VtP.^ BOUGHT WITH THE INCOME FROM THE SAGE ENDOWMENT FUND THE GIFT OF Hetirg M. Sage 1891 AinMSM. fULjiuC 3081 Cornell University Library QB 219.M16 V.1 Verification and extension of La Caille' 3 1924 012 313 437 *.... Cornell University Library The original of this book is in the Cornell University Library. There are no known copyright restrictions in the United States on the use of the text. http://www.archive.org/details/cu31924012313437 VERIFICATION AND EXTENSION OF LA CAILLE'S ARC OF MERIDIAN AT THE CAPE OF GOOD HOPE; BY SIR THOMAS MACLEAR, ASTRONOMER ROYAL AT THE CAPE OF GOOD HOPE. IN TWO VOLUMES. Vol. I. CONTAINING Identification of La Caille's Stations, and Comparison of the Ancient and Modern Measures. Description of the Modern Geodetic and Astronomical Instruments. Geodetic Operations for the Extension of the Arc. Abstract of the Astronomical Operations. PUBLISHED BY ORDER OF THE LORDS COMMISSIONERS OF THE ADMIRALTY. 1866. 3) VERIFICATION AND EXTENSION OF LA CAILLE'S ARC OF MERIDIAN AT THE CAPE OF GOOD HOPE. INSTRUCTIONS TO THE BINDER. Volume I. to begin with Title Page, Advertisement by the Editor, Index to Volume I. After this, the sheets of the first stitched book, Signatures B to I (its Title Page to be cancelled) : and the sheets of the second stitched book. Signatures K to G G (its Title Page to be cancelled) : and the unbound sheets. Signatures A to Z, 2 A to 2 P, A to Z, A 1 to 1 Z. 2 A to 2 F. The Plates to be inserted as follows : — Plates I., IL, III , IV., V., VI., all to face page 66. Plates VII., VIII., IX., X., XL, XII., XIII, XIV., XV., XVI., all to face page 80. Plates XVII., XVIII., XIX., all to face page 242. Plate XX., " Zwartland Base Line" (not numbered in the engraving), to face page 344. Plate XXL, views of rocks (not numbered in the engraving), to face page 447. Plate XXIL, long sheet of triangles (not numbered)") . r f.,r. Plate XXIIL, short sheet of triangles (not numbered) 5 Plate XXIV., (not numbered) modern triangulation between the north and south termini of La Caille's Arc, to face page 619. Volume II. to begin with Title Page, Index to Volume IL After this, the sheets, Signatures A to Z, A A to Z Z, 2 A to 2 Z, 3 A to 3 Z, 4 A to 4 M, B and C (unsigned) to G. There are no Plates. VERIFICATION AND EXTENSION OF LA CAILLE'S ARC OF MERIDIAN AT THE CAPE OF GOOD HOPE. INDEX TO VOLUME I, Introduction ----------- Identification of La Caille's Station in Cape Town ______ Identification of La Caille's Station in Klyp Fonteyn ______ Identification of La Caille's Stations on Riebeek's Castel and Kapoc Berg _ _ _ Triangulation for connecting La Caille's Observatory, the Modern Observatory, and Sir John Herschel's Large Reflecting Telescope _______ Results of the triangulation _________ Triangulation for connecting La Caille's Sector-Station at Klyp Fonteyn, the Modern Sector-Station, and the Neighbouring Hills ________ Results of the triangulation _________ Appendix, containing Official Documents from 1710 to 1772 _ _ - _ _ Plate I. Showing the position of La Caille's Sector in Cape Town, 1751 and 1752, and' Bradley's Sector (Maclear's) in 1838 Plate II. Plan of the Buildings, &c., at Klyp Fonteyn - Plate III. Small triangulation near Cape Town - Plate IV. Views of the mountains near Klyp Fonteyn Plate V. Plan of the mountains near Klyp Fonteyn - Plate VI. Small triangulation near Klyp Fonteyn Description of Bradley's Sector, with which the Astronomical Observations of Mr. Maclear were made __________ Notes on the history of the instrument, &c. _______ Plate VII. Plate VIII, Plate IX. Plate X. Plate XI. Plate XII. Plate XIII Plate XIV. Plate XV. Plate XVI. _ History of the operations with Bradley's Sector for the verification of the astronomical amplitude of La Caille's Arc ---------- Methods employed for the reduction of the observations -__--- Results for the amplitude of the arc ___--_-_ Comparison of La Caille's amplitude with Maclear's amplitude _ _ _ _ _ ^Latitude of La Caille's Station in Cape Town,^ , - Page 1 6 11 19 20 35 46 55 y £icing p. 66 67 76 =■ Plans of Bradley's Zenith Sector - facing p. 80 81 92 106 111 112 ( 6 ) Page - 113 Sector observations at Klyp Fonteyn, unreduced _----" Sector observations at Cape Town, unreduced _-_--" Mean Zenith Distances of stars at Klyp Fonteyn -----~ Mean Zenith Distances of stars at Cape Town _----" Measurement of the Base ____---" Plate XVII. ^ Plate XVIII. i Plans of the Base Apparatus ----- - facing p. 242 Plate XIX. ) _ _ 243 Cape Standards of Measure ------- 245 Measurement of the Zwartland Base - - -- - ~ ~ ~ Tabular detail of the Measurement _------" ^'^ Errors of Alignment --_------" "•■■" • SIR Level observations for sections of the Base Line ----- ~ ~ ''^° Level observations from the Base Line to Saldanha Bay ----- ~ "•^^ Reduction of Microscope intervals to 62° Fahrenheit - - - - " - ooc Verification of the Base by triangulation -------- """ Plate XX. Triangulation of Base Line ------- facing p. 344 Comparisons of the Compensation Bars vrith the Standard Iron Bars _ - - - 346 Expansion of the Cape 10-feet Iron Bars ------- 350 Reduction of Standards B and A to 62° Fahrenheit (table) - - - - - 361 Abstract of comparison of Compensation Bars with Standards ----- 365 Relative lengths of Standards A and B- - - - - - - -371 Experiments in London, on the thermal expansion of A and B, and on their relative lengths as compared with Ordnance Standards, R. Astronomical Society's Scale, and Mr. Simm's Scale 383 Character of the country, for the Extension of the Arc ------ 395 Description of the Theodolites, Signals, &c. ------- 397 Historic Abstract of the progress of the triangulation ------ 402 Observed Horizontal Angles, preliminary explanation, with details of one angle by each instrument 419 Description of Stations ---------- 427 Plate XXI. Rocks on the summit of Kapoc Berg ----- facing p. 447 Abstract of the Horizontal Angles observed at the several stations - - - - 475 Investigation of corrections to be applied to the Horizontal Angles, to satisfy geometrical relations - 485 Calculation of the principal triangles -------- 533 Calculation of the secondary triangles --__---_ 547 Calculation of the meridional distances of stations ------- 559 Calculation of the geodetic latitudes and longitudes of stations ----- 575 Observed zenith distances of stations, and calculation of their altitudes above the sea - - 591 Astronomical determinations of azimuth - - - - _ -._ - 605 Final results of the observed latitudes, the calculated latitudes, and the distances of the parallels, of the sector-stations ------___ 009 Plate XXII. Triangulation of the Meridian Arc, from Cape Point Sector-Station to North End Sector Station, Bushman's Flat ------- facing p. 610 Plate XXIII. Triangulation from the neighbourhood of Cape Town to Cape L'Agulhas - facing p. 610 Investigation of the length of La Caille's measure in terms of the Modern Base - - _ 611 Plate XXIV. Modern Triangulation between the north and south termini of La Caille's Arc - facing p. 619 Errata - - - -- - - _ _ _ facing p. 1 VOL. I. EERATA ET ADDENDA. PAGE FOR BEAD 36 7th line from bottom 101-739 101-084 *) 6th „ „ „ 45"-01 45'-30 4tli J) J. » sight site 262 Series 88 52-5 52-25 280 Notes. 2nd line from bottom 240 340 281 Notes. 8th line from bottom 946 346 315 6th line from bottom 0-000023 0-000232 334 5th line from top give gives 335 TopUne , from of 355 Bottom line 434-41 434-31 J) j; if ■■• ••■ ... ••• 0-021721 0-021716 360 2nd line from top 0-021721 0-021716 71 4th line from top 0-000277 0-000282 364 Heading of Table XI made at the Base line made at the Royal Observatory. 402 Top line smooth smooths. 404 5th line from bottom ing omit ing 429 Angle Sneeuwkop to 75°-43'-46-26 156-14-19-14 ft Danger Point 75-4311-47 156-13-44-35 431 a nd 432, 433, 443, 482 Noah's Arc Noah's Ark. 435 4th line from bottom 79-15-11-06 72-15-1 1 -06 438 5th line from top supercedes supersedes 442 5th Une from bottom Cape HangMp pile Cape HangUp point. 453 Middle of page Winter Beig, heUostat ... Whitzenberg heUostat. 465 18th line from top over the terminal point ... over the angle point. 468 4th line from bottom 306°-54'-32" 306°-54"-39' }) 5th Mne from bottom between the disc between Louis Fontein 549 A 72 137204-41 feet 137200-44 555 AS 102,103,203 Blaau Berg Blaauberg Meridian pillar 576 Log. Distance, No. 8 5-1991810 5-1991310 576 Log. Distance, No. 1 1 5-5039042 5-2763846 585 a' Diff. in Long. No. 109 356-42-10-95 336-42-10-95 OPERATIONS THE VERIFICATION AND EXTENSION OF THE ABBE DE LA CAILLE'S ARC OF MERIDIAN, THE CAPE OF GOOD HOPE. PART I. ON THE POSITION OF LA CAILLE'S STATIONS. § 1. Introduction, The astronomical celebrity of the Abb6 De la Caille's visit to the Cape of Good Hope, in the last century, together with the remarkable result from his arc of the meridian, naturally prompted me to take an early opportunity of becoming acquainted with his principal stations, and to connect the southern, which was his Observatory in Cape Town, with the present Observatory. I soon found that the lapse of eighty-five years had obliterated all local evidence of the French astronomer's operations ; and the fact that he had been here at all, was mainly kept alive by the inquiries of Captain Everest in the year 1820. I except from this apathy a few scientific gentlemen, whose connexion with the colony is of comparatively recent date. Having read with attention the papers published by him in the M6m. de I'AcadSm. des Sciences, and having carefully perused his printed journal, I 2 VERIFICATION AND EXTENSION OF LA CAILLe's ARC OF MERIDIAN. applied to His Excellency, Sir Benjamin D'Urban, for leave to inspect the official records between 1750 and 1753, which was obligingly granted; and, although I did not succeed in procuring a copy of the order of Governor Tulbagh for building the Observatory, under the superintendence of M. DE RuYTER, which I had hoped would allude to the spot where it stood, nor the order to M. Muller, to assist him in the measurement of the base line; still several letters and notices were brought to light interesting to the astronomer, particularly the recommendatory letter of the Prince of Orange to the Governor of the Cape, signed by his serene highness, the official correspondence, the memorial of the Academy of Sciences of France to the Dutch ambassador, and the report of the States-General on the occasion. It now became necessary to pursue an indirect course — to trace the residences and property of all persons of the name of Bestbier, the name of the person in whose house the Abbe states he resided, and on whose premises the Observatory was built. I ascertained from the records in the Transfer Office, that only one person of the name of Bestbier held property in Cape Town in the year 1751; and he answers to the description given by La Caille. By tracing down the successive transfers of this property to the present time, I was led to the house in Strand Street, now occupied by Mrs. De Witt, which is the house referred to by Captain Everest. This lady permitted me to inspect her title-deeds and diagram : they exactly agree with the records in the Transfer Office. I may further mention, that the position and form of the premises correspond with several remarks made by La Caille in his operations, which will be particularly alluded to in the sequel. In the meantime, my predecessor, Mr. Henderson, desirous to assist the investigation, presented the Observatory library with a copy of Wales and Bailey's Astronomical Observations, wherein there is a description of a triangulation by Mr. Wales, for joining the spot where he observed with La Caille's position. But Mr. Wales omitted to register his own position ; and all the inquiries made, occupying several days, led to no conclusion. His triangles, he states, correspond with the form of the intervening streets. By adapting them to Grave Street, across the Parade, the last angle (being obtuse) leads to Mrs. De Witt's front door, and not to the Observatory, which was at the bottom of the yard behind, as will be seen presently. Tliis INTRODUCTION. 3 fixes Mr. Wales's position, (which, he says, is the same with Mason and Dixon's,) in Concordia Gardens,* a noted club-house sixty years back. Captain Cook lodged at the house of a Mr. Brandt, whose daughter-in- law I have seen. She shewed me a copy of Cook's Voyages, presented to her father " by the Lords Commissioners of the Admiralty, for his attention to Captain Cook and other English sojourners at the Cape." Her father's residence was in the Heerengraght, nearly opposite to a noted house in the present day — George's Hotel. Mr. Sloman, a linendraper, now occupies the house, and a north-east triangulation from it would lead to the anchorage in Table Bay. I particularise names, because, where there is no remarkably well-described monument of a residence in a town liable to changes in the buildings, it can only be traced by a reference to the Registry Office, where names are the principal elements. Having undeniable proof of the identity of Bestbier's house with that • now occupied by Mrs. De Witt, the search for the position of the Ob- servatory was brought within narrow limits ; for La Caille states it was in the court of the house where he lived. I therefore proceeded to connect the house with the Royal Observatory by triangulation, being resolved to spare no pains in the execution, as I entertained a hope that I should thus detect whether Table Mountain affected his plumb-line. In the meantime, I had communicated my views and proceedings to Captain Beaufort, who is ever ready to countenance and support any , proposal for the advancement of science ; and to Mr. Airy, the Astronomer Royal, from whom I shortly afterwards received a letter, informing me that he had written to the Secretary of the Admiralty, requesting permission of the Lords Commissioners of the Admiralty to send out Bradley's zenith sector, that I might verify at once the amplitude of the arc. This was exactly my wish, 'provided I could identify the northern station. The first step, therefore, was to ascertain this point. Accordingly, I called upon Mr. Hertzog, the assistant surveyor -general, who accompanied Captain Everest to Klyp Fonteyn in the year 1820. His duties at this time were too pressing to justify his absence ; but he was so kind as to lend me the drawings he made in 1820, and to supply a description of the platform of the granary referred to by Captain Everest, together with the names and • See Appendix, No. 1. 4 VERIFICATION AND EXTENSION OF LA CAILLE's ARC OF MERIDIAN. residences of persons to whom I should apply for information. Lieut. Williams, of the Royal Engineers, a zealous officer, and devoted to his profession, volunteered to accompany me. We took the opportunity to visit La Caille's triangulating points on Capoc Berg and Riebeck's Castel, and to traverse the direction of his base line on Zwartland Plain. So many changes had taken place at Klyp Fonteyn within the last fifty years, that, besides an examination of the buildings and ruins, a close investigation into the history of the proprietors became necessary ; for when I saw the old foundation, described as the platform of the granary by Captain Everest, and compared its dimensions with La Caille's statement, and remarked its position and distance from the old house, so unlike the arrange- ments of the Dutch farmers, I had strong reason for doubting its identity with the granary of La Caille. I was about to undertake a responsible and a very important task, and it became my duty to receive nothing for granted that admitted of a question. My doubts were further confirmed on referring to Jerrit Cotsee, who has resided at or near the spot for sixty-eight years, and whose testimony will be described hereafter. I beg it may be distinctly understood, that I by no means undervalue Captain Everest's exertions and discrimination in his own inquiries. But, without charging the inhabitants with a desire to mislead, I may state that a longer residence in this colony has taught me that, in their readiness to afford an affirmative answer on all occasions, they are apt to affect a knowledge of circumstances which they do not possess. Captain Everest will readily grant this, and will see its force, when he learns that the aforesaid platform on which he stood was within eighty yards of two foundations, of which there was not a vestige above ground to indicate their existence. This general outline being premised, I proceed to the description of the two stations, and to the discussion of the evidence upon .which they rest. As I before stated, the only records I could obtain of La Caille's visit consist in the official letters that passed between the government authorities on the occasion, and two or three notices, which may be enumerated as follows : — The first (Appendix, No. 3) is a memorial from the Academy of Sciences, delivered by the Marquis de Puysieulx at Versailles, to M. Lestevenon, the Dutch ambassador. This letter displays in a strong light the jealousy of the Dutch authorities with reference to the Cape colony. " II n'a besoin INTRODUCTION. O d'aucun domestique, d'aucun aide, il restera en pension dans le lieu que Ton lui indiquera Les Hollandois, qui ont accorde a M, Krosick la permission d'entretenir au Cap un astronome Prussien, destine a executer preeisement le meme projet dont il s'agit, ne peuvent raisonnablement la refuser au roi pour un astronome de son academic, qui se tiendra exacte- ment dans le lieu qu'on lui assignera, soit dans le fort, soit dans I'interieur des terres ! " The Abbe, however, was not confined to one spot : he was hospitably entertained and respected, as he acknowledges on several occasions. The second (Appendix, No. 4) is an extract from the journal of the States-General, noticing the receipt of Mr. Lestevenon's letter, in which the Marquis de Puysieulx's Memorial is communicated, and referring it to the consideration of the Representatives of the States-General and the Directors of the Dutch East India Company at Amsterdam. • The third (Appendix, No. 5) is an extract from the same journal, noticing the receipt of an answer from the Representatives and Directors at Amster- dam, and granting permission to M. de La Caille to proceed to the Cape. The fourth and fifth (Appendix, Nos. 6 and 7) are from the Representatives and Directors at Amsterdam to the Councillor Extraordinary and expected Governor at the Cape of Good Hope, inclosing the resolutions of the States- General. The sixth (Appendix, No. 8) is a letter from his Serene Highness the Prince of Orange, addressed to Governor Tulbagh, introducing and recom- mending La Caille to his Excellency. The seventh (Appendix, No. 9) is the Governor's reply. The eighth (Appendix, No. 10) is an extract from the journal then kept by the Secretary to the government at the Cape of Good Hope, dated 19th April, 1751, announcing La Caille's arrival, his objects, &c. The ninth (Appendix, No. 11) appears to be the official envelope covering private letters to La Caille. The tenth (Appendix, No. 12) is at this time particularly interesting : it is an application from M. Mltller, the engineer of the fortress, to Governor Tulbagh, for an extension of leave of absence for the reasons therein stated. La Caille says, (MSm. de I'AcadSmie, 1751, page 425): " M. Tulbagh, gouverneur de la colonic, ayant approuv^ le projet que je lui presentai sur ce sujet, et ayant nomra6 M. Mullek, capitaine d'artillerie et ing^nieur de la b VERIFICATION AND EXTENSION OF LA CAILLE S ARC OF MERIDIAN. forterpsse, pour etre temoin de mes operations," &c. Again {Journal, page 1 85) : " M. MuLLER, capitaine d'artillerie, arrive a Drie-Fonteyn le 5 pour assister a mes observations, vint me rendre visite sur Riebek-Castel, et s'en r^tourna un peu aprfes." La Caille was detained eleven days and nights on Riebeck's Castel by bad weather, waiting an opportunity to observe the signals on Capoc Berg and Klyp Fonteyn, which explains the delay, the cause of MiJLLER's letter. The eleventh (Appendix, No. 13) is an extract from the journal of the Secretary, stating the heights of the neighbouring mountains. The twelfth (Appendix, No. 14) is an extract from the journal of the Secretary, registering La Caille's departure from the Cape. Authenticated translations of these letters and notices are annexed.* I have seen the originals. I expected to find Count Bentinck's letter to the governor ; also La Caille's survey of Hout's Bay, made at the request of the governor ; and the order for building the Observatory : but neither these, ' nor the memorial on the arc, are registered in the journals. § 2. Identification of La Caille's Station in Cape Town. The Abbe arrived at the Cape on the 19th of April, 1751. He says {Mkm. de VAcadtmie, 1751, page 522) : " J'allai le lendemain me presenter a M. TuLBAGHj gouverneur du Cap, muni d'une lettre du feu Prince d'ORANCE ; elle fut suivie d'autres lettres de la Compagnie de Hollande et de M. le Comte de Bentink. M. Tulbagh me re9ut avec beaucoup de politesse ; je fus accueilli de meme trfes-gracieusement par tons les principaux officiers de cette colonic. Un des premiers bourgeois de la ville, nomm6 M. Bestbier, AUemand de naissance, et qui a servi autrefois dans les troupes de France, m'offrit obligeamment sa maison, et la disposition absoljfe de tout ce qu'il avoit chez lui. On verra, dans la suite de ce discours, qu'il ne tint pas a lui que toutes les observations que j'ai entrepris de faire pendant mon sejour au Gap, n'eussent tout le succes possible M. le gouverneur apprit que je me disposois a faire batir un logement expr^s pour y placer mes instrumens; il donna aussitot ses ordres pour que les ouvriers que la Compagnie de Hollande entr6tient a ses gages y travaillassent incessamment, • See the Appendix. IDENTIFICATION OF LA CAILLE S STATION IN CAPE TOWN. 7 suivant le plan que j'en donnerois, et que les materiaux fussent tires des magasins de la colonie. J'employai tout le mois de Mai a faire construire cet observatoire, ou rien ne fut 6pargn6 de tout ce qui pouvoit contribuer a lui procurer toutes les commodit^s n^cessaires, et ce qui est le plus important dans I'astronomie pratique, toute la solidity possible aux pie- destaux sur lesquels mes grands instrumens devoient 6tre places." Again (page 526) : " Je trouvois toutes sortes de facilites, et dans la complaisance de M. Bestbieii, mon bote, qui s'empressoit a me procurer toutes les com- modites possibles, reglant meme les heures de ses repas sur les momens ou je pouvois etre libre," &c. Also (page 529) : " M. Bestbier, cet bote si obligeant chez qui je demeurois, me fit sentir," &c. &c. These extracts prove that La Caille lived in the house of M. Bestbier, and that the latter was one of the principal burgesses of Cape Town ; that the Observatory was built by order of Governor Tulbagh, and by government ^workmen, the materials being supplied from the magazines of the Company ; and that the pillars to carry his larger instruments were constructed with all possible solidity. To prove the position of the Observatory, I extract the following from page 398. " L'observatoire ou j'ai place mes instrumens, etoit un batiment fait expres par ordre de M. Tulbagh, gouverneur de la colonie. II etoit place au fond de la cour de la maison ou je demeurois, sur un terrein klevi de 7 a 8 pieds sur le niveau de la mer." Thus his Observatory was built at the bottom or further end of the court of the house where he lived, upon the ground, seven or eight feet above the level of the sea. I make no apology for these copious extracts, as no doubt should remain on the subject they are meant to clear up. There is only one person of the name of Bestbier registered in the Transfer- Office in the year 1751, and only two since. The following is an authentic translation of the register in which the name Bestbier first occurs, furnished by Mr. Zastron, chief clerk in the Transfer Office : — " Daniel Pfiel and Jacob Leeven, commissioned members of the Board of Orphan Masters, as administering to the estate of the Burgeen, Eaap St. Johannes Blanckenberg, cede and transfer certain houses and premises in this Table Valley in Zee Street (now, 1835, Strand Street) in block ^, to "Jan Laurens Bestbier, 31 July, 1737. Arend de Waal, 17 Jan. 1766. 8 VERIFICATION AND EXTENSION OF LA CAILLE S ARC OF MERIDIAN. Petrus Johannes de Witt, 4 June, 1794. Johannes Henricus De Witt, 7 Feb. 1797." The widow of the last-named J. H. De Witt, now about seventy years old, still occupies the house, and holds the title-deeds, which she permitted me to inspect. They, with the diagram annexed to them, exactly correspond with the above extract from the office-register, and with the diagram attached to the original grant of the land where the house stands, made by Governor Der Steel in 1701, to Blanckenberg, who built the house and became a bankrupt. Mr. Alexander Van Breda, of Newlands, now about eighty years old, remembers, when he was a little boy, M. Bestbier living in the same house ; and states further, that the two Bestbiers, late of the Cape Flaats, and now residing in Zwartland, are his grandsons. Mr. Hertzog, the assistant surveyor-general, possesses a map of Cape Town, made in 1751, now of considerable local value. He kindly permitted^ me to copy it, on the condition that it was only to be employed for the purposes of the present inquiry. I annex this copy * that it may be com- pared with the plan of Mrs. De Witt's and the adjoining houses, lately made by Lieutenant Williams and myself, from actual measurement. The extract from the Transfer Office refers the house to block <^ : the same is marked on the old map. La Caille attaches a note to an observation on the station of Riebeck's Castel {Mim. 1751, p. 429). "Remarque. — Le coin de la rue dite Heeren- straat, au Cap, est a 73 degres du sud vers Test, du coin oriental de I'Obser- vatoire, a la distance de lllg^ pieds. II se distinguoit fort bien, etant d'un blanc de chaux, et projete sur la mur du grand attelier de la Compagnie, lequel est peint en noir et fort eleve." The great workshop of the company here referred to is "de Ed. Comp. Warf." block <^ on the map of 1751. The naval yard and stores, smiths' and carpenters' shops, were in this block, and only removed as late as 1813, when the station was changed to Simon's Town. The naval commissioner's dwelling, next to the corner house, is now the custom-house, and the corner house is a prison ; the street, which is a prolongation of Heerenstraat, alias Heeregraght or Gentleman's Street, assumes the name of " Justice Street." On placing myself in this street, towards the top, the line of sight to the * This copy is not here given ; but the position of the house may be seen in Plate I. IDENTIFICATION OF LA CAILLE S STATION IN CAPE TOWN. 9 second peak of Riebeck's Castel is a tangent to the opposite corner of Mrs. De Witt's block; while the distance, 111|^ feet, and the beapng, 73°, carries us into Mrs. De Witt's yard to the point marked on the plan, as the pro- bable site of the Observatory. This almost accidental remark of La Caille is alone sufficient evidence of the position of his Obervatory. There is one more (page 456), " La mer s'^lfeve tres peu au Cap de Bon Esp^rance. II y avoit en face de la maison ou je demeurois des roches en mer, qui sont presque a fleur d'eau," &c. The rocks here alluded to still exist, and I have lately had an ample opportunity of verifying his remarks upon them. I could produce the observed azimuth of Dassenberg Rock, and the angle between it and the Capoc Berg signal rock ; but I hope enough has been brought forward to fix the identity of Mrs. De Witt's house in 1838 with that of Jan Laurens Bestbier in 1751, and to prove that La Caille's Observatory stood in the yard of that house. The meridian of his Observatory passes to the east of Mrs. De Witt's house, a couple of degrees to the left of the high projection into the yard constituting her kitchen and pantry stores, and over the east end of Table Mountain ; one-third of which, from the top, must have been exposed to his view.* Mrs. De Witt's is the second house in Strand Street, counting westward from the Heeregraght, on the side next the Bay. It is of the description of a good London house. The accommodation it affords may be inferred from the circumstance that, in the year 1806, Sir David Baird and the present Right Hon. Lord Glenelg, and, in the present year, his Serene Highness Prince Frederick of Orange, lodged in it. Such events are a sort of registry in this colony, and for this reason I mention them, as well as for the purpose of shewing the quality of the house.f I inclose a faithful sketch of the front taken from the corner of the Parade, and another of the back premises from the roof of Roggebay Guard-house, both by Mr. C. Piazzi Smyth ; which, together with the plan, will convey an adequate conception of the spotj I should mention that this guard-house was built about the year 1789. From * Since writing this paragraph, I have laid down the direction of the meridian on the walls of the house. The meridian of his sector, I believe, passed over the high building. I believe /3 Hydri was his lowest sub-polar star. f The value of the house and premises is estimated at 5000Z. X These sketches are not here given ; but the plan of the premises may be seen in Plate I. C 10 VERIFICATION AND EXTENSION OF LA CAILLE'S ARC OF MERIDIAN. the north-west wall of the kitchen within the yard projects the pin, or spike, alluded to by Captain Everest, flattened at the end, where it is slightly turned downwards.* In the flat portion there is a hole, and underneath, on the wall, is drawn a rectangular quadrilateral, bisected perpendicularly. A pencil of light through the hole, falls on the middle vertical line at apparent noon. Mrs. De Witt informs me that this meridian line was there in her father's time (Arend de Waal), from whom she always understood it was put up by the French astronomer. I have not seen another of the same kind at the Cape. She further informs me that her late husband erected the high building of two stories now covering the west side of the premises from the dweUing-house to the back street (Rogge Bay), for the reception of merchandise, in the year 1816: likewise the low buildings at the bottom of the yard (between which is the back entrance), to let as tenements to poor people. The upper story of the high building is let to sail-makers, and the low buildings f [lower story?] to fishermen. The latter occupy the site of the Observatory. It appears by La Caille's description % that the Observatory was a sub- stantial building : the floor, five feet above the level of the yard, resting on sand, the pillars must have been tolerably free from vibrations. Whether their diagonal position, as described by him, was a matter of choice or not, I do not pretend to say ; but I may remark, that such a position would place the Observatory nearly square with the house : and it has occurred to me, that it might have been so placed with the ulterior view of making it subservient to domestic purposes by removing the elevated floor. If so, it may have been in existence when M. De Witt erected the buildings before mentioned. However, by the arrangement in the corner, the instruments were in less danger of disturbance, more room was obtained, and the clock was advantageously posted for observation. It is very probable the founda- tion-stones are still below the surface, but it is impossible now to get at them without endangering the walls. The yard and passage are paved at this time with large irregularly shaped stones. * This pin is in the meridian of the Observatory, and may have supported the threads he suspended for the purpose of keeping the instrument in the meridian, as stated by himself. t It appears from the plan (Plate I.), and also from the zenith-sector observations, that the high building occupies the site of the Observatory. — G. B. A. X See Mem. de I'Acad. des Sciences, for 1751, page 398. IDENTIFICATION OF LA CAILLe's STATION AT KLYP FONTEYN. 1 1 § 3. Identification of La Caille's Station at Klyp Fonteyn. The station at Klyp Fonteyn cannot be so readily traced as that in Cape Town. I have already expressed my doubts as to the situation fixed on by Captain Everest, and that they were further confirmed by the testimony of Jerrit Cotsee, to whom I was referred for information by Mr. Hertzog. When I told this man Captain Everest's opinion, and the source from which the Captain derived his information, he replied with some degree of vehemence that it was the foundation of his father's house, and that the granary was to the east of it, close to the foot of the hill. He immediately walked to the supposed site of the granary and searched about, but no remains could be found where he looked for them. He stated as follows : — He is now seventy- six years old ; he came with his father at eight years old to reside at Klyp Fonteyn ; and the house they lived in was over that foundation. The roof became faulty ; his father repaired it : afterwards he built the house over the stream (the present old house), and the other went to ruin.* La Caille says (Mim. de VAcad. page 426) : " Je plaf ai dans la grange de cette habitation le secteur de six pieds de rayon." And (Journal, page 180) : " Le lieu ou nous couchions, M. Bestbier, moi, et Poitevin, 6toit un emplace- ment d'une grange, long de six pieds et large de sept, separ6 de celui ou 6toit le secteur par une toile, qui faisoit une espece de cloison ; nous y avions pos6 les deux matelats de mon lit de camp, a cote I'un de I'autre, sur des sacs a demi remplis de paille. Au dela de cet endroit ^toit une autre petite place, ou couchoient les esclaves." Captain Everest gives the following {Mem. Astron. Soc. Vol. L p. 261) : " In reference to this matter, it may not be amiss to mention that the daughter of the quondam proprietor of Klyp Fonteyn, now an aged lady named Letchie Schalkeveck, is still in existence, and not only gives a narration perfectly agreeing, but has pointed out the very platform on which the granary once stood ; and states further that the signal fires were so large and brilliant, that those of Riebeck's Castel were visible from Klyp Fonteyn, a distance of more than forty-five miles, with the naked eye at night. The same lady relates, also, that the Abbe De La Caille observed the stars with * For the elucidation of this part of the Memoir, see the plan in Plate II. Also the Appendix, No. 15. 12 VERIFICATION AND EXTENSION OF LA CAILLE's ARC OF MERIDIAN. his instrument (the sector, I suppose,) in the granary (an aperture having been made in the thatched roof for the purpose) until the day when the fires were hghted; when, having previously sent M. Poitevin, his assistant, to make simultaneous observations at Riebeck's Castel, he placed it, or some other, at some paces in front of the fire : and as this account taUies with what I have before observed in my remark respecting Riebeck's Castel, it leads directly to the extraordinary conclusion, that not only the signals in these operations were ill defined, but that the instrument for measuring the horizontal angles was not placed over the centres of the stations." Captain Everest acknowledges elsewhere that he had not seen La Caille's papers in the Mim. de FAcadSmie, which explains the conclusion he arrives at in the latter part of this paragraph ; for La Caille did reduce his angles to the centre, and he gives the bearings and distances from which the reductions were computed at the stations — Cape Town, Capoc Berg, Riebeck's Castel — not for Klyp Fonteyn ; for the reason, I presume, that the point at which the angle between Capoc Berg and Riebeck's Castel, at Klyp Fonteyn, was first measured, was over the picket where the fire was afterwards to be made. Poitevin must have been sent to Riebeck's Castel to superintend that signal ; for it appears that La Caille measured all the angles himself with the 3^-feet quadrant. This is the only part of Letchie Schalkeveck's statement that seems improbable. We can trace La Caille through the several stages of this work. He left Cape Town on the 11th of September, and arrived at Klyp Fonteyn on the 14th. He observed there with the sector from the 16th to the 25th. October 13th he enters this note in his journal : " Le soir, un peu avant I'heure des feux, Riebek Castel se couvre de nuages ; je descendis ce soir de la montagne, apres y avoir reste neuf jours et neuf nuits de suite. Comme le tems de la moisson des orges approchoit, j'avois rSsolu de remettre d, faire les feux d, Picquet-Berg (Klyp Fonteyn) apres avoir mesuri la base, pour laquelle operation," &c. On the 17th he commenced the measurement of the base, and on the 26th he was on a visit to the governor at Rondebosch. I suspect the Klyp Fonteyn fire was lighted on the 14th or 15th of October, twenty days after the sector observations terminated. La Caille being on Riebeck's Castel at the time. But, returning to the important investigation, the platform alluded to by Captain Everest consists of a foundation wall, 63 feet long by 24 in breadth. A considerable portion of it on the west side is two feet above IDENTIFICATION OF LA CAILLe's STATION AT KLYP FONTEYN. 13 the ground, and it is situated at a distance of 630 feet from the present old house. 1st. If this was the granary inhabited by La Caille, it must have been at the time nearly full of grain or something else, otherwise there could be no necessity for the confined dimensions (6 feet by 7) of the place where he, Bestbier, and Poitevin slept. 2d. The Cape harvest takes place in October and November. La Caille arrived at Klyp Fonteyn on the 14th of September, just before harvest, when there is seldom a full granary ; therefore, most probably, it was not occupied by grain. 3d. Where was the dwelling-house of the proprietor ? Jerrit Cotsee distinctly states that his father built the present old dwell- ing fifty years back. He, Jerrit, must then have been twenty-six years old, and living on the spot, which he did not leave for his present residence, only about one mile off, until 1792. This objection is corroborated by the custom of the Dutch farmers, who, as far as I have seen, build their offices close to their dwellings. I confess L. Schalkeveck's account generally is plain enough, and carries with it the stamp of truth ; for I have been told by Mr. Hertzog, that she mentioned La Caille's little dog, " Grisgris," by name. {Journal, p. 97.) The steps which, in the midst of such conflicting testimony, it remained for me to take, were, first to search out the Schalkeveck family ; for, ac- cording to the common course of nature, the old woman was dead ; 2dly, To investigate the authenticity of Jerrit Cotsee's statement ; and 3dly, To examine the place by turning up the soil. No one of these could be undertaken immediately, but I laid my plans for their execution ; and, on returning from Klyp Fonteyn, I lost no opportunity to inquire after the ScHALKEVECKS, but uo One recollected the old lady. I again applied to Mr. Hertzog, and obtained a detailed account of his journey with Captain Everest. It appears they travelled together to Klyp Fonteyn, where they separated. Captain Everest went off" in the direction of Riebeck's Castel in search of L. Schalkeveck, in consequence of some information he re- ceived ; while he (Mr. Hertzog) went to Jerrit Cotsee, to whom he read the extract just quoted from La Caille's journal, to make him comprehend the kind of building they were in search of. Captain Everest brought up Letchie Schalkeveck's son to point out the site according to directions from 14 VERIFICATION AND EXTENSION OF LA CAILLE S ARC OF MERIDIAN. the mother. It appears the old lady lived at a considerable distance, and did not attend herself, but sent her son. It is to be regretted that Jerrit CoTSEE was not brought to the place at the same time ; and it is here I conceive the misunderstanding originated ; for I can shew, by the testimony of Jerrit Cotsee, aged 76 — of his sister, Mrs. Lambritz, of Keptyn's Kloof, aged 71 — of his sister-in-law, Mrs. Dirk Cotsee, of Klyp Fonteyn, aged 65 — of Mrs. Lambritz, of Groene Fonteyn, aged 69 — that no person of the name of Schalkeveck has resided at or near Klyp Fonteyn within their memories ; consequently, the son could not have any local knowledge of the place ; and it is very probable his mother told him he would find the ruin to the east of the stream of water on the rise of the hill, and he did find a ruin on the rise of the hill, and referred to it. I now applied at the Transfer Office for a list of the proprietors of Klyp Fonteyn, from the year 1751 downwards. The first notice of that property in the Transfer Office is dated 1792, when Jerrit Cotsee divided it, and sold the half on the west side of a mountain (which we afterwards named La Caille's Mount) to Jacobus Gideon Low, which includes the farm-houses and the ruins in question, retaining for himself the portion in the basin or valley bounded by the said mountain on the west, and Piquet Berg on the east and north, where he built a house for himself, and where he still resides. In explanation, why there is no existing earlier notice or record, I am informed that, as the colony and population increased, the Dutch Company, with the view of bringing the land into cultivation, permitted applicants to locate on loan * places, on the condition that the land and tenements should annually revert to the government, provided they were claimed ; but they were rarely claimed, except for public purposes. Such lands, in the end, were usually granted on the payment of quit-rent.f This may have been the case with Klyp Fonteyn ; for, although it is a beautiful romantic spot, with the advantage of a considerable stream of water issuing from underneath a rock, about 300 yards above the habitation, it is * Loan places, so called because they were lent to the applicants. t After this paper was sent to England, I discovered a document which I had long been seeking. (See the Appendix, No. 14.) From this it is clear that the father of Letchie Schalkeveck was not a proprietor of Klyp Fonteyn from 1744 to 1758, although he resided there. This shews that her statement on that point to Captain Everest was not correct. IDENTIFICATION OF LA CAILLE S STATION AT KLYP TONTEYN. 15 SO insulated by a desert of deep sand, that agricultural produce cannot be conveyed to Cape Town at a less expense than is required to raise it. It is therefore probable that the occupier in La Caille's time was poor. He says (Journal, page 181), "En general cette habitation, quoique fort petite, nous fournit tout ce dont nous avions besoin. Ella est situee dans un coin de la grande plaine de Sable, qui est entre Berg riviere, et le Piquet Berg, et la mer, a I'endroit on la montagne sans nom dont j'ai parle, s'approche le plus du Piquet Berg." When preparing for my second journey with Bradley's sector, I made arrangements for exploring the place. I applied to his Excellency General Napier, and obtained a corporal of sappers and a private from the artillery corps, under my old companion, Lieut. Williams. I had, besides, a young Dutchman to act as interpreter (and servant), to prevent misconception, and Joseph Gibbs, carpenter to the Observatory ; a number of pick-axes and spades were also put into the waggon. On my way up, I called upon Schalkeveck, of Orange Fonteyn, near Capoc Berg, and on Schalkeveck, of Matjies Fonteyn, near the Berg river. Both families trace up their pedigree to Dirk Schalkeveck, of Groene Fonteyn, about fifteen miles south of Klyp Fonteyn, the place where La Caille slept on his way with the sector. {Journal, page 179.) They had no knowledge of Letchie Schalkeveck, nor had they heard of the French astronomer. At Klyp Fonteyn, I found an old woman residing with her son-in-law, Hendrick Thiark, the present proprietor; her maiden name was Clark, and her age 65. She is the widow of Dirk Cotsee, brother of the present Jerrit Cotsee ; was married at the age of seventeen, and has known Klyp Fonteyn forty-eight years. On her marriage, she resided with her mother-in-law, Mrs. Jacobus Cotsee, who died at the age of eighty, and has been dead thirteen years. She often heard her mother-in-law speak of the French astronomer's visit ; and says no one of the name of Schalkeveck resided at Klyp Fonteyn within her recollection. When made acquainted with my errand, she took me to a spot where there was a ruin in her early years, stated by her mother-in-law to be the ruins of Oker Schalkeveck's house. There was nothing to be seen in the shape of a ruin. The sappers and Gibbs were set on, and exposed in a couple of days the foundation 16 VERIFICATION AND EXTENSION OF LA CAILLE'S AKC OF MERIDIAN. of a building, fifty-four feet by twelve, with three partition walls ; also the remains of an oven at the north end, without the wall, where a quantity of ashes were turned out. (See the plan in Plate II.) In the meantime, I had frequent communication with Jerrit Cotsee, who often visited us. He called my attention to a mound of clay, where an oven had lately been made, but had fallen down. He said there was formerly an old ruin there. The sappers were set to work upon it, and, at the depth of three feet, encountered a wall, which they traced and cleared with great labour in three or four days. This foundation, like the other, is of stone and clay, well put together. It is twenty-two feet by twelve, and generally from two to three feet below the common surface of the ground. I attribute the depth to the sliding down of the soil from above, for the ground over it is much inclined. Portions of chaff or short straw lay deep in the clay ; but I place little confidence in this as an indication of a granary, for it may have been carried down by ants or mice. The ground is hard and dry, and of the kind that is used for making bricks. When the measure- ment for the plan of the farm-houses was finished, and the bearings of these ruins taken, they were again covered over without disturbing the stones, so that they may be easily re-examined. Jerrit Cotsee could not give any account of this last-mentioned spot ; there was no roofed building there within his recollection ; neither could he satisfactorily describe the situation of his father's granary, which he formerly said was to the east of the house ; and the position he then assigned to it, about seventy yards eastward, would place the signal fire at his father's door ; for La Caille says he chose a place thirty-six toises due west of the granary. Jerrit furnished me with the following list of the proprietors of the farm : — 1. Hendrick Moal. 2. Cornelius Cotsee, Jerrit's ancestor, a French emigrant.* 3. Oker Van Schalkwyck (I suppose the father of Letchie). 4. Jacobus Cotsee, Jerrit's father. 5. Jasper Cotsee, Jerrit's brother. 6. Jerrit Cotsee, the informant, who divided the property, and sold Klyp Fonteyn to 7. Jacobus Gideon Low. * See the Appendix, No. 15. IDENTIFICATION OF LA CAILLE's STATION AT KLYP FONTEYN. 17 8. Mr. Brant. 9. Mr. Melk. 10. Mr. LoRCHSPUR. 11. Hendrick Thiark, the present proprietor. With regard to the veracity of this man Jerrit, I cannot, as may be supposed, speak positively ; he is a healthy, intelligent, active old man, con- nected by marriage with the most respectable farmers of the neighbourhood, by whom he is designated " father ;" and, by the appearance of his house, garden, and farm, I should say he is an age in advance of those about him. Lieut. Williams rode down to Groene Fonteyn in search of local information ; on his return he gave the following account : — " I saw Mrs. Lambritz, now sixty-nine years old, whose maiden name was Fister. She has resided at Groene Fonteyn forty-one years. Her husband bought the place of Munick, who was proprietor for only one year. Munich bought it of Dirk Schalkwyck, who went to reside at Matjies Fon- teyn, where he and his wife died. They left one son, named Tunis, since dead ; Tunis left two sons and five daughters ; one of the daughters married Fister, of Matjies Fonteyn ; the two sons reside there also.* She knew no other Schalkwyck. On asking her whether there might not be another of that name about twenty miles from Klyp Fonteyn, she seemed to think not. She recommended me to call on Anne Lambritz, a very old lady, who had long known Klyp Fonteyn ; I rode to Keptyn's Kloof and saw her, but she could give no further information. She is sister to Jerrit Cotsee, and is five years younger." We obtained no other information relating to this family. It is possible she (Letchie) gave Captain Everest her maiden name,f for it is very unlikely * We have seen them. — T. M. t I have lately been fortunate enough to trace out the residence of Letchie Schalkeveck. She was never married nor had any children. She had a sister who was married to a person of the name of Watcherhouse (I think), with whom she lived near Riebeck's Castel. After his death, she lived with his son. She died at that place. The son now resides near Saldanha Bay. I am not quite sure of his name. With regard to the spelling of names in this Colony, I have found the following varieties : — Kepteyn's Kloof — Captain's Kloof — Kaptayn's Kloof. Schalkeveck — Schalkewtk — Schalkevyck. Cotsee — Cotzee — Coetsee. Rubeck's Castle — Riebeck's Kasteel. Klip Fontein — Klyp Fonteyn. D 18 VERIFICATION AND EXTENSION OF LA CAILLE's ARC OF MERIDIAN. that in such a place as Zwartland she could have been entirely forgotten in the space of seventeen years, supposing she died shortly after he saw her. CoTSEE understood that Oker Schalkeveck's sons went to the eastern province. It is now clear that there is no one living whose testimony relative to Klyp Fonteyn can be put in competition with Jerrit Cotsee's, and his extends only as far back as 1762, ten years after La Caille was there. We might naturally conclude that much alteration could not have occurred within those ten years, and that his father would have resided in Oker Schalkeveck's house, but he denies this to have been the case ; then, who built the house he did reside in ? to what use was it applied in 1752, if it was then built? for we have the evidence of his mother, through Mrs. Dirk CoTSEE, that Oker Schalkeveck occupied a house which we discovered according to her directions, exactly under the spot to which she led us. Mr. Hertzog's solution of the difficulty explains the whole ; and, if he can support it by any satisfactory testimonial, we are pretty certain of La Caille's granary. He believes that Oker Schalkeveck and Cornelius Cotsee, Jerrit's grandfather, were joint proprietors;* and that Jacobus Cotsee succeeded to his father Cornelius's share at his death, and after- wards purchased Schalkeveck's. By this explanation, the platform of Cap- tain Everest was old Cotsee's dwelling-house, as Jerrit asserts it to have been : Oker Schalkeveck's we know, and the granary was on the foundation which I lately exposed, to the west of the others ; and in the same relative position with respect to them as such offices usually occupy in Zwartland, and I believe elsewhere. The dimensions of this foundation are too circumscribed for a dweUing- house, and its masonry is too good for the purpose of supporting the flimsy hut of a Hottentot, or slave ; buildings of the latter kind are besides not oblong, but circular, and are never constructed of more substantial materials than mud, except at the missionary institutions. I am unable to explain why La Caille was so much confined for room, or to understand his arrangements, if they had any reference to the walls. He says "the place where he, Bestbier, and Poitevin, slept, was six feet by seven, separated from the sector by a curtain which formed a sort of * See the Appendix, wherein this matter is cleared up. IDENTIFICATION OF LA CAILLE's STATIONS ON RIEBECK's CASTEL, ETC. 19 partition : beyond, was a little place for the slaves." (He had eight slaves.) This building is 22 feet by 12 nearly. Oker Schalkeveck's house and the granary are on the same parallel : the meridional distance between Jacobus Cotsee's house and the granary is 210 feet, rather more than 2'', the granary being to the north of the house. (See the Plan, Plate II.) There are at this time three families residing on the farm, in a very primitive condition ; for two of them occupy buildings put up about 1820, by Mr. Melk, for out-houses. Their names are Hendrick Thiark, Jasper Thiark, and Mr. Castor. The latter is only a renter, and has no property in the soil. A fourth building was burnt in the interval between my visits. They usually cook their food in the open air, behind a screen of brushwood collected for the purpose. Their ovens for baking bread are likewise out in the open air, not very unlike large ant-hills, formed of brick, earth, and stones, and the place altogether exhibits poverty and degeneracy. On the east side of the stream there are two threshing-floors, or places for treading out corn by means of oxen. The largest of these occupies a large portion of Jacobus Cotsee's ruin. This floor being flat, clean, and firm, afforded a convenient bearing for Bradley's Sector and the Repeating Circle. Behind the floor within the old foundation, and towards its north end, is a small mud-wall inclosure, about five feet high, which they roofed over, in a rough way, at the time I was carrying on the observations, as a receptacle for straw. Many of the particulars alluded to in this inquiry may appear trifling; they are not, however, without importance in the discussion, and they will, I hope, serve, in conjunction with the map and bearings, to distinguish the ruins now so important from the heaps of rubbish that must ere long cover the place. § 4. Identification of La Caille's Stations on Riebeck's Castel and Capoc Berg. The signals on the triangulating points of Riebeck's Castel and Capoc Berg are easily recognised, and are well described by Captain Everest. I covered over the charcoal remnant of the signal fire on Riebeck's Castel with stones, previously abstracting a portion as an interesting relic. The top of 20 VERIFICATION AND EXTENSION OF LA CAILLE's ARC OF MERIDIAN. this rugged mountain offers nothing inviting to visitors ; the ascent is laborious and difficult: hence the reason why the signal remained undis- turbed, and we were able to enjoy the sight of one undeniable mark of La Caille's work. These points are admirably suited for triangulation. The Cape district, with Cape Town on one side, Zwartland and Naraaqua land on the other, are seen without interruption. The whole of Zwartland plain, excepting the cultivated patches, is covered with brushwood : the soil on the south side of the Berg river is a mixture of pot or brick-clay and sand, tolerably firm, particularly towards Capoc Berg. On the north side of the river sand prevails, and is in general loose and deep. The base line was measured on the south side ; and, although the run is unusually level, I cannot conceive how it could be cleared and measured twice in seven days. If a similar operation should be undertaken hereafter, the base would most probably be measured on the same ground, and, of course, on tressels. In that case, several portions of the line need not be cleared ; where the brushwood is short it might be cut down expeditiously with some sharp tool, as a scythe ; but where it is dense, and above three feet high, considerable labour would be required. I may safely say there is no place within 300 miles of Cape Town, in the proper direction, so well suited for the purpose. § 5. Triangulation for connecting La Caille's Observatory, the Modern Observatory, and Sir John Herschel's large Reflecting Telescope. I now proceed to describe the operation for connecting the observatories, and afterwards to notice the heights, distances, and bearings of the mountains about Klyp Fonteyn. Another position is included with the former, one that must ever excite the feelings and enthusiasm of the admirers of genius : I need scarcely name the scene of Sir John Herschel's recent labours. When made acquainted with my intention, he opposed it on the ground that his observations being differential, they were not necessarily connected with one spot more than another; and he only submitted, in the end, to that which he could not easily prevent. Although the distance between the points to be connected is compara- SMALL TRIANGULATION IN THE NEIGHBOURHOOD OF CAPE TOWN. 21 tively insignificant, as much care is obviously required in the measurement of the base, and greater attention in placing the signals, than in operations on a large scale. Furthermore, the house in Strand Street is nearly invisible from the Observatory ; the front parapet and chimney only emerge above the rising ground half way between the Observatory and Cape Town. The hne of sight thus passing close to the ground, the chimney can scarcely be distinguished when the atmosphere is dry, or in strong sunshine. Sir John Herschel's position is hid from the Observatory by the high ground occupied by the village of Rondebosch. The house is masked by a grove of high trees, and is invisible from any other commodious station. It is situate close to the foot of Wynberg Hill on the north side ; and I may here mention, as a ready means of identifying the place, that Sir John pur- chased it, in the year 1834, from V. A. Schonnberg, and sold it in the year 1838 to Rice J. Jones. It is known by the name of Feldhausen. About half-way up the north side of Wynberg Hill, there is a stone sunk into the ground ; its upper oblong end is about sixteen inches above the surface, and the direction of its longer axis is towards the Blockhouse battery on Devilsberg. This stone is a boundary or land-mark, where four estates join, one of them being Sir John Herschel's. It is visible from the south avenue leading up to his front door, and onwards past the orchard, where the twenty-feet reflector and equatorial room stood. On the top of Wynberg Hill there is a huge weather-rounded granite rock, known by the name of "Wynberg Stone." The distance between it and the boundary stone is 2576 feet ; and both are visible from the Royal Observatory. The east end of Table Mountain and Devilsberg intervening between Cape Town and Sir John Herschel's position, it became necessary to choose a fourth station. Accordingly, " King's Blockhouse" battery, about half-way up the east face of Devilsberg, was fixed upon. The platform of the battery is paved with large flat stones, well cemented together with mortar, and is in good repair. It commands a view of the other stations and the base line. The wings of the Royal Observatory are some feet higher than the meridian rooms ; so that Cape Town cannot be seen from the shutter above the transit instrument, while the west dome intercepts a view of King's Blockhouse from the same point. I therefore chose a station on the west wing, and reduced the distances afterwards to the transit instrument.* * See the plan of the triangulation in Plate III. 22 VERIFICATION AND EXTENSION OF LA CAILLE's ARC OF MERIDIAN. I was desirous, in the measurement of the base, to make it subservient to other useful purposes, particularly as the Rhineland measure, which has hitherto been employed in this colony, is so far a fiction, that there is no authorised standard in the Colonial Office for reference. But I found that the position of the line best adapted for the present purpose might not always be convenient for measurement by the chain ; a second, therefore, was afterwards measured in a suitable position in Cape Town. The site of the base is on the sandy plain to the north of the Observatory. The east end is defined by the centre of the pillar serving for the north meridian mark of the transit-instrument, and the west by a gun. The line is so httle elevated above the sea, that a large portion of it is covered by water at spring-tides. The Liesbeck stream intersects the line about one-fourth of its length from the meridian mark, over which a temporary platform was placed. In the month of October 1836, I applied to Colonel Lewis, Commandant of the Royal Engineers, for an unserviceable gun, and for assistance in the measurement, which he readily granted ; and I here acknowledge the alacrity displayed by the engineer department to meet my wishes on this and several other occasions, and to Sir Benjamin D'Urban, the governor, at the period alluded to, when I had occasion to trouble him. On the 10th of October, Lieut. Williams brought up the gun. A pit was dug, seven feet deep, in a slightly elevated mound, at the west end of the line. The bottom being well lined with stones and mortar, a large flat stone, hollowed in the centre for the reception of the gun, was let down ; the gun was then lowered, and firmly fixed by ramming down the soil, about a foot of the muzzle being left above ground, and painted white. Almost the whole of the apparatus for the measurement was constructed at the Observatory ; and although the screws, brass-work, &c. were homely in appearance, they answered the pur- pose very well. The measuring rods were three in number (distinguished by the letters A, B, C), constructed of well-seasoned white deal, on the model of those employed by General Roy on Hounslow Heath, excepting a few minor details corresponding with the contemplated method of using them. The square brass ferule covering each extremity was perforated perpendicularly with a hole, three-eighths of an inch in diameter; the ferule was then driven on and firmly fixed. A brass screw, a quarter of an inch in diameter, and nearly two inches long, was passed into the wood through the hole SMALL TRIANGULATION IN THE NEIGHBOURHOOD OF CAPE TOWN. 23 without touching the ferule, and both were ground down together perfectly flat. The screw-head was to carry the division that defined the length of the rod, and could only be affected by the expansion of. the wood. Eight tressels were constructed on the model of General Roy's, six of them having wood screws and moveable teak-wood tables. Also, teak-wood clamps with steel screws working in brass sockets, for clamping the rods to the tressels, and clamps with screws, for driving up the rods to adjustment, with the usual equipment of boning rods and pickets. The standard rod was twenty feet long. It was only trussed laterally, but, to prevent vertical flexure, the depth was increased to eight inches, and it rested on a smooth plank, ten inches deep and three inches thick. Two stout brass plates, three inches long and five deep, were fixed to the sides near each end with bolts and nuts, for transferring the length of the rod to the measuring rods. Their tops projected two inches (the depth of the measuring rods) above the upper surface. Five brass pins were screwed into the upper surface of the rod, four feet from each other, their tops ground down smooth to receive the divisions in laying off the rod. A microscopic beam compass was contrived by fixing, with brass plates, a micrometer microscope to each end of a deal plank, four feet long. Two blocks were fixed to the beam, of such a depth, that, when they rested on a smooth surface, that surface was in the focus of the microscopes. While these instruments were in progress, I had several consultations with Sir John Herschel, who, always ready to assist me with his advice, entered warmly into the contrivances for measuring the base. If there had been plenty of time and mechanical means for carrying one of the plans he proposed into effect, there is little doubt that the length of the base would have been determined as accurately as the standard rod, by means of the beam compass. I had contrived to prevent the ends of the rods touching in the measure- ment, and proposed to measure the space between the divisions by means of a scale. He suggested the trial of making the space a constant quantity, which would prevent mistakes in registering, and which might be effected by a piece of mica. Accordingly a couple of crosses were drawn on a slip of mica, 2'3 inches, nearly, from each other, with a fine point ; then, turning the divided surface downwards to prevent parallax, the crosses were seen 24 VERIFICATION AND EXTENSION OP LA CAILLE'S ARC OF MERIDIAN. through the transparent mica hke spider lines, and being placed over a fine Hne on brass, a neat bisection of the cross was easily effected. This con- trivance was afterwards found to answer well in practice with the assistance of a common magnifier. Every thing being ready by the 4th of April, 1837, for laying off the rods, the opportunity was offered to the Colonial Government for comparing their standard of measure with the brass scale at the Observatory, and some of the official gentlemen were invited to witness our proceedings. Accordingly Colonel Bell, the colonial secretary. Major Michel, the surveyor-general. Colonel Lewis and Lieut. Williams, of the Royal Engineers, and Sir J. Herschel, met at the Observatory. A straight line on the standard rod was defined by a fine silver wire stretched by means of a weight : where it passed over the brass heads, a hne was drawn with a cutter. The brass scale was then removed from its case, and placed on the trussing of the rod, with a thermometer upon it, and another at some distance. Sufficient time having been allowed for equahzing the temperature of the scale and the room, the beam compasses were placed upon the scale, and the micrometer screws turned until the first and last divisions of the scale bisected the cross wires. A zero division having been previously cut on the first brass head of the standard rod, the beam compass was transferred from the scale to the rod ; and one of the microscopes was brought over the division, which was made to bisect the cross wire by gentle taps on the foot of the compass, taking care to keep the second microscope exactly over the longitudinal division on the second brass head. A t square, got up for this purpose, was then clamped to the rod, and the edge brought under the second microscope was made to bisect the cross wire ; the cutter was then applied, and the second division drawn. The compass was now returned to the scale to verify the position of the wires. Thus the five lengths of the scale were laid off, the gentlemen present having an opportunity to examine each bisection before and after the cutter was applied. The thermometer on the scale indicated 71°-8 at the beginning, and 72° at the termination : the temperature of the room as shewn by the distant thermometer was 72°. For the purpose of transferring the first and last divisions to the upper edges of the brass plates, an oblong piece of teak-wood, of the depth and thickness of the measuring rods, with a thin brass plate screwed on its upper SMALL TRIANGULATION IN THE NEIGHBOURHOOD OF CAPE TOWN. 25 surface, was smoothed, and its angles squared. A hole, half an inch in diameter, was drilled through it from above downwards, and a portion of the side cut away below to admit light. A piece of mica, with a cross-line on its under surface, was cemented on the lower end of the hole ; so that, on looking through from above, the cross appeared in the centre of the field. The block being placed over one of the end divisions and clamped to the rod, the division was made to bisect the cross on the mica. The t square was now clamped to the upper surface of the block and brass plate of the rod, and a line was cut on both. The block was then removed to the other brass plate, and fixed as before over the division below, and the division on the top was continued to the brass plate by means of the t square and cutter. It is obvious that the relative longitudinal distance between the cross on the mica and the line on the upper surface of the block, must be equal to the relative longitudinal distance of the divisions on the brass pin and the plate ; consequently the length between the divisions on the plates was equal to the length between the divisions on the pins, provided the direction of the block was the sarne at both operations. Other engagements interfering, I had not leisure to examine the standard rod until the 28th and 29th of May, 1837, The examination was then under- taken. The scale was placed on' the trussing of the rod as formerly, and by means of the compasses each length of four feet was compared with the scale in rotation, as follows : — Temperature of the scale, 59°-5 ; of the room, 59°-8. 1st interval + 28'2 divisions. 2d + 24-2 3d + 20-0 ■ 4th + 24-2 5th + 12-9 Sum + 109-5 Run of micromeLui- B over one-tenth of an inch = 565*7 divisions. A subsequent experiment gave 565*4 divisions. Then ,„ _ x 0'°-l = 0'°'01936, by which the standard rod appears to exceed 20 feet of 565-7 -' rr the brass scale, both being at the temperature 59°-5. The temperature engraved on the scale is 70°. And suppose the expansion of white deal is -0000022685 for 1° of Fahrenheit's scale. r. of brass -0000103077 E 26 VERIFICATION AND EXTENSION OF LA CAILLE's ARC OF MERIDIAN. Then -0000080392 x 240 x 10-5 = 020259 is the estimated relative contraction of the rod with regard to the brass scale, for 10°'5 of the thermometer; and the difference, or -0009, may be taken as the error of the rod at 70°. Five comparisons gave the following results : — Computed Thermometrical Therm. relative contraction of the Observed Difference Deal Rod. of the Rod and Scale. O in. i". 59..5 0-02026 0-01936 by Mr. Maclear. 58-5 0-02219 0-0-2319 Ditto. 58-9 0-02142 0-02307 Mr. C. P. Smyth. ,58-75 0-02171 0-02202 Ditto. 58-9 0-02142 0-02206 Mr. Maclear. Mean 0-02140 0-02194 The difference between the two means, 0'°-00054, may be considered as the quantity by which the standard rod of 20 feet exceeds 20 feet of the brass scale, both being at the temperature of 70°. The scale is by Dollond. It is a thin brass bar, inclosed in a mahogany case lined with green baize. Sir John Herschel was so good as to take charge of this scale, on his return to England, for the purpose of comparing it with the Royal Astronomical Society's Standard.* The measurement of the base-line commenced on the 17th of June, 1837, in the presence of the gentlemen before mentioned. Sir John Herschel, Lieutenant Williams, Mr. C. P. Smyth, and myself performing the work. The previous day was spent in boning the line, driving pickets, and the like preparations. As the point on the meridian pillar, meant to define the east end of the line, was considerably elevated, a hole was drilled in a stone let into the ground close to the pillar, for a convenient starting point. Two tressels being placed in position and levelled, rod a was laid on ; and a cylindrical plummet in the form of a tube, with cross-wires on the lower surface, was * The 4-feet brass scale, here alluded to, was compared with the standard scale of the Royal Astronomical Society by Sir John Herschel and Mr. Baily; and the mean of sixty-three comparisons shewed that the 4-feet brass scale is equal to 47-997083 inches of the standard yard of the Society. The comparisons were made on March 5th-9th, 1839, both days inclusive; the thermometer varying from 32°- 8 to 44° during those days. The 4-feet scale was sometimes placed next to the observers, and at other times the Society's scale : and the comparisons were made with the two several 4-feet of the Society's scale. The results were very accordant and satisfactory. [I am informed by Mr. Baily that no correction was applied for temperature G. B. A.] SMALL TRIANGULATION IN THE NEIGHBOURHOOD OF CAPE TOWN. 27 suspended from the end of the rod through a tin tube (to guard it against the wind) over the hole in the stone. The rod was then shifted until the cross wires, as seen from above through the plummet with an opera-glass, coincided with the centre of the hole. It was then clamped ; and rod b being placed, the piece of mica, before mentioned, was laid on end 2 of rod a, and held down by a weight ; by gentle taps on the weight, the division was made to bisect the cross. End 1 of rod b was now driven up until its division bisected the other cross ; the rod was then clamped, and the bisection again examined. Rod c was in like manner brought into line, and the mica transferred to the junctions of b and c. As the rods were successively brought up and placed, the bisections were always re-examined before the mica was removed from its last position. The twenty-inch transit was placed about the middle of the line directed towards the advancing rods ; through the telescope the intervening cross-bars of the boning-rods were seen as one, the telescope being parallel to the horizon, and the axis on the same level with the bars. Lozenge-shaped holes, in triangular pieces of wood of equal dimensions, were fixed to the rods, one at each end ; so that by looking through one end of the series, a concentric line of gradually diminishing apertures would prove the rods to be in a right line. They were soon abandoned, for they were either not truly placed with reference to the axes of the rods, or the test was too delicate for practice : I believe the former to have been the case. The progress this day was inconsiderable, in a great measure owing to the delay in levelling and adjusting the tressels where the ground was uneven and cut up by floods. A pig of lead, weighing fifty-six pounds, was sunk in the ground at the end of the twenty-seventh rod. The plummet being supended from the advancing end of the rod through the tube, a cross was cut on the lead and adjusted to the plummet, then covered with sand. Lieutenant Williams, Mr. C. P. Smyth, and myself, continued the mea- surement on the 18th; we were deprived of the valuable assistance of Sir John Herschel, who was suffering from the damp and cold of the preceding day, but he paid us a visit. In the afternoon a. brisk breeze sprung up from the N. W. I was in the act of adjusting the sixty-sixth rod, when a sudden gust blew it and the next off the tressels. I caught hold of the third and saved it. One was entirely destroyed ; the other being clamped, the feet broke off close to the clamps 28 VERIFICATION AND EXTENSION OF LA CAILLE's ARC OF MERIDIAN. and it went over slowly. This accident compelled us to postpone the mea- surement until November ; for, before a new rod could be made, and the other repaired, the winter had set in and the floods had spoiled the line, and we could not calculate upon four days' fine weather. I may here remark that, although the contrivance adopted for preventing a similar accident proved effectual, rods of this description are unfitted for a windy country like the Cape ; they are liable to short vibrations whiqh no clamping can control. They should only be used in calm weather ; but a continuance of such weather at the Cape is not very common. I certainly should be unwilhng to hazard them on a six-mile hne. The measurement was recommenced from the meridian pillar on the 8th of November, 1837. Hooks were now fixed on the trussing of each rod, so that a cord could be linked on loose, the other end being attached to a weight resting on the ground. A 220-feet sash-line was stretched with the force of four men over the tops of the pickets to direct the advancing foot of each tressel, and was moved from time to time as the rods came up. The party consisted of Lieutenant Williams, Mr. C. P. Smyth, myself, Joseph Gibbs, two sappers, and a common labourer. Each confined himself to his assigned department of the work, which went on with regularity and precision. On reaching the twenty-seventh rod, the lead was uncovered that was placed there in June : the plummet fell short of the mark upon it nearly half an inch. It is not improbable that, as the place was frequently covered with water in the winter, the lead may have shifted. At sunset, a pig of lead was sunk in the ground at the end of the forty-sixth rod. The next morning was foggy, but sufficiently clear to admit of the boning rods being seen. Towards one o'clock the tide unexpectedly flowed over the hne immediately in advance, at the same time indications of approaching rain caused us to drop the plummet, having this day measured only twenty- eight rods. The 10th was rainy; we resumed on the 11th late in the forenoon, and by sunset completed thirty-eight rods. We began at sunrise on the 13th, and reached the gun, marking the west end, at noon, having measured thirty- two rods. The muzzle of the gun being considerably higher than the level of the rods, and the last rod falling short of the gun, a smooth deal plank was SMALL TRIANGULATION IN THE NEIGHBOURHOOD OF CAPE TOWN. 29 levelled ; one end resting on the gun at the intersection of the cross-wires stretched on the muzzle, the other on a tressel lowered into the ground. A plumb-line was shifted along the plank until the apex of the bob coincided with the division on the last rod. The point of suspension being marked and afterwards measured at the Observatory, shewed that the last, or 144th rod, fell short of the gun 7'* 10"-825. I should state that four equidistant grooves were cut in the muzzle with a file, to receive two wires stretched by weights. The intersection of the wires is supposed to be the centre of the muzzle. To obtain the distance between the crosses on the mica employed in joining the ends of the rods, it was laid on the graduated ring of the mural circle ; and the angular distance, measured by the microscopes of the instru- ment, gave 3° 17' 16" = 2^-2752. But as it is difiBcult to observe the coinci- dence of the intersections of cross wires with cross lines of different inclina- tions, and as the mica, moreover, required to be held on with the hand, the result was discarded. Q.OO The mean of five measures on the brass scale gave 2^'3 — ^- x 0'"*1 = 2'"-29843, none differing from the mean more than -^^ of an inch. The distance between the divisions and extreme ends of the rods from which the plumb-line was occasionally dropped, proved to be, — Rod A, end 1 = 1-034 inch. 2 = 1-018 — Rod B, end 2 = 1-025 — Rod C, end 2 = 1-050 — 30 VERIFICATION AND EXTENSION OF LA CAILLE'S ARC OF MERIDIAN. At the commencement, rod A was first laid on ; the hne hung from end I : at the twenty-seventh rod, the line hung from end 2 of rod C ; a new elevation was there taken, and the next start was made from end 1 of A, leaving off at night from end 2 of A. The sum of these is =4-136 inches. Second day, Rod A, ends 1 and 2 = 2052 — Third day, Rod A, end 1 ; B, end 2 . . = 2-059 — Fourth day. Rod A, end 1 =1-034 — The rods were compared with the standard on the morning of the first day ; they were of exactly the same length. The air all day was hot and dry. Mean of the thermometers attached to the rods, 83°. The second day was foggy and moist. Mean of the thermometers, 65°. The rods were compared with the standard immediately after returning from the field, when the former were wet. in Rod A exceeded the standard 0-012 — B 0-020 _ C 0-025 On the morning of the third day. Rod A exceeded the standard 0-012 — B 0-022 — C 0-025 Again, on returning. Rod A exceeded the standard 0-025 — B 0-000 _ C 0-011 This day was gloomy ; mean of the thermometers, 68°-4. Fourth day, in the afternoon. Rod A exceeded the standard O'OOO — B 0-017 _ C 0-025 The atmosphere dry and cloudy ; mean of the thermometers, 71°*3. On remarking the above variation, I was informed by those who removed the rods on the third morning from the room, that one of them encountered a brass plate of the standard. I immediately compared the plates with the divisions below on the brass heads, and found the distance between the latter longer than between the former by about tt of an inch, so that the indications SMALL TRIANGULATION IN THE NEIGHBOURHOOD OP CAPE TOWN. 31 of the standard rod at the latter comparisons were less than they should be by that quantity. The observed correction from the comparisons is + 0-294 inch. The expansion of white deal on 20 feet is 0'000544 inch for 1° of Fahrenheit. The temperature of the large room where the standard was kept, was almost uniformly 65° ; then the computed reduction of the base to the standard rod will be. 0-0000 1st day -000544 x 46 x 83°-0— 65°= +0-4504 2d — - 3d — - 4th— - X 28x65° -65°= x38x ,°-4_65°= +0-0703 X 32 x71°-3-65°= +0-1097 Sum =+0-6304 The computed correction was adopted. LENGTH OF THE BASE. 1st day, 46 rods =920 -i 4 plumb-line values 4-136 (. 44 mica lengths 8 5-131 [ 2d day, 28 rods =560 -i 2 plumb-line values 2-052 I. 27 mica lengths 5 2-058 J 3d day, 88 rods =760 -i 2 plumb-line values 2-059 1, 37 mica lengths 7 1-042 J 4th day, 32 rods =640 1 plumb-line value 1-034 31 mica lengths 5 11 -25 1 Deal plank 7 10-825 Correction for temperature of measuring rods to 65° +0-630 Correction for temperature of standard rod, from 65° to 70° —0-392 Correction for error of standard rod at 70° +0-078 Length of base as it would be shewn by the brass scale, supposing it used at the tem- perature 70° of Fahrenheit 928 9-267 565 4-110 767 3-101 653 11-110 0-316 >.. = 2915 3-904 J = 2915-325 The east-end base-signal, when I was measuring the angles, was placed over the stone from which the base-measure was begun ; therefore the above 32 VERIFICATION AND EXTENSION OF LA CAILLE S ARC OF MERIDIAN. value was used in the triangulation. Subsequently the distance between the stone and the intersection of two diagonal lines, drawn on the top of the pillar, was ascertained (by suspending a plummet from a plank) to be 4*'-040 : therefore the distance between the centre of the gun and the centre of the pillar appears to be 2919'*-365. The angles were measured in the latter part of 1836, while the apparatus for measuring the base-hne was in progress. I employed the repeating instrument by Dollond, described in the first volume of the Memoirs of the Royal Astronomical Society. The "tell-tale" level, for checking a shift in the horizontal circle while the verniers are moved, was in England for repair. I had calculated upon receiving it in time for this work, but was finally com- pelled to proceed without it, adopting whatever precautionary measures I could think of; such as always driving the tangent screw in one direction, and repeating backward as well as forward. In the employment of this instrument for measuring horizontal angles, it is presumed that the stand is secure against horizontal flexure or shift, over which the "tell-tale" level can have no control. To guard against this danger, I had a heavy stand constructed of teak-wood, the legs braced with cross bars ; and, to increase their steadiness, a 14 lb. weight was attached to each. Three conical grooves of brass were let into the top of the stand, the direction of the grooves coinciding with three lines at equal angles radiating from the centre of the top. The feet of the instrument readily fell into their places in these grooves, and were equally strained during the motion of the verniers. This instrument is very powerful for its dimensions. As an altitude instrument, its precision is astonishing; and if a telescope could be attached to the horizontal circle, I should not hesitate to use it on the most extensive survey. A fair mean was taken of all the measures of each angle, and as all the angles were measured, I had the usual check on the work ; yet, on the return of the level from England, I thought it right to repeat those of the base-line. The difference was trifling. The signals on the Blockhouse Battery, Observatory, and base-line stations, were tripods surrounded by hoops, and covered with white cloth. They were placed over their respective stations by means of a plummet suspended from the inside of their conical tops. The signal at Mrs. De Witt's was a circular disc painted on the east chimney. This chimney is SMALL TRIANGULATION IN THE NEIGHBOURHOOD OF CAPE TOWN, 33 narrow, and the distance considerable. The disc, as seen from the Observ- atory, coincides with the centre of the chimney ; as seen from the Block- house it is a trifling distance to the right. The Blockhouse signal was twice destroyed by wind ; finally, a disc projecting from an arm was nailed to the chimney behind the battery, and the angles were reduced to the first station on the battery. OBSERVATORY STATION. On the west wing, 33" 8'"-5 to the north of the dome. The place of the plummet-point (defining the position of the axis of the circle) is marked on the lead. 1836. Nov. 23/ ^"^'' ^'*''''° ^'' ^^ H^^^chel's Boundary-stone-, g^o ^ ,^^,,^ L and King's Blockhouse, 10 repetitions J Nov. 23 J Angle between east end of Base and west end of"l Dec. 2 \ Base, 92 repetitions J 1837. [Day not entered]. The same, 40 repetitions 42 15 22-75 1836. Dec. 2 f Angle between Blockhouse and west end of Base, 1 ,_-S .„ . . > 84 35 13*57 19 L 46 repetitions J Remark.* — The observations of Dec. 19 were made on the disc on the Battery Chimney, 33"- 349 from the station on the platform of the Battery. The azimuth of the disc (as seen from the platform), measured from the centre of the dome in the direction of N.E.S.W., is 156° 17' 5". The Reduction adopted in forming the number above is + 4' 32"'98. Dec. 2 r Angle between Blockhouse and Mrs. De Witt's "i o ; ,/ J ^ !- 51 52 54-71 9 L Chimney, 44 repetitions '} EAST END OF BASE. The circle placed over the stone close to the Meridian Pillar. 1836. Nov. 23 f Angle between Observatory and west end of Base, T o / ,, •i-w ini mn ^-i- }• 101 55 16-57 Dec. 12 L 73 repetitions J * This remark stands thus in the MS. : — " Those of Dec. 19 from the disc on the Battery " Chimney 33"- 349 from the station on the platform. N.E. bearing of the centre of the dome as " seen from the platform 156° 17' 5". Reduction -|- 4' 32''-98." I have altered the wording in the only way in which the remark can have any meaning, with due reference to the numerical values. It would seem however that, either the direction of the azimuth ought to be opposite to that which I have assumed, or the sign of the reduction ought to be changed. The numbers also would agree better if the azimuth angle were 156° 57' 5". But this is not important, as the values of the angles of the triangle are given in the text as finally corrected. — G. B. A. F 34 VERIFICATION AND EXTENSION OF LA CAILLE's ARC OF MERIDIAN. WEST END OF BASE. The plummet of the circle 1 1 inches from the intersection of the cross-wires on the muzzle of the gun. The gun, as seen from the circle, bore 30° 43' to the left of the Meridian Pillar (east end of Base). 1836. Nov. 23 r Angle between Observatory and east end of Base, "i „ ° ,„' if-Vno Dec. 12 1 31 repetitions (Reduction + 7"-76) J With "tell-tale" level, 41 repetitions. -i 1837. [Date not entered] a , „ Blockhouse, 119 repetitions J ^^ ^^ ^°'^'' Reduction of window to station on west wing — 2 58-19 Reduction to centre (from the actual position of the "i circle to Mrs. De Witt's Chimney) J + 1 1 "65 True angle 35 15 24-23 SIR JOHN HERSCHEL'S BOUNDARY-STONE STATION. The axis of the circle six inches due west of the centre of the stone. Nov. 28. Angle between the King's Blockhouse Battery and T o , « Observatory, 100 repetitions (Red. + 4"-76) . . J ^^ ^* ^°'°^ / 84 35 12' 24 2 46 71 22 2 180 SMALL TRIANGULATION IN THE NEIGHBOURHOOD OF CAPE TOWN. 35 RESULTS. Angles observed. Angles used in calculation. Observatory 42° 15' 22"-7 42° 15' 23" East end of base 101 55 16 -7 101 55 16 West end of base 35 49 19-6 35 49 21 Sum of angles 179 59 59 180 Base line 2915-325 feet.. Observatory to east end of base 2537-396 — — to west end of base 4241-881 — Observatory 84 35 13'-'6 King's Blockhouse 24 2 47 West end of base 7122 2-2 Sum of angles 180 2-8 Blockhouse to west end of base 10363-817 feet. to Observatory 9864-600 — Observatory 51 52 Si'j 51° 52 SS" King's Blockhouse 92 5138-1 92 5138 Mrs. De Witt's Chimney 35 15 24-2 35 15 24 Sum of angles 179 59 57 180 Observatory to Mrs. De Witt's Chimney 17067-951 feet. King's Blockhouse to ditto 1 3444-955 — Observatory 39° o' 33'-'3 39° o' 33" King's Blockhouse 117 4 57-7 117 4 57 Sir J. Hersch el's Boundary-stone 23 54 30-1 23 54 30 Sum of angles 180 1-1 180 Observatory to Sir J. Herschel's Boundary-stone . . 21671-645 feet. King's Blockhouse to ditto 15321 -025 — To measure direct, from a point immediately above the middle of the axis of the transit instrument, the angle between Mrs. De Witt's chimney and the dot on the meridian pillar in the meridian of the ten-feet transit instru- ment, or the azimuth of the chimney as seen from the middle of the transit axis, a high stage would be required on the roof of the transit-room, which would not only incur considerable expense, but would be attended with risk, where there is so much danger from the force of the wind. I therefore preferred measuring the angle between these objects on the west wing, and reducing it to the transit instrument. I measured on the west wing the angle between the signal at the east end 36 VERIFICATION AND EXTENSION OF LA CAILLE's ARC OF MERIDIAN. of the base and the dot on the pillar. Ten repetitions gave 6' 47"-7. Apply- ing this quantity to the angle between the chimney and signal derived from the preceding angles, the angle between the chimney and the dot, as observed on the west-wing station, is 75° 4' 29"*3. The same was measured direct. Forty repetitions gave 75° 4' 39"-l. The distance between the west-wing station and a plumb-line dropped on the intersection of the axes of the transit instrument, carefully measured with a trussed rod, levelled by means of a spirit level, was found to be 28" l'""81. '1 191 45 35 The angle as observed on the west wing between the meridian dot and ~1 o i n plumb-line J between Mrs. DEWiTx'sChim- " ney and plumb-line . . between Sir J. Herschel's t Boundary-stone and plumb- 1 100 51 55 line J Therefore, the reduction to the transit instrument for Mrs. De Witt's Chimney is - 36' 54"-2 ; and, adopting 75° 4' 39"- 1, The azimuth of the chimney from the north towards the west, as "i o / « ... !> 74 27 449 seen from the transit instrument, is J The distance between the chimney and transit instrument 17096 feet. Therefore the chimney is 4579"'5 north from the perpendicular. And 16471 -l west from the meridian. Assuming the compression ^gg. 1" in lat. 33° 56' = 101"-739; therefore the difference in latitude = 45"'01 : and, if the latitude of the Royal Observ- atory is 33° 56' 3"-25, the latitude of the chimney is 33° 55' 18"-24. The chimney is southwesterly of the supposed sight of La Caille's Observatory about 120 feet, or, reduced to the meridian of the Observ- atory, 115 feet; consequently, the latitude of La Caille's Observatory is 33° 55' 17"-11. La Caille assumed it to be 33° 55' 15".* * La Caille first adopted for his latitude 33° 55' 14"-5 or 33° 55' 15", in the Memoirs of the Academy of Sciences for 1751, pages 411 and 412 : but on revising his computations in the Fundamenta AstronomicB , published in 1757, he found it to be 33° 55' ]3"-3 : and in a paper read to the Academy of Sciences in 1756, but revised and read again in 1758, and published in 1761, in the volume of the Memoirs for 1755, page 569, he latterly determined the latitude to be 33° 55' 12"-6. And the Baron de Zach states that, on recomputing the observations of La Caille he found the latitude to be 33° 55' 12"-45 — (Zach's Correspondance Astronomique, vol. n\. p. 615). [For this note I am indebted to Professor Henderson G. B. A.] SMALL TRIANGULATION IN THE NEIGHBOURHOOD OF CAPE TOWN. 37 The angle at the west-wing station, between Sir John Herschel's"] Boundary-stone and the dot in the meridian of the transit-instru- ll65 57 57-3 ment, computed from angles already observed, is The same observed direct, 31 repetitions 166 57 49-8 The supplement (eastward) observed direct, 14 repetitions 194 1 54-7 Reduction to the transit instrument 42 26'44 Adopting the direct observations, we have Azimuth from north, westward, as seen from the transit instrument .... 165 15 23*4 eastward 194 44 2M Defect from 360°=15"-5. The stone is visible from the roof of the transit instrument ; but the form of the shutter prevented the axis of the circle being placed exactly over the instrument. The plummet fell 8"5 inches to the east, and 3 inches north ; therefore the reduction is 63""4< : this is applied to form the following numbers : — O / // Six repetitions westward, on the roof of the transit instrument, gave . . 165 }5 30-5 — ' eastward, gave 194 44 14-1 Defect from 360° = 15"-4. I cannot explain this defect, which is constant for both stations, on any other hypothesis than a drag of the lower circle, or stand. The stone was whitewashed, and the observations from the transit-roof were made on a gloomy morning, when there could not be any deception from a phase of the signal. The mean of the results for eastward angle, from the direct observations on the west wing, is 194° 44' 28"-85: that from the direct observations on the roof of the transit instrument is 194° 44' 21"-8. The mean of these two, giving them the respective weights 45 and 12 (the whole number of direct observations at each place) is 194° 44' 27""3, or the azimuth of the stone from the south point westward is 14° 44' 27"-3. And the distance from the meridian, 5514-3 feet to the west; from the perpendicular, 20958*4 feet to the south. It may not be amiss to introduce the continuation of the triangulation from the boundary-stone, to the south avenue leading up to Sir John Her- schel's house, made by Sir John Herschel himself, with a small theodolite. The angle between " Wynberg stone" and the Boundary-stone, observed on 38 VERIFICATION AND EXTENSION OF LA CAILLE's ARC OF MERIDIAN. the west-wing station with Dollond's circle, is 5° 9' 33"-44. Between the centre of the chimney of the Block-house Battery and "Wynberg stone," 33° 54' 21"-62. The nearest distance between the centre of the west dome and the line of sight to the former, 9" 0'°-6; the same to the latter, 12* 3*". Sir John measured a small base-line in his avenue of 516*'-21 ; and he found, by observation, the following angles (they are corrected for calculation) : — BOUNDARY-STONE STATION. Between both ends of base 7 1 6 52 Between Wynberg Stone and Royal Observatory 125 41 28 Between Wynberg Stone and north-west end of base 122 28 40 " WYNBERG STONE" STATION. Between Royal Observatory and Boundary-stone 49 8 59 Between Boundary-stone and north-west end of base 30 4 46 SOUTH-EAST END OF BASE STATION. Between Boundary-stone and north-west end of base 136 32 6 NORTH-WEST END OF BASE STATION. Between Boundary-stone and south-east end of base 36 11 2 Between Boundary-stone and " Wynberg stone" 27 26 34 Hence, ft Distance between Observatory station and " Wynberg stone" = 23268*90 between Boundary- stone and " Wynberg stone" ^ 2576*45 between Boundary-stone and east end of base = 2404"65 between Boundary-stone and west end of base = 2801*88 between " Wynberg stone" and the Boundary-stone, T calculated from the Observatory base-line J The difference between the determinations of the distance between the Wynberg and Boundary stones, from the two base-lines, is only 1™'8. I may here mention, that, in the expected triangulation round Table Mountain, for the purpose of obtaining the difference of latitude between the sector stations on the north and south sides of the mountain, there will be an opportunity of intersecting the roof of the dwelling-house from two points. Sir J. Herschel further found, by prolonging his base above mentioned, and letting fall on it a perpendicular from the centre of the twenty-feet SMALL TRIANGULATION IN THE NEIGHBOURHOOD OF KLYP FONTEYN. 39 reflector, the following values of the co-ordinates of that centre, as referred to the base : — Abscissa = distance of the perpendicular from the north-west ex-T '' 1551-0 tremity of the base, in the direction of the base continued . . Ordinate = perpendicular offset to centre of the reflector 56'69 In like manner were the co-ordinates of the centre of the equatorial instrument (supposed coincident with that of the circular building containing it) ascertained, as follow : — Abscissa = distance from the north-west extremity of the base, 1 of a perpendicular let fall on its prolongation from the centre ? = 645-73 of building J Ordinate = perpendicular offset to centre = 95-86 § 6. Triangulation for CONNECTING La Caille's Sector-Station at Klyp FoNTEYN, THE MoDERN SeCTOR-StATION, AND THE NEIGHBOURING HiLLS. The Klyp Fonteyn station is in the north-east corner of Zwartland Plain, where a range of high mountains, twelve or fifteen miles long, known by the name of Picquet Berg, abruptly terminates. La Caille's map in the Mem. de rAcadimie, 1751, shews this range continued further to the north, which incHnes me to think he neither ascended that mountain nor journeyed north of the farm. About half a mile north of the parallel of the farm, the mountain makes a sudden turn to the west, and terminates in a kloof or valley to the north of and in the meridian of La Caille's station. The north front of this turn is steep, like a gigantic wall, nearly as perpendicular as the north front of Table Mountain, and, from the ground below, cannot be less than 2500 feet high. From the before-mentioned valley, another mountain rises on the west, running, first west, about a mile, then north-west, where it terminates in Zwartland Plain. This is the "montagne sans nom" of La Caille. To the north of it, close up, there are two or three irregular masses; these gradually dwindle into an undulating ridge of low hills northwards, about ten or twelve miles. Near their north extremity, a very remarkable-shaped mountain rises from the plain, called "Little Table Mountain" (Kleintze Tafel Berg). There is no eminence north of this one nearer than fifty or sixty miles. 40 VERIFICATION AND EXTENSION OF LA CAILLE's ARC OF MERIDIAN. But to the N.N.E. of Klyp Fonteyn, the country undulates for a considerable distance ; and, fifty or sixty miles off, there are several very high mountains. Lieut. Williams and myself started off on horseback, with the intention of exploring the nature of the country north of Klyp Fonteyn. We did not find it necessary to go further than "Little Table Mountain." From a comparatively low hill near to it, we had an uninterrupted view to the north of about sixty miles, over a plain, apparently of loose sand, covered with brushwood, bounded by the sea-shore on the west, and on the north- east by undulating hills and the mountains before-mentioned. Returning, we had a good view of the north extremity of Picquet Berg and the " nameless mountain." Some weeks would be required to make a perfect survey of the mountains about this station. I did not, therefore, attempt to carry a chain of triangles round them, as I had other pressing engagements that could not be post- poned. But I ascertained the heights, distances, and bearings of the culminating points with considerable exactness ; and from these a map was made, which will convey an idea of their form and their probable influence on the zenith distances. They consist almost entirely of solid rock with little interstitial earthy matter, sandstone mixed with quartz ; specimens of which are transmitted with this communication. The inclination of the strata is westward, and above 20°. Their tops are rugged, with irregular masses of naked rock. There is no hill of consequence from the west point to twelve degrees east of south, nearer than Zwartberg. La Caille's station is on the rise of a hill, inclosed within the corner formed by the westward turn of Picquet Berg. This hill, which he does not mention in his Journal, like the rest, is composed of sandstone ; and its top rises 700 feet above the granary. Some of the rocks at its base are within ninety yards of the station : indeed, the latter may be understood as placed on the west slope of a mountain of solid rock, at an elevation of 400 feet above the level of the sea. The circle and Bradley's sector were placed on the corn-floor, on Jacobus Cotsee's foundation, before the foundation of the granary was discovered; and, as the place was comparatively convenient, and the in- fluence of the surrounding masses nearly common to both, I went on where I began. SMALL TRI ANGULATION IN THE NEIGHBOURHOOD OF KLYP FONTEYN. 41 I soon found that I must distinguish the several masses from each other by names, to prevent confusion in the entries.* Accordingly, the "moun- tain without a name" was called "Castle Hill," from a remarkable rock on the nearest summit resembling a castle. The mountain close to the sector, " La Caille's Mount." The west termination of Picquet Berg, " Hunchback," from its figure. A mass of rock to the south, in the plain, with three remarkable peaks, the " Three BernouUis," Daniel being the middle one. Another mass, eleven degrees more to the west, which resembled a fortifica- tion, " Fort Azimuth ;" for, on its west summit, there is a sharply defined conical rock, which supplied an excellent natural and permanent signal. This rock was compared with the sun, to get the direction of the meridian, and the angles all round were connected with it. The station may be recovered at any future time from the bearings and distances of Fort Azimuth, the three BernoulHs, the north culminating point of La Caille's Mount, the south culminating point of the same, two rocks near the station, a group of rocks above the spring, and the Castle. Besides, a pit was dug in the corn-floor, under the axis of the sector, three feet and a half deep, where the rock was met with. A hollow was chiselled in the rock to receive a quart bottle, containing the following memorandum, written in large round hand : — "Bradley's IS^^-feet zenith sector was 'placed over this spot (supposed to be the north extremity of La Caille's arc of the meridian), for the purpose of verifying the astronomical portion of that work, on the 27th day of March, 1838. The observations began on Wednesday, the 28th, and continued to the 21st day of April, when the instrument was taken down. "The party consisted of Thomas Maclear, H.M. Astronomer; Lieut. Williams, Royal Engineers; J. Smith, Serjeant, Royal Engineers; — Sharpe, Gunner, Royal Artillery ; Joseph Gibbs, Carpenter and Labourer to the Royal Observatory ; Conrad Engelbraght, Johnny Wallace, Servants. Signed by " Thomas Maclear. "John Williams." On the other side of the paper : — " Over this there is a stone 1*' 11*" long, 13|- inches in breadth, and 5 J inches deep, with the letters B^ Sr 1838. Whoever disturbs this is requested to replace it with care, and to notice the circumstance." * See the sketches and elevations in Plates IV. and V., and the triangulation in Plate VI. G 42 VERIFICATION AND EXTENSION OF LA CAILLE's ARC OF MERIDIAN. The scroll was inclosed in a piece of blotting paper, and then covered with a thick coat of sealing-wax. The bottle being warmed, the scroll was introduced, and the cork covered with sealing-wax. The bottle was then rolled up in a cloth dipped in tar, and placed in the hollow cut out of the rock at the bottom of the pit, and covered over with the stone above described, over which the earth was rammed down firm, and the surface smoothed as before. Mr. Lambritz, nephew of Jerrit Cotsee, and Hendrick Thiark, the proprietor, were made acquainted with the object of the memorandum. The position of the repeating circle was exactly 21" 11" eastward of the spindle of the sector. Before' it was placed, a perpendicular was drawn to the face of the sector, on which the plummet of the circle was dropped. The base-line was measured by Lieut. Williams and the sappers, on the plain to the west, with a common Gunter's chain. They went over the line seven times to get rid of inconstant errors. The temperature of the ground was 85°. The chain, in the temperature 57°, was found to be 66" 1"-1. The mean of the seven measures was 27* 1'"; consequently, the length of the base was 1784."-907. Only one artificial signal was put up, viz. a flagstaff on Castle Hill, towards the furthest extremity. CIRCLE STATION NEAR SECTOR. Angle between signal rock on Fort Azimuth and south end of base, ;ie ueiweeu siguai lucK. uii rori rtzirauui ana souin ena 01 Dase, ■) o I ,/ 24 repetitions J ^^ 2 37-5 Angle between north and south ends of base, 26 repetitions 42 41 8-5 Angle bet\yeen south end of base and flagstaff on Castle Hill, 19 repetitions I 97 44 21-3 Theodolite readings for all the points observed in a sweep round (the angle between any two points may be obtained by taking the difference of their readings) : — Reading for culminating rock at north end of La Caille's foot 0° l' I2" for culminating rock at south end of ditto 6 5 40 for north rock of La Caille's Mount 45 40 30 for middle 5116 20 for south ■ 54 Q Q for middle of a large rock, distant from the circle 263"-7 58 1 1 20 SMALL TRIANGULATION IN THE NEIGHBOURHOOD OF KLYP FONTEYN, 43 CIRCLE STATION NEAR SECTOR (continued). Reading for a large rock, which, in the line of sight, appears to be -i the termination of the range south-east of the circle ; it I 82 35 30 is distant 324"-5 , J for Daniel Bernoulli 106 41 for Fort Azimuth signal-stone 117 33 10 for the culminating point of the apparent west termination of Castle Hill r 274 41 304 50 } for flagstaff on the third peak from the west, of Castle Hill . . 277 20 10 for Castle Rock, west end, 285° 36' 0" T '„„ „ ,„ ]■ 286 22 35 • east end, 287 9 10 J for a large group of stones (or rocks) on the lower part of ' Castle Hill, immediately above the spot where the water springs from the ground ; they are in a line with a group of willow-trees (the middle large rock observed) for the apparent middle of the Kloof between Castle Hill T i 323 4 20 and the Hunchback termination of Picquet Berg .... J for first object, or starting point 360 1 10 SECOND SWEEP. Reading for signal rock on Fort Azimuth 1 18 for second peak on Riebeck's Castel, La Caille's siarnal "1 , , , ,„ . ^ ° ^ 1 15 40 station ; it just emerges above Zwartberg J for culminating point of Dassenberg 8 23 33 for a very distant culminating peak, Drakenstein (?) 8 39 36 — '■ — for knob on a distant Hunchback mountain 8 59 ■ for culminating point of Baviansberg 23 47 10 for culminating point of Katzenberg 24 52 20 for niche between Baviansberg and Katzenberg 26 11 30 for culminating point of Contre Berg 26 44 20 for culminating point of another mountain 27 36 for west escarpment of Table Mountain 28 46 32 for culminating point of Capoc Berg 31 18 40 for culminating point of Klyp Berg 36 37 10 for a whale-back looking mountain 48 38 50 for a small moundlike hill 60 17 30 for a hill towards Saldanha Bay 66 49 '0 for another 69 43 for 1st of four flagstaves at the corners of Okeu Schal- ■) keveck's ruined dwelling house J for 2d 205 23 8 for 3d •. . 207 52 35 for 4th 211 25 58 44 VERIFICATION AND EXTENSION OF LA CAILLE S ARC OF MERIDIAN. CIRCLE STATION NEAR SECTOR (continued). Reading for La Caille's Foot 243 52 4o" for La Caille's Head 248 32 53 for niche on James Bernoulli 348 4 43 for Daniel Bernoulli 349 8 3 . for John Bernoulli 350 39 7 for a large rock on Picquet Berg 328 45 20 for Fort Azimuth, the starting point 360 45 Drag on circle, — 33" ZENITH DISTANCES. The observations were made thus: — Vernier a clamped to zero (the mean of the three verniers is then constantly 9", sub- tractive); contact made and level adjusted ; circle turned half-round in azimuth; verniers undamped ; second contact made (level-bubble brought to centre, if necessary, by the foot-screw previously) ; the reading is double the'zen. dist. Off/ Zenith distance of north extremity of La Caille's Mount 75 38 27'7 of middle peak 75 41 33-9 of Daniel Bernoulli 88 21 51-4 of signal rock on Fort Azimuth 89 49 41 "4 of second peak on Riebeck's Castel 89 42 42*2 of flagstaff on Castle Hill (the culminating point of 1 , . ^ , . . }■ 83 51 39"0 the mountam), 4 repetitions J of second peak on Castle Hill from west, 4 repetitions 82 16 25-6 of Castle Rock on Castle Hill, 4 repetitions 81 53 16-8 NORTH END OF BASE. HORIZONTAL ANGLES. Angle between south end of base and signal at station near sector, "i o , „ "- ,... ' [ 55 56 2-6 7 repetitions J culminating point of Picquet T R r, .-.• [ 57 16 7-7 Berg, 7 repetitions J rock above sector 63 47 45 — vertical group 60 52 10 jiorth peak of La Caille's Mount 53 49 36 middle peak 51 25 54 south peak 49 49 23 Daniel Bernoulli 3 10 27 ' Fort Azimuth (westward) 5 55 54 SMALL TRIANGULATION IN THE NEIGHBOURHOOD OF KLYP FONTEYN. 45 NORTH END OF BASE (continued). Angle between south end of base and flagstafFon Castle Hill (westward) 196 59 38 - Hunchback termination of"i Picquet Berg group of rocks over Klyp "1 Fonteyn spring / 92 13 48 88 53 ZENITH DISTANCES. Zenith distance of culminating point of Picquet Berg, 4 repetitions . . 83 14 35*5 of flagstaff on Castle Hill, 4 repetitions 82 15 31 "5 of Castle Rock 80 46-4 ■ of Hunchback termination of Picquet Berg .•. 83 57 50-5 of rock on La Caille's Foot, immediately above } 85 21 40-5 sector station of north culminating point of La Caille's Head 83 20 33-9 of south do. do. 83 13 16-4 of Daniel Bernoulli 88 12 43-0 of Fort Azimuth signal 89 28 12-2 SOUTH END OF BASE. HORIZONTAL ANGLES. Angle between north end of base and flagstaff on Castle Hill 1 3 33 28 . signal at station near sector, 5 repetitions culminating point of Picquet signal at station near sector, T J* 81 23 24 5 repetitions J I 117 4 44-5 Berg, 3 repetitions Daniel Bernoulli 176 15 53 Fort Azimuth (eastward) 187 6 27 north peak of La Caille's Head 106 29 53 middle do. 109 51 53 south do. 117 3 13 Hunchback termination of "I Picquet Berg J north culminating point. La "1 y oo 1 Caille's Foot J south do. 88 35 centre of Castle Rock 32 10 46 VERIFICATION AND EXTENSION OF LA CAILLE S ARC OF MERIDIAN. SOUTH END OF BASE {continued) ZENITH DISTANCES. O / II Zenith distance of flagstafF on Castle Hill, 8 repetitions 83 48 29-3 of culminating point of Picquet Berg 82 54 44-7 f ____ do. do. 82 54 26-5 of south peak of La Caille's Head 81 52 8-9 ^ of south peak of La Caille's Foot w 84 47 18-9 of north do. 84 58 of Hunchback termination of Picquet Berg 84 5 17-2 of Daniel Bernoulli 87 53 18 of Fort Azimuth 89 16 45-6 The last observation uncertain, for the day was closing in fast. Angles used in calculation. 42° 41' 8" 55 55 46 81 23 6 180 RESULTS. Angles observed, Station near sector 42°4r 8""5 North end of base 55 56 2-6 South end of base 81 23 24 -0 Sum of angles 180 35 -1 Base 1784-907 feet. Station near sector to north end of base 2603-0 — ^ to south end of base 2180-8 — Angles used in calculation. Picquet Berg 5° 39' 8" South end of base 117 4 44 North end of base 57 16 8 Sura of angles ..180 Picquet Berg to north end of base 16136-13 feet. to south end of base 15245- 15 — ■ to station near sector 13533-13 — Castle Hill flagstaff 17° 52' 31" Station near sector 55 3 13 North end of base* 107 4 16 Castle Hill flagstaff 14° 26' 1" Station near sector 97 44 21 South end of base . . 67 49 38 * The angle given in the MS is 107° 4' 36"; but this is inconsistent with the observations at the north end, and gives an erroneous quantity for the sum of the three angles. It has however, apparently, been used in computing the .side " flagstaff to sector by north end," but the error is insensible ; the side ought to be increased about 0"-2. — G. B. A. SMALL TRIANGULATION IN THE NEIGHBGUKHOOD OF KLYP FONTEYN. 47 RESULTS {continued). Castle Hill flagstaff to north end of base 6951'22 feet. to south end of base 8670-00 — to station near sector, by north end of base 8106'45'| to station near sector, by south end of base 8102'20j 8104-33 feet. Fort Azimuth 1 3° 24' 34" Station near sector 1 04 43 46 North end of base 61 51 40 Fort Azimuth 12° 14' 1" Station near sector 62 2 38 South end of base 105 43 21 Fort Azimuth to north end of base 10855-41 feet to south end of base , . . 9090-75 — • to station near sector, by north end of base . . 9897-64 to station near sector, by south end of base 1-9902-16 feet. 9906-67 J Hunchback termination of Picquet Berg 14° 12' 32" North end of base 92 13 48 South end of base 73 33 40 Hunchback to south end of base 7266-24 feet. to north end of base 6974-50 — to station near sector 51 14-38 — Daniel Bernoulli 1 1°38' 45" Station near sector 115 36 56 North end of base . .' 52 45 19 Daniel Bernoulli 1 2° 12' 24" Station near sector 72 54 49 South end of base 94 52 47 Daniel Bernoulli to north end of base 1 1629-23 feet. , south end of base 9858-86 station near sector, by north end of base 10265-16 station near sector, by south end of base 10276 I6y 10270-94 feet. North peak of La Caille's Mount 19°40' 31" South end of base 106 29 53 North end of base 53 49 36 North peak to north end of base 5083-10 feet. south end of base 4279-44 — station near sector 2483-70 — Middle peak of La Caille's Mount 18° 42' 13" North end of base 51 25 54 South end of base 109 51 53 Middle peak to north end of base 5234-94 feet. south end of base 4351-97 — station near sector 2647-84 — 48 VERIFICATION AND EXTENSION OF LA CAILLE S AKC OF MERIDIAN. RESULTS {continued). South peak of La Caille's Mount 13° T 24" South end of base 117 3 13 North end of base 49 49 23 South peak to north end of base 700 M 9 feet. south end of base 6006-67 — station near sector 4421 '80 — Castle Rock 24° 0' 7" South end of base 49 13 6 Station near sector 1 06 46 47 Castle Rock to south end of base 5133'0 feet. station near sector 4059'6 — Several points on La Caille's Mount were observed from the station near the sector, and apparently the same points were observed at the ends of the base I'ine ; but, from the contiguity of the hill to the sector, the culminating points were somewhat hid. The observations at the end of the base line are therefore preferred in the computations. OBSERVATIONS AT THE STATION NEAR THE SECTOR, FOR THE AZIMUTH OF FORT AZIMUTH. Tuesday, April 24, 1838. Comparison of the sun in azimuth with Fort Azimuth : — O I // Reading of horizontal circle for Fort Azimuth 359 59 38-3 — sun's preceding limb,* at 19^ 43?" 41'*5 by"! „ ,„ , , , . . ^ 'r ^,^ 269 43 30 chron. (angles increasing from N. to E.)J sun's following limb, at 19'' 45"' 15» 270 1 43-3 Azimuth of sun's preceding; limb from Fort Azimuth, at first observation! ■ <• o Tr\ ^ 90 16 8-3 (mcreasmg from S. to E,) J Azimuth of sun's following limb from Fort Azimuth, at second observation . . 89 57 55 Mean of readings of vertical circle for zenithT •• ■" • ■» >19 49 39 distances of the sun's limb, at J 50 45 51 62 U9 50 45-33 .... 0095 * In the MS. this is called the N.L. The alteration made above seems to be supported by the agreement of the difference between the two observations, with the difference between the sun's diameter and the suti's motion in azimuth during the interval. The words following 41''5 are added by me. — G. B. A. SMALL TRIANGULATION IN THE NEIGHBOURHOOD OF KLYP FONTEYN. 49 h m 8 Mean of reading's with circle reversed* .... 19 53 44-5"l ° h m s OIK 54 51 U9 54 50-17 .... 148 2 6-7 55 55 J Tlierefore the sun's apparent lenith distance at 19 52 47-75 = 74 58-6 Chronometer fast, 33=-03. And the azimuth of the signal rock on Fort Azimuth is 25° 52' 16' from the south point towards the east. The sun cannot be seen from the station at sunrise, from the intervention of La Caille's Mount. At sunset I was always engaged with the sector ; but the above determination is near enough for the purpose. Lieutenant Williams and myself examined the relative heights of the base-line and corn-floor with an excellent 18-inch level, sent out by Capt. Beaufort for these inquiries. We found the north end 72-2 feet, and the south end 68"3 feet, lower than the corn-floor. The axis of the repeating circle was four feet above the floor. These quantities are taken into account in the computation of the altitudes, together with the refraction : the zenith distances having been observed at ioth ends of the base, the mean of the results was taken. * Upon repeating the calculations, it appears that these observations were taken on the morning of Wednesday (April 25, civil reckoning), and that both the series of observations of zenith distance were made on the sun's upper limb. — G. B. A. R 50 VERIFICATION AND EXTENSION OF LA CAILLE S ARC OF MERIDIAN. Heights,* Distances, and Azimuths referred to the Repeating Circle 21" 11'" due East of the Axis of Bradley's Sector, placed on the Ruin of Jacobus Cotsee's Dwelling-house, 210 feet on the Meridian South of La Caille's Granary: — Fort Azimuth Daniel Bernoulli West terminal rock of La Caille's Foot Large remarkable rock of ditto La Caille's south peak middle peak north peak Culminating point of Picquet Berg La Caille's Foot, group of rocks Ditto another group Hunchback termination of Picquet Berg Valley between Hunchback and Castle Hill Group of rocks above and close to the Klyp Fon-T teyn spring (largest rock) J Castle Rock on Castle Hill Castle Hill flagstaff North end of base-line South end of ditto Height above the Floor. feet. 35-0 300-0 10-0 10-0 781-0 679-0 529-0 1844-0 213-0 204-0 681-0 588-0 878-0 -72-2 -68-3 Distance from the Repeating Circle. feet. 9902-2 10271-0 324-5 263-7 4422-0 2648-0 2484-0 13533-0 979-0 748-0 5114-0 1569-0 4060-0 8107-0 2603-0 2180-8 Azimuth reckoned East- ward from the South Point. 25 52 16 36 44 26 60 49 56 85 14 6 91 26 45 92 11 14 97 45 102 44 19 137 19 46 143 24 14 154 58 43 180 198 35 27 217 2 51 226 5 16 281 8 30 323 49 38 With the view of obtaining an estimate of the height of the sector-station above the level of the sea, I compared the readings of the barometer in the sector tent at 9' 30™ p.m., with the corresponding readings at the Royal Observatory, as follow : — « In preparing Plate VI. for the engraver, the lines have been drawn in conformity with the numbers in this table, and without regard to the numbers of the triangulation, which (m respect to some of the points of La Caille's Mount) are scarcely reconcilable with these G. B. A. SMALL TRIANGULATION IN THE NEIGHBOURHOOD OF KLYP FONTEYN. 51 Klyp Fon TEYN. Barom. Therm. March 29 29-614 o 66 30 •661 65-7 31 •564 68 April 4 •605 59 5 •681 60 6 •662 61-8 7 •578 70-8 10 •624 70 11 •606 67-5 15 •730 59-8 16 •466 62-9 18 •822 56-1 20 •630. 61 21 •480 64 eans . . 29-623 63-8 Royal Obsi^vatohy. Barom. Therm, 30^058 59°3 -104 67^2 •024 57^4 •062 59-7 -180 61 30-152 62-5 29-993 57-6 30^080 62-5 •030 59-5 30-253 54 29-985 56-6 30-352 59 •184 60-4 •001 61-7 30^104 59^9 The comparison of the barometers shewed that the indications of the portable one are less than the Observatory standard by O'^'OOO. The neutral point of the former, aQ'"'* ; capacity, ^ ; temperature, 54°. Applying these, and estimating the height of the Observatory standard at 35 feet above the level of the sea, the height of the sector above the same level is 396'4 feet, or, in round numbers, 400 feet. Since writing the above, the height of the cistern of the standard baro- meter above the mean level of the sea, in Table Bay, has been found, by careful leveUing, to be 37 feet; THOS. MACLEAR. September 30, 1838. APPENDIX. APPENDIX. No. 1. By the good offices of M. Hertzog, and of Mr. Moody, a gentleman engaged in examining the records of the Colonial Office, I have been enabled to collect the follow- ing documents identifying the place of Wales and Bailey's observations. Extract from the Day-book "Colonial Office, Saturday, Z\st October, 1772." " The Astronomers, W. Wales and William Bailey (arrived with Captain Cook), allowed to erect an Observatory for their observations in the garden of the Burgher, Pieter Zeeman." In the Transfer Office, the following records of transfers were found : — " Jacob Van Dam transfers to Johannes Rogiers a house and land (in extent 1 morgan and 250 square rods) on 26th July, 1717. " Maria Van Mullan, widow of Johannes Rogiers, transfers the same to Henricus Chaywagen on 24th December, 1759. " Henricus Craywagen transfers the same to Pieter Zeeman on 7th March, 1761. " Catherine Verbeck, widow of Pieter Zeeman, transfers the same to Abraham A DE Haan on 27th April, 1779. "Abraham a de Haan transfers the same (by the name of Rosenberg or Concordia) to the Concordia Society, 1798." Thus Pieter Zeeman's garden is the same with Concordia Gardens, the place to which I was guided by repeating Mr. Wales's triangles, starting from the front door of Mrs. De Witt's house in Strand Street. 56 APPENDIX. No. 2. Extract from the Resolutions of the Governor of the Cape of Good Hope, Sfc. n February, \1\0. "The Astronomer, Pieter Colbe, who arrived here in the year 1705, in the ship called the Ulme, from Europe ; and who has for a considerable time been idling about, without attending to his astronomical observations or rendering any burgher-service : — it was thought advisable to demand from him whether he intends remaining here much longer, in which case he will in ftiture be considered as a burgher, and thus become liable to taxes and doing burgher-duty ; otherwise we shall give him his discharge, so that he may return to Europe." This curious resolution has been extracted because of its connexion with the letter or memorial presented through the Marquis De Puisieulx, wherein the leave to reside at the Cape granted to Colbe is employed as an argument to procure a similar boon for La Caille. [It appears from the remark prefixed to La Caille's Critical Notes on Kolbe's work {Journal du Voyage au Cap, edition 1763, page 317), that there existed other reasons for the inquietude of the Dutch colonial government with regard to the employ- ments of Kolbe. His whole occupation, besides drinking and smoking, consisted in collecting the complaints of the Dutch settlers against the local government (which when sent by other channels had always been intercepted), and forwarding them to Europe. The effect of the publication of these after Kolbe's return to Europe was, that the central government recalled and punished nearly all the officers of the Cape government. — G. B. A.] No. 3. Memoire sur le Proj it propose par le Si. De La Caille, Astronome de I'Academie Roy ale des Sciences. " Les savans qui ont eu jusq'ici un vrai z^le pour le progr^s de I'astronomie, et par consequent pour perfectionner la geographic et la navigation, ont reconnu, qu'il serait presqu' impossible de parvenir a quelque chose d'exact, principalement a I'egard de la partie qui a pour objet la determination des longitudes sur mer par les observa- tions de la lune, a moins que des observateurs les plus exerces et les mieux fournis de bons instrumens ne concertassent ensemble pour faire en m6me terns des observations du soleil et de la lune, dans les lieux de la terre les plus eloign^s qu'il est possible dans le sens du meridien. APPENDIX. 57 " C'est dans cette vue que depuis plus d'un si^cle plusieurs astronomes c^l^bres out entrepris de longs voyages ; mais, malheureusement, celui qui etoit le plus important pour les longitudes a 6te celui qui a eu le moins de succ^s. En 1705, M. De Krosieck, Conseiller Prive du Roy de Prusse, envoye a ses frais M. Kolbb au Cap de Bonne Esperance, muni de plusieurs instrumens et d'une permission des 6tats de Hollande, pour y faire toutes sortes d'observations astronomiques ; sans doute, que le pen d'ex- p6rience de M. Kolbe pour les observations, et peut-dtre aussi I'imperfection de ses instrumens, ont ete cause que I'astronomie ni la geographic n'ont tire aucune utilite de ce voyage. " Deux circonstances, extremement favorables pour obtenir un succ^s complet, se presentent dans le cours de I'annee 1751 ; une opposition de Mars pr^s de son p6rihelie, et une conjunction inf^rieure visible de Venus : c'est pour profiter d'une occasion si rare que le Si. De La Caille, exerce depuis plus de treize annees aux observations les plus delicates, et fourni de tous les instrumens les plus propres pour des recherches si desir^es des astronomes, et si utiles h la navigation, demande qu'on luy procure les moyens de passer une ann^e au Cap de Bonne Esperance, qui est a tous 6gards le seul lieu avantageusement situ6, parcequ'il est le plus eloigne de Paris, et en meme tems le plus proche du meridien qui passe par le milieu de I'Europe : deux conditions absolument essentielles, et sans lesquelles on ne pent esperer un succ^s raisonnable. " Voyez, done, les observations qui le Si. De La Caille se propose de faire pendant son s6jour : — "1. II d^terminera exactement la vraye position de ce fameux Cap, sur laquelle les plus cel^bres g^ograpbes different d'environ 100 lieues : et quoique M''^ de la Com- pagnie des Indes, ayent charge de ce soin M. D'Apkes, capitaine de leurs vaisseaux, tr^s capable de bien etablir cette position, tant par son habilite dans les observations, que par les instrumens qu'ils luy ont fait faire expr^s, cependant cet habile officier ne pourra y parvenir que par des methodes indirectes et par consequent peu susceptiBles de precision, parceque les Eclipses des satellites de Jupiter ne pourront ^tre visibles pendant le tems de relache que les afiaires de la Compagnie luy permettront de prendre, " 2. II d6terminera par des observations concertees, la parallaxe de la lune, Element le plus important, et le moins connu de la theorie de cet astre. Tous les astronomes conviennent que c'est la la seuie maniere de I'etablir avec toute la precision que Ton pent desirer. " 3. II observera la parallaxe du soleil, element encore plus incertain a proportion que n'est la parallaxe de la lune : les deux ph6nomenes rares dont il a ete parle cy-dessus, en fourniront plusieurs moyens egalement surs. " 4. 11 complettera le catalogue des principales etoiles fixes, par la meme methode, et avec les m^mes instrumens avec lesquels il a deja etabli les positions exactes des etoiles bor^ales : celles du zodiac qui sont australes ne peuvent etre determin6es que I 58 APPENDIX. tr^s imparfaitement dans I'Europe, a cause qu'elles se levent trop peu et trop lentement sur I'horison : c'est pour cette raison qu'on a ete oblige jusqu'icy d'eviter de comparer la lune a ces etoiles, parce-que les observations 6toient trop incertaines. " A I'egard de I'execution de ce projet les moyens en sont extremement simples. " II n'y a aucune depense a faire pour la construction des instrumens; elle cohsiste toute dans la traversee et dans la nourriture du Si. De La Caille seul, pendant environ une annee. II n'a besoin d'aucun aide, d'aucun domestique ; il restera en pension dans le lieu que Ton luy indiquera ; la nature de ses observations n'exige qu'un sejour tranquille dans un m^me lieu, et tout lieu sera propre pour y etablir ses instru- mens. Les Hollandois, qui ont accorde a Mr. Krosieck la permission d'entretenir au Cap un Astronome Prussien, destine a executer precisement le m^me projet dont il s'agit icy, ne peuvent raisonnablement la refuser au Roy pour un Astronome de son Academic, qui se tiendra exactement dans le lieu qu'on luy assignera, soit dans le fort, soit dans I'interieur des terres : ce projet regardant d ailleurs le bien commun de toutes les nations." [Here the memorial terminates abruptly without signature.] No. 4. Extract from Journal of the States-General. " 25th August, 1750. " Received a letter from Mr. Lestevenon van Berkeneode, their H. M. Am- bassador at the Court of France, dated at Paris, the 20th of this current month, intimating that, being at Versailles, the Marquis de Puisieulx had handed to him the memorial annexed to the said letter; and added, that he felt persuaded that their H. M. would permit M. De La Caille to proceed to the Cape of Good Hope, for the purpose of prosecuting his Astronomical Observations there, as detailed in the said memorial, since M. De Krosieck, Privy Councillor of the King of Prussia, had obtained a similar permission from their H. M. in the year 1705. "Which having been deliberated on, it was thought proper and resolved that a copy of the said letter and annexure be sent to the Representatives of their H M and the Directors of the Dutch East India Company, at their Presidial Chambers at Amsterdam, in order to obtain their advice on the matter. " N. S. VANDERVELDE." APPENDIX. 59 No. 5. Extract from Journal of the States -General. 23d November, 1750. " Received a letter from the Representatives of his Highness and the Directors of the Dutch United' East India Company, giving cover to a Resolution of the Chamber of XVII. adopted at a meeting held in Amsterdam on the 20th instant, in compliance with a Resolution of their H. M. of the 25th August last, and requesting advice on a Memorial handed by the Marquis de Puisieulx to Mr. Lestevenon van Berkenrode, their H. M. Ambassador at the Court of France, praying that their tl. M. may be pleased to permit Mr. De La Caille to proceed to the Cape of Good Hope, in order effectually to prosecute his astronomical observations there, as more fully detailed in the said Memorial. " After deliberation on the subject, it was thought proper and resolved to permit Mr. De La Caille, as he is permitted by these presents, to proceed to the Cape of Good Hope for the purpose set forth in the said Memorial. " Extract of this Resolution of their H. M. to be sent to the said Representatives and Directors in the Chamber of XVII. at Amsterdam aforesaid, in order that the same may be communicated to the Government of the Cape of Good Hope, and cause them to take such precautions as to prevent any improper use being made of this permission ; and a like extract also to Mr. Lestevenon van Berkenrode, for his information and guidance. " P. VERSEHOOR, Pt. " H. FOGEL. " J. SWEERS." No. 6. , Letter from the Representatives of the Prince of Orange and the Directors of the Dutch East India Company to the Authorities of the Cape Colony. To the Councillor Extraordinary and the Expected Governor of the Cape of Good Hope. Much respected Sir, After the separation of the last Annual Meeting of Council [of XVII.], we received their High Mightinesses' Resolution of the 23d instant, which, together 60 APPENDIX. with the Memorial of the Marquis de Ptjisieulx, therein alluded to, we herewith transmit to you accordingly : and remain, Your good friends, The Representatives of His Highness, And the Directors of the E. I. Company of Amsterdam, and out of the same, PHILIP VAN DER GHIESSEN, JOSUA VAN DER POORTEN, J. WALTERS, JACOB ALEWYN, J. BORN VAN WAVEREN, Amsterdam, Tlth Nov. 1750. GROOFLAND JANSON. No. 7. Extract from Letter from the Representatives and Directors, Sfc. to the Governor of the Cape Colony. " The Presidial Chamber, in a letter of the 27th Nov. 1750, after the separation of the Annual Meeting, having forwarded to you their H. M. Resolution of the 23d, together with a Memorial of the Marquis de Puisieulx, on the subject of Mr. Db La Caille's departure to, and sojourn at, the Cape, for the purpose of prosecuting his Astronomical Observations, we, agreeing thereto, do hereby accordingly direct you to comply with the directions contained in the said Resolution. "P. VAN GHIESSEN, " J. VAN DER POORTEN, &c. &c." No. 8. Letter from the Prince of Orang^ to the Governor of the Cape of Good Hope. To the Governor of the Cape of Good Hope. SlE, Mr. De La Caille, Member of the Royal Academy of Sciences at Paris, who intends to proceed to, and remain at, the Cape for some time, with the APPENDIX. 61 view of pursuing his Astronomical Observations, having applied to their High Mighti- nesses for the necessary permission to that effect, — and we being also disposed to comply with the request made to us in that respect by this gentleman, do therefore hereby recommend him to you, trusting that you will render him such assistance as he may stand in need of during his temporary residence there. Recommending you in God's holy protection and keeping. We remain, sir, Your well-disposed friend, (Signed) PRINCE D'ORANGE AND NASSAU. By order of His Highness, On the Loo, In the absence of the Private Secretary, nth October, 1750. (Signed) J. D. HORST. No. 9. Letter from the Governor of the Cape to the Prince of O RANGE. To His Highness the Prince of Orange and Nassau. Most Illustrious Prince and Sir, Mr. De La Caille, who arrived here on the 19th of this present month of April, having handed over to me your Highness's letter, dated on the Loo, the 17th October last, I have, in dutiful compliance with the desire therein expressed, not only permitted that gentleman to remain at this place for some time for the purpose of proceeding with his Astronomical Observations, but I shall also not fail to render him such assistance as may be in my power towards bringing that work to a desirable conclusion ; of which, I humbly trust, your Highness is fully convinced, as also that I shall ever consider it as the greatest happiness in having an opportunity of subscribing myself, with sentiments of profound respect and esteem. Most illustrious Prince and Sir, Your Highness's most faithful, most obedient, and most humble servant, (Signed) R. TULBAGH. In the Castle of Good Hope, the 2\ St April, 1751. 62 APPENDIX. No. 10. Extract from the Journal kept at the Office of the Secretary of the Government at the Cape of Good Hope. "Monday, \%th April, 1751. " Arrivred, the French ship Le Glorieux, carrying 14 guns and 115 men, which left Port rOrient on the 21st November last year, under the command of Captain D'Apres DE Mannevillettb, bound to the Island Mauritius, having on board Mr. De La Caille, Member of the Royal Academy of Sciences at Paris, who will remain here for some time, with the view of making Astronomical Observations ; he having for that purpose applied to and obtained the requisite permission from their High Mightinesses, as is expressed in a letter from His Most Illustrious Highness the Prince of Orange and Nassau to His Excellency the Governor, of which Mr. De La Caille himself was the bearer." No. 11. Envelope enclosing Letters to La Caille. To the Governor and Council at the Cape. It has pleased His Serene Highness the Prince of Orange and Nassau, &c., to send us two Letters addressed to Mr. De La Caille, Member of the Academy of Sciences at Paris, who is at present at the Cape of Good Hope, in order that we should send them to him by the first opportunity : we have, therefore, considered it expedient to forward the said two Letters to yon, for the purpose of handing them to Mr. De La Caille. Recommending you to the protection of God, we remain. Your good friends, THE REPRESENTATIVES, Amsterdam, I6th Sept. 1751. &c. &c. APPENDIX. 63 No. 12. Letter from Mr. Muller {Officer of Engineers accompanying La Caille) to the Governor of the Cape of Good Hope. Sir, Mr. De La Caille not having as yet completed his Astronomical Observa- tions, partly owing to a neglect of keeping a fire kindled at Piquetberg, and partly from the cloudy state of the weather, wherefore we have to await a clear sky, so that we may commence the measurement of the base-line ; and as Mr. De La Caille's application to you is only to obtain assistance in the matter before stated, I therefore beg you will be pleased to grant me a few days' more leave, in order that I may be enabled to fulfil your orders in the measurement of the base-line. And as the time of the yearly muster is approaching, I beg you will be pleased to order the oflacer of the mainguard to assist with the artillerymen. By doing which, you will much oblige him who has the honour, with all due respect, to subscribe himself, Your most obedient humble servant, Africa, Uth October, 1752. E. B. MULLER. Favoured by M. Best bier. No. 13. Extract from the Journal kept in the Office of the Secretary to the Government of the Cape of Good Hope. " Thursday, 23d September, 1751. " Mr. Abb6 De La Caille, who is still at this place pursuing his Astronomical Observations, having recently taken the height of Table and Wind Mountains, and of the Lion's Head and Rump, went yesterday, in order to eflect the measurement with more accuracy, to the top of Table Mountain, and found the heights of the said moun- tains to be as follows : — " The height of Lion's Rump 1102"^ ^ Lion's Head 2085 =2 west corner of Table Mountain 3353 \ a east ' 3302 Windberg 3106 all calculated from the level of the sea ; the length of Table Mountain, east and west, being 8346 Parisian feet." 64 appendix- No. 14. Extract from the Journal kept in the Office of the Secretary to the Government of the Cape of Good Hope. " Thursday, 8th March, 1753. " This afternoon the French ship Le Puisieux, after having saluted and received a contra salute, proceeded on her voyage to the Mauritius, having on board Mr. De La Caille, who had completed his Astronomical Observations at this place." No. 15. After the foregoing memoir was sent to England, I learned, by accident, that Klyp Fonteyn was formerly included in the Clan William district. The records in the Treasurer-General's Office were therefore examined, wherein was discovered the original permission granted to Cobnelis Coetsee to locate at Klyp Fonteyn, dated 31st August, 1744. Likewise the notice to quit of Jan de Lang (who, it appears, married the widow of Cornelis Coetsee) dated 15th September, 1758. These dates include the epoch of La Caille's visit. Jacobus Coetsee, Jerrit's father, took up his residence in 1762. The following translations of these documents from the Dutch language are by a sworn translator. The original copies are signed by the Treasurer-General, W. H. Harvey, Esq. " Fo. 22. " Stellenhosch. " It is hereby permitted to the agriculturist, Cornelis Coetsee, for a period of " one whole year, to resort to, and graze his cattle at, the Klip Fontein, at the corner " of Picquet Berg (being the abandoned place of Jan Pieterz), and for which he has " already paid — agreeably to the Resolution of Council, dated 24th January, 1741 — " two good and serviceable oxen, of four years old, as tribute to the Hon. Company; " remaining, moreover, obliged, after this shall have been registered in the Secretary's " Office, to pay into the Company's treasury a fine of twelve rix dollars, and to renew " this permission within one month after its expiration ; in default of which he shall " incur such fines as are prescribed in the several proclamations on that head. He APPENDIX, 65 " being, moreover, bound to deliver at the Castle, for the Government or the Company, "the tithe, or one tenth part of the whole he may raise on the land in question. This " permission to be previously produced to the landrost. " In the Castle of Good Hope, 31st August, 1744. (Sigped) " H. SWELLENGREBEI., " Received, W. V. KERKHOFF, " Entered by mc, ER. SCHOOR." "On this, the 15th Sept. 1758, the soldier, Jan de Lang (as having a verbal order " to that effect from his wife, the widow of the late agriculturist, Cornelis Coetsee), " gives notice that, with the knowledge of His Excellency the Governor, he leaves the " aforesaid cattle post, after having duly paid nine serviceable oxen as a tribute for " three years, instead of the ordinary taxes, and in reduction of thirteen years' arrears, " which he has delivered at the Company's post De Schuur, as per Receipt of the " Overseer, Jan Hendkick Hofmeybr, dated 14th September of this year, — being " held bound, from time to time, to pay up the remaining ten years' dues. (Signed) " H. ROUNENKAMP, Chief Clerk. A true translation, (Signed) B. J. Van de Sandt. The next paragraph in the record of this land is the grant of it to Jacobus Coetsee, the father of Jeerit, so often mentioned, dated 1758. Thus we see that the real proprietor of the place in 1752 was Cornelis Coetsee; that Letchie Schalkwyk's father was not a proprietor, but a householder at the will of Coetsee. Jerrit Coetsee's general testimony is supported, and we have no reason to doubt his recollection of his father's residence, which was his own residence in his youth. There is scarcely a shadow of doubt remaining, therefore, that the foundation exposed by us (page 16, line 8) is that of the granary wherein La Catlle made his sector-observations. LONDON: 1 PRINTED EY MOVES AND BARCLAY, CASTLE STREET) LEICESTER SQUARE. a Fhted'. -}xalwny ojfvdy XrAmj-iofi of la^ Chulles .Aro of Jle^jdian . ■ MeniofJtxij'.Jslriin.Si'cJ'LiLXr.l'lak'X. |^|*^\V^-;-^., ffo yg REFERENCE S. 1 . J^oiaile posiiWTi, ofZa CaiUetp Sectsr. 2. FosidoTh of Sradlqy's Se4aoT. in, Jlir^J)&Witii Tard.iiL February IS3S. 3 J)?- ..J)?..... in. Jto^^eSc0' Guard. Mouse, tti Mm' emd. June l838. 4. Fositum ofDudJin, prajedzTy /rom -ffie Wall; supposed to have hcen. placed ^lere 7rv laCaille. Ven/uxObOfb oTtd. £xiemto?b of la. Gizlles ,Jro of Jde^-zdiAfo . ■ _^ ^"^^ 3'^-^ ylstran. Soc. VolMMate^. 'S^la?t f i/ie .Buildmjrs at ^Jhrm called jrf/^Jbntey, Toniiyn. IfendnckThaackis the proprietor of fhrs TR-nn .April .i838. 3- Stdbles. 12\ A.Mour TniU. \ 1 5- WaSs of a rtaned Junise. 6 . Temp or OP}' Mitt. 1 . Oven.. SmaJLBam: this titUding was ^latched Soring -ffie -time of o&seri •ation.. 9. Sector tent:-ffie centre of wTach.sheM'S ihe positioTt of SradZ^'S See/x^r jfoo iiet above -ffie lex'elof&ie Secb. 10.2'osition of repeating (zrde. 11. Soldier.? Tent. H.Fotmdaiions opened ijiAprillSSS: supposed sits ofOTter Sdi£il/av)'/cj 7umse,in.i-;^,-theyearIaCcdIle made his oiservaHons. '^.Fomidatian. opencdinJprillSSS: the proial/le site of -ffie Graiwr)' in yhinhZa CaiSes Sector was placed/ . 14 . Slee^m^ Tent^. l338 . "ib. Assumed position. ofZaCaiU^ s^nalYzre. 3© . The dotted Une round 8 and 9 marks lite foundaiion. of ofComeHiis Cotzees Twuse; -ffie proprietor in ij^. The^ Granojy Tiatforni of Everest- Jf£asire. sculp. I'lafe'Iir. Ve9'"ifi.ca-iw?i- ami J:'a>te-nswn. of Zco l}if^lles^4n 'T 0-/ Mem. of Ay Asbvri. Soc. Virl.XL.I-Jj7& IE. J^Sastre saHp. t,z y octt«>c//6/ and/ JUai&iswny of Zoy entiles ^ ire of' .J/en/I/arL Views of the/ l^ozcntazns &:a. m. th^ nayfibourTwoi' of £2^^p S'oniespv ■ Mm,. o/Jliry. Ajtron.Soc. rolMI'Lit£ IV. I ^ > t :pz>2 tp'Wljf ^''^'■^WPO '^T llTlOjp ' • ij]moiiJpg^< 1 I I ^ I ^S S .^ I ft; t N »; Si Phyte /: I r/7///;////i// ,,,/,/ /:.r/t:jis/ii// ,■/'/,// //////rs. l/r o/' . Ur/Vf////// . ■ Mirn RoY-Mo-on.SocVi't Xll'luf^^. /'lUi r/- ///,■ J/r////fi////.v ,(v /// ///,' /ir/i//i/iiii//-/iiii),/ ,//' /\'////j /''i'///r//// .^ ,»' > 'jt 'aJ4»:*a --« ^^ '.-ft ,i'^ ,<• J?.'" J^'^^ihfcre. srn/p. Tlate. W. Ver^fu:-attO'n' and J^xienswfv of lay Ckilles . //r of ^-feS V \. il ■a- A I' <»s 1 ^ «! Ot ^ ^ S K| ^ , !^ te; -^ -, ■ n u R w h u B M «■ J S a d d, a ffi /^rul/aji . Mail. ofJiiTy. -Astran . Soc. YolXT -Plate "VI. ^>- JfBasirc sculp. OPERATIONS FOR THE VERIFICATION AND EXTENSION OF THE ABBE DE LA CAILLE'S ARC OF MERIDIAN, THE CAPE OF GOOD HOPE. PART II. VERIFICATION OF THE ASTRONOMICAL AMPLITUDE OF LA CAILLE's ARC. § 7. Description of Bradley's Sector, with which the Astronomical Observations of Mr. Maclear were made.* Of Bradley's sector, an instrument not more remarkable for its historical » interest than for the general excellence of its construction, no sufficient account exists. Bradley himself, in the Phil. Trans. Vol. XLV. (1748), p. 7, has referred generally to the description of the sector used by the French astronomers for the degrees of meridian in Lapland and in France (see the D6gr6 du MSridien entre Paris et Amiens). It will be found, however, on comparing the plates of the French work with those shortly to be explained, that some important parts in the construction of Bradley's sector are omitted in the description of that used by the French astronomers. A general view * The whole of this section is written by me G. B. A. 68 VERIFICATION AND EXTENSION OF LA CAILLE's ARC OF MERIDIAN. of the sector, as mounted at Greenwich, is given in Bradley's Miscellaneous Works, edited by Professor Rigaud ; but the details of construction are there necessarily omitted. When the Lords Commissioners of the Admiralty, on my recommenda- tion, had determined to send this instrument to the Cape of Good Hope, I thought it desirable to preserve drawings of it in such detail as might (if it were desired) enable a modern artist to construct an exact copy of the instru- ment in the event of its loss or injury on its voyage. A draughtsman, Mr. B. Sly, was accordingly employed to make drawings under my direction. The instrument was taken to pieces, and some parts were separated which probably had never been unscrewed since the sector left the hands of its maker. Before describing the sector in the state in which it was sent to the Cape of Good Hope, it will be proper to premise an account of the alterations which were made to adapt it to this service. The instrument, when at Greenwich, was suspended to a bracket fixed to the wall of the Quadrant Room ; and there was no means of reversing it in azimuth, except by taking it down from that bracket and carrying it to another bracket on the opposite wall of the same room : an operation which, as I am informed by Mr. Henry (the only assistant now at the Royal Ob- servatory who remembers its use), occupied a whole morning. When the instrument was prepared for use at different field-stations at the Cape of Good Hope, a new cast-iron bracket of smaller size was made, and was attached to a vertical spindle turning in azimuth within a large tripod-stand ; upon this bracket the brass work was mounted in exactly the same manner as upon the original brackets. To the lower part of the spindle an iron bar was screwed, for attaching the ends of the brass frame that carries the weight-pulleys and steadies the plumb-line shade (which frame was formerly attached to the wall) ; and also another iron bar, for supporting the back arch by means of two flat horizontal pieces, with long screw-holes, that project backwards from the back arch. A wooden sliding arc of a circle, carrying a flat board for a lamp-stand, was placed on the spindle opposite to the illuminator of the telescope. A four-glass diagonal eyepiece was made : the original eye-glass being a single lens. These are all the changes made under my direction. The object-glass, whose convex lens is thin, was found so much pinched DESCRIPTION OF BRADLEy's SECTOR. 69 in its cell that the coloured rings were exceedingly distorted. It was reheved. The image of a star, as now shewn by the telescope, is extremely neat. The whole of this work was done by Mr. Simms in the summer of 1837. DESCRIPTION OF THE PLATES. Fig. 1, Plate VII. Side view of the top of the great spindle, the top of the cast-iron bracket, and the brass work which it carries (the lower part of the great spindle and of the bracket being cut off). On the side of the bracket are seen two screw-heads ; these screws, and two similar ones inserted the opposite way in the opposite cheek of the bracket, are for supporting j^a;ec?/y an iron-piece of the shape f] partly seen in fig. 2, This iron is part of the original work. Its middle side is next to the spindle, but distant at le^st two inches from the spindle. This iron-piece supports movably a brass plate, shaped like an imperfect horse-shoe, whose edge is seen in fig. 1. The motion of this brass plate is circular in azimuth ; it is effected by the opposite tangent screws seen in figs, 1 and 2 ; it is limited to circularity of motion by three small screws passing through elon- gated holes in the brass and screwed in the iron : they are seen well in fig. 2. This brass plate supports movably another brass plate of a complete horse- shoe form, whose edge is seen in fig. 1, and whose flat is entirely seen in fig. 2. The motion of this upper brass plate is rectilinear, viz. to and from the spindle ; it is effected by a screw (whose large milled head is seen in figs. 1 and 2), which works in a cock of the lower brass plate with shoulder and pinned collar ; and in the upper brass plate by the thread of its screw. The motion is limited to rectilinear direction by three pins carried by the lower brass plate which enter elongated holes in the upper : these are not visible in fig. 1, but may be seen in fig. 2, where the two that are farthest from the spindle are partially concealed by the edge of a small plate above the upper brass piece. This small plate, whose end is seen in fig. 1, is merely for attachment of the upper end of the plumb-line shade. There are also seen sideways in fig. 1 the heads of two screws with washers, which pass through or into the upper plate : I do not at all recollect their use, but suppose that it may be to hold the upper brass plate down to the lower brass plate. 70 VERIFICATION AND EXTENSION OF LA CAILLE's ARC OF MERIDIAN. Fig. 2. This contains an end view (from the top) of the great spindle, shewing its back edge bar, which, at the middle of the spindle's length, is deep. An iron ring is fixed near the top to give hold for raising it. At the top of the spindle is seen the plate (of brass or of iron) with deep conical hole, in which the conical point of the fixed pivot of the tripod-stand enters. All the rest of the work has been described in the account of fig. 1. The elongated holes of the lower brass plate are seen here through larger holes of the upper brass plate, which are made for convenience of access to the screws. There are also three other sets of screw-holes, which seem to have been intended for some other place of mounting. Figs. 3, 4, 5, Plate VIII., are a perspective view, a plan, and a front view, of the triangular frame which stands upon the upper brass plate of figs. 1 and 2, and supports the pivots of the telescope. The triangular frame stands on the points of three screws : small holes for two.of them (the two front screws) are made in the upper brass plate, and may be seen in fig. 2. In figs. 3, 4, and 5, the following parts may be seen : the back Y (or that nearest to the spindle) with a semicylindrical cover : the front Y without a cover : the piece shaped thus J |, which carries the plumb-line adjustment ; this piece is movable by hand to and from the spindle in a dovetail groove, but there is no screw motion : the plumb-line adjustment carried by the last. The suspending piece is moved upon the piece of the form J |j_ by a screw (with pinned collar, I suppose, but it is not so represented), whose point abuts on the point of another screw for adjustment to steadiness ; the thread of the screw works in the suspending piece ; the plumb-wire passes over two notches on the suspending piece, and its end is pinched by the shoulder of a small screw in the suspending piece. The dovetail groove below the front of the trian- gular frame is for the sliding piece which carries the microscope for viewing the wire and pivot dot. Fig. 4 shews also the microscope in position, sliding in a split tube, which is carried by a stalk that turns in a small split tube carried by the dovetail slider. The front of the triangular piece, as shewn in fig. 5, bears the appearance of having been cut in two places, or having been formed by inserting a front piece which has no connexion with the sides except by means of two subsidiary corner pieces : this appearance is represented quite correctly. I can give no further account of it. DESCRIPTION OF BRADLEY's SECTOR. 71 Fig. 6, Plate IX., shews the upper end, or object-glass end, of the telescope. The object-glass cell is screwed upon a brass tube, which is thrust into the tele- scope tube, and is held there by friction only. The upper collar of the tele- scope tube is of brass, but the rest of the telescope tube is of tin-plate. The upper collar carries the two pivots ; the back pivot is plain ; the front pivot has, screwed upon its end with three screws, a smaller pivot, on the centre of which is a gold pin, in which is the fine dot over which the plumb-line is made to pass. This dot is so excentric that it is absolutely necessary to adjust the plumb-Hne for every observation. Fig. 6 shews also the lower end with the six screw-holes for the screws by which the eyepiece is attached : the milled edge at the bottom is a part of the tube. Fig. 7 shews again the upper pivot: it also shews the illuminator. This is a small piece of speculum-metal carried by a stalk which is thrust in at one side of the tube : the metal is cut at an angle of 45°. On the opposite side of the tube is a hole with a glass cover for the light to shine in at. Fig. 8, Plate X., is a perspective view of the sector-arc and the eyepiece- plate to which it is fixedly attached. Farthest from the eye is the milled head of a screw for moving the roller-frame ; it turns in a cock, being held by a shoulder and pinned collar. On the upper ring are seen six screws, which are for attaching the eyepiece-plate to the telescope-tube (see the bottom of fig. 6). This upper ring is thrust into the bottom of the telescope-tube, and the screws pass through the holes of the tube, and their threads lay hold of the upper ring. Below the lowest ring are seen the heads of two flat-headed screws, which hold the eyepiece-cell, with play for motion in azimuth. At the right hand of the stout ring is seen the small mirror or plate of very hard steel (the hardest, Mr. Simms says, that he ever touched).. The face of this mirror is pressed, in observation, by the point of the micrometer-screw; Below this may be seen a very small portion of another similar mirror of brass (nearly hidden in the figure by the sector-arc); it is to receive the action of the guarding-screw, that the steel mirror may not be in perpetual contact with the micrometer-screw when observation is not going on. The steel mirror, when not in use, was formerly covered by a brass or copper cap: it is now covered by a zinc cap. In front is the sector-arc (in a vertical plane), behind which may be indistinctly seen its back-edge-piece. 72 VERIFICATION AND EXTENSION OF LA CAILLE's ARC OF MERIDIAN. connected with it by knee-pieces. The two stoutest knee-pieces are those at the corner of the square plate, by which the connexion of the eyepiece-plate' and the sector-arc is made. Below the five-minute divisions of the sector-arc are the gold pins, on which nice round points are made for bisection with the plumb-line. The sector-arc is of steel ; the rest of the work is of brass. Fig. 9, Plate XI., is a plan of the same, as seen from the upper side. The screw with shoulder and pinned collar is seen well (its thread works in part of the roller-frame not seen here). The use of the square holes at the corners (which are omitted in fig. 8, but shewn in figs. 9 and 10) I forget ; but as they correspond in position with the pivots of the two rollers of the roller-frame, they are probably made for access to them. Near the left-hand upper corner in fig. 9, and near the right-hand upper corner in fig. 10, is a small circle : this ought to have been represented as a hole, into which enters the pin (secured by a screw) in which works the thread of the screw that gives azimuth motion to the eyepiece. The explanation of other parts may be taken from fig. 8. Fig. 10 is a plan of the same, as seen from the lower side. Besides the parts shewn in the other, there are two long rectangular holes at the two sides (omitted in figs. 8 and 9) for the pins which limit the motion of the roller- frame to rectilinearity. There are also seen raised the flat heads of the four screws which allow azimuthal motion to the eyepiece. The other screws I beheve are for holding fixedly the stout ring and other parts. Fig. 11 is a view of the same endways in regard to the arc. At the left is the arc, fore-shortened. In the centre are the two mirrors, the steel one above and the brass one below. Under the arc's back-edge, but above the eyepiece-plate, is a thicker piece, by which (I believe) the arc and the eyepiece-plate are connected. Fig. 12, Plate XII., is an elevation of the eyepiece-cell. To the left is the thick pin described in the end of the account of fig. 9 : it enters the circular hole in figs. 9 and 10, and is secured by a washer with square hole and a flat-headed screw. The thread of the tangent-screw which gives azimuthal motion to the eyepiece-cell works in this thick pin. The other end of the screw works with shoulder and pinned collar in another thick pin that turns DESCRIPTION OF BRADLEY's SECTOR. 73 in the flat of the eyepiece-cell. It has a square end, for a common key, not represented here. Near the bottom of fig. 12 is seen a hole in the side of the cell: I think that it must have been for observation with a diagonal mirror, but I have not found any which fit to the cell. Fig. 13 is a perspective view of the same cell, with the new diagonal eyepiece. The tangent-screw is partly concealed, but the four elongated holes of the flat are well seen ; these are for the four screws partly seen in fig. 8, but better seen in fig. 10, and seen in profile in fig. 11. Within the eyepiece-tube is seen the frame carrying the cross-wires : I believe that it is merely thrust in, but I did not dislodge it. Fig. 14, Plate XIII., is a perspective view of the roller-frame. Under each of the two sides are seen the double square pins, with a screw and long spring, which slide in the long rectangular holes (described under fig. 10). At two corners are seen the two rollers which run along the front-edge of the back- arch. To the side between these two rollers is attached the great curved spring, carrying at its point a third roller, which runs along the back-edge of the back-arch. At the bottom of the great spring is a hole, through which passes the screw (freely) that is mentioned at the beginning of the description of figs. 8 and 9. The thread of that screw works in the small piece which, in fig. 14, is nearer to the eye. Fig. 15 is a perspective view of the eyepiece-plate and sector-arc (broken off at the end) carrying the eyepiece-cell, the diagonal eyepiece, and the roller-frame, exactly in the state in which they are attached for observation to the telescope tube. Fig. 16, Plate XIV., is a perspective view of the slider, which slides upon the ' back-arch, and is clamped on it at the proper place for each observation. At the top are seen two clamping-screws, whose threads work in the upper plate of the slider, and whose points press downwards, upon the back-arch, the ends of a long broad spring that lies under the upper plate. This upper plate takes hold of the under side of the back-arch by the cramp-shaped pieces at the two ends (seen imperfectly in fig. 16, the end of one is seen perfectly in fig. 17). When mounted on the back-arch, the length of the upper plate is 74 VERIFICATION AND EXTENSION OF LA CAILLE's ARC OF MERIDIAN. parallel to the length of the back-arch. Upon recollection, I am inclined to think that the right-hand screw presses with its point upon the upper plate, and draws upwards (by its thread) a sliding cramp-shaped piece ||[ "J. To the upper plate is attached (or rather is in the same piece of plate-brass) a plate projecting forwards (i. e. farther from the great spindle), carrying the concave screw of the micrometer ; below it, the concave screw of the guard- screw ; on one side, the machinery for registering the whole number of- turns. The micrometer-head is divided into thirty-four parts, intended (I suppose) for seconds. The micrometer-axis has a pinion of eight, working in a concealed wheel of forty, which carries a pinion of seven, working in a wheel of forty-two : a portion of this wheel is seen through a cut in the end plate, carrying figures for the whole revolutions. The concave screw of the micrometer is spht, and a screw, whose head is seen in fig. 16, nearly in the line of the micrometer axis, presses the two parts together. Below this are seen, in fig. 16, two small screws ; they merely hold on a small plate which covers up the screw threads. The end of the micrometer screw is not pointed, but nearly spherical. The guard screw works in a brass split crossways. There is a small piece at the left-hand extremity of fig. 16, which I do not remember or understand. Fig. 17 is an end view of the slider, looking at the micrometer head; every part of it has been described under fig. 16. When the observer has turned his face towards the great spindle, the micrometer and guard-screws are at his right hand. Fig. 18, Plate XV. This is a perspective view of the sector, as mounted on its spindle, complete. At the top is the transverse beam of the tripod top. A brass block is attached to its lower surface, and in this the pivot (whose upper part is cut with a deep screw-thread) works, so that the conical point of the pivot can be brought down to the depression requisite for entering properly into the deep conical hole at the top of the spindle shewn in fig. 2. The circular piece with holes for handspikes is a part of the pivot. Above it is a circular piece with milled head ; this works on the thread of the upper part of the pivot, and is to lock it fast. The bracket, seen partially in figs. 1 and 2, is here seen well. The plumb-line shade is seen well ; at the top it is firmly attached to the piece mentioned under fig. 1 ; near the DESCRIPTION OF BRADLEY's SECTOR. 75 bottom it is attached to the frame carrying the counterpoise weights, but not firmly ; there being a screw to move it through a small distance sideways. At the bottom the plumb-line shade carries a stirrup of brass, whose bottom is a circular plate, on which stands the plumb-bob pot. To one side of this stirrup is screwed (by a milled-head screw) a piece carrying a stalk, which carries the split tube for the lower microscope : this stalk is moved endways by a milled-head screw. The bottom of the spindle is seen ; it turns with a conical hole on a conical point, as at the top ; but the point has no adjustment upwards. This point is attached to or part of a sort of inverted dish ; in the sides of the dish are four powerful screws, which press against the sides of a large stud that is firmly fixed to the lower cross-beam of the tripod, for adjustment sideways. To the face of the spindle, at the bottom, is attached a projecting piece of brass; and on the inverted dish are two stops, by which the spindle can be reversed in azimuth almost exactly : there is a milled-head screw passing through the piece of brass, for fixing it to either stop, and thus setting the spindle fast in azimuth. The back edge- bar of the spindle can be seen, deepest in the middle. The slider for the illuminating lamp can be seen. The iron bar on the spindle, to which the counterpoise frame is attached, can be seen. The back arch can be seen well, but the iron bar by which it is carried cannot be seen ; on the right hand, two screws, which connect it with the projecting pieces that fasten it to the iron bar, can be seen. The slider is seen upon the back arch, and the roller-frame, &c. attached to the telescope ; and the figure shews the relative position which they always have, the two rollers being included between the two cramp-pieces, with sufficient play for the action of the micrometer-screw. The great spring is seen, spanning over the back arch. The counterpoise weights are for the purpose of pressing the steel mirror with proper force against the point of the micrometer-screw. Fig. 19, Plate XVI., is a perspective view of the tripod-stand and its sur- rounding stage, without the spindle or any part of the sector. The lower transverse bar has a good back edge-bar. The apertures, in the upper frame, between the transverse bar and the triangular sides, serve for the telescope to look through in opposite positions of the spindle. The surrounding stage is for the observer to walk round, for examining the bisection of the upper dot ; it does not touch the tripod-stand any where. The whole is so constructed 76 VERIFICATION AND EXTENSION OF LA CAILLE's ARC OF MERIDIAN. that it may be taken to pieces and packed in cases for transportation. The legs of the tripod are, I think, but 2 inches thick ; but the bracing makes the tripod very stiff and firm. I shall now subjoin a few notes on the history of the instrument and the changes which it has undergone. The instrument was completed, it appears, in August 1727 {Phil. Trans. Vol, XXXV. p. 643), and was mounted at Wansted ; where it remained apparently till 1749. The history of its removal to Greenwich is contained in the following statement extracted from a manuscript in Bradley's hand- writing preserved in the Safe-Room at the Royal Observatory.* " In the year 1749, lOOOZ. was given by His Majesty, to be paid by the Treasurer of the Navy out of monies arising from the old stores of the navy (upon the representation of the Lords of the Admiralty, and principally upon Lord Anson's recommendation), to buy some astronomical instruments for the use of the Royal Observatory, when it was proposed by Mr. Folks, Mr. Graham, and Mr. Robins, who were consulted with on that occasion, that, in the catalogue of instruments to be purchased, a parallactick sector should be inserted as very useful for observing stars near the zenith ; and the sector which I had formerly hung up at Wansted in 1727 (with which I had after- wards discovered the laws of the aberration of the fixed stars, as also the nutation of the earth's axis), being judged by them worthy of a place at the Royal Observatory, I removed it from Wansted in July 1749, and procured a new apparatus for suspending it (made by Mr. Hearn, as the old one was) ; and I likewise took care, while the rooms of the new Observatory were building, that there might be made convenient places for hanging the sector, both in the new Quadrant-Room and in the Transit-Room. My view (in providing for its suspension in either room) was to render it useful for setthng the true zenith distances of such stars as come within its reach (or within 6^° on either side of the zenith), thereby errors of the lines of collimation of the tele- scopes of the mural quadrants may be found with greater ease and certainty." I cannot extract this account without expressing my astonishment that no better method was devised by Bradley for reversing the instrument than carrying it from one wall to another. * The number of this manuscript, in the present arrangement of the MSS. at the Royal Observatory, is 204. DESCRIPTION OF BRADLEY's SECTOR, 77 It appears probable, from an estimate cited by Professor Rigaud from Bradley's papers (Bradley's Miscellaneous Works, p. Ixxvi.), that the price of the sector was 4:51. The next entry that I find is the following : * " 1750, Aug. 13. Examining the object-glass of the parallactick sector, I found that the screw (which should press it firm in the cell) was loosened, so that when I had pressed the glass down as much as I could in the cell, the screw had room to turn a great way before it touched the glass again. I therefore screwed it in as far as I could without injuring the glass, and then made a mark on it opposite to the middle of that end of the axis on which the plummet hangs, and so let it remain in that situation in order to find whether the line of coUimation is altered by what I did to the object-glass ; for I suspect that the difference between the zenith point, as found now and last January, may be owing to the glass not lying fixed in the same position in the cell. " From the mean of all the observations, taken from Aug. 3 to Aug. 2Z> the zenith point of the sector is 38° 23' 45|", or about 1^" different from what I before found in January last." Nothing further, except occasional notices of the shifting of the sector from room to room, of the zenith point, &c., occurs in the few papers of Bradley's preserved at the Royal Observatory. In some of his manuscripts, at the Bodleian Library, at Oxford, (which Professor Johnson, at my request, has had the goodness to examine), there occur repeated determinations of the value of the divisions ; of which the following are the principal results : Manuscript marked B : "In these comparisons the zenith point of the sector is 38° 23' 45"-5. The angle shewn by the sector greater than that by the new quadrant 2"-25 for every degree, and greater than that shewn by the old quadrant 1"*25 for every degree, by the 96 division. " The above numbers are the mean of the observations made from Aug. 14, 1750, to October, 1752." Manuscript marked D. It is stated that, in January and February 1754, the zenith point was found to be 38° 23' 45"-35 ; the angle shewn by the sector, when in the Transit-Room, was greater by 2"-6 in a degree than by the new quadrant, and by 2"-l in a degree greater than by the old quadrant with Mr. Bird's * MS. No. 201. 78 VERIFICATION AND EXTENSION OF LA CAILLE'S ARC OF MERIDIAN. division ; and, when in the Quadrant-Room, greater by 2"*3 in a degree than by the new quadrant, and greater by 1"'5 in a degree than by the old. In September, 1754, the angle was found to be greater by 2" in a degree than that shewn by either quadrant. These numbers were found by comparing the zenith distances of stars several degrees apart, as found with the sector and with the quadrants (manuscript marked C). The following notes occur in Dr. Maskelyne's papers, and are for the most part printed in his Observations. 1768, July 12.* " This day Mr. Bird set up the zenith sector of 12J feet radius, which he has cleaned and put in order, in the Transit-Room. He has also altered the manner of suspension of its plumb-line, which before was hung from a notch made precisely at the centre of the instrument ; but it is now suspended from a notch a httle above the centre, and the notch is moved by means of a screw, so that the silver wire, which is the plumb-line, may appear through a microscope to pass over and bisect a fine point placed at the centre." 1776, Nov. 5. "Weight added to the plummet : it now weighs l|^lb." 1776, Nov. 6. " Found the instrument bear too little on southernmost of three triangular screws at top ; altered the bearing of this and the opposite screw till, on moving the instrument to different zenith distances, the plumb- line still kept to the point in the centre. Before, on only turning the micro- meter-screw nine revolutions, the plumb-line shifted a great deal with respect to the central point." f In the printed Transit Observations, Vol. II. p. 160 (1779, October 22), is a long note describing several alterations made in the buildings in the summer of 1779, in which, after mentioning that the flat ceilings had been taken away from the Transit and Quadrant-Rooms, Dr. Maskelyne says, " The western wall of the Quadrant-Room thus raised has been applied to good use, as a new place of support from whence to suspend the zenith sector, when removed from the eastern wall of the same room in order to be turned into a contrary position, instead of placing it on the western wall of the Transit-Room, which was less commodious, being at too great a distance from the mural quadrants." * MS. No. 329. t It would seem from this that the form of the pivot was faulty. DESCRIPTION OF BRADLEY's SECTOR. 79 The brackets and the attachments for the back arch, for mounting the. sector in its two positions, were in the Quadrant-Room (one on the eastern wall, the other on the western wall) till within a short time. They were removed on the occasions of converting the western side of the Quadrant- Room into a fire-proof-room (in 1839), and of making some alterations in the Computing-Room, which required the erection of a staircase and the piercing of new doorways on the eastern side of the Quadrant-Room (in 1841) : the openings in the roof remain as they were. " 1785.* A steel arch with divisions to every five minutes of zenith- distance upon gold pins has been substituted, instead of the brass arch by the late Mr. Sisson, so that now the instrument requires no correction, either for the total arc or for the different rates of expansion and contraction of the arch and telescope by heat and cold, as they are both made of the same metal. Moreover, the horizontal wire in the focus of the telescope has been sunk in a deep groove, that it may never touch the vertical wire, as was done with the wires in the focus of the transit and south quadrant telescope in 1784. A guard, also, has been applied to the plumb-line, to defend it from the impulse of the air, and the plummet-pot has been fixed to the guard, with a short broad plummet, that the observations may now be made, even in the zenith, without ever taking up the plummet ; a circumstance which much facilitates the observing a number of stars in succession in the same night. The placing the lamp for enhghtening the wires at a much greater distance from the object-glass than formerly, as well as the enlargement made in the opening of the roof in 1779, cannot but conduce to the greater exactness of the observations." The name of the artist who constructed the new arc is not mentioned ; but from the next entry it appears beyond doubt that it was Troughton. This is the arc which is still on the sector. The illuminating apparatus here described as new is probably that now used ; the old one being probably a small disk in front of the object-glass. " 1785, Nov. 19. The plummet of the zenith sector weighed 9f [ounces, I suppose]. The plumb-line broke in air with 19| ounces. I took out 14 ounce, to reduce it to 18 ounces. Mr. Troughton soldered lead on the inside to make it weigh exactly 18 ounces." • MS. No. 329. 80 VERIFICATION AND EXTENSION OF LA CAILLE's ARC OF MERIDIAN. At the end of Dr. Maskelyne's printed Quadrant Observations for 1801 is the following note, of which I have not found the original manuscript, although a short memorandum is contained in MS. No. 338 : — "An excellent achromatic object-glass, with an aperture of 3|- inches diameter, has been fitted by Mr. Dollond to the same tube, instead of the original one of the common sort, and of about 3 inches longer focal length ; and the finest wires of about j^ of an inch in diameter fixed in the focus, instead of the former ones of about — of an inch. The same eyeglass is retained as before, for the convenience of observing, with the plumb-hne always remaining in its place, stretched by the plummet immersed in water. The telescope magnifies about seventy times, as before. The thickness of the gilt silver wire plumb-line is ^jg of an inch, and it is stretched by a weight of 18 ounces, as before." This is the object-glass now in the sector. The increase of focal length explains the insertion of the tube in the object end of the telescope, exhibited in fig. 6. The method of using the sector has always been the following : — Direct the telescope to the expected place of the star, and clamp the slider (fig. 16, &c.) By means of the adjusting piece seen in figs. 3, 4, and 5, cause the plumb-line to pass truly over the upper dot. Then, if there is sufficient time before the star's entry into the field, use the micrometer-screw (fig. 16, &c.) to make the nearest dot of the limb pass under the plumb-line, and read off" its number of turns and subdivisions. When the star enters the field, use the same micrometer-screw to make the wire in the field of view bisect the star. The difference between the two readings is evidently the quantity, which must be added to or subtracted from the reading expressed by the graduation of the dot, to give the star's zenith distance, still subject to an error of coUiraation, which will be eliminated by reversing the instrument. If time permit, it is prudent again to read the micropieter with the dot under the plumb-line, as the observer will thus ascertain the firmness of the slider-clamp during the observation. In judging of the merits of this instrument, it must be remarked that, in common with all other instruments of the same class, it is liable to one of these inconveniences ; that, if the plumb-line hangs at a sensible distance Ycrvftavtwri cmd IxUnswrio/La. Cailks ArcofMndmn. Plcais of Braxlhys "lemtk Sector. Iig. Z.lTtd view ofth top of the great. spouUcti TMe^. Fig./l Syj£ vi£w ofthttop ofth£ gnat spindfl/i ({■• /'/.r//7/.i-/ii/i ci/' /,ii (/ii7/fs . I/v i/f J1('/-n/iiI/i J'/,j//.y of Srtu/lt'ils .'/'/iit/i ,)/•/•/-//• 7v//. IS I'} fir (if Sf.r/'i'/' ,'/,(• ///a7i///n/ 0/1 lis s/JUii//c Ufiper h as from the heavy sands, and the poverty of oxen at this season of the year, he doubted if I should be more fortunate elsewhere. On renewing the negotiation, only one waggon and two span of oxen could be engaged for the whole journey; and the super- intendant, that I might not be detained, was so good as to lend the institution- waggon for the next stage. The gathering together of the oxen from the downs, with other delays on the part of the Hottentots, kept us at Groene Kloof three days. We set out on the 20th, at i*" p.m., and reached field cornet Schalkwyk's, on Zwartland Plain, shortly after nightfall. March 2 1st. Hired a waggon and span of oxen from the field cornet. 86 VERIFICATION AND EXTENSION OF LA CAILLe's ARC OF MERIDIAN, Started at noon, and arrived at Uly Kraal, the farm of Jasper Smidt, by nightfall. It is proper to mention, that the order on the field cornets was not so eflScient as I expected ; I therefore sent off a letter to the Civil Commissioner in Cape Town, to ascertain the real extent of its power, in order that I might not be delayed on my return. I received Mr. Borchard's reply at Klyp Fonteyn with a more imperative mandate inclosed ; but I was not compelled to use it. March 22d. Jasper Smidt's oxen were at a distant farm ; but he supplied me with a waggon and horses. We started at l*" p.m. and reached Portuguese Fonteyn by 10'' at night. Observed latitude of Portuguese Fonteyn, 33° 1' 13". March 23d. Hired a waggon and span of oxen of Mr. Bester. Set out at 1'' 45°, and arrived at Mr. Melk's of Kerston Fonteyn, on the Berg river, at 7" P.M. March 24th. With a waggon and oxen hired from Mr, Melk, we set out early in the morning, and reached I^lyp Fonteyn about sunset. In the selection of a spot for the sector, I was guided in some measure by the facilities afforded in a large firm circular floor (for treading out corn), composed of pot-clay, situated at and rather within the south extremity of the ruin supposed by Captain Everest to be the granary of La Caille ; and in part by the uncertainty whether the local investigation about to be under- taken by the sappers would prove successful. Within the limits of inquiry there could be no sensible diflference of effect on the plumb-line from local causes, while any point could be referred to the floor. The straw and rubbish having been swept off, the sector was taken from its case, laid on the floor, and carefully cleaned. In this necessary operation the several pieces forming the bearings and upper adjustments of the tube were separated and cleared from sand and dust. In the meantime the tripods were raised, and lines drawn on the floor in the direction of the meridian and perpendicular, by means of the sun's transit. The tent was next raised and fixed to iron pins driven into the floor ; after which the tube was placed on its bearings, and the two barometers suspended from the sector tripod. At the distance of 21 feet exactly, and due east of the sector axis, a nail HISTORY OF SECTOR OBSERVATIONS AT THE CAPE OF GOOD HOPE. 87 was driven into the floor, over which the axis of the repeating circle was placed. As all remarks relating to the weather, with other memorandums con- nected with the sector-work, are annexed to the observations in their proper places, it is only necessary here to state, that the night of March 27th was spent in the adjustment of the sector by transits over the meridian, that the observations for zenith distance began on the 28th, and that they were discontinued on the 21st of April, a sufficient number having been made for settling the question of the amphtude. March 28th. From fresh information obtained on the spot, the sappers and GiBBS began their operations by cutting trenches in various directions. They soon encountered a foundation, which being traced proved to be that of a dwelling-house, distant about 70 yards north of the sector. The ground being dry and hard, and the weather extremely hot, this work took up nearly five days. April 6th. This day the sappers succeeded in discovering another foundation to the west of the former, some of it from two to three feet below the surface. The dimensions in some measure correspond with the description given by La Caille, in his journal, of the granary he occupied. April 12th. Lieut. Williams and the sappers were engaged in making a map of the farm by actual measurement with the chain. April 14th. Started with Lieut. Williams, — Gibbs, Conrad Engel- braght, and a guide, at daybreak for the summit of Piquet Berg, which we reached at nine o'clock. Before our departure the barometers were com- pared ; their indications were No. 518 t= 29°693. Ther. 58°. No. 249 = 29-698. Ther. 57. On the mountain. No. 249 was suspended from a small tripod made of cane. At 9'' 12", the time arranged for simultaneous observation, the mercury stood at 27"'-603 ; thermometer, 49°-l. The day was unfavourable for obtaining an extensive view of the sur- rounding country ; misty with mizzling rain. About noon it partially cleared up. On our return, the barometers were again compared, when the pointer of the stationary one was found separated from the vernier. The observer had marked the height of the column on the scale at the time appointed 88 VERIFICATION AND EXTENSION OF LA CAILLE's ARC OF MERIDIAN. = 29'°'764. However, as some uncertainty attaches to his observation, and as it gives the altitude of the mountain about 170 feet greater than was afterwards obtained with the repeating circle, no use has been made of it. From this day to the 20th, Lieut. Williams, with the sappers and Gibbs, were continually engaged in their investigations on the ruins and plan of the place, and in the measurement of a base line. On the latter day, the exposed foundations were closed in. The 21st, 22d, and 24th, were employed in taking horizontal angles and zenith distances with the circle, and in levelling from the sector station to the base line. I set out with Lieut. Wil- liams and a guide at daybreak, on the morning of the 23d, to examine the character of the country north of the station. We rode on about fifteen miles, where, from a hill, we obtained a view of about seventy miles, so com- manding as to render a closer investigation of it unnecessary. Our time, with other circumstances, precluded the possibility of a longer journey. On our return, the sappers had dug a pit under the axis of the sector (that instrument having been dismounted on the 22d) to the depth of rather more than three feet, where they encountered a rock, in which they chiselled a hollow to receive a quart bottle, as is described in Part I. page 41. April 25th. Having agreed with Conrad Cotsee, a farmer, for three span of oxen and two waggons for the whole way to Cape Town, we left Klyp Fonteyn at l"" p.m. this day, and halted at nightfall at the farm, Zout Kloof (Salt valley). Observed latitude, 32° 54' 0". April 26th. Started at S"" a. m. and reached Mr. Melks on the Berg river at daybreak, where we halted till 2'' p. m. when we again started and reached an open outspan. Observed latitude, 3i3° 1' 0". April 27th. Left at 4'" a. m. Halted at Mr. Fister's farm about daybreak, from whence we started at 2'' p. m. and reached an open outspan in the night. Observed latitude, 33° 25' 0". April 28th. Left at 4'' a.m. Reached Uly Kraal by break of day, near to the place where La Caille's base-line traverses the waggon-way. ' Accompanied by Lieut. Williams, I took this opportunity to explore the direction of the line. At l"" p.m. we proceeded on our journey, and by 8^ p.m. we arrived on the Capoc Berg ridge, near to Contre Berg. HISTORY OF SECTOR OBSERVATIONS AT THE CAPE OF GOOD HOPE. 89 April 29th. Set off at 4'' a.m. and arrived at the Groene Kloof Missionary Station about 7^ from whence we started at 2" p.m. and reached Drie Fonteyn, the farm of Mr. Kuss, at 6" 40"'. Observed latitude, 33° 39' 0", April 30th. Started from Drie Fonteyn at 5" 30" a.m. and arrived at Mr, Fester's farm by sunrise; from whence we started at 1''p.m. and arrived at Mr. Bester's, of Langflea, at 7^ p. m. May 1st. Left Mr. Bester's at 9'" a.m.; arrived at the Observatory at 4" p. M. ; but the waggons proceeded on to Cape Town with the instruments, where Wm. Field, Esq. H. M. Collector of Customs, kindly permitted them to be deposited in his private store. It is now necessary to state why the sector was taken a second time to Cape Town. A cursory comparison of the observations shewed that those made at the south extremity did not deserve the confidence required in a work of this kind, where the length of a few feet is a matter of importance, and, as was very properly stated in the instructions, " it is indispensable that the observa- tions be of unexceptionable goodness." The list of stars had been increased, partly to supply the place of those daily becoming invisible from gliding into daylight; and the substitution of cobweb for the unusually thick wires admitted of greater precision in the bisections of the smaller stars ; to which may be added that increased accuracy might now be expected from the increased experience in the observer. I knew from the past that good observations could not be obtained under a tent in Mrs. De Witt's yard ; I therefore sought for some building close to the station, in which the sector could have fair play ; and fixed upon Roggebay Guardhouse, a building in charge of the Board of respective Officers, and let by them to a tenant at will. Having obtained leave of the tenant, the Board granted permission to make a hole in the roof and to sink the floor, so that the sector might be brought underneath the rafters, I undertaking to reinstate all in its former condition when the observations should be completed. I must here acknowledge my obligations to my friend Lieut. Williams, who smoothed the way for obtaining this favour, and to Col. Lewis, the 90 VERIFICATION AND EXTENSION OF LA CAILLE's ARC OF MERIDIAN. commandant, for various kinds of assistance throughout the work ; indeed, the value of the zealous co-operation of the engineer department can only be estimated by those acquainted with the Cape of Good Hope. In the friendship of these two gentlemen I was particularly fortunate. The brick floor was taken up, and the soil underneath removed to the depth of three feet in the centre of the room, where the sector was erected on the 7th of May, one week after my return from Klyp Fonteyn. The winter having set in early, no observations could be obtained until the 12th. Afterwards frequent interruptions occurred from the state of the weather ; six weeks, from this cause, were expended on a work that in fair weather might have been performed in two. The sector was dismounted on the 30th of June and removed to the Customhouse, from whence it was carried to the Observatory by coolies on the 2d of July, and again erected in the sector-room. On inspection, the instrument was found as perfect as when I received it, without the slightest mark of injury. The only alterations in its details are the substitution of spider lines for thick wires, and the addition of trays to the tripod, for supporting the lamp opposite the upper dot. At the guardhouse I was compelled to shorten the feet of the stage, but on the return of the instrument to the Observatory new ones were made. As a field instrument it is only defective in one particular, viz. in a con- trivance for referring the plane of the arch to a fixed mark. Merely looking along the arch is not sufficient, as the lower end of the plumb-Kne-shade intercepts the line of sight along the divided surface. A telescope cannot be fixed to the tube ; if attached to the spindle, its parallelism with the arch might vary, and is difficult to verify. As a substitute, small sight vanes are now constructing to clamp on the flanch of the arch. They will be very light, and it is hoped will save much time in the adjustments, and much calculation (as will be presently seen), and will expel that want of confidence as to the azimuthal position, which has been the cause of many hours being devoted to trial-and-error adjustments, that would otherwise have been spent in the real objects of the sector. On this point it may be right to explain more at length the importance of referring to a fixed mark. 1st. In the absence of an azimuth-circle, the two stops require two inde- HISTORY OF SECTOR OBSERVATIONS AT THE CAPE OF GOOD HOPE. 91 pendent adjustments, and several transits are required for each. These are reduced to one by means of a fixed meridian mark with two points on it. 2dly. In a climate where the variations in temperature within twenty-four hours often amount to 45°, the frame-work is liable to swerve ; therefore it requires a constant check. 3dly. The coefficient for the error in azimuth within the limits of the arch is small, and the transit at one wire being liable to an error of half a second, several transits must be observed on the same night, thus dividing the attention; and experience teaches me that the attention should not be so divided, as, for instance, when the thundering noise of the wind com- pels the observer to hold a box-chronometer to his ear while he is bisecting a star. By these remarks I must not be understood to imply that transits over the meridian should be neglected ; on the contrary, I conceive the observer is in duty bound to produce them, not only for his own satisfaction, but to satisfy the public that the instrument was in its proper position. For this purpose, three or four observations will be sufficient, as an error of observa- tion, amounting to half a second or more, when the instrument is kept nearly in the meridian by the mark, is of no consequence. In other respects Bradley's sector is a perfect instrument; the inde- pendence of its parts and the simplicity of their combination are worthy of the master hand that contrived it. The position of the sector in the Guard-house has been permanently marked in the following way : — Before the hollow occupied by the sector was filled up, a block of granite, about three feet long, was placed upright on a base of brick and mortar, so that its top should be even with the floor. It was then inclosed in a case of masonry, by building it round with brick and mortar. The floor was then raised and paved with bricks. The top of the block is dressed smooth and contracted to one foot square, and is even with the floor. The centre of the square surface is the position of the axis of the sector. 92 VERIFICATION AND EXTENSION OF LA CAILLE's ARC OF MERIDIAN. § 9. Methods employed for the Reduction of the Observations, and Abstract of the Result of all the Observations. The barometers employed at Klyp Fonteyn were made by Mr. Thomas Jones, and are the property of the Royal Engineer department. From a comparison of their indications with the meteorological journal kept at the Royal Observatory, it appears that the station at Klyp Fonteyn is 485 feet above the mean level of the sea. The barometer employed in the Guard-house was made by Mr. Dollond, and is the property of the Observatory. This station is close to the sea-beach. The feet of the sector could not be more than two or three feet above high water. The chronometer employed at both stations is by Arnold, and numbered 326. It beats half-seconds. It went solar time at Klyp Fonteyn ; but, find- ing the inconvenience of this in sidereal observations, I had the rate altered to sidereal time before the observations in the Guard-house began. The per- formance at Klyp Fonteyn was good ; at the Guard-house the reverse ; for which I am unable to assign any cause beyond the circumstance, that in my absence it was on one occasion allowed to run down. The error of the chronometer at Klyp Fonteyn was usually obtained by altitudes near the prime vertical : that in Cape Town by means of journey- man pocket -chronometers carried to and from the transit -clock at the Observatory. From some unaccountable cause (perhaps misplacement of the comparison entries) a portion of them is not available. However, as the error and rate, when the latter is tolerably regular, are eliminated in the solution of the equations for determining the error in azimuth, the investigation of the rate by independent means is little more than a matter of prudent curiosity. Shortly after the commencement of the observations at Klyp Fonteyn, the error of coUimation in right ascension of the meridian wire was found to be inconveniently large in the adjustment of the arch by transits. An attempt was made on the 3d of April to diminish it ; but, from stiffness in the frame, proved unsuccessful. Therefore, before the error in azimuth can be de- termined, it is necessary to know the distance of the meridian wire from the visual axis. As the transit of a star within a few minutes of the zenith is little affected by the error in azimuth ; if we assume the rate of the chronometer to be METHODS OF REDUCTION OF THE SECTOR OBSERVATIONS, 93 constant, the successive transits of a star in the alternate positions of the limb east and west ought to give the error of coUimation of the middle wire. Let T, T', T", be the times by chronometer of the successive transits, c the error of coUimation expressed by its value in time for an equatorial star, r the rate of the chronometer in 24; hours, M. the star's right ascension, y the secant of its declination, and e the error of the chronometer, then, jR + e + cy =T M. + e — cy+ r =:T jH + e + ci/ +2r- = T" Hence +r-2c2/ = r-T ^ T' + T-2T' ^, rr,, and c = — ^ . + r +2c2/ =T"-T' 4.y An analogous process applies when one of the intervals of the transits is not a single day. Thus, KLYP FONTEYN. Astro. Society's Catalogue, No. 1969; Zenith Distance, 0° 14' North; cy = c x M85. h m s April \5,M + e — cy =15 31 58-0, face West \Q, Si + e + cy + r = 15 28 4-0 East 18, Jl + e-cy + 3r = 15 20 7-0 West \9, M. + e -\r cy + Ar = 15 16 16-0 East 20, iR + e-cy + 5r = 15 12 15-0 West 2\,M. + e + cy + Qr = \S 8 23-5 East By 15th, 16th, and 18th, c x 7-110 = 9-0 By 16th, 18th, and 19th, c x 7-110 = 15-0 By 18th, 19th, and 20th, c x 4-740 = 10-0 By 19th, 20th, and 21st, c x 4-740 = 9-5 _ 43-5 _ j^gg _ ^^j ^j^g middle wire is between the spindle and visual axis. 23-7 Astro. Society's Catalogue, No. 848 ; Zenith Distance, 0° 22' North ; cy = c x 1-184. April 1,^ + e + cy = ^ ^ ^^-O, face East 4, ^ + e — cy + 3 r = 5 54 5-0 West 5, ^ + e + cy + 47- = 5 50 15-0 East 6^^ + e-cy + 5r = 5 46 13-0 West 9, 7il+c + cy + 8r = 5 34 30-0 East 94; VERIFICATION AND EXTENSION OF LA CAILLE's ARC OF MERIDIAN. By 1st, 4th, and 5th, c x 9-472 = 24°0 By 4th, 5th, and 6th, c x 4-736 = 12-0 By 5th, 6th, and 9th, c x 9-472 = 23-0 59-0 c = = 2-49. 23-68 Astro. Society's Catalogue, No. 1378; Zenith Distance, 0° 18' South; cy ■=■ c y. 1-192. h m s April 15, tR + e — cy = 10 11 0-5, face West 16, ^ + e + cy + r = 10 1 9-0 East 18, iR + e - cy + 3 »• = 9 59 12-5 West 13-5 ^ = 7-:T62=^-«^- Astro. Society's Catalogue, No. 1070; Zenith Distance, 0° 6' North; cy = c x 1-187. April 6,M + e — cy = 7 39 13-0, face West 9, ^ + e + cy + 3»- = 7 27 29-5 East lQ,M-\- e-ircy = 7 23 34-5 East \\,M-^ e — cy -^-r =7 19 33-5 West 15, ^ + e - cy =73 52-5 West 16, ^ + e + cy + r =7 0-5 East By 6th and 9th, c x 4-748 = 6-5 By 10th and 11th, combined with 15th and 16th, c x 4-748 = 9-0 15-5 s ''^ 9^496 =^-^32. The chronometer error was applied in this case, as found by independent means.* Giving to the four results for c the respective vfeights 6, 5, 3, 2, the mean = l''71f expressed in solar time, r-72 was employed in the calculations. * There appears to be no doubt of the correctness of the process by which the three first values of c are obtained above. Mr. Maclear, in the manuscript, had however given the values 1-661, 1-971, and 1-416. The remark as to the application of chronometer error seems to apply only to the observations of April 6 and 9. — G. B. A. t For the reasons given in the last note, this value appears to be slightly in error. METHODS OF REDUCTION OF THE SECTOR OBSERVATIONS. 95 CAPE TOWN. Astro. Society's Catalogue, No. 1915; Zenith Distance, 0° 4' South; cy = c x 1-206. h m s May 2Q,M. + e-cy =16 39 23-0, face West 27, iR + e + cy + r = 39 29-5 East 29, Jl + e-cy + 3r = 39 19-0 West June 17, Jl + e — cy = 39 .55-5 West \^, M+e + cy + r = 39 57-0 East 19, ^ + e — cy + 2»-= 39 42-0 West 21, jR, + e + C2/ + 4r = 39 36-0 East 23, ^ + e + cy = 39 17-5 East 2A,M.+e-cy+ r= 39 1-5 West 25, JR. + e + cy + 2/- = 38 59-5 East 26, jR, + e - cy + 3r = 38 46-5 West 27, JR. + e + cy + 4r = 38 45-0 East s Weights. By May 26, 27, and 29, c x 7-236 = 23-5. 0-41 By June 17, 18, and 19, c x 4-824 = 16-5. 0-28 By June 18, 19, and 21, c x 7-236 = 24-0. 0-40 By June 23, 24, and 25, c x 4-824 = 14-0. 0-34 By June 24, 25, and 26, c x 4-824 = 11-0. 0-44 By June 25, 26, and 27, c x 4-824 = 11-5. 0-42 Mean c = 2^-66,* by which the wire is too near the spindle. The second value should be rejected. If a weight is given to each in proportion to the reciprocal of the square of its probable error, the mean is 2'"55.* 2'-65 was employed in the calculations. It appears that the collimation in right ascension altered about 0'*94 in the journey from Klyp Fonteyn to Cape Town ; which perhaps arises from one of two causes. The first is, an alteration in the position of the sliding tube which contains the object-glass, and which must be pushed in before the instrument can be packed in its case. The second is, a flexure in the tube by jolting in the waggon, notwithstanding the support of the blocks. ' The removal from and refixing of the wire frame to the tube is not likely to be the cause of a variation to this amount. For the investigation of the error in azimuth (Z), the following list of stars is selected; whose right ascensions were determined for this purpose with the 10-feet transit instrument. * These numbers are probably erroneous to a small amount. 96 VERIFICATION AND EXTENSION OF LA CAILLE S ARC OF MERIDIAN. No.of Ast. Soc. Cat. Mean Right Ascen- sion, Jan. 1, 1838. Zenith Distance South End of Arc. Zenith Distance North End of Arc. 903 h m s 7 11 25-52 S. 2° 53' 20" s. O 1 /( 4 6 35 957 7 39 29-14 S. 3 39 25 s. 4 52 40 1433 12 19 47-18 S. 4 13 40 s. 5 26 53 1527 13 11 30-80 s. 3 9 30 1821 15 49 24-32 S. 4 30 s. 5 13 45 2007 17 22 36-86 S. 3 3 28 s. 4 16 43 2043 17 38 50-10 S. 3 3 50 s. 4 17 5 791 6 14 5-84 N. 3 55 30 N. 2 42 16 869 5 52 15-73 N. 5 9 50 N. 3 56 36 915 7 17 41-29 N. 4 55 40 N. 3 42 25 1084 8 43 15-18 N. 3 49 57 1243 10 19 44-99 N. 3 40 15 N. 2 27 1774 15 28 43-34 N. 4 40 33 N. 3 27 18 1866 16 9 18-69 N. 3 24 30 N. 2 11 15 2079 17 55 24-23 N, 3 30 N. 2 16 45 2741 22 48 41-05 N. 3 26 40 N. 2 13 25 The error of coUimation in right ascension having been applied with the sign + face west, and — face east, to the observed time of transiting the meridian wire, the star's apparent right ascension was subtracted, and the diflFerence (w), (ji), &c. for each star was arranged in equations of the following form : — e—Za +r6 — n = e — Za' +rb' —n' =0 e + Zo" +r6"-«" = e + Za"'+r6"'-«"'= Where e is the error of the chronometer on sidereal time ; a, a, &c. = — ' ' '■ ; b the time from sidereal noon expressed in decimals of twenty-four hours. Subtracting the equations for stars south of the zenith from the equations for stars north of the zenith, equations of the following form take place : — Z (a" + a) + r (6" _ 6) - «" + m =0 Z (a'" + «') + »• (*'" - V) - »'" + «' = METHODS OF REDUCTION OF THE SECTOR OBSERVATIONS. 97 Treating groups of such equations by the method of least squares, and eliminating r, Z becomes known. Thus, KLYP FONTEYN, March 31st, No.of Ast. Soc. Cat. Chron. Time of Transit. * App. m.. n. n', &c. 903 h m s 7 11 8-17 fa m 3 7 11 25-87 ^^^ 17-70 2007 17 21 17-13 17 22 37-99 — 20-86 2043 17 38 31-95 17 38 51-16 — 19-21 957 7 39 2-76 7 39 29-63 — 26-87 1821 15 48 52-02 15 49 25-79 — 33-77 869 6 53 30-09 6 52 16-05 + 74-04 1084 8 44 28-27 8 43 16-04 + 72-23 915 7 18 52-76 . 7 17 41-73 + 71-03 1774 15 29 51-10 15 28 44-79 + 66-01 791 6 15 5-84 6 14 5-97 + 59-87 2079 17 56 20-72 17 55 25-16 + 55-56 2741 22 49 35-77 22 48 40-67 + 55-10 1866 16 10(18-35) 16 9 20-03 + (58-32) No. 1866 is marked doubtful in the original observations. The equations given by the individual stars are e-Zx e-Zx e-Zx e — Zx e-Zx e + Zx e + Z X e + Z X e + Zx e + Zx e + Zx e + Z X e + Z X -089 +r X •093 +rx •093 +rx -107 +r X -116 +rx -078 +r X •076 +r X •074 +r X •069 +r X ■055 + r X -046 + r X -045 +rx •044 + r X -300 + -724 + -735 + -319 + -659 + -286 - •363 - -304 - ■645 — •260 — -747 - •951 - ■673 - 17-70 20-86 19^21 26^87 33-77 74-04 72-23 71-03 66-91 59-87 55-56 55-10 58-32 98 VERIFICATION AND EXTENSION OF LA CAILLE's ARC OF MERIDIAN. And the equations formed by differences of the equations above are Z X -194 -r X -373 -107'81 = Z X -183 +r X -044 - 99-10 = Z X -167 -r X -431 - 90-24 = Z X -162 —rx -079 - 87-77 = Z X -144 -r X -040 — 77-57 = Z X -162 +r X -088 - 89-33 = Z X -152 +r X -632 — 81-97 = Z X -137 —rx -062 - 77-53 = Z X -171 —rx -456 — 94-90 = Z X -165 — r X -063 — 89-93 = Z X -181 —rx -015 — 97-90 = Z X -162 —rx -090 - 86-12 = Z X -148 -r X -464 - 80-73 = From these the following are formed by the method of least squares : — + Z X -351486 - »- X 0-189579 - 191-74758 = - Z X -189579 + r X 1-181205 + 104-59669 = Of which the solution is Z = 544-95 = 2° 16 15 r = -1-09 Substituting the value of Z thus found in the terms Z a, Z a, &c., of the original equations, the following results are found : — No.ofAst. Soc. Cat. Values of e. 903 + 30-80 -r X -300 2007 + 29-82 —rx -724 2043 + 31-47 -r X -735 957 + 31-44 —rx -319 1821 + 29-44 —rx -659 869 + 31-53 -r X -286 1084 + 30-81 —rx -363 915 + 30-70 - »• X -304 1774 + 29-31 -rx -645 791 + 29-90 -r X -260 •2079 + 30-49 -rx -747 2741 + 30-58 -rx -951 1866 + (34-34)-r X -673 METHODS OF REDUCTION OP THE SECTOR OBSERVATIONS. 99 From these. Chronometer error at sidereal noon = + 30-52 — r x "524 The same by independent observations = 30-90 — r x -429 No. 1866, marked uncertain, should have been rejected. KLYP FONTEYN, April 6th. No. of Ast. Soc. Cat. Chron. Time of Transit. * App. M. n. 1527 h m s 13 12 2-72 h m 3 13 11 32-51 + 30-21 903 7 11 55-76 7 11 25-73 30-03 2007 17 23 8-39 17 22 38-21 30-18 2043 17 39 22-05 17 38 51-38 30-67 957 7 39 59-37 7 39 29-49 29-88 1821 15 49 55-63 15 49 25-95 29-68 1433 12 20 18-32 12 19 48-78 29-54 869 6 52 47-93 6 52 15-93 32-00 1774 15 29 17-56 15 28 44-94 32-62 791 6 14 37-20 6 14 5-84 31-36 1243 10 -20 18-46 10 19 46-18 32-28 2079 17 55 58-11 17 55 25-37 + 32-74 e- Z X -068 e—Zx -089 e — Zx -093 e—Zx -093 e — Zx -107 e—Zx -116 €-Zx -121 e + Z X -078 c + Z X -069 e + Z X -055 e + Z X -050 e + Z X -046 + r X + r X + r X + r X + r X + r X + r X + r X + r X + r X + r X + r X •550 •300 •724 ■735 -319 -659 -514 -286 ■645 -260 -430 -747 30-21 . 30-03 30-18 30-67 29-88 29-68 ■ 29-54 ■ 32-00 . 32-62 ■ 31-36 - 32-28 - 32-74 100 VERIFICATION AND EXTENSION OF LA CAILLE's ARC OF MERIDIAN. Z X -199 — r- X -228 — 2-46 = Z X -185 — r X -014 — 2-94 = Z X -162 — r X -059 — 1-48 = Z X -143 - r X -305 - 1-61 = Z X -139 + r X -023 — 2-56 = Z X -167 —r X -014 — 1-97 =0 Z X -137 +rx -095 - 2-41 == Z X -176 - r X -254 - 1-82 = Z X -166 — r X -229 — 2-60 = Z X -153 +r X -428 — 2-86 = Z X -171 - r X -449 — 1-33 = Z X •162. — r X -079 — 2-44 = Z X -144 - r X -040 — 1-33 = + Z X -34466 — r X -19983 — 4-52216 = - Z X -19983 +r X -66802 + 1-59689 = Z = 14^2 = 3 33 r = - 1-86 Values of e, 3l'l8 +7-X -550 31-29 +rx -300 31-50 +r X -724 31-99 +r X -735 31-40 +r X -319 31-33 + r X -659 31-26 +r X -514 30-89 +r X -286 31-64 +r X -645 30-58 + »• X -260 31-57 +r X -430 32'09 +r X -747 The concluded value of e, the"! „ „^ ., , ' . [31-39 + 7- X -514 error at sidereal noon, isj By independent observations 32-27 — r x '422 In a similar way the value of Z has been found each night, presuming the invariability of the position throughout the night. That this .was not strictly correct is evident on carrying the eye over the columns ; still it is probable that the fluctuations were within such limits as to be insensible on the zenith distances. METHODS OF REDUCTION OF THE SECTOR OBSERVATIONS. 101 The observations of the 28th and 29th of March have not been included in the calculations, because the error in azimuth on those nights was about the same as on the 30th and 31st, and because the transits on those nights are not sufficiently numerous to prove the exact value ; also the chronometer rate at the time was very irregular from the recent journey. I shall now give the final equations* for each night in a tabular form. AZIMUTHAL ERROR AT KLYP FONTEYN. Dav. Position of Face. Equations. Values of Z. 1838. Mar. 30 31 April 1 East. West. East. West. East. ! give) = 0j + Zx-366824-rx0-33162 -159-714 =0 -Zx-33152 +rx 130-981 + 10-779 =0 — Zx-35146 -rxO-189579 +191-7476 = + Zx -189579 +»-x 1-181205 -104-5967 fOnly six observations altogether; three stars Zx-330 +r-xO-000 -175-20 Z is so small that it may be neglected The sector was adjusted on the 3d. fThe east stop was not adjusted on the 3d. This night it was accomplished by trial and error. The night being favourable for observation, the zenith distances were recorded, to be employed in the determination of the amplitude. In the calculation of the values of Z for the fol- lowing intervals, the error of the chronometer derived fronl extra-meridional altitudes has been employed. From 5 33 to 7 11 7 11 7 36 7 36 8 40 8.40 9 20 9 20 10 10 13 40 13 40 22 48 436-85 = 544-95 O i II 1 49 13 2 16 15 530-9 = 2 12 44 0-00 181-7 = 45 23 442-2 = 1 50 33 45-8 = 11 27 83-4 = 20 51 55-3 = 13 50 66-3 = 16 35 13-6 = 3 24 * In the manuscript which reached me, the decimal points were universally omitted from the coefficients of these equations, and many of the signs were obviously wrong. Not having leisure 102 VERIFICATION AND EXTENSION OF LA CAILLE S ARC OF MERIDIAN. AZIMUTHAL ERROR AT KLYP FONTEYN (continued). Day. Position of Face. Equations. Values of Z. 1838. April 6 West. f+Zx-34466 -rx i-Zx -19983 +rx -19983 — 4-5222 •66802 + 1-5969 ::i s 14-2 o / // = 3 33 7 East. f+Zx-24503 -rx (-Zx-14883 +rx •14883 — 3-5158 •45205 + 3^65943 ::i 11-8 = 2 57 9 East. f+Zx-1228 +rx ^+Zx-100 +rx •100 - r9409 •72 - 2^151 ::i 15-1 = 3 46 10 East. f+Zx-3747 -rx l-Zx-180 +rx •180 - 9^1000 •14644 + 7^2367 ::i 24-5 = 067 11 West. f+Zx-2029 -rx }-Zx-1545 +rx •1545 — 8-9423 -2028 + 7-6396 ::i 36-6 = 099 (The seconds of No. 1527 and 869 are incorrect.) 15 West. f- Zx -380434 -rx 1+Zx -250102 +rx -250102 +37-22053 -931297-24-14079 ::i 98-1 = 24 31 16 East. f+Zx-385583-rx 1-Zx -157957 +rx -157957-35-09605 i-11311 +21-7120 ::i 88-2 = 22 3 18 West. f+Zx-2628 +rx l+Zx -55259 +rx -55259 —20-41655 •24410 —47-4433 ::i 81-1 = 20 16 19 East. f+Zx-26788 +rx -4124 -11-26549 l+Zx-4124 +rx 116-04 -51-9724 ::i 41-6 = 10 24 20 West. (+ZX-2952 —rx l+Zx-959 — rx -959 -10-7287 97-79 -45-112 ::i 36-0 = 090 21 East. f+Zx-371578-rx I- Zx -45925 +rx -45925 - 9-9490 -884-289+ 5-2787 ::i 26-9 = 6 44 The value of Z at the south station being always within certain limits, and the rate of the chronometer variable, the equations were formed so as to diminish the effect of the latter as much as possible. The method of least squares was adopted in only a few cases. to repeat from the beginning Mr. Maclear's investigation, I t-ave contented myself with finding, bv trial, such positions for the decimal points, and such signs, as are consistent with the values of Z. No figures are altered. — G. B. A. METHODS OF REDUCTION OF THE SECTOR OBSERVATIONS. 103 AZIMUTHAL ERROR AT CAPE TOWN. Day. Position of Face. Equations. 1 Values of Z. 1838. ' -\ May 12 West .. Insensible. 13 East rC- Z x-168 + 7- X -083 + 8-19 = 01 » mi \ V to 13 20 \- Z x-166 + r X -013 + 6-99 = j C+ Z x-137 —r xO-14 -4-18 = 1 from 13 20 ' 1+ Z x-160-r xO-90 -3-75 = 1 to 22 48j 40-86 = 10 13" 32-08= 8 jO 15 West j + Z x-327 +rx -596 - 2-76 \ +Z x-275 + rx -250 - 3-45 ::i 25-87 = 6 28 17 West f +ZX-26535 -rx 1-2740 - 11-64259 |-Zx-255 +rx73-23 +169-3641 = 1 = j 32-72= 8 11 21 East f +Z x-144165 + rx -57708 - 11-08782 \ +ZX-14026 -rx -573966- 9-9866 ::i 76-02 = 19 22 West f+Zx-486 -rx -097 -40-75 1 + Z x-022 +rx -234 - 1-68 ::i 83-71=20 56 26 West f +ZX-874 +rx -369 - 63-37 1 -Z x-010 -rx 1-5211 + 1-52 ::i 72-28 = 18 4 27 East r + Z x-819 +rx -311 - 26-51 |-Zx-037 -rx 1-686 - -074 ::i 32-66= 8 10 28 West f Only two stars for this determination. l+Zx-179 +rx -015 -10-14 = ol 56-66= 14 10 29 West f +ZX-921 -rx -0078 —46-420 j +ZX-034 +rx -2872 - 2-740 ::i 50-43 = 12 37 June 2 East 1 1 Insensible. 3 East f Five observations only this night. 1 + Z x-166 -r X -09 - 6-10 = oj 36-2 = 93 r The transits for azimuth are all north of zenith in i consequence of interruptions from clouds 4 Fast ■ +ZX-271 +rx -283 - 9-57 [+ZX-034 — rx -314 — -960 = = . 34-59= 8 39 6 East j Z x-648 +2-117 - 25-96 = °l 36-80= 9 12 When the instrument was not reversed, a reference to the original observations will explain the reason. 104 VERIFICATION AND EXTENSION OF LA CAILLE'S ARC OF MERIDIAN. AZIMUTHAL ERROR AT CAPE TOWN {continued). Day. Position of Face. Equations. Values of Z. 1838. f+Zx l+Zx 101 + 111 + r X -236 - 9-65 r X -025 — 8^59 h m = Olfrom 5 50' = 03 to 11 30 75-6 =18' 54" June 7 West j+Z X 070 — 071 + 144- r X -014 - 0^57 r X •OlO- 1^05 r X -110- 12-52 = 0) from 11 30 = of to 14 1 from 14 ^ ^\ to 15 30 12-8 = 3 12 87^0 =21 45 f+Zx i-Zx 625- 79 + r X -79 - 6-219 r x3^33 + 6-79 = OjfromlS 30 = o| to 22 48 IM = 2 47 8 East f +Zx I +Zx •1596 •053 — rx -425 — — r X 1-448 — 5^1650 = 1 2^370 =03 32-24= 8 4 14* West f +Z X 1 +Zx •138 •138 + r X -023 - + rx -012 — 8^53 = 1 8^81 = j 83-11=20 47 17t West r-z 1 +Zx •640 + rx -178 + -rx -18 - 3^20 = 1 0^703 = j 11-04= 2 45 18 East f +Zx { +Zx •823 •40 + r X -944 - 29-240 = | -r X •27-08 +153-8 = j 28-53= 7 8 19 West 1 • .. •• 1 Insensible. 21 East f +Zx 1-Zx •955 •01 + r X ^869 - + r X 1^696 + 21-020 =01 14-170 = j 29-6 = 7 24 22 West f +Z X } +Zx •774 ■018 + rx ^719 - + r X VIM - 38-990 = ■ 17-220 = 41^62 = 10 24 23 East f +Z X 1 +Zx •439 •01 + r X ^009 — + rx •Sll + 10-570 = j 5-188 = j 24^3 = 65 24 West f +Zx i-Zx •398 ■006 + r X -006 — + r X ^253 + 14-863 • = 1 1-646 = j 37^23= 9 18 25 East f H-Zx I -Zx •161 •012 - r X -072 - + rx -314 + 6-53 = 1 2-89 = j 37^08= 9 16 26 West ( +Zx i +Zx •163 •001 — rx -204 — + r X ^285 — 3-86 =01 2-54 = ] 34^84= 8 42 27 East j-Zx / +Zx •1632 1.0227 + r X 7^3975 + -r X 1'632 - 10-5248 = \ 18-9703 = \ 16^87= 4 13 * It appears probable that one of the coefficients of Z on this day is erroneous, t Probably a coefficient of Z has been omitted. METHODS OF REDUCTION OF THBl SECTOR OBSERVATIONS. 105 The correction of the observed zenith distance depending on the value of (Z) was computed from the formula 72 2 cos Latitude x sin Zen. Dist. sin I" cos Declination. where Z is supposed to be expressed in seconds of time. The computations were verified by means of the line of squares on the sliding rule. The corrections for precession, aberration, and nutation were calculated by means of the constants in the Royal Astronomical Society's Catalogue, recomputed for the year 1838 ; excepting for the three stars which have the numerals of the Brisbane Catalogue. The run of the micrometer at Klyp Fonteyn was ascertained on the morning after the observations terminated. The temperature during the examination was 79°-5 ; at one period 83°. At Cape Town, the second morning after the observations there, in the temperature of 61°. One Revolution at Klyp Fonteyn = 33'-6153 at Cape Town = 33-6143 It appears by this that a variation of 19° of temperature is insensible in the run. The details of the examinations will be found below. In the arrangement of the results, all the corrections are entered in detail with the view of checking the calculations or facilitating combinations. Comparing the error of coUimation on the 30th and 31st of March with the error of coUimation afterwards, the disturbance of the wire frame does not appear to have produced any sensible difference. In like manner, com- paring the observations before the 19th of June with those of the 20th and 21st, the removal of the object-glass on the 19th is not sensible ; but the removal on the 23d produced a sensible variation. With two or three ex- ceptions, the whole list was observed on the 30th and 31st of March, therefore the mean zenith distance for each star will not be affected at Klyp Fonteyn ; the other is a matter of calculation. Assuming in the reductions of each star the line of coUimation to have remained constant at each station, we have the following results : 106 VERIFICATION AND EXTENSION OF LA CAILLE S ARC OF MERIDIAN. RESULTS FOR THE AMPLITUDE OF THE ARC. I, ^ i' rz22 /r w 33 m 7.1 .- 3,a// i', 52 no iij - Jsi'-'i/ no i> 2ZH, Zds-I BY STARS NORTH OF THE ZENITH AT CAPE TOWN. Star's No. in Ast. Soc. Cata- logue. Star's Name. At Cape Town. At Klyp Fonteyn. Resulting Amplitude. Star's Mean Zen. Dist. 1838, Jan. 0. Error of Collim. Star's Mean Zen. Dist. 1838, Jan. 0. Error of Collim. 1947 1797 1378 1070 1969 848 1562 1579 1356 1866 2741 2079 1243 791 1115 1774 915 869 k Scorpii A Lupi (28 Craterisj.^/{7,-:..v.-. « Pixidis Nauticse . . u Scorpii X Canis Majoris i Centauri k Centauri „ . . Brisbane, 2566 Brisbane, 3350 (19 Crateris . i... *-.... p Scorpii f » Piscis Australis 7 \ (Fomalhaut) . . \ A Sagittarii a Antlise Pneumaticee Brisbane, 2823 ^ Canis Majoris e Pixidis Nauticse . . 40 Librse / // N. 2 0-39 111.17. M.^ 47 37-01 ,^i^ 54 49-29 //fe 1 18 52-69 py 1 26 54-96 ,ti.y 1 35 42-28 /i,%i 1 41 57-00 /4.,fil 1 43 59-51 n.ill 28 1-63 /X^2 49 54-61 /2.?i 2 57 32-61 //, 3.24 49-52 iLcr 3 26 30-08 /^Jy3 30 9-08 mt 3 40 32-29 //,:'-3 48 54-24 lUl 3 S5 28-47 7«4 12 48-06 n.il 4 40 53-46 /5.^4 55 44-74 N. 5 9 52-15 a4'-63 23-61 23-34 22-64 23-54 23-80 24-02 24-37 24-06 23-95 24-28 24-00 23-74 24-64 24-07 24-01 24-42 22-55 23-54 23-85 23-97 1 II S. 1 11 14-44 S. 25 36-81 S. 18 24-62 N. 5 38-52 0I3 40-84 22 28-09 28 43-21 30 45-30 1 14 47-78 1 36 40-45 1 44 17-44 2 11 35-58 2 13 19-22 2 16 54-78 2 27 18-15 2 35 40-15 2 42 14-70 2 59 33-60 3 27 40-42 3 42 30-49 N. 3 56 36-75 29'-'88 29-56 29-59 30-87 29-82 29-04 29-51 29-53 30-13 30-10 30-11 30-17 29-27 28-93 29-64 30-44 28-72 31-44 30-26 30-87 30-23 Q 1 II 1 13 14-83 13-82 13-91 14-17 14-12 14-19 13-79 14-21 13-85 14-16 15-17 13-94 (10-86) 14-30 14-14 /^;^ 13-73 13-77 14-46 13-04 14-25 1 13 15-40 M Canis Majoris s Canis Majoris ,Y) w "■' y '•^■" RESULTS OF THE SECTOR OBSERVATIONS. 107 RESULTS FOR THE AMPLITUDE OF THE ARC {continued). BY STARS SOUTH OF THE ZENITH AT CAPE TOWN. Star's No. in Ast. See. Cata- logue. /yet. ii'ffg lip' /Sn H /ze-'r; (ni, 'Ho I. 1915 699 1889 2110 1661 1061 1604 732 1527 1015 1299 1742 1835 2101 903 2007 2043 957 1821 1433 Star's Name. At Cape Town. Star's niean Zen. Dist. 1838, Jan. 0. Error of Collim. I Scorpii a, Columbse . . . « Normse 6 Sagittarii . . . c^ Centauri .... ,3 PixidisNauticse 5 Centauri ,8 Columbse .... ( Centauri q ArgAs in Puppi ip2 Lupi fl Lupi ^ Telescopii .... ?r ArgAs A Scorpii y Telescopii .... c Argfts in Puppi D Lupi M Centauri S. /7.»; llf.D'J im t'-,^^ li,X 1 '■■■: 1 a; 2^ 2 '/. i " 2 mm' 2 Ihi 2 /^::r2 /«,3z3 lt.l\ 4 S. 4 4 15-25 14 37-13 25 23-09 31 56-07 33 1-23 48 .57-79 38 53-74 54 44-13 56 4-48 14 24-03 20 49-86 21 1-50 25 59-97 52 52-14 53 22-16 3 22-89 3. 44-00 39 28-42 19-67 13 20-14 24-49 23-95 23-49 23-73 23-40 23-34 24-70 24-42 24-77 23-48 23-93 23-96 24-05 24-23 23-93 24-14 23-95 23-57 24-18 23-86 At Klyp Fonteyn. Star's Rlean Zen. Dist. 1838, Jan. 0. 1 17 30-20 1 27 49-24 1 38 38-76 1 45 10-80 1 46 15-98 2 2 12-83 2 52 9-30 3 7 58-48 3 9 20-07 3 27 38-84 3 34 5-14 3 34 16-63 3 39 14-66 4 6 6-47 4 6 36-78 4 16 38-20 4 16 59-08 4 52 43-49 5 13 34-62 5 26 35-15 Error of Collim. 30-40 30-28 30-5) 30-04 29-94 31-13 29-80 30-97 30-25 30-72 30-25 30-23 29-75 30-12 30-01 29-24 29-39 29-69 28-95 28-57 Resulting Amplitude. 1 13 14-95 12-11 15-67 14-73 14-75 15-04 15-56 14-35 15-59 14-81 15-28 15-13 14-59 14-33 14-62 15-31 15-08 15-07 14-95 1 13 15-01 Giving to the result from each star a weight proportional to the number of observations of that star, we have Amplitude as deduced from the observations of 20 stars north of| o ^^ 14-163 the zenith at Cape Town J Amplitude as deduced from the observations of 20 stars south of"i ^ ^^ 14.347 the zenith at Cape Town J Mean of the two 1 13 14-505 The result from No. 2741 (Fomalhaut) has been rejected, perhaps also that for No. 699 {a'Columbce) ought not to be retained. I am not aware of p 108 VERIFICATION AND EXTENSION OF LA CAILLE S ARC OF MERIDIAN. the cause of the discrepancy, unless it be from swerving of the frame at the time of their transits, when the temperature at-Klyp Fonteyn was usually 90°. If we give to the result from each star a weight proportional to the product, of the smallest number of observations of that star in either position of the sector at one station by the smallest number of observations of the same star at the other station, we find for the amphtude By the stars north of the zenith at Cape Town 1 13' 14-173 By the stars south of the zenith at Cape Town 1 13 14'961 If we give to each result a weight proportional to the quotient of the square of the number of observations of each star by twice the sum of the squares of the errors at both stations, we find for the amplitude O / n By the stars north of the zenith at Cape Town 1 13 14-173 By the stars south of the zenith at Cape Town 1 13 14-953 The results for the two methods may be considered identical : and the stars north of the zenith give the amplitude less by 0""78 than the stars south of the zenith. The number of observations at Klyp Fonteyn is 464 at the Guard-house 669 therefore, errors of observation are reduced to nothing. That the change in the line of coUimation on the 23d has little effect in producing the discrepancy, is shewn by the following table, where the means of the observations before that day are compared with the means of the following days. M expresses the seconds of mean zenith distance for each star by the observations preceding the 23d of June ; M' the same after the 23d of June ; c and c the errors in collimation corresponding with M and M'. No. of A.S.C. M M' c' M-M' c—c' 699 37-21 24-"07 36-94 23-65 It + -27 + "42 732 44-15 24-71 43-95 23-71 + -20 + 1-00 791 28-61 24-83 27-98 23-27 + -63 + 1-56 848 42-24 24-17 42-24 23-36 -00 + -81 869 52-22 24-19 51-71 23-16 + -51 + 1-03 903 22-13 24-13 22-23 23-43 - -10 + -70 REMARKS ON THE VALUE OF THE RESULTS. 109 No. of A.S.C. M e M' o' M- -M' C-C' 915 44-57 23-98 45-"i6 23-53 -.59 + -45 957 28-24 23-87 28-46 22-87 — -21 + 1^00 1015 .... .... .... .... .... 1061 57-76 23-73 58-17 22-02 — -41 + b71 1070 .... .... .... .... 1115 .... .... .... .... . . .... (2566)* .... .... .... .... .. .... (2823)* .... .... .... 1243 32-26 24-38 32-39 23-33 — -13 + 1-05 1299 49-94 24-00 49-33 23-44 -f -61 + -56 (3350)* .... .... .... .... .. 1356 32-68 24-56 32-64 23-33 + -04 + 1-23 1378 49-41 23-41 48-89 23-07 + -52 + -34 1433 20-08 24-03 20-23 23-34 — -15 + -69 1527 4-28 25-09 4-90 23-99 — -62 + 1-10 1562 57-03 24-17 56-88 23-29 + -15 + -88 1579 59-54 24-63 59-61 23-30 — -07 + 1-33 1604 53-61 24-95 54-11 23-78 — •50 + 1-17 1661 1-18 23-55 1-27 22-90 — -09 + -65 1742 1-50 24-11 1-46 23-39 + -04- + -72 1774 53-55 23-61 53-14 23-41 + •41 + -20 1797 36-99 23-78 37-16 22-90 — -17 + -88 1821 19-75 24-42 19-32 23-45 + •43 + -97 1835 60-02 24-14 59-76 23-73 + -26 + -41 1866 49-60 24-28 49-42 23-03 + •18 + 1-25 1889 •22-99 23-71 2.3-15 22-90 — -16 + -81 1915 15-28 24-63 14-94 23-88 + -34 + ^75 1947 0-54 24-80 0-02 24-07 + •52 + -73 1969 55-01 23-74 55-11 22-92 — •10 + ^82 2007 22-86 24-37 22-67 23-39 + -19 + -98 2043 44-04 24-16 43-44 23-17 + •60 + -99 2079 9-13 24-91 9-32 23-77 — •19 + 1-14 2101 52-06 24-49 52-05 23-43 + •01 + 1-06 2110 ■ 55-98 24-01 55-94 22-85 + •04 + 1-16 M-M' = + 0-07 + 0-90 f M-M' = Mean i , _ \ c — c = * Numerals of Brisbane's Catalogue. 110 VERIFICATION AND EXTENSION OF LA CAILLE'S ARC OF MERIDIAN. If each star had been observed an equal number of times in both positions of the arch after tiie 23d, the final result would have remained unaffected by e — Heavy dew. ' A dense fog over the plain. The Mean of 5 Altitudes of Sirius corrected for Index error of Spica .... T o / // h m s j = 40 36 29 at 9 44 19-1 by Chron. = 47 9 30 m s By the 1st the Chronometer is fast 9 32-56"] • By the 2d 9 32-17 10 15 58-2 on Mean Time. After the night's observations with the sector were finished the minute hand was put back 9" OBSERVATIONS WITH THK SECTOR AT KLYP FONTEYN, UNREDUCED. 115 March 31st, 1838, Face of Sector West. No. of Ast. Soc. Cat. Time by Chronometer. Micr. for Plumb-line on Dot. Micr. for Observa- tion of Star. Micr. for Plumb-line on Dot. Mean of Micr. for Plumb-line on Dot. Star's Apparent Zenith Distance. Barom. Therm. 732 h m s rev. pts. rev. pta. 19 17-6 rev. ptB. 21 26-2 rev. pts. O / rev. pts. —3 10 4-2 8-6' 29-614 82 791 5 40 41 12 15-7 9 11-2 12 15-4 12 15-55 + 1 40 -f3 4-35 810 48 18 12 11-2 7 32-5 12 11-2 12 11-2 4-0 15+4 12-7 869 6 18 59 10 13-8 8 14-8 10 13-4 10 13-6 -f3 55+1 32-8 903 36 34 13 10-4 17 21-4 13 10-8 13 10-6 —4 5-4 10-8 915 44 17-5 10 24-3 7 6-8 10 24-5 10 24-4 + 3 40 +3 17-6 957 7 4 24 11 21-3 17 338 11 22-4 11 21-85 —4 50—6 11-95 977 17 34-5 9 28-5 5 26-4 9 28-4 9 28-45 + 2 45 +4 2-05 1007 32 40 10 12-8 16 26-5 10 13-2 10 13-0 _2 40-6 13-5 1015 37 37-5 10 13-2 7 21-3 10 13-4 10 13-3 -3 30+2 26-0 29-608 75 1070 .... .... 10.15-3 10 13-6 ■ • • • +0 5-0 1-7 1084 8 9 39 10 13-2 10 33-8 10 12-5 10 12-85 + 3 50-0 20-95 1115 29 17 10 5-3 11 33-0 10 5-5 10 5-4 + 3 0-1 27-6 (2566)* 56 1 10 4-4 11 21-7 10 5-2 10 4-8 + 1 15-1 16-9 29-650 71-3 (2823)* 9 24 30 9 29-7 9 26-1 9 30-1 9 29-9 + 2 35+0 3-8 1243 .... 9 22-0 6 21-0 9 21:8 9 21-9 +2 25+3 0-9 1299 10 8 50-5 10 17-6 10 12-8 10 17-8 10 17-7 -3 35 +0 4-9 (3350)* 21 12-5 10 5-9 8 11-7 10 5'7 10 5-8 + 1 35+1 28-1 1356 50 39 10 2-7 3 20-0 10 2-6 10 2-65 + 1 40+6 16-65 1378 11 9 54 10 12-9 8 26-5 10 12-7 10 12-8 -0 20-1 20-3" 29-564 68 1527 .... 10 2-8 10 12-4 10 3-0 10 2-9 -3 10-0 9-5" 1562 13 1 39 10 7-9 4 27-5 10 7-9 10 7-9 + 25 +5 14-4 1579 7 30 10 7-9 1 7-4 10 7-7 10 7-8 + 25 +9 0-4 : 1604 21 29 10 7-3 15 14-9 10 7-3 ' 10 7-3 -2 50-5 7-6 1661 ' .... 9 26-7 13 11-8 9 26-8 9 26-75 -1 45—3 19-05 29-564 65 1742 14 36 46 10 1-3 1:0 5-2 10 1-4 10 1-35 —3 35 —0 3-85 1774 . 53 56 9 5-7 14 11-8 9 6-0 9 5-85 + 3 30-5 5-95 1797 15 5 11 8 32-3 11 7-2 8 32-5 8 32-4 -0 25-2 8-8 1821 12 53 8 24-5 7 19-8 8 24-3 8 24-4 -5 15+1 4-6 1835 19 48 8 22-0 8 22-1 8 22-0 8 22-0 -3 40-0 0-1^ a i] I'hermometer at i loon this da f in the heat was 101°. '' The heat seems to affect the sector frame. -= s tar leaving the £ eld. d Calm. * Numerals of Brisbane's Catalogue. 116 VERIFICATION AND EXTENSION OF LA CAILLE S ARC OF MKRIDIAN. March 31st, 1838, Face or Sector West (continued). No. of Ast. Soc. Cat. Time by Chronometer. Micr. for Plumb-line on Dot. Micr. for Observa- tion of Star. Micr. for Plumb-line on Dot. Mean of Micr. for Plumb-line on Dot. Star's Apparent Zenith Distance. Barom. Therm. 1866 h m s 15 34(16?) rev. ptB. 8 30-8 rev. pu. 7 4-2 rev. ptB. 8 30-8 rev. ptB. 8 30-8 / rev. pu. +2 10 -fl 26-6 m. o 1889 .... 9 31-7 8 24-9 9 31-7 9 31-7 -1 40+1 6-8 29-544 65 1915 16 3 51 10 20-8 7 11-2 10 20-8 10 20-8 — 1 20 +3 9-6 1947 18 19-5 9 22-0 13 1-3 9 22-2 9 22-1 -1 10—3 13-2 1969 30 54-5 9 12-3 12 27-3 9 11-3 9 11-8 -1-0 15-3 15-5 2007 45 3 8 4-5 12 13-3 8 4-9 8 4-7 _4 15-4 8-6 2043 17 2 15 8 4-9 13 0-9 8 4-6 8 4-75 _4 15-4 30-15 2079 20 1 8 15-3 5 32-7 8 15-3 8 15-3 + 2 15+2 16-6 2101 30 2 8 5-8 11 14-2 8 5-8 8 5-8 _4 5-3 8-4 2110 37 r4-5 7 30-6 9 12-2 7 31-0 7 30-8 -1 45—1 15-4' 2741 22 12 28 13 14-2 17 5-2 13 13-9 13 14-05 + 2 15—3 25-15 29-652 93-5 « Th e weather is calm and hot. Zenith Distance of Sirius taken"! o / » '' ™ ' „, = ., , . . , ^= 54 19 55 at 9 54 49-25 by Chron. ; Chron. fast 28-53>i with the repeating circle .... J oiSpica = 42 54 20-5 at 10 2 44-25 33-67 56 3 8 at 10 31 37-8 Mean of 5 double Altitudes ofl Sirius, taken with sextant * . of Spices =108 22 3 at 10 39 47-1 ^ I cannot explain the discrepancy in these results. Mean. 33-50 27-90 30-9 on ,Mean Time. April 1st, 1838, Fac E OF Sector East. No. of Ast. Soc. Cat. Time by Chronometer. Micr. for Plumb-line on Dot. Micr. for Observa- tion of Star. Micr. for Plumb-line on Dot. Mean of Micr. for Plumb-line on Dot. Star's Apparent Zenith Distance. Barom. Therm. 791 h m s 5 36 19 rev. ptB. 11 19-5 rev. ptB. 16 12-6 rev. ptB. 11 20-5 rev. ptfl. 11 20-0 O / rev. pta. + 2 40 +4 36-6' 810 44 23 11 24-5 8 29-8 11 24-3 11 24-4 + 15-2 28-6 848 6 5 59 11 32-4 16 32-2 U 32-4 11 32-4 -fO 20-J-4 33-8 869 15 3-5 11 8-8 14 32-9 11 8-6 11 8-7 + 3 55-1-3 24-2 903 32 41 9 28-4 7 10-4 9 28-0 ■ 9 28-2 -4 5-2 17-8 915 35 21 10 33-0 16 11-2 10 33-4 10 33-2 + 3 40 -f 5 12-0 977 7(13)39-5 10 31-4 7 28-9 10 29-6 10 30-5 + 2 50-3 1-6 » Milky atmosphere. Ovfercast, accompanied with lightning to the west, north-west, and west-south-west. * The index error of the sextant is 11' 28", to be subtracted from the numbers in the text. The numbers thus corrected are the double altitudes. OBSERVATIONS WITH THE SECTOR AT KLYP FONTEYN, UNREDUCED. 117 Monday, April 2d, was cloudy with rain. The weather cleared up on Tuesday, and the night was spent in examining the adjustments of the sector, principally by means of transits at the extreme ends of the arch. The coUimation in right ascension appears considerable, which renders the meridian adjustment difficult. To remove the former, the wire frame was undamped, and moved according to the indications of the successive transits ; but from some stiffness in the dovetail this could not be properly accomplished, and there was not time to unscrew and examine the frame. The greater part of the night having passed in this occupation, only one star south of the zenith remained of greater zenith distance than 4°, and none to the north. Assum- ing the chronometer error, as obtained by the observations recorded below, to be 31''2 fast, the differences between it and the errors obtained by transits over the middle wire of the sector were finally as follows : FACE WEST. h m M 16 20 Zen. Dist. O / S. 1 40 a Difference 39 S. 1 15 54 S. 1 10 17 6 N. 15 22 S. 4 2 The stop of the azimuth motion was clamped to this position. There not being an azimuth circle to the sector (which in field-work would be an advantage), the position face east cannot be placed, by mere mechanical means, 180° from position face west, consequently the east stop was not disturbed. As the extreme differences in temperature in this sheltered spot are con- siderable, with corresponding hygrometric variations, humid in the night, dry and hot in the day, the frame not guarded as it would be under a building, it may swerve without the knowledge of the observer ; to keep a check on it (so far as stars close to the zenith will be a check) in future the times of all the transits will be recorded. The observations made before the wire frame was disturbed this night must be reduced separately from the observations to be made hereafter. 118 VERIFICATION AND EXTENSION OF LA CAILLE S ARC OF MERIDIAN. Zenith distance of Siriusl , ° „„' ,,„" ^ ._™ J_i ^i /-i. r ^ r,n"r,n\ f- = 42 38 IV at 8 47 7-5 by Chron. ; Chron. fast 29-90 with repeating circle . , . . j = 46 40 1 at 9 6 32-5 Altitude of iSmai with sextant = 34 55 52+ at 9 47 2-8 Zenith distance of Spica "i with repeating circle .... J 37 26 22-5 at 10 19 39-5 31-19 32 on (Mean Time. Mean 31-24 April 4th, 1838, Face of Sectob West. No. Thin clouds. <: Uncertain. ^ 15" past middle wire. + This must be diminished by 5' 44" for index error. — G. B. A. * Numerals of Brisbane's Catalogue. OBSERVATIONS WITH THE SECTOR AT KLYP FONTEYN, UNREDUCED. 119 April 4th, 1838, Face of Sector West (continued). No. of Ast. Soc. C»t. Time by Chronometer. Mior. for Plumb-line on Dot. Mior. for Obseryra- tion of Star. Micr. for Plumb-line on Dot. Mean of Micr, for Flumb-lipe on Dot, Star's Apparent Zenith Distance. Barom. Ther;n. 1433 11° 29 12 ret. ptB. 10 14-4 rev. pta. 14 11-0 rev. pta. 10 14-7 rev. pta. 10 14-55 / rev. pta. —5 26—3 30-45 In. 1527 12 20 46 10 15-0 10 14-8 10 15-4 10 15-2 -3 10 -fO 0-4 1562 45 42 11 16-6 16 1-9 11 16-6 11 16-6 + 30-3 19-3 29-569 53-5 1579 51 40 11 16-6 11 14-3 11 16-6 11 16-6 + 30+0 2-3 1604 13 6 18-5 11 30-9 16 32'8 11 31-2 11 31-05 -2 50-5 1-76 1661 42 48 JO 31-9 14 14-5 10 32-1 10 32-0 -1 45-3 16-5 1742 14 21 45 9 15-0 9 9-2 9 15-2 9 15-1 -3 35 +0 5-9 29-582 54-5 1774 37 37-5 9 2-2 14 19-8 9 1-9 9 2-05 + 3 30-5 17-75 1797 49 32 9 2-4 11 12-4 9 2-6 ' 9 2-5 -0 25-2 9-9 1821 58 13 9 10-2 7 24-7 9 9-8 9 10-0 -5 15+1 19-3 1835 15 4 47 10 13-2 10 2-8 10 13-1 10 13-15 -3 40 +0 10-35 1866 18 6 9 12-1 7 26-7 9 11-8 9 11-95 + 2 10+1 19-25 1889 29 33 11 5-0 9 30-8 11 5-0 11 5-0 — 1 40+] 8-2 1915 48 22 11 2-4 7 25-6 11 2-4 11 2-4 -1 20 +3 10-8 29-582 .54-6 1947 16 2 49-5 11 16-3 14 27-8 11 16'4 ' 11 16-35 -1 10-3 11-45 1969 15 9 11 14-0 14 30-4 11 14-0 11 14-0 + 16-3 16-4 2007 31 10 11 28-2 16 23-0 11 29-0 11 28-6 -4 15-3 28-4 2043 47 21 11 29-0 16 9-8 ill 28-9 11 28-95 -4 15-4 14-85 2079 17 3 53 . 11 4-8 8 30-0 11 5-0 11 4-9 +2 15+2 8-9 . 2101 15 6 11 18-4 14 15-8 11 18-4 11 lS-4 —4 5—2 31-4' 2110 21 50-5 11 31-8 13 9-5 11 31-8 '■ 11 31-8 -1 45-1 11-7 2741 21 56 21-5 10 19-8 14 17-6 10 19-6 10 19-7 +2 15-3 31-9 ' Good bis ections throughout the night. { Mean of 6 Altitudes oiiSirius = 34 68 27 at 9 42 24-8 by Chron. ; Chron. fast 30-16 | ,5>° Mean of 5 Altitudes of Spica = 47 22 22 at 9 48 23-4 30-84 ) Yme. Mean 9 45 30-50 120 VERIFICATION AND EXTENSION OF LA CAILLE S ARC OF MERIDIAN. Aprfl 5th, 1838, Face or Sector East. No. of Ast. Soc. Cat. Time by Chronometer. Micr. for Plumb-line on Dot. Micr. for Observa- tion of Star. Micr. for Plumb-line on Dot. Mean of Micr. for Plumb-line on Dot. Star's Apparent Zenith Distance. Barom. Therm. 699 h m s 4 40 20 rev. pts. 10 13-7 rev. pts, 15 3-7 rev. ptfl. 10 14-0 rev. pts. 10 13-85 O / rev. pts. -1 30+4 23-85= In. o 791 5 20 46 10 19-0 15 7-2 10 18-8 10 18-9 + 2 40 +4 22-3 810 28 40-5 10 21-2 7 31-7 10 20-8 10 21-0 +0 15—2 23-3" 848 50 15 11 27-8 16 29-7 11 28-4 11 28-1 + 20 +5 1-6 29-680 70 869 58 54 11 22'3 15 4-5 11 22-5 11 22-4 + 3 55+3 -16-1' 915 6 24 34 10 21-7 15 30-6 10 22-0 10 21-85 +3 40 +5 8-75 957 45 41 10 29-0 6 24-9 10 29-0 10 29-0 -4 50-4 4-1'' 977 57 31 11 16-8 8 6-4 11 15-7 11 15-75 —2 50—3 9-35 1007 7 13 32-5 .... 15 16-4 10 31-2 .... —2 45 +4 19-2 1015 18 37 .... 16 6-3 11 7-0 .... -3 30+4 33-3' 1061 39 52-5 10 27-5 7 16'5 10 27-5 10 27-5 -2 0—3 11-0 1070 .... 10 33-3 12 25-1 10 33-1 10 33-2 + 5+1 25-9' 1084 49 28 11 18-4 12 14-2 11 19-0 11 18-7 + 3 .50+0 29-5 1115 8 9 13 11 15-9 11 8-7 11 16-4 11 16-15 + 3 0-0 7-45 (2566)* 36 15 11 7-4 11 14-4 11 7-5 11 7-45 + 1 15— ■ 6-955 (2823)* 9 4 28 11 16-7 13 6'0 11 16-7 11 16-7 + 2 35+1 23-3'' 1243 26 5 11 13-5 15 31-2 11 13-3 11 13-4 + 2 25 +4 17-8' 1299 55 7 11 7-6 13 15-3 ■ 11 7-3 11 7-45 -3 35 +2 7-85 (3350)* 10 1 16-5 11 15-3 14 30-5 11 15-1 11 15-2 + 1 35+3 15-3 1356 30 42 11 13-5 10 20-5 11 13-7 11 13 6 + 1 45-0 27-1' 1433 11 25 26 10 7-8 8 0-8 10 7-0 10 7-4 -5 25 —2 6-6 29-682 58-3 1527 12 16 59 10 13-4 12 7-5 10 13-4 10 13-4 -3 10+1 28-1 1562 41 50 9 26-0 7 32-6 9 26-0 9 26-0 + 30-1 27-4 1579 47 48 9 26-0 11 20-1 9 25-8 9 25-9 + 30+1 28-2' 1604 13 2 28 9 29-3 6 22-8 9 29-5 9 29-4 -2 50-3 6-6 > Too much wind ; plumb-line unsteady; moved the sector in azimuth by means of a Columbte on the wire. " Fai at; 10' past middle wire. ■= Moved the sector in azimuth. '' Moved the sector in azimuth. e Not good. ' Bisected W past the middle wire. s Moved the sector in azimuth. " Mo ired the sector in azimuth. ' Leaving the field. '' Moved the sector in azimuth. > Mo ifed the sector in azimuth. * Numerals of Brisbane's Catalogue. OBSERVATIONS WITH THE SECTOR AT KLYP FONTEYN, UNREDUCED. 121 April 5th, 1838, Face of Sector East {continued). No. of Ast. Soc. Cat. Time of Chronometer. Micr. for Plumb-line on Dot. Micr. for Observa- tion of Star. Micr. for Plumb-line on Dot. Mean of Micr. for Plumb-line on Dot. Star's Apparent Zenith Distance. Barom. Therm. 1661 h m s 13 37 57-5 rev, pts. I 26-1"' rev. ptB. 7 4-6 reT. ptB. 9 26-2'" rev. pu. I 26-15 / rev. ptH. -1 45-1 21-55" in. 1742 14 17 54-5 10 22-0 12 22-5 10 21-9 10 21-95 —3 35+2 0-55 1774 33 44-5 11 11-0 7 22-8 11 11-2 11 11-1 + 3 30 -.3 22-3 1797 44 44 11 24-4 11 7-9 11 24-3 11 24-35 -0 25—0 16-45 1821 54 24-5 12 1-4 15 11-5 12 1-4 12 1-4 -5 15+3 10-1 1835 15 56-5 12 26-7 14 29-5 12 26-3 12 26-5 —3 40 +2 3-0 29-678 55 1866 14 13-5 13 24-3 17 3-8 13 24-0 13 24-15 + 2 10+3 13-65 1889 25 42 11 26-3 14 30-6 11 25-6 11 25-95 -1 40 +3 4-65 1915 44 31-5 11 8-2 16 14-4 11 8-0 11 8-1 -1 20 +5 6-3 1947 58 58-5 9 31-6 8 13-7 9 31-0 9 31-3 -1 10-1 17-6 1969 .... 11 5-2 9 16-4 11 5-0 11 5-1 + 15-1 22-7 2007 16 27 21 11 2-4 8 33-3 11 2-0 11 2-2 -4 15—2 2-9 29-680 57-2 2741 21 52 30 11 20-4 9 13-7 11 20-2 11 20-3 + 2 15—2 6-6 ■" The revolutions of the micrometer were regist ered 9 rev. The number should be 8, by comparing this with other observations of the same star. It was stated on April 3d that only the west stop was adjusted. Having this day computed the times by chronometer when each star should transit the middle wire, the east stop was undamped, and when a star entered the field it was kept bisected, while the sector was moved in azimuth, so that the star should transit at the specified moment. Finally no difference remained beyond the estimated error in collimation of two seconds, and the stop was then clamped. Therefore, in the reductions, the times by chronometer of the transits must be examined. . Mean of 5 Altitudes of Spica = 47° 44' 24" at 9'' 46"' 21= by Chron. ; Chron. fast 31»-11 on Mean Time. 122 VERIFICATION AND EXTENSION OF LA CAILLE'S ARC OF MERIDIAN. April 6th, 1838, Face of Sector West. No. of Ast. Soo. Cat. Time by Cht-onoraeter. Micr. for Plumb-line oti Dot. MiCr. for Observa- tion of Star. Micr. for Plumb-line on Dot. Mean of Micr. for Plumb-line on Dot. Star's Apparent Zenith Distance. Barom. Therm. 699 O 1 . II 4 36 24 Tev. pta. 9 28-2 rev. pts. 6 33-7 rev. pts. 9 28'2 rev. pta. 9 28'2 / "V. pta. -1 30 -f 2 28-5 29-710 o 82 791 5 16 37 9 24-8 6 29-7 9 24-4 9 24-6 +2 40 -f 2 28-9 848 46 i? 13 54 41-5 10 1-3 6 25-4 10 1-5 10 1-4 -fO 20 -f 3 10-0 29-710 75 869 9 28-2 8 5-2 9 27-8 9 28-0 + 3 55 -fl 22-8 903 6 13 46 10 6-6 14 4-1 10 7-0 10 6-8 -4 5-3 31-3 915 . . • ■ 9 25-7 6 16-2 9 25-5 9 25-6 + 3 40+3 9-4" 957 41 45 10 10-4 16 7-8 10 11-8 10 11-1 -4 50 -5 30-7 977 53 28 9 20-1 14 23-4 9 20-1 9 20-1 -i-2 50-5 3-3 1007 7 9 35 10 9-2 7 18-0 10 9-4 10 9'3 -2 45 -f 2 25-3 1015 14 40 10 11-2 7 7-8 10 11-1 10 11-15 -3 30 -f 3 3-35" 1061 35 53 10 9-5 15 13-8 10 9-5 10 9-5 -2 0—5 4-3 1070 39 13 10 3-5 10 6-0 10 3-6 10 3-55 + 5-0 2-45 1084 45(21) 10 0-5 10 33-5 10 0-5 10 0-5 + 3 50-0 33-0 1115 8 5 9-5 10 1-7 12 5-3 10 .2-5 10 2-1 -1-3 0-2 3-2-= (2566)* 32 12 .... 12 8-0 10 21-7 .... -t-1 15-1 20-3 29-688 64-5 (2823)* 9 27 10 5-0 10 8-0 10 5-2 10 5-1 + 2 35-0 2-9 1243 21 38 10 6-4 7 12'0 10 6-5 10 6-45 + 2 25 +2 28-45 1299 50 37-5 10 26-0 10 9-5 10 26-2 10 26-1 + 3 35 +0 16-6 (3350)* 57 20-5 10 14-7 8 24-4 10 14-4 10 14-55 + 1 35-1-1 24-15 1356 10 26 45 10 14-4 12 32-9 10 14-4 10 14-4 + 1 45-2 18-5 1378 46 23 10 4-2 8 17-0 10 4-0 10 4-1 — 20 -fl 21-1 1433 11 21 18 10 20-6 14 16-6 10 20-7 10 20-65 -5 25 -3 29-95 1527 12 12 54 10 17-0 10 16-0 10 17-0 10 17-0 -3 10 -fO 1-0 1562 37 41 10 21-4 14 3-3 10 21-5 10 21-45 + 30 -1-3 15-85 1579 43 50 10 21-5 10 16-5 10 21-5 10 21-5 -f-0 30 +0 5-0 1604 58 26 10 32-5 15 31-0 10 32-6 10 32-55 -2 50 -4 32-45 1661 13 34 57 10 32-6 14 11-5 10 32-6 10 32-6 -1 45-3 12-9 29-635 59 1742 14 13 53-5 11 lO'O 11 0-7 11 9-7 11 9-85 -3 35 -fO 9-15 1774 29 46-5 10 18-0 15 31-4 10 17-5 10 17-75 + 3 30-5 13-65 1797 41 41 10 33-6 13 6-4 11 0-0 10 33-8 -0 25-2 6-6 1821 50 21 11 250 10 3-4 11 25-1 11 25-05 -5 15-1 21-65 " 20» past m iddle wire. ^ Warm evening. <= Becoming cool. * Numerals of Brisbane's Catalogue. OBSERVATIONS WITH THE SECTOR AT KLYP FONTEYN, UNREDUCED. 123 April 6th, 1838, Face or Sector West (continued). No. of Aat. Soc. Cat. Time by Chronometer. Micr. for Plumb-line on Dot. Micr. fur Observa- tion (if Star. Micr. for Plumb-line on Dot. Mean of Micr. for Plumb-line on Dot. Star's Apparent Zenith Distance. Barom. Therm. 1835 h m s 14 56 55 rev. pts. 10 29-4 rev. pt.. 10 17-2 rev. ptB. 10 29'6 rer, pts. 10 29-5 O / rev. pti. -3 40+0 12-3 in. 1889 15 21 42 10 15-9 9 3-0 10 15-3 10 15'6 -1 40 -fl 12-6 1915 41 31 10 21-8 7 6-4 10 21-0 10 21-4 -1 20 -f 3 15-0 29-603 57-5 1947 54 59 10 21-7 13 28-8 10 21-4 10 21-55 -1 10-3 7-25 1969 16 7 18-5 10 20-9 14 0-2 10 20-8 10 20-85 -fO 15—3 13-35 2007 23 18-5 10 31-2 14 23-7 10 31-2 10 31-2 —4 15—3 26-5 2043 39 29-5 10 31-2 15 97 10 31-4 10 31-3 —4 15-4 12-4 2079 56 3 9 25-5 7 13-8 9 25-5 9 25-5 +2 15+2 11-7 2101 17 7 14-5 10 6-3 12 33-9 10 6-5 10 6-4 -4 5-2 27-5 2110 13 59 10 6-0 11 13'3 10 5-2 10 5-6 _1 45_l 7-7'» 29-614 56 ■> The air feels very cold. Bad images throughout the night. Mean of 5 Altitudes of Sinus "i o , „ , i, a , i, h m . withsexfant 1^ (57 19 4- 11 10) x | = 28 33 57 at 10 5 0-13 by Chron. Spica =(106 46 15—11 10) x J = 53 17 33 at 10 II 52-8 Chronometer fast on mean time, by Sirius 32'-47, by Spica 32^-06. April 7, 1838, Face of Sector East. No. of Ast.Soc. Cat. Time by Chronometer. I\Iicr. for Pluml)-line on Dot. Micr. for Otiserva- tion of Star. Micr. for Plumb-line on Dot. Mean of Micr. for Plumb-line on Dot. Star's Apparent Zenith Distance. Barom. Therm. 869 h m s 5 50 50 reT. ptH. 10 3-2 rev. pti. 14 11-1 lo' 30'-'4 rev. ptt. 10 30-3 O / rev. pts. + 3 55 +3 14-8' ID. o 903 6 9 55 10 16-2 8 10-5 10 15-0 10 15-6 —4 5-2 5-1 29-586 83 957 37 (12) 10 15-3 8 24-2 10 15-3 10 15-3 -4 50-1 25-1 977 49 37-5 10 14-0 7 2-8 10 14-8 10 14-4 + 2 50-3 11-6 1007 7 5 42-5 9 32-3 14 15-0 9 32-4 9 32-35 -2 45 +4 16-65 1015 10 48-5 9 31-2 14 26-0 9 30-6 9 30-9 -3 30+4 29-1 1061 32 2-5 9 28-5 6 18-2 9 29-3 9 28-9 -2 0—3 10-7 1084 41 31-5 9 24-0 10 17-1 9 24-3 9 24-15 + 3 50+0 26-95 (2566)* 8 28 J9-5 9 20-1 9 24-4 9 20-4 9 20-25 + 1 15 +0r 4-15 » Thin clouds c learing off. * Numeral of Brisbane's Catalogue. 124 VERIFICATION AND EXTENSION OF LA CAILLE S ARC OF MERIDIAN. April 7, 1838, Face of Sector East (continued). No. of Ast. Soc. Cat. Time by Chronometer. Micr. for Plumb-line on Dot. Micr. for Observa- tion of Star. Micr. for Plumb-line on Dot. Mean of Micr. for Plumb-line on Dot. Star's Apparent Zenith Distance. Barom. Therm. (2823)* h m s 8 56 35 rev. ptfl. 9 30-5 rev. pli. 11 19-3 rev. ptB. 9 30-7 rev. pta. 9 30-6 / rev. pte. + 2 35 -fl 22-7 29-583 o 72-5 1243 9 17(46) 9 11-0 13 30'7 9 11-0 9 11-0 +2 25+4 19-7" (3350)* 58 28 9 10-3 12 26-7 9 10-5 9 10-4 -fl 35 -+-3 16-3 1356 10 22 53 9 2-4 8 9-3 9 2-7 9 2-55 -1-1 45-0 27-25 1378 42 29-5 9 l-O 12 11-7 9 1-2 9 1-1 -0 20 -f 3 10-6 1433 11 17 25-5 9 1-5 6 27-7 9 2-0 9 1-75 -5 25-2 8-05 29-574 69 1527 12 9 1 9 20'0 11 12-8 9 20-0 9 20-0 -3 10-f 1 -26-8 1562 33 57-5 10 14-8 8 21-7 10 15-4 10 15-1 -J-0 30-1 27-4 1579 40 58 10 15-4 12 9-5 10 15-5 10 15-45 + 30 -fl 28-05 1604 54 33-5 .... 7 30-8 11 5-2 .... -2 50-3 8-4 29-539 66 1661 13 31 4 11 17-5 9 28-8 11 18-0 11 17-75 -1 45-1 22-95 1742 14 10 11 4-4 13 3-7 11 4-0 11 4-2 —3 35 -fl 33-5 1774 25(53) 10 32-1 7 7-8 10 32-0 10 32-05 -fS 30-3 24-25 1797 .... 10 17-9 10 0-5 10 18-0 10 17-95 -0 25-0 17-45' 1821 46 29 10 29-6 14 5-7 10 29-6 10 29-6 -5 15+3 10-1 1835 .... 10 20-6 12 23-4 10 21-4 10 21-0 —3 40+2 2-4" 1889 12 23-5 15 27-2 12 23-0 12 23-25 -1 40+3 3-95' I" The second of time uncertain. ° Wind and clouds rising. ^ Bisected 15' past middle wire. <> Bisected 16' past middle wire ; cloudy; the sky was soon totally overcast. * Numerals of Brisbane's Catalogue. Four Readings for Zenith Distances of Sirius with the Repeating Circle as follows : At 8 40 5 by Chron. 0° o' 9 8 42 51 89 26 57 I ? 44 43 24 at 8 41 28 by Chronometer. 8 47 21-5 8 49 25 89 26 57 181 46 28-3 gave 46 9 45-7 at 8 48 23-25 Chronometer fast on mean time, by the first pair 30=-41, by the second pair 30»-83. Sunday, April 8, was cloudy ; also part of Monday. OBSERVATIONS WITH THE SECTOR AT KLYP FONTEYN, UNREDUCED. 125 April 9th, 1838, Face of Sector East. No. of Ast. Soc. Cat. Time by Chronometer. Micr. for Plumb-line on Dot. Micr. for Observa- tion of Star. Micr. for Plumb-line on Dot. Mean of Micr. for Plumb-line on Dot. Star's Apparent Zenith Distance. Barom. Therm. 848 h m s 5 34 30 rev. ptB. 11 29-9 rev. ptB. 16 31-7 rev. pts. 11 29-9 rev. ptB. 11 29-9 O / rev. pll. + 20-1-5 1-8 in. 29-620 78° 869 42 57-5 10 14-3 13 31-4 10 14-3 10 14-3 4-3 55+3 17-1 903 6 2 2 8 13-7 6 9-3 8 14-2 8 13-95 -4 5-2 4-65 957 30 1 8 28-5 4 24-6 8 28-7 8 28-6 _4 50 -4 4-0 29-616 74 977? 40 29 .... 12 2-3 10 14-0 .... +2 50+1 22-3 1007 57 51-5 9 32-5 14 16-5 9 32-5 9 32-5 -2 45 +4 18-0 1015 7 9 31-3 14 28-5 9 30-7 9 31-0 -3 30+4 31-5 1061 24 10 9 32-3 6 24-5 9 31-9 9 32-1 -2 0-3 7-6 1070 27 29-5 9 19-6 11 10-0 9 19-5 9 19-55 +0 5+1 24-45 1084 33 40 11 15-4 12 11-6 11 15-5 11 15-45 + 3 50+0 30-15 29-625 72-5 1115 53 26 11 17-8 11 8-2 11 17-8 11 17-8 + 3 0-0 9-6 (2566)* .... 11 4-0 11 8-7 11 4-2 11 4-1 + ] 15+0 4-6' 1579 12 32 5-5 10 12-8 12 6-3 10 11-5 10 12-15 + 30+1 28-15" 1604 46 42 9 4-7 5 30-6 9 4-8 9 4-75 —2 50—3 8-15 > 15' past meridian. '■ Dense clouds. * Numeral of Brisbane's Catalogue. At 8'' M. T. dense clouds ascended from the north with strong wind, indicating an approach- ing storm. About midnight the sky again became clear, but about 13'' it was entirely overcast. The lunar eclipse consequently could not be observed. 126 VERIFICATION AND EXTENSION OF LA CAILLE S ARC OF MERIDIAN. April 10th, 1838, Face of Sector East. No. of Ast. Soc. Cat. Time by Chronometer. Alicr. for Plumb-line on Dot. Micr. for Observa- tion of Star. Micr. for Plumb-line on Dot. Mean of Micr. for Plumb-line on Dot. Star's Apparent Zenith Distance. Barom. Therm. 699 h m 5 4 20 44-5 rev. pts. 8 31-2 rer. pts. 13 17-5 rev. ptg. 8 31-2 rCT. pts. 8 31-2 O / rev. pts. -1 30 +4 20-3 in. 732 32 10 9 1-0 4 17-2 9 0-4 9 0'7 -3 5-4 17-5 29-620 87 791 5 58 10 4'6 14 25-8 10 4-8 10 4-7 + 2 40 +4 21-1 848 30 34 9 30-2 14 30-8 9 30-2 9 30-2 + 20 +5 0-6 869 39 2-5 10 13-8 13 29-2 10 13-8 10 13-8 + 3 55 -f 3 15-4 903 58 6 9 32-6 7 28-0 9 31-5 9 32-05 _4 5_2 4-05* 915 .... .... 15 14-6 10 12-0 .... + 3 40 +5 2-6'' 957 6 25 24° 9 17-4 7 27 '4 9 17-8 9 17-6 -4 50-1 24-2 977 36 33 20 6-4 16 29-6 20 6-6 20 6-5 + 2 50-3 10-9" 1007 53 55 10 21-6 15 4-7 10 21-7 10 21-65 -2 45 +4 16-05 1015 59 1 10 3-8 14 32-6 10 3-5 10 3-65 -3 30 +4 28-95' 1061 7 20 14 10 2'2 6 25-3 10 2-0 10 2-1 -2 0-3 10-8 29-632 74-2 1070 23 34-5 9 26-7 11 19-0 9 26-8 9 26-75 + 5+1 26-25 1084 29 44 10 19-1 U 14-2 10 19-7 10 19-4 -f3 50 +0 28-8 1115 49 31 10 18-7 10 9-8 10 19-2 10 18-95 -1-3 0-0 9-15 (2566)* 8 16 33 10 17-5 10 21-8 10 17-8 10 17-65 + 1 15 -fO 4-15 (2823)* 44 47-5 10 27-0 12 16-2 10 27-4 10 27-2 + 2 35 +1 230 29-628 71-6 1243 9 5 58 10 29-5 15 14-7 10 29-6 10 29-55 + 2 25 -f 4 19-15 1299 35, 17 10 11-4 12 18-6 10 11-2 10 11-3 -3 35 +2 7-3 (3350)* 41 41 10 23'3 14 3-4 10 23-3 10 23-3 -f 1 35 +3 14-1 1356 10 11 5 10 23-6 9 29-2 10 24'0 10 23-8 + 1 45—0 28-6 1378 30 43 10 17-8 13 28-8 10 17-8 10 17-8 -0 20 +3 11-0 1433 11 5 47-5' 10 9-2 8 1-8 10 9-4 10 9-3 -5 25—2 7-5 29-620 68 1527 57 14 10 8-3 12 1-0 10 7-9 10 8-1 -3 10 +1 26-9 1562 12 22 10 10 27-3 8 33-9 10 27-2 10 27-25 -1-0 30—1 27-35 1579 28 9'5 10 27-2 12 21-1 10 27'3 10 27-25 -1-0 30 4-1 27-85 29-602 68 1604 42 46-5 10 17-0 7 7-9 10 17-2 10 17-1 -2 50-3 9-2 1661 13 19 7 10 12-2 8 24-2 10 12-2 10 12-2 -1 45-1 22-0 a Not sufficient illumination. " 25» past middle wire. ' e*" 26"' 24' ? d Touched the arch with my hand. ' Upper dot not attended to. ' Should be 37''5. * Numerals of Brisbane's Catalog-ue. OBSERVATIONS WITH THE SECTOR AT KLYP FONTEYN, UNREDUCED. 127 Apuil 10th, 1838, Face of Sector East {continued). No. of Ast. Soc. Cat. Time by Chronometer. Micr. for Plumb-line on Dot. Micr. for Observa- tion of Star. Micr. for Plumb-line on Dot. Mean of Micr. for Plumb-line on Dot. Star's Apparent Zenith Distance. Barom. Therm. 1742 h m s 13 58 12-5 rev. ptB. 10 8-3 rev. pts. 12 7-0 rev. pts. 10 8'5 rev. pu. 10 8-4 O / rev. pu. -3 35 -t-1 32-6 29-602 o 66 1774 14 14 7 11 0-9 7 10-7 11 1-1 11 1-0 -f3 30-3 24-3 1797 26 10 21-3 10 3-8 10 21-2 10 21-25 -0 25-0 17-45 1821 34 40-5 10 23-7 13 32-5 10 24-1 10 23-9 -5 15 -i-3 8-6 1835 41 14 10 26-9 12 28-8 10 27-0 10 26-95 -3 40 -f 2 1-85 1866 54 34-5 11 5-1 14 17-8 11 6-0 11 5-55 + 2 10 -f3 12-25 1889 15 6 1 10 20-5 13 24-5 10 20-9 10 20-7 -1 40+3 3-8 1915 24 51-5 10 122 15 17-2 10 12-2 10 12-2 -1 20+5 5-0 1947 39 18 10 14-5 8 29-5 10 14-5 10 14-5 -1 10-1 19-0« 1969 51 37 10 15-5 8 23-4 10 15-3 10 15-4 + 15-1 26-0 2007 16 7 38 10 12-6 8 7-7 10 12-6 10 12-6 -4 15—2 4-9 2043 23 49 10 12-6 7 21-0 10 12-4 10 12-5 -4 15-2 25-5 29-602 64-5 2079 40 23-5 10 17-8 14 16-3 10 17'6 10 17-7 +2 15+3 32-6 2101 51 32-5 10 12-2 9 7-8 10 12-6 10 12-4 -4 5-1 4-6 2110 58 18 10 11-7 10 27-0 10 12-0 10 11-85 -1 45-0 15-15 2741 21 32 62-5 10 12-8 8 4-8 10 11-5 10 12-15 + 2 15-2 7-35 f North wind springing up. Zenith Distance of Sir-IMS by repeating circle = 54 22 -26 at 8 26 33-835 by chron. Error + 32-27 Antares = 54 36 59-7 at 10 52 45-665 • Error +32-21 Chronometer fast on mean time, by Sirius 32^-27, by Antares 32'-21. 128 VERIFICATION AND EXTENSION OF LA CAILLE's ARC OF MERIDIAN. April 11th, 1838, Face of Sector West. No. of Ast. Soc. Cat. Time by Chronometer. Micr. for Plumb-line on Dot. Micr. for Observa- tion of Star. Micr. for Flumb-line ou Dot. Mean of Micr. for Flumb-line on Dot. Star's Apparent Zenith Distance. Barom. Therm. 732 b m 5 reT. ptB. 12 5-4 rev. pts. 18 13-0 rev, PtB. 12 5-6 rev. ptB. 12 5-5 O / rev. ptB. -3 5-6 7-5» in. o 791 12 4-3 9 7-8 12 3-8 12 4-05 -f 2 40 +2 30-25" 848 5 26 33 12 1-5 8 25-4 12 1-7 12 1-6 -t-0 20 -f 3 10-2 869 35 4 11 22-2 9 32-9 11 21-8 11 22-0 + 3 55 -fl 23-P 903 54 4 10 10-8 14 7-7 10 10-8 10 10-8 -4 5-3 30-9 29-600 82 915 6 25 9 23-8 6 15-8 9 23-8 9 23-8 H-3 40 -1-3 8-0 957 .... 10 10-6 16 5-9 10 10-3 10 10-45 -4 50 -5 29-45* 977 .... 9 21-8 14 27-4 9 21-8 9 21-8 +2 50 -5 5-6= 1007 49 53 9 33-0 7 9-0 9 33-2 9 33-1 -2 45 +2 24-1 29-600 75 1015 54 59 9 26-8 6 25-8 9 27-3 9 27-05 -3 30 -f 3 1-25 1061 7 16 12-5 9 31-8 15 3-7 9 31-0 9 31-4 -2 0-5 6-3' 1070 19 33-5 9 29-8 10 0-6 9 29-7 9 29-75 + 5-0 4-85 1084 25 45 9 28-2 10 30-4 9 28-0 9 28-1 -f3 50-1 2-3 1115 45 51-5 9 29-2 12 1-4 9 29-2 9 29-2 +3 0-2 6-2 (2566)* 8 12 32-5 9 33-5 11 21-7 9 33-5 9 33-5 + 1 15-1 22-2 (2823)* 40 48 9 3M 10 1-3 9 30-7 9 30-9 + 2 35-0 4-4 1243 9 2 9 31-3 7 5-4 9 31-2 9 31-35 4-2 25—2 25-85 29-606 67-5 1356 10 7 6 10 9-9 12 30-5 10 9-7 10 9-8 -1-1 45—2 20-7 1378 26 43 10 32-2 9 14-4 10 32-5 10 32-35 — 20+1 17-95 1433 11 1 35 10 30-2 14 28-8 10 30-4 10 30-3 -5 25 -3 32-5 1527 53 9 10 27-1 10 27-0 10 26-9 10 27-0 -3 10-0 0-0 1562 12 18 12 10 26-4 14 11-0 10 26-8 10 26-6 + 30—3 18-4 1579 24 9-5 10 26-8 10 28-1 10 26-4 10 26-6 +0 30-0 1-5 1604 38 46 11 15-5 16 15-3 11 15-7 11 15-6 -2 50-4 33-7 1661 13 15 16 9 14-0 12 28-7 9 14-0 9 14-0 -1 45-3 14-7 • 20»i last middle wire. '' 20* past middle wire. ' The second at transit probably incorrect. ■■ lO'i ast middle wire. ' 10' past middle wire. ' Bad images. * Numerals of Brisbane's Cataloo-ue. A dense fog and strong north wind sprung up at lA^ M. T. Zenith Distance of Sirius with repeating circle 54° 12' 5"'5 at 9'' 11" 0'-165 by chronometer. Chronometer fast on mean time 31'-79. The 12th, 13th, and 14th, were rainy or cloudy. OBSERVATIONS WITH THE SECTOR AT KLYP FONTEYN, UNREDUCED. 129 April 15th, 1838, Face of Sector West. No. of Ast. Soc. Cat. Time by Chronometer. Micr. for Plumb-line on Dot. Micr. for Observa. tion of Star. Micr. for Plumb-line on Dot. Mean of Micr. for Plumb-line on Dot. Star's Apparent Zenith Distance. Barom. Therm. 732 h m s 4 12 24-5 rev. ptB. 11 5-3 rev. pts. 17 16-2 reT. ptB. 11 5-3 rev. ptB. 11 5-3 O / rev. pts. -3 5-6 10-9° in. o 791 41 21-5 8 13-9 5 17-2 8 14-4 8 14-15 -f 2 40 +2 30-95 848 5 10 54 9 2-4 5 26-4 9 2-6 9 2-5 + 20+3 10-1 869 5 19 27 8 27-6 7 6-4 9 27-8 9 27-7 + 3 55+1 21-3" 903 38 17 9 16-2 13 13-0 9 16-2 9 16-2 -4 5-3 30-8 915 44 48-5 8 26-0 5 17-3 8 26-4 8 26-2 + 3 40+3 8-9 29-734 66-2 957 6 6 15 9 29-3 15 28-8 9 29-5 9 29-4 -4 50-5 33-4 977 18 12-5 .... 14 9-9 9 4-3 + 2 50 -5 5-6 1007 .... 9 25-0 6 1-2 9 25-2 9 25-1 -2 45 +3 23-9 1061 7 1 (29) 9 19-4 14 25-7 9 19-2 9 19-3 -2 0-5 6-4 1070 3 52-5 .... 9 10-8 9 5-2 . . • • + 5-0 5-6° 1084 10 9 9 11-3 10 13-7 9 11-4 9 11-35 + 3 50+1 2-35 1115 29 54 9 8-7 11 14-5 9 8-5 9 8-6 + 3 0—2 5-9 (2566)* 56 54 9 16-2 11 5-3 9 16-0 9 16-1 + 1 15-1 23-2 (2823)* 8 5 11 9 8-7 9 14-7. 9 8-8 9 8-75 + 2 35-0 5-95 29-744 60-5 1243 46 21 9 4-2 6 12-3 9 4-0 9 4-1 + 2 25+2 25-8 1299 9 15(31) 10 29-2 10 15-5 10 29-4 10 29-3 -3 35+0 13-8 (3350)* 21 2-5 9 21-1 7 33-6 9 21-3 9 21-2 + 1 35+1 21-6 1356 51 27-5 9 25-2 12 12-4 9 25-2 9 25-2 + 1 45-2 21-2 1378 10 11 0-5 10 2-0 8 18-6 10 2-0 10 2-0 -0 20+1 17-4 1433 .... 10 7-4 14 6-7 10 7-5 10 7-45 -5 25-3 33-25^ 1562 12 2 32 10 10-1 13 30-0 10 10-1 10 10-1 + 30-3 19-9 1579 8 30 10 10-1 10 7-8 10 lO-O 10 10-05 + 30+0 2-25 29-716 59 1604 23 11 0-4 16 2-8 11 1-2 11 0-8 —2 50—5 2-0° 1661 59 33 10 27-8 14 11-3 10 28-4 10 28-1 -1 45—3 17-2 1742 13 38 26 10 13-7 10 8-4 10 13-3 10 13-5 —3 35 +0 5-1 1774 54 32 9 11-7 14 29-0 9 11-7 9 11-7 + 3 30-5 17-3 1797 14 6 19-5 10 0-5 12 11-2 10 0-5 10 0-5 -0 25-2 10-7 1821 14 51 10 4-3 8 21-2 10 4-5 10 4-4 —5 15+1 17-2 1835 21 28 10 0-0 9 24-5 10 0-0 10 0-0 -3 40+0 9-5 »Wind " Crabby images. ° Bad images. "* Observed 10* past middle wire. ' Images blotchy. Numerals of Brisbane's Catalogue. 130 VERIFICATION AND EXTENSION OF LA CAILLE S ARC OF MERIDIAN. April 15th, 1838, Face of Sector West (continued). No. of Ast. Soc. Cat. Time by Chronometer. Micr. for Plumb-line on Dot. Micr. for Observa- tion of Star. Micr. for Plumb-line on Dot. Alean of Micr. for Plumb-line on Dot. Star's Apparent Zenith Distance. Barom. Therm. 1866 h m s 14 34 .57-5 reT. pts. 8 32-8 rev. pti. 7 14-1 rev. ptB. 8 33-4 rev. pts. 8 33-1 O J rev. pts. + 2 10-1-1 19-0 In. o 1889 46 18 9 5'7 7 30-2 9 5-5 9 5-6 -1 40 -1-1 9-4 1947 15 19 36 9 7-8 13 19-1 10 7-8 10 7-8 -1 10-3 11-3 29-665 58 1969 31 58 10 6-4 13 22-8 10 6-2 10 6-3 -f-0 15—3 16-5 2007 48 50 11 1-7 14 30-8 11 1-3 11 1-5 -4 15-3 29-3 2043 16 4 1 11 1-3 15 17-7 11 1-5 11 1-4 -4 15—4 16-3 2079 20 45 11 7-0 8 30-8 11 7-0 11 7-0 +2 15+2 10-2 2101 31 46-5 10 30-2 13 26-2 10 300 10 aO'l —4 5-2 30-1 2110 38 35-5 10 33-7 12 10-8 10 33-7 10 33-7 -1 45-1 IM 2741 21 13 14 10 20-5 14 15-7 10 20'1 10 20-3 + 1 15-3 29-4 The sector frame had slightly swerved in position, produced apparently by the effect of the late rains on the corn-floor. Altitude oi Antares with sextant from 5 observations = 43° 19' 21" at ll"" ll" l4'-2 by chron. Chronometer fast on mean time 34''56. April 16th, 1838, Face of Sector East. No. of Ast. Soc. Cat. Time by Chronometer. Micr. for Plumb-line on Dot. Mior. for OI)serva- tion of Star. Micr. fur Plumb-line on Dot. Mean of Micr. for Plumb-line on Dot. Star's Apparent Zenith Distance. Barom. Therm. 971 h m s 4 37 28-5 rev. pts. 9 17-2 reT. ptH. 14 5-3 rev. pts. 9 17-2 rev. pts. 9 17-2 / rev. pts. 4-2 40 -f 4 22-1 29'518 o 82 869 5 15 36 9 33-8 13 15-6 9 34-0 9 33-9 -f-3 55+3 15-7 903 34 26-5 9 9-5 7 4-6 9 9-5 9 9-5 _4 5-2 4-9'' 915 40 56 9 6-8 14 8-7 9 7-0 9 6-9 + 3 40+5 1-8 29-500 75 957 6 2 25 9 4-6 4 31-3 9 4-2 9 4-4 _4 50—4 7-1 977 13 3-5 9 31'9 11 20-2 9 31-9 9 31-9 + 2 50+1 22-3'' 1007 30 17'5 10 2-7 14 19-0 10 2-7 10 2-7 -2 45 +4 16-3 1015 35 23 10 3-7 14 32-5 10 3-7 10 3-7 -3 30+4 28-8 1061 .... .... 6 24-8 9 33-8 .... -2 0—3 90" 1070 7 0-5 10 4-8 11 29-4 10 4-8 10 4-8 + 5+1 24-6 1084 6 16 5 10 1-3 10 29-5 10 1-3 10 1-3 + 3 50+0 28-2 » Beautiful. 'Go od. c Upper d )t bisected ? ■i 20» past middle wire. OBSERVATIONS WITH THE SECTOR AT KLYP FONTEYN, UNREDUCED. 131 April 16th, 1838, Face of Sector East (continued). No. of \st. Soc. Cat. Time by Chronometer. Micr. for 'Inmb-line on Dot. Micr. for Obaerva- tion of Star. Micr. for Plumb-line on Dot. Mean of Micr. for Plumb-line on Dot. Star's Apparent Zenith Distance. Barom. Therm. 1115 h m s 7 26 1 rev. pts. 10 1-7 rev. ptB. 9 27-4 rev. pts. 10 2-3 rev. ptB. 10 2-0 / "'• pt«- -f3 0-0 8-6 iQ. o (2566)* 53 1 9 28-7 9 33-2 9 29-5 9 29-1 -fl 15-1-0 4-1 29-472 65-5 (2823)* 8 21 18 9 28-4 11 17-8 9 28-5 9 28-45 + 1 35+1 23-35 1243 42 28 .... 14 10-6 9 25-5 .... 4-2 25+4 19-1 1299 9 11 38-5 9 7-6 11 14-5 9 7-6 9 7-6 -3 35 +2 6-9 (3350)* 18 9-5 9 12-5 12 27-0 9 12-5 9 12-5 -f 1 35+3 14-5 1356 47 40 9 10-4 8 14-8 9 10-0 9 10-2 + 1 45—0 29-4 1378 10 7 9 9 13-3 12 22-8 9 13-3 9 13-3 — 20+3 9-5 1527 11 33 36 9 7-2 10 32-8 9 7-0 9 7-1 -,3 10+1 25-7 1662 58 38 9 18'3 7 22-7 9 17-8 9 18-05 + 30-1 29-35' 1579 12 4 37 9 17-8 11 10-7 9 17-8 9 17-8 + 30+1 26-9' 1604 19 9 9 6-9 5 31-4 9 6-9 9 6-9 -2 .50-3 9-5 e 1661 55 41 9 5-3 7 14-8 9 5-2 9 5-25 — 1 45—1 24-45 1742 13 34 34 9 6-8 11 4-8 9 6-6 9 6-7 _3 35 +1 32-1 29-460 68-2 1774 50 38-5 9 23'3 5 32-8 9 22-9 9 23-1 + 3 20-3 24-3" 1821 14 11 8 19-5 11 28-1 8 19-7 8 19-6 _5 15+3 8-5 1835 17 36 8 23-8 10 25-4 8 24-2 8 24-0 -3 40 +2 1-4 29-466 59 1866 31 4-5 • . . > 13 18-1 10 5-9 + 2 10 +3 12-2 1889 42 25-5 10 6-5 13 8-9 10 6-0 10 6-25 — 1 40+3 2-65 1915 15 1 15 10 3-4 15 8-0 10 3-8 10 3-6 _1 20+5 4-4 1947 15 42-5 9 29-0 8 10-5 9 29-0 9 29-0 — 1 10-1 18-5 1969 28 4 10 9-4 8 18'5 10 9-0 10 9-2 + 15—1 24-7 2007 43 58-5 10 10-0 8 6-6 10 10-0 10 10-0 -4 15-2 3-4 2043 16 9 10 10-0 7 20-7 10 10-2 10 10-1 _4 15-2 23-4 29-453 58-8 2079 17 52-5. 11 0-5 15 1-2 11 0-8 11 0-65 + 2 15 +4 0-55 2101 27 54-5 11 3-8 10 0-0 11 3-6 11 3-7 _4 5-1 3-7 2110 34 43-0 10 32'3 11 14'0 10 32-1 10 32-2 -1 45 +0 15-8 2741 21 9 21-5 10 31-0 8 24-6 10 31-0 10 31-0 +2 15—2 6-4* « Bad light. ' Crabby. ^ Blotchy. ■> Light air. ' Very bad image. * Numerals of Brisbane's Catalogue. o I II h m s Altitude of Antares with sextant from 5 observations = 43 54 14 at 11 10 4-6 by chronometer. a Chronometer fast on mean time 34-42. Rather a heavy fall of rain in the night of the 17th. 132 VERIFICATION AND EXTENSION OF LA CAILLE S ARC OF MERIDIAN. April 18th, 1838, Face of Sector West. No. of Ast. Soc. Cat. Time by Chronometer. Micr. for Plumb-line on Dot. Micr. for Observa- tion of Star. Micr. for Plumb-line on Dot. Mean of Micr. for Plumb-line on Dot. Star's Apparent Zenith Distance. Barom. Therm. (2566)* h m s 7 45 1 rev. ptB. 10 17-4 rev. pta. 12 8-8 rev. ptB. 10 17-4 rev. pt9. 10 17-4 O / rev. pts. -j-1 15-1 25-4 in. (2823)* .... 9 30-3 10 2-3 9 30-3 9 30-3 -f 2 35 +0 6-0 1243 8 34 23 9 22-6 6 31-3 9 22-8 9 22-7 -f 2 25 +2 -25-4 29-828 58-6 1299 9 3 54 10 14-5 10 1-5 10 14-4 10 14-45 -3 35 4-0 12-95 1356 39 31-5 10 2-0 12 24-5 10 2-0 10 2-0 + 1 45-2 22-5 1378 59 12-5 10 4-4 8 21-0 10 4-3 10 4-35 -0 20 + 1 17-35 1433 10 34 18-5 10 21-3 14 22-3 10 24-5 10 22-9 -5 25-3 33-4^ 1527 11 25 51 10 13-0 10 15-0 10 13-0 10 13-0 -3 10-0 2-0 1562 50 41 10 0-0 13 22-0 10 0-2 10 0-1 + 30-3 21-9" 1579 56 39-5 10 1-4 9 33-6 10 1-2 10 1-3 +0 30+0 1-7 1604 12 11 22-5 10 13-4 15 16-0 10 13-0 10 13-2 —2 50-5 2-8 1661 47 50-5 10 12-2 13 29-4 10 12-3 10 12-25 -1 45-3 17-15 29-815 53-5 1742 13 26 54-5 10 19-6 10 1-52 10 19-4 10 19-5 —3 35 +0 4-3 1774 42 31-0 9 17-5 15 1-7 9 17-7 9 17-6 + 3 30-5 18-1 1797 54 32 9 28-8 12 5-6 9 28-8 9 28-8 -0 25-2 10-8 29-815 52-2 1821 14 3 22 10 23-4 9 7-2 10 25-0 10 24-2 —5 15+1 17-0 1835 9 52 10 22-2 10 13-8 10 22-2 10 22-2 -3 40+0 8-4 1866 22 39-5 9 33-5 8 14-7 9 33-5 9 33-5 +2 10+1 18-8 1915 53 23 10 29-0 7 18-7 10 29-0 10 29-0 -1 20+3 10-3 1947 15 7 50 10 30-7 14 6-7 10 30-7 10 30-7 — 1 10—3 10-0 1969 20 7 11 12-5 14 29-5 11 12-3 11 12-4 + 15-3 17-1 2007 36 17-5 12 19-2 16 14-3 12 19-3 12 19-25 -4 15-3 29-05 2043 52 27-5 12 19-3 17 0-3 12 19-5 12 19-4 -4 15-4 14-9 29-781 52 2079 16 8 48-5 12 16-8 10 8-2 12 16-8 12 16-8 + 2 15+2 8-6 2101 20 12-5 11 0-7 13 3M 11 1-2 11 0-95 —4 5-2 30-15 2110 26 52 11 9-7 12 21-0 11 9-6 11 9-65 -1 45-1 11-35'= 2741 21 1 15 10 20-2 14 19'7 10 19-8 10 20-0 +2 15-3 33-7'' 29-852 69 » A probable mistake in reading off one o f the dots. "> Upper dot not previously examined. " The stars hare been steady this night. ^ Bad image. * Numerals of Brisbane's Catalogue. After the transit of No. 869 the instrument was shifted in azimuth, as indicated by the next following stars. It appears to have been disturbed during my absence yesterday. OBSERVATIONS WITH THE SECTOR AT KLYP FONTEYN, UNREDUCED. 133 April 19th, 1838, Fac E OF Sector East. No. of Ast. Soc. Cat. Time by Chronometer. Micr. for Plumb-line on Dot. Micr. for Observa- tion of Star. Micr. for Plumb-line on Dot. Mean of Micr. for Plumb-line on Dot. Star's Apparent Zenith Distance. Barom. Therm. 869 h m s 5 3 38 rev. ptB. 11 22-0 rev, pts. 15 4-0 rev. ptB. 11 22-2 rev. ptB. 11 22-1 O / rev. ptB. -f 3 55 +3 15-9'' in. 903 22 51 11 4-2 8 32-9 11 4-2 11 4-2 —4 5-2 5-3" 29-750 71 915 28 59-5 10 24-8 15 24-8 10 25-0 10 24-9 + 3 40 -1-4 33-9° 957 51 52 10 21-7 6 15-8 10 21-7 10 21-7 _4 50 -4 5-9 977 6 2 26 10 26-0 7 14-4 10 25-0 10 25-5 4-2 50-3 IM 1007 18 37-5 10 24-2 15 7-7 10 24-0 10 24' 1 -2 45 +4 17-6 1061 9 27-8 6 15-5 9 27-8 9 27'8 -2 0-3 12-3 29-750 65 1070 9 21-0 11 10-0 9 20-8 9 20-9 + 5 4-1 23'1'' 1084 9 30-4 10 22-4 9 30-4 9 30-4 4-3 50 4-0 26-0 1115 9 26-3 9 15-7 9 26-4 9 26-35 4-3 0-0 10-65 (2823)* 9 20-4 11 5-9 9 20-6 9 20-5 4-2 35 4-1 19-4' 1243 9 26-2 14 8-3 9 26-6 9 26-4 4-2 25 4-4 15-9 1356 10 5-3 9 10-0 10 5-3 10 5-3 4-1 45-0 29-3 1378 11 1-6 14 10-8 11 2-0 11 1-8 — 20 4-3 9-0' 1579 11 0-4 12 26-3 11 0-5 1 1 0-45 4-0 30 4-1 25-85 1604 . . . 10 31-7 7 21-3 10 31-7 10 31-7 -2 50-3 10-4 1666 10 28-4 9 4-8 10 28-4 10 28-4 -1 45-1 23-6 1742 13 22 55-5 10 12-6 12- 9-9 10 12-4 10 12-5 -3 35 4-1 31-4 1774 38 43 10 3-7 6 11-8 10 2-8 10 3-25 4-3 30—3 25-45^ 1797 .... 9 29-4 9 10-8 9 29-0 9 29-2 -0 25-0 18-4*' 1821 59 35-5 9 33-7 13 7-8 9 33-7 9 33-7 —5 15 4-3 8-1 29-682 55-5 1835 14 5 57-5 9 26-4 11 27-8 9 26-0 9 26-2 -3 40 4-2 1-6 1866 . . . .• 10 3-7 13 14-7 10 3-7 10 3-7 4-2 104-3 11-0 1889 30 42 10 5-3 13 7-6 10 5-1 10 5-2 -1 40 4-3 2-4 1947 15 14 58 10 5-3 8 20-8 10 ; 5-8 10 5-55 -1 10-1 18-75 1969 16 16 10 19-8 8 28-4 10 20-0 10 19-9 4-0 15-1 25-5 2007 48 24, 10 15-2 8 12-5 10 15-4 10 15-3 —4 15 4-2 2-8 2043 48 34 10 15-4 7 25-8 10 15-8 10 15-6 —4 15-2 23-8 2079 16 14 59-5 10 21-0 14 21-0 10 21-0 10 21-0 4-2 15 4-4 0-0 2101 20 10 19-4 9 17-5 10 19-4 10 19'4 -4 5-1 1-9 29-652 53 2110 23 2-5 10 11-0 10 27-2 10 10-8 10 10-9 -1 45 4-0 16-3 2741 20 57 26-5 10 5-6 8 4-7 10 6-3 10 5-95 4-2 15-2 1-25' " Stria [Cirri). '' Indications of s trong wind. "= Table mountain is visible, capped with cloud. <> Chron ometer is employed with the repeating ci rcle. « Very faint. ' Cloudy. eBad. ^ Leaving the fie Id. ' Bad image, flickering. * Numeral of Brisbane's Catalogue. 134 VERIFICATION AND EXTENSION OF LA CAILLE S ARC OF MERIDIAN. Aprtl 20th, 1838, Face of Sector West. No. of Ast. Soc. Cat. Time by Chronometer. Micr. for Plumb-line on Dot. Micr. for Observa- tion of Star. Micr. for Plumb-line on Dot. Mean of Micr. for Plumb-line on Dot. Star's Apparent Zenith Distance. Barom. Therm. 699 h m s rev. pti. 9 10-7 rev. pts. 6 13-1 rev. pta. 9 10'7 rev pts. 9 10-7 O / rev. pts. -1 30+2 31-6=" In. 732 .... 9 10-5 15 20-3 9 10-5 9 10-5 -3 5-6 9-8 29-653 79 791 4 21 35-5 9 15-7 6 20-0 9 15-7 9 15-7 -1-2 40 +2 29-7 29-653 77-5 869 .... 9 25-8 8 2-8 9 25-6 9 25-7 + 3 55+1 22-9" 903 5 18 39-5 11 16-7 15 15-2 11 16-7 11 16-7 —4 5-3 32-5"= 915 25 ) 11 1-0 7 29-2 11 1-0 11 10 + 3 40 +3 5-8 957? .... 11 ,1-4 14 18-3 11 2'0 11 1-7 -4 50-3 16-6 977 58 26 9 18-4 14 23-0 9 18-0 9 18-2 + 2 50-5 4-8 1007 6 14 29-5 10 24-6 7 33-5 10 24-8 10 24-7 —2 45 +2 25-2" 1015 19 35 10 27-4 7 26-2 10 27-7 10 27-55 -3 30 +3 1-35 29-653 68 1070 .... .... 10 32-4 10 29-2 .... + 5-0 3-2» 1084 50 19-5 10 27-4 11 28-6 10 27-2 10 27-3 +3 50-1 1-3 1115 7 10 7-5 10 21-5 12 27-8 10 22-3 10 21-9 + 3 0-2 5-9 (2566)* 37 9 10 24-0 12 12-6 10 24-2 10 24-1 + 1 15-1 22-5 (2823)* 8 5 24-5 10 24-8 10 31-8 10 24-8 10 24-8 +2 35-0 7-0 1243 26 35-5 10 24-7 7 33-8 10 24-7 10 24-7 +2 25 +2 24-9 1299 55 52 12 9-1 11 31-7 12 9-7 12 9-4 -3 35 +0 11-7 (3350)* .... 1 1 7-8 9 21-9 11 7-6 11 7-7 + 1 35 +1 19-8 1356 9 31 42 11 2-8 13 26-5 11 3-0 11 2-9 + 1 45-2 23-6 1378 51 28 10 26-3 9 9-2 10 26-0 10 26-15 -0 20 -hi 16-95 29-630 61 1433 10 26 9-5 14 8-0 10 7-6 .... -5 25 -4 0-4 1527 11 17 49-5 9 27-2 9 29-3 9 27-0 9 27-1 -3 10—0 2-2 1562 42 46 9 26-1 13 13-3 9 25-9 9 26-0 + 30—3 21-3 1579 48 46 9 25-9 9 26'2 9 25-6 9 25-75 + 30—0 0-45 1604 12 3 21 10 8-2 15 11-1 10 8-8 10 8-5 -2 50-5 2-6' 1661 39 52 10 7-3 13 23-7 10 7-1 10 7-2 -1 45-3 16-5 1742 13 18 47 10 17-4 10 12-8 10 17-4 10 17-4 -3 35 +0 4-6 1774 34 44-5 10 1-6 15 20-9 10 2-0 10 1-8 + 3 30-5 19-1 1821 54 16-5 10 19-5 9 2-2 10 20-0 10 19-75 -5 15 -t-1 17-55 1835 14 1 51 10 23-4 10 15-1 10 23-2 10 23-3 -3 40 +0 8-2 «20sp ast middle wire, invisible on entering the field. "Wind -= Wind. « Calm. «20'p ast middle wire. ' Bad images, brilliant ski f- * Numerals of Brisbane's Catalogue. OBSERVATIONS WITH THE SECTOR AT KLYP FONTEYN, UNREDUCED. 135 April 20Tn, 1838, Face or Sector West {continued). No. of Ast. Soc. Cat. Time by Chronometer. Micr. for Plumb-line on Dot. Micr. for Observa- tion of Star. Micr. for Plumb-line on Dot. Mean of Micr. for Plumb-line on Dot. Star's Apparent Zenith Distance. Barom. Therm. 1866 h m s 14 15 12-5 reT. pts. 10 4-5 rev. pts. 8 18-9 rev. pts. 10 4-5 rev. ptB. 10 4-5 t rev. pta. + 2 10+1 19-6 in. o 1889 26 37 10 20-6 9 10-8 10 20-6 10 20-6 -1 40 -fl 9-8 1915 45 26-5 11 4-0 7 26-7 11 3-6 11 3-8 -1 20+3 11-1 1947 59 .53-5 11 3-8 14 14-5 11 4-0 11 3-9 -1 10-3 10-6 29-560 54 1969 15 12 15 10 32-2 14 15-4 10 31-8 10 32-0 + 15-3 17-4 2007 28 13 11 18-4 15 13-5 11 18-5 11 18-45 -4 15—3 29-05 2043 44 23 11 18-5 16 0-0 11 18-3 11 18-4 -4 15-4 15-6 2079 16 1 11 5-0 8 29-4 11 5-0 11 5-0 + 2 15+2 9-6 2101 12 8-5 11 30-0 14 27-1 11 30-5 11 30-25 -4 5-2 30-85 2110 18 55 12 1-5 13 11-8 12 1-5 12 1-5 -1 45-1 10-3 2741 20 53 27 10 17-3 14 13-2 10 16-9 10 17-1 + 2 15-3 30-1 Zenith Distance of Antares with repeating circle ^ 44° 3' 53" at 1 P 3™ 59'-67 by chronometer. Chronometer fast on mean time 32'-13. April 21st, 1838, Face of Sector East. No. of Ast. Soc. Cat. Time by Chronometer. Micr. for Plumb-line on Dot. Micr. for Observa- tion of Star. Micr. for Plumb-line on Dot. Mean of Micr.for Plumb-line on Dot. Star's Apparent Zenith Distance. Barom. Therm. 699 h m s 3 37 32 rev. pte. 14 15-0 rev. pts. 19 4-3 rev. pts. 14 14-8 rev. pts. 14 14-9 O / rev. pts. -I 30+4 23-4 29°550 o 80 732 48 59 14 11-9 9 31-4 14 12-3 14 12-1 _3 5-4 14-7 869 4 55 44-5 12 30-0 16 16-8 12 30-2 12 30-1 + 3 55 +3 20-7 903 12 3-8 10 0-1 12 4-8 12 4-3 _4 5_2 4-2 = 915 5 6 5 11 18-0 16 17-8 11 18-0 11 18-0 + 3 40 +4 33-8 957 42 55-5 11 8-4 7 5-0 11 8-6 11 8-5 _4 50 -4 3-5 977 54 33 11 6-7 7 30-8 11 6-2 11 6-45 +2 50 -3 9-65 29-523 75-5 1007 10 6-4 14 24-5 10 6-4 10 6-4 —2 45 +4 18-1 1015 6 15 50 9 23-5 14 19-8 9 23-5 9 23-5 -3 30 +4 30-3 1061 39 2 10 7-5 6 30-8 10 8-1 10 7-8 -2 0-3 11-0" 1084 46 27 9 16-9 10 8-4 9 16-8 9 16-85 + 3 50+0 25-55 " 20" past middl e wire. b Much lightning. 136 VERIFICATION AND EXTENSION OF LA CAILLE S ARC OF MERIDIAN. April 21st 1838, Face of Sector East (continued). No. of Ast.Soc. Cat. Time by Chronometer. Micr. for Plumb-line on Dot. Micr. for Observa- tion of Star. Micr. for Plumb-line on Dot. Mean of Micr. for Plumb-line on Dot. Star's Apparent Zenith Distance. Barom, Therm. 1115 h m s 7 6 14 rev. pta. 9 1-9 rev. ptA. 8 25-8 rev. pts. 9 2-1 rev, pM. 9 2-0 O / rev. ptfl. + 3 0—0 10-2 in. o (2566)* .... 9 16-8 9 20-2 9 16-8 9 16-8 + 1 15-1-0 3-4' (2823)* 8 1 31 9 23-4 11 10-4 9 23-4 9 23-4 + 2 35 + 1 21-0 1243 22 42 9 21 '0 14 3-4 9 20-8 9 20-9 + 2 25+4 16-5 1299 52 6 .... 12 18-8 10 12-0 .... -3 35+2 6-8 '^ (3350)* 58 26 11 0-4 14 13-2 11 0-5 11 0-45 + 1 35+3 12-75 1356 9 27 49-5 10 8-7 9 13-5 10 8-3 10 8-5 + 1 45—0 29-0 1378 47 28-5 10 7-8 13 17-5 10 8-.0 10 7-9 —0 20 +3 9-6 29-482 64-2 1433 10 22 29-5 9 33-7 7 24-6 9 33-5 9 33-6 -5 25—2 9-0' 1527 11 14 1-5 9 31-3 11 23-3 9 31-4 9 31-35 —3 10+1 25-95 1562 38 56-5 8 32-7 7 4-8 8 33-1 8 32-9 + 30—1 28-1 29-468 63 1579 44 55 8 33-2 10 26-6 8 33-1 8 33-15 + 30+1 27-45 1661 12 36 4 .... 7 29-4 9 18-8 > > ■ ■ -1 45-1 23-4 1742 13 15 3 9 11-3 11 9-3 9 11-1 9 11-2 -3 35+1 32-1 29-450 61-2 1774 30 49 9 32-5 6 8-7 9 32-0 9 32-25 + 3 30—3 23-55 1797 42 47 10 3-8 9 19-1 10 3-8 10 3-8 -0 25-0 18-7 1821 51 33-5 9 27-4 13 2-5. 9 27-6 9 27-5 -5 15+3 9-0' 1835 58 4-5 9 22-2 11 23-9 9 22-0 9 22-1 -3 40+2 1-8 1866 14 11 20 9 18-7 12 30-4 9 18-5 9 18-6 + 2 10 +3 11-8 29-436 60-5 1889 22 49 9 18-8 12 22-2 9 18-6 9 18-7 -1 40 +3 3-5 1915 41 38-5 9 20-4 14 26-0 9 20-4 9 20-4 — 1 20+5 5-6 1947 56 5 9 21-5 8 5-0 9 21-7 9 21-6 -1 10-1 16-6 1969 15 8 23-5 9 27-4 8 3-5 9 26-5 9 26-95 + 15-1 23-45« 2007 24 28-5 9 19-0 7 16-7 9 19-0 9 19-0 -4 15-2 2-3 2043 40 39 9 19-0 6 30-3 9 18-8 9 18-9 -4 15 -2 22-6 29-418 59-5 2079 57 7-5 10 7-5 14 8-5 10 7-6 10 7-55 + 2 15 +4 0-95 2101 16 8 24-5 10 33'6 9 31-5 10 33-4 10 33-5 -4 5-1 2-0 2110 15 6'5 10 19-8 11 3-5 10 19-4 10 19-6 -1 45+0 17-9 2741 20 49 34 8 19'3 6 16-3 8 18-9 8 19-1 +2 15-2 2-8 29-504 74 <= Clou iy at transit ; bisected 10" af ter. ,„ 30 4 1-0 4 4 10 22 0-7 4 5-7 17 29-0 " = 33-633 ^0 ^ gg.ggg 40 4 32-7 5 17 29-2 30 22 27-9 4 20 4 2-6 17 29-5 17 29-1 „„ ,„„ 40 4 32-4 4 10 4 20 21 31-7 4 2-2 17 29-5 " = 33-583 ^0 = 33-580 50 4 2-4 20 ^ 33.597 17 28-3 40 21 30-7 17 28-5 4 30 4 8-7 17 28-3 20 _ 33-608 50 4 2-2 4 20 22 3-0 17 28-2 ^ 40 _ 33.641 1 4 1-3 17 28-4 4 30 4 8-8 50 = 33-597 50 21 29-7 17 27-9 Arch to the Right. 1 1 4 1-8 4 4 25-0 17 29-8 : '4 _ 33.594 Arch to the Right. 4 10 22 20-8 17 28-7 4 ^0 _ 33.533 4 10-7 17 29-5 4 4 26-1 4 ^0 ^ 33.597 10 22 6-2 17 29-4 4 10 4 19-2 17 28-6 4 30 4 10-8 4 20 4 10 22 13-8 4 19-3 17 28-5 The arithmetical mean is 33"-616. 10 4 9-3 17 29-5 In the above calculation 20 22 4-8 4 20 4 17-4 the mean of the results for the 17 29-5 17 29-3 direct and retrograde motion 10 4 9-3 4 30 4 20 22' 12-7 4 17-6 17 29-1 of the motion of the screw over each interval is taken. 20 4 12-7 The screw head is divided 30 22 8-1 17 17 29-4 29-0 Mean temperature (indi- cated by the thermometers into 34 parts, and (adding together all the results for all the measured arcs) 10620' 15" 20 4 13-1 hanging from the sector frame) during the examina- of these parts correspond to 30 4 11-8 tion = 79°-5. 10500" of the arch. There- 17 28-7 The observations com- , 34x10500" QQ"filrg fo-^^ 10620-15 -33-6153 40 22 6-5 17 29-3 menced at 9'' A.M. 30 4 11-2 forthe value of one revolution. 138 VERIFICATION AND EXTENSION OF LA CAILLE's ARC OF MERIDIAN. Klyp Fonteyn. Table for Converting the Readings of the Micrometer into Minutes and Seconds of the Arch. Div. 0' r 2' 3' 4' 5' 6' 33-615 1 7-231 l' 40-846 2 14'-'461 2 48-077 3 21-692 1 0-989 34-604 1 8-220 1 41-835 2 15-450 2 49-066 3 22-681 2 1-977 35-592 I 9-208 1 42-823 2 16-438 2 50-054 3 23-669 3 2-966 36-581 1 10-197 1 43-812 2 17-427 2 51-043 3 24-658 4 3-955 37-570 1 11-186 1 44-801 2 18-416 2 52-032 3 25-647 5 4-943 38-559 1 12-175 1 45-790 2 19-405 2 53-020 3 26-635 6 5-932 39-547 1 13-163 1 46-778 2 20-393 2 54-009 3 27-624 7 6-92] 40-536 1 14-152 1 47-767 2 21-382 2 54-998 3 28-613 8 7-909 41-525 1 15-141 1 48-756 2 22-371 2 55-986 3 29-601 9 8-898 42-513 l 16-129 1 49-744 2 23-359 2 56-975 3 30-590 10 9-887 43-502 1 17-118 1 50-733 2 24-348 2 57-964 3 31-579 11 10-876 44-491 1 18-107 1 51-722 2 25-337 2 58-953 3 32-568 12 11-864 45-479 1 19-095 1 52-710 2 26-325 2 59-941 3 33-556 13 12-853 46-468 1 20-084 1 53-699 2 27-314 3 0-930 3 34-545 14 13-842 47-457 1 21-073 1 54-688 2 28-303 3 1-919 3 35-534 15 14-830 48-446 1 22-061 1 55-676 2 29-291 3 2 907 3 36-522 16 15-819 49-434 1 23-050 1 56-665 2 30-280 3 3-896 3 37-511 17 16-808 50-423 1 24-039 1 57-654 2 31-269 3 4-885 3 38-499 18 17-796 51-411 1 25-027 1 58-642 2 32-257 3 5-873 3 39-488 19 18-785 52-400 I 26-016 I 59-631 2 33-246 3 6-862 3 40-477 20 19-774 53-389 1 27-005 2 0-620 2 34-235 3 7-851 3 41-466 21 20-762 54-377 1 27-993 2 1-608 2 35-223 3 8-839 3 42-454 22 21-751 55-366 1 28-982 2 2-597 2 36-212 3. 9-828 3 43-443 23 22-740 56-355 1 29-971 2 3-586 2 37-201 3 10-817 3 44-432 24 23-728 57-343 1 30-959 2 4-574 2 38-189 3 11-805 3 45-420 25 24-717 58-332 1 31-948 2 5-563 2 39-178 3 12-794 3 46-409 26 25-706 59-321 1 32-937 2 6-552 2 40-167 3 13-783 3 47-398 27 26-695 1 0-310 1 33-926 2 7-541 2 41-156 3 14-772 3 48-387 28 27-683 1 1-298 1 34-914 2 8-529 2 42-144 3 15-760 3 49-375 29 28-672 1 2-287 1 35-903 2 9-518 2 43-133 3 16-749 3 50:364 30 29-661 1 3-276 1 36-892 2 10-507 2 44-122 3 17-738 3 51-353 31 30-649 1 4-264 1 37-880 2 11-495 2 45-110 3 18-726 3 52-341 32 31-638 1 5-253 1 38-869 2 12-484 2 46-099 3 19-715 3 53-330 33 32-627 1 6-242 1 39-858 2 13-473 2 47-088 3 20-704 3 54-319 34 33-615 1 7-231 1 40-846 2 14-461 2 48-077 3 21-692 3 55-307 OBSERVATIONS WITH THE SECTOR AT CAPE TOWN, UNREDUCED. 139 § 11. Observations with the Sector at Cape Town, unreduced. May 12th, 1838, Face of Sector West. No. of Ast. Soc. Cat. Time by Chronometer. Micr. for 'lumb-Iine on Dot. Micr. for Observa. tion of Star. Micr. for ?lumb-.line on Dot. Mean of Micr. for Plumb-line on Dot. Star's Apparent Zenith Distance. Barom. Therm. 1115 h m s 9 2 55 rev. pts. 10 15-0 rev. pts. 6 19-1 rev. pts. 10 14-8 rev. pts. 10 14;9 / rev. pts. + 4 0+3 29-8 in. o (2566)* 30 1-5 9 32-8 14 22-1 9 33-0 9 32-9 + 2 30-4 23-2 (2823)* 58 19 10 2-8 13 9'1 10 3-0 10 2-9 + 3 50-3 6-2 1243 10 19 33-5 10 3-4 10 13-0 10 3-6 10 3-5 + 3 40—0 9-5" 1299 .... 9 16-7 12 3-1 9 16-7 9 16-7 -2 20-2 20-4 (3350)* .... .... 10 12-7 8 33-2 +2 50-1 13-5 1433 12 19 35 9 26-9 7 31-8 9 27-0 9 26-95 —4 15+1 29-15" 1527 13 11 18-5 9 18-4 12 22-2 9 18-4 9 18-4 -1 55-3 3-8° 1562 36 17 9 14-4 7 6-1 9 14-4 9 14-4 + 1 40+2 8-3 1579 42 17 9 14-4 3 17-9 9 14-3 9 14-35 + 1 40+5 30-45 1604 56 57-5 10 1-2 9 7-2 10 1-2 10 1-2 -1 40+0 28-0 1661 14 33 33-5 10 1-6 7 21-8 10 1-5 10 1-55 -0 35+2 13-75 1742 15 12 36-5 9 33-0 12 29-3 9 32-8 9 32-9 -2 20—2 30-4 1774 28 29 9 19-1 9 6-5 9 18-9 9 19-0 + 4 40 +0 12-5 1797 40 27 9 19-7 14 33-2 9 19-7 9 19-7 + 50-5 13-5 1821 49 11 9 24-2 11 8'0 9 24-2 9 24-2 -4 0-1 17-8 1835 ■ • • ■ 9 13-9 12 5-7 9 14-0 9 13-95 -2 25 -2 25-75 1866 .... 9 10-4 10 26'2 9 11-0 9 10-7 + 3 25-1 15-5 1889 16 20 34 .... 11 7-3 9 17-7 .... — 25—1 23-6 1915 39 27 9 19-6 9 8-3 9 19-6 9 19-6 — 5+0 11-3 1947 • ■ . • 9 21-4 15 31-4 9 21-4 9 21-4 + 5-6 10-0 1969 17 6 16-5 9 19-7 7 5-4 9 19-9 9 19-8 + 1 25+2 14-4 2007 22 21-5 9 14-5 7 11-4 9 14-1 9 14-3 -3 5+2 2-9 2043 38 35 9 14-2 7 31-6 9 14-2 9 14-2 -3 5+1 16-6 2079 55 8 8 23-3 9 14-1 8 23-4 8 23-35 + 3 30-0 24-75 2101 18 6 24 9 7-0 6 5-8 9 7-0 9 7-0 -2 55 +3 1-2 2110 13 8-5 9 3-4 13 12-4 9 3-2 9 3-3 _0 30-4 9-1" » The second of transit is doubtful. ' Perfectly calm. ■= Fine definition. <• The upper dot was not examined before bisection ; afterwards the error for this star was found to be O^'-S = 0"-297. * Numerals of Brisbane's Catalogue. The barometer is by Dollond : its indications are lower by 0'°-051 than those of the standard barometer at the Observatory. T 140 VERIFICATION AND EXTENSION OF LA CAILLE S ARC OF MERIDIAN. May 13th, 1838, Face or Sector East. No. of Ast. Soc. Cat. Time by Chronometer. Micr. for Plumb-line on Dot. Micr. for Observa- tion of Star. Micr. for Plumb-lint on Dot. Mean of Micr. for Plumb-line on Dot. Star's Apparent Zenith Distance. Barom. Therm. 848 h m 3 6 43 37 rev. ptB. 8 23-2 rev. pts. 10 15-7 rev. pts. 8 23'0 lev. pts. 8 23-1 / «v. pts. -f 1 35 -fl 26-6 in. o 869 52 8-5 9 5-2 9 11-0 9 5-1 9 5-15 -f5 10+0 5-85 903 7 11 11-5 9 29-8 13 11-8 9 29-4 9 29-6 -2 55-1-3 16-2 957 39 11-5 9 10-2 10 26-5 9 10-2 9 10-2 -3 40 -fl 16-3 1007 8 7 9 10 8-6 11 15-0 10 8-6 10 8-6 -1 30+1 6-4 1015 .... 10 8-5 11 26-2 10 8-5 10 8-5 —2 15+1 17-7 30-142 1061 33 32-5 10 14-0 12 2M 10 14-2 10 14-1 — 50 +2 7-0 " 1070 36 54 10 23-7 8 32-9 10 24-0 10 23-85 + 1 20—1 24-95 1084 43 7 11 27-0 9 4-3 11 27-0 11 27-0 + 5 5—2 22-7 . 1115 9 2 56 9 8-4 14 14-7 9 8-6 9 8-5 + 4 10 +5 6-2 (2566)* 30 1-5 .... 5 31-3 9 7-5 .... + 2 30-3 10-2 (2823)* 58 21-5 9 9-3 7 15-0 9 9-3 9 9-3 + 3 50-1 28-3 1243 10 19 35-5 9 7-2 10 9-3 9 7-3 9 7-25 + 3 40+1 2-05 1299 48 56-5 8 24- 1 7 13-7 8 23'5 8 23-8 -2 20—1 10-1 (3350)* 55 22-5 9 7-7 9 5-6 9 7-5 9 7-6 + 2 50-0 2-0 1356 11 24 52 9 14-2 14 1-0 9 14-5 9 14-35 +2 55+4 20-65 1378 44 33 9 14-5 9 6'0 9 14-1 9 14-3 + 55—0 8-3 1433 12 19 30-5 9 30-8 13 3-4 9 30-3 9 30-55 —4 15+3 6-85 1579 13 42 15 10 17-8 17 25-5 10 17-8 10 17-8 + 1 40+7 7-7» 1604 56 58-5 10 1-7 12 7-5 10 1-7 10 1-7 -1 40+2 5-8 1661 14 33 33-5 10 2-7 13 27-2 10 2-7 10 2-7 — 35+3 ■24-5'' 30-131 1742 15 12(36?) 9 7-0 7 22-7 9 7-0 9 7-0 —2 20—1 18-3 1774 28 26 9 25-7 11 13-5 9 26-0 9 25-85 +4 40+1 21-65 1797 40 26 9 30-8 5 29-3 9 30-8 9 30-8 + 50-4 1-5 1835 55 46 9 15-5 8 0-4 9 15-3 9 15-4 -2 25—1 15-0 1866 16 9 2 9 26-0 9 21-5 9 25-8 9 25-9 + 3 25—0 4-4 1889 20 35 9 13-4 9 1-2 9 13-3 9 13-35 — 25-0 1215 1915 39 26-5 9 19-5 11 8-2 9 19-4 9 19-45 -0 5+1 22-76 1947 53 55-5 9 IM 13 10-2 9 11-3 9 11-2 0+3 33-0 = 1969 17 6 16-5 9 21-8 13 12-7 9 21-8 9 21-8 + 1 25+3 24-9 2007 22 24 9 16-7 12 30-2 9 16-3 9 16-5 -3 5+3 13-7 30-140 2043 38 37 9 16-3 12 9-5 9 16-5 9 16-4 -3 5+2 27-1 2079 54 6 9 32-4 10 20-2 9 32-5 9 32-45 + 3 30+0 21-75 2101 18 6 27. 9 13-5 4 29-4 9 12-7 9 13-1 -2 50-4 17-7 2110 13 9 8 33-8 6 2-6 8 33-6 8 33-7 -0 30-2 31-1 ' Mov( >d the sector a lit tie eastward in azimuth at IS* 36" fi idereal time. <> Bad images. ' Bad images. * Numerals of Brisbane's Catalogue. On the whole, this, though clear, was a bad observing night; the images indifferent and torch-like. OBSERVATIONS WITH THE SECTOR AT CAPE TOWN, UNREDUCED. 141 May 15th, 1838, Face or Sector West. No. of Ast. Soc. Cat. Time by Chronometer. Micr. for Plumb-line on Dot. Micr. for Observa. tion of Star. Micr. for Plumb-line on Dot. Mean of Micr. for Plumb-line on Dot. Star's Apparent Zenith Distance. Barom. Therm. (3350)* h m s 10 56 13 rev. pts. 9 32-8 rev. pts. 11 13-2 rev. pts. 9 32-8 rev. ptB. 9 32-8 / rev. ptB. + 2 50—1 14-4 in. 1356 11 25 43 10 9-2 7 0-7 10 9-5 10 9-35 + 2 55+3 8-65 1378 45 22-5 10 24'0 12 9-5 10 23-8 10 23-9 + 55-1 19-6 1433 12 20 21 9 29-1 8 1-0 9 29-1 9 29-1 -4 15+1 28-1 29-924 1562 13 37 7-5 9 9-8 7 2-8 9 10-0 9 9-9 + 1 40+2 7-1 1579 43 6'5 9 10-0 3 15-2 9 9-8 9 9-9 + 1 40+5 28-7 1604 57 45 9 8-1 8 16-2 9 8-1 9 8-1 — 1 40+0 25-9 1661 14 34 21-5 9 2-7 6 24-2 9 2-7 9 2-7 — 35 +2 12-5 1797 15 39 21 9 19-45 9 7-4 9 19-2 9 19-33 +4 40+0 11-93" 1866 16 9 55 8 20-4 10 3-5 8 20-4 8 20-4 + 3 25—1 17-1 1889 21 22-5 9 8-2 10 32-4 9 8-2 9 8-2 -0 25—1 24-2 " 1915 40 14 9 9-4 8 33-4 9 9-3 9 9-35 -0 5 +0 9-95 1947 54 54 9 26-75 7 6-6 9 26-40 9 26-58 0+2 19-98 1969 17 7 6 9 24-5 7 10-4 9 24-4 9 24-45 + 1 25+2 14-05 2007 23 8 9 33-7 7 31-7 9 33-7 9 33-7 -3 5+2 2-0 2043 .... 9 33-7 8 17-3 9 33-5 9 33-6 -3 5+1 16-3 2079 .... 9 33-1 10 25-7 9 33-3 9 33-2 -3 5-0 26-5 2101 18 7 (9-5)? 10 3-2 15 32-7 10 3-2 10 3-2 —2 50—5 29-5 2110 13 57 10 7-6 14 17-5 10 7-6 10 7-6 — 30—4 9-9 2741 22 49 10-5 10 32-0 8 27-3 10 31-8 10 31-9 + 3 25+2 4-6 30-015 '■ The micrometer *as movee twice for e< ich dot-bisec tion, and the mean taken. ' Cloudy. * Numeral of Brisbake's Catalogue. The stars have been difficult of bisection to-night ; bad and unsteady images. The day was warm and lowering. The chronometer was allowed to run down in my absence, but was set in motion several hours before the observations commenced. 142 VERIFICATION AND EXTENSION OF LA CAILLE S ARC OF MERIDIAN. May 16th, 1838, Face of Sector East. No. of Ast. Soc. Cat. Time by Chronometer. Micr. for Plumb-line on Dot. Micr. for Observa- tion of Star. Micr. for Plumb-line on Dot. Mean of Micr.for Plumb-line on Dot. Star's Apparent Zenith Distance. Barom. Therm. 699 1562 1579 1604 1651 h m 3 13 36 56 42 55 57 36 14 34 11-5 rev. pis. 8 33-2 9 25-3 9 25-3 9 20-4 9 23-3 To 13''3 4 12-4 8 0-4 11 27-3 13 14-6 a rev. p(8. 8 33-2 9 25-3 9 25-1 9 20-4 9 23-5 Rain in the rev. pts. 8 33-2 9 25-3 9 25-2 9 20-4 9 23-4 morning. o / rev. pts. -0 15+1 14-1' + 1 45-5 12-9 + 1 45-1 24-8 -1 40+2 6-9 -0 35+3 25-2 in. 30-138 o 62 Now totally overcast. A warm cloudy day with occasional separations near the zenith. Mat 17th, 1838, Face of Sector West. No. of Ast. Soc. Cat. Time by Chronometer. Micr. for Plumb-line on Dot. Micr. for Observa- tion of Star. Micr. for Plumb-line un Dot. Mean of Micr. for Plumb-line. ou Dot. Star's Apparent Zenith Distance. Barom. Therm. 869 h m s 6 52 9 rev. pts. 10 31-0 rev ptB. 12 3-4 rev. pts. 10 30-8 rev. pts. 10 30-9 O / rev. pts. + 5 10-1 6-5 in. o 903 7 11 0-5 11 28-1 9 23-6 11 28-0 11 28-05 -2 55 +2 4-45 30-185 61-5 915 17 31 .... 9 7-6 9 19-4 .... +4 55 +0 11-8 957 39 14 9 26-1 9 22-3 9 26-3 9 26-2 -3 40 +0 3-9 • 1115 9 2 52 9 3-0 5 8-4 9 3-0 9 3-0 + 4 10+3 28-6 (2566)* 29 59-5 9 6-2 13 30-3 9 6-4 9 6-3 + 2 30-4 24-0 30-185 61-2 (2823)* 58 18-5 9 5-0 12 11-6 9 4-8 9 4-9 + 3 50-3 6-7 1243 10 19 32 9 3-5 9 14-5 9 3-5 9 35 + 3 40-0 11-0 1299 48 54-5 9 2-4 11 25-3 9 2-2 9 2-3 -2 20-2 23-0 1356 11 24 50 8 18-6 5 11-9 8 18-6 8 18-6 + 2 55+3 6-7 30-185 61-2 1378 44 30 8 15-4 10 1-3 8 15-4 8 15-4 + 55-1 19-9" 1562 13 36 14-5 9 3-3 15 28-8 9 3-3 9 3-3 + 1 45-6 25-5 1604 56 52-5 9 0-8 8 9-2 9 0-6 9 0-7 -1 40 +0 25-5 1661 14 33 29 8 26-1 6 1.5-0 8 25-9 8 26-0 -0 35+2 11-0 1742 15 12 30-5 8 32-7 11 31-5 8 32-7 8 32-7 -2 20—2 32-8 = 1774 28 28-5 8 16-2 8 5-2 8 16-0 8 16-1 -1-4 40+0 10-9^ 1797 40 23-5 8 12-3 13 25-2 8 12-4 8 12-35 +0 50-5 12-85 1821 49 2-5 8 19-8 10 7-4 8 19-8 8 19-8 —4 0-121-6 > Clouds coming ove r from the s( luth. '' Hazy atmosphere. "^ Hazy I atmosphere. ^ Bad images. * Numerals of Brisbane's Catalogue. OBSERVATIONS WITH THE SECTOR AT CAPE TOWN, UNREDUCED. 143 May 17th, 1838, Face or Sector West {continued). No. of Ast. Soo. Cat. Time by Chronometer. Micr. for Plumb-line on Dot. Micr. for Observa- tion of Star. Micr. for Plumb-line on Dot. Mean of Micr. for Plumb-line on Dot. Star's Apparent Zenith Distance. Barom. Therm. 1835 1 15 m 3 55 38 rev. pts. 8 10-0 1ei. pli. 11 4-3 rev. ptB. 8 10-0 rev. pts. 8 10-0 O / rev. ptB. —2 25—2 28-3 in. o 1866 .... 7 26-7 9 9-8 7 26-7 7 26-7 + 3 25-1 17-1' 1889 le 20 29 8 9-2 10 0-8 8 9'3 8 9-25 -0 25-1 25-55 1915 39 21 -5 8 12-3 8 3-2 8 12-3 8 12-3 -0 5-fO 9-1 1947 53 51 8 19-6 6 07 8 19'6 8 19-6 4-2 18-9 1969 .... 8 16 9 15 2-9 8 16-9 8 16-9 -f 1 30-6 20-0 2007 17 22 15-5 8 23-3 6 23-3 8 23-4 8 23-35 -3 5-f2 0-05 2043 38 28-5 8 23-4 7 9-5 8 23-4 8 23-4 -3 5-fl 13-9" 2079 55 6-5 8 7-9 9 0-2 8 7-8 8 7-85 + 3 30-0 26-35 2101 18 6 18-5 8 28-6 14 25-8 8 28-7 8 28-65 -2 50-5 31-15 2110 13 4-5 8 17-6 12 28-2 8 17-6 8 17-6 —0 30-4 10-6 30-150 61 » 1 5' past the middle wire. ■i Bad definition. A dense fog came on and continued the remainder of the night. May 18th, 1838, Face or Sector East. No. of Ast. Soc. Cat. Time by Chronometer. Micr. for Plumb-line on Dot. Micr. for Observa- tion of Star. Micr. for Plumb-line on Dot. Mean of Micr. for Plumb-line on Dot. Star's Apparent Zenith Distance. Barom. Therm. 1661 h m s 14 33 33 rev. pu. rev. pts. 12 13-3 rev. pts. 8 25-0 rev. pti. O / rev. pts. -0 35 -f 3 22-3 iu. o 1742 15 12(41?) 8 24-2 7 4-8 8 24-2 8 24-2 -2 20-1 19-4" 1774 28 12-5 8 33-6 10 22-6 8 33-6 8 33-6 -f4 40+1 23-0" 1797 40 23-5 9 7-0 5 6-6 9 7-0 9 7-0 -fO 50-4 0-4" 1821 49 25-5 8 11-5 8 3-5 8 11-5 8 11-5 -4 0-0 8-0^ 1835 55 53 8 3-9 6 22-2 8 3-9 8 3-9 -2 25-1 15-7 1866 .... 9 28-4 9 23-2 9 28-4 9 28-4 + 2, 25-0 5-2' 1889 16 20 35 8 33-8 8 19-8 8 33-6 8 33-7 -0 25-0 13-9 1915 .... 8 19-2 10 8-2 8 19-2 8 19-2 -0 5-fl 23-0 30-143 60-8 » Tlie sec tor appears to ha ve shifted in azimuth. ■> Slightly £ id justed in azi muth. <: Ditto. "i Ditto. « Ditto. Totally overcast. The plane of the arch did not continue at a constant distance through- out its extent when carried north and south. Star No. 1661 did not continue well bisected through the middle of the field. These errors were corrected, the latter by hitching the stop. i Scorpii No. 1915 remained bisected at transit. These circumstances must be attended to in the reductions. 144 VERIFICATION AND EXTENSION OF LA CAILLE S ARC OF MERIDIAN. Saturday, May 19, was cloudy without any indication of clearing up, and I returned to the Royal Observatory. Sunday, May 20, was cloudy with indications of rain ; but late in the evening the sky became clear, and the remainder of the night was fine, yet too far advanced to encourage a visit to the sector. May 21st, 1838, Face of Sector East. No. of Ast. Soe. Cat. Time by Chronometer. Micr. for Plumb-line on Dot. Micr. for Observa- tion of Star. Micr. for Plumb-line on Dot. Mean of Micr. for Plumb-line on Dot. Star's Apparent Zenith Distance. Barom. Therm. 869 h m s 6 51 63 rev. pta. 9 12-5 rev. pta. 9 21-0 rev. pta. 9 13-2 rev. pta. 9 12-85 O / rev. pta. H-5 10 +0 8-15 in. 30-211 o 61-8 915 .... 8 32-4 12 16-4 8 32-7 8 32-55 +4 55 +3 17-85* 1015 8 12 19 8 2-3 9 21-0 8 2-0 8 2-15 -2 25 -f 1 18-85" 1061 33 32-5 8 18'2 10 27-2 8 18-4 8 18-3 -0 50+2 8-9 1115 9 2 43-5 9 1-8 14 9-8 9 1-8 9 1-8 -t-4 lO-t-5 8-0 (2566)* 29 53-5 9 1-2 3 25-5 9 1-2 9 1-2 -f2 30—3 9-7 (2823)* 58 11 9 5-4 7 12-7 9 5-2 9 5-3 -f3 50-1 26-6 1243 10 19 24-5 9 7-2 10 10-0 9 7-4 9 7-3 + 3 40+1 2-7 1356 11 24 44-5 10 8'5 14 29-4 10 8-7 10 8-6 + 2 55 +4 20-8 1378 44 29-5 10 4-3 9 30-8 10 3-8 10 4-05 + 55-0 7-25 1527 .... 9 16-3 7 24-3 9 16-3 9 16-3 -1 55—1 26-0 30-215 61-7 1562 13 36 14 8 32-7 3 18-9 8 32-7 8 32-7 + 1 45-5 13-8 1579 .... 8 32-7 7 8-3 8 32-7 8 32-7 + 1 45—1 24-4 1604 .... 8 13-4 10 18-5 8 13-4 8 13-4 -1 40+2 5-1"= ■ 1661 14 33 35 8 25-8 12 16-4 8 25-8 8 25-8 -0 35+3 24-6 1742 15 12 42 8 9-8 6 24-3 8 9-6 8 9-7 -2 20-1 19-4 1774 28 24-2 9 6-7 10 30-2 9 6-9 9 6-8 + 4 40+1 23-4'' 1797 40 27-5 .... 4 17-7 8 19-3 .... + 50-4 1-6 1821 49 19-3 7 31-9 7 25-1 7 32-0 7 31-95 -4 0-0 6 85' 1835 «... 8 6-4 6 25-4 8 6-4 8 6-4 -2 25-1 15-0^ 1866 16 9 0-8 8 9-4 8 6'6 8 9-4 8 9-4 + 3 25-0 2-8^ 1915 39 37-5 7 33-7 9 23-5 7 33-7 7 33-7 -0 5+1 23-8 1947 53 57-5 7 23-3 11 22-0 7 23-1 7 23-2 0+3 32-8 1969 17 6 17 8 8-4 12 0'8 8 8-6 8 8-5 + 1 25+3 26-3 2007 ■ ■ . . 8 7-8 11 21-7 8 7-8 8 7-8 -3 5+3 13-9" 2043 38 43 8 7-8 11 2-7 8 8-0 8 7-9 -3 5+2 28-8 2079 55 6-3 8 26-7 9 15-5 8 26-5 8 26-6 + 3 30 +0 22-9 2101 18 6 32-5 8 17-3 3 33-8 8 17-5 8 17-4 -2 50-4 17-6 2110 13 13-5 8 32-2 6 0-8 8 32-1 8 32-15 -0 30-2 31-35 » 10' past the middle w ire. ■> Milky atmos phere. " 10» past the middle wire. ^ Faint. ' Nearly invisible. ' Faint. E Dense haze. )> Leaving the field. * Numerals of Brisbane's Catalogue. OBSERVATIONS WITH THE SECTOR AT CAPE TOWN, UNREDUCED. 145 May 22nd, 1838, Face OF Sector West. No. of Ast. Soc. Cat. Time by Chronometer. Micr. for Plumb-line on Dot. Micr. for Observa- tion of Star. Micr. for Plumb-line on Dot. Mean of Micr.for Plumb-line on Dot. Star's Apparent Zenith Distance. Barom. Therm. 1356 h m s 11 24 27-5 rev. pt9. 7 12-6 rev. ptB. 4 4-5 rev. ptB. 7 12-5 rev. pts. 7 12-55 O / rev. pts. +2 55+3 8-05 30'°il5 o 62 1579 13 42 1-5 8 5-8 11 11-3 8 5-8 8 5-8 + 1 45-3 5-5'' 1604 .... 8 17-8 7 27-4 8 17-8 8 17-8 -1 40 -fO 24-4" 1661 8 15-5 6 6-2 8 15-5 8 15-5 — 35 4-2 9-3'= 1742 15 12 29-5 8 19-6 11 19-7 8 19'5 8 19'55 -2 20-3 0-15^ 1774 28 11 8 19-2 8 8-9 8 19-2 8 19-2 -i-4 40-1-0 10-3 1797 .... 8 16-5 13 32-4 8 16-5 8 16-5 -fO 50-5 15-9 = 1821 49 7-5 9 6-4 10 28-8 9 6'4 9 6-4 -4 0-1 22-4' 1835 55 38 9 5-2 12 0-3 9 5-2 9 5-2 —2 25—2 29-18 1866 .... 8 18-9 10 4-7 8 18-8 8 18-85 +3 25-1 19-85*' 1889 16 20(25?) 8 33-5 10 26-3 8 33-9 8 33-7 — 25—1 26-6' 1915 39 17 8 24-8 8 16-4 8 24-8 8 24-8 -0 5+0 8-4 1947 ; • . . . 8 25-6 6 10-7 8 25-6 8 25-6 0-1-2 14-9' 1969 17 6 5-5 8 27-3 6 14-4 8 27-1 8 27-2 + 1 25 -f 2 12-8 2007 22 18-5 9 4-8 7 5-0 9 4-8 9 4-8 -3 5-fl 33-8 2043 38 31-5 9 4-8 7 26-2 9 4-7 9 4-75 -3 5-fl 12-55 2079 54 54-2 8 21-7 9 14-5 8 21-7 8 21-7 -f3 30-0 26-8 2101 18 6 21 9 2-2 15 0-6 9 2-0 9 2-1 —2 50 -t- 5 32-5 2110 .... .... 13 21-6 9 10-3 -0 30-4 11-3 '■ Cloudy day. " Clear ng up ; hot air. "= 10' past the mi ddle wire. "> Seen through thin cloud. ' 8' past the middle wire 'Seen through haz 3. s Very faint. ■> Faint. ' Faint. ' 15« pa ist the middl e wire. May 23, cloudy day ; heavy rain in the night. May 24, heavy rain with thunder. May 25, heavy rain at intervals. May 26, cleared up. 146 VERIFICATION AND EXTENSION OF LA CAILLE S ARC OF MERIDIAN. May 26th, 1838, Face of Sector West. No. of Ast. Soc. Cat. Time by Chronometer. Micr. for Plumb-line on Dot. Micr. for Observa- tion of Star. Micr. for Plumb-line on Dot. Mean of Micr. for Plumb-line on Dot. Star's Apparent Zenith Distance. Barom. Therm. 791 h m s rev. pts. 9 24-8 rev. ptB. 9 25-0 rev. pts. 9 24-8 rev. pts. 9 24-8 O / rev. pts. -f 3 55-0 0-2'' 30'°400 61°5 869 6 51 47 9 27-8 10 33-8 9 27-8 9 27-8 +5 10-1 6-0 1061 8 33 25-5 9 29-3 9 0-7 9 29-3 9 29-3 -0 50+0 28-6 (2823)* 9 57 33-6 9 8-5 12 15-6 9 8-0 9 8-25 + 3 50—3 7-35 1356 11 24 38-5 8 28-8 5 22-9 8 28-8 8 28-8 +2 55 -f 3 5-9 1378 44 23 8 29-3 10 21-8 8 29-3 8 29-3 + 55-1 26-5 1433 12 19 33-5 8 29-0 7 4-4 8 29-2 8 29-1 -4 15-t-l 24-7" 1527 13 11 14 8 19-9 11 28-2 8 20'0 8 19-95 -4 15—3 8-25 1562 .... 8 13-6 15 7-5 8 13-5 8 13-55 + 1 45-6 27-95 1579 .... 8 13-5 11 20-6 8 13-5 8 13-5 + 1 45-3 7-1 1604 56 53-5 8 29-0 8 6-1 8 28-8 8 28-9 -1 40 -f 22-8 30-422 61-2 1661 14 33 ll\l 8 31-1 6 21-7 8 31-2 8 31-15 -0 35 +2 9-45 1774 15 28 17-5 9 6-0 8 31-6 9 6-0 9 6-0 +4 40 -fO 8-4 1797 .... 9 19'3 15 1-2 9 19-3 9 19-3 + 50-5 15-9 1821 49 11-7 10 1-2 11 23-6 10 M 10 1-15 -4 0-1 22-45 1835 55 43-5 10 2-0 12 32-6 10 2-0 10 2-0 -2 25-2 30-6 1866 .... 9 27-0 11 12-8 9 27'0 9 27-0 + 3 25-1 19-8-= 1915 16 39 23 9 32-0 9 26-6 9 32-0 9 32-0 -0 5-fO 5-4 1947 .... 9 9-3 6 28-4 9 9-3 9 9-3 -t-2 14-9 1969 17 6 11-5 9 18-8 7 7-2 9 18-8 9 18-8 + \ 25+2 11-6 2007 22 23-5 10 4-7 8 7-7 10 4-9 10 4-8 -3 5+1 31-1 2043 38 37 10 4-9 8 26-7 10 4-9 10 4-9 -3 5+1 12-2 2079 55 0-5 9 27-0 10 20-5 9 26-8 9 26-9 + 3 30-0 27-6 2101 18 5 56-5 10 4-7 16 3-8 10 4-7 10 4-7 -2 50-5 33-1 2110 13 7-5 10 13-5 14 24-6 10 13-5 10 13-5 -0 30-4 11-1 Occasional inte rruptions fro m clouds. "B ad light. "^ 10' past the middle wire. * Numeral cf Brisbane's Catalogue. OBSERVATIONS WITH THE SECTOR AT CAPE TOWN, UNREDUCED. 147 May27th, 1838, Face OF Sector East. No. of Ast. Soc. Cat. Time by Chronometer. Micr. for Plumb-line on Dot. Micr. for Observa- tion of Star. Micr. for Plumb-line on Dot. Mean of Micr. for Plumb-line on Dot. Star's Apparent Zenith Distance. Barom. Therm. 699 h m 3 5 33 31 reT. pts. 9 32-3 rev. pts. U 14-9 rev. pts. 9 32'3 rev. pta. 9 32-3 O / rev. pta. -0 15 +1 16-6 In. o 732 11 13-0 10 2-2 ■ > . • -1 55 -fl 10-8 30-287 61 791 6 13 48-5 10 16-7 12 0-5 10 16-8 10 16-75 + 3 55+1 17-75 848 43 32 10 16-2 12 13-4 10 16-2 10 16-2 + 1 35 +1 31-2 869 51 57-5 10 24-8 11 0-8 10 24-8 10 24-8 -5 10+0 10-0 903 7 11 32 10 29-4 14 15-4 10 29'0 10 29-2 —2 55+3 20-2 9'15 11 13-9 13 6-4 11 13'9 11 13-9 +4 55+1 26-5 1061 10 28-3 13 5-2 10 28-3 10 28-3 -0 50+2 10-9' (2566)* 9 29 56-5 10 1-8 6 28-4 10 1-8 10 1-8 + 2 30-3 7-4" (2823)* 58 14 9 14-7 7 23-5 9 14-7 9 14-7 + 3 60-1 25-2 1243 10 19 29 7 23'4 8 27-9 7 23-0 7 23-2 + 3 40+1 4-7 1299 48 59 8 0-0 6 27-3 8 0-0 8 0-0 -2 20-1 6-7 (3350)* 55 17'5 8 33-0 8 32-9 8 33-0 8 33-0 + 2 50-0 0-1 1378 11 44 30 9 2-7 8 30-5 9 2-6 9 2-65 + 55-0 6-15 1433 .... 9 3'7 12 10-6 9 3-7 9 3-7 -4 15+3. 6-9 1527 13 11 20 9 4-2 7 13-8 9 4-4 9 4-3 -1 55-1 24-6 1562 36 16 9 32-3 4 19-7 9 32-2 9 32-25 + 1 45-5 12-55 1579 42 15-5 9 32-2 8 8-4 9 32-2 9 32-2 + 1 45-1 23-8 1604 56 59 10 1-4 12 7-5 10 1-4 10 1-4 -1 40 +2 6-1 1661 14 33 34-5 9 25'4 13 15-3 9 25-4 9 25-4 -1 35+3 23-9 1774 15 28 28-5 11 4-2 12 27-0 11 4-2 11 4-2 + 4 40 + 1 22-8 30-200 61 . 1797 40 29-5 11 4-3 7 3'4 11 4-2 11 4-25 + 50—4 0-86 1821 49 15-5 10 33-8 10 25-8 10 33-6 10 33-7 _4 0—0 7-9 1835 55 48-5 10 18-0 9 2-4 10 17-9 10 17-96 -2 25-1 15-55 • • 1866 16 9 4 .... 10 23-5 10 25-8 .... + 3 25-0 2-3 1889 20 37-2 9 20-6 9 7-8 9 20-6 9 20-6 —0 25-0 12-8 30-148 60-8 1915 39 29-5 9 18-5 11 7-7 9 18-4 9 18-45 —0 5+1 23-25. 1947 54 56-5 9 21-2 13 20'7 9 21-2 9 21-2 0+3 33-5 1969 17 6 19 9 28-3 13 20-2 9 28-3 9 28-3 + 1 25+3 25-9 2007 .... .... 13 7-4 9 27-2 .... -3 5+3 14-2" 2079 55 9-5 12 17-5 13 7-3 12 17-5 12 17-5 + 3 30+0 23-8 2101 18 6 30-5 8 27-2 4 11-1 8 27-2 8 27-2 -2 50-4 16-1 30-115 60-7 2110 13 13-7 8 30-6 6 0-0 8 30-6 8 30-6 -0 30 -2 30-6^ * 15' past middle wire. *> Milky atmosphere. ' Hurried. >■ Torch like. * Numerals of Brisbane's Catalogue. 148 VERIFICATION AND EXTENSION OF LA CAILLE S ARC OF MERIDIAN. May 28th, 1838, Face of Sector West. No. of Ast. Soc. Cat. Time by Chronometer. Micr. for Plumb-line on Dot. Micr. for Observa- tion of Star. Micr. for Plumb-line on Dot. Mean of Micr. for Plumb-line on Dot. Star's Apparent Zenith Distance. Barom. Therm. 699 h m s 5 33 22-5 rev. 9 ptj. 3-0 rev. ptB. 9 0-1 rev. pts. 9 3-0 rev. pl8. 9 3-0 O / rev. pl». -0 15-1-0 2-9 30-075 o 61 732 44 51-5 9 3-2 9 7-6 9 3-2 9 3-2 -1 55-0 4-4' 903 .... 9 32-8 7 28-7 9 33-2 9 33-0 -2 55-F2 4-3' 915 7 17 9-5 9 13-8 9 2-2 9 13-8 9 13-8 4-4 55 -f 9-6' 957 39 7 10 9-2 10 4-6 10 9-2 10 9-2 -3 40 +0 4-6 30-075 61 1015 8 12 6-5 10 12-7 10 6-5 10 12-7 10 12-7 -2 15 -f 6-2* 1061 33 20-3 10 15-2 9 19-8 10 15-5 10 15-35 -0 50 +0 29-55 (2566)* 9 29 44 11 3-8 15 28-7 11 3-7 11 3-75 +2 30-4 24-95 (2823)* 58 2-5 11 0-4 14 8-4 11 0-4 11 0-4 + 3 50—3 8-0 1243 .... 10 16-5 10 29-8 10 16-7 10 16-6 + 3 40-0 13-2 1299 10 48 47-5 10 10-4 13 0-5 10 10-5 10 10-45 -2 20-2 24-05 (3350)* 9 29-5 11 13-4 9 29-7 9 29-6 +2 50-1 17-8 1356 11 24 35-5 10 1-7 6 31-0 10 1-7 10 1-7 -2 55+3 4-7 1378 44 20-5 10 5-0 11 26-3 10 5-2 10 5-1 + 55-1 21-2 a Clouds coming o ver. " Cloud y- <^ Good ob8< rvation. ^ Very faint. * Numerals of Brisbane's Catalogue. The sky totally obscured. May 29th, 1838, Face of Sector West. No. of Ast. Soc. Cat. Time by Chronometer. Micr. for Plumb-line on Dot. Micr. for Observa- tion of Star. Micr. for Plumb-line on Dot. Alean of Micr. for Plumb-line on Dot. Star's Apparent Zenith Distance. Barom. Therm. 699 h m s 5 33 21 rev, pla. 10 30-2 r«T. ptB. 10 25-5 rev. pts. 10 30-2 rev. pta. 10 30-2 J rev. pt>. -0 15+0 4-7 30'°225 o 71 732 44 51 10 28-5 10 31-3 10 28-6 10 28-55 — 1 55-0 2-75 791 6 13 36-5 10 32-4 10 30-3 10 32-3 10 32-35 + 3 55+0 2-05 869 51 45 10 26-2 11 28-6 10 26-1 10 26-15 + 5 10-1 2-45 903 7 11 2-8 10 8-7 8 1-4 10 8-7 10 8-7 -2 55+2 7-3 915 . • • • 10 5-6 9 2.5-1 10 5-4 10 5-5 +4 55 +0 14-4 957 39 7 10 24-3 10 18-1 10 24-3 10 24-3 -3 40+0 6-2 1061 8 33 21-2 10 21-4 9 23-9 10 21-4 10 21-4 -0 50+0 31-5 OBSERVATIONS WITH THE SECTOR AT CAPE TOWN, UNREDUCED. 149 May 29th, 1838, F ACE OF Sector West (continued). No. of Ast. Soc. Cat. Time by Chronometer. Micr. for plumb-line on Dot. Micr. for Observa- tion of Star. Micr. for Plumb-line on Dot. Mean of Micr. for Plumb-line on Dot. Star's Apparent Zenith Distance. Barora. Therm. 1070 b m s rev. pts. 10 19-3 rev. pts. 13 19-3 1 rev. ptB, 10 19-5 rev. pts. 10 19-4 O / rev. pts. + 1 20—2 33-9» In. o (2566)* 10 21-8 15 10-5 10 22-0 10 21-9 +2 30—4 22-6 (2823)* 9 58 2-5 • • • • 14 7-3 11 1-3 • . . • + 3 50-3 6-0 1243 10 19 16 10 20-8 10 31-8 10 21-0 10 20-9 4-3 40-0 10-9'' 30-190 61-1 . 1299 48 49-5 10 14-3 13 1-3 10 14-4 10 14-35 -2 20 -2 20-95 (3350)* .... .... 11 33-0 10 17-4 .... + 2 50-1 15-6" 1356 11 24 36-5 10 19-3 7 12-3 10 19-3 10 19-3 -i-2 55 +3 7-0 1378 44 20 10 22-4 12 7-5 10 22'5 10 22-45 -fO 55-1 19-05 1527 13 11(39-5?) 9 20-2 12 27-6 9 20-2 9 20-2 -1 55—3 7-4 1562 .... 9 33-5 16 26-2 9 33-5 9 33-5 -f 1 45—6 26-7 1579 42 5-5 9 33-5 13 4-2 9 33-5 9 33-5 + 1 45-3 4-7 1604 56 49 10 11-7 9 22-0 10 11-7 10 11-7 -1 40 -fO 23-7 1661 14 33 25 10 16-3 8 4-8 10 16-3 10 16-3 -0 35 4-2 11-5 1742 15 12 29-5 10 20-6 13 19-7 10 20-6 10 20-6 -2 20—2 23-1 1774 28 16-5 10 20-3 10 10-7 10 20-2 10 20-25 + 4: 40-i-O 9-55 1797 40 16-8 .... 15 15-7 10 0-4 .... -f-0 50-5 15-3 1821 49 6 .... 13 0-3 11 12'0 .... -4 0-1 22-3 1835 55 38-5 11 3-1 13 33-2 11 2-9 11 3-0 -2 25-2 30-2 1866 16 9 (4?) 9 10-6 10 29-0 9 10-6 9 10-6 -f3 25-1 18-4 1889 20 27 9 10-2 11 2-4 9 10-2 9 10-2 — 25-1 26-2 1915 39 19 9 11-4 9 3-7 9 11-4 9 11-4 — 5 4-0 7-7 •1947 54 48-5 9 12-7 6 29-4 9 12-6 9 12-65 4-2 17-25 1969 17 6 8-5 9 24-3 7 12-3 9 24-3 9 24-3 4-1 25 4-2 12-0 2007 22 18 10 6-9 8 8-4 10 6-9 10 6-9 -3 5 4-1 32-5 2043 38 31-5 10 6-9 8 27-2 10 7-0 10 6-95 -3 5+1 13-75 ,' 2079 54 58-5 10 1-7 10 28-6 10 1-7 10 1-7 4-3 30-0 26-9 2101 18 6 21 10 14-7 16 12-8 10 14-7 10 14-7 —2 50—5 32-1 2110 13 3-5 10 12-3 14 22-7 10 12-5 10 12-4 -0 30—4 10-3 5741 22 48 14-5 10 5-8 7 31-8 10 5-8 10 5-8 4-3 25 4-2 8-0 " 20' past the n liddle wire. '■ The second i lot certain. "" A fine observing night. * Numerals of Brisbane's Catalogue. Before the observations commenced the telescope was moved in azimuth by the upper adjusting screw, to place the axis of suspension truly perpendicular to the back arch, from which it had deviated. 150 VERIFICATION AND EXTENSION OF LA CAILLE S ARC OF MERIDIAN. May 30th, 1838, Face of Sector East. No. of Ast. Soc. Cat. Time by Chronometer. Micr. for Plumb-line on Dot. Micr. for Observa- tion of Star. Micr. for Plumb-line on Dot. Mean of Micr. for Plumb-line on Dot. Star's Apparent Zenith Distance. Barom. Therm. 869 1356 1378 1433 h m 3 6 52 8'5 11 24 51-5 44 29-5 12 19 20-5 rev. pts. 12 13-6 8 31-8 9 2-7 8 27-8 rev. ptB. 12 26-7 13 21-6 8 30-2 11 33-8 rev. pts. 12 13'8 8 32-4 9 2-5 8 27'8 rev. pts. 12 13-7 8 32-1 9 2-6 8 27-8 O / rev. pts. +5 10+0 13'0 + 2 55+4 23-5 + 55—0 10-4 -4 15 +3 6-0 in. O Overcast. The sector was moved a little eastward in azimuth after the above observations. May 3lst. Heavy rain. Great difficulty in keeping the sector dry. June 1st. Cloudy. June 2nd, 1838, Face of Sector East. No. of Ast. Soc. Cat. Time by Chronometer. Micr. for Plumb-line on Dot. Micr. for Observa- tion of Star. Micr. for Plumb-line on Dot. Mean of Micr. for Plumb-line on Dot. Star's Apparent Zenith Distance. Barom. Therm. 791 h m s 6 13 44 rev. pts. 13 26-2 rev. pts. 15 9-7 rev. pts. 13 26-0 rev. ptB. 13 26-1 O / rev. pts. + 3 55+1 17-6 in. 30-062 59° 2 869 51 55 10 9-6 10 21-2 10 9'9 10 9-75 + 5 10+0 11-45^ 903 7 11 2-5 9 15-0 13 3'0 9 15-1 9 15-05 -2 55 +3 21-95 957 .... 9 2-4 10 24-7 9 2-5 9 2-45 —3 40+1 22-25'' 1070 .... 8 24-6 7 4-2 8 24-2 8 24-4 + 1 20-1 20-2 (2823)* 9 58 1-5 9 6-2 7 15-3 9 6-2 9 6-2 + 3 50—1 24-9'' 1243 10 19 16-2 9 8-3 10 13-9 9 8-3 9 8-3 + 3 40+1 5-6^ 1299 48 48 9 12-8 8 6-5 9 12-7 9 12-75 -2 20-1 6-25 1378 12 26-1 12 20-2 12 26-1 12 26-1 + 55-0 5-9 » This transit shews the s Bctor too we iterly; movf id it. *> Faint: indifferent observation. " Faint. 1579 41 58 7 10-2 5 21-7 7 10-2 7 10-2 + 1 45-1 22-5 1604 56 42 7 20-4 9 26-3 7 20-6 7 20-5 -1 40 +2 5-8 30-020 60-2 1835 i . • • 9 26-6 8 12-4 9 26-6 9 26-6 —2 25-1 14-2 ■ 1915 16 19 11 10 5-8 11 30-2 10 5-8 10 5-8 -0 5+1 24-4 » Mist. 1" Faint; the upper dot not examined. At 14^ 33™ S.T. dense volumes of cloud from the south-west, occasionally becoming thinner. 15h 40m misty rain, and heavy rain on the morning of the 5th. The instrument has not been reversed in azimuth, in the hope of procuring observations of those stars which have not been seen for several days. 152 VERIFICATION AND EXTENSION OF LA CAILLE S ARC OF MERIDIAN. June 5th, 1838, Face of Sector East. No. of Ast. Soc. Cat. Time by Chronometer. Micr. for Plumb-line on Dot. Micr. for Observa- tion of Star. ■ Micr. for Plumb-line on Dot. Mean of Micr. for Plumb-line on Dot. Star's Apparent Zenith Distance. Barom. Therm. 1527 1569 1579 1604 b m s 13 Jl 59-5 35 56-5 56 39-5 rev. pu. 9 17-5 10 6-2 10 6-1 10 12-5 lev. pt.. 7 28-3 4 28-0 8 16-7 12 18-4 ireT. pl8. 9 17-5 10 6-1 10 5-8 10 12-3 rev. pt8. 9 17-5 10 6-15 •10 5-95 10 12-4 / rev. pt8. -1 .55—1 23-2 + 1 45-5 12-15 + 1 45-1 23-25 -1 40 +2 60 in. O Rain. June 6th, 1838, Face of Sector East. No. of Ast. Soc. Cat. Time by Chronometer. Micr. for Plumb-line on Dot. Micr. for Observa- tion of Star. Micr. for Plumb-line on Dot. Mean of Micr. for Plumb-line on Dot. Star's Apparent Zenith Distance. Barom. Therm. 1356 h m s 11 24 22 rev, pts. 11 27-3 rev. pts. 16 16-4 rev. pta. 11 27-1 rev. pts. ' 11 27-2 O / rev. pts. + 2 55 +4: 23-2 30'"288 o 59 1378 44 6 8 33-2 8 27-4 8 33-0 8 33-1 + 55-0 5-7 1433 12 19 13-5 8 29-0 12 1-7 8 29-0 8 29-0 -4 15-1-3 6-7 1527 13 10 54-5 9 7-4 7 16-3 9 7-4 9 7-4 -1 55-1 25-1 1562 35 51 9 9-1 3 30-9 9 9-1 9. 9-1 4-1 45-5 12-2 1579 41 50-5 9 9-1 7(29-3) 9 9-1 9 9-1 + 1 45-1 13-8' 1604 56 34-5 10 5-9 12 11-5 10 5-8 10 5-85 — 1 40 +2 5-65 30-284 58-8 1742 15 12 14-5 9 25-6 8 6-0 9 25-6 9 25-6 -2 20-1 19-6 1774 28 2-5 9 7-2 (11)29-8 9 7-0 9 7-1 -1-4 4-)-l 22-7'' 1797 40 (3?) 8 26-8 4 24-6 8 27-2 8 27-0 + 50-4 2-4 1821 .... 9 33-5 9 26-7 9 33-7 9 33-6 —4 0-0 6-9 1835 • • . . 9 28-9 8 13-8 9 28-8 9 28-85 -2 25-1 15-05 1866 16 8 38 11 1-0 10 32-1 11 1-0 11 1-0 + 3 25-0 2-9 1889 20 13 9 33-0 9 20-5 9 32-8 9 32-9 — 25—0 12-4 1915 39 3-5 9 30-1 11 19-4 9 29-8 9 29-95 -0 5+1 23-45 ; 1947 .... 9 13-2 13 12-5 9 13-2 9 13-2 0+3 33-3 1969 17 5 53 9 24-0 13 16-3 9 24-0 9 24-0 + 1 25 +3 26-3 2007 22 1-5 9 23-0 13 5-0 9 23-0 9 23-0 -3 5+3 16-0 2079 54 43-5 10 6-3 10 31-0 10 6-3 10 6-3 + 3 30 +0 24-7 2101 18 6 4-5 10 6-7 5 24-2 10 6-6 10 6-65 —2 50+4 16-45 2110 13 47-5 9 33-8 7 3-2 9 33-6 1 9 33-7 -0 30—2 30-5 » There is a mistake of 10 divisions in reading off: the reading for the star ought to be T 19<''3. ■• The micrometer reading for the star should be 10' 29P-8. OBSERVATIONS WITH THE SECTOR AT CAPE TOWN, UNREDUCED. 153 June 7th, 1838, Face OF Sector West. No. of Ast. Soo. Cat. Time by Chronometer. Micr. for Plumb-line on Dot. Micr. for Observa- tion of Star. Micr. for Plumb-line on Dot. Mean of Micr. for Plumb-line on Dot. Star's Apparent Zenith Distance. Barom. Therm. 699 h tn s 5 32 56-5 rev. ptB. 10 19-2 rev. ptB, 10 16-2 rev, PtB. 10 19-2 rev. ptB. 10 19-2 / rev. ptB. -0 15 +0 3-0 30'-260 o 59 732 44 20 10 7-8 10 11-6 10 7-9 10 7-85 -1 55—0 3-75" 791 .... 9 30-7 9 28-2 9 30-5 9 30-6 + 3 35 -fO 2-4 1299 10 48 16-5 11 17-3 14 6-8 11 17-3 11 17-3 _2 20-2 23-5 (3350)* .... 12 29-7 11 14-2 .... + 2 50-1 15-5 1356 11 24 17-5 11 17-0 8 11-2 11 17-0 11 17-0 +2 55+3 5-8'' 1378 43 54-5 11 14-7 13 1-7 11 14-7 11 14-7 + 55-1 21-0 1433 .... 11 23-4 9 31-8 11 23-7 11 23-55 -4 15+1 25-75 1527 .... 11 13-8 14 21-7 11 14-0 11 13-9 -1 55-3 7-8 1562 13 35 40 9 24-6 16 20'0 9 24-5 9 24-55 + 1 45-6 29-45 1579 41 40-5 9 24-5 12 32-5 9 24-5 9 24-5 + 1 45-3 8-0 1604 56 19-5 10 I'O 9 14-6 10 1-0 10 1-0 — 1 40+0 20-4'= 1661 14 32 57-5 10 6-7 7 32-4 10 6-8 10 6-75 -0 35 +2 8-35 1742 15 12 4 10 7-2 13 8-2 10 7-2 10 7-2 -2 20-3 1-0 1774 27 48 10 8-2 9 33-6 10 8-3 10 8-25 + 4 40 +0 8-65'' 1797 39 51 10 6-5 15 22-4 10 6-5 10 6-5 + 50-5 15-9 1821 48. 35-5 10 32-7 12 22-3 10 32-7 10 32-7 -4 0-1 23-6 1835 55 9-5 . * • . 13 29-4 10 32-0 .... -2 25-2 31-4' 1866 16 8 28 .... 13 6-3 11 19-1 .... + 3 25-1 21-2 1889 19 59 11 8-4 13 1-8 11 8-4 11 8-4 — 25—1 27-4 1915 38 51 10 19-6 10 12-4 10 19-5 10 19-55 -0 5+0 7-15 1947 53 21 10 24-5 8 8-1 10 24-4 10 24-45 0+2 16-35 30-240 58 1969 17 5 42-5 10 24-9 8 14-2 10 24-7 10 24-8 + 1 25 +2 10-6 2007 21 48 10 3-5 8 6-3 10 3-5 10 3-5 -3 5+1 31-2 2043 .... 10 3-5 8 26-2 10 3-3 10 3-4 -3 5+1 11-2 2079 54 35 10 0-0 10 28-8 10 O'O 10 0-0 + 3 30-0 28-8 2101 18 5(13-5?) 10 17-0 16 16'4 10 17'0 10 17-Q -2 50—5 33-4 2110 12 36 10 4-''4 14 16-2 10 4-3 10 4-35 — 30-4 11-85 » After tl lis transit th e sector was moved a little in azimuth. '> After this transit the sec tor was mov ed a little m ore eastward. ° After this transit moved the sector in azimuth. ^ After ti lis transit moved the sector i a azimuth. 'Star s ratlier crabby. * Numeral of Brisbane's Catalogue. This has been the first good observing night since the 1st of May. Many of the smaller stars visible at Klyp Fonteyn now transit in the day time and cannot be observed. If the weather had been favourable, the observations at the present station could have been completed last month. 154 VERIFICATION AND EXTENSION OF LA CAILLE S ARC OF MERIDIAN. June 8th, 1838, Face of Sector East. No. of Ast. Soc. Cat. Time by Chronometer. Micr. for Plumb-line on Dot. Micr. for Observa- tion of Star. Micr. for Plumb-line on Dot. Mean of Micr. for Plumb-line on Dot. Star's Apparent Zenith Distance. Barom. Therm. 699 h m 3 5 32 58-5 rev. pts. 9 7-1 rev. pts. 10 27-3 rev. pts. 9 6-5 rev pts. 9 6-8 O / rev. pts. -0 15+1 20-5 30'-i45 o 58-4 732 44 28 9 10-4 10 25-5 9 10-4' 9 10-4 -1 55+1 15-1 848 .... 9 24-1 11 23-0 9 24-3 9 24-2 + 1 35+1 32-8 869 6 51 24 8 33-4 9 11-7 8 33-6 8 33-5 + 5 10+0 12-2 903 7 10 39 8 17-2 12 5-8 8 17-0 8 17-1 -2 55 +3 22-7 915 •16 50-2 9 18'4 11 14-4 9 18-3 9 18-35 +4 55 +1 30-05 1061 8 32 59 9 12-8 11 24-7 9 12-8 9 12-8 -0 50+2 11-9' 1243 10 18 54-5 9 3-8 10 9-5 9 3-8 9 3-8 +3 40+1 5-7" 1299 48 25-5 9 7-5 7 32-7 9 7'4 9 7'45 -2 20-1 8-75= 1356 11 24 14 8 33-6 13 21-3 8 33-2 8 33'4 + 2 55 +4 21-9 1378 43 57 9 29-8 9 23-3 9 29-8 9 29-8 + 55—0 6-5 1433 12 19 4 9 9-7 12 14-7 9 9-5 9 9-6 -4 15+3 5-1" 1527 13 10 46 10 19-8 8 28-4 10 19-6 10 19'7 -1 55-1 25-3 1562 35 43 9 20-9 4 8-3 9 20-9 9 20-9 + 1 45-5 12-6 30-135 58 1579 41 42-5 9 20-9 7 30-5 9 20-8 9 20-85 + 1 45-1 24-35 1604 56 26 9 14-4 11 21-2 9 14-4 9 14-4 -1 40+2 6-8 1661 14 33 1 9 10-1 12 33-9 9 10-1 9 10-1 -0 35 +3 23-8 1742 15 12 6 9 10-3 7 26-5 9 10-3 9 10-3 -2 20-1 17-8 30-112 58 1774 27 55 9 24-7 11 16-1 9 24-7 9 24-7 + 4 40+1 25-4 1797 39 54-5 9 32-3 5 32'2 9 32'3 9 32-3 + 50-4 0-] 30-111 58 1821 48 42-5 8 3-7 7 30-9 8 3'3 8 3-5 -4 0-0 6-6 » Faint. •■Good • 'Fain >• Faint. Called ofF suddenly to the Observatory. The sky became cloudy on the 9th; stormy weather succeeded, with thunder and heavy rain, which ceased on the 13th. OBSERVATIONS WITH THE SECTOR AT CAPE TOWN, UNREDUCED. 155 June 14th, 1838, Face of Sector West. No. of Ast. Soc. Cat. Time by Chronometer. Micr. for Plumb-line on Dot. Micr. for Observa. tion of Star. Micr. for Plumb-line on Dot. Mean of Micr. for Plumb-line on Dot. Star's Apparent Zenith Distance. Barom. Therm. 1579 h m ■ s 13 41 4-5 rev. pts. 9 21-8 rev. pts. 12 29-4 rev. pts. 9 21-8 rev, ptB. 9 21-8 O / rev. pt«. -1-1 45-3 7-6 30-134 56° 1915 16 38 13-5 9 16-0 9 11-0 9 160 9 16-0 —0 5 +0 5-0 1947 52 43 9 19-6 7 .5-0 9 19-6 9 19-6 0+2 14-6 1969 - . . . .... 7 1-3 9 12-2 .... -1-1 25+2 10-9 2007 17 21 5 9 21-1 7 24-5 9 21-0 9 21-05 -3 5+1 30-55 2043 37 18 9 21-0 8 11-0 9 2M 9 21-05 -3 5+1 10-05 2079 54 1 9 8-3 10 3-5 9 8-5 9 8-4 + 3 30—0 29-1 2101 .... 9 11-8 15 11-7 9 11-8 9 11-8 -2 50-5 33-9' 2110 18 11 57 9 15-6 13 28-8 9 15-6 9 15-6 -0 30-4 13-2 MO ■ past tlie m ddle wire. Heavy rain again came on, which continued on the 15th and 16th. The winter has set in unusually early. June 17th, 1838, Face or Sector West. No. of Ast. Soc. Cat. Time by Chronometer. Micr. for Plumb-line on Dot. Micr. for Observa- tion of Star. Micr. for Plumb-line on Dot. Mean of Micr. for Plumb-line on Dot. Star's Apparent Zenith Distance. Barom. Therm. 699 h in s 5 32 0-5 rev. ptB. 9 15-3 rev. pts. 9 6-5 rev. pts. 9 15-2 rev. pts. 9 15-25 O / rev. pts. — 15+0 8-75 30- 150 o 58 732 43 26 9 11-9 9 9-8 9 11-9 9 11-9 -1 55+0 2-r, 1061 8 31 8 9 12-6 8 13-7 9 12-6 9 12-6 -0 50+0 32-9 1356 11 23 17 9 2-0 5 30-3 9 2-1 9 2-05 +2 55 +3 5-75 1378 42 58 8 29-8 10 17-3 8 29-7 8 29-75 + 55-1 21-55 1433 12 17 58 8 20-9 6 31-2 8 21-0 8 20-95 —4 15 +1 23-75 1527 13 9 45 8 28-8 12 3-7 8 28-7 8 28-75 -1 55—3 8-95 30-235 58-2 1562 34 43-5 8 33-5 15 29-1 8 33-5 8 33-5 + 1 45—6 29-6 1579 40 43-2 8 33-5 12 6-8 8 33-5 8 33-5 + 1 45-3 7-3 1604 54 24-5 9 16-0 8 29-4 9 16-0 9 16-0 -1 40+0 20-6 1661 14 32 0-5 9 13-3 7 6-5 9 13-3 9 13-3 -0 35 +2 6-8 30-235 58-2 » After this t ransit the se ctor was mo red in azimut 1 a small quantity. 156 VERIFICATION AND EXTENSION OF LA CAILLE S ARC OF MERIDIAN. June 17th, 1838, Face of Sector West (continued). No. of Ast. Soc. Cat. Time by Chronometer. Micr. for Plumb-line on Dot. Micr. for Observa- tion of Star. Micr. for Plumb-line on Dot. Mean of Micr. for Plumb-line on Dot. Star's Apparent Zenith Distance. Barom. Therm. 1742 h m s 15 11 4 rev. pts. 9 10-2 rev. plB. 12 13-2 lev. ptB. 9 10-2 rev. pts. 9 10-2 O / rev. pts. -2 20-3 3-0 in. o 1774 26 56-5 8 22-6 8 17-9 8- 22-8 8 22-7 +A 40 +0 4-8 1797 38 55-2 8 29-7 14 15-2 8 29-7 8 29-7 + 50-5 19-5 1821 47 39 10 0-5 11 27-5 10 0-4 10 0-45 _4 0-1 27-05 1835 54 13-5 9 12-6 12 13-4 9 12-6 9 12-6 -2 25—3 0-8 1866 9 10-8 10 32-7 9 10-8 9 10-8 + 3 25-1 21-9 1889 16 19 3-5 9 16-9 11 13-1 9 16-9 9 16-9 -0 25-1 30-2 1915 37 55-5 9 18-0 9 13-0 9 18-0 9 18-0 -0 5+0 5-0 1947 52 25 7 1-1 9 14-5 .... 0+2 13-4 1969 17 4 46-5 9 3-3 6 29-3 9 3-3 9 3-3 + 1 25+2 8-0 2007 20 52-5 9 15-8 7 20-5 9 15-8 9 15-8 -3 5+1 29-3 30-235 58-2 2043 37 5-5 9 15-8 8 6-4 9 16-0 9 15-9 -3 5+1 9-5'' 2079 53 38 8 26-4 9 21-7 8 26-6 8 26-5 + 3 30-0 29-2 2101 18 4 55-2 9 21-3 15 22-7 9 21-3 9 21-3 —2 50—6 1-4 2110 11 40 9 28-1 14 8-8 9 28-2 9 28-15 —0 30—4 14-65 2741 22 46 52-5 9 2-5 6 27-] 9 2-0 9 2-25 + 3 25+2 9-15 b Beautiful de inition. « Columbce this day transits at noon ; but it will continue to be entered under the head of the following day, with the great mass of the observations, for convenience. June 18th, 1838, Face of Sector East. No. of Ast. Soc. Cat. Time by Chronometer. Micr. for Plumb-line on Dot. Micr. for Observa- tion of ■ Star. Micr. for Plumb-line on Dot. Mean of Micr. for Plumb-line on Dot. Star's Apparent Zenith Distance. Barom. Therm. 869 h m 5 6 52 33 rev. ptSi 9 32-4 rev* pts. 10 13-6 rev. plB. 9 32-1 rev. pts. 9 32-25 O / rev. pts. + 5 10+0 15-35' 30-215 58°2 915 7 17 58-5 9 13-9 11 11-7 9 13-9 9 13-9 +4 55+1 31-8 1243 10 20 1 8 26-6 9 32-5 8 26-8 8" 26-7 + 3 40+1 5-8 1299 49 23-2 7 32-1 6 25-2 7 31-9 7 32-0 -2 20-1 6-8 1356 11 25 18-7 9 31-5 14 20-2 9, 31-5 9 31-5 + 2 56 +4 22-7 » Advanced the c ainute hand of the chronoi neter 2°". OBSERVATIONS WITH THE SECTOR AT CAPE TOWN, UNREDUCED. 157 June 18th, 1838, Face of Sector East {continued). No. of Ast. Soc. Cat. Time by Chronometer. Micr. for Plumb-line on Dot. Micr. for Observa- tion of Star. Micr. for ?lumb-line on Dot. Mean of Micr. for Plumb-line on Dot. Star's Apparent Zenith Distance. Barom. Therjn. 1378 h m s 11 44 56-5 rev. ptB. 9 7-5 rev. pts. 8 33-1 rev. ptB. 9 7-2 rev. pts. 9 7-35 O / rev. pt*. -1-0 55-0 8-25 in. o 1433 12 19 59-5 8 20-2 11 26-3 8 20-2 8 20-2 -4 15 -f3 6-1 1527 .... 8 27-8 7 1-7 8 27-6 8 27-7 -1 55-1 26-0 1562 13 36 46 9 5-2 3 25-7 9 4-8 9 5-0 + 1 45-5 13-3 30-200 58-2 1579 42 55-5 9 4-8 7 13-8 9 4-8 9 4-8 + 1 45-1 25-0 1604 57 24-6 8 24-0 10 27-9 8 23-8 8 23-9 -1 40+2 4-0 1661 14 34 (1?) 9 15-3 13 2-7 9 15-1 9 15-2 -0 35 +3 21-5 1742 15 13 4 9 23-5 8 1-7 9 23-5 9 23-5 -2 20-1 21-8 1774 29 2 10 13-0 11 33-2 10 12-8 10 12-9 ^-4 40-1-1 20-3 1797 40 57-2 9 23-3 5 18-4 9 23-1 9 23-2 -fO 50-4 4-8 1821 49 38-5 9 15-3 9 5-3 9 15-3 9 15-3 —4 0-0 10-0 1835 56 13 8 30-3 7 12-2 8 30-4 8 30-35 -2 25-1 18-15 1866 . • • • 8 27-1 8 21-2 8 27-1 8 27-1 -t-3 25-0 5-9 1889 16 21 4-5 10 3-4 9 23-5 10 3-4 10 3-4 -0 25-0 13-9 1915 39 57 9 22-0 11 9-4 9 21-8 9 21-9 -0 5-M 21-5 1947 .54 26-7 8 31-3 12 29-2 8 31-5 8 31-4 0-f3 31-8 1969 17 6 48-3 8 27-2 12 17-4 8 27-3 8 27-25 -1-1 25 +3 24-15 2007 22 50-5 10 10-7 13 22-8. 10 10-4 10 10-55 -3 5-1-3 12-25 2043 39 4 10 10-4 13 2-7 10 10-4 10 10-4 -3 5 +2 26-3 30-112 58 2079 55 41-5 10 24-5 11 11-3 10 24-5 10 24-5 + 3 30+0 20-8 2101 18 6 54 10 4-7 5 20-7 10 4-5 10 4-6 -2 50-4 17-9 2110 13 40-2 10 11-7 7 14-4 10 11-5 10 11-6 — 30-2 31-2 2741 48 56-5 10 12-0 14 3-1 10 12-0 10 12-0 + 3 25 +3 25-1 There is a deposit of damp on the inside or lower surface of the object-glass which cannot be removed without unscrewing the glass. It was dispersed for a time by applying my warm hand upon the glass with a warm cloth interposed, but it returned when the glass regained the tem- perature of the room. I am unwilling, as the weather is fine, to risk an alteration in the coUimation by removing the glass. No doubt it arises from the dampness consequent upon so much rain, which has made its way into the tube. 158 VERIFICATION AND EXTENSION OF LA CAILLE S ARC OF MERIDIAN. June 19th, 1838, Face of Sector West. No. of Ast. Soc. Cat. Time by Chronometer. Micr. for Plumb-line on Dot. Micr. for Observa- tion of Star. Micr. for Plumb-line on Dot. Mean of Micr. for Plumb-line on Dot. Star's Apparent Zenith Distance. Barom. Therm. 699 h m s 5 33 49-5 re». pis. 10 0-3 rev. ptB. 9 24-2 rev. pt8. 10 0-3 rev. pts. 10 0-3 O / rev. pt8. -0 15+0 10-1 30-'T20 o 58 732 45 16-8 10 0-2 9 31-3 10 0-0 10 0-1 -1 55 +0 2-8 791 6 14 7-5 9 25-7 9 18-3 9 25-7 9 25-7 + 3 55 +0 7-4 869 52 17-3 9 17-8 10 18'2 9 17-8 9 17-8 + 5 10—1 0-4 903 7 11 26-5 9 26-5 7 15-8 9 26-4 9 26-45 -2 55 +2 10-65 915 17 42-5 9 12'8 8 29-4 9 12-8 9 12'8 +4 55 +0 17-4 957 ■ 39 30-2 10 17-8 10 8-5 10 17-8 10 17-8 -3 40 +0 9-3 1243 8 33-4 9 8'2 8 33-3 8 33-35 + 3 40—0 8-85" 1299 10 49 11-5 9 17-7 12 5-6 9 17-7 9 17-7 -2 20—2 21-9 1356 11 25 3-5 9 31-8 6 24-7 9 31-8 9 31-8 +2 55+3 7-1 1378 45 45-5 10 2-2 11 22-8 10 2-2 10 2-2 + 55-1 20-6 1433 12 19 48 10 5-5 8 13'7 10 5-2 10 5-35 -4 15+1 25-65 1527 13 11 32-5 9 23-2 12 31-8 9 23-3 9 23-25 -1 55-3 8-55 1562 36 32 9 21-3 16 16-3 9 21-1 9 21-2 + 1 45-6 29-1 1579 42 31-5 9 21-1 12 28-4 9 21-0 9 21-05 + 1 45-3 7-35 30-087 58 1604 57 12-5 10 4-4 9 17-4 10 4-2 10 4-3 -1 40 +0 20-9 1661 14 33 48-5 10 5-6 7 .32-2 10 5-6 10 5-6 -0 35 +2 7-4 30-100 59 1742 15 12 52-5 10 15-0 13 17-9 10 15-2 10 15-1 -2 20-3 2-8 1774 28 45-5 9 30-4. 9 24-3 9 30-4 9 30-4 +4 40+0 6-1 1797 .... 10 1-4 15 20-0 10 1-5 10 1-45 + 50-5 18-55'' 1866 .... 11 2-3 12 24-3 11 2-3 11 2-3 + 3 25-1 22-0 30-140 59 1889 16 20 51-5 10 11-2 12 6-7 10 11 1 10 11-15 -0 25-1 29-55 1915 39 42 9 33-7 9 28-5 9 33-6 9 33-65 — 5 +0 5-15"^ 30-142 59 »10=p ast the middle w ire. I" About 15" past the midc le wire. ' The second of transit is uncert ain. Rain came on. Shortly before this day's observations commenced, the quantity of vapour collected on the under surface of the object-glass v?as so great, that obviously the smaller stars could not be seen through it. Therefore it became necessary to remove the object-glass for the purpose of clearing it oflP, and to allow a stream of dry air to pass through the tube. This was accordingly done, and in replacing the glass it vcas screwed in with the same number of turns required in taking it out, and to a point marked on the bra^s previously. It is therefore probable that the coUimation will not be altered. OBSERVATIONS WITH THE SECTOR AT CAPE TOWN, UNREDUCED. 159 June 20th, 1838, Face of Sector East. No. of Ast. Soc. Cat. 699 Time by Chronometer b m s 5 33 50-5 Micr. for Plumb-line on Dot. res. iits. 9 .31-2 Micr. for Observa- tion of Star. rev. pts. 11 21-0 Micr. for Plui nb-line on Dot. rev. 9 Pi». 31-2 Mean of Micr. for Plumb-line on Dot. Star's Apparent Zenith Distance. rev. ptB. 9 31-2 O / rev. pts. -0 15-1-1 23-8 Barom. 30-250 Therm. 59 Cloudy, with occasional showers. June 21st, 1838, Face of Sector East. No. of Ast. Soc. Cat. Time by Clironometer. Micr. for Plumb-line on Dot. Micr. for Observa- tion of Star. • Micr. for Plumb-line on Dot. Mean of Mici-. for Plumb-line on Dot. Star's Apparent Zenith Distance. Barom. Therm. 957 h m s 7 39 21-5 rev. pts. 10 3-6 rev. ptB. 11 27-8 rev. pta. 10 3-4 rev. pts. 10 3-5 O J rev. pts. -3 40 -fl 24-3' 36-430 o 58 1299 10 49 3-5 10 5-4 8 31-4 10 5'4 10 5-4 -2 20-1 8-0 1356 11 24 59 10 4-1 14 27-2 10 4-1 10 4-1 4-2 55 -f 4 23-1 1378 44 40 9 13-9 9 6-5 9 13-9 9 13'9 -4-0 55-0 7-4 1433 12 19 39-5 8 33-1 12 4-3 8 33-1 8 33-1 -4 15+3 5-2 1527 13 11 24-5 9 3-2 7 11-8 9 3-3 9 3-25 — 1 55-1 25-45 1562 36 26 9 3-2 12 22-6 9 3-2 9 3-2 -1-1 40 -f 3 19-4 1579 42 25-5 9 3'2 16 10-3 9 3-1 9 3-15 + 1 40 +7 7-15 1604 57 4-5 9 1-0 11 5-0 9 0-9 9 0-95 _1 40 H- 2 4-05 30-430 58 1661 14 33 41 8 32-6 12 21-3 8 .32-7 8 32-65 -0 35 -f 3 22-65 1742 15 12 43-5 9 1-6 7 14-3 9 1-6 9 1-6 -2 20-1 21-3 1774 28 51-5 9 21-2 11 9-4 9 21-2 9 21-2 +4 40-1-1 22-2 1797 40 37 9 18-1 5 14-6 9 18-2 9 18-15 -1-0 50-4 3-55 1821 49 17-5 9 15-9 9 5-8 9 15-8 9 15-85 -4 0-0 10-05 1835 55 52-5 9 17-8 8 0-3 9 17-6 9 17-7 -2 25—1 17-4 1889 16 20 43-5 .... 10 12-1 10 26-7 .... -0 25-0 14-6 1915 39 36 10 1-3 11 23-4 10 1-1 10 1-2 -0 5-M 22-2 1947 55 5-5 10 2-8 14 0-0 10 2-8 10 2-8 0-h3 31-2 1969 17 6 27-5 9 20-3 13 10-4 9 20-1 9 20-2 -f 1 25 -f- 3 24-2 » Cloudy at the transi t of a ColumbcB. 160 VERIFICATION AND EXTENSION OF LA CAILLE S ARC OF MERIDIAN. June 21st, 1838, Face of Sector East (continued). No. of Ast. Soc. Cat. Time by Chronometer. Micr. for Plumb-line on Dot. Micr. for Observa- tion of Star. Micr. for Plumb-line on Dot. Mean of Micr. for Plumb-line on Dot. Star's Apparent Zenith Distance. Barom. Therm. 2007 h m s 17 22 30-5 rev. ptB. 9 6-0 rev. pta. 12 18-5 rev. pts. 9 6-0 rev. pts. 9 6-0 O / rev. ptB. -3 5 -t-3 12-5 in. o 2043 38 43-7 9 6-0 11 33-2 9 6-0 9 6-0 -3 5 +2 27-2 2079 55 21 9 3-3 9 25-0 9 3-4 9 3-35 + 3 30-1-0 21-65 2101 18 6 33 9 0-0 4 16-8 8 33-5 8 33-75 -2 50-4 16-95 30-430 57-6 2110 13 10 9 19-8 6 22-6 9 19-8 9 19-8 -0 30-2 31-2 2741 22 48 35-5 9 33-0 13 24-6 9 33-0 9 33-0 + 3 25 -f 3 25-6 30-400 56-6 The past has been a good observing night. June 22nd, 1838, Face of Sector West. No. of Ast. Soc. Cat. Time by Chronometer. Micr. for Plumb-line on Dot. Micr. for Observa- tion of Star. Micr. for Plumb-line on Dot. Mean of Micr. for Plumb-line on Dot. Star's Apparent Zenith Distance. Barom. Therm. 732 h m 8 rev. pts. 10 20-3 rev. pts. 10 16-3 rev. pts. 10 20-2 rev. pts. 10 20-25 O / rev. pts. -1 55 -fO 3-95 30-400 o 57 791 .... 10 4-7 9 30-0 10 4-8 10 4-75 + 3 55 -f 8-75 848 6 43 27-5 9 28-9 9 7-2 9 28-9 9 28-9 -f 1 35 4-0 21-7 30-400 57-5 869 51 55-2 9 22-2 10 22-3 9 22-4 9 22-3 -f5 10-1 0-0" 903 .... 10 15-6 8 5-2 10 15-6 10 15-6 -2 55 +2 10-4 915 7 17 14 10 19-6 10 0-7 10 19-6 10 19-6 +4 55+0 18-9" 957 39 12 10 31-4 10 20-1 10 31-4 10 31-4 -3 40-f-O 11-3 1061 8 33 25 10 20-7 9 20-3 10 20-7 10 20-7 -0 50+1 0-4 1299 .... 10 27-7 13 15-2 10 27-5 10 27-6 -2 20 -2 21-6"= 1356 11 24 39-5 10 17-3 7 9-2 10 17-3 10 17-3 +2 55+3 8-1 1378 44 22-5 11 3-3 12 23-3 11 3-0 11 3-15 + 55—1 20-15 30-350 58 1433 12 19 29-5 10 2-7 8 12-6 10 3-5 10 3-1 -4 15+1 24-5 1562 .... 9 12-8 7 10-2 9 12-8 9 12-8 + 1 40+2 2-6 1579 13 42 8 9 12-8 3 22-6 9 12-8 9 12-8 + 1 40+5 24-2 » Before this transit moved the s eotor easterly a small quantity. "> After his transit r noved the se Btor in azimuth to the former position. ■^ This 8 ar was not c etected unti 1 near leaving the field, but the observation is good. OBSERVATIONS WITH THE SECTOR AT CAPE TOWN, UNREDUCED. 161 June 22nd, 1838, Face of Sector West {continued). No. of Ast. Soo. Cat. Time by Chronometer. Micr. for Plumb-line on Dot. Micr. for Observa- tion of Star. Micr. for Plumb-line on Dot. Mean of Mior. for Plumb-line on Dot. Star's Apparent Zenith Distance. Barom. Therm. 1604 h m 9 13 56 51-5 rev. pts. 9 14-8 rev. pt3. 8 27-4 rev. pts. 9 J 4-7 rev. ptfl. 9 14-75 O / rev. ptB- -1 40-1-0 21-35 In. 1661 14 33 36-2 9 13-0 7 5-0 9 12-6 9 12-8 -0 35-1-2 7-8 1742 15 12 31-2 9 15-7 12 18-1 9 15-8 9 15-75 -2 20-3 2-35 1774 28 19-2 9 7-2 9 1-0 9 7-4 9 7-3 +4 40-1-0 6-3 1797 40 20 9 15-7 14 33-0 9 15-7 9 15-7 + 50-5 17-3 1835 55 40-5 9 29-7 12 29-0 9 29-7 9 29-7 -2 25—2 33-3" 1889 16 20 29-5 9 21-5 11 18-5 9 21-7 9 21-6 -0 25—1 30-9 1915 .... 9 20-9 9 16-3 9 20-9 9 20-9 -0 5-1-0 4-6 30-353 56 1969 17 6 10-5 7 11-3 5 2-3 7 11-0 7 11-15 -i-1 25 -(-2 8-85 2007 22 19-5 7 23-0 5 25-7 7 23-1 7 23-05 -3 5 -1-1 31-35° 2043 38 32 7 23-1 6 12-2 7 23-0 7 23-05 -3 5-fl 10-85? 2079 55 0'5 8 3-0 8 33-4 8 3-4 8 3-2 4-3 30-0 30-2 2101 18 6 21-5 9 0-4 15 0-1 9 0-4 9 0-4 -2 50 -6 33-7 2110 13 5 9 2-7 13 15-4 9 3-2 9 2-95 -0 30-4 12-45 30-350 56-2 2741 22 48 15-2 8 26-2 6 15-4 8 26-1 8 26-15 4-2 25 -1-2 10-75 I" Vapour is again depos ted on the lower surface of the object-glass. « Opened t lie hole in the tube occu] ied by the r sflector, to let in air. ' Faint. Several stars this night were barely visible, and some were lost, from the quantity of aqueous vapour on the under surface of the object-glass. The opening in the roof of the building is close to the object-glass, and the entrance door is kept open to equalise the temperature, yet the quantity of vapour does not diminish. 162 VERIFICATION AND EXTENSION OF LA CAILLE S ARC OF MERIDIAN. June SSrd, 1838, Face of Sector East. No. of Ast. Soc. Cat. Time by Chronometer. Micr. for Plumb-line on Dot. Micr. for Observa- tion of Star. Micr. for Plumb-line on Dot. Mean of Micr. for Plumb-line on Dot. Star's Apparent Zenith Distance. Barom. Therm. 699 h m s rev. pts. 9 IM rev. Jits. 11 2-8 rev. pts. 9 11-1 rev. pts. 9 IM O / rev. pts. -0 15+1 25-7» in. o 732 5 44 51-5 9 15-3 10 33-5 9 15-4 9 1.5-35 -1 55-i-l 18-15 30-335 56-6 791 6 13 46 10 17-7 12 5-3 10 17-3 10 17-5 + 3 55+1 21-8 848 43 26 10 17-0 12 19-1 10 17-2 10 17'1 + 1 35+2 2-0 869 51 56-5 10 17-0 10 31-0 10 16-8 10 16-9 + 5 10 +0 14-1 903 7 11 1 10 0-3 13 26'0 10 0-3 10 0-3 -2 55+3 25-7 915 10 23-6 12 22-2 10 23-7 10 23'65 + 4 55+1 32-55'' 957 39 4 9 21-2 11 11-4 9 21-1 9 21-15 -3 40+1 24-25 1243 10 19 23 9 33-1 11 4-3 9 33-1 9 33-1 +3 40+1 5-2 1299 48 45-8 9 14-4 8 7-4 9 14-4 9 14-4 -^2 20—1 7-0 1356 11 24 40-5 9 26-3 14 13-5 9 26-2 9 26-25 +2 55+4 21-25 1378 44 21-5 9 21-7 9 13-8 9 21-7 9 21-7 + 55-0 7-9'= 1433 12 19 22 9 10-7 12 15-4 9 10-7 9 10-7 _4 15+3 4-7 1527 13 11 6-5 8 18-6 6 24-8 8 18-5 8 18-55 -1 55-1 27-75 1562 36 7-5 8 29-8 3 14-5 8 29-8 8 29-8 + 1 45-5 15-3 1579 42 7 8 29-8 7 3-0 8 29-7 8 29-75 + 1 45—1 26-75 1604 56 46'5 8 9-7 10 12-1 8 9-7 8 9-7 -1 40+2 2-4 30-315 56-1 1661 14 33 22-5 8 8-4 11 29-7 8 8-5 8 8-45 -0 35+3 21-25 1742 15 12 25 8 24-2 7 1-2 8 24-2 8 24-2 —2 20-1 23-0* ' 1774 28 22-5 8 32-8 10 19-7 8 32-8 8 32-8 + 4 40-1 20-9 1797 40 18 9 3-2 4 33-0 9 3-4 9 3-3 + 50-4 4-3 1821 48 59 9 5-5 8 28-8 9 5-3 9 5-4 —4 0-0 10-6 1835 55 33-5 8 32-4 7 13-9 8 32-4 8 32-4 —2 25—1 18-5 1889 16 20 25-5 9 25-5 9 10-3 9 25-5 9 25-5 -0 25-0 15-2 1915 39 17-5 9 26-2 11 13-3 9 26-2 9 26-2 -0 5+1 21-1 1969 17 6 9-5 10 0-8 13 24-6 10 1-0 10 0-9 + 1 25 +3 23-7 2007 22 12 9 9-8 12 22-3 9 9-8 9 9-8 -3 5+3 12-5 = Fa nt ; obliged to r emove the ol ject-glass. '> 15' past the middle wire. 'Mc ved the sector a [ittle in azin mth, eastwa rd. Vapour is becoming deposited on the object-glass. OBSERVATIONS WITH THE SECTOR AT CAPE TOWN, UNREDUCED. 163 June 23rd, 1838, Face or Sector East (continued). No. of Ast. Soc. Gat. Time by Chronometer, Micr. for Plumb-line on Dot. Micr. for Observa- tion of Star. Micr. for Plumb-line on Dot. Mean of Micr. for Plumb-line on Dot, Star's Apparent Zenith Distance. Barom. Therm. 2043 h m s 17 38 25 rev. pts. 9 9-8 rev. pts. 12 1-4 rev. pts. 9 9-8 rev. pts. 9 9-8 O- / rev. ptB. -3 5 +2 25-6, in. o 2079 55 2-5 10 1-8 10 23-8 10 2-4 10 2-1 + 3 30+0 21-7 2101 18 6 15 8 7-8 3 23-5 8 8-0 8 7-9 -2 50—4 18-4 2110 13 1-5 8 16-3 5 18-4 8 16-4 8 16-35 -0 30-2 31-95 30-330 56 2741 22 48 15-5 8 29-7 12 19-7 8 29-7 8 29-7 -f3 25 +3 24-0 It became absolutely necessary to remove the object-glass immediately after the transit of a Columbce, from the dense collection of vapour settled on its under surface. It was restored in the same manner and with the precautions adopted on Tuesday the 19th. June 24th, 1838, Face of Sector West. No. of Ast. Soc. Cat. Time by Chronometer. Micr. for Plumb-line on Dot. Micr. for Observa- tion of Star. Micr. for Plumb-line on Dot. Mean of Micr. for Plumb-line on Dot. Star's Apparent Zenith Distance. Barom. Therm. 699 h m s rev. pts. 8 8-8 rev. pts. 7 31-2 rev, pts. 8 8-6 rev. pts. 8 8-7 O / rev. pts. —0 15 +0 11-5 3d°332 56° 2 732 5 44 36-5 8 26-3 8 21-5 8 26-1 8 26-2 -1 55 -fO 4-7 791 6 13 22-5 8 14-4 8 5-1 8 14-3 8 14-35 + 3 55 +0 9-25 848 43 6 8 20-3 7 31-1 8 20-0 8 20-15 + 1 35+0 2305 869 51 31-5 8 16-4 9 14-3 8 16-3 8 16-35 + 5 10-0 31-95 903 • • ■ ■ 8 27-8 6 14-7 8 27-6 8 27-7 -2 55+2 13-0 915 7 16 56-5 8 24-8 8 5-8 8 24-8 8 24-8 + 4 55+0 19-0 957 38 51 9 10-1 8 31-7 9 9-8 9 9-95 -3 40+0 12-25 1061 8 33 5 9 10-3 8 8-8 9 10-3 9 10-3 -0 50+1 1-5^ 1243 • ■ > • 8 28-7 9 2-7 8 28-7 8 28-7 + 3 40-0 8-0- 30-320 57-5 1356 11 24 19-5 8 32-8 5 24-7 8 32-8 8 32-8 +2 55+3 8-1 1378 44 3 9 6-2 10 26-7 9 6-4 9 6-3 + 55-1 20-4 1433 12 19 9-5 9 19-8 7 28-4 9 19-9 9 19-85 —4 15+1 25-45 30-320 57-5 » Very fa mt. 164 VERIFICATION AND EXTENSION OF LA CAILLE S ARC OF MERIDIAN. June 24th, 1838, Face of Sector West (continued). No. of Ast. Soc. Cat. Time by Chronometer. Micr. for Plumb-line on Dot. Micr. for Observa. tion of Star. Micr. for Plumb'line on Dot. Mean of Micr. for Plumb-line on Dot. Star's Apparent Zenith Distance. Barom. Therm. 1527 h m s 13 10 51-5 rev. pts. 9 16-3 rev. ' pts. 12 24-8 rev. pts. 9 16-3 rev. pts. 9 16-3 O 1 rev. pts. -1 55-3 8-5 In. o 1562 35 48-5 8 32-6 15 27-1 8 32-6 8 32-6 -f 1 45-6 28-5 1579 41 48-2 8 32-6 12 4-7 8 32-6 8 32-6 + 1 45-3 6-1 1604 56 36 9 7-1 8 19-7 9 7-3 9 7-2 -1 40+0 21-5 1661 14 33 6-5 9 7-'6 6 33-9 9 7-6 9 7-6 —0 35+2 7-7 1742 15 12 11-5 9 8-7 12 10-6 9 8-6 9 8-65 -2 20 -3 1-95 1774 28 9 5-5 8 32-4 9 5-4 9 5-45 +4 40 +0 7-05 1797 40 0-5 8 33-4 14 17-2 8 33-4 8 33-4 + 50-5 17-8 1821 48 47-5 9 21-3 11 11-2 9 21-3 9 21-3 -4 0-1 23-9 1835 55 20-2 9 23-1 12 2M 9 23-0 9 23-05 -2 25 -2 32-05 30-320 57 1866 16 8 36 9 8-7 10 29-4 9 8-6 9 8-65 + 3 25-1 20-75 1889 20 9-5 9 12-3 11 7-2 9 12-3 9 12-3 — 25—1 28-9" 1915 39 1-5 9 10-7 9 4-2 9 10-6 9 10-65 -0 5 +0 6-45 1947 53 30-5 9 9-3 6 28-4 9 9-3 9 9-3 0+2 14-9 1969 17 5 51 9 5-7 6 29-8 9 5-6 9 5-65 + 1 25+2 9-85 2007 21 59-5 9 23-0 7 25-0 9 22-9 9 22-95 -3 5+1 31-95 2043 38 12-5 9 22-9 8 10-5 9 22-9 9 22-9 -3 5+1 12-4 2079 54 41-5 9 14-8 10 8-5 9 14-9 9 14-85 + 3 30-0 27-65 2101 18 6 2 9 29-2 15 28-3 9 29-2 9 29-2 -2 50-5 33-1 2110 12 45-5 9 27-1 14 4-7 9 27-1 9 27-1 -0 30-4 11-6 30-320 57 <> Beautiful. A fine observing night ; the stars very steady ; no vapour on the object-glass. Although a Columba (No. 699) transits before noon, it is entered a day later for convenience of arrangement. OBSERVATIONS WITH THE SECTOR AT CAPE TOWN, UNREDUCED. 165 June 25th, 1838, Face of Sector East. No. of . Ast. Soc. Cat. Time by Chronometer. Micr. for !>lumb-line on Dot. Micr. for Observa- tion of Star. Micr. for Plumb-line on Dot. niean of Micr. for Plumb-line on Dot. Star's Apparent Zenith Distance. Barom. Therm. 699 h m s 5 33 5-5 rev. ptB. 9 16-6 rev. pti. 11 7-4 rev. pts. 9 16-6 rev. pts. 9 16-6 O / rev. pta. -0 15+1 24-8" 30-'320 59° 732 44 12-5 .... 10 29-1 9 9-3 .... -1 55-t-l 19-8 848 6 43 7 9 5-7 11 8-3 9 5-7 9 5-7 + 1 35+2 2-6 869 51 38-5 9 7-2 9 22-7 9 7-2 9 7-2 + 5 10 -1-0 15-5 30-300 61 . 903 7 10 41 9 5-6 12 32-3 9 5-7 9 5-65 -2 55+3 26-65 915 17 2-5 9 24-7 11 23-5 9 24-7 9 24-7 + 4 55+1 32-8" 1061 8 33 2-5 9 8-4 11 2M 9 8-4 9 8-4 -0 50 +2 12-7 1243 10 19 5-5 9 19-5 10 25-6 9 19-7 9 19-6 + 3 40+1 6-0 1356 11 24 21or23 9 24-6 14 13-3 9 24-5 9 24-55 + 2 55 +4 22-75 1378 44 3 9 25-7 9 18-4 9 25-7 9 25-7 + 55-0 7-3 1433 12 19 2 9 21-7 12 27-2 9 21-8 9 21-75 -4 15+3 5-45 1527 13 10 47-5 9 28-5 8 1-5 9 28-5 9 28-5 -1 55-1 27-0 30-287 60 1562 35 49-5 10 2-1 4 22-0 10 2-0 10 2-05 + 1 45-5 14-05 1579 41 49-5 10 2-0 8 9'6 10 1-9 10 1-95 + 1 45-1 26-35 1604 56 27-5 9 1-0 11 3-8 9 1-1 9 1-05 -1 40+2 2-75 1661 14 33 4-5 9 18-5 13 5-5 9 18-7 9 18-6 -0 35+3 20-9 1742 • • > • 9 12-2 7 24-1 9 12-0 9 121 -2 20-1 22-0 1774, 15 28 55 9 25-8 11 12-1 9 25-8 9 25-8 + 4 40+1 20-3 1821 48 40-5 8 26-7 8 16-4 8 26-7 8 26-7 _4 0-0 10-3 1835 54 15-5 .... 7 13-3 8 31-2 .... -2 25-1 17-9 1866 16 8 39-5 9 25-0 9 17-4 9 25-0 9 25-0 + 3 25-0 7-6 1889 20 7 9 33-8 9 17-2 9 33-8 9 33-8 -0 25—0 16-6 1915 38 59-5 9 23-0 11 9-2 9 23-2 9 23-1 -0 5+1 20-1 1947 53 29 9 22-3 13 17-8 9 22-3 9 22-3 0+3 29-5 1969 17 5 51 9 26-7 13 15-2 9 26-7 9 26-7 + 1 25+3 22-5 2007 21 53 9 31-7 13 8-4 9 31-7 9 31-7 -3 5+3 10-7 2043 38 6-5 9 31-7 12 22-7 9 31-8 9 31-75 -3 5 +2 24-95 2079 54 45 10 2-7 10 22-9 10 2-6 10 2-65 + 3 30+0 20-25 2101 18 5 56-5 9 26-1 5 5-5 9 26-1 9 26-1 -2 50-4 20-6 2110 12 43 9 24-2 6 24-3 9 24-0 9 24-1 -0 30-2 33-8 30-265 59 > South-east end. '' No. 957 1 nust have esc iped unseen behind the wire. 166 VERIFICATION AND EXTENSION OF LA CAILLE S ARC OF MERIDIAN. June 26th, 1838, Face of Sector West. No. of Ast.Soc. Cat. Time by Chronometer. Micr. for Plumb-line on Dot. Micr. for Observa- tion of Star. Micr. for Plumb-line on Dot. Mean of Micr. for Plumb-line on Dot. Star's Apparent Zenith Distance. Barom. Therm. 699 h m B 5 32 52-5 rev. pt8. 9 7-7 rev. pta. 8 29-8 rev. pta. 9 7-7 xev. pta. 9 7-7 / «V. plB. -0 15+0 11-9 30-'238 59° 733 44 21 9 9-1 9 3-2 9 9-2 9 9-15 -1 55+0 5-95 791 6 13 8 9 7-8 8 32-3 9 7-6 9 7-7 + 3 55 +0 9-4 869 51 17 8 32-7 9 30-4 8 32-8 8 32-75 +5 10-0 31-65 903 .... ■9 24-8 7 11-7 9 24-8 9 24-8 -2 55+2 13-1 915 7 16 42-5 9 15-3 8 28-7 9 15-5 9 15-4 +4 55+0 20-7 = 1061 8 32 50-5 10 4-2 9 1-4 10 4-2 10 4-2 -0 50 +1 2-8 30-230 60 1243 .... 9 25-3 9 32-2 9 25-3 9 25-3 + 3 40—0 6-9'' 1299 10 48 16-5 10 8-2 12 27-9 10 8-1 10 8-15 -2 20-2 19-75 1356 11 24 5-5 9 24-2 6 15-1 9 24-2 9 24-2 + 2 55+3 9-1 1378 43 48-5 9 12-8 10 31-2 9 12-8 9 12-8 +0 55-1 18-4 1433 12 18 54 9 29-7 8 3-5 9 29'8 9 29-75 -4 15+1 26-25 1527 13 10 37 9 30-0 13 3-8 9 30-0 9 30-0 — 1 55—3 7-8 1562 35 34 9 10-3 16 3-4 9 10-3 9 10-3 + 1 45-6 27-1 1579 41 33-5 9 10-3 12 15-6 9 10-3 9 10-3 + 1 45-3 5-3 1604 56 16-5 9 21-0 9 32-3 9 21-0 9 21-0 -1 40-0 11-3' 1661 14 32 52 9 20-1 7 11-4 9 20-1 9 26-1 — 35+2 8-7 1742 15 11 56-5 9 12-6 12 14-5 9 12-7 ' 9 12-65 -2 20-3 1-85 1797 39 45-5 9 2-0 14 18-3 9 2-1 9 2-05 + 50—5 16-25 1821 48 32-5 9 25-2 11 15-6 9 24-8 9 25-0 —4 0-1 24-6 1835 55 5 9 20-7 12 19-2 9 20-5 9 20-6 —2 25—2 32-6 1866 16 8 21-5 9 0-3 10 19-7 9 0-3 9 0-3 + 3 25-1 19-4 1889 19 54 9 6-0 11 0-7 9 6-5 9 6-25 -0 25—1 28-45 1915 38 46-5 9 9-3 9 3-2 9 9-3 9 9-3 — 5+0 6-1 1969 17 6(5?) 36-5 10 0-0 7 22-6 10 0-0 10 0-0 + 1 25 +2 11-4 30-230 59 2007 21 44-5 10 28-6 8 31-3 10 28-7 10 28-65 -3 5+1 31-35 2043 37 57 10 28-7 9 16-6 10 28-7 10 28-7 —3 5+1 12-1 2079 54 27 10 7-8 11 0-8 10 7-8 10 7-8 + 3 30-0 27-0 2101 18 5 47 10 25-3 16 24-4 10 25-3 10 25-3 -2 50-6 33-1 2110 12 30-5 10 26-1 15 3-5 10 26-1 10 26-1 — 30—4 11-4 ° Flickering images. "• Very faint. " An error committed in the reading for the star ; mo St probably the micrometer for the star was 8'" 32P'»-3, and the zenith distance —1° 40' +22i"»-7; the reading being ' near Zero, the revolution next to coincidence catches the eye. A beautiful observing night ; the stars surrounded by rings ; the centre of the image a small orange nucleus. OBSERVATIONS WITH THE SECTOR AT CAPE TOWN, UNREDUCED. 167 June 27th, 1838, Face of Sector East. No. of Ast. Soc. Cat. 869 957 1243 1299 1356 1378 1433 1527 1579 1604 1661 1774 1797 1821 1835 1866 1889 1915 1947 1969 2007 2043 2079 2101 2110 Time by Chronometer. Micr. for Plumb-line on Dot. 6 51 24-5 10 18 48 11 24 6-5 43 47-5 13 10 33 41 33-5 56 13 14 32 50 15 27 48-5 39 44-5 48 26 55 1 16 8 23 19 51-5 38 45 53 13-5 17 5 35-5 21 38 37 51 54 28 8 5 40-5 . 12 27-5 rcT. pts. 10 29-5 10 28-7 9 14-6 9 26-3 9 27-5 9 8-4 8 27-8 9 3-8 9 8-4 9 20-3 10 8-6 10 11-8 10 32-4 10 16-5 10 26-2 10 25-0 10 20-8 10 13-7 10 12-8 9 23-8 9 23-8 10 4-3 9 12-0 9 15-0 Micr. for Observa- tion of Star. Micr. for Plumb-line on Dot. rev. pts. 10 30-0 12 23-8 12 0-7 8 8-7 14 13-7 9 19-7 12 13'3 6 33-7 7 11-1 II 9-8 13 5-7 11 28-4 6 6-7 10 21-1 8 31-8 10 18-8 10 7-5 12 7-3 14 9-0 14 1-6 12 33-5 12 14-5 10 24-7 4 25-8 6 14-8 rev. pts. 10 29-5 10 32-5 10 28-8 9 14-4 9 26-4 9 27-4 9 8-0 8 27-8 9 3-6 9 8-3 9 20-3 10 8-6 10 11-8 10 32-5^ 10 16-3 10 26-4 10 24-6 10 20-8 10 13-7 10 12-8 9 23-8 9 23-7 10 4-5 9 11-8 9 14-8 Mean of Micr. for Plumb-line on Dot. Star's Apparent Zenith Distance. Barom. rev. pts. 10 29-5 10 28-75 9 14-5 9 26-35 9 27-45 9 8-2 8 27-8 9 3-7 9 8-35 9 20-3 10 8-6 10 11-8 10 32-45 10 16-4 10 26-3 10 24-8 10 20-8 10 13-7 10 12-8 9 23-8 9 23-75 10 4-4 9 11-9 9 14-9 O / rev. ptB. +5 10+0 0-5» -3 40-fl 25-3'> + 3 40-t-l 5-95 —2 20-1 5-8" + 2 55-i-4 21-35 + 55-0 7-75 -4 15+3 5-1 -1 55—1 28-1 + 1 45-1 26-6 — 1 40 +2 1-45 — 35+3 19-4 +4 40+1 19-8 +0 50-4 5-1 _4 0-0 11-35 —2 25—1 18-6 + 3 25-0 7-5 -0 25-0 17-3 -0 5+1 20-5" -0 0+3 29-3 + 1 25+3 22-8' — 3 5+3 9-7 -3 5+2 24-75 + 3 30 +0 20-3 —2 50-4 20-1 -0 30—3 0-1 30-146 Therm. 61 30-145 30-145 60-8 60-1 30-080 60 1 There must be some error in reading off the micrometer for the star. t The sector axis has been deranged since last night. '" 12' past tlie middle wire. d The stars are flickering and difficult to bisect ; south wind. ' The wind is south. A change took place in the verticality of the sector since last night: adjusted it. The plummet was sluggish : I introduced clean water ; then re-examined the adjustments. 168 VERIFICATION AND EXTENSION OF LA CAILLE S ARC OF MERIDIAN. June 28th, 1838, Face of Sector East. Examination for Runs. Arch to the Left. Arch to the Left. Arch to the Left. / rev. pts. rev. ptB. O / rev. ptB. rev. pti. 1 rev. ptB. rev. Jits. , 10 4 10-4 17 28-0 50 4 9-4 17 29-0 1 20 4 9-2 17 29-2 22 4-4 17 28-2 40 22 4-4 17 29-6 1 10 22 4-4 17 29-0 10 4 10-2 17 28-2 50 .4 8-8 17 29-0 1 20 4 9-4 17 28-9 22 4-4 17 28-1 40 22 3-8 17 28-4 1 10 22 4-3 17 29-0 10 4 10-3 17 28-2 50 4 9-4 17 28-1 1 20 4 9-3 17 29-0 22 4-5 40 22 3-5 1 10 22 4-3 Mean = 17 28-14 1 Mean = 4 12-3 17 28-82 17 29-1 Mean = 17 29-02 20 4 10-8 17 28-9 50 22 7-4 17 29-0 1 20 22 8-3 17 28-9 10 22 5-7 17 29-0 1 4 12-4 17 28-8 1 30 4 13-4 17 28-6 20 4 10-7 17 28-9 50 22 7-2 17 28-9 1 20 22 8-0 17 28-6 10 22 5-6 17 28-9 1 4 12-3 17 28-7 1 30 4 13-4 17 28-4 20 4 10-7 17 28-9 50 22 7-0 1 20 22 7-8 17 28-6 10 22 5-6 Mean = 17 28-90 1 30 4 13-2 Mean = 17 28-92 1 22 ^-5 Mean = 17 28-62 17 28-7 1 10 4 10-8 30 20 30 20 4 10-4 22 4-7 4 10-3 22 4-7 17 28-3 17 28-4 17 28-4 17 28-3 1 1 10 1 1 10 22 5-4 4 9-4 22 4-8 4 8-4 17 28-6 17 30-0 17 29-4 17 30-4 1.30 1 40 1 30 1 40 22 2-3 4 7-2 22 2-3 4 7-3 17 29-1 17 29-1 17 29-0 17 28-8 30 4 10-4 17 28-2 Mean = 17 29-42 1 30 22 2-1 17 28-9 20 22 4-6 The last repeated the bob- after clean- 1 40 4 7-2 Mean = 17 28-32 ing out cistern and Mean = 17 28-98 introdu cing clean water. 40 4 10-4 17 28-8 1 10 22 6-8 17 29-5 1 40 22 9-0 17 29-3 30 22 5-2 17 29-0 1 4 11-3 17 29-5 1 50 4 13-7 17 29-4 40 4 10-2 17 29-1 1 10 22 6-8 17 29-1 , 1 40 22 9-1 17 28-9 30 22 5-3 17 29-0 1 4 11-7 17 28-9 1 50 4 14-2 17 29-0 40 4 10-3 17 28-8 1 10 22 6-6 17 29-1 1 40 22 9-2 17 29-0 30 22 5-1 1 4 11-5 1 50 4 14-2 Mean = 17 28-94 Mean = 17 29-22 Mean = 17 29-12 OBSERVATIONS WITH THE SECTOR AT CAPE TOWN, UNREDUCED. Examination for Runs {continued). 169 Arch to the Left. Arch to the Right. Arch to the Right. / rev. pts. rev. pu. C5 / rev. pts. rev. ptB. / rev, pts. rev. ptB. 1 50 22 2-1 17 28-6 5 10 23 3-4 17 28-2 2 22 2-7 17 29-0 2 4 7-5 17 28-8 5 5 9-2 17 28-2 1 50 4 7-7 17 29-0 1 50 22 2-3 17 29-0 5 10 23 3-4 17 28-4 2 22 2-7 17 29-0 2 4 7-3 17 28-2 5 5 9-0 17 28-4 1 50 4 7-7 17 29-0 1 50 22 1-5 17 28-2 5 10 23 3-4 17 28-4 2 22 2-7 17 29-1 2 4 7-3 5 5 9-0 1 50 4 7-6 Mean = 17 28-56 Mean = 17 28-32 Mean = 17 29-02 3 20 4 10-9 Repeated. 3 10 22 6-0 17 29-1 17 29-1 5 5 10 3 33-7 21 28-7 17 29-0 10 21 31-7 17 29-8 3 20 4 10-9 17 28-8 5 3 33-4 17 29-3 4 1-9 17 29-4 3 10 22 5-7 17 28-7 5 10 21 28-3 17 28-9 10 21 31-3 17 29-6 3 20 4 11-0 17 28-7 'i .T 1.T-8 17 28-5 4 1-7 17 29-4 3 10 22 5-7 t^ V o oo o 17 28-5 10 21 31-1 Mean = 17 28-88 5 10 21 28-3 Mean = 17 28-84 4 1-6 Mean = 17 29-6 17 29-56 5 22 9-3 17 28-7 3 20 22 6-3 5 10 5 5 10 5 5 10 4 14-6 22 9-4 4 14-7 22 9-5 4 14-8 17 28-8 17 28-7 17 28-8 17 28-7 3 10 3 20 3 10 3 20 3 10 4 10-8 22 6-3 4 11-0 22 6-2 4 10-9 17 29-5 17 29-5 17 29-3 17 29-2 17 29-3 Mean = 17 28-74 Mean = 17 29-36 The mean of 1 he whole = l'? 28*885 for 10' of the Arch. .•. 1 rev = Sil=33"-6143oftheArch. This value is almost identical with the value obtained at Klyp Fonieyn. Throughout th e examination the thermometer stood at 61°. 170 VERIFICATION AND EXTENSION OF LA CAILLE's ARC OF MERIDIAN. Table for Converting the Micrometer Readings info Minutes and Seconds of the Arch. Pts. Qrev. l«v. orev. 3«v. 4«»- 5"'- grev. ft ' 33-614 / 7'-229 1 40-843 2' 14"457 2 48-072 3 2l'-'686 1 0-989 34-603 8-217 41-832 2 15-446 2 49-060 3 22-674 2 1-977 35-592 9-206 42-820 2 16-435 2 50-049 3 23-663 3 2-966 36-580 10-195 43-809 2 17-423 2 51-037 3 24-652 4 3-955 37-569 11-183 44-798 2 18-412 2 52-026 3 25-640 5 4-943 38-558 12-172 45-786 2 19-401 2 53-015 3 26-629 6 5-932 39-546 13-161 46-775 2 20-389 2 54-003 3 27-618 7 6-921 40-535 14-149 47-764 2 21-378 2 54-992 3 28-606 8 7-909 41-524 15-138 48-752 2 22-366 2 55-981 3 29-595 9 8-898 42-512 16-126 49-741 2 23-355 2 56-969 3 30-584 10 9-887 43-501 17-115 50-730 2 24-344 2 57-958 3 31-572 11 10-875 44-490 18-104 51-718 2 25-332 2 58-947 3 32-561 12 11-864 45-478 19-092 52-707 2 26-321 2 59-935 3 33-550 13 12-853 46-467 20-081 53-695 2 27-310 3 0-924 3 34-538 14 13-841 47-456 21-070 54-684 2 28-298 3 1-913 3 35-527 15 14-830 48-444 22-058 55-673 2 29-287 3 2-901 3 36-516 16 15-818 49-433 23-047 56-661 2 30-276 3 3-890 3 37-504 17 16-807 50-421 24-036 57-650 2 31-264 3 4-879 3 38-493 18 17-796 51-410 25-024 1 58-639 2 32-253 3 5-867 3 39-482 19 18-784 52-399 26-013 59-627 2 33-242 3 6-856 3 40-470 20 19-773 53-387 27-002 2 0-616 2 34-230 3 7-845- 3 41-459 21 20-762 54-376 27-990 2 1-605 2 35-219 3 8-833 3 42-448 i22 21-750 55-365 28-979 2 2-593 2 36-208 3 9-822 3 43-436 ■ 23 22-739 56-353 29-968 2 3-582 2 37-196 3 10-811 3 44-425 24 23-728 57-342 30-956 2 4-571 2 38-185 3 11-799 3 45-413 .25 24-716 58-331 31-945 2 5-559 2 39-174 3 12-788 3 46-402 .26 ■25-705 59-319 32-934 2 6-548 2 40-162 .3 13-777 3 47-391 ;27 26-694 1 0-308 33-922 2 7-537 2 41-151 3 14-765 3 48-379 28 27-682 1 1-297 34-911 2 8-525 2 42-140 3 15-754 3 49-368 '29 28-671 1 2-285 35-900 2 9-514 2 43-128 3 16-742 3 50-357 i30 29-660 I 3-274 36-888 2 10-503 2 44-117 3 17-731 3 51-345 31 30-648 1 4-263 37-877 2 11-491 2 45-105 3 18-720 3 52-334 32 31-637 1 5-251 38-866 2 12-480 "2 46-094 3 19-708 3 53-323 33 32-626 1 6-240 39-854 2 13-469 2 47-083 3 20-697 3 54-311 34 33-614 1 7-229 40-843 2 14-457 2 48-072 3 21-686 3 55-300 MEAN ZENITH DISTANCES OF STARS OBSERVED AT KLYP FONTEFN. 171 § 12. Collection of all the Results of Observation of each Star at Klyp FONTEYN, AND DEDUCTION OF MeAN ZeNITH DISTANCE, 1838, JANUARY 0. Note. — The Reduction for Azimuthal Error is always to be applied subtractively to the Zenith Distance. The Refraction is always to be applied additively. The Precession, Aber- ration, and Nutation, have the sign which is proper for reducing the Apparent South Polar Distance of the Star to its Mean South Polar Distance, 1838, Jan. 0; and therefore are to be applied with the sign given in the Table when the star is North of the Zenith, and with the opposite sign when the star is South of the Zenith. The numbers included in parentheses in the column " Mean Zenith Distance, 1838, Jan. 0," are omitted in taking the mean. Where an asterisk is affixed to the Day of observation it denotes that there is some circumstance affecting the value of the observation for which it will be necessary to refer to the section of Unreduced Observations. 172 VERIFICATION AND EXTENSION OF LA CAILLE S ARC OF MERIDIAN. Star's No. in Ast. Soc. Cat., Name, Face of Sector E AST. Day of Observa- tion, 1838. Apparent Reduction Precession, Resulting Mean Zenith Distance, and Position with regard to the Zenith. Zenith Distance from unreduced Observation. for Azimuthal Error. Refraction. Aberration, and Nutation. 1838, Jan. 0, and Mean of separate Re- sults uncorrected for Error of CoUimation. A. S. C. 699, April 5 o / // 1 27 21-96 0-47 // 1-42 + 6-42 / // 1 27 16-49 a Columbse, 10 25-47 o-o'i . 1-37 5-88 20-95 South. 21 22-40 0-01 1-38 + 4-32 Mean 19-45 1 27 18-96 A. S. C. 732, April 10 3 7 31-76 0-02 2-93 + 6-52 3 7 28-15 /3 Columbse, 21 29-00 0-02 2-96 + 5-07 26-87 South. Mean 3 7 27-51 A.S. C. 791, Mar. 30 2 42 35-21 4-77 2-59 + 7-00 2 42 40-03 ^ Canis Majoris, April 1 40-76 7-04 2-59 6-93 43-24 North. 5 36-51 0-82 2-62 6-73 45-04 10 35-32 0-01 2-53 6-42 44-26 16 36-31 0-19 2-54 + 5-89 44-55 Mean 2 42 43-42 A. S. C. 848, Mar. 30 22 49-66 0-67 0-36 + 8-10 22 57-45 X Canis Majoris, April 1 47-88 1-00 0-36 8-09 55-33 North. 5 49-66 0-12 0-36 8-02 57-92 9 49-86 0-00 0-35 7-87 58-08 10 48-67 0-00 0-35 + 7-84 Mean 56-86 22 57-13 • MEAN ZENITH DISTANCES OF STARS OBSERVED AT KLYP FONTEYN. 173 Face of Sector West. Resulting Mean Resulting Error of Zenith Distance, 1838,Jan.O, com- pletely corrected; Day of Apparent Reduction Precession, Resulting Mean Zenitli Distance, Observa- Zenith Distance for Aberration, 1838, Jan. 0, and CoUima- and Position with from unreduced Azimutlial and Mean of separate Re- tion. regard to the Observation. Error. Nutation. sults uncorrected for Error of CoUimation. Zenith. / // n " n „ O , II April 4* 1 28 25-73 0-00 1-41 + 6-52 1 28 20-56 6 24-59 0-00 1-39 6-32 19-66 30-28 1 27 49-24 20* 21-53 0-02 1-39 + 4-49 Mean 18-31 South. 1 28 19-51 Mar. 31 3 8 44-27 9-20 2-96 + 7-42 3 8 30-61 April 4 32-87 0-00 3-01 7-11 28-77 11* 29-11 0-04 3-04 6-43 (25-68) 30-97 3 7 58-48 15 32-47 0-30 3-06 5-94 29-29 South. 20 31-38 0-04 2-98 + 5-23 Mean 29-09 3 8 29-44 Mar. 31 2 41 45-15 7-42 2-55 + 6-96 2 41 47-24 April 4 37-23 0-00 2-59 6-80 46-62 6 35-80 0-01 2-59 6-68 45-06 11* 37-14 0-03 2-62 6-33 46-15 28-72 2 42 14-70 15 37-83 0-24 2-64 5-98 46-21 North. 20 36-60 0-03 2-57 + 5-46 Mean 44-60 2 41 45-98 April 4 21 50-93 0-00 0-36 + 8-05 21 59-34 6 50-73 0-00 0-36 8-00 59-09 11 50-93 0-00 0-36 7-78 59-07 15 50-83 0-03 0-36 + 7-53 Mean 58-69 29-04 22 28-09 North. 21 59-05 174 VERIFICATION AND EXTENSION OF LA CAILLE S ARC OF MERIDIAN. Star's No. in Face of Sector East. Ast. Soc. Cat., Name, and Position with regard to the Zenith. Day of Observa- tion, 1838. Apparent Zenith Distance from unreduced Observation. Reduction for Azimuthal Error. Refraction. Precession, Aberration, and Nutation. Resulting Mean Zenith Distance, 1838, Jan. 0, and Mean of separate Re- sults uncorrected for Error of Collimation. A. S. C. 869, Mar. 30 O t II 3 56 61-91 II 6-87 3-'79 -f 7'-'53 3°57' 6-36 i Canis Majoris, April I 64-77 10-15 3-79 7-53 5-94 North. 5 56-76 1-19 3-82 7-48 6-87 7 55-48 0-01 3-71 7-44 6-62 9 57-75 0-01 3-75 7-38 8-87 10 56-07 0-02 3-69 7-35 7-09- 16 56-37 0-28 3-71 7-03 6-83 19 56-57 0-06 3-82 6-83 7-16 21 61-31 0-03 3-73 4-6-68 Mean (11-69) 3 57 6-97 A. S. C. 903, Mar. 30 4 6 22-16 7-84 3-98 -f 9-51 4 6 8-79 % Arg4s, April 1 24-83 11-59 3-98 9-56 7-66 South. 7 12-27 001 3-87 9-61 6-52 9 11-83 0-01 3-94 9-59 6-17 10 11-24 0-02 3-85 9-58 5-49 16 12-08 0-32 3-92 9-39 6-29 19 12-47 0-07 3-99 9-23. 7-16 21* 11-38 0-03 3-92 -f 9-10 Mean 6-07 4 6 6-77 A.S. C. 915, Mar. 30 3 42 56-28 6-48 3-59 + 8-11 3 43 1-50 41 Canis Majoris, April 1 59-94 9-56 3-59 8-16 2-13 North. 5 56-73 6-64 3-59 8-20 1-88 10* 50-65 0-02 3-47 8-17 2-37 16 49-86 0-26 3-53 8-00 1-13 19 48-98 0-06 3-59 7-86 0-37 21 48-87 0-02 3-53 + 7-76 Mean 0-14 3 43 1-36 MEAN ZENITH DISTANCES OF STARS OBSERVED AT KLYP FONTEYN. 175 Face of Sector West. Resulting Error of CoUima- tion. Resulting Mean Zenith Distance, 1838,Jan.0,com- pletely corrected; and Position with regard to the Zenith. Day of Observa- tion, 1838. Apparent Zenith Distance from unreduced Observation. Reduction for Azimuth al Error. Refraction . Precession, Aberration, and Nutation. Resulting Mean Zenith Distance, 1838, Jan. 0, and Mean of separate Re- sults uncorrected for Error of CoUimation. Mar. 31 3° 55 66"04 10''69 // 3-72 + 7"53 3° 56' 6-60 " , ,, April 4 54-28 0-00 3-78 7-50 5-56 6 56-16 O-OI 3-79 7-47 7-41 11 56-45 0-05 3-83 7-30 7-53 15 54-67 0-35 3-86 7-10 5-28 20 56-26 0-05 3-76 + 6-76 6-73 30-23 3 56 36-75 North. • Mean -t-9-54 3 56 6-52 Mar. 31 4 7 25-14 12-21 3-93 4 7 7-32 April 4 13-92 0-00 4-05 9-61 8-36 6 11-79 0-01 3-95 9-62 6-11 11 11-40 0-05 3-99 9-55 5-79 15 20 11-30 12-98 0-40 0-05 4-02 3-92 9-42 + 9-17 5-50 7-68 30-01 4 6 36-78 South. Mean 4 7 6-79 Mar. 31 3 41 58-25 10-08 3-55 + 8-13 3 41 59-85 April 4 44-70 0-00 3-65 8-19 56-54 6* 50-14 0-01 3-56 8-20 61-98 11 48-76 0-05 3-60 8-15 60-46 30-87 3 42 30-49 15 49-65 0-33 3-62 8-04 60-98 North. 20 46-58 0-04 3-54 + 7-82 57-90 Mean 3 41 59-62 176 VERIFICATION AND EXTENSION OF LA CAILLE S ARC OF MERIDIAN. Star's No. in Ast. Soc. Cat., 1 Face oj Sector East. Name, and Position with regard to the Zenith. Day of Observa- tion, 1838. Apparent Zenith Distance from unreduced Observation. Reduction for Azimutha Error. Refraction Precession Aberration and Nutation. Resulting Mean ' Zenith Distance, , 1838, Jan. 0, and Mean of separate Re- sults uncorrected for Error of Collimation. A. S. C. 957, Mar. 30 4° 52 30''68 9-40 4-73 + 10"l6 4° 52' 15-85 c Argfts in puppi, April 5 18-52 0-10 4-73 10-46 12-69 South. 9 18-42 0-01 4-69 10-57 12-53 16 21-48 0-38 4-66 10-57 1519 19 20-29 0-09 4-73 10-50 14-43 21 17-92 0-04 4-66 + 10-44 Mean 12-10 4 52 13-80 A. S. C. 1015, April 5* 3 27 12-62 0-07 3-35 + 10-95 3 27 (4-95) q ArgAs in puppi. 7 16-77 0-00 3-33 11-08 9-02 South. 9 14-40 0-01 3-33 11-18 6-54 10 16-92 0-02 3-32 11-25 8-97 16 17-07 0-27 3-30 11-42 8-68 21 15-58 0-02 3-30 + 11-47 Mean 7 39 3 27 8-12 A. S. C. 1061, Mar. 30 2 1 56-07 3-79 1-97 + 10-57 2 1 43-68 /3 Pixidis Nauticse, April 5 51-72 0-04 1-97 11-14 42-51 South. 7 51-43 0-00 1-96 11-31 42-08 9 48-36 0-00 1-96 11-45 38-87 10 51-52 0-01 1-95 11-52 41-94 16* 49-74 0-15 1-94 11-81 (39-72) 19 53-01 0-03 2-00 11-90 43-08 21 51-72 0-01 1-94 + 11-93 Mean 41-72 2 1 41-98 A. 8. C. 1070, Mar. 30 5 58-43 0-17 0-09 + 10-27 6 8-62 a Pixidis Nauticse, April 5 59-22 0-00 0-09 10-83 10-14 North. . 9 57-79 0-00 0-09 11-13 9-01 10 59-57 0-00 0-09 11-20 . 10-86 16 57-94 0-01 0-09 11-48 9-51 19 56-45 0-00 0-09 + 11-58 Mean 8-12 6 9-38 MEAN ZENITH DISTANCES OF STARS OBSERVED AT KLYP FONTEYN. 177 Face of Sector West. Resulting Mean Resulting Error of Collima- tion. Zenith Distance, 1838,Jan.0,com. pletely corrected ; and Position with regard to the Zenith. Day of Observa- tion, 1838. Apparent Zenith Distance from unreduced Observation. Reduction for Azimuthal Error. Refraction. Precession, Alierration, and Nutation. Resulting Mean Zenith Distance, 1838, Jan. 0, and Mean of separate Re- sults uncoirected for Error of Collimation. Mar. 31 O / // 4 53 33-51 14'63 // 4-67 -f 10-24 / // 4 53 13-31 // O / // April 4 19-47 0-00 4-81 10-42 13-86 6 11 15 18-43 17-19 21-10 0-01 0-07 0-47 4-69 4-74 4-78 10-48 10-58 -flO-58 12-63 11-28 14-83 29-69 4 52 43-49 South. Mean 4 53 13-18 Mar. 31 3 28 27-06 10-20 3-34 -flO-57 3 28 9-63 April 4 17-77 0-00 3-41 10-88 10-30 6 11 15-84 17-92 0-01 0-05 3-39 3-36 11-02 11-29 8-20 9-94 30-72 3 27 38-84 South. 20 17-82 0-04 3-36 -f 11-47 9-67 Mean 3 28 9-55 April 4 2 2 52-63 0-00 2-01 -I-11-06 2 2 43-58 6 11 52-33 54-31 0-00 0-03 2-00 1-98 11-22 11-57 43-11 44-69 30-99 2 2 12-97 South. 15 54-41 0-19 2-02 + 11-77 44-47 Mean 2 2 43-96 Mar. 31 4 58-32 0-26 0-09 + 10-37 . 5 8-52 April 6 57-58 0-00 0-09 10-92 8-59 11 . 15 55-21 54-46 0-00 O-Ol 0-09 0-09 11-25 11-44 6-55 5-98 30-87 5 38-52 North. -20* 56-84 . 0-OX) 0-0,9 + 11-60 8-63 Mean 5 7-65 178 VERIFICATION AND EXTENSION OF LA CAILLE S ARC OF MERIDIAN. Star's No. in Face or Sector East. Ast. Soc. Cat., Name, and Position with regard to the Zenith. Day of Observa- tion, 1838. Apparent Zenith Distance from unreduced Observation. Reduction for Azimutbal Error. Refraction Precession, Aberration, and Nutation. Resulting Alean Zenith Distance, 1838, Jan. 0, and Mean of separate Re- sults uncorrected fur Error of Collimation. A. S. C. 1115, Mar. 30 2° 59 57''03 5-26 2'-'89 + 10-19 O / /' 3 4-85 s Pixidis Nauticae, April 5 52-63 0-19 2-90 10-83 6-17 North. 9 50-51 0-01 2-88 11-19 4-57 10 50-95 0-02 2-87 11-26 5-06 16 51-50 0-21 2-85 11-64 5-78 19 49-47 0-05 2-93 11-79 4-14 21 49-92 0-02 2-85 + 11-86 Mean 4-61 3 5-03 Brisbane (2566), Mar. 30 1 15 7-91 2-23 1-21 + 10-83 1 15 17-72 North. April 5 6-87 0-04 1-23 11-63 19-69 7 4-10 0-00 1-19 11-86 17-15 9 4-55 0-00 1-20 12-07 17-82 10 4-10 0-01 1-20 12-19 17-48 16 4-05 0-09 1-21 12-72 17-89 21 3-36 0-01 1-21 + 13-07 Mean 17-63 1 15 17-91 Brisbane (2823), Mar. 30 2 35 63-47 4-.58 2-52 + 11-00 2 36 12-41 North, April 5 56-65 0-07 2-57 11-87 11-02 7 56-06 0-00 2-40 12-13 1059 10 56-36 0-01 2-50 12-50 11-35 16 56-70 0-19 2-51 13-14 12-16 19 52-80 0-04 2-54 13-40 8-70 21 54-38 0-02 2-52 + 13-56 Mean 10-44 2 36 10-95 MEAN ZENITH DISTANCES OF STARS OBSERVED AT KLYP FONTEYN. 179 Face of Sector West. Resulting Mean Resulting Error of Collima- tion. Zenith Distance, 1838, Jan. 0, com- pletely corrected; and Position with regard to the Zenith. Day of Observa- tion, 1838. Apparent Zenith Distance from unreduced Observation. Reduction for Azimuthal Error. Refraction. Precession, Aberration, and Nutation. Resulting Mean Zenith Distance, 1838, Jan. 0, and Mean of separate Re- sults uncorrected for Error of Collimation. Mar. 31 2° 58 59'l0 8'- 19 2'-89 + 10-31 / // 2 59 4-11 // O / ;/ April 4 48-32 0-00 2-95 10-73 2-00 6 49-61 0-01 2-93 10-92 3-45 11 46-64 0-04 2-90 11-33 0-83 31-44 2 59 33-60 15 46-84 0-27 2-96 11-47 1-00 North. 20 46-84 0-04 2-91 + 11-88 1-59 Mean 2 59 2-16 Mar. 31 1 14 9-68 3-47 1-20 + 10-98 1 14 18-39 April 4 4-34 0-00 1-23 11-50 17-07 6 6-31 0-00 1-22 11-74 19-27 11 4-44 0-02 1-21 12-28 17-91 15 3-45 0-11 1-23 12-65 17-22 30-13 1 14 47-78 North. 18 1-27 0-08 1-24 12-88 15-31 ft 20 4-14 - 0-02 1-21 + 13-02 Mean 18-35 1 14 17-65 Mar. 31 2 34 63-76 7-13 2-50 + 11-15 2 35 10-28 April 4 55-16 0-00 2-55 11-73 9-44 6 57-13 0-00 2-54 12-01 11-68 11 55-65 0-03 2-52 12-61 10-75 15 54-12 0-23 2-56 13-03 9-48 30-44 2 35 40-51 North. 18 54-07 0-16 2-58 13-31 9-80 20 53-08 0-03 2-52 + 13-48 Mean 905 2 35 10 07 AA 180 VERIFICATION AND EXTENSION OF LA CAILLE S ARC OF MERIDIAN. Star's No. in Ast. Soc. Cat., Name, Face of Sector Ei kST. Day of Observa- tion, 1838. Apparent Reduction Precession, Resulting Mean Zenith Distance, and Position with regard to tlie Zenith. Zenith Distance from unreduced Observation. for Azimuthal Error. Refraction. Aberration, and Nutation. 1838, Jan. 0, and Mean of separate Re- sults uncorrected for Error of CoUimation. A. S. C. 1243, April 5 o / // 2 27 32-06 010 // 2-43 + 12''l7 / // 2 27 46-56 a. Antlise Pneu- 7 33-94 0-00 2-35 12-46 48-75 maticse. 10 33-39 0-01 2-36 12-87 48-61 North. 16 33-35 0-18 2-38 13-59 49-14 19 30-18 0-04 2-40 13-90 46-44 21 30-77 0-02 2-38 + 14-09 Mean 47-22 2 27 47-79 A. S. C. 1299, Mar. 30 3 33 50-99 6-77 3-47 + 11-81 3 33 35-88 South. April 5 45-01 0-16 3-54 13-01 35-38 10 45-55 0-02 3-44 13-91 35-06 16 45-95 0-28 3-47 14-89 34-25 21 46-05 0-03 3-48 + 15-60 Mean 33-90 3 33 34-89 Brisbane (3350), Mar. 30 1 36 60-77 2-87 1-56 + 11-57 1 37 11-03 North. April 5 55-97 0-07 1-59 12-64 10-13 7 56-96 0-00 1-54 12-97 11-47 10 54-79 0-01 1-55 13-46 9-79 16 55-18 0-12 1-56 14-30 10-92 21 53-45 0-01 1-56 + 14-93 Mean 9-93 1 37 10-55 A. S. C. 1356, Mar. 30 1 44 36-67 3-09 1-69 + 11-70 1 44 46-97 19 Crateris, April 5 33-21 0-07 1-72 12-82 47-68 North. 7 33-06 0-00 1-68 13-17 47-91 10 31-72 0-01 1-67 13-68 47-06 16 30-93 0-13 1-68 14-61 47-09 19 31-03 0-03 1-70 15-03 47-73 21 31-33 0-01 1-69 + 15-30 Mean 48-31 1 44 47-54 MEAN ZENITH DISTANCES OF STARS OBSERVED AT KLYP FONTEYN. 181 Face of Sector West. Resulting Error of Collima- tion. Resulting Mean Zenith Distance, 1838, Jan. 0, com. pletely corrected ; and Position with regard to the Zenith. Day of Observa- tion, 1838. Apparent Zenith Distance from unreduced Observations. Reduction for Azimuthal Error. Refraction. Precession, Aberration, and Nutation. Resulting Mean Zenith Distance, 1838, Jan. 0, and Mean of separate Re- sults uncorrected for Error of Collimation. Mar. 31 O 1 II 2 26 41-74 6-75 2-36 + 1 1'-'38 Q / If 2 26 48-73 // O / // April 4 33-18 0-00 2-41 12-02 47-61 6 35-36 0-00 2-40 12-32 50-08 11 32-79 0-03 2-38 13-00 48-14 15 32-74 0-22 2-42 13-47 48-41 29-64 2 27 18-15 18 32-34 0-15 2-44 13-80 48-43 North. 20 31-85 0-03 2-38 + 14-00 Mean 48-20 2 26 48-51 Mar. 31 3 34 55-16 10-54 3-46 + 1201 3 34 36-07 April 4 45-12 0-00 3-52 12-81 35-83 6 43-59 0-01 3-50 1319 33-89 15 46-36 0-34 3-53 14-73 34-82 30-25 3 34 5-14 18 47-20 0-23 3-56 15-18 35-35 South. 20 48-43 0-05 3-47 ^15-47 Mean 36-38 3 34 35-39 Mar. 31 1 35 61-40 4-47 1-56 + 11-76 1 36 10-25 April 4 55-46 0-00 1-58 12-47 9-51 6 57-49 000 1-57 12-81 11-87 15 20 54-97 53-19 0-14 0-02 1-59 1-56 14-17 + 14-81 Mean 10-59 9-54 30-10 1 36 40-45 North. 1 36 10-35 Mar. 31 1 43 38-16 4-82 1-68 + 11-89 1 43 46-91 April 4 31-91 0-QO 1-71 12-64 46-26 6 34-48 0-00 1-70 13-00 49-18 11 32-30 0-02 1-68 13-84 47-80 15 31-81 0-16 1-72 14-46 47-83 30-11 1 44 17-44 18 30-52 O-Il 1-73 14-90 47-04 North. 20 29-44 0-02 1-71 + 15-17 Mean 46-30 1 43 47-33 182 VERIFICATION AND EXTENSION OF LA CAILLE's ARC OF MERIDIAN. Star's No. in Ast. Soc. Cat., Name, Face of Sector East. Day of Observa- tion, 1838. Apparent Reduction Precession, Resulting Mean Zenith Distance, and Position with regard to the Zenith. Zenith Distance from unreduced Observation. for Azimiithal Error. Refraction. Aberration, and Nutation. 1838, Jan. 0, and Mean of separate Re- sults uncorrected for Error of Collimation. A. S. C. 1378, Mar. 30 0°18' 7-29 0'^7 o''30 + ll'-'73 0° 17 55-29 28 Crateris, April 7 8-67 0-00 030 13-33 55-64 South. 10 8-28 0-00 0-30 13-89 54-69 16 9-76 0-02 0-30 14-92 55-12 19 10-26 0-01 0-30 15-40 55-15 21 9-66 0-00 0-30 + 15-70 54-26 Mean 17 55-03 A. S. C. 1433, Mar. 30 5 26 24-73 10-57 5-33 + 11-35 5 26 8-14 u Centauri, April 5 13-76 0-24 5-41 12-80 6-13 South. 7 15-19 0-01 5-27 13-21 7-24 10 14-65 0-03 5-29 13-87 6-04 21 16-13 0-04 5-31 + 16-07 - 5-33 » Mean 5 26 6-58 A. S. C. 1527, Mar. 30 3 8 66-02 5-95 3-08 + 10-96 ^ 3 8 52-19 ( Centauri, April 5 58-60 0-14 3-13 12-27 49-32 South. 7 59-89 0-00 3-05 12-70 50-24 10 59-79 0-02 3-06 13-32 49-51 16 60-98 0-24 3-08 14-51 49-31 21 60-73 0-02 3-07 + 15-45 Mean 48-33 3 8 49-82 A. S. C. 1562, Mar. 30 28 61-77 0-86 0-46 + 11-13 29 12-50 i Centauri, April 5 59-30 0-02 0-46 12-29 12-03 North. 7 59-30 0-00 0-46 12-67 12-43 10 59-34 0-00 0-46 13-22 13-02 16 57-37 0-03 0-46 14-28 12-08 21 58-60 0-00 0-46 + 15-11 14-17 Mean 29 12-71 MEAN ZENITH DISTANCES OF STARS OBSERVED AT KLYP FONTEYN. 183 Face of Sector West. Resulting Mean Resulting Error of CoUima- tion. Zenith Distance. 1838,Jan.0,cona- pletely corrected ; and Position with regard to the Zenith. Day of Observa- tion, 1838. Apparent Zenith Distance from unreduced Observation. Reduction for Azimuthal Error. Refraction. Precession, Aberration, and Nutation. Resulting Mean Zenith Distance, 1838, Jan. 0, and Mean of separate Re- suits uncorrected for Error of CoUimation. Mar. 31 o / // 19 6-31 0-88 0'-'30 + ll'-94 O 1 tt 18 53-79 // t It April 4 7-11 0-00 .0-31 12-75 54-67 6 5-52 0-00 0-30 13-14 52-68 11 8-64 0-00 0-30 14-07 54-87 15 9-18 0-03 0-31 14-75 54-71 18 9-23 0-02 0-31 15-24 54-28 29-59 18 24-62 20 9-63 0-00 0-31 -)- 15-55 Mean 54-39 South. 18 54-20 April 4 5 27 10-95 0-00 5-44 -M2-53 5 27 3-86 6 10-46 0-01 5-34 12-98 2-81 11 12-98 0-07 5-30 14-07 4-14 15 13-72 0-53 5-40 14-90 3-69 18 13-87 0-36 5-43 15-50 3-44 28-57 5 26 35-15 20 14-86 0-07 5-37 + 15-87 Mean 4-29 South. 5 27 3-71 Mar. 31* 3 9 69-39 9-27 3-06 + 11-18 3 9 51-76 April 4 59-60 0-00 3-15 12-06 50-69 6 59-01 0-01 3-09 12-49 49-60 11 60-00 0-04 3-07 13-59 49-51 18 61-98 0-21 3-15 14-60 50-32 30-25 3 9 20-07 20 62-18 0-04 3-11 + 15-27 Mean 49-98 3 9 50-31 South. Mar. 31 27 62-31 1-34 0-46 + 11-33 -28 12-76 April 4 60-07 0-00 0-47 12-10 12-64 6 63-48 0-00 0-47 12-51 16-46 11 60-96 0-01 0-46 13-40 14-81 15 59-48 0-04 0-47 13-23 13-14 18* 57-50 0-03 0-48 14-62 12-57 29-51 28 43-21 North. 20 58-10 0-01 0-47 + 14-95 Mean 13-51 28 13-70 184 VERIFICATION AND EXTENSION OF LA CAILLe'S ARC OF MERIDIAN. Star's No. in Face of Sector East. Ast. Soc. Cat., Name, and Position with regard to the Zenith. Day of Observa- tion, 1838. Apparent Zenith Distance from unreduced Observation. Reduction for Azimuth al Error. Refraction. Precession, Aberration, and Nutation. Resulting Mean Zenith Distance, 1838, Jan. 0, and Mean of separate Re- sults uncorrected for Error of Collimation. A. S. C. 1579, Mar. 30* 0°30'(60'5l) 0"92 0-50 + ll-'07 0°3r(ll"l6) k Centauri, April 5 61-50 0-00 0:50 12-23 14-23 North. 7 61-35 0-00 0-49 12-60 14-44 9 61-45 0-00 0-49 12-96 14-90 10 61-15 0-00 0-49 13-14 14-78 16 60-21 0-04 0-50 14-19 14-86 19 59-17 0-01 0-50 14-69 14-35 21 60-76 0-00 0-49 + 15-03 Mean 16-28 31 14-83 A. S. C. 1604, Mar. 30 2 51 52-66 5-40 2-80 + 10-35 2 51 39-71 6 Centauri, April 5 47-37 0-01 2-85 11-58 38-63 South. 7 49-15 0-00 2-79 11-97 39-97 9 48-90 0-01 2-76 12-37 39-28 10 49-94 0-02 2-78 12-56 40-14 16 50-24 0-22 2-80 13-70 39-12 19 51-13 0-05 2-84 + 14-26 Mean 39-66 2 51 39-50 A. S.C. 1661, Mar. 30 1 45 60-11 3-29 1-73 + 9-94 1 45 48-61 c* Centauri, April 5 54-92 0-00 1-76 11-04 45-64 South. 7 56-31 0-00 1-72 11-50 46-53 10 55-37 0-01 1-72 11-92 45-16 16 57-79 0-13 1-73 12-95 46-44 19 56-95 0-03 1-75 13-46 45-21 21 56-75 0-01 1-73 + 13-78 Mean 44-69 1 45 46-04 MEAN ZENITH DISTANCES OF STARS OBSERVED AT KLYP FONTEYN. 185 Face of I Sector West. I Resulting Error of Collima- tion. Resulting Mean Zenith Distance, 1838, Jan. 0, com- pletely corrected; and Position with regard to the Zenith. Day of Observa- tion, 1838. Apparent Zenith Distance from unreduced Observation. Reduction for Azimuthal Error. Refraction. Precession, Aberration, and Nutation. Resulting Mean Zenith Distance, 1838, Jan. 0, and Mean of separate Re- sults uncorrected for Error of Collimation. Mar. 31 0°30' 2-93 l'-43 0-49 -1-11 '-27 0°30'l3"26 " O 1 11 April 4 2-27 0-00 0-51 12-04 14-82 6 4-94 0-00 0-50 12-41 17-85 11 15 1-48 2-22 0-01 0-05 0-49 0-50 13-32 14-02 15-28 16-69 29-53 30 45-30 North. 18 1-68 0-03 0-51 14-53 16-69 20 0-45 0-01 0-50 -1-14-86 15-80 Mean 30 15-77 Mar. 31 2 52 55-59 8-40 •2-78 -1-10-55 2 52 39-42 April 4 49-81 0-00 2-86 11-37 41-30 6 46-54 0-01 2-84 11-78 37-59 11 15 47-78 50-05 0-04 0-27 2-79 2-84 12-76 13-52 37-77 39-10 29-80 2 52 9-30 18 50-85 0-19 2-89 14-07 39-48 South. 20 50-65 0-04 2-83 + 14-44 Mean 39-00 2 52 39-09 Mar. 31 1 46 59-«8 5-12 1-73 -f-10-13 1 46 46-16 April 4 57-16 0-00 1-77 10-86 48-07 6 53-59 0-00 1-75 11-21 44-13 11 15 18 55-38 57-85 57-80 0-02 0-17 0-11 1-72 1-76 1-78 12-10 12-80 13-29 44-98 46-64 46-18 29-94 1 46 15-98 South. 20 57-16 0-02 1-76 -1-13-62 Mean 45-28 1 46 45-92 186 VERIFICATION AND EXTENSION OF LA CAILLE's ARC OF MERIDIAN. Star's No. in Ast. Soc. Cat., Name, and Position with regard to the Zenith. Face of ' SECTOR East. Day of OI)serra- tion, 1838. Apparent Zenith Distance from unreduced Observation. Reduction for Azimuthal Error. Refraction. Precession, Aberration, and Nutation. Resulting Mean Zenith Distance, 1838, Jan. 0, and Mean of separate Re- sults uncorrected for Error of CoUimation. A. S.C. 1742, Mar. 30* 3°(32 10"-24) II 6-77 3-49 + 8-"79 O / // (p2 Lupi, April 5 33 52-23 0-01 3-57 9-79 3 33 46-00 South. 7 53-26 0-00 3-47 10-12 46-61 10 54-15 0-02 3-48 10-61 47-00 16 54-65 0-28 3-52 11-58 46-31 19 55-34 0-06 3-53 12-05 . 46-76 21 54-65 0-03 3-49 + 12-37 Mean 45-74 3 33 46-40 A. S, C. 1774, Mar. 30 3 27 62-89 6-05 3-38 + 10-26 3 28 10-48 40 Librae, April 5 57-11 0-01 3-45 11-02 11-57 North. 7 55-18 0-00 3-36 11-26 9-80 10 55-13 0-02 3-37 11-62 10-10 16 55-13 0-25 3-40 12-32 10-60 19 53-99 0-05 3-45 12-67 10-06 21 55-87 0-02 3-38 + 12-89 Mean 12-12 3 28 10-68 A. S.C. 1797, Mar. 30 25 17-50 0-78 0-42 + 9-03 25 8-11 A Lupi, April 5 16-26 0-00 0-43 9-83 6-86 South. 7 17-25 0-00 0-42 10-09 7-58 10 17-25 0-00 0-42 10-49 7-18 19* 18-19 0-01 0-43 11-64 6-77 21 18-49 0-00 0-42 + 11-89 Mean 7-02 25 7-25 MEAN ZENITH DISTANCES OF STARS OBSERVED AT KLYP FONTEYN. 187 Face of ' Sector W EST. Resulting Error of Collima- tion. Resulting Mean Zenith Distance, 1838, Jan. 0, com- pletely corrected ; and Position with regard to the Zenith. Day of Observa. tion, 1838. Apparent Zenith Distance from unreduced Observation. Reduction for Azimuthal Error. Refraction. Precession, Aberration, and Nutation. Resulting Mean Zenith Distance, 1838, Jan. 0, and Mean' of separate Re- sults uncorrected for Error of Collimation. Mar. 31 3°34'63''81 10-54 3'-48 + 8-96 3° 34' 47-79 // O / // April 4 54-17 0-00 3-56 9-63 48-10 6 50-95 0-01 3-53 9-96 44-51 15 54-96 0-34 3-54 11-42 46-74 30-23 3 34 16-63 18 55-75 0-23 3-59 11-90 47-21 South. 20 55-45 0-05 3-54 + 12-21 46-73 Mean 3 34 46-85 Mar. 31 3 26 66-04 9-42 3-37 + 10-39 3 27 10-38 April 4 54-37 0-00 3-44 10-57 8-38 6 58-43 0-01 3-42 11-14 12-98 15 54-82 0-31 3-43 12-21 10-15 30-26 3 27 40-42 18 54-03 0-21 3-48 12-56 9-86 North. 20 53-04 0-04 3-44 + 12-78 9-22 Mean 3 27 10-16 Mar. 31 26 15-93 1-22 0-42 + 9-17 26 5-96 April 4 17-02 0-00 0-43 9-70 7-75 6 15 13-76 17-81 0-00 0-04 0-42 0-43 9-96 11-13 4-22 7-07 29-56 25 36-81 South. 18 17-91 0-03 0-43 + 11-51 6-80 Mean 26 6-36 B B 188 VERIFICATION AND EXTENSION OF LA CAILLE S ARC OF MERIDIAN. Star's No. in Face or Sector East. Ast. Sec. Cat., Name, and Position with regard to the Zenitli. Day of Observa- tion, 1838. Apparent Zenith Distance from unreduced Observation. Reduction for Azimuth al Error. Refraction. Precession, Aberration, and Nutation. Resulting Mean Zenith Distance, 1838, Jan. 0, and Mean of separate Re- sults uncorrected for Error of Collimation. A. S. C. 1821, Mar. 30 O / // 5 13 18-13 10''l3 // 5-12 + 7-'54 5° 13 5-58 n Lupi, April 5 9-17 0-01 5-23 8-41 5-98 South. 7 9-17 0-01 5-09 8-60 5-65 10 10-65 0-03 5-10 9-14 6-58 16 10-75 0-41 515 10-01 5-48 19 11-15 0-09 5-22 10-44 5-84 21 10-26 0-04 5-12 -f 10-73 Mean 4-61 5 13 5-67 A. S. C. 1835, Mar. 30 3 38 57-42 6-94 3-57 + 7-87 3 38 46-18 6 Lupi, April 5 49-80 0-01 3-65 8-67 44-77 South. 7 50-40 0-01 3-55 8-94 4500 10 50-94 0-02 3-56 9-33 45-15 16 51-39 0-28 3-60 10-13 44-58 19 51-19 0-06 3-65 10-53 44-25 21 50-99 0-03 3-58 + 10-79 Mean 43-75 3 38 44-81 ■ A. S. C. 1866, Mar. 30 2 11 58-05 3-89 2-14 + 9-27 2 12 5-57 p Scorpii, April 5 54-34 0-00 2-19 9-87 6-40 North. 10 52-96 0-01 2-13 10-37 5-45 16 52-91 0-16 2-15 10-95 5-85 19 51-72 0-04 2-18 11-24 5-10 21 52-51 0-01 2-14 + 11-42 Mean 6-06 2 12 5-74 MEAN ZENITH DISTANCES OF STARS OBSERVED AT KLYP FONTEYN. 189 Face of Sector W EST. Resulting Mean Resulting Error of Collima- tion. Zenith Distance, 1838, Jan. 0, com. pletely corrected ; and Position with regard to the Zenith. Day of 01)serva- tion, 1838. Apparent Zenith Distance from unreduced Observation. Reduction for Azimuthal Error. Refraction. Precession, Aberration, and Nutation. Resulting Mean Zenith Distance, 1838, Jan. 0, and Mean of separate Re- sults uncorrected for Error of Collimation. Mar. 31 o / tl 5 14 21-84 15-76 5-10 + 7-69 5 14 3-49 It / II April 4 7-30 0-00 5-22 8-27 4-25 6 4-98 0-01 5-19 8-56 1-60 15 9-38 0-51 5-19 9-86 4-20 18 20 9-58 9-03 0-35 0-07 5-28 5-22 10-30 + 10-58 4-21 3-60 28-95 5 13 .34-62 South. Mean 5 14 3-56 Mar. 31 3 39 60-10 10-80 3-56 + 8-00 3 39 44-86 April 4 49-77 0-00 3-64 8-54 44-87 6 47-84 0-01 3-62 8-80 42-65 15 50-61 0-35 3-63 10-00 43-89 18 20 51-70 51-89 0-24 0-05 3-69 3-64 10-39 + 10-66 44-76 44-82 29-75 3 39 14-56 South. Mean 3 39 44-31 Mar. 31 2 10 59-91 6-05 2-13 + 9-37 2 11 5-36 April 4 52-65 0-00 2-18 9-78 4-61 15 52-40 0-20 2-17 10-85 5-22 18 20 52-20 52-99 0-13 0-03 2-20 2-18 11-14 + 11-33 5-41 6-47 30-17 2 11 35-58 North. Mean 2 11 5-41 190 VERIFICATION AND EXTENSION OF LA CAILLE S ARC OF MERIDIAN. Star's No. in Ast. Soc. Cat., Name, and Face of Sectok, E AST. Day of Apparent Zenith Distance Reduction for Precession, Aberration, Resulting Mean Zenith Distance, 1838, Jan. 0, and Position with regard to the Zenith. Observa- tion, 1838. from unreduced Oiiservatiou. Azimuthal Error. and Nutation. Mean of separate Re- suits uncorrected for Error of Collimation. A. S. C. 1889, Mar. 30 O / '/ 1 38 18-66 3"05 l'-61 + 7'-'85 1°38' 9'-'37 a, Normae, April 5 14-56 0-00 1-64 8-48 7-72 South. 7 15-25 0-00 1-60 8-70 8-15 10 15-40 0-01 1-60 9-01 7-98 16 16-53 0-12 1-62 9-64 8-39 19 16-78 0-03 1-64 9-95 8-44 21 15-69 0-01 1-61 + 10-16 Mean 7-13 1 38 8-17 A. S. C. 1915, Mar. 30 1 17 11-20 2-39 1-26 + 7-55 1 16 62-52 £ Scorpii, April 5 5-69 0-00 1-29 8-07 58-91 South. 10 6-98 0-01 1-26 8-51 59-72 16 7-57 0-10 1-27 9-04 59-70 21 6-39 0-01 1-27 + 9-48 Mean 58-17 1 16 .59-80 A. S. C. 1947, Mar. 30 1 10 54-38 2-19 1-16 + 7-26 1 10 46-09 h. Scorpii, April 5 51-02 0-00 1-19 7-70 44-51 South. 10 52-40 0-01 1-16 8-07 45-48 16 51-91 0-11 1-17 8-52 44-45 19 52-15 0-02 1-19 8-75 44-57 21 50-03 001 1-16 + 8-90 Mean 42-28 1 10 44-56 A. S. C. 1969, April 5 14 3-94 0-41 0-22 + 7-79 14 11-54 u Scorpii, 10 0-68 0-00 0-22 8-09 8-99 North. 16 1-97 0-02 0-22 8-44 10-61 19 1-17 0-00 0-22 8-62 10-01 21 3-20 0-00 0-22 + 8-74 12-16 Mean 14 10-66 MEAN ZENITH DISTANCES OF STARS OBSERVED AT KLYP FONTEYN. 191 Face of Sector West. Regal ting £rror of CoUima- tion. Resulting Mean Zenith Distance, 1838, Jan. 0, com- pletely corrected ; and Position nitb regard to the Zenith. Day of 1 Observa- tion, 183S. Apparent Zenith Distance from anreduced Observation. ReductiuD for Azimutlial Error. Refraction. Precession, Aberration, and j Natation, i 1 Resulting Mean Zenith Distance, 1838, Jan. 0, and Mean of separate Re- sults uncorrected for Error of CoUimation. Mar. 31 1° 39 19'66 4''74 l'-60 + 7"96 1°39 8'-56 // O / II April 4 18-28 0-00 1-64 8-38 11-54 6 13-93 0-00 1-63 8-59 (6-97) 15 20 17-09 16-70 015 0-02 1-63 1-64 9-53 + 10-06 9-04 8-26 30-59 1 38 38-76 South. Mean 1 39 9-35 Mar. 31 I 18 9-66 3-71 1-26 + 7-63 1 17 59-58 April 4 8-48 000 1-29 7-98 61-79 6 18 4-32 8-97 0-00 0-08 1-28 1-30 8-16 9-22 (57-44) 60-97 30-40 1 17 30-20 20 8-18 0-02 1-29 + 9-44 Mean 60-01 South. 1 18 0-59 Mar. 31 1 11 53-90 3-41 1-16 + 7-33 1 11 44-32 April 4 52-17 0-00 1-18 7-62 . 45-73 6 48-01 0-00 1-18 7-77 (41-42) 15 18 52-02 50-73 0-11 0-08 1-18 1-20 8-44 8-67 44-65 43-18 29-88 1 U 14-44 South. 20 51-33 0-01 1-18 + 8-82 Mean 43-68 1 11 44-31 Mar. 31 13 3-83 0-63 0-22 + 7-50 13 10-92 April 4 2-94 0-00 0-22 7-74 10-90 6 5-96 0-00 0-22 7-85 (14-03) 15 18 20 2-84 2-25 1-95 0-02 001 0-00 0-22 0-22 0-22 8-38 8-54 + 8-68 Mean 11-42 11-00 10-85 29-82 13 40-84 North. 13 11-02 192 VERIFICATION AND EXTENSION OF LA CAILLE S ARC OF MERIDIAN. Star's No. in Ast. Soc. Cat., Name, and Position with regard to the Zenith. Face oi' Sector East. Day of Observa- tion, 1838. Apparent Zenith Distance from Tinreduced Observation. Reduction for Azimuthal Error, Refraction. Precession, Aberration, and Nutation. Resulting; Mean Zenith Distance, 1838, Jan. 0, and Mean of separate Re- sults uncorrected for Error of Collimation. A. S. C.2007, Mar. 30 4°16'22''65 8-18 4-21 + 5'-'60 O 1 II 4 16 13-08 A Scorpii, April 5 10-10 0-01 4-25 5-92 8-42 South. 10 12-08 0-03 4-18 6-19 10-04 16 10-59 0-33 4-21 6-55 7-92 19 10-00 0-07 4-29 6-73 7-49 21 9-51 0-03 4-20 + 6-86 Mean 6-82 4 16 8-96 A. S. C. 2043, Mar. 30 4 16 41-93 8-19 4-22 + 5-22 4 16 32-74 y Telescopii, April 10 - 32-25 0-03 4-18 5-62 30-78 South. 16 30-37 0-33 4-21 5-88 28-37 19 30-76 0-07 4-29 6-02 28-96 21 29-58 0-03 4-20 + 6-11 27-64 Mean 4 16 29-70 A. S. C. 2079, Mar. 30 2 17 17-53 4-04 2-24 + 7-09 2 17 22-82 y Sagittarii, April 10 1308 0-01 2-23 7-19 22-49 North. 16 15-01 0-16 2-24 7-23 24-32 19 14-46 0-04 2-28 7-26 23-96 21 15-40 0-02 2-23 + 7-28 24-89 Mean 2 17 23-70 A. S. C. 2101, Mar. 30 4 5 47-21 7-83 4-04 + 4-65 4 5 38-77 /8 Telescopii, April 10 38-16 0-02 4-01 4-72 37-43 South. 16 37-27 0-32 4-04 4-80 36-19 19 35-49 0-07 4-11 4-85 34-68 21 35-59 0-03 4-03 + 4-89 34-70 Mean 4 5 36-35 MEAN ZENITH DISTANCES OF STARS OBSERVED AT KLTP FONTEYN. 193 Face of Sector West. Resulting Mean Resulting Error of Collima' tion. Zenith Distance, 1838,Jan.0,com- pletely con ected ; and Position with regaj'd to tlie Zenith. Day of Observa. tion, 1838. Apparent Zenith Distance from unreduced Observation. Reduction for Azimuthal Error. Refraction. Precession, Aberration, and Nutation. Resulting Mean Zenith Distance, 1838, Jan. 0, and Mean of separate Re- sults uncorrected for Error of Collimation. Mar. 31 O / //' 4 17 22-96 12-74 4-17 + 5"65 4° 17' 8-74 // I II April 4 8-92 0-00 4-26 5-86 7-32 6 15 7-05 9-82 0-01 0-41 4-24 4-25 5-97 6-49 (5-31) 7-17 29-24 4 16 38-20 South 18 9-57 0-28 4-31 6-67 6-93 20 9-57 0-06 4-27 + 6-80 Mean 6-98 4 17 7-43 Mar. 31 4 17 44-27 12-75 4-17 + 5-25 4 17 30-44 April 4 29-14 0-00 4-27 5-39 • 28-02 6 15 26-72 30-58 0-01 0-41 426 4-25 5-47 5-84 (25-50) 28-58 29-39 4 16 59-08 18 29-19 0-28 4-32 5-97 27-26 South. 20 29-88 0-06 4-27 + 6-06 Mean 28-03 ' 4 17 28-47 Mar. 31 2 16 23-64 2-69 2-22 + 7-10 2 16(30-27) April 4 16-03 0-00 2-27 7-13 25-43 6 15 18-80 17-32 0-00 0-20 2-27 2-26 7-15 7-22 (28-22) 26-60 28-93 2 16 54-78 18 15-73 0-14 2-30 7-26 25-15 North. 20 16-72 0-03 2-27 + 7-28 Mean 26-24 2 16 25-85 Mar. 31 4 6 49-15 12-19 4-00 + 4-65 4 6 36-31 April 4 38-28 0-00 4-09 4-67 37-70 6 15 34-42 36-99 0-01 0-40 4-08 4-07 4-68 4-78 (33-81) 35-88 30-12 4 6 6-47 18 37-04 0-27 4-14 4-83 36-08 South. 20 37-73 0-05 4-09 + 4-86 Mean 36-91 4 6 36-58 194 VERIFICATION AND EXTENSION OF LA CAILLE S ARC OF MERIDIAN. Star's No. in Ast. Soc. Cat., Name, and Position with regard to the Zenith. Face or Sector East. Day of Observa- tion, 1838. Apparent Zenith Distance from unreduced Observation. Reduction for Azimuthal Error. Refraction Precession Aberration and Nutation. Resulting Mean Zenith Distance, 1838, Jan. 0, and Mean of separate Re- sults uncorrected for Error of Collimation. A.S.C. 2110, i Sagittarii, South. Mar. 30 April 10 16 19 21 1°44'49''42 45-02 44-38 43-88 42-30 * // 325 0-01 0-13 0-03 0-01 1-73 1-71 1-72 1-76 1-72 + 5-30 5-27 5-27 5-28 + 5-29 Mean 1°44' 42-60 41-45 40-70 40-33 38-72 1 44 40-76 A.S.C. 2741, » Piscis Australis (Fomalhaut), North. Mar. 30 April 5 10 16 19 21 2 13 46-00 46-24 45-50 46-44 51-53 50-00 3-94 0-00 0-01 0-16 0-04 001 2-18 2-20 2-17 2-18 2-22 2-12 + 2-27 + 0-92 -0-23 - 1-62 -2-32 — 2-79 Mean 2 13 46-51 49-36 47-43 46-84 51-39 49-32 2 13 48-48 MEAN ZENITH DISTANCES OF STARS OBSERVED AT KLYP FONTEYN. 195 Face or Sector West. Day of Observa- tion, 1838. Mar. 31 April 4 6 15 18 20 Apparent Zenith Distance from unreduced Observation. 1 4.5 48-84 45-18 41-23 44-59 44-84 43-80 Reduction for Azimuthal Error. Mar. 31 April 4 15 18 20 5-07 0-00 0-00 0-16 0-11 0-02 Refraction, 2 12 54-29 47-62 50-09 45-84 49-39 6-13 0-00 0-20 0-14 0-03 1-71 1-75 1-74 1-74 1-77 1-75 Precession, Aberration, and Nutation. + 5-30 5-28 5-27 5-27 5-28 + 5-29 Mean 2-05 2-21 2-20 2-17 2-21 Resulting Mean Zenith Distance, 1838, Jan. 0, and Mean of separate Re- suits uncorrected for Error of CoUimation. o / /' 1 45 40-18 41-65 (37-70) 40-90 41-22 40-24 I 45 40-84 + 2-05 + i-l5 -1-39 -2-09 -2-55 Mean 2 12 52-26 5J>98 50-70 45-78 49-02 2 12 49-95 Resulting Error of CoUima- tion. 30-04 Resulting Mean Zenith Distance, 1 838, Jan. 0, com- pletely corrected; and Position with regard to the Zenith. 1 45 10-80 South. 29-27 2 13 19-22 North. C C 196 VERIFICATION AND EXTENSION OF LA CAILLE S ARC OF MERIDIAN. § 13. Collection of all the Results of Observation of each Star Star's No. in Face of Sector East, Ast. Soc. Cat., Name, and Position with regard to the Zenith. Day of Observa- tion, 1838. Apparent Zenith Distance from unreduced Observation. Reduction for Azimuthal Error. Refraction. Precession, Aberration, and Nutation. Resulting Mean Zenith Distance, 1838, Jan. 0, and Mean of separate Re- sults uncorrected for Error of Collimation. A. S. C. 699, May 16 0°14' I2'-45 o'bo 0-24 - 0-'79 o / // 14 13-48 a. Columbse, 27 9-97 0-00 0-24 3-60 13-81 South. June 3 6-51 0-00 0-24 5-51 12-26 4 6-42 0-00 0-24 5-80 12-46 8 6-12 0-00 0-24 6-93 13-29 20 2-86 0-00 0-24 10-43 13-53 23 0-98 0-00 0-25 11-32 12-55 25 1-87 0-00 0-25 -11-91 Mean 14-03 14 13-18 A. S. C. 732, May 27 1 54 15-71 0-02 1-92 — 2-68 1 54 20-29 /3 Columbse, June 3 12-99 0-02 1-91 4-59 19-47 South. 4 11-90 0-02 1-91 4-87 18-66 8 11-46 0-02 1-93 6-00 19-37 23 8-44 0-01 1-94 10-40 20-77 25 6-81 0-03 1-93 -11-00 19-71 Mean 1 54 19-71 MEAN ZENITH DISTANCES OF STARS OBSERVED AT CAPE TOWN. 197 AT Cape Town, and Deduction of Mean Zenith Distance, 1838, January 0. Face of Sector West. Resulting Mean Resulting Error of qpllima- . tion. Zenith Distance, 1838,Jan.O, com- pletely corrected ; and Position with regard to the Zenith. Day of Observa- tion, 1838. Apparent Zenith Distance from unreduced Observation. Reduction for Azimuthal Error. Refraction. Precession, Aberration, and Nutation. Resulting Mean Zenith Distance, 1838, Jan. 0, and Mean of separate Re- sults uncorrected for Error of Collimation. May 28 o / // 14 57-13 o'oo // 0-24 - 3-86 o / // 14 61-23 " O / // 29 55-35 0-00 0-24 4-14 59-73 June 7 57-03 0-01 0-24 6-64 63-90 17 51-35 0-00 0-24 9-54 61-13 19 50-01 0-00 0-24* 10-13 60-38 23-95 14 37-13 24 48-63 0-00 0-25 11-61 60-49 South. 26 48-24 0-00 0-24 -12-20 60-68 Mean 15 1-08 May 28 1 54 64-35 0-06 1-91 - 2-95 1 55 9-15 29 62-72 0-05 1-89 3-23 7-79 June 7 63-71 0-11 1-93 5-71 11-24 17 57-92 0-01 1-93 8-62 8-46 19 57-23 0-00 1-92 9-21 8-36 24-42 1 54 44-13 22 56-10 0-03 1-95 10-11 8-13 South. 24 55-35 0-03 1-95 10-70 7-97 26 54-12 0-02 1-93 -11-30 Mean 7-33 1 55 8-55 198 VERIFICATION AND EXTENSION OF LA CAILLE S ARC OF MERIDIAN. Star's No. in Ast. Soo. Cat., Name, and Position with regard to the Zenith. Face of Sector East. Day of Observa- tion, 1838. Apparent Zenith Distance from unreduced Observation. Reduction for Azimuthal Error. Refraction. Precession, Aberration, and Nutation. Resulting Mean Zenith Distance, 1838, Jan. 0, and Mean of separate Re- sults uncorrected for Error of CoUimation. A.S. C. 791, May 27 o / // 3 55 51-16 0'-'04 3-96 - l'-06 3 55 54-02 ^ Canis Majoris, June 2 51-01 0-00 3-94 2-47 52-48 North. 4 52-89 0-04 3-94 2-96 53-83 23 55-17 0-02 4-00 -7-91 51-24 Mean 3 55 52-89 A. S. C. 848, May 13 1 35 59-91 0-02 1-60 + 4-09 1 36 5-58 X. Canis Majoris, 27 64-46 0-02 1-61 + 1-36 7-41 North. June 8 66-04 0-02 1-61 - 1-40 6-23 23 69-21 0-01 1-62 -5-24 5-58 25 69-80 0-02 1-62 -5-78 Mean 5-62 1 36 6-08 A. S. C. 869, May 13 5 10 5-78 0-08 5-18 + 4-00 5 10 14-88 ^ Canis Majoris, 21 8-06 0-27 5-19 + 2-62 15-60 North. 27 9-89 0-05 5-21 + 1-47 16-52 30 12-85 0-56 5-19 + 0-86 18-34 June 2 11-32 0-00 5-19 + 0-22 16-73 ■ 3 10-88 0-06 5-18 + 0-01 16-01 4 11-52 0-06 5-18 -0-21 16-43 8 12-06 0-05 5-23 - 1-06 16-18 18 15-18 0-04 5-23 -3-46 16-91 23 13-94 0-03 5-27 — 4-76 14-42 25 15-32 0-06 5-24 -5-20 Mean 15-30 5 10 16-12 MEAN ZENITH DISTANCES OF STARS OBSERVED AT CAPE TOWN. 199 Face of S ECTOR West. Resulting Error of CoUima- tion. Resulting Mean Zenith Distance, 1838, Jan. 0, com- pletely corrected ; and Position with regard to the Zenith. Day of Observa- tion, 1838. Apparent Zenith Distance from unreduced Observation. Reduction for Azimuthal Error. Refraction. Precession, Aberration, and Nutation. Resulting Mean Zenith Distance, 1838, Jan. 0, and Mean of separate Re- sults uncorrected for Error of CoUimation. May 26 3° 54 SQ-SO 0-19 3''97 - 0-83 3 5°5 2-75 " 1 II 29 62-03 0-09 3-88 1-52 4-30 June 7 62-37 0-20 3-97 3-71 2-43 19 67-32 0-00 3-96 6-83 4-45 24-42 3 55 28-47 22 68-65 0-06 4-00 7-64 4-95 North. 24 69-15 0-05 4-00 8-18 4-92 26 69-29 0-04 3-97 — 8-72 Mean 4-50 3 55 4-04 June 22 1 35 21-45 0-03 1-63 -4-98 1 35 18-07 24 22-79 0-02 1-62 -5-51 18-88 23-80 1 35 42-28 North. Mean 1 35 18-48 May 17 5 9 19-96 0-05 5-19 + 3-33 5 9 28-43 26 20-45 0-24 5-22 + 1-67 27-10 29 23-96 0-12 5-11 + 1-06 30-01 June 19 25-99 0-00 5-21 -3-71 27-49 22 24 26-39 28-41 0-08 0-06 5-27 5-27 -4-45 -4-95 27-13 28-67 23-97 5 9 52-15 North. 26 28-71 0-06 5-22 -5-45 28-42 Mean 5 9 28-18 200 VERIFICATION AND EXTENSION OF LA CAILLE S ARC OF MERIDIAN. Star's No. in Face of Sector East. Ast. Soc. Cat., Name, and Position with regard to the Zenith. Day of Observa- tion, 1838. Apparent Zenith Distance from unreduced Observation. Reduction for Azimuthal Error. Refraction. Precession, Aberration, and Nutation. ResultinfT Mean Zenith Distance, 1838, Jan. 0, and Mean of separate Re- sults uncorrected for Error of Collimation. A.S.C. 903, May 21 2° 52 63" 14 0-16 2-90 + 6''62 2°52' 59-26 ic ArgAs, 27 59-19 0-03 2-91 -t-4-09 57-98 South. June 2 57-46 0-00 2-90 + 2-82 57-54 3 56-81 0-04 2-89 4- 2-60 57-06 8 56-72 0-03 2-91 + 1-44 58-16 23 53-75 0-02 2-94 -2-35 59-02 25 52-81 0-04 2-93 — 2'88 Mean 58-58 2 52 58-23 A.S.C. 915, May 21 4 55 58-49 0-26 4-95 -f4-35 4 56 7-53 1) Canis Majoris, 27 59-81 0-05 4-97 + 3-31 8-04 North. June 3 62-38 0-06 4-94 + 1-97 9-23 8 63-32 0-05 4-97 + 0-94 9-18 18 65-05 0-04 4-99 - 1-28 8-72 23 65-80 0-03 5-02 - 1-46 9-33 25 66-04 0-06 5-00 -2-94 Mean 8-04 4 56 8-58 A.S.C. 957, May 13 3 39 10-27 0-06 3-67 + 8-58 3 39 5-30 c ArgAs in Puppi, June 2 4-39 0-00 3-67 + 5-28 2-78 South. 21 2-36 0-03 3-69 + 1-00 5-02 23 2-41 0-02 3-72 + 0-50 5-61 27 1-37 0-01 3-67 — 0-52 5-55 Mean 3 39 4-85 A. S.C. 1015, ft May 13 2 J4 8-89 0-04 2-25 + 10-38 2 14 0-72 q ArgAs in Puppi, 21 7-75 0-13 2-25 + 9-49 0-38 South. Mean 2 14 0-55 1 MEAN ZENITH DISTANCES OF STARS OBSERVED AT CAPE TOWN. 201 Face of Sector West. Resulting Mean Resulting Error of Collima- tion. Zenith Distance, 1838,Jan.0,com- pletely corrected ; and Position with regard to the Zenith. Day of Observa- tion, 1838. Apparent Zenith Distance from unreduced Observation. Reduction for Azimuthal Error. Refraction. Precession, Aberration, and Nutation. Resulting Mean Zenith Distance, 1838, Jan. 0, and Mean of separate Re- sults uncorrected for Error of Colliraation. May 17 2°53' 48"37 0-03 2-90 + 5-97 O 1 It 2 53 45-27 " O / // 28 48-52 0-09 2-89 -f3-89 47-43 29 45-56 0-07 2-85 4-3-68 44-66 June 19 22 42-24 42-49 0-00 0-05 2-91 2-95 - 1-29 — 2-08 46-44 47-47 23-93 2 53 22-16 South. 24 39-92 0-04 2-94 -2-61 45-43 26 39-82 0-03 2-92 -3-15 Mean 45-86 2 53 46-08 May 17 4 55 11-67 0-05 4-95 + 4-98 4 55 21-55 28 9-49 0-14 4-94 + 3-12 17-41 29 14-24 0-11 4-87 H-2-94 21-94 June 19 17-20 0-00 4-97 -1-52 20-65 22 24 18-69 18-78 0-08 0-06 5-01 5-03 -2-22 — 2-70 21-40 21-05 23-85 4 55 44-74 North. 26 20-47 0-05 4-98 -3-18 Mean 22-22 4 55 20-89 May 17 3 39 56-14 0-04 3-67 + 8-04 3 39 51-73 28 55-45 0-12 3-66 6-24 52-75 29 53-87 0-09 3-61 6-05 51-34 June 19 50-81 0-00 3-69 1-49 53-01 23-57 3 39 28-42 22 48-83 0-06 3-73 0-75 51-75 South. 24 47-89 0-05 3-73 + 0-25 Mean 51-32 3 39 51-98 May 28 2 14 53-87 0-07 2-24 + 8-53 2 14 47-51 23-48 2 14 24-03 South. 202 VERIFICATION AND EXTENSION OF LA CAILLE S ARC OF MERIDIAN. Star's No. in Ast. Soc. Cat., Name, and Position with regard to the Zenith. Face or Sector East. Day of Observa- tion, 1838. Apparent Zenith Distance from unreduced Observation. Reduction for Azimuthal Error. Refraction. Precession, Aberration, and Nutation. Resulting Mean Zenith Distance, 1838, Jan. 0, and Mean of separate Re- sults uncorrected for Error of Collimation. A. S. C. 1061, May 13 0°48'45"85 o'-'oi o''82 + 1 1 "so 0° 48 35'36 ,3 Pixidis Nauticse, 21 43-97 0-05 0-82 10-59 34-15 South. 27 42'00 0-01 0-82 9-89 32-92 June 8 41-01 0-01 0-82 8-13 33-69 25 40-22 0-01 0-83 + 4-89 36-15 . Mean 48 34-45 A. S. C. 1070, May 13 1 19 1-72 0-00 1-31 + 11-01 1 19 14-04 a. Pixidis Nauticee, North. June 2 6-42 0-00 1-32 -f 8-86 Mean 16-60 1 19 15-32 A.S. C. 1115, May 13 4 12 .54-20 0-06 4-22 + 11-68 4 13 10-04 s Pixidis Nauticee, North. 21 55-98 0-22 4-23 + 11-18 Mean 11-17 4 13 10-61 Brisbane (2566), May 13 2 28 907 0-04 2-47 + 13-46 2 28 24-96 North. 21 9-57 0-13 2-47 13-14 25-05 27 11-84 0-02 2-48 + 12-76 27-06 Mean 2 28 25-69 Brisbane (2823), May 13 3 48 58-41 0-06 3-82 + 14-38 3 49 16-55 North. 21 60-09 0-20 3-82 14-24 17-95 27 61-47 0-04 3-84 14-02 19-29 June 2 61-77 0-00 3-83 + 13-62 19-22 Mean 3 49 18-25 MEAN ZENITH DISTANCES OF STARS OBSERVED AT CAPE TOWN. 203 Face of Sector W F.ST. Resulting Error of Collima- tion. Resulting Mean Zenith Distance, 1838,Jan.0,com. pletely corrected ; and Position with regard to the Zenith. Day of Observa- tion, 1838. Apparent Zenith Distance from unreduced Observation. Reduction for Azimuth al Error. Refraction. Precession, Aberration, and Nutation. Resulting Mean Zenith Distance, 1838, Jan. 0, and Mean of separate Re- sults uncorrected for Error of Collimation. May 26 O / /* 49 31-73 0'-'04 0-83 + 10'-'02 0° 49 22'-'50 " O / ,/ 28 30-79 0-03 0-82 9-76 21-82 29 28-86 002 0-83 9-62 20-05 June 17 22 27-47 25-99 0-00 0-01 0-82 0-83 6-51 5-51 21-78 21-30 23-34 48 57-79 24 24-90 0-01 0-83 5-10 20-62 South. 26 23-62 0-01 0-82 + 4-68 Mean 19-75 49 21-12 May 29* 1 18 19-26 0-01 1-30 4- 9-40 1 18 30-05 22-64 1 18 52-69 North; May 12 17 4 12 10-31 9-12 0-00 0-04 4-22 4-23 -fll-72 -fll-46 Mean 4 12 26-25 24-77 22-55 4 12 48-06 North. 4 12 25-51 May 12 2 27 22-61 0-00 2-47 4-13-48 2 27 38-56 17 28 21-82 20-88 0-02 0-07 , 2-47 2-46 13-33 12-68 37-60 35-95 24-06 2 28 1-63 29 23-20 0-06 2-43 + 12-60 Mean 38-17 North. 2 27 37-57 May 12 3 48 13-03 0-00 3-82 + 14-38 3 48 31-23 17 12-53 0-04 3-82 14-33 30-64 26 28 11-89 11-25 0-18 0-11 3-85 3-81 14-04 13-93 29-60 28-88 24-01 3 48 54-24 29 13-23 0-09 3-76 + 13-88 Mean 30-78 North. 3 48 30-23 DD 204 VERIFICATION AND EXTENSION OF LA CAILLE S ARC OF MERIDIAN. Star's No. in Ast. Soc. Cat., Name, Face of Sector E^ ST. Day of Observa- tion, 1838. Apparent Reduction Precession, Resulting Mean Zenith Distance, and Position with regard to the Zenith. Zenith Distance from unreduced Observation. for Azimuthal Error. Refraction. Aberration, and Nutation. 1838, Jan. 0, and Mean of separate Re- sults uncorrected for Error of Collimation. A. S. C. 1243, May 13 3° 40' 35''64 0''06 3-68 + 15-25 3°40' 54'-'51 a, Antlise Pneu- 21 36-28 0-19 3-68 15-25 55-02 maticae. 27 38-26 0-04 3-70 15-11 57-03 North. June 2 39-15 0-00 3-69 14-84 57-68 4 39-84 0-04 3-67 14-72 58-19 8 39-25 0-03 3-70 14-45 57-37 18 39-35 0-03 3-71 13-56 56-59 23 38-76 0-02 3-74 13-00 55-48 25 39-55 0-05 3-72 1276 55-98 27 39-50 0-01 3-68 + 12-50 Mean 55-67 3 40 56-35 A. S. C. 1299, May 13 2 20 43-60 0-04 2-36 + 17-64 2 20 28-28 South. 27 40-24 0-02 2-37 18-01 24-58 June 2 39-79 0-00 2-36 17-93 24-22 4 40-49 0-03 2-35 17-88 24-93 8 42-27 0-02 2-37 17-71 26-91 18 40-34 0-02 2-38 17-09 25-61 21 41-52 0-02 2-37 . 16-83 27-04 23 40-54 0-01 2-39 16-63 26-29 27 39-35 0-01 2-36 + 16-21 Mean 25-49 2 20 25-93 Brisbane (3350), May 13 2 49 58-02 0-04 2-83 + 16-67 2 50 17-48 North. 27 59-90 0-03 2-85 + 16-92 19-64 Mean 2 50 18-56 MEAN ZENITH DISTANCES OF STARS OBSERVED AT CAPF TOWN. 205 Face of Sector W) EST. Resulting Error of CoUima- tion. Resulting Mean Zenith Distance, 1838,Jan.0,com. pletely corrected; and Position with regard to the Zenith. Day of Observa- tion, 1838. Apparent Zenith Distance from unreduced Observation. Reduction for Azimuthal Error. Refraction. 'recession, Aberration, and Nutation. Resulting Mean Zenith Distance, 1838, Jan. 0, and Mean of separate Re- sults uncorrected for Error of CoUimation. May 12 3° 39 50 -61 o'-'oo 3-68 + 15-24 O / // 3 40 9-53 // O / " 17 49-13 0-04 3-68 15-28 8-05 28 46-95 0-11 3-67 15-07 5-58 29 49-22 0-09 3-69 15-03 7-85 June 19 24 51-25 52-09 0-00 0-05 3-70 3-73 13-45 12-88 8-40 8-65 24-07 3 40 32-29 North. 26 53-18 0-04 3-70 + 12-63 9-47 Mean 3 40 8-22 May 12 2 21 27-40 0-00 2-36 + 17-60 2 21 12-16 17 29-97 0-02 2-36 17-83 14-48 28 31-01 0-07 2-35 18-00 15-29 . 29 27-94 0-06 2-36 17-99 12-25 June 7 30-46 0-13 2-38 17-77 14-94 23-93 2 20 49-86 19 28-88 0-00 2-37 17-00 14-25 South. 22 . 28-58 b-04 2-40 16-72 14-22 26 26-75 0-03 2-37 + 16-32 12-77 Mean 2 21 13-80 May 12 2 49 13-04 0-00 2-83 + 16-27 2 49 32-14 15 12-15 0-02 2-81 16-75 31-69 28 8-79 0-08 2-83 16-91 28-45 23-95 2 49 54-61 29 10-96 0-07 2-84 16-90 30-63 North. June 7 11-06 0-15 2-86 + 16-65 Mean 30-42 2 49 30-67 206 VERIFICATION AND EXTENSION OF LA CAILLE S ARC OF MERIDIAN. Star's No. in Ast. See. Cat., Name, and Position with regard to the Zenitli. Face of Sector E \ST. Day of Observa- tion, 1838. Apparent Zenith Distance from unreduced Observation. Reduction for Azimuthal Error. Refraction. Precession, Aberration, and Nutation. Resulting Mean Zenith Distance, 1838, Jan. 0, and Mean of separate Re- sults uncorrected for Error of Collimation. A. S. C. 1356, May 13 2° 57 34'87 0''05 2"96 + 17-40 2°57'55-'l8 19 Crateris, 21 35-02 0-16 2-96 17-78 55-60 North. 30 37-69 0-33 2-96 17-96 58-28 June 4 37-89 0-03 2-95 17-94 58-75 6 37-39 0-04 2-99 17-90 58-24 8 36-11 0-03 2-98 17-87 56-93 18 36-90 0-02 2-98 17-47 57-33 21 37-30 0-02 2-98 17-29 57-55 23 35-47 ■ 0-02 3-01 17-16 .55-62 25 36-95 0-04 2-98 17-02 56-91 27 35-57 0-01 2-96 + 16-86 55-38 Mean 2 57 56-89 A. S.C. 1378, May 13 54 51-79 0-01 0-91 + 18-21 55 10-90 28 Crateris, 21 52-83 0-05 0-91 18-74 12-43 North. 27 53-92 0-01 0-91 19-00 13-82 30 49-72 0-10 0-91 19-09 • 9-62 • June 2 54-17 0-00 0-91 19-15 14-23 4 54-96 0-01 0-91 19-17 15-03 6 54-37 0-01 0-92 19-17 14-45 8 53-57 0-01 0-92 19-16 13-64 18 51-84 001 0-92 18-95 11-70 21 52-68 0-01 0-92 18-82 12-41 23 52-19 0-01 0-92 18-71 11-81 25 52-78 O-Ol 0-92 18-61 12-30 27 52-34 0-00 0-91 + 18-49 Mean 11-74 55 12-62 MEAN ZENITH DISTANCES OF STARS OBSERVED AT CAPE TOWN. 207 Face of Sector West. Day of Observa- tion, 1838. May 15 17 22 26 28 29 June 7 17 19 22 24 26 Apparent Zenith Distance from .unreduced Observation. May 1.5 17 26 28 29 June 7 17 19 22 24 26 2 56 49-40 47-47 48-80 46-68 45-49 47-76 46-58 46-53 47-86 48-85 48-85 49-84 Reduction for Azimuthal Error. Refraction. Precession, Aberration, and Nutation. 0-02 0-03 0-19 0-14 0-09 0-07 0-16 0-00 0-00 0-05 0-04 0-03 54 7-01 6-71 (0-19) 5-43 7-55 5-62 5-08 6-02 6-47 6-22 . 8-20 0-01 0-01 0-04 0-03 0-02 0-01 0-00 0-00 0-01 0-01 0-01 2-94 2-96 2-95 2-98 2-95 2-97 2-98 2-98 2-97 3-01 3-00 2-98 + 17-52 1761 17-82 17-99 17-94 17-95 17-88 17-52 17-42 17-23 17-09 + 16-93 Mean Resulting Mean Zenith Distance, 1838, Jan. 0, and Mean of separate Re- sults uncorrected for Error of CoUimation. 2 57 0-90 0-91 0-92 0-91 0-91 0-92 0-92 0-91 0-92 0-92 0-91 + 18-36 18-50 18-97 19-03 19-06 19-17 18-99 18-91 18-77 18-66 + 18-54 Mean 9-84 8-01 9-38 7-51 6-29 8-61 7-28 7-03 8-25 9-04 8-90 9-72 2 57 8-32 54 26-26 26-11 25-34 27-50 25-70 24-99 25-84 26-15 25-79 27-64 54 -26-13 Resulting Error of CoUima- tion. 24-28 Resulting Mean Zenith Distance, 1838, Jan. 0, com- pletely corrected; and Position with regard to the Zenith. 2 57 32-61 North. 23-25 54 49-37 North. 208 VERIFICATION AND EXTENSION OF LA CAILLE S ARC OF MERIDIAN. Star's No. in Ast. Soc. Cat., Name, and Position with regard to the Zenith. Face of Sector East. Day of Observa- tion, 1838. Apparent . Zenith Distance from unreduced Observation. Redaction for Azimutbal Error. Refraction, Precession, Aberration, and Nutation. Resulting Mean Zenith Distance, 1838, Jan. 0, and Mean of separate Re- suits uncorrected for Error of Collimation. A. S. C. 1433, May 13 o / " 4 13 12-39 0-07 4-24 + 19'45 t It 4 12 57-11 u Centauri, 27 12-34 0-05 4-26 20-79 55-76 South. 30 13-23 0-51 4-24 20-99 55-97 June 4 11-84 0-05 4-23 21-27 54-75 6 12-53 0-06 4-28 21-36 55-39 8 14-12 0-04 4-26 21-43 56-91 18 13-13 0-03 4-28 21-58 55-80 21 14-02 0-04 4-31 21-57 .56-72 23 14-51 0-03 4-31 21-53 57-26 25 13-77 0-06 4-26 21-49 56-48 27 14-12 0-01 4-24 +21-43 Mean 56-92 4 12 56-28 A. S. C. 1527, May 21 1 55 59-32 0-11 1-95 + 19-93 1 55 41-23 » Centauri, 27 57-84 0-02 1-95 20-48 39-29 South. June 5 56-55 0-03 1-94 21-18 37-28 6 58-43 0-03 1-96 21-27 39-09 8 58-63 0-02 195 21-38 39-18 18; 59-32 0-02 1-96 21-81 39-45 21 58-78 0-02 1-97 21-89 38-84 23 61-05 0-01 1-97 21-93 41-08 25 60-31 0-03 1-96 21-95 40-29 27 61-40 0-01 1-94 + 21-96 Mean 41-37 1 55 39-71 MEAN ZENITH DISTANCES OF STARS OBSERVED AT CAPE TOWN. 209 Face of Sector West. Resulting Mean Resulting Error of Collima- tion. Zenith Distance, 1838, Jan. 0, com- pletely corrected; and Position with regard to the Zenith. Day of Observa- tion, 1838. Apparent Zenith Distance from unreduced Observation. Reduction for Azimuthal Error. Refraction. Precession, Aberration, and Nutation. Resulting Mean Zenith Distance, 1838, Jan. 0, and Mean of separate Re- sults uncorrected for Error of Collimation. May 12 O / /' 4 13 57-57 o'-'oo 4-24 + 19-33 O / y/ 4 13 42-48 II /' II 15 58-60 0-03 4-21 19-68 43-10 26 61-97 0-22 •4-27 20-73 45-29 June 7 60-93 0-01 4-27 21-41 43-78 17 62-91 0-01 4-27 21-58 45-59 19 61-03 0-00 4-26 21-58 43-71 22 62-16 0-07 4-30 21-55 44-84 23-86 4 13 20-14 24 61-22 0-06 4-30 21-51 43-95 South. 26 60-43 0-05 4-26 +21-46 43-18 Mean 4 13 43-99 May 12 1 56 44-60 0-00 1-94 + 18-77 1 56 27-77 26 49-00 0^10 1-96 20-37 30-49 29 48-16 0-05 1-95 20-65 29-41 June 7 48-56 0-01 1-96 21-32 29-19 17 49-69 0-00 1-96 ■ 21-77 29-88 19 49-30 0-00 1-95 21-84 29-41 l^-ll 1 56 4-48 24 49-25 0-03 1-97 21-94 29-25 South. 26 48-56 0-02 1-95 +21-96 28-53 Mean 1 56 29-24 210 VERIFICATION AND EXTENSION OF LA CAILLE S ARC OF MERIDIAN. Star's No. in Ast. Soc. Cat., Name, and Position with regard to tlie Zenith. Face of Sector East. Day of Observa- tion, 1838. Apparent Zenith Distance from unreduced Observation. Reduction for Azimuthal Error. Refraction. Precession, Aberration, and Nutation. Resulting Mean Zenith Distance, 1838, Jan. 0, and Mean of separate Re- sults uncorrected for Error of Collimation. A. S. C. 1562, May 16 I°4l'59''l8 0-02 l'-69 + 18-53 '/ // 1 42 19-38 i Centauri, 21 58-29 0-09 1-70 19-05 18-95 North. 27 59-52 0-02 1-70 19-60 20-80 June 4 60-21 0-02 1-69 20-21 22-09 5 59-92 0-02 1-69 20-28 21-87 6 59-97 0-02 1-71 20-34 22-00 8 59-47 0-02 1-71 20-46 21-62 18 58-78 0-01 1-71 20-91 21-39 21 60-02 0-01 1-72 20-99 22-72 23 56-80 0-01 1-72 21-03 19-54 « 25 58-04 0-02 1-71 + 21-07 Mean 20-80 1 42 21-02. A. S. C. 1579, May 13 1 44 2-91 0-02 1-73 + 18-09 1 44 22-71 k Centauri, 16 1-87 0-02 1-73 18-44 22-02 North. 21 2-26 0-09 1-73 18-97 22-87 27 2-86 0-02 1-74 19-53 24-11 June 4 4-14 0-02 1-73 20-15 26-00 5 3-40 0-02 1-73 20-22 25-33 6 2-86 0-02 1-75 20-28 24-87 8 2-31 0-02 1-74 20-41 24-44 18 1-67 0-01 1-74 20-88 24-28 21 2-37 0-01 1-76 20-97 25-09 23 43 59-94 0-01 1-76 21-02 22-70 25 60-34 0-02 1-74 21-07 23-13 27 60-09 0-00 1-73 +21-09 Mean 22-91 1 44 23-88 i MEAN ZENITH DISTANCES OF STARS OBSERVED AT CAPE TOWN. 211 Face of Sector West. Resulting Mean Resulting Error of Collima- tion. Zenith Distance, 1838, Jan. 0, com. pletely corrected ; and Position with regard to the Zenith. Day of Observa- tion, 1838. Apparent Zenith Distance from unreduced Observations. Reduction for Azimuthal Error. Refraction. Precession, Aberration, and Nutation. Resulting Mean Zenith Distance, 1838. Jan. 0, and Wean of separate Re- suits uncorrected for Error of Collimation. May 12 1° 41' 15"44 o'-'oo l"70 + 18'-'07 f II 1 41 35-21 // / // 15 14-25 o-oi 1-68 18-41 34-33 17 13-10 0-02 1-70 18-63 33-41 26 10-68 0-08 1-71 19-52 31-83 29 11-92 0-04 1-70 19-77 33-35 June 7 9-20 0-01 1-71 20-40 31-30 17 9-05 0-00 1-71 20-87 31-63 19 9-54 0-00 1-70 20-93 32-17 24-02 1 41 57-00 22 9-80 0-03 1-72 21-01 32-50 North. 24 10-14 0-02 1-72 21-05 32-89 26 11-52 0-02 1-70 -I-21-08 Mean 34-28 1 41 32-99 May 12 1 43 18-18 0-00 1-73 + 17-97 1 43 37-88 15 16-45 0-01 1-72 18-33 36-49 22 13-72 Oil 1-73 1906 34-40 26 12-14 0-08 1-74 19-44 33-24 29 14-51 0-04 1-73 19-70 35-90 June 7 11-25 0-01 1-74 20-34 33-32 14 11-64 0-07 1-75 20-72 34-04 17 11-94 0-00 1-75 20-84 34-53 24-37 1 43 59-51 19 11-89 0-00 1-74 20-91 34-54 North. 22 12-00 0-03 1-75 21-00 34-72 24 13-13 0-02 1-75 21-04 35-90 26 13-92 0-02 1-74 + 2108 36-72 Mean 1 43 35-14 EE 212 VERIFICATION AND EXTENSION OF LA CAILLE S ARC OF MERIDIAN. Star's No. in Ast. Soc. Cat., Name, and Position with regard to the Zenith. Face of . Sector East. Day of Observa- tion, 1838. Apparent Zenith Distance from unreduced Observation. Reduction for Azimuthal Error. Refraction. Precession, Aberration, and Nutation. Resulting Mean Zenith Distance, 1838, Jan. 0, and Mean of separate Re- sults uncorrected for Error of Collimation. A. S. C. 1604, May 13 / // 1 38 47-04 0-02 l'-66 -f is-'io 1° 38 30-58 6 Centauri, 16 45-95 0-02 1-65 18-50 29-08 South. 21 47-73 0-12 1-66 19-13 30-14 27 46-74 0-02 1-67 19-81 28-58 June 4 47-04 0-02 1-65 20-60 28-07 5 46-84 0-02 1-65 20-69 27-78 6 47-19 0-03 1-67 20-77 28-06 8 46-05 0-02 1-67 20-93 26-77 18 48-82 0-02 1-67 21-60 28-87 21 48-77 0-02 1-67 21-76 28-66 23 50-40 0-01 1-68 21-84 30-23 25 50-05 0-03 1-67 21-92 29-77 27 51-34 0-01 1-66 +22-00 Mean 30-99 1 38 29-04 A. S. C. 1661, May 13 32 54-94 0-01 0-56 + 17-03 32 38-46 c' Centauri, 16 54-24 0-01 0-56 17-42 37-37 South. 18, 57-11 (0-12)*" 0-56 17-67 39-88 21 54-84 0-03 0-56 18-03 37-34 27 55-53 0-01 0-56 18-72 37-36 June 8 55-63 0-01 0-56 19-89 36-29 18 57-90 o-oo 0-56 20-65 37-81 21 56-76 0-00 0-57 20-84 36-49 23 58-15 0-00 0-57 20-95 37-77 25 58-49 0-01 0-66 21-06 37-98 27 59-98 0-00 0-56 + 21-18 39-36 Mean 32 37-83 * Se^ the remark following the observations of May 18, page 143. MEAN ZENITH DISTANCES OF STARS OBSERVED AT CAPE TOWN. 213 Face of Sector West. Resulting Error of Collima- tion. Resulting Mean Zenith Distance, 1838,Jan.O, com- pletely corrected; and Position with regard to the Zenith. Day of Observa- tion, 1838. Apparent Zenith Distance from unreduced Observation. Reduction for Azimuthal Error. Refraction. Precession, Aberration, and Nutation. Resulting Mean Zenith Distance, 1838, Jan. 0, and Mean of separate Re- sults uncorrected for Error of Collimation. May 12 I 39 32"32 o'-'oo l'-66 -f 17-96 1° 39 16'-'02 // / It 15 34-39 0-01 1-65 18-37 17-66 17 34-79 0-02 1-66 18-63 17-80 22 35-88 0-14 1-65 19-25 18-14 26 37-46 0-11 1-67 19-70 19-32 29 36-57 0-05 1-66 20-02 18-16 June 7 39-83 0-01 1-67 20-86 20-63 17 19 39-63 39-34 0-01 0-00 1-67 1-66 21-54 21-67 19-75 19-33 24-70 1 38 53-74 22 38-89 0-03 1-68 21-81 18-73 South. 24 38-74 0-03 1-68 21-88 18-51 26 (37-56) 0-02 1-67 + 21-96 Mean 17-25 1 39 18-44 May 12 33 39-18 0-00 0-56 + 16-90 33 22-84 15 40-4L 0-00 0-55. 17-29 23-67 17 41-90 0-01 0-56 17-55 24-90 22 43-58 0-04 0-56 18-15 25-95 26 43-43 0-03 0-56 18-37 25-59 29 41-40 0-01 0-56 1893 23-02 June 7 44-52 0-04 0-56 19-80 25-24 17 19 46-05 45-46 0-00 0-00 0-56 0-56 20-57 20-7^ 26-04 25-30 23-40 33 1-23 South. 22 45-06 0-01 0-56 20-90 24-71 24 45-16 001 0-56 21-01 24-70 26 44-17 0-01 0-56 + 21-11 Mean 23-61 33 24-63 214 VERIFICATION AND EXTENSION OF LA CAILLE S ARC OF MERIDIAN. Star's No. in Ast. Soc. Gat., Name, Face of Sector East. Day of Observa- tion, 1838. Apparent Reduction Precession, Resulting Mean Zenith Distance, and Position witli regard to the Zenith. Zenith Distance from unreduced Observation. for Azimuthal Error. Refraction. Aberration, and Nutation. 1838, Jan. 0, and lUean of separate Re- sults uncorrected for Error of Cullimation. A.S. C. 1742, May 13 2°20'5l''71 u 002 11 2-36 -H5'-60 2°20' 38''45 ip« Lupi, 18 52-79 (0-53)* 2-36 16-27 38-35 South. 21 52-79 0-23 2-36 16-65 38-27 June 6 52-99 0-03 2-38 18-52 36-82 8 51-21 0-02 2-37 18-73 34-83 18 55-17 0-02 2-38 19-67 37-86 21 54-67 0-02 2-40 19-93 37-12 23 56-35 0-01 2-40 20-09 38-65 25 55-37 0-03 2-38 -)-20-24 37-48 Mean 2 20 37-54 A. S. C. 1774, May 13 4 40 55-02 0-04 4-69 + 15-12 4 41 14-79 40 Libra, 18 56-35 0-98 4-70 15-56 15-63 North. 21 56-75 0-24 4-70 15-82 17-03 27 56-16 0-05 4-70 16-30 17-11 June 6 56-06 0-06 4-74 17-03 17-77 8 58-73 0-04 4-72 17-17 20-58 18 53-68 0-03 4-73 17-77 16-15 21 ■ 55-56 0-04 4-77 17-93 18-22 23 54-28 0-02 4-77 18-02 17-05 25 53-68 0-06 4-73 18-12 16-47 27 53-19 001 4-70 + 18-21 Mean 16-09 4 41 16-99 * See the remark following the observations of May 18, page 143. MEAN ZENITH DISTANCES OF STARS OBSERVED AT CAPE TOWN. 215 Face of Sector W EST. Resulting Mean Resulting Error of CoUima- tion. Zenith Distance, 1838,Jau.0,com- pletely corrected ; and Position with regard to tlie Zenith. Day of Observa. tion, 1R38. Apparent Zenith Distance from unreduced Observation. Reduction for Azimuthal Error. Refraction. 2-36 Precession, Aberration, and Nutation. Resulting Mean Zeniih Distance, 1838, Jan. 0, and Mean of separate Re- sults uncorrected for Error of CoUimation. May 12 2°2l'37''28 0-00 + 15-46 2''2l'24'-'l8 // O , /, 17 39-66 0-02 2-36 16-13 25-87 22 40-99 0-16 2-35 16-78 26-40 29 39-95 006 2-36 17-63 24-62 June 7 41-83 0-17 2-38 18-63 25-41 17 43-81 0-00 2-38 19-59 26-60 19 43-61 0-00 2-37 19-76 26-22 22 43-17 0-04 2-39 20-01 25-51 23-96 2 21 1-50 24 42-77 0-03 2-39 20-16 24-97 South. 26 42-67 0-03 2-37 +20-31 Mean 24-70 2 21 25-45 May 12 4 40 12-36 0-00 4-69 + 15-02 4 40 32-07 15 11-80 0-03 ■ 4-66 15-29 31-72 17 10-78 0-04 4-70 15-47 30-91 22 10-18 0-30 4-67 15-90 30-45 . 26 8-30 0-22 4-73 16-22 29-03 29 9-44 0-11 4-70 16-46 30-49 June 7 8-55 0-32 4-73 17-10 30-06 17 4-75 0-01 4-73 17-71 27-18 23-54 4 40 53-46 19 6-03 0-00 4-71 17-82 28-56 North. 22 6-23 0-07 4-75 17-97 28-88 24 6-97 0-06 4-75 + 18-07 Mean 29-73 4 40 29-92 216 VERIFICATION AND EXTENSION OF LA CAILLE S ARC OF MERIDIAN, Star's No. in Face or Sector East. Ast. Soc. Cat., Name, and Position with regard to the Zenith. Day of Observa- tion, 1838. Apparent Zenith Distance from unreduced Observation. Reduction for Azimuthal Error. Refraction. Precession, Aberration, and Nutation. Resulting Mean Zenith Distance, 1838, Jan. 0, and Mean of separate Re- sults uncorrected for Error of Collimation. A. S. C. 1797, May 13 0°47' 44'b6 o'-'oi 0"79 -fl4'-'48 o / // 47 59-32 A Lupi, 18 45-15 0-17 0-79 15-02 60-79 North. 21 43-96 0-04 0-79 15-34 60-05 27 44-70 0-01 0-79 15-94 61-42 June 6 43-17 0-01 0-80 16-89 60-85 8 45-44 0-01 0-79 17-06 63-28 18 40-80 0-01 0-80 17-88 59-47 21 42-03 0-01 0-80 18-10 60-92 23 41-29 0-00 0-80 18-24 60-33 27 40-50 0-00 0-79 -1-18-50 59-79 Mean 48 0-62 A. S. C. 1821, May 18 4 7-91 0-93 4-02 + 14-45 3 59 56-55 D Lupi, 21 6-77 0-23 4-03 14-85 55-72 South. 27 7-81 0-04 4-03 15-61 56-19 June 6 6-82 0-05 4-06 16-81 54-02 8 6-53 0-04 404 17-04 53-49 18 9-89 0-03 4-05 18-11 55-80 21 9-94 0-04 4-08 18-41 55-57 23 10-48 0-02 4-08 18-60 55-94 25 10-18 0-05 4-05 18-79 55-39 27 11-22 0-01 4-03 + 18-97 Mean 56-27 3 59 55-49 MEAN ZENITH DISTANCES OF STARS OBSERVED AT CAPE TOWN. 217 Face of Sector West. Resulting Mean Resulting Error of Collima- tion. Zenith Distance, 1838, Jan. 0, com- pletely corrected; and Position with regard to the Zenith. Day of Observa- tion, 1838. Apparent Zenith Distance from unreduced Observation. Reduction for Azimuthal Error. Refraction. Precession, Aberration, and Nutation. Resulting Mean Zenith Distance, 1838, Jan. 0, and Mean of separate Re- sults uncorrected for Error of Collimation. May 12 0° 46 SS'-'SS 0-00 0-79 + 14-37 0°47' 13"74 // O 1 „ 17 59-23 0-01 0-79 1491 14-92 22' 56-21 0-06 0-79 15-44 12-39 26 56-21 0-04 0-80 15-85 12-82 29 56-80 0-02 0-79 16-15 13-72 June 7 56-21 0-00 0-80 16-97 13-98 17 52-65 0-00 0-80 17-80 11-25 23-61 47 37-01 19 53-59 0-00 0-79 17-95 12-33 North. 22 54-82 0-01 0-80 18-17 13-78 24 54-33 0-01 0-80 18-31 13-43 26 55-86 0-01 0-79 + 18-45 Mean 15-09 47 13-40 May 12 4 51-21 0-00 4-02 + 13-66 4 41-57 17 54-97 0-04 4-03 14-32 44-64 22 "55-76 0-28 4-01 14-97 44-52 26 .55-81 0-21 4-06 15-48 44-18 . 29 55-66 0-10 4-03 15-85 43-74 June 7 56-95 0-00 4-05 16-92 44-08 24-18 4 19-67 17 60-36 0-00 4-06 1801 46-41 South. 24 57-24 0-06 4-07 18-70 42-45 26 57-94 0-05 4-05 + 18-88 43-06 Mean 4 43-85 218 VERIFICATION AND EXTENSION OF LA CAILLE S ARC OF MERIDIAN. Star's No. in Ast. Soc. Cat., Name, and Position with regard to tlie Zenith. Face or Sector East. Day of Observa- tion, 1838. Apparent Zenith Distance from unreduced Observation. Reduction for Azimuth al Error. Refraction. Precession, Aberration, and Nutation. Resulting Mean Zenith Distance, 1838, Jan. 0, and nieau of separate Re- sults uncorrected for Error of CoUimation. A. S. C. 1835, May 13 2° 25 48"44 0-02 2-44 + 13-'58 O / 11 2 25 37-28 t Lupi, 18 49-14 0-55 2-44 14-18 36-85 South. 21 48-44 0-14 2-44 14-54 36-20 27 48-99 0-03 2-45 15-24 36-17 June 4 47-65 0-03 2-44 16-11 33-95 6 48-49 0-03 2-47 16-33 34-60 18 51-56 0-02 2-46 17-53 36-47 21 50-82 0-02 2-48 17-80 35-48 23 51-90 0-01 2-48 17-98 36-39 2.5 51-31 0-03 2-46 18-15 35-59 27 52-00 0-01 2-44 + 18-32 Mean 36-11 2 25 35-92 A. S. C. 1866, May 13 3 24 55-65 0-03 ■ 3-42 + 13-37 3 25 12-41 p Scorpii, 18 54-86 0-72 3-42 13-78 11-34 North. 21 57-23 0-18 3-42 14-02 14-49 27 57-73 0-03 3-42 14-49 15-61 June 6 57-13 0-04 3-45 15-22 15-76 18 54-17 0-03 3-44 16-02 13-60 25 52-49 0-04 3-44 16-44 12-33 27 52-59 0-01 3-42 + 16-55 12-55 Mean 3 25 13-51 MEAN ZENITH DISTANCES OF STARS OBSERVED AT CAPE TOWN. 219 Face or Sector West. Day of Observa- tion, 1838. May 12 17 22 26 29 June 7 17 22 24 26 Apparent Zenith Distance from unreduced Observation. May 12 15 17 22 26 29 June 7 17 19 24 26 2 26 32-69 35'21 36-00 37-48 37-09 38-27 41-63 40-15 38-92 39-46 Reduction for Azimuthal Error. 3 24 11-06 9-48 9-48 6-76 6-81 8-20 5-43 4-73 4-64 5-87 7-21 0-00 0-03 0-17 0-12 0-06 0-00 0-00 0-04 0-03 0-03 Refraction. Precession, Aberration, and Nutation. 0-00 0-02 0-03 0-22 0-16 0-08 0-00 0-00 0-00 0-04 0-04 2-44 2-45 2-44 2-46 2-45 2-46 2-46 2-47 2-47 2-46 + 13-46 14-07 14-66 15-12 15-46 16-44 17-43 17-89 18-07 + 18-23 Mean Resulting Mean Zenith Distance, 1838, Jan. 0, and Mean of separate Re- sults uncorrected for Error of CoUimation. 2 26 21-67 23-56 23-61 24-70 24-02 24-29 26-66 24-69 23-29 23-66 2 26 24-02 3-42 3-39 3-42 3-41 3-45 3-42 3-45 3-45 3-43 3-46 3-44 + 13-29 13-53 13-70 14-10 14-41 14-64 15-29 1.5-96 16-08 16.38 + 16-49 Mean 3 24 27-77 26-38 26-.57 24-05 24-51 26-18 24-17 24-14 24-15 . 25-67 27-10 3 24 25-52 Resulting Error of CoUima- tion. 24-05 Resulting Mean Zenith Distance, 1838,Jau.0,com- pletely corrected ; and Position with regard Co the Zenith. 2 25 59-97 South. 24-00 3 24 49-52 North. F F 220 VERIFICATION AND EXTENSION OF LA CAILLE S ARC OF MERIDIAN. Star's No. in Ast. Soc. Cat., Name, and Position with regard to the Zenith. Face of Sector E AST. Day of Observa- tion, 1838. Apparent Zenith Distance from unreduced Observation. Reduction for Azimuthal Error. Refraction. Precession, Aberration, and Nutation. Resulting Mean Zenith Distance, 1838, Jan. 0, and Mean of separate Re- sults uncorrected for Error of Collimation. A. S. C. 1889, May 13 / // 25 12-01 0-00 0-43 + 12'-42 0°24' 60'-02 a, Normse, 18 13-74 0-09 0-43 12-92 61-16 South. 27 12-66 0-00 0-43 13-80 59-29 June 6 1226 0-01 0-43 14-73 57-95 18 13-74 0-00 0-43 15-79 58-38 21 14-43 0-00 0-43 16-04 58-82 23 15-03 0-00 0-43 16-20 59-26 25 16-41 0-01 0-43 16-36 60-47 27 17-10 0-00 0-43 -f 16-51 61-02 Mean 24 59-60 A.S.C. 1915, May 13 4 3-89 0-00 0-08 H-11-43 3 52-54 6 Scorpii, 18 3-65 0-02 0-08 11-87 51-84 South. 21 2-86 0-00 0-08 12-13 50-81 27 3-40 0-00 0-08 12-66 50-82 June 4 2-26 0-00 0-08 13-35 48-99 6 3-20 0-00 0-08 13-52 49-76 18 5-13 0-00 0-08 14-52 50-69 21 4-44 0-00 0-08 14-76 49-76 23 5-53 0-00 0-08 14-92 50-69 25 6-51 0-00 0-08 15-07 51-52 27 6-12 0-00 0-08 + 15-23 50-97 Mean 3 50-76 MEAN ZENITH DISTANCES OF STARS OBSERVED AT CAPE TOWN. 221 Face of Sector W EST. Resulting Mean Resulting Error of Colllma- tion. Zenith Distance, 1838, Jan. 0, com- pletely corrected ; and Position with regard to the Zenith. Day of Observa- tion, 1838. Apparent Zenith Distance from unreduced Observation. Reduction for Azimuthal Error. Refrabtion. Precession, Aberration, and Nutation. Resulting Mean Zenith Distance, 1838, Jan. 0, and Mean of separate Re- sults uncorrected for Error of CoUimation. May 12 0° 25 56-95 o'-'oo 0-43 -f 12-32 0° 25 45-06 // O / // 15 57-54 0-00 0-42 12-62 45-34 17 58-88 0-00 0-43 12-82 46-49 22 59-91 0-03 0-43 13-31 47-00 29 59-52 0-01 0-43 13-99 45-95 June 7 60-70 0-00 0-43 14-83 46-30 17 19 63-47 62-83 0-00 0-00 0-43 0-43 15-71 15-87 48-19 47-39 23-49 25 '23-09 South. 22 64-16 0-01 0-43 16-12 48-46 24 62-19 0-01 0-43 16-28 46-33 26 61-74 0-00 0-43 -J- 16-43 Mean 45-74 -25 46-57 May 12 4 48-83 0-00 0-08 -t- 11-34 4 37-57 15 50-16 0-00 0-07 11-60 38-63 17 51-00 0-00 0-08 11-78 39-30 22 51-70 0-00 0-08 12-21 39-57 26 54-66 0-00 0-08 12-57 42-17 29 52-39 0-00 0-08 13-02 39-45 June 7 52-93 0-00 0-08 13-61 39-40 14 17 19 55-06 55-06 54-91 0-00 0-00 0-00 0-08 0-08 0-08 14-19 14-44 14-60 40-95 40-70 40-39 24-49 4 15-25 South. 22 55-45 0-00 0-08 14-84 40-69 \ 24 53-62 0-00 0-08 14-99 38-71 26 53-97 0-00 0-08 -fl5-15 Mean 38-90 4 39-73 222 VERIFICATION AND EXTENSION OF LA CAILLE S ARC OF MERIDIAN. Star's No. in Face of Sector East. Ast. Soc. Cat., Name, and Position with regard to the Zenith. Day of Observa- tion, 1838. Apparent Zenith Distance from unreduced Observation. Reduction for Azimuthal Error. Refraction. Precession, Aberration, and Nutation. Resulting Alean Zenith Distance, 1838, Jan. 0, and Mean of separate Re- sults uncorrected for Error of CoUimation. A. S. C. 1947, May 13 0° 2 13"47 o'-'oo 0'-'03 + 10-62 0° 2 24-'l2 k Scorpii, 21 13-27 0-00 0-03 11-26 24-56 North. 27 13-96 0-00 0-03 11-74 25-73 June 6 13-77 0-00 0-03 12-54 26-34 18 12-28 0-00 0-03 13-50 25-81 21 11-69 0-00 0-03 13-73 25-45 25 10-01 0-00 0-03 14-04 2408 27 988 0-00 0-03 -f 14-19 24-10 Mean 2 25-02 A. S. C. 1969, May 13 I 27 5 46 0-01 1-45 -HO-12 1 27 17-02 u Scorpii, 21 6-8.5 0-08 1-45 10-63 18-85 North. 27 6-45 0-01 1-45 11-03 18-92 June 6 6-85 0-02 1-44 11-71 19-98 18 4-72 001 1-46 12-53 18-70 21 4-77 0-01 1-47 12-73 1896 23 4-27 0-01 1-47 12-86 18-59 25 3-09 002 1-46 13-00 17-53 27 3-38 0-00 1-45 -1-13-13 17-96 Mean 1 27 18-50 MEAN ZENITH DISTANCES OF STARS OBSERVED AT CAPE TOWN. 223 Face op Sector West. Resulting Error of CoUima- tion. Resulting Mean Zenith Distance, 1838,Jan.0,com. pletely corrected ; and Position witli regard to the Zenith. Day of Observa. tion, 1838. Appnrent Zenith Distance from unreduced Observation. Reduction for Azimutlml Error. Refraction. Precession, Aberration, and Nutation. Resulting Mean Zenith Distance, 1838, JHn, 0, and Mean of separate Re- sults uncorrected for Error of CoUimation. May 12 15 17 22 26 29 June 7 14 17 24 o / // 1 28-43 26-98 25-91 21-96 21-96 24-28 23-39 21-66 20-48 2) -96 o'-'oo 0-00 0-00 0-00 0-00 0-00 0-00 0-00 0-00 0-00 o-b3 0-03 0-03 0-03 0-03 0-03 0-03 0-03 0-03 0-03 ■ + 10-53 10-78 10-94 11-34 11-66 11-90 12-62 13-18 13-42 + 13-96 Mean o ' /' 1 38-99 37-79 36-88 33-33 33-65 36-21 36-04 . 34-87 33-93 35-95 1 35-76 24-63 O / It 2 0-39 North. May 12 15 17 22 26 29 June 7 14 17 22 24 26 1 26 21-47 21-12 18-54 19-87 18-70 19-09 17-71 18-01 15-14 15-98 16-97 18-50 0-00 0-01 0-01 009 0-07 0-03 0-00 0-06 0-00 0-02 0-01 0-02 1-45 1-44 1-45. 1-44 1-46 1-45 1-46 1-46 1-46 1-47 1-47 1-46 + 10-05 10-24 10-37 10-73. 10-94 11-17 11-78 12-25 12-46 12-80 12-93 + 13-07 Mean 1 26 32-97 32-79 30-35 31-95 31-03 31-68 30-95 31-66 29-06 30-23 31-36 33-01 23-54 1 26 54-96 North. I 26 31-42 224 VERIFICATION AND EXTENSION OF LA CAILLE S ARC OF MERIDIAN. Star's No. in Ast. Soc. Cat., Name, and Position with regard to the Zenith. A. S. C. 2007, A Scorpii, South. A. S. C. 2043, yTelescopii, South, Face or Sector East. Day of Observa- tion, 1838. May J3 21 27* June 6 18 21 23 25 27 Apparent Zenith Distance from unreduced Observation. 3 3 May 13 21 June 18 21 23 25 27 5-61 5-42 5-12 3-34 7-05 6-80 6-80 8-58 9-57 Reduction for Azimuthal Error. 0-03 0-17 0-03 0-04 0-02 0-03 0-02 0-04 0-01 3 25-98 24-30 26-77 25-98 27-36 28-11 28-30 0-03 0-17 0-02 0-03 0-02 0-04 0-01 Refraction 3-07 3-07 3-07 3-09 3-09 3-11 3-11 3-09 3-07 3-07 3-08 3-09 3-12 3-12 3-09 3-07 Precession, Aberration, and Nutation Resulting Mean Zenith Distance, 1838, Jan. 0, and Mean of separate Re- sults uncorrected for Error of Collimation. -f- 8-41 9-04 9-53 10-39 11-46 11-74 11-92 12-10 -M2-28 Mean -f 7-35 7-80 10-11 10-37 10-55 10-72 -f 10-90 Mean 2 60-24 59-28 58-63 56-00 58-66 58-14 57-97 59-53 60-35 3 2 58-76 3 21-67 19-41 19-73 18-70 19-91 20-44 20-46 3 3 20-05 MEAN ZENITH DISTANCES OF STARS OBSERVED AT CAPE TOWN. 225 Face of Sector West. Resulting Mean Resulting Error of Collima- tion. Zenith Distance, 1838,Jan.0,com- pletely corrected; and Position with regard to the Zenith. Day of Observa- tion, 1838. Apparent Zenith Distance from unreduced Observation. Reduction for Azimutlial Error. Refraction. Precession, Aberration, and Nutation. Resulting Mean Zenith Distance, 1838, Jan. 0, and Mean of separate Re- sults uncorrected for Error of Collimation. May 12 3° 3'49''90 0-00 3-07 + 8-33 3° 3' 44-64 " / /, 15 50-79 0-02 3-04 8-56 45-25 17 52-72 0-03 3-07 8-72 47-04 22 52-97 0-21 3-06 9-12 46-70 26 55-64 0-16 309 9-45 49-12 29 54-26 0-08 3-07 9-70 47-55 June 7 55-54 0-00 3-09 10-48 48-15 24-14 3 3 22-89 14 56-18 0-13 3-10 11-10 48-05 South. 17 57-42 0-00 3-09 11-38 49-13 22 55-39 0-05 3-12 11-83 46-63 24 54-80 0-04 3-11 12-01 45-86 26 55-39 0-04 3-09 + 12-19 Mean 46-25 3 3 47-03 May 12 3 4 9-97 0-00 3-07 + 7-29 3 4 5-75 15 10-27 0-02 3-05 7-49 5-81 17 12-64 0-03 3-08 7-62 8-07 22 13-98 0-21 3-06 7-97 8-86 26 14-33 0-16 3-10 8-26 9-01 29 12-79 0-08 3-08 8-48 7-31 June 7 15-31 0-00 3-10 9-19 9-22 23-95 3 3 44-00 14 16-45 0-13 3-10 9-77 9-65 South. 17 16-99 0-00 3-10 10-02 10-07 22 15-66 0-05 3-12 10-46 8-27 24 14-13 0-04 3-11 10-63 6-57 26 14-42 0-04 3-09 -f 10-81 Mean 6-66 3 4 7-94 226 VERIFICATION AND EXTENSION OF LA CAILLe's ARC OF MERIDIAN. Star's No. in Face of Sector E AST. Ast. Soc. Cat., Name, and Day of Apparent Zenith Distance Reduction for Precession, Aberration, Resulting Mean Zenith Distance, 1838, Jan. 0, and Position witli regard to the Zenith. Observa- tion, 1838. from unreduced Observation. Azimutlial Error. Refraction. and Nutation. Mean of separate Re- sults uncorrected for Error of CoHimation. A. S. C. 2079, May 13 3''30'2l'-'50 0-03 3-51 + 7'-'62 3° 30 32''60 . A Sagittai'ii, ^ North. 21 22-64 0-19 3-51 7-80 33-76 27 23-53 0-03 3-51 7-97 34-98 June 6 24-42 0-04 3-54 8-28 36-20 18 20-56 0-03 3-53 8-75 32-81 21 21-41 0-03 3-56 8-88 33-82 23 21-45 0-02 3-56 8-97 33-96 25 20-02 0-04 3-53 9-06 32-57 27 20-07 0-01 3-51 + 9-15 32-72 Mean 3 30 33-71 A. S.C. 2101, May 13 2 52 31-96 0-02 2-89 + 5-56 2 52 29-27 /3 Telescopii, 21 31-86 0-10 2-89 5-92 28-73 South. 27 30-38 0-02 2-89 6-23 27-02 June 6 30-72 0-02 2-92 6-84 26-78 18 32-15 0-01 2-90 7-68 27-36 21 31-22 0-02 2-94 7-90 26-24 23 32-65 0-01 2-93 8-06 27-51 25 34-82 0-02 2-91 8-22 29-49 27 34-33 0-01 2-89 + 8-38 28-83 Mean 2 52 27-91 MEAN ZENITH DISTANCES OF STARS OBSERVED AT CAPE TOWN. 227 Face or Sector West. lesulting Error of Collima- tion. Resulting Mean Zenith Distance, l838,Jan.0,com- pletely corrected; ind Position with regard to the Zenith. Day of Observa- tion, 1838. Apparent Zenitii Distance from unreduced Observation. Reduction for Azimuthal Error. Precession, _ , ^. Aberration, lefraction. and Nutation. Resulting Mean Zenith Distance, 1838, Jan. 0, and Mean of separate Re- sults uncorrected for Error of Collimation. May 12 o / // 3 29 35-53 0-00 3-51 + 7-06 O 1 It 3 29 46-10 // / // 15 33-80 0-02 3-48 7-66 44-92 17 33-95 0-03 3-51 7-71 45-14 22 33-50 0-22 3-50 7-83 44-61 26 32-71 0-17 3-54 7-94 44-02 29 33-41 0-08 3-51 8-03 44-87 June 7 31-53 0-00 3-54 8-32 43-39 24-64 3 30 09-08 14 31-23 0-14 3-54 8-58 43-21 North. 17 31-13 0-00 3-54 8-70 43-37 22 30-14 0-06 3-57 8-92 42-57 24 32-66 0-04 3-56 9-01 45-19 26 33-31 0-04 3-53 -1-9-10 Mean 45-90 3 29 44-44 May 12 2 53 17-97 0-00 2-89 -I-5-51 2 53 15-35 15 17-24 0-01 2-87 5-64 14-46 17 18-87 0-02 2-89 5-73 16-01 22 20-20 0-13 2-88 5-97 16-98 26 20-80 0-09 2-92 6-18 17-45 29 19-81 0-05 2-89 6-34 16-31 June 7 21-09 0-00 2-92 6-90 17-11 24-23 2 52 52-14 14 21-59 0-08 2-92 7-38 17-05 South. 17 23-07 0-00 2-91 7-60 18-38 22 21-39 0-03 2-94 7-98 16-32 24 20-80 0-03 2-93 8-14 15-56 26 20-80 0-02 2-91 -f 8-30 Mean 15-39 2 53 16-36 G G 228 VERIFICATION AND EXTENSION OF LA CAILLE S ARC OF MERIDIAN. Star's No. in Ast. Soc. Cat., Face of Sector East. Name, and Position with regard to the Zenith. Day of Observa- tion, 1838. Apparent Zenith Distance from unreduced Observation. Reduction for Azimuthal Error. Refraction. Precession, Aberration, and Nutation. Resulting Mean Zenith Distance, 1838, Jan. 0, and Mean of separate Re- sults uncorrected for Error of CoUimation. A. S. C. 2110, May 13 0°3l' 37"98 o'-'oi 0-53 + 5-63 0°3r32'87 i Sagittarii, 21 38-22 0-03 0-54 5-87 32-86 South. S7 37-48 0-01 0-53 6-07 31-93 June 6 37-38 0-01 0-54 6-51 31-40 18 38-08 0-00 0-54 7-15 31-47 21 38-08 0-00 0-54 7-33 31-29 23 , 38-82 0-00 0-54 7-46 31-90 25 40-65 0-01 0-54 7-58 33-60 27 40-94 0-00 Q'53 + 7-71 33-76 Mean 31 32-34 A. S. C. 2741, June 18 3 27 5-66 0-03 3-47 -14-73 3 26 54-37 ac Piscis Australia 21 6-15 0-03 3-52 15-18 54-46 (Fomalhaut), 23 4-57 0-02 3-51 -15-44 52-62 North. Mean 3 26 53-82 MEAN ZENITH DISTANCES OF STARS OBSERVED AT CAPE TOWN. 229 Face of Sector West. Resulting Error of Collima- tion. Resulting Mean Zenith Distauce, 1838, Jan. 0, com. pletely corrected, and Position with regard to the Zenith. Day of Observa- tion, 1838. Apparent Zenith Distance from unreduced Observation. Reduction for Azimuthal Error. Refraction. Precession, Aberration, and Nutation. Resulting Mean Zenith Distance, 1838, Jan. 0, and Mean of separate Re- suits uncorrected for Error of Collimation. May 12 0° 32 23'45 o'-oo 0''53 + 5-'61 0°32' 18-37 " O / n 15 24-25 0-00 0-53 5-68 19-10 17 24-94 0-01 0-53 5-74 19-72 22 25-63 0-04 0-53 5-89 20-23 26 25-43 0-03 0-54 6-04 19-90 29 June 7 24-64 26-17 0-01 0-00 0-54 0-54 6-15 6-56 19-02 20-15 23-73 31 56-07 South. 14 27-51 0-02 0-54 6-92 21-11 17 28-94 0-00 0-54 7-09 •22-39 22 26-77 0-01, 0-54 7-39 19-91 24 25-93 0-01 0-54 7-52 18-94 26 25-73 0-01 0-54 + 7-65 Mean 18-61 32 19-79 May 1,5 3 26 11-78 0-02 3-44 - 8-30 3 26 6-90 29 June 17 22 15-14 16-27 17-86 0-08 0-00 0-05 3-46 3-48 3-51 11-23 14-58 -15-31 Mean 7-29 5-17 6-01 23-74 3 26 30-08 North. 3 26 6-34 OPERATIONS FOB THE VERIFICATION AND EXTENSION OF THE ABBE DE LA CAILLE'S AEG OF THE MERIDIAN, AT THE CAPE OF GOOD HOPE. PAET III. MEASUREMENT OF THE BASE. § ]. Introductory History.* While Mr. Maclear was engaged in the small surveys in the neighbourhood of Cape Town and Klyp Fontein, he informed me that he possessed no proper standard of length, and that there was no standard, of even the roughest kind, in the Cape Colony. I considered it my duty to represent this deficiency to the Lords Commissioners of the Admiralty, and to state that, as well for the civil requirements of the colony, as for the contemplated geodetic survey, it was highly desirable that this deficiency should be supplied. On April 24, 1838, I received their Lordships' authority for the construc- tion of two iron 10-feet bars, similar in size and general arrangement to those used by Colonel Colby (afterwards Major-General Colby), for reference in his measure of the base near Lough Foyle, in Ireland, and instructions were immediately given to Mr. Simms to proceed with the fabrication of these bars. * This section is written by G. B. Airy, Esq., Astronomer Eoyal, excepting where quotation marks are annexed. — T. M. 232 In the autumn of the same year (1838), I received a letter from Mr. Maclear, dated June 1, 1838, giving me the result of an approximate calculation of the observations of La Caille's arc (contained in part II of this work), and summing up the conclusion as follows: — " It is clear that we cannot hope for any explanation [of the anomalous cha- racter of La Caille's result] from this re-observation of the amplitude. I am therefore fully prepared, on the receipt of my observations at home, to hear that the geodetic work is to be undertaken." I proceeded without loss of time to make applications to various departments of the Government for the assistance which Mr. Maclear would require for the survey. Several circumstances, however, prevented me from acting efficiently till the year 1839 On Feb. 8, 1 839, I ascertained from Colonel Colby, that it would be entirely agreeable to him, that the compensation bars invented by him, and used by him for the measure of the base by Lough Foyle, should be employed for the measure at the Cape of Good Hope. And, application having been made by the Lords Commissioners of the Admiralty to the Master-General and Board of Ordnance for the loan of these bars, I had the satisfaction of learning on May 17, 1839, that the Master-General and Board assented to this request. The official order for the delivery of the compensation bars was given on July 1 6. In the month of April, 1839, observations (to be detailed hereafter) were made to determine the thermal expansion of the iron bars, and to compare their lengths with the lengths of the Astronomical Society's scale, and of Colonel Colby's two iron bars. Previously to the month of July, the compensation bars had been placed by Colonel Colby in the hands of Mr. Simms, for general examination and small repairs, and clean- ing, — and were then packed in travelling cases. Every part of the base apparatus being thus ready for des])atch, advantage was taken of the departure of Mr. Mann (recently appointed second assistant at the Cape of Good Hope) to place them under his care. Mr. Mann sailed, with the base apparatus in his charge, about the 20th of July, 1839. The Board of Ordnance, in announcing their willingness to lend the compensation bars, had suggested that it might be desireable that an Officer of the Corps of Royal Engineers, who had already had some experience in the use of the compensation bars, should accompany them to the Cape of Good Hope, and should there assist in the mea- sure of the base. The Lords Commissioners of the Admiralty having been pleased to refer this suggestion to me, I stated as my opinion, founded on the best information to which I had access, that it would be necessary to have the assistance of soldiers in many parts of the work, — and that for this reason, as well as for the more obvious reason of placing the bars under the immediate charge of a person accustomed to use them, it was desirable that an Officer of the Engineers should go to the Cape. Accordingly on Octo- ber 1 1, 1839, Captain Henderson was selected for this service, and a small party of Sappers and Miners was placed under his command. Captain Henderson, however, (being then engaged in the survey of Scotland) did not sail with his party till April 8, 1840. 233 On December 10, 1839, I suggested to the Lords Commissioners of the Admiralty that it would be highly advantageous to the progress of the survey, that the Commander of the Garrison of Cape Town should be empowered to grant to Mr. Maclear the further assistance of soldiers from the garrison ; and I learned by letter from the Secretary of the Admiralty, dated 1839, December 23, that their Lordships had used their influence with the Principal Secretary of State for the Colonies to this effect, and that he had complied most liberally with their request. Captain Henderson and his party arrived at the Cape of Good Hope on July 6, 1840, and operations of various kinds, comparisons of the iron bars, trials of the com- pensation bars, preparations of supports and signals, &c., were immediately commenced by Mr. Maclear. " On the 20th of August Mr. Maclear applied for, and obtained, from His Excel- lency Sir George Napier, the Governor and Commander-in-Chief at the Cape, the services of Lieutenant Cust, a talented young officer of the 25th Regiment of the line, and of a working party from the same regiment, consisting of a non-commissioned officer and twelve men : and on the 2nd of September the whole party moved off for Zwartland plain, where La Caille measured his base." By a series of tentative operations Mr. Maclear, with the assistance of Mr. Mann, were led to fix upon a small swell of ground, without a stone or any distinguishing mark, ■ either above the surface or below it to the depth of three feet, as the place of the west end of La Caille's base.* Starting from this point, with the known direction of the base-line, they were enabled to trace its whole course. The first 1^ mile is good close hard ground, " excepting a sheet of water about 60 yards wide :" then it becomes sandy, and spongy from the great number of mole holes. It then declines rather abruptly towards the course of a winter river (the Salt River) : a watercourse which in the summer consists merely of a series of stagnant brackish lagoons, but in the winter is a running stream. Mr. Maclear states that he had not seen this river before : nor is it mentioned at all by La Caille in the Memoirs de I'Academie, or in his Journal. It intersects the plain from a mile south of the Coggera farm to Uyle Kraal, a distance of five or six miles, " and finally opens into the Berg River." The next mile of the base line is in part sandy and spongy, rising to the more elevated ridge on which the Coggera farm stands, but north of that farm. From this point to the eastern extremity the ground is hard. The valley of the winter river is entirely concealed from the eastern extremity, by the undulating of the Coggera ridge. Upon the whole, in Mr. Maclear's opinion, the line was not the best which might have been chosen, (a) * "La Caille applies the terma soulh and rwrth to his terminal points; but his line inclines more to the prime vertical than to the meridian. — T. M." (a) " The explanation may in part he found by tracing his movements. On his scouring visit to the plain he travelled on horseback from Groenekloof, and the road was probably the same that now exists. From the point of the road where the line he afterwards measured crossed it, he could see to his left the quartz rock (which he fancied was A2 234 After consultation with Captain Henderson, Mr. Maclear felt himself at liberty to select a new line for his base. The considerations which weighed with him were the following: — 1st. No error in La Caille's base could be detected by examination of the same hne, since none of La Caille's works remain. 2nd. The spongy ground is unfit for the support of compensation bars upon tressels, however, well it might be suited for deal rods lying upon the ground. 3rd. Several portions of the line are too much marked by intervening undulations. Mr. Maclear then examined a line two miles south of La Caille's line. It was in many respects good, but it was rejected, because the intervention of rising ground pre- vented the observation of one end of the line from the other end. Finally a line was adopted, beginning about 462 yards south-west of La Caille's west end, passing through La Caille's west end, " passing along the N.W. edge of the sheet of water," crossing the " Salt River," rising to the slightly elevated table land, then declining, and finally rising to the end. The line is in general hard, and its parts are less screened from each other, and from the terminal points, than any other which could be found. The length of this line is about 8*1 miles. As viewed from the west end, the line is more inclined to the north than La Caille's by about two degrees. As soon as the line was adopted, Mr. Maclear proceeded to build in an unoccupied house, about f of a mile from its west extremity, two piers for carrying the microscopes, intended for comparison of the compensation bars, with the standard iron bar B ("stand- ard A was left at the Observatory"). The microscopes of the compensation apparatus were examined and adjusted; and the pier defining the western extremity of the base was built. It is a firm structure of masonry, enclosing an iron pipe into which a brass plug is fixed with lead (a), in the centre of the brass a platinum wire is inserted, and its end is polished off": upon this end is the dot. On October 21 the work of measuring was actually begun, and on October 27, 1701 feet were completed. The end of this measure being preserved by a dot, on a brass pin, carried by a strong picket, — the measure was recommenced from the west end on the 30th, and on November 4 the same point was again reached ; and the coincidence of the measures was most satisfactory. After this time no measure was repeated, " except two or three sets of bars of doubtful accuracy." As the measure proceeded, it was found that very great delay would be caused by bringing the standard bar, and compensation bars, to the microscopes fixed in the unoccupied house, Mr. Maclear, therefore, constructed a microscopic beam compass, marble, journal page 174), but not the intervening sheet of water (Kotzee's Vlei); and to the right apparently even ground, ascending at the distance of six miles to a low ridge. " He seems to have comraenccii the original measurement at the east end; and to a certainty at that end, when he repeated the measure with a cord, to discover if he had miscounted. The locality of his east point is not mentioned, cither In his journal or memoir; its position, however, was on a swell, where there is a mound similar to, but larger than the one at the west end. The east terminal point of the new line is upon the same undulation, distant from La Caille's about 620 yards. — T. M." (a) " The plug is hour glass shaped." 235 consisting of a trussed wooden frame, carrying two microscopes, which was transported to different points of the base, and was there mounted on temporary " bearings," built under temporary shelter. The east end of the base was reached on April 5, 1841, and the permanent mark was established in nearly the same form as that at the west end, on April 20. On April 24, the triangulation for connecting different portions of the base (in order to ascertain that no serious error, as by the omission of a bar, had occurred in any part) was commenced. The levelhng of the base line, and the levelling from a point of the base line to the sea at Saldanha Bay, were conducted at nearly the same time. On June 21, Mr. Maclear finally returned to the Observatory. On August 19, 1841, comparisons of the compensation bars with the two standard iron bars, and of the standard iron bars with each other, were commenced at the Observatory. On December 13, 1842, the compensation bars, and the standard bar B (used for comparison with the compensation bars, throughout the measure of the base) were brought to Greenwich. On September 12, 1843, B was compared with the two Ordnance bars (Col. Colby's) at Mr. Simm's shop; and in 1844, March and April, the comparisons were repeated at the Ordnance Survey OfBce, in Southampton. § 2. Measuring Apparatus. As the account of a geodetic operation would be defective without a description of the instruments that were employed, the Astronomer Royal, Mr. Airy, applied to the late Colonel Colby for a copy from the three plates, which illustrate the elaborate details of the construction of the compensation bars, drawn up by Captain William Yolland, of the Royal Engineers, and published in the " Account of the measurement of the Loch Foyle Base" These plates are numbered XVII, XVIII, XIX, in the present work. So much of Captain Yolland's descriptive letter press, as will explain the mechanical construction of the apparatus in reference to these plates, will be extracted from his work. For the record of the instructive temperature experiments, made prior to the determina- tion of the positions of the compensation points, the work itself should be consulted. The theory of the compensation point is exceedingly simple and beautiful ; but the mechanical definition of its position is quite another matter. The expansion of metals in relation to the thermometer does not appear, in broad evidence, with the required preci- sion. In the instance of a bar, the temperature of the portion in immediate contact with the bulb may be indicated on the scale; but in varying temperatures,--upon the con- ducting power of the metal, upon its volume and the condition of its surface, — will mainly depend whether the indications be partial or general. 236 An interesting experiment was made in comparison shed M, while measuring the Cape base, where there was no apparent reason for doubting the stability of the micros- cope pillars. The standard iron bar B was placed under the microscopes, and its varying lengths were compared with the varying temperatures, at short intervals, during twenty- four consecutive hours without a break. At 3 o'clock, p.m., when the temperature was stationary, the length of the bar was still increasing. Near 5 o'clock the length was stationary, but the temperature had descended several degrees. Shortly before sunrise the temperature was at its lowest point and stationary, but the length was still contracting. Near 8 o'clock, a.m., the temperature had risen several degrees, and the bar, which had been stationary for half an hour, was beginning to lengthen. On comparing the results, the mean drag of bar motion appeared to be nearly two hours after the temperature. The long bulbs of the thermometers, bent to right angles with their stems, were in holes within the substance of the bar, surrounded by olive oil : these stems were screwed to the bars. That the thermal connexion between the thermometer bulbs and the iron, through the medium of the olive oil, was not complete, is more than probable; yet, making due allowance for the imperfect connexion, there is a residual amount of time chargeable to the rate of absorption and radiation (the bar was painted ) sufficient to vitiate com- parisons in varying temperatures, where the bars are not nearly identical with respect to material, volume, shape, and surface covering. Hence the disheartening difficulties Colonel Colby encountered when fixing the positions of the compensation points, which will be found concisely and clearly recorded by Captain Yolland, in the account of the measurement of the Loch Foyle Base : their geometric positions, derived from the calculated expansions of the brass and iron, was an easy task to determine. * Let a a' hV be two bars of brass and iron joined together at their centres by a steel Fig 1. bar, JO q, but free to expand from and contract towards their centres, independent of each other; an a'n' are flat steel tongues at the extremities of these bars, moving freely on conical brass pivots, allowing them to be inclined at small angles with the lines perpen- dicular to aa' b hi . At the temperature of 62° Fahrenheit, the bars are assumed to be precisely of the same length, and the tongues consequently at right angles to ad bb'. Imagine these bars to receive an increase of temperature and length, and, from the inequality of their expansions, the brass to become c c', and the iron d d', the position of the tongues now being cdn c'd'n!; it will then be apparent that if the points, nn', be so determined that ac : b d :: an : bn distance of the distance of the Expansion of Brass : Expansion of Iron : : compensated point : compensated point from the Brass from the Iron, the positions of the points, nn', can only vary within very narrow limits for any differ- ences of temperature arising from atmospheric changes. * Account of the measurement of the Loch Toyle Base, page 9. I'LATK XVII. 237 In the construction of instruments on a similar principle, such, for example, as compensation pendulums or balances, it is assumed that the metals of which they are composed change their temperatures, and consequently their lengths, at an equal rate. But although this may be nearly true with respect to such instruments, and the error arising from a contrary supposition scarcely, if at all, appreciable, yet, with regard to the apparatus in question, composed of considerable masses of metal, and exposed to greater and more sudden variations of temperature, such an assumption might lead to very fallacious results. It is obvious, from the nature of such a construction, that any diiference in the tem- / peratures of the two bars would produce a greater error in the distance between the two points, nm', than a variation to the amount of the difference in the temperatures of a single bar would produce in its length ; hence the necessity of adopting every possible precaution to guard against such an occurrence, and of devising some means of producing perfect equality between the two metals, so far as regards their rate of changing temperature. The metals may have different capacities for heat — their surfaces may have different powers of radiation and absorption : two modes therefore presented themselves of produ- cing the desired equality of temperature, either to have made the bars of different dimen- sions, or to have varied their surfaces till, by means of increased or diminished radiation and absorption, the desired equality was produced. To have attempted the first mode would have required a previous determination of the extent of the inequality, and would thus have occasioned considerable delay. The second was therefore chosen, and a series of experiments were made on the heating and cooling of brass and iron cylinders, with a view of ascertaining the best means of so preparing their surfaces as to induce them to acquire or part with equal increments of temperature (when similarly exposed) in the same periods of time.* 1. " Compensation Bar. The compensation bar consists of two bars, a a' b b', of brass and iron, 10 feet, 1*5 § 2. inch long, 0*5 inch broad, and 1'5 inch deep, placed ri25 inch apart, supported on brass rollers, r r', at one-fourth and three-fourths of their length, and firmly fixed together Apparatus. at their centres by the transverse steel cylinders, ss', 1'5 inch in diameter, and being free ^'s- 1'^- to expand from, or contract towards, their centres independently of each other. At the '^' extremity of, and at right angles to, each of these bars is a flat steel tongue, a' n', 6'2 j-jg, g, 7, $. inches long l-l inch broad, and 025 inch thick ; projecting 3-25 inches on the side of the iron bar, and moving freely on conical brass pivots, rivetted into the brass and iron Fig. 2, e, 7, 8. bars, each axis being perpendicular to the surface of the tongue, allowing it to be inclined at slightly different angles to these bars according to their expansion from, or contraction * The experiments here alluded to are published in the " Account of the measurement of the Loch Foyle Base." PLATE XVII. Kg. 2, 3. Fig. 9. Fig. 2, 4. I'LATE XIX. Fig. 3. 238 § 2, to, their centres. The centres of the two axes are at 0"5 inch and 23 inches from the ApparatuT" end of the tongue next the brass bar. On the tongue, and flush with its upper surface, Fig. 6. j^gyj. ^}jg extremity, n, is inserted a silver pin, with a dot marked on it, as the compen- sation point. S'ig. ■>, 3. The bars are placed in wooden boxes, e g f h, to the bottoms of which are fixed the plates that hold the brass rollers on which they are supported, and having in the middle a vertical brass stay, t, screwed on the box, and passing upwards between the two steel cylinders, ss', to prevent the bars being moved longitudinally in their casing. To protect the tongue carrying the compensated point (which projects beyond the wooden box) Fig. 2. from injury, nozzles, oo', are fixed to the boxes, having a small circular orifice with a lid on the upper side, to allow the dot or compensation point to be seen. On one side of the connecting steel cylinders, and attached to the brass bar only, is placed the longitudinal level, /, the lid of the box being furnished with a glass window and shutter, W, to enable it to be observed. Over the rollers which support the bars are two pieces of metal, »« m', for preventing any sudden jar from striking the bars against the lid of the box. At each end, on the outside of the bar box a thick metal plate, t, t, t, t, is screwed, for the purpose of firmly fixmg a three-armed grooved stand, ss's", intended to support the tripod of the compensation microscope ; and at each end of the box are two vane sights, v, (which shut down with hinges into grooves), used for placing the bars approximately in line. Fig. 1. On both sides, at one-fourth and three-fourths of the length, are brass plates, with holes for receiving the screw which clamps the plate, C, of the tripod-stand (technically called a camel) to the box, for the purpose of adjusting the bar in a longitudinal direc- tion. The wooden boxes are of well-seasoned straight-grained deal, selected by Sir F. Fig. 4. Knowles, F.R.S., from one of the Dockyards. The compensation bars are six in number, and designated by the letters A, B, C, D, JS, and G ; the weight of each bar with its two brass ends, t, t, t, t, is 136 lbs. 2. " Compensation Microscope. PLATE xvn. The compensation microscope consists of three microscopes, mn, co, m' n', placed ^'s- 3. three inches from centre to centre, connected by two bars, aa' b b', of brass and iron, 7 inches long, 0-6 inch broad, and 0'375 inch thick, 2'5 inches apart, firmly secured together by means of a brass collar and cylinder, forming part of the tube of the centre or telescopic microscope. The two bars carrying with them the outer microscopes, TO n m'n', of two inches focal distance, being free to expand from, and contract towards, the central microscope, c o, independently of each other ; and thereby forming with it small angles of inclination similar to the steel tongues of the compensation bars. The compensated point of each is so adjusted as to be in the outer focus of its object-glass. Fig. 1,2,3. The microscopes revolve on the axis of the telescopic microscope in a tube fastened to a horizontal plate attached to a tripod-stand with levelling screws, ss's", and furnished with longitudinal and lateral adjusting screws, h h'. On one side, secured to the brass DESCRIPTION, &c., OF THE BASE-LINE APPARATUS. 239 bar, is the spirit level, I, for levelling the microscopes, and on the other, firmly fixed to § 2. the centres of the bars by a brass plate, is a telescope, t, embraced by a brass collar with AralatuT"^ a small cylinder projecting from one side, which turns in a socket attached to the plate ; thus affording it a vertical motion, allowing objects to be seen in opposite directions. The telescopic microscope is provided with an adjusting screw, /, for altering the focal distance within certain limits, as well as moveable object-glasses of different focal lengths fitting into the lower end of the tube, for purposes which will be explained when the mode of proceeding in measuring the base is entered on. The compensation microscopes are seven in number, distinguished by the letters M, N, 0, P, Q, R, and S ; the weight of each microscope is 5 lbs. 4. Micrometer Microscope. In the event of its being necessary to remeasure any portion of the base, it became requisite to adopt means for ascertaining the value of any minute differences of length which might be observed in the first and second trials; accordingly a micrometer micro- scope was devised for measuring differences not varying much from six inches, consisting of a solid arm of brass, with a collar at one end and a counterpoise at the other, moving freely on a pivot, the stem of which is secured on a tripod stand ; attached to the arm is a level, similar to those belonging to the compensation microscopes. 5. Adjustments, Sfc* — Compensation Bar. The bar requires but one adjustment, viz : to place the longitudinal spirit level Adjustments. parallel to the line joining the upper surfaces of the tongues at the compensation point. This is managed with facility by removing the nozzles (the bar resting on its camels) and placing a large Y spirit level a few yards off, in such wise, that the tongues shall be exactly in focus as the telescope is pointed to each in succession, without altering its focus-screw. Next, the Y spirit level is to be rigorously adjusted, and the upper surfaces of the tongues brought to coincidence with the horizontal wire by means of the camel- screws. The lower edge of a piece of white card, resting smoothly on the tongue, forms a good mark for the wire. Lastly, the centres of the bubble and scale of the longitudinal spirit level are to be brought to coincide by means of its adjusting screws, to which the preceding arrangement is subsidiary. Compensation Microscope, The several adjustments of the microscopes demand much patience and nice hand- ling. If, generally, instead of the head slit, square heads worked by keys had been given to the screws, nine-tenths of the counter pressure needed, when turning them, might have been avoided. This remark applies, in particular, to the adjustment which causes the optical axis of the side telescope to describe a plane parallel to the vertical * The methods of adjustment here described were those pursued by me on the Zwartland Base, without reference to any collateral authority. — T. M. B PLATE XVII. Fig. 2, 3. PLATE XVllI, 240 VERIFICATION AND EXTENSION OF LA CAILLE'S ARC OF THE MERIDIAN. § 2. plane, passing through the optical axis of the outer microscopes, — the most liable to be Apparatus, deranged by casual rough handling, and upon which depends the continuation of a right Adjustments, jjjjg through the several compensation points (a). CoUimating the Telescopic Microscope. This adjustment may be conveniently managed, the microscope resting on a bar arm, and a " point carrier " underneath it at the desired elevation. The mode of proceeding is, to a certain extent, similar to coUimating the telescope of a Y spirit level, the dot on the " point carrier" affording the mark ; but in the present case, the object glass is moved by the coUimating screvFs, instead of the wire frame (b). The first step is to place the microscope vertical by means of the side level : the second, to rotate the microscope on its axis, and to note the deviation of the wire from the image of the dot. One half of the deviation is to be corrected by moving the object glass, the other by moving the dot on the " point carrier." The operation is to be continued by trial and error until the dot remains bisected in all positions of the outer microscopes. Adjusting the wires of the outer Microscopes to t?ie length of the six-inch Standard Scale. A block of lead resting upon a strong trestle forms a good support for the 6-inch Standard Scale and the Microscope to be adjusted: a groove in the lead receives the scale over which the microscope is mounted, and levelled by means of its side level and foot screws (theodolite fashion) : the standard is then to be shifted, until one of the dots defining the six inches is bisected by the wire of the outer microscope which chances to be over it : the microscope is then reversed, and if the wire bisects the other terminal dot, the adjustment for that outer microscope is correct, otherwise half of the error is to be removed by the coUimating screws, vvv v, and the other half by moving the micros- Fig. 1,3.6. cope longitudinally, by means of the dovetail screw of the microscope stand, hh'. In a similar way the other outer microscope is to be adjusted. The thermometer of the 6-inch standard should be registered at the commencement and termination, and the mean taken for the temperature of the standard at the time of adjustment. No pains should be spared to effect this adjustment with rigorous accuracy. Adjusting the Telescope to move in a vertical Plane, sensibly parallel to the vertical Plane passing through the optical axes of the outer Microscopes. It is convenient to divide this adjustment into two steps, and to re-examine the first, for if the screws move stiffly, it may have been disturbed by the second operation. An angle of 30^ may be obtained by suspending a plumb-line in front of the telescope, in such wise that its image may be seen reflected in a basin of water or mercury (the (a) The microscope adjustments throughout the measurement of the Zwartland Base were made by myself, which afforded ample opportunities for estimating the weakness of this part of the arrangement. — T. M. (b) It should, of course, be understood that the preliminary step in the several microscope adjustments is to place the axis upright, by means of the attached level and foot screws. DESCRIPTION, &c., OF THE BASE-LINE APPARATUS. 241 microscopes having been previously levelled) : then, by means of screws jopjo, adjust the §2. telescope, so that its vertical wire shall bisect the plumb-line and its reflected image. ApparatuT"^ The second step consists in bringing this vertical plane into parallelism with the foci of ^'^J'^stments. the microscopes : for this purpose, a board about nine inches in breadth, painted black, '^it^l."^^'''' having two white dots, whose centres are horizontally distant from each other, by twice the distance of the optical axis of the side telescope from the centre of its vertical axis, is placed upright about 60 or 70 yards off, in the line of the sight-vanes of the 6-inch standard. A similar board is set up by the same means in the opposite direction. The body of the microscope is then turned on its axis, until the scale dots appear in the middle of the narrow space between the lateral wires of the outer microscopes : next, the telescope is directed to the corresponding mark on one of the uprights, and the upright shifted until the wire bisects the mark ; the telescope is then directed to the other upright, which is shifted, if necessary, until the corresponding mark upon it is bisected. The body of the microscope is now to be turned 180° in azimuth, with respect to the scale dots, and the telescope pointed to the second mark on each upright, which instantly detects if the plane described by the telescope is not parallel to the plane passing through the optical axes of the outer microscopes. The deviation, if any, is to be corrected, half by driving one and drawing the other of the two screws, which secure the telescope to the collar : the other half by the outer screws, pp. This result is to be considered only in the light of the first approximation. The microscope is now to be carefully re-levelled, and the plane described by the telescope re-examined by means of the plumb-line and its reflected image, and corrected if necessary. The line joining the dots on the standard, are to be brought to coincide correctly with the line joining the centres of the uprights, by moving the former the requisite small quantity in azimuth (or by moving the upright) : — the reversion is to be repeated, and any residual deviation corrected. Those who are familiar with the adjustment of a transit instrument, will have little difficulty in managing the one under consideration. The line from the middle point between the marks on one upright, to the corresponding point on the other upright, may be regarded as the meridian; with which the vertical plane passing through the optical axes of the outer microscopes, and the dots on the six-inch standard, must coincide. Then, with respect to the telescope, the short axis it works on should be placed horizontal, and the deviation from parallelism (regarded as an error in azimuth) should be corrected, each by means of its proper screws; the plumb-line and its reflected image guiding the former, and the marks on the uprights, the latter. " 6. Bar Tripods or Camels, Trestles, and Triangular Frames* The box, containing a compensation bar, is supported at one fourth and three-fourths plate xix. of its length, by means of strong brass tripods (technically called camels), with small (* Page 22.) B2 242 VERIFICATION" AND EXTENSION OP LA CAILLE'S ARC OP THE MERIDIAN. §2. Description of Apparatus. PLATE XIX. Fig. 2. Kg. 1. Kg. 2. I'ig. 1. rollers, o o, on the upper surface. One of the camels is provided with a tangent screw, g, and both' with lateral screws, /, as well as a powerful elevating screw, e, wherewith to alter the height and level of the compensation points. These camels rest on strong wooden trestles, T T', of 3" x 2" scantling, varying in height from 6 to 30 inches, with a framed top forming an equilateral triangle, with the angles rounded oif, of 14-inch side, with a hole in the centre to allow the elevating screw, e, to pass through and be worked from below ; the legs of the same scantling well braced together, being placed on stout triangular frames of wood, RR', 29 in. on the side, 5" x 3" scantling, and supported by three wooden pickets, P P', generally about five inches in diameter, whose length is regulated by the nature of the soil into which they are driven. Kg. 3. PLATE XTII. Fig. 9, 10. Kg. 10. Kg. 9. " 7. Microscope Stand (a). The tripod of the compensation microscope rests on a three-armed grooved stand, ss's", supported by a brass plate, tttt, screwed to the end of the bar box. The first bar in the series has a stand attached to each end, and supports two of the microscopes ; whereas each of the other bars in the series has only one microscope, and that attached to the advanced end. "8. Directing Theodolite (b). This is a small five-inch theodolite supported on pillars in lieu of Y's to allow it to revolve on its axis, its feet resting in grooves, on a brass plate, moved by means of a screw, in a dovetail brass frame, firmly secured to a solid piece of lead 8 in. x 7 in., and 0'6 in. thick. The movement in the dovetail is to afford the means of its being shifted transversely into line by observing the upright planks, both in front and rear of the prolongation of the base, until the inner edges coincide. The theodolite is principally used for placing the bars and microscopes approximately in line, and laying out the line of pickets. " 9. He/erring Points, or Point- carriers. These are of various kinds ; one of the most simple consists of a solid triangular cast- iron plate, Y, 15-6 inches on the side, 26 inches thick, with a short, flat, hollow cylinder of brass screwed on to its upper surface, enclosing a moveable disk, in which is inserted a silver pin having a dot engraved on it ; this dot is adjusted to its proper position, by means of three screws passing through the cylinder, placed at equal distances on its circumference. Another sort is represented at Y', and is formed of a cylinder of brass, which moves in a hollow cylindrical tube attached to a cast-iron slab laid on the ground, an excavation being made for the tube (c). The brass cylinder has at its summit an (a) Page 22. (b) Page 23. This instrument was not used on the Zwartland Base. (c) These were not used on the Zwartland Base. 'A < >^ ^ ^ \\ I \ fH sfe W/A + 3 nil '"^ .il ^ '/>yr //■,./, ,,,,,/( .r/f//.Uf// /'/ "^r, f,,///,'.!. Yyro/^ //ry/,/ff laATj: -Will. rip-. 4 ijj^ '?! rig-. 5 « > ' ^ '« ' 4 -^ () 1 U ) N AN ( ■ V, S I^ R^"E Y, J5 ;i s e Apparatus. PLATJvIl. rig. 6 ris-.3 ^ .■-o W ft W ^, '««' M >M9 li)' ill s»f i DESCKIPTION', &c., OF THE BASE-LINE APPARATUS. 243 adjustable disk similar to the former, this construction being adopted to obviate the §2. necessity for frequently changing the object glasses of the telescopic microscope, by rais- Apparatus. ing or lowering the cylinder to the proper focal distance ; a clamp being provided above the cast-iron plate for fixing the brass cylinder and disk at the required height. " 10. Base Tents (a). The base tents are formed of wooden frames 9 feet long, 7 feet broad, 2" x 2" scantling, the several parts being firmly screwed together by bolts and nuts. Two of these frames are joined together at one end by strong double-jointed hinges, so as to receive El pole plate on the top, and a strong canvass covering is then laid over the double frame, the side bars of which are passed through a hem on the outer sides of the canvass, prior to the parts being bolted together. The canvass is secured to the lower bar or stretcher of the frame, by points similar to those used for the reef of sails ; and as this stretcher prevents the canvass being brought close to the ground, a valance of strong, but inferior canvass, is attached to the lower part to prevent gusts of wind deranging the apparatus. These tents are constructed to shade the compensation bars and microscopes from the direct rays of the sun, and are only used on very hot and bright days ; and, in order to admit of a sufficiency of light for making the bisection of the dots, &c. ; the points at the bottom on one side are loosened, and the canvass run up the sides of the frame by means of the casing or hem. After the days measurement is completed, the bars are placed on skidding with all the apparatus alongside, under two of the frame tents ; and to secure the whole from the weather, two triangular frames, also covered with canvass, are placed against the ends. § 3. Cape Standards of Measure. g 3_ Cape Stand- ards of These consist of two ten-feet iron bars, marked A and B, respectively ; constructed Measure. by Messrs. Troughton and Simms in the year 1838 : and a six-inch brass standard, by the same artists, constructed in the year 1839. A brass four-feet scale by Dollond, divided to inches and tenths of inches, was unfortunately bent near its middle through the negligence of the man who had temporary charge of it while shifting the camp in Zwartland. 1 . Cape ten feet Iron Standards, A and B. These bars being alike, a description of one will serve for both. Bar B is of wrought iron, J 22-22 inches long, 1'46 inch broad, and 2-6 inches (a) Page 23. 244 VERIFICATION AND EXTENSION OF LA CAILLE'S ARC OF THE lilERIDIAN. §3- deep, supported at one-fourth and three-fourths of its length on brass rollers, secured to ardsof the bottom of its wooden enclosing box, and prevented from moving longitudinally by a pin attached to the box, which enters a small hole in the centre of the under surface of the bar. At each end, about 2 inches in length and 1*3 inches in depth, are cut away, leav- ing surfaces which are supposed to coincide with the neutral axis of the bar : into each of these surfaces a gold pin is inserted, to carry the punctures or dots, meant to define the length often feet of the British Imperial standard (a). A spirit level, in length about 9^ inches, is attached to the middle of the upper surface of the bar by adjusting screws : and about half way between it and each end there is a cylindrical hole to admit the oblong bulb, one inch in length, of a delicate thermometer, bent at right angles to its stem, — which stem is fastened to the surface of the bar by mill-headed screws, to facilitate its removal, when oil or other conducting fluid is to be placed in the hole, for the purpose of connecting the temperature of the bar with the bulb. The spirit level and thermometers are protected by hinge shutters attached to the case. At each end, about two inches of the bar, projects through a hole in the case, for the purpose of exposing the dots to the microscopes. A brass ring surrounds the hole, to which a cylindrical brass cap screws on when the bar is not in use. The bars are covered with stone coloured paint, except the two inches of surface in the neutral axis, where the gold pins are inserted. 2. Six-inch Brass Standard. This standard is a brass bar, twelve inches nearly in length, 1*7 inch in breadth, and 0-35 inch in depth. On the lower surface, at each end, a brass plate is screwed on, of the breadth of the bar, 2'45 inches in length, and 0'25 inch thick. Hence when the bar rests upon a plane surface, 7'1 inches of its middle do not touch the bearing. At each end, a sight-vane is fixed (by removeable mill-headed screws), for the purpose of indicating the position of a mark in the vertical of the dots, which define six inches, to facilitate the adjustment of the side telescopes of the microscopes. A thermometer 8 inches in length, the stem bent to a right angle with the bulb, is fixed to the upper surface of the bar, the bulb being received within a hole in the bar, which hole is filled up with olive oil, or other conducting fluid while experimenting. The length of six inches is defined by two faint punctures on silver studs ; and upon the upper surface of the bar is engraved : " Standard at 62° Faht. " Troughton & SiMMS, London." =") (a) The length will be discussed in another section. MEASUREMENT OF THE ZWARTLAND BASE. 245 Mr. Simms furnished the following information with the bar: — §3. Cape Stand- " 136, Fleet-street, 20th July, 1839. MeZre. " Compared the 6-inch Standard Scale for the Cape of Good Hope, with to 6 " inches upon the Standard Scale of the Royal Astronomical Society, and found the " lengths identical. " 5 feet scale, " Thermometers : 6-inch scale. "No. 1, 66°-5 " „ 2, 67 -1 " „ 3, 67 -2 66°-5. " The comparison was made by laying the scales side by side, upon a plane surface, " and attaching two microscopes to a sliding frame, one over each scale. "W. Simms." § 4. Measurement of the Zwartland Base. § 4. Measurement of Zwartland I. Terminal Points of the Base. For the reasons assigned in the introductory history (§1) page 234, the attempt to re-measure La Caille's line, was abandoned in favour of one better suited for compensa- tion bar measurement. The ztfesf terminal position of the new line is on the top of a gradual ascent, in the direction of a kloof between Klipberg and Capocberg. The ground consists of pot-clay mixed with loose small stones. A farm-house named Koekoek Vallei, built in part with the broken up quartz rock referred to by La Caille in his journal, is distant about two-thirds of a mile to the northward (a). There is no other house within a couple of miles. A pyramidal shaped block of stone and lime masonry, rises from a depth of between three and four feet, to rather more than one foot above the surface of the ground, where the area of the block somewhat exceeds four feet square. The stones are large, and well bedded in mortar, and the upper surface is dressed so as to resemble stone flooring. A brass plug, 2|- inches in length, hour-glass shaped, with a platinum wire driven into its centre, is fixed by lead into an iron pipe built in the centre of the block. The upper surface of the plug is smoothed off, and even with the surface of the masonry. A dot (puncture) on the platinum stud marks the terminal point. The position of the east terminal point is on a swell, somewhat similar to, but more commanding than, the west. Rock, of loose texture, is found within a foot of the surface, (a) The farm derives its name from that of a sheet of water near to which the line passes; and, in the year 1841, the occupier's name was Kotze. Base. 246 VERIFICATION AND EXTENSION OF LA CAILLE'S ARC OF THE MERIDIA.N. § 4- and becomes solid at the depth of three feet, which is about the depth of the excavation Measurement of Zwartiand for the foundation of the masonry. The structure for carrying the point is like that at the west end, but instead of an iron pipe in the centre, a hole is drilled in the large centre stone, for the reception of the brass plug and platinum stud which carries the terminal dot. The plug is hour-glass shaped, and is fixed in the hole with lead. There are two farm-houses in the neighbourhood : one, at the distance of about one thousand yards in the vale to the south, was occupied, in 1841, by a Mrs. Buckle ; the other, about a mile (?) to the north west, was the property, at that period, of a farmer named Basson. After effecting the triangulation in the neighbourhood of the base, provision was made for the permanent preservation of the points, by a substantial pyramid of stone and lime masonry erected over each, ten feet square at the base and ten feet altitude,— the outside neatly dressed. A niche, at the height of six feet in the eastward face of the west pyramid, and in the westward face of the east pyramid, carries a slab of Robben Island stone, with an inscription cut in the stone. These slabs are vertical within the slant surfaces. It is proper to record also, that the stone within each pyramid, which is immediately over the point, is hollow, so as to arch over a teakwood case laying on the point, which case contains an inscription etched on a slip of glass, and a few of the current coins of Her Majesty. Each pyramid is encompassed by a trench and a quantity of loose stones, to prevent the approach of cattle or waggons to the structure. 2. Alignment of the Base. The instruments employed were a 30-inch transit instrument, by Jones, supported on a cast-iron stand ; a 20- inch transit instrument, by Dollond, supported on a cast-iron stand; and a 12-inch altitude and azimuth circle, by Dollond. By means of the 30-inch transit, adjusted and centered over the west terminal point, normal pickets were driven at convenient intervals along the prominent ground ; then along the low ground, as in the Salt River vale, by centering the same instrument over normal pickets. On each incline to this vale a pole was firmly fixed in position, because the terminal points were not visible from below. Temporary poles were then placed to guide the men in clearing the ground of bush to the width of about 20 feet. The 12-inch theodolite was used in the early part of the measurement, for placing the uprights to guide the side telescopes of the microscopes, also for bringing the micros- cope directors into line : it was set aside afterwards in favour of the 20-inch transit instrument for these services. The pickets, for registering lengths along the line, were in general about four feet long and four inches in diameter, hooped with iron at the upper end, and driven home MEASUREMENT OF THE ZWARTLAND BASE. 247 with heavy mallets : the tops were then smoothed off, and a brass pin two or three inches § ■*. •' ^ . f^ Alignment of long and sliglitly serrated, was inserted to carry the dot. the Basa Uprights, or sti-uts as they were termed on the base line, each consisting of an upright board about six inches broad, joined to a cross foot-piece, and kept at right angles to it by a brace, were erected on opposite sides of the line at normal pickets, and placed vertical by a plummet, suspended from a short projecting piece at the top : and being painted alternately black and white, their inner edges could be brought into exact line with great facility by means of the transit instrument. Two lines of similar struts, but of less dimensions, were placed one on each side of, and parallel to the true line (the line passing through the compensation points), each distant from it, by the interval between the centre of the microscope and the optical axis of the side telescope; in other words, between the vertical plane passing through the foci of the microscopes, and the plane described by the optical axis of the side telescope, — the line to the left painted black, the other to the right painted white ; and forming a lane or avenue, along the middle of which the true line ran. The struts were distant in line from each other, according to the nature of the ground, from 200 to 250 yards. The contrast between white and black prevented mis- takes when pointing the side telescope, in succession, to the inner edges right and left forward on reversing the telescope ; and right and left backward to corresponding white and black marks, painted on the axis of the lining transit or theodolite. Upon the inner edges of these struts being exactly in their respective lines, and the side telescopes correctly parallel to the foci of their microscopes, depend, whether the measured base be a measured right line or a measured zigzag. 3. Measurement. The superintendent of four picket drivers, being provided with s ten feet straight Mode of pro- edge having a spirit level fixed to it, and one of three feet similarly provided, — also with measuring a chain having marks at the proper distances, — commences operations by laying off points for pickets in the line of measurement, at distances of 5 feet 6 inches and 5 feet alternately, these being the centres of a series of triangles of about 17 inches, placed thus : direction of measurement, the points indicating where the pickets are to be driven to the proposed height above the surface. The direction of the central pickets is given by the officer at the theodolite or transit telescope ; their heads are levelled first, and this normal level regulates the heads of the lateral pickets. The wooden triangular frame, R {triangles in base line plate i.x. language) are then laid on the pickets, and their steadiness and level exammed. The trestles, T, are next placed on the triangles, with their feet over the picket heads : next 248 VERIFICATION AND EXTENSION OF LA CAILLE'S ARC OF THE MERIDIAN, §4. Mode of pro- ceeding In measuring the Base. PLATE XIX. Kg. 3. PLATE XTIII. Fig. 1, 4. the camel cups and camels are placed on the trestles, and finally the compensation bars, in succession, on the camels. In the meantime the officer who works the first bar (A) stands centinel over the point-carrier, and when the bar is laid on the camels, the theo- dolite officer comes forward, the sight vanes are raised, and by directions from him, the bar is brought roughly into line, levelled and clamped. The sights of that bar are then lowered and those of the following raised, that it may be brought roughly into line, levelled and clamped, and so on to the end of the series. The theodolite officer now returns to his instrument : the compensation microscopes are taken from their carrying box, and placed on the bar arms, ss's", with the points of the levelling foot screws of the tripod in the grooves. The officer at the "look down" of bar A levels his microscope, and brings the compensation dot into focus by means of the foot screws, and moves his end of the bar to bring the " look down " (central micros- cope) over the dot on the point-carrier: then the officer next to him adjusts the left hand microscope for level and focus, and so on to the end of the series, the several officers adjust their microscopes for level and focus. The button of the director, d, is then inserted in the eye-hole of the centre or telescopic microscope, resting on the left or advanced arm of bar A, and the microscope is turned at right angles to the alignment, for the purpose of distinguishing it from the other microscopes, as seen through the theodolite telescope. The officer at the theodolite directs the telescope to the avenue between the inner edges of the line of struts, and bisects it with the middle wire, — then communicates, by signal or call, the direction, and the quantity in terms of the director, which the bar should be moved by the transverse screw of the camel, to bring the director into line. This done, the microscope is restored to the alignment, the director is placed in the eye-hole of the third microscope, which microscope is turned to right angles to the alignment, and the bar is moved by the camel screw, until the director is reported to be bisected by the theodolite wire. The same process is continued to the end of the series of microscopes. It will be evident that the lateral movement of the advanced end of bar A into line, will carry the look down from over the point-carrier dot; both camel screws must therefore be worked simultaneously. Similarly the movement of the advanced end of bar B will carry the third microscope from over the left compensation dot of bar A ; both camel screws of bar B must therefore be worked simultaneously, and so on for the other bars. It is, of course, understood that the officer who works the director shall take care that the bars are level, that each microscope is kept correctly level, that the adjacent compensation points are in exact focus, and bisected on reversing the outer microscopes, — otherwise the final alignment, through the agency of the side telescopes, will be much impeded. The officer who is responsible for the accuracy of the work, now re-examines the adjustments of the microscope over the point-carrier, bisects the dot on the compensation MEASUREMENT OF THE ZWARTLAND BASE. 249 point, and the dot on the point-carrier, then reverses the microscope to be certain that § '^■ ... • 1 'p 1 • • Mode of pro- the SIX inches are exactly bisected; if not, he notes which side of the microscope is eeedmgin ji'ii '■■1 II- /• measuring towards him, that the opposite side may be towards him in the following series. The the Base.' distance between the foci of the outer microscopes may be correct, although, from thick oil or dirt on the axis, the reversion may not be satisfactory; but an early reference to the six-inch standard should be made when there is any doubt. Another officer directs the side telescope of the second microscope forward, to the inner edge of the line of struts which is on the telescope side of the microscope, — and, if necessary, moves the bar by the transverse screw of the camel, until the telescope wire coincides with the edge of the struts, — the compensation point at the time being in the focus of the microscope. He then reverses the microscope and telescope, and directs the latter to the inner edge of the opposite line of struts. In a similar way he points, in succession, to two objects in the rear, which are in the line of the struts prolonged backward. If the left compensation dot of bar A appears in the middle of the space between the lateral wires in the focus of the right outer microscope, and the right compensation point, also the dot on the point-carrier, are in similar position with respect to the foci of the left outer of the first microscope and look down ; while, in succession, the bisecting wire of the telescope coincides with the inner edges of the double line of struts forward, and with their prolongations backward ; bar A is in the true alignment, and the telescope is in adjustment. The back marks, during the greater part of the measurement of the Zwartland base, were two rings painted on the axis of the 20-inch transit instrument, — one on each side of the telescope: that being white in the prolongation of the white line of struts, the other black; and the distance between them equal to twice the perpendicular distance of the optical ixis of the side telescope, from the line joining the foci of the outer microscopes. The setting up of struts properly is a delicate and a tedious operation : those in advance have to be removed as the measurement advances; the lining theodolite, or (in the present case) lining transit, is generally centered over a point-carrier which has been left two or three series of bars behind ; therefore it is exactly in the measured line. The description which has been given of the method pursued to bring the first bar, A, into true alignment, applies to the other bars of the series, with this diiference only, that the first and last bars include the consideration of the look down telescopes. Before the termination of the side telescope alignment, the soft surface ground is paired off from beneath the advanced end of the last bar, to afford a flat firm bearing for a point-carrier {a). Where there is loose deep sand, a box of greater breadth than depth should be bedded in it, and nearly filled with sand to receive the point-carrier : where the ground is soft and moist, strong pickets should be driven deep for support. The bars and microscopes having been placed truly in line, the next step is the (a) Flat point-carriers, excepting one instance, were employed on the Zwartland base. C2 250 VERIFICATION AND EXTENSION OF LA CAILLE'S ARC OF THE IIERIDIAN. Iiodeof pro- careful bisection of the several dots, by the transverse wires in the foci of the microscopes LtS and look down. the Base. -pjjg responsible officer placed at the first look down rotates his microscope, examines the side level, bisects the compensation and point-carrier dots, — the former by means of the microscope slide, the latter by means of the side camel-screw, — reverses the micros- cope to ascertain if the six inches are bisected, and if so he calls out "correct;" other- wise he notes the particulars. The officer at the next bar follows the same manoeuvre, bisects the left compensation dot of bar A and the right of bar B, then signifies " correct."' And so on to the end of the series, excepting the advanced look down. If there are not a sufficient number of officers, those at the beginning of the series move forward. For greater security, the responsible officer now examines the several bisections, and on reaching the advanced end of the series, — the adjustments of the last microscope ; then, by means of the three screws which move the disk of the point-carrier, brings the dot upon it to bisection by the wire of the look down : a box is then inverted over the point-carrier from which the series started, and a quantity of earth is strewed over the box, to screen it from the direct action of the sun. (Three point-carriers are usually left in position at the same time, as zeros for re-mea- surement in case of doubt.) Each officer now carefully removes his microscope, and places it in the "carrying box" (a): and the responsible officer remains guarding the advanced point-carrier, while the tents and bars are being carried forward ; and as it is a standing rule to keep the bars as much as possible out of sunshine, the movement is conducted accordingly. A spare set of triangles and trestles having been placed upon the advanced pickets for the next series, the tent is removed from over the commencing point-carrier of the series just measured, and placed over the advanced carrier, and picketted down, — simulta- neously bar A and its camels are moved forward, laid on and covered, and the others, in succession, in the same manner. The last point-carrier of the day is protected in the following manner. When its position becomes known, but before the adjustment of the dot, a box, some inches larger every way than the carrier, is pressed down so as to leave the trace of its edges on the ground ; it is then removed, and four long iron or wooden pickets (according to the hardness of the soil) are driven at the inner corners of the trace, leaving five or six inches of their tops above ground. Four other wooden pickets are driven close to the trace on its outside at the middle of the sides, their tops also projecting a few inches. When the dot has been adjusted, the box is pressed down over the inner and within the outer pickets, and fastened to the latter by screws passing through them. Earth is then piled over the box, and a base line tent is secured over it in the usual way for the night, or until the continuation of the measurement. But if the work is likely to be (a) The microscope carrying box is provided with fitting partitions to keep them steady. Personal MEASUREMENT OF THE ZWARTLAM) BASE. 251 interrupted for several days, a strong register picket is driven, and a brass pin inserted to § *■ carry the dot ; protected by a box, mound of earth, and tent in the way just described. At night the bars v^ere wrapped up in hair cloth, and placed side by side, together with the whole of the measuring apparatus, under line tents, securely fastened down. 4. Personal Force on the Measurement of the Zwartland Base, and their duties. The party consisted of the following : — Tbos. Maclear, H.M. Astronomer, and Responsible Superintendent. ^'"■"■ Charles Piazzi Smyth, and | Assistants to the Astronomer, employed "William Mann, j on the work in rotation (a). Captain Alexander Henderson, Royal Engineers. Lieutenant Cust, 25th Regiment. Serjeant John Hemming, \ Two Corporals, l Royal Sappers and Miners. Five Privates, ) Serjeant Wm. Calderhead, ) Twelve Privates, [ 25th Regiment. Joseph Gibbs, the Carpenter attached to the Observatory. Total : four officers, four non-commissioned officers, and eighteen men including Mr. Gibbs. Shortly after the commencement of the operation, it was perceived that the party was not sufficiently strong. Each bar requires a qualified officer, or non-commissioned officer, for the consumption of time rests chiefly with the preliminary adjustments in lining and levelling the bars and microscopes, the details of which are partly consecutive, but chiefly simultaneous ; and the only non-commissioned ofiicer, who from talent and survey experience was qualified for a position at the bars (Jb), had charge of the stores. Of the men, three were on the sick list at an early period, and the camp duties re- quired in general two, the forge one, and the carpentry one; leaving about 14 or 15 for the labouring work of the measurement. The order of the officers, with respect to their several duties and their positions at the bars, established at the beginning of the measurement was adhered to throughout ; excepting where the ground was unfavourable, or trivial instances of an officer being engaged elsewhere. The order at the bars was as follows : — Bar A, Mr. Maclear, first microscope over point-carrier. B, Mr. Smyth or Mr. Mann. C, Captain Henderson. D, Lieutenant Cust, E, Mr. Smyth or Mr. Mann. G, Mr. Maclear, last microscope over point-carrier. (a) One of the two Assistant Astronomers had, in rotation, charge of the Observatory. (b) Serjeant Hemming. 252 VERIFICATION AND EXTENSION OF LA CAILLE'S ARC OP THE MERIDIAN. Personal After the 40th set (a) it became necessary to dispense with bar D ; then Captain Henderson did not shift from bar C, nor Lieutenant Cust from E, Captain Henderson in general, but not always, worked the "directors" and side telescopes of the microscopes. Mr. Maclear invariably examined the bar dot bisections after they had been declared to be correct, and managed the point-carriers. The directing theodolite, or transit, was in charge of an Assistant Astronomer. Serjeant Calderhead superintended the picket, triangle, and trestle party, and personally levelled the picket heads. The most intelligent of the men assisted in the bar adjustments. § 5. ^5. Detail of the Measurement. The measurement was begun at the west terminal point on the 21st of October, 1840 ; and on the 27th a register picket was driven, marking 1701 feet. The precision of this length was tested, by re-commencing at the west terminal point on the 30th : on November 3rd it passed over the supposed position of La Caille's west end, and on the 4th reached the register picket before mentioned, when the wire of the "look down" telescope was seen bisecting the dot on the register pin. On the 6th, shortly after two o'clock, while adjusting the 41st series, (6) the air pre- viously calm and hot, a whirlwind suddenly sprung up, and advancing rapidly with a hissing noise, forced the tent pins (which were not well secured), and drove the tent frames against the line of bars resting on their trestles. Bars D and E were thrown off and fell to the ground, the others were held on the camels by the parties who chanced to be near to them at the moment : the microscopes were fortunately in their carrying box. Upon examination, and by comparison with the standard 10 -feet iron bar B, it appeared that bar E had not sustained any injury; but the right hand tongue of D was bent downward about one-tenth part of an inch, and therefore disabled from taking any further share in the measurement. While the examination of bars D and E was going on, 15 sets were measured with the four bars A, B, C, G. On the 9th bar E was restored in the 56th series, and no other accident worth recording occurred during the remainder of the operation, nor of any description whatever that could affect the precision of the measurement. Of the retardations arising from uneven surface, or loose ground, they chiefly occurred in the sandy soil at, and in the neighbourhood of the Salt River : deep cuts had to be made in its banks, but fortunately there was little water in its bed at the time of crossing it. A register picket was driven at the advanced end of series No. 808, on the 3rd of April, 1841 ; on the 5th another was driven at the advanced end of series 810, — distant (a) A series of bars was termed a set of bars in the register entries, and in conversation. (b ) Thermometer 9 1°'3. , DETAIL OF THE MEASUREMENT. 253 3 1 -5 feet from the intended east terminal point. These pickets and the intervening § s- point-carrier (protected as usual by boxes and mounds of earth, and sheltered by tents) remained thus while the masonry of the terminal point was effected and became firm. On the 20th, series Nos. 809 and 810 were re-measured : the dot on the brass stud of 810 required no correction; but the dot on the point-carrier left between pickets 808 and 810 was in error 0-02 inch, the cause of which was afterwards explained. Bars A, B, and C having been advanced to find the position of the intended ter- minal point, C, was removed to allow of the centre stone being drilled for the reception of the brass plug carrying the platinum stud. This done the three bars were adjusted, and a puncture made in the stud, at the distance of 31-5 feet from the 810th series. The total length of the base, in terms of the compensation bars and microscopes in the accidental temperature during the measurement, is represented by — 40 series of 63 feet = 2520. Apparent 15 „ 42 „ = 630. length of the 754 „ 52-5 „ = 39585. I „ 62-25 „ = 52-25, No. 88, of Nov. 12. 1 „ 31-5 „ = 31-5. Total, = 42818-75 feet. No beam compass nor measure of length, other than the compensation bars and microscopes, were used for any fraction of the distance. Of the 158 days — between October 30, 1840, and April 5, 1841 — 88 were occupied wholly, or in part, measuring. The greatest length measured on any one day was 787*5 feet, effected in 1 1|- hours. On these days, each series of 52-5 feet averaged 46 minutes ; and this is about the maximum speed that can be attained over favourable ground with the personal force employed, paying close attention to the adjustments of the bars, &c. Of the remaining 70 days, 12 were devoted to relaxation and private affairs at the termination of the year ; 21 were Sundays; leaving 37 chargeable to shed building, camp shifting, instrumental experiments and adjustments, and unfavourable weather. Two independent registers of the daily measurement were kept, one by Captain Henderson, the other by myself. The ^rst column of the following tabular detail of the measurement, gives the date. Tabular detau The second column gives the hour and minute when each series was completed. The third gives the number of the series. The fourth gives the titular or identifying letter of the bar. The fifth gives the same of each microscope. The sixth gives the temperature of the air when each series was completed. The thermometer rested upon a bar box near the middle of the line of bars, with its bulb freely exposed to the air, but sheltered from the suns rays. The seventh column gives the length of each series in terms of the bars and microscopes. of the Measu- rement. DETAIL OF THE MEASUEEMENT. 256 VERIFICATION AND EXTENSION OP LA CAILLE'S ARC OF THE MERIDIAN. DATE. TIME. No. of Series. n Micro- Bcopes, Therm. Apparent Length. DATE. TliME. No.of Series. Micro- Bcopes. Therm. Apparent Length. 1840. h m o feet 1840. h m o feet Oct. 30 1 A i^N \ M Oct. 31 7 A UN 1 M B B C P C P D Q D Q p.m. E R p.m. E R 2 45 2 G A B C D E IS UN 1 M P Q R 69-2 63 1 10 8 G A B C D E UN \ M O P Q R 73-7 63 4 8 3 G A B C D E IS UN \ M P Q R 67- 63 2 29 9 G A B C D E UN \ M P Q R 73-8 63 5 50 G IS 61-4 63 3 45 G |S 68-1 63 Oct. 31 4 A UN 1 M 10 A UN \ M O B B C P C P D Q B Q a.m. E R E R 8 5 5 G A B C D E UN 1 M P 61-4 63 4 50 11 G A B C D E iJN 1 M O P Q R 64-7 63 9 25 G JS 66-5 63 5 53 G is 62-4 63 6 A B C D E i|N 1 M P Q R Nov. 2 a.m. 12 A B C D E UN 1 M O P Q R 10 53 G JS 73-0 63 (378) 8 18 G iS 64; 7 63 (756) The " directors " lined with the 20-iiich transit instrument ; C. P. Smyth worked the transit. Order of observers: T. Maclear at half N, "look down;" C. P. Smyth at M; Capt. Henderson a1 0; Lieut. Oust at P; T. Maclear and Lieut. Oust at Q; C. P. Smyth at E; T. Maclear at half S, and "look down." The thermometer rests on a har box towards the middle of the series, with its bulb exposed; but \ vithout touching the box. The outer microscope of half N. or of half S, which precedes in one series of bars, follows in the next; thus any inequality in the bisection of the six inches, disappears from an even number of series. DETAIL OP THE MEASUEBMENT OF THE ZWARTLAND BASE.-CAPE OP GOOD HOPE. 257 DATE. TIME. No. of Series. a) Micro- scopes. Therm. Apparent Length. DATE. TIME. No. of Series i Micro- scopes. Therm. Apparent Length. 1840. h m o feet 1840. h m feet Nov. 2 13 A UN \ M Nov. 2 19 A liN 1 M B B C P C P D Q B Q E R E R 9 36 G iS 68-5 63 5 40 * G JS 70-0 63 14 A UN 1 M „ 3 20 A UN \ M B * B C P C P D Q B Q E R a.m. E R 10 55 15 O A B C B UN 1 M P Q 79-3 63 11 46 21 G A B C B IJN \ M P Q 74-2 63 p.m. E R p.m. E R 12 16 G A B C B E UN j M P Q R 83-9 63 1 17 22 G A B C B E UN 1 M P Q R 74-6 63 1 38 17 G A B C B E )|N M P Q R 82-0 63 2 40 * 23 G A B C B E UN 1 M P Q R 72-6 63 2 55 18 G A B C D E UN M P Q R 80-8 63 3 49 24 G A B C B E UN M P Q R 72 1 63 4 15 G |S 78'2 63 (1134) 5 47 G ^s 66-6 63 (1512) 19. The lining of G bar uncertain, owing to the lining instrument having been inadvertently removed, and no time to re-adjust. 20. The "point carrier" dot under Microscope i N out of Hue 07 inches — (see note to series 19); therefore placed bar A obliquely, to bring the advancing end into line. Correction = ■00033 feet subtractive. 22. Microscope S of this series supposed to be over La Caille's west end. 258 VERIFICATION AND EXTENSION OF LA CAILLE'S ARC OF THE MERIDIAN. 1840. Nov. 4 TIME. p.m. 1 No. of S Series, jn 25 2 50 3 55 5 18 a.m. 9 20 26 27 28 29 30 10 35 Micro- scoies. M O P Q R IS iN M O P Q R JS JN M O P Q R IS M O P Q R IS IN M O P R Q IS Therai. 73-3 73-3 Apparent Leugih. 63 63 1840. Nov. 5 71-1 63 67-3 67-7 76-6 (1890) 63 63 63 p.m. 17 1 26 3 4 No. of Series 31 32 33 34 4 18 5 35 a.m. 8 15 35 36 Micro- scopes. Therm. IN 'M O P Q R IS IN M O P Q R |S IN M O P Q R IS N M O P Q R S N M O P Q R rN 'M O P Q R ^S 81-0 82-9 78-6 76-7 Apparent Length, 63 63 63 63 73-6 68-3 63 63 (2268) 25. Microscope N thrown off its arm by the tent canvas, owing to strong wind. Compared its length with that of E, by means of the adjusted bar dots; the 6 inches do not appear to be exactly bisected. 27. The "look down" wire of Microscope S bisects the dot on the register picket planted on October 27, marking 1701 feet ! ! 29. By mistake Mcroscope R was placed on bar D, and Microscope Q on bar E. Strong wind on the 5th. DETAIL OF THE MEASUREMEKTT OP THE ZWARTLAND BASE —CAPE OF GOOD HOPE. 259 DATE. TIME. No. of . Micro- Tllerm. Apparent DATE. TIME. No. of i Micro- Therm Apparent Scries. " scopes. Length. Series. « scopes. Length. 1840. h m o feet 1840. h m o feet Nov. 6 37 A B C UN 1 M P Nov. 6 p.m. 43 A B C UN \ M R D Q 5 55 G JS 77-8 42 E R 9 35 38 G A JS UN \ M 83-7 63 „ 7 a.m. 44 A B C UN t M P B O 8 30 G IS 79-8 42 C P D E Q R 45 A J|N ■ M 11 5 G IS 87-8 63 B C P 39 A B C D UN \ M P Q 9 18 46 G A B |S UN M 82-4 42 p.m. E R C P 1 10 40 # G A B C JS UN \ M O P 91-4 63 10 18 47 G A B C IS UN \ M P 90-0 42 D Q 11 20 G |S 94-8 42 E R ^ ( 2 22 G JS 91-3 63 (2520) 48 A B UN M 41 A B UN 1 M pm. 35 C G P IS 92-6 42 3 58 C G R 840 42 49 A B UN \ M 42 A B UN M 1 22 C G P IS 93-7 42 4 45 C G R JS 82-8 42 (2604) 2 27 50 A B C G UN ■ M P IS 88-4 42 (2940) 40. After completing this series, and the bars were about to be removed from the tr( 3stles, a sudden gust of wind carried the tents against the bars : J) and E were thrown off, and fell to the ground wi th violence. These two bars were removed to Kotze's barn to be examined, in the mean time the measurement was c arried on with the other four bars. Fortunately the microscopes had been taken off. Observers: Maclear, Smyth, Cust, Mann; Maclear for series 44, 45, 46, 47, 50, 51, 52 53, 54, 55. Maclear, Smyth, Mann, Henderson; Maclear for 48, 49. 260 VERIFICATION AND EXTENSION OF LA CAILLE'S ARC OF THE MERIDIAN. DATE. TIME. No. of m Micro- Therm. Apparent DATE. TIME. No. of Micro- Therm. Apparent Series. B scopes. Length. Series. n scopeB. Length. 1840. h m o feet 1840. h m o feet Nov. 7 51 A UN 1 M Nov. 9 58 A UN t M B B p.m. C P C P 3 14 52 G A B C UN \ M P 86-7 42 a.m. 10 6 59 E G A B R IS f|N ) M 87-9 52-6 4 G IS 85-8 42 C E P R 53 A B C UN \ M P 11 13 60 G A IS UN 1 M 83-1 52-5 4 56 G iS 82-9 42 B C P 54 A B UN \ M p.m. 27 E G R IS 85-2 52-5 6 27 55 C G A P IS |N 1 M 83-6 42 61 » A B C E UN 1 M O P R B 1 24 G |S 82-8 ,52-5 C P 6 15 * G IS 77-1 42 (3150) 62 A UN 1 M „ 9 56 * A B UN \ M B C E O P R C P 2 20 G |S 82-2 52-5 a.m. E R / 1 -«T 7 41 G JS 73-5 52-5 63 A UN 1 M P R 57 A B UN 1 M B C E C P 3 23 G IS 81-9 62-5 9 5 E G R |8 81-1 52-5 (3255) 4 30 64 » A B C E G UN 1 M P R IS 80-8 (3 52-5 622-5) Mr. Smyth returned to the Observatory on the 8th, and Mr. Mann took his place at the lining ins trument, &c. 53. Commenced fixing the line-tents with iron pickets. 56. Bar E restored in this set. Bar D having been injured by the fall must henceforth be dispens ed with. Order of observers : Maclear, Mann, Henderson, Cust, Mann, Maclear. 61. Crossing the road from Kotze's house to his barn. 64. Clay soU as hard as sun-burned bricks. Directors Uned with Dollond's repeating Tl leodolite DETAIL OP THE MEASUREMENT Oi;.THE ZWARTLAND BASE.— CAPE OP GOOD HOPE. 261 DATE. 1840. Nov. 9 10 TIME. 5 36 6 30 a.m. 8 6 9 17 No. of Series. 65 66 67 68 69 10 23 11 35 p.m. 0-53 70 71 Micro- scopes. M O P R ^S IN M O P R hS N M O P R 8 {' (IN [ M O P R IS ;|N ' M O P R IS ■|N M O P R IS IN M O P R IS Therm. 76-4 73-0 67-4 Apparent Length 52-5 52-5 52-5 74-8 81-4 83-8 1840. Nov. 10 52-5 52-5 52-5 76-5 (3 52-5 990-0) TIME. No. of Series. „ 11 p.m. 1 52 3 5 72 73 4 2 5 a.m. 8 20 74 75 76 9 15 10 5 77 78 Micro- scopes. f|N [ M O P R |8 IN M O P R IS I|N I M O P R |8 f|N I M O P R IS f|N [ M O P R IS IN M O P R IS Therm. 78-0 Apparent Length. 62-5 76-2 52-5 74-0 64-7 71-2 52-5 52-5 52-5 73 2 52-5 72-8 (4 52-5 357-5) 68. Microscope E does not "telescope" correctly. 75. Left off in haste, from indications of a N.W. gale. 262 VERIFICATION AND EXTENSION OF LA CAILLE'S ARC OF THE MERIDIAN. DATE. TIME. No. of Series. s P Micro- scopes. Therm. Apparent Lenglli, DATE. TIME. No. of Series. 1 Micro- scopes. Therm. Apparent Length. 1840, h m o feet 1840. li m feet Nov. 11 79 A UN 1 M Nov. 12 86 A UN \ M B B C P C P a.m. E R a.m. E R 11 27 80 G A UN M 74-5 52-5 8 35 87 G A iS UN 1 M 64-7 52-6 B B O p.m. V C E P R C E P R 19 81 G A B C E UN M P R 76-4 52-5 10 3 p.m. 88 * G A B C E IS R 78-0 52-5 2 5 82 • G A B C E ]|N t M P 73-8 52-5 1 89 G A B C E JS UN j M P R 79-0 52-5 3 83 G A B C E JS UN 1 M P R 73-0 52-5 2 10 90 G A B C E IS UN 1 M P R 75-8 52-5 4 4 84 G A B C E iS |iN \ M P R 70-5 52-5 3 5 91 G A B C E IS UN \ M P R 73-0 52-5 5 85 G A B C E UN 1 M P R 68-5 52-5 4 1 92 « G A B C E IS UN 1 ¥ P Q 68-9 52-5 6 6 G 1 S 1 64-6 52-5 4 54 G IS 67-5 52-5 ! (4 825 -0) (50 92-25) 82. Eepeating Theodolite corered with sand raised by the wind. 84. Sandy soil near the swamp (Kotze's Valei). 86 and 87. Lieutenants "Wilmot and Maclean, Eoyal Artillery, observed — vice Henderson. 88. A descent : Microscope Q placed on bar A vice M, and M placed on bar C, with its " look dov m " on bar E. Only 3 inches of M employed. 92. Microscope Q used on bar E instead of R, which accidentally fell, by which its telescope adjustm 3nt was disturbed. DETAIL OP THE MEASUREMENT OP THE ZWARTLAND BASE.— CAPE OP GOOD HOPE 263 DATE. 1840. Nov. 12 13 14 p.m. 5 51 a.m. 7 45 8 36 9 53 No.o< Series, 11 11 p.m. 25 8 45 93 94 95 96 97 98 # 99 Micro- scopes. iN M O P Q UN 1 M O P Q iS UN [ M O P Q UN ' M O P R JS IN M O P Q JS JN M O P Q iS N M O P Q S Therm. 1* 64-6 63-4 71-4 75-2 76-1 75-0 80-1 (54 Apparent Length, feet 52-5 52-5 52-5 52-5 52-5 52-5 52-5 .59-75) DATE. 1840. Nov. 14 TIME. a.m. 9 43 10 44 11 49 p.m. 44 1 46 3 12 4 15 No. of Series, 100 101 102 103 104 105 106 B C E G A B C E G B C E G A B C E G Micro- scopes. i* :N M O P Q S N M O P Q s JN M O P Q JN M O P Q IS JN M O P Q JS UN \ M O P Q iS Therm, 85-6 92-5 94-9 86-7 84-5 81-8 81-7 (58 Apparent Length, feet 52-5 52-5 52-5 52-5 52-5 52-5 52-5 27-25) 98. Obliged to leave off owing to strong wind. H. absent from 104 and the following four sets. 102. The heat oppressive. 264 VERIFICATION AND EXTENSION OF LA CAILLE'S ARC OF THE MERIDIAN, DATE. TIME. No. of s Micro- Therm. Apparent DATE. TIME. No. of t Micro- Therm, Apparent Series. S scopes. Length. Series n scopes. length. 1840. h m o feet 1840. li m o feet Nov. 14 107 A jJN 1 M Nov. 16 114 A UN \ M B B C P f C P p.m. E R p.m. E Q 5 19 108 G A B C E IS UN 1 M P R 79-9 52-5 2 44 115 G A B C E IS UN 1 M P Q 94-2 52-5 6 25 G iS 76-0 52-5 3 37 G |S 82-6 52-5 „ 16 a.m. 109 A B C E UN \ M P Q 116 A B C E i|N 1 M P Q ' 7 59 110 G A B C E UN 1 M P Q 66-7 52-5 4 26 117 G A B C E |8 i|N ■ M P Q 74-1 52-5 9 16 111 G A B C E IS |N 1 M P Q 77-6 62-5 5 26 118 G A B C E IS UN M P Q 70-4 52-5 10 18 G iS 82-0 52-5 6 9 G IS 66-9 52-5 112 A B C E UN *^ P Q „ 17 a.m. 119 » A B C E ||N 1 M P Q 11 47 113 G A B C IS UN 1 M P 85-0 52-5 9 22 120 G A B C IS i|N M P 73-4 52-5 p.m. E Q E Q 1 46 G IS 91-8 52-5 10 20 G i8 81-1 52-5 1 (61 94-75) (65 62-25) 113. Drove a register picket at the advanced end of this series, to carry a pin with a gross marked upon it. 114. Lieut. Cust absent from this set. DETAIL OF THE MEASUREMENT OP THE ZWARTLAND BASE.— CAPE OF GOOD HOPE. 265 DATE. TIME. . No. of Series. Micro- scopes, Therm. Apparent Length. DATE. TIME. No. of Series a Micro- sci'pes. Therm. Apparent Length. 1840. h m feet 1840. h m feet Not. 17 121 A UN 1 M Nov. 20 128 A UN 1 M B B C P C P a.m. E Q E Q 11 26 122 G A B C 38 UN 1 M P 76-0 52-5 11 22 129 * G A B C |8 UN 1 M P 99-7 52-5 p.m. E Q p.m. E Q 41 123 G A B C E UN 1 M P Q 76-7 52-5 40 130 G A B C E IS UN \ M P Q 100-1 52-5 1 42 124 G A B C E IJN P Q 77-0 52-5 3 12 131 G A B C E IS UN 1 M P Q 96-9 52-5 2 36 125 * G A B C E IS UN t M P Q 74-4 52-5 4 6 132 G A B C E IS (JN 1 M P Q 93-1 52-5 3 38 G 58 73-4 52-5 5 1 G IS 90-7 52-5 „ 20 126 A B C E IIN p Q 133 A B C E UN M P Q ~ a.m. G 5S 92-2 52-5 6 11 G IS 84-2 52-5 9 41 127 A B C E UN i M p Q „ 25 134 A B C E (IN M P Q 10 31 G |S 97-6 52-. 5 8 20 G IS 70-8 52-5 (69 29-75) (72 97-25) 125. Obliged to discontinue the measurement, owing to the violence of the wind: also for the same reason on the 18th and 19th. Spent the time comparing the Bars with the standard B, and adjusting microscopes. 129. The heat too oppressing to continue the measurement. 133. Barometer 29'702, thermometer 80 at 94 p.m. A north-wester advancing. The north-wester set in on ' Saturday morning, 21st ; Mr. Maclear seized the opportunity to visit the Observatory: returned on the 24th. 266 VERIFICATION AND EXTENSION OF LA CAILLE'S ARC OP THE MERIDIAN. DATE. TIME. No. of Series, Micro- scopes. Therm. Apparent Length. DATE. TIME. No. of Series. n Micro- scopes. Therm. Apparent Length. 1840. h m feet 1840. b m o feet Nov. 25 135 A (|N \ M Nov. 25 142 A ||N 1 M O B B C P C P E Q p.m. E Q 9 20 136 G A B C E |S ||N M P Q 73-5 52-5 3 38 143 G A B C E |S J|N p Q 73-8 52-5 10 13 137 O A B C E IS (IN ■ M P Q 77-0 52-5 4 30 144 G A B C E IS UN M P Q 71-7 52-5 . 11 15 G IS 80-8 52-5 5 26 G |S 74-3 52-5 138 A B C ||N \ M P „ 26 145 A B C UN t M P p.m. E Q a.m. E Q 6 139 G A B C E |S (IN 1 M P Q 83-2 52-5 9 6 146 G A B C E IS UN 1 M P Q 68-0 52-5 55 G IS 84-7 52-5 11 9 * G IS 65-5 52-5 140 A B C E (IN 1 M P Q „ 27 a.m. 147 A B C E UN 1 M O P Q 1 53 141 G A B C E |S UN \ M P Q 77-9 52-5 7 37 148 G A B C E IS UN \ M P Q 67-9 52-5 2 48 G IS 75-5 (76 52-5 64-75) 8 42 G IS 73-1 (80 52-5 32-25) 146. A register picket driven at the advanced end of this series, carrying the usual hrass pin with dot. The position is 52-5 feet on the east side of the Uyle Kraal road. Left oflf at the following series on account of rain. Lieut. Gust absent on leave, from November 27 to December 3: unwell. DETAIL OF THE MEASUREMENT OP THE ZWARTLAND BASE.-CAPE OF GOOD HOPE, 267 DATE. 1840. Nov. 27 TIME. a.m. 9 32 10 37 11 36 p.m. 41 1 34 2 35 3 27 No. cf Series. 149 150 151 152 153 154 155 Micro- scopes. UN 1 M O P Q J8 I^N I M O P Q iS HN t M o p Q UN I M O P Q is UN I M O P Q JS liN I M O P Q IJN I M O P Q Therm. 75-0 77-0 76-1 76-3 73 2 73-7 71-2 C83 Apparent Length. feet 52-5 52-5 52-5 52-5 52-5 52-5 52-5 99-75) DATE. 1840. Nov. 27 28 TIME. p.m. 4 18 5 17 a.m. 7 12 8 5 9 10 7 11 19 No. of Series. 156 157 158 159 160 161 162 Micro- Bcopes, 1|N I M O P Q js UN I M O P Q ^8 UN I M O P Q |S UN I M O P Q JS (JN [ M O P Q JS [^N [ M O P Q hs UN M O P Q Therm. 70-8 68-0 68-0 72-1 70-6 75-5 76-9 (87 Apparent Length. feet 52-5 62-5 52-5 52-5 52-5 52-5 52-5 67-25) 162. Removed the Azimuth circle of DoUond's Theodolite, to save the divisions from injury by sand. 268 VERIFICATION AND EXTENSION OF LA CAILLE'S ARC OP THE MERIDIAN. DATE. TIME. No. of Series. 1 Micro- scopes. Therm. Apparent Length. DATE. TIME. No. of Series. E n Micro- scopes. Therm. Apparent Length. 1840. h m o feet 1840. li m o feet Nov. 28 163 A UN 1 M Dec. 1 170 A UM B B C P C P p.m. E Q E R 26 164 G A B C E IS ( JN {m p Q 790 52-5 11 26 p.m. 171 G A B C E IS IM N P R 80-4 52-5 3 22 165 G A B C E UN M P Q 75-0 52-5 24 172 G A B C E IS PS? p R 76-7 52-5 4 13 166 G A B C E IS UN 1 M P Q 75-0 52-5 3 54 173 G A B C E IS UM 1 N O P R 74-1 52-5 5 5 * G iS 71-0 52-5 4 44 G IS 73- 1 52-5 Dec. 1 167 A I N 174 A UM 1 N B B C P C P a.m. E R E R 8 24 168 G A B C E |8 UM P R 68-6 52-5 5 34 175 G A B C E IS UM 1 N P R 72-4 52-5 9 23 G IS 75-0 52-5 6 37 G IS 68-4 52-5 169 A B C E ]|M ( N P R „ 2 a.m. 176 A B C E i|M 1 N O P R 10 23 G IS 77-0 (91 52-5 34-75) 7 13 G |S ?68-2 (95 52-5 02-25) 166. Indications of a N.W. breeze: measurement concluded in consec[uence. Kain came on at 7''. Nov. 30. Capt. Henderson and Mr. Mann comparing the compensation with the standard bar B ; Mr. Maclear engaged examining and adjusting Microscopes. Microscope Q cannot convenientlyhe adjusted to bisect 6 inches on rotation, because a screw of one of the outer is broken, and the object glass is held fast with wire in consequence. Microscopes M and N wiU therefore change places on bar A. The levels of Microscopes Q and E are not steady: the tubes are fast in their frames. They have been frequently examined and cleaned, without discovering the cause of their unsteadiness. The side telescopes require constant attention : they are frequently getting out of adjustment, probably from being touched when removing the Microscopes from their bearings to their carrying box. 167. Microscope E replaces Q on bar E. 170. Str ong wind. 176. The" rher. not oi lits b ir: 5 8 register ed instea dof 68? 1 DETAIL OP THE MEASUREMENT OF THE ZWARTLAND BASE.— CAfE OF GOOD HOPE. 269 DATE. TIME. No. of Series. Micro- scopes. Tlierm. Apparent Length. DATE. TIME. No. of Series. i Micro- scopes. Therm. Apparent Lengtl). 1840. h m o feet 1840. Ii m o feet Dec. 2 177 A 1 N Dec. 2 184 A UM 1 N B B C P C P a.m. E R p.m. E R 8 14 178 G A B C E P R 71-3 52-5 5 42 185 G A B C E i^M 1 N O P R 69-0 52-5 9 10 G iS 75-1 52-5 6 30 G iS 65-0 52-5 179 A B C E p R ;, 3 a.m. 186 A B C E UM * g P R 10 4 180 G A B C E P R 79-9 52-5 7 25 187 G A B C E |8 UM 1 N P R 61-4 52-5 11 12 * 181 G A B C ^8 SJM ' I P 83-4 52-5 8 12 188 G A B C UM u p 65-1 52-5 p.m. E R E R 14 182 G A B C E p R 86-7 52-5 9 39 189 G A B C E |8 UM * I P R 70-4 52-5 4 8 183 G A B C E * I p R 74-5 52-5 10 23 190 G A B C E UM P R 71 3 52-5 5 G JS 70-5 (98 52- -5 69-75) 11 14 G IS 73-0 (102 52-5 37-25) 180. A register picket driven at the £ idvanced end of this series, marking 9712'25 feet. The centre of the dot on the pin is one-third of its breadth too n 3ar the east end of the Base. 270 VERIFICATION AND EXTENSION OF LA CAILLE'S ARC OF THE MERIDIAN. DATE. TIME. No. of 3eries. i Micro- scopes. Therm. Apparent Length, DATE. TIME. No. of Series. Micro- scopes. Therm. Apparent Length. 1840. h m feet 1840. h m o feet Dec. 3 191 A i N Dec. 4 198 A 1 N B B a P C P p.m. E R a.m. E R 3 192 a A B C E P R 75-2 52-5 8 48 199 G A B C E IS p R 71-3 52-5 3 19 193 G A B C E J8 P R 77-1 52-5 9 38 200 G A B C E IS ■ N P R 75-5 52-5 4 6 194 O A B C E ' I p R 74-7 52-5 10 32 p.m. 201 G A B C E IS ilM 1 N P R 78-3 52-5 5 195 G A B C E P R 72-1 52-5 23 202 G A B C E IS i|M 1 N P R 80-0 52-5 5 56 196 G A B C E J8 P R 68-6 52-5 1 11 203 G A B C E IS i|M 1 N P R 79-8 52-5 6 46 G |S 65-1 52-5 4 26 G IS 74-0 62-5 „ 4 a.m. 197 A B C E p R 204 « A B C E P R 7 40 * G iS 61-2 (loe 52-5 04-75) 6 46 G IS 69-5 (lOE 52-5 72-25) 197. Thermometer in its box had not attained the temperature of the air. 204. Left off at 5^ 46°' to afford time for putting up struts. DETAIL OF THE MEASUREMEIVT OF THE ZWARTLAND BASE.— CAPE OF GOOD HOPE. 271 DATE. TIME. STcof . Mlcpo- Therm, Apparent DATE. TIME. No. of i Micro- Therm. Apparent r^erles. n scopos. Lenglh, Series. n scopes. Length. 1840. h m o feet 1840. h m O feet Dec. 5 205 A Dec. 5 212 A 1|M B B C p C P a.m. E R pm. E R 7 10 206 G A UM 1 N 64-5? 52-5 141 213 G A J8 80-0 52-5 B B C P C P E R E R 8 2 207 G A B C E p R 72-3 52-5 2 23 214 G A B C E ■ N O P R 77-7 52-5 9 6 G iS 77-8 52-5 4 40 G IS 74-6 52-5 208 A B C E I N P R » 7 a.m. 215 A B C E 1 N P R \ 9 55 209 G A B C E |8 P R 77-8 52-5 7 55 216 G A B C E HM I N p R 72-1 52-5 10 54 210 G A B C E 1 N P R 82-9 52-5 8 39 217 G A B C E IS p R 74-5 52-5 11 49 211 G A B C 1 N P 81-4 52-5 10 9 218 G A B C IS i|M ■ N P 78-9 52-5 p.m. E R E R 38 G JS 79 6 (113 52-5 39-75) 11 17 G IS 80-0 (117 52-5 07-25) 205. As yesterday: the Therm, had not been removed from its box in time to attain the temperature ot the air. 214. A register picket driven at the end of this series, marking U497-25 feet. When adjusting Microscope P m this series it did not bisect the compensation point in reversed positions : the level and side telescope were also out of adjustment, indicating the effect of a fall, though seemingly unknown to any one. Six inches were measured between the adjacent compensation points, by placing on bar B as a test for P. P was found to rotate correctly, but the unlettered outer Microscope exceeded three inches of 0, by about one-third part of the silver stud carrying the compen- sation point. The series was completed by re-placing P on bar C, measuring six inches by rotating the lettered end. In same way series 213 was re-measured and found correct, shewing the injury to have been sustained when removing the Microscope between series 213 and 214. P was adjusted on the six-inch standard, in the temperature 59 -4, early on the following morning 272 VERIFICATION AND EXTENSION OF LA CAILLE'S ARC OF THE MERIDIAN. DATE. TIME. No. of aeries. 1 Micro- scopes. Therm. Apparent Length. DATE. TIME. No. of Series. Micro- scopes. Therm. Apparent Length, 1840. h m feet 1840. b m o feet Dec. 7 219 A Dec. 8 226 A UM B B C p C P p.m. E R p.m. E R 24 220 a A B C E p R 80-4 52-5 1 30 227 G A B C E f sM P R 89-2 52-5 1 41 221 G A B C E IS P R 81-1 52-5 2 38 228 G A B C E isM I N P R 88-0 52-5 3 30 * G |8 76-5 52-5 3 55 G IS 86-1 52-5 » 8 a.m. 222 A B C E HM 1 N P R 229 A B C E 1|M p R 7 58 223 G A B C E |8 1 N P R 71-5 52-5 6 23 230 G A B C E |S ||M P R 82-0 52-5 9 5 G iS 76-4 52-5 6 35 G IS 76-2 52-5 224 A B C E UM ' I P R „ 10 a.m. 231 A B C E UM 1 N O P R 10 36 G iS 84-1 52-5 7 38 G IS 68-0 52-5 225 A B C E i^M 1 N P R • 232 A B C E i|M 1 N P R 11 59 G IS 90-0 (120 52-5 74-75) 10 15 G IS 72-0 (124 52-5 42-25) 220. Captain Henderson otherwise engaged. 221. Obliged to leave off owing to the violence of the south wind. Microscope P was again foiu ad this morning out of order. The lettered half only used. Strong wind on the 8th. December 9 devoted to planting directing pickets in the low ground nea and to the examination of Microscopes. r the Salt Eiver, The dot on the six-inch brass scale near the Thermometer bulb is 17 divisions of the Microm eter Microscope belonging to the bar apparatus, designed for measuring small quantities. 12"'-253 of the Micrometer sc rew = O'l inch of the four feet brass scale, in temperature 76 ; .-. 17 divisions = 0'°'0013874 = the diameter of the dot. The temperature of the six-inch brass standard rose from 88 to 100°, which afforded an estimate of the compensation oJ ' the Bar Micros- DETAIL OF THE MEASUKEMENT OF THE ZWAUTLAND BASE.-CAPE OF GOOD HOPE. 273 DATE. 1840. Dec. 10 TIME. a.m. 11 40 p.m. 34 No. of Series, 233 234 235 1 42 11 3 6 a.m. 8 12 9 19 10 3 236 237 238 239 Micro- scopes. I N O Q R JS UM I N O Q R IS I N o Q R IS I N O Q R I N O Q R JS I N O Q R I N o Q R Therm. 76-4 74-5 84-3 Apparent Length feet 52-5 52-5 DATE. 1840. Dec. 11 TIME. 52-5 80-0 73-8 84-4 88-5 (128 52-5 52-5 52-5 52 -.5 09.75) No. of Series, 240 a.m. 11 11 49 p.m. 34 241 242 243 1 28 2 23 3 35 4 20 244 245 246 Micro- scopes. I N o Q R IS i|M I N o Q R IS i|M I N O Q R IS JIM I N O Q R IS I JM I N O Q R IS {|M I N O Q R IS M N O Q R IS {* Therm. Apparent Len^h, feet 87-2 88-4 52-5 52-5 83-8 82-3 52-5 525 81-9 81-5 81-3 (131 52-5 52-5 52-5 77-25) copes by comparing the wire on one side with the dot, while the wire of the other outer Microscope bisected the opposite dot. Taking the expansion of brass at -000009959 for one degree =-000059754 for 6 inches, and for 23°-0013743, &c. Subtracting the temperatures when the Microscopes were adjusted on the 30th of November from the temperatures of to-day while experimenting, the computed value in terms of the dot for the difference was compared with the observed displacement, and as far as the eye coxild detect they exactly agreed; implying that the wires remained firm and the Microscopes unaffected by changes of temperature. The method is rough, but suflScient for the object in view. The side telescopes were next examined, aid slight deviations from adjustment corrected, excepting P, which will be re- placed by Q on the present work. 239. The plumb-line dropped on the point-carrier brass plate. 241. R seems to be out of adjustment. 274 VERIFICATION AND EXTENSION OF LA CAILLE'S ARC OF THE MERIDIAN. DATE. TIME. No. of aeries. i Micro- Bcopes. Therm. 4ppareiit Length. DATE. TIME. No. of Series. i Micro- scopes. Therm. Apparent Length. 1840. h m o feet 1840. h m o feet Dec. 11 247 A 1 N Dec. 14 254 A I|M 1 N B B C Q C Q p.m. 5 13 E R a.m. E R G IS 80-6 52-5 11 55 G IS 74-0 52-5 248 A 1|M 255 A j|M ' N B » B C Q C Q E R p.m. E R 554 249 G A 80-5 52-5 1 22 ■256 G A IS ||M 74-1 52-5 B B * C E Q R C E Q R 6 41 G IS 75-6 52-5 3 G IS 74-5 52-5 » 12 250 A ||M 257 A ||M 1 N B B O C Q C Q a.m. E R E R 8 11 * G IS 64-9 52-5 3 56 G IS 71-9 52-5 „ 14 251 A B C E i|M 1 N Q R 258 A B C E i|M Q R 9 17 G IS 71-5 52-5 4 58 G IS 67-8 52-5 252 A „ 15 259 A ||M B B ^ C Q C Q E R E R 10 5 253 G A B C E |S ' I Q R 73-0 52-5 7 44 260 « G A B C E IS ||M Q R 73-0 62-5 11 8 G IS 74-5 (135 52-5 44-75) 8 35 G IS 79-2 (13S 52-5 12 '25) 249. Microscope Q was carefully cleaned on the evening of the 1 1th, and the edge of the plate of the brass case that touched the outside of the stem was filed away: this done the instrument rotated correctly. 250. While measuring set 251, one of the party engaged in placing the "point-carrier," accidentally hit Microscope S with his head and it fell to the ground. The side telescope was thrown out of adjustment, and the measurement was therefore stopped. The adjustment for length was made the same evening in temperature 66°: also the case of was removed, the collar and axis cleaned, and the brass of the case, where it pressed on the axis, was filed away. December 14. Commenced by re-measuring series 250. 255. A rather abrupt ascent: the Bars placed on the triangles without tressels. 258. Indications of the approach of "a north-wester" with rain. 260. Measuring over a spongy mound of sand. DETAIL OF THE MEASUREMENT OP THE ZWARTLAND BASE.— CAPE OP GOOD HOPE. 275 DATE. TIMF. JfO.ff i Micro- Therm. Apparent DATE. TIME. No. of E Micro- Apparent A Length. Series m scopes. Length. 1840. h m feet 1840. h m o feet Dec. 15 a.m. 261 A B C E |M 1 N Q R Dec. 17 a.m. 268 A B C E i|M 1 N Q R 9 38 262 G A B C E IS j |M 1 N Q R 79-9 52-5 11 21 p.m. 269 G A B C E |S J|M 1 N Q R 100-5 52-5 10 52 263 » G A B C E IS 1|M * I Q R 81-8 52-5 25 270 G A B C E IS f|M ' I Q R 98-0 52-5 G IS 80-5 52-5 1 27 G IS 97-6 52-5 „ 17 a.m. 264 A B C E ||M O Q R 271 A B C E <|M 1 N Q R 7 46 265 G A B C E IS (|M Q R 82-2 52-5 2 40 272 G A B C E IS i|M 1 N Q R 95-3 52-5 8 31 266 G A B C E IS ^ I Q R 84-9 52-5 3 55 273 G A B C E IS i|M Q R 92-4 52-5 9 24 267 G A B C E IS S|M Q R 91-4 52-5 4 42 274 G A B C E IS i|M Q R 91-0 52-5 10 17 G IS 94-8 52-5 6 54 G IS 77-5 52-5 (142 79-75) (146 47-25) 263. Stopped measuring for the purpose of comparing the Compensation-bars with the standards, by means of the Microscopic beam compass lately constructed. December 16. The day distressingly hot: it was in part spent comparing bars. 276 VERIFICATION AND EXTENSION OF LA CAILLE'S ARC OF THE MERIDIAN. DATE. TIME. No. of Series. i Micro- Bcopes. Therm. Apparent Length. DATE. TIME. No. of Series. Micro- scopes. Therm. Apparent Length, 1840. h m o feet 1840. b m feet Dec. 18 275 A ■ N Dec. 18 282 A B B C Q C Q a.m. E R p.m. E R 7 6 276 O A B C E Q R 63-1 52-5 4 44 283 G A B C E N Q R 78-0 52-5 8 25 G iS 77-8 52-5 6 15 « G iS 68-5 52-5 277 A ■ N „ 21 284 A J5M N B B G Q C Q E R a.m. E R 9 23 278 G A B C In Q 75-1 52-5 7 35 285 G A B C 1 N Q 70-4 52-5 p.m. E R E R 35 * 279 G A B C E {%^ Q R 88-6 52-5 8 46 286 G A B C E 1 N Q R 78-4 .52-5 1 35 280 G A B C E |8 1 N Q R 81-1 52-5 10 13 287 G A B C E Q R 86-5 52-5 245 281 G A B C E IN Q R 80-8 52-5 11 22 p.m. 288 G A B C E i N Q R 930 52-5 3 45 G iS 79-7 (150 52-5 14-75) 1 14 G JS 93-5 (153 62-5 32-25) 278. At the advanced end of this series a register picket was driven, marking 14857'25 apparent feet. An ohlong dot inadvertently made on the pin. The true position of the " look down" wire, one-third of the diameter of the dot towards the east of its centre. '283. Drove a strong register picket at the advanced end of this series, marking 15119-75 feet; for reference, if necessary, while measuring over the soft ground near the river. The dot is rather oblong, but its centre is the correct point. 284. Strong south wind. DETAIL OF THE MEASUREMENT OF THE ZWARTLAND BASE.-CAPE OP GOOD HOPE. 277 DATE. 1840. Dec. 21 „ 22 TIUE. p-m. 2 53 a.m. 9 46 11 12 No. of Series, 289 290 291 p.m. 17 1 19 3 12 4 32 292 293 294 295 Micro- scopes. 1 N o Q R IS HM I N o Q R IS UM 1 N O Q R iS J|M I N O Q R iS I N O Q R IS I N O Q R IS ||M O Q R *S Therm. 90-2 82-7 Apparent Length. feet 52-5 52-5 88-0 52-5 83-4 85-3 77-1 71-7 (157 DATE. 1840. Dec. 22 1841. Jan. 6 TIME. p.m. 6 18 p.m. 1 8 No. of Series, 296 297 52-5 52-5 52-5 52-5 49-75) 2 42 4 17 5 42 a.m. ■ 7 35 9 21 298 299 300 301 302 Micro- scopes, i|M 1 N O Q R IS ( iM I N O Q R IS I|M i N O Q R IS f|M [ N O Q R IS ■|M N O Q R IS |M N O Q R IS Therm. 65-0 Apparent Length. feet 52-5 73-8 71-3 68-9 52-5 52-5 65-4 66-6 81-4 (161 52-5 52-5 52-5 52-5 17-2.5) 291. Passing along the south side of a pool of water, one of the lagoons of the Salt River. This locality is the worst part of the line, and swampy in the winter season. La Caille does not mention the place. 295. Difficult work, the tents generally obstructing a view of the lining struts from the Theodolite, owing to the unevenness of the ground. 296. Drove a register picket at the end of this set, marking 15802-25 feet. Two dots on the pin, corresponding to the wire in reversed positions, viz. : separated by double of the error in colMmation. The middle of the interval is the true point. January 6, series 297. Engaged in the forenoon comparing Bars, and in making deep cuts for the Bars in the banks of the Salt River. Progress retarded by the nature of the ground, and by showers of sand raised by brisk wind. 278 VERIFICATION AND EXTENSION OP LA CAILLE'S ARC OP THE MERIDIAN. DATE. 1841. Jan. 8 TIME. a.in. 11 15 No. of Series. 303 p.m. 48 2 19 3 48 5 3 6 15 a.m. 7 19 304 A 305 306 307 308 309 Micro- scopes. Therm, N O Q R iS ■ JM N O Q R IS ' s Q R IS ;^M I N O Q R JS [JM I N O Q R ^S I N O Q R ( iM I N O Q R 94-5 A-pparent Length. 95-1 103-0 90-7 88-2 85-7 feet 52-5 66-3 (164 52-5 52-5 52-5 52-5 52-5 52-5 84-75) DATE. TIME. 1841. Jan. 9 a.m. 8 12 9 7 No. of Series. 310 311 10 12 11 4 p.m. 3 53 2 4 312 313 314 315 316 Micro- scopes. ;M N O Q R :S ,M N O Q R iM N O Q R JM N O Q R IS |M N O Q R JS JM N O Q R J8 ;jM I N o Q R Therm. 71-4 73-1 74-8 77-2 78-8 Apparent Length. 52-5 52-5 52-5 52-5 52-5 52-5 80-2 (168 52-5 52-25) Mr. 0. P. Smyth has replaced Mr. Mann, the former taking charge of the Royal Observatory. 300. This set crossed the Salt River at its mean hend. January 7. Engaged with Captain Henderson and Mr. Smyth clearing the nozzles of sand: cleaning clamps, camels, microscopes, &c. The men were employed cutting through the sand banks on the east side of the Salt River. 305. Thermometer bulb not properly exposed: the temperature of the air was about 95°. DETAIL OP THE MEASUREMEJfT OF THE ZWAETLAND BASE.-CAPE OP GOOD HOPE. 279 DATE. 1841. Jan. 9 11 TIME. No.cf Series. p.m. 3 15 a.m. 8 59 317 318 p.m. 3 12 1 59 319 320 321 a.m. 8 50 10 18 11 27 322 323 Micro- scopes. N O Q R .8 iM N O Q R S N 1* O Q R {* M N O Q R |M O Q R IS I* Therm. 76-9 Apparent Length. feet 52-5 75-8 89-7 52-5 52-5 83-4 81-3 52-5 81-7 84-9 (172 52-5 52-5 52-5 19-75) DATE. 1841. Jan. 12 TIME. p m. 46 No. of Series. 324 2 14 325 a.m. 8 25 9 46 326 327 328 11 p.m. 15 1 17 329 330 Micro- Bcopes. N O Q R JS M O Q R iS 1|M I N O Q R IS 1|M \ N O Q R IS [|M i N O Q R IS IM N O Q R IS M |M I N O Q R Therm. Apparent Length. feet 81-2 52-5 82-0 78-9 52-5 52-5 90-8 52-5 94-7 52-5 88-3 86-0 (175 52- 5 52-5 87-25) 317. Left off to compare Bars. January 1 1, at 10i> 20" a.m., a sudden gust of wind drove the tent against Bar A, which was faJling off the trestles, but Mr. Maclear being at Microscope M, over the " point-carrier," held up that end of the Bar, though he could not pre- vent the left end and Microscqpe N from reaching the ground : neither sustained any injury. The accident arose from neglecting to secure the guy and foot ropes to the pickets, a common practice in calm weather, hut which cannot he too strongly reprobated. The former accident led to a general order on this subject, and the present shews how necessary, in addition, is personal superintendence. January 12. The measurement delayed by the examination of Microscopes. N was found correct in temperature 66°-5 and M in 62°-0. J J t f 280 VERIFICATION AND EXTENSION OF LA CAILLE'S AEG OF THE MERIDIAN. DATE. TIME. 1841. Jan. 14 p.m. 3 11 4 11 16 6 5 No. of Series. 331 332 333 a.m. 7 53 8 55 9 56 10 44 334 335 336 337 Micro- scopes. Therm. N O Q R JM "N O Q R Q R iS Q R IS (iM 'g Q R iS Q R IS ||M I N O Q R 82-4 78-2 75-1 Apparent Length. feet 52-5 52-5 52-5 DATE. 1841. Jan. 16 79-2 85-6 88-3 88-0 (179 52-5 52-5 52-5 52-5 54-75) TIME. 11 54 p.m. 52 2 11 18 No. of Serie?. 338 339 340 341 3 12 4 23 a.m. 7 33 8 25 342 343 344 Micro- |M N O Q R IS |M N O Q R |S |M N O Q R IS [|M I N O Q R IS (|M I N O Q R |S O Q R IS ||M I N O Q R IS Therm. 90-7 93-3 92-3 Apparent Length. feet 52-5 52-5 52-5 88-1 84-4 81-4 52-5 52-5 52-5 87-6 (183 52-5 22-25) 325. The wind rising and the ground loose sand, the measurement was stopped, and the men set to work on a place in advance for comparing Bars. 329. The tent-frames are becoming rickety from constant shifting. 333. Left off for the purpose of planting uprights (struts). Strong wind in gusts. 334. Drove a strong register picket at the advanced end of this series, marking 17797-25 feet. Two dots were made on the pin, corresponding to the reversed positions of the wire; the middle of the space between them is the correct point. 240. Sudden pufis of wind from the south. Difficult to drive pickets, as the rock is close to the surface. 342. Left off measuring from being too close to the picket drivers, and the wind dangerously strong. DETAIL OF THE MEASUREMENT OF THE ZWARTLAND BASE.-CAPE OF GOOD HOPE. 281 DATB" 1841. Jan. 18 19 TIME. a-m. 9 56 a.m. 8 3 9 21 11 16 No. of Series. 345 346 347 348 p.m. 11 1 2 1 56 349 350 351 Micro- scopes. 1 N o Q R iS 1 N O Q R HM I N O Q R HM I N o Q R IS HM I N o Q R HM I N o Q R iS |M N O Q R Therm. 90-7 93-6 Apparent Length feet 52-5 52-5 97-6 96-2 96-2 94-8 (186 52-5 DATE. 1841. Jan. 19 p.m. 2 52 No. of Series, 352 353 52-5 52-5 52-5 52-5 89-75) 3 54 4 49 5 45 6 30 7 15 „ 21 a.m. 9 354 355 356 357 358 Micro- scopes. HM o Q R iS {|M 1 N O Q R IS HM I N o Q R |8 HM t N O Q R IS ;|M N O Q R IS |M N O Q R IS |M N O Q R IS Therm. 101-7 Apparent Len^h. feet 52-5 98-9 93-7 52-5 52-5 86-7 84-9 81-4 81-9 (190 52-5 52-5 52-5 52-5 57-2.5) 345. Left off measuring, because the wind is dangerously strong. 946. Found the level tube of Microscope O broken, replaced it by the level belonging to Microscope P. January 19. Judge Menzies, Mr. Stuart, the High Sheriff, and several gentlemen visited the camp this day to witness the nature of the operation. 349. The Thermometer was registered 86°'2, which must be in error 1 0° : the numbers have been altered accordingly. 357. There was little light when closing this series, and the dots were consequently not distinct: it wiU therefore be re-measured. This days work seemed to overpower the party. January 20. Thunder and rain towards the middle of the day. Compared Bars early in the morning, and when the rain came on, compared the Microscopes with the 6-inch standard. ■ 282 VERIFICATION AND EXTENSION OF LA CAILLE'S ARC OF THE MERIDIAN. DATE. TIME. No. of Series. IB Micro- Bcopes. Therm. Apparent Length. DATE. TIME. No. of Series. i Micro- scopes. Therm. Apparent Length. 1841. h m feet 1841. h m feet Jan. 21 359 A Jan. 21 366 A ■ N B B C Q C Q a.m. E R p.m. E R 9 55 G J8 86-0 52-5 6 50 G JS 79-6 52-5 360 A „ 22 367 A N B B C Q C Q E R a.m. E R 10 51 361 « G A B C E Q R 89-7 52-5 7 12 368 G A B C E ' I Q R 77-3 52-6 11 57 362 G A B C 1 N Q 91-2 52-5 8 42 369 G A B C 58 UM 1 N Q 88-6 52-5 p.m. E R E R 1 5 363 G A B C E Q R 89-4 52-5 10 17 p.m. 370 G A B C E Q R 90-6 52-5 2 13 364 G A B C E Q R 88-1 52-5 9 371 G A B C E JS jJM 1 N Q R 93-2 52-5 3 19 365 G A B C E Q R 86-9 52-5 1 10 372 G A B C E JS t N Q R 90-2 52-5 4 28 G iS 84-8 (194 52-5 24-75) 2 30 » G JS 88-3 (197 52-5 92-25) 361. The surface of the rock is only a few inches below the surface of the ground. 372. West end of G Bar orer a road from Coggera to XJyle KraaL DETAIL OP THE MEASUREMENT OP THE ZWARTLAND BASE—CAPE OP GOOD HOPE. 283 DATE. 1841. Jan. 22 23 TIME. p.m. 3 38 Nccf Tories. 373 374 4 43 a.m. 7 56 9 7 375 376 377 10 10 378 11 2 379 11 54 B C Q E R G iS Micro- scopes. !* I N O Q R IS ■JM N O Q R 1 N o Q R JS ||M 1 N O Q R I N o Q R Therm. 89-3 87-2 79-2 83-9 83-8 Apparent Length, feet 52-5 52-5 52-5 83-0 52-5 83-0 (201 52-5 52-5 52-5 59-75) DATE. 1841. Jan. 23 25 TIME. p m. 40 No. of Series. 380 1 45 381 382 2 31 3 23 4 6 383 384 5 3 a.m. 8 47 385 386 Micro- scopes. Tlierra. N O Q R iS |M N O Q R IS 1 N O Q R IS J|M I N O Q R IS i|M 1 N O Q R IS [|M O Q R IS l|M I N O Q R IS 80-6 Apparent liengtli, feet 79-8 52-5 52-5 77-2 76-3 52-5 52-5 73-8 52-5 71-7 71-6 (205 52-5 52-5 27-25) 374. Left off to compare bars. 284 VERIFICATION AND EXTENSION OF LA CAILLE'S AKC OF THE MERIDIAN. DATE. TIME. No. of Series. s Micro- scopes. Therm. Apparent Length. DATE. TIME. No. of Series. Micro- scopes, Therm. Apparent Length. 1841. b m feet 1841. li m o feet Jan. 25 387 A ■ N Jan. 25 394 A 1 N B B C Q C Q a.m. E R p.m. E R 9 42 388 G A B C E i8 Q R 73-3 52-5 4 59 395 G A B C E Q R 72-4 52-5 10 44 G JS 76-3 52-5 6 1 G ^8 70-3 52-5 389 A N „ 26 396 A ■ N B B C Q C Q E R a.m. E R 11 54 390 G A I N 79-0 62-5 9 19 397 G A IS ■ N 77-6 52-5 B B C Q C Q p.m. E R E R 1 4 391 G A B C E ^8 ['^ Q R 80-3 52-5 10 13 398 G A B C E |S 1 N Q R 80-3 52-5 1 58 392 G A B C E Q R 78-9 52-5 11 2 399 G A B C E IS ' I Q R 81-3 52-5' 2 53 393 G A B C E ' I Q R 77-3 52-5 11 58 p.m. 400 G A B C E IS i|M ( N Q R 82-8 52-5 3 57 G iS 76-5 (208 52-5 94-75) 47 G IS 84-2 (212 52-5 62-25) DETAIL OF THE MEASUREMENT OF THE ZWARTLAND BASE.-CAPE OF GOOD HOPE. 285 DATE. 1841. Jan. 26 Feb. 1 TIME. No. of Series. p.m. 1 42 3 18 a.m. 9 13 10 12 402 403 404 11 5 p.m. 1 2 17 405 406 407 401 A B C E Q Micro- scopes. N O Q R IS 'S Q R IS f|M 'S Q R IS [|M I N O Q R IS ;|M N O Q R IS ■|M N O Q R IS Therm. 83-2 80-6 87-0 Apparent Length. feet 52-5 52-5 52-5 DATE. 1841. Feb. 1 91-6 94-2 89-6 85-4 (216 52-5 52-5 52-5 52-.5 29-75) No. of Series. p.m. 3 15 4 21 5 24 408 409 410 6 31 a.m. 7 31 8 25 10 37 411 412 413 414 Micro- scopes. |M N O Q R |S |M N O Q R IS |M N O Q R JS |M N O Q R rM 'N O Q R P M N O Q R JS Therm. 83-5 82-7 Apparent Length, 52-5 52-5 75-7 69-8 52-5 52-5 731 73-8 85-4 (219 52-5 52-5 52-5 97-25) 402. Drove a strong register picket at the advanced end of this series, marking 21367-25 feet: the centre of the puncture on the brass pin — the true point. The moving of the camp forward, and clearing more ground, occupied January 27, 28, 29, and .SO. The oppor- tunity was taken to make several sets of comparisons, and to examine Microscopes. The Microscopes were adjusted in the accidental temperature of the six-inch brass standard. 403. The Thermometer may be in error 1°. 407. Detained by a side screw having been forced, and the threads crossed. 286 VERIPICATIOlir AND EXTENSION OP LA CAILLE'S ARC OF THE MERIDIAN. DATE. TIME. (fo.of Series. 2 Micro- scopes. Therm. Apparent Length, DATE. TIME. So. of Series. Micro- scopes. Therm. Apparent Length. 1841. b m o feet 1841. b m o feet Feb. 2 a.m. 415 « A B C E ■ N Q R Feb. 3 a.m. 422 » A B C E j|M ■ N Q R 11 48 416 G A B C Q 86-8 52-5 6 56 423 G A B C |S |M N Q 70-1 52-5 p.m. E R E R 40 417 G A B C E IS u Q R 86-9 52-5 8 17 424 G A B C E |8 i|M ■ N Q R 77-2 52-5 1 42 418 G A B C E IS ^ I Q R 87-1 52-5 9 57 425 G A B C E IS ilM 1 N Q R 81-4 52-5 2 45 419 G A B C E Q R 85-7 52-5 11 21 p.m. 426 G A B C E IS (|M ' I Q R 85-7 52-5 3 46 420 G A B C E IS j|M I N Q R 84-9 52-5 45 427 G A B C E IS 1 N Q R 84-6 52-5 4 51 G |S 78-2 52-6 2 17 G |8 84-8 52-5 421 A B C E jIM 1 N Q R „ 5 a.m. 428 * A B C E ||M Q R 6 14 G IS 72-7 (223 52-5 64-75) 6 54 G IS 68-0 (227 62-5 32 -25) 415. Whirlwind gusts from the south: partial as to locality, and rarely exceeding 100 yards in diameter. The Base line tent frames nearly unfit for use : not more than two have perfect hinges. Four men sick in the camp, and three Sappers sick in Cape Town. The efiective force insufficient for removing the Bars to the comparison shed this morning. Lieut. Cust is most active. 422. Bar B over a waggon road. 424. Delayed hy the picket drivers. Five men sick in camp to-day: Lieut. Cust, C. P. Smyth, and myself, assist in carrying Bars and moving on the tents. 426. Hard ground: iron pickets only can be driven. 428. Low ground: the " myrtle hush " lining pole masked, .". the near struts are relied on for the continuation of the direction. DETAILOP THE MEASUKEMEHT OP THE ZWARTLAND BASE.— CAPE OE GOOD HOPE. 287 DATK. 1841. Feb. 5 TIME. a.m. 7 41 8 33 9 26 10 35 11 39 p.m. 33 No. of Series. 429 430 431 432 433 1 19 434 435 Micro- scopes. N o Q R N O Q R N O Q R hS iM N O Q R iS N O Q R iM N O Q R iS I N O Q R IS Therm. 75-2 79-9 84-0 89-6 91-2 90-1 ^8-5 (230 Apparent Length. feet 52-5 52-5 52-5 525 52-5 52-5 52-5 99-75) DATE. 1841. Feb. 5 p m. 2 13 No. of Series, ^ 436 3 437 3 57 4 45 439 5 28 6 19 a.m. 6 59 440 441 442 Micro- scopes, Therm. I N O Q R JS [ N O Q R JS JM N O Q R In o Q R ^S UM 1 N O Q R HM 1 N o Q R N O Q R iS 87-5 84-9 82-7 80-7 77-2 73-8 72-3 (234 Apparent Length, 52-5 52-5 52-5 52-5 52-5 52-5 52-5 67-25) 432. Microscope E accidentally touched, and thrown from off its bar by one of the men. It was immediately compared with Q when their lengths appeared to be equal, but it does not rotate correctly. To be examined in the evening. 439. The signal pole referred to in the morning is now visible, and the preceding direction appears to be exactly inline. 288 VERIFICATION AND EXTENSION OP LA CAILLE'S ARC OP THE MERIDIAN. TIME. 1841. Feb. 6 a.m. 7 59 No. of Series. 443 444 445 10 57 11 47 p.m. 48 446 447 448 1 48 2 44 449 Micro- scopes. JM N O Q R iS 'N O Q R JS N O Q R :^M N ' O Q R i ^M [ N O Q R is i N o Q R SIM O Q R 77-3 79-8 Apparent Length. feet 52-5 52-5 81-6 82-8 83-1 83-1 82-2 (238 52-5 DATE. 1841. Feb. 6' p.m. 3 41 4 35 52-5 52-5 52-5 52-5 34-75) 5 34 No. of Series. 450 451 452 453 a.m. 7 23 8 21 9 34 10 37 454 455 456 M icro- scopes. N O Q R iS JM N O Q R JS JM N O Q R IS ;|M [ N O Q R [ |M I N O Q R l« !|M { N O Q R IS ||M I N O Q R Therm. 79-8 77-9 66-4 Apparent Length, feet 52-5 52-5 52-5 52-5 73-9 81-3 80-7 (242 52-5 52-5 52-5 02-25) 445. Drove a register picket at the advanced end of this series, marking 23624-75 conTentional feet. The dot on the hrass pin is small and deep, and marks the true point. 452. Drove a register picket at the advanced end of this set, marking 23992-25 conventional feet. The dot on the brass pin marks the true point. This position commands a better view of Coggera than picket 445. February 9. Mr. Charles Bell, Assistant Surveyor-General, was present at the measurement of series 453 to 460. DETAIL OF THE MEASUREMENT OF THE ZWARTLAND BASE.— CAPE OF GOOD HOPE. 289 DATE. TIME. Xo. of Series. i Pi Micro- scopes. Therm. Apparent Length. DATE. TIME. No. of Series. n Micro- scopes. Therm. Apparent Length, 1841. h in o feet 1841. h m o feet Feb. 9 » 457 A ■ N Feb. 10 464 A B B C Q C Q a.m. E R a.m. E R 11 44 G IS 77-6 52-5 6 44 G iS 61-3 52-5 1 458 A B C 1 N Q 465 A B C Q p.m. E R E R 50 459 G A |8 82-6 52-5 7 47 466 G A ||M 1 N 71-9 52-6 B B C Q C Q E R E R 1 38 460 G A B C E UM * I Q R 82-4 52-5 8 42 467 G A B C E JIM Q R 74-6 52-5 2 41 461 G A B C E i|M Q R 80-8 52-5 9 48 468 G A B C E Q R 78-3 525 3 50 462 G A B C E 1 N Q R 79-7 52-5 10 51 469 G A B C E Q R 78-9 52-5 4 48 463 G A B C E |8 Q R 74-6 52-5 11 35 p.m. 470 G A B C E Q R 79-8 52-5 5 45 G IS 72-1 (245 52-5 69-75) 26 G sS 81-7 (249 52-5 37-25) 290 VERIFICATION AND EXTENSION OF LA CAILLE'S ARC OF THE MERIDIAN. DATE. 1841. Feb. 10 TIME. 12 p.m. 1 32 No. of Series. 471 472 2 25 3 13 4 y 473 474 a.m. 7 25 8 18 9 10 475 476 477 Micro- scopes. Therm. N O Q R 1 N ' O Q R JS [ N O Q R I N O Q R N O Q R iS iM N O Q R IS Apparent Length. 79-7 79-6 78-8 52-5 52-5 TIME. 1841. Feb. 12 52-5 7o-7 71-0 72-1 52-5 52-5 52-5 78-6 (253 52-5 04-75) a.m. 10 6 No. of Series. 478 479 10 52 11 47 480 481 p.m. 40 1 43 2 39 3 25 Micro- scopes. 482 483 484 N O Q R I' Therm. M N O Q R iM N O Q R iS JM N Q R iS JM N O Q R JS ;jM t N O Q R IS (|M { N O Q R IS 84-9 Apparent Length. 52-5 86-7 52-5 87-4 91-3 90-4 52-5 52-5 52-5 91-1 88-6 (256 52 5 52-5 72 '25) 471. The state of the Bar tents much impedes the progress of the operation: bar B from this cause was exposed to the sun for some time. It may be proper to record again, that from the beginning up to the present time, the lettered half of the Micros- cope at each end of the series, which measures the three inches between the compensation point and the "point carrier," is used alternately with the unlettered half,— viz. : if the former, for example, is employed for series 471 the latter is employed for 472, to eliminate any constant error depending on the reversion of the outer Microscopes, in other words the bisection of the six inches. The distance between the foci of the outer Microscopes remain steady, whereas the half which depends on the mechanism of the collar work, does not. February 11. Engaged finishing comparison shed No. 3, comparing bars, and clearing the line in advance of bush. DETAIL OF THE MEASUREMENT OF THE ZWARTLAND BASE.-CAPE OF GOOD HOPE. 291 DATE. 1841. Feb. 12 13 TIME. p.m. 4 21 5 32 a.m. 10 31 11 22 p.m. 22 2 10 3 No. of Series. 485 486 487 B C E G 489 A B C E G 490 491 Micro- scopes. [ N O Q R |8 [^M I N O Q R iS N O Q R {' M N O Q R [ N O Q R N O Q R iS JM N O Q R IS Therm. 82-1 90-0 89-6 93-8 94-3 92-7 Apparent Length. feet 52-5 52-5 52-5 52-5 52-5 52-5 52-5 (260|39-75) DATE. 1841. Feb. 13 TIME. 15 p.m. 4 4 No. of 492 493 a.m. 8 15 9 16 10 14 494 495 11 14 p.m. 4 1 4 496 497 Micro- scopes. Q R I N O Q R IS I N o Q R is I N O Q R HM I N o Q R IS jiM I N O Q R iS l|M [ N O Q R Therm. 89-1 76-3 81-7 90-8 97-2 Apparent Length. feet 52-5 52-6 52-5 88-6 52-5 52-5 52-5 97-7 52-5 (26407-25) 490. Drove a register picket at the advanced end of this series, marking 25987'25 conventional feet. Two dots on the brass correspond to the wire on reversion: the middle between them is the true point. 292 VERIFICATION AND EXTENSION OF LA CAILLE'S ARC OP THE MERIDIAN. DATE. 1841. Feb. 15 TIME. 16 No. of Series. p.m. 2 20 3 23 499 500 * 501 4 34 602 5 58 7 14 8 14 9 14 503 504 505 Micro- Bcopes. Therm. UM Q R iS Q R ^S UM ^S Q R JS Q R Q R IS Q R iS i N O Q R 93-7 Apparent Length. 91-3 86-3 81-4 69-4 74-6 feet 52-5 52-5 52-5 DATE. 1841. Feb. 16 52-6 84-0 (267 52-5 52-5 52-5 74-75) TIME. a.m. 10 4 10 59 p.m. 3 50 No. of Series, 506 507 508 509 510 1 38 2 30 3 32 511 512 Micro- ECOpeB. N o Q R |S iM N O Q R iS iM N O Q R N O Q R [ N O Q R ^s [ N O Q R (JM [ N O Q R Tlicrm. 87-5 92-5 94-7 96-2 96-9 Apparent Length, feet 52-5 52-5 52-5 52-5 52-5 52-5 90-6 (271 52-5 42-25) 500. The cast-iron handle of the Microscope "carrying box" broke while in the hands of the man who was shifting it forward. The box fell, but the contents escaped injury. 512. Left off to compare Bars, and to afford an opportunity for clearing ground in advance. DETAIL OP THE MEASUREMENT OF THE ZWARTLAND BASE.-CAPE OF GOOD HOPE. 293 DATE. 1841. Feb. 19 No. of Series. a.m. 7 18 8 2 8 41 9 15 10 8 10 56 11 39 513 514 515 516 517 518 519 Micro- scopes, I N O Q R ^S UM 1 N O Q R I N o Q R UM I N O Q R iS I N O Q R 1 N O Q R IS M N O Q R IS {* Therm. 64-8 67-8 72-3 72-6 77-6 80-7 73-7 (275 Apparent Length. 52-5 52-5 62-5 52-5 52-5 52-5 52-5 09-75) 1841. Feb. 19 TIME. p.m. 37 1 23 2 14 No. of Series. 520 521 522 3 3 42 4 37 5 13 523 524 525 526 Micro- scopes . 1 N O Q R |8 I N O Q R IS ||M I N O Q R |8 JIM I N O Q R IS Q R IS UM Q R IS (|M I N O Q R IS Therm. 77-5 74-0 74-6 73-2 73- 1 72-4 69-7 (278 Apparent Length. feet 52-5 52-5 52-5 52-5 52-5 52-5 52-5 77-25) 515. The sky clouded, which allowed of the two following measured in less than 1 1^ hours. being measured without tents. 787-5 feet were 294 VERIFICATION AND EXTENSION OP LA CAILLE'S ARC OP THE MERIDIAN. DATE. TIME. No. of Series. s Micro- scopes, Therm. Apparent Length, DATE. TIME, No. of Seriet. Micro- scopes. Tlierm, Apparent Length, 1841. h m O feet 1841. b m o feet Feb. 19 527 A ■ N Feb. 20 534 A 1|M 1 N * B B C Q C Q p.m. E R a,m. E R 5 59 G JS 65-7 52-5 11 31 G ^8 79*1 52-5 „ 20 a.m. 528 A B C E u Q R p.m. 535 A B C E N Q R 6 40 529 G A B C E |8 Q R 63-5 52-5 24 536 » G A B C E J8 Q -R 82-1 62-5 7 25 530 G A B C E ' I Q R 57-8 52-5 1 13 537 G A B C E J8 1 N O Q R 83-3 52-5 8 2 531 G A B C E I N Q R 66-0 52-5 2 13 538 G A B C E ^8 Q R 80-2 52-5 9 12 532 G A B C E IN Q R 73-4 52-5 3 7 539 « G A B C E Q R 78-8 52-5 9 69 G iS 75-4 52-5 4 10 G 18 76-9 52 5 533 A 1 N „ 24 540 A i N • B C E Q R a.m. B C E Q R 10 41 G ^8 75-0 (282 52-5 44-75) 7 58 G ^8 76-6 (286 52-5 12 •25) 527. Measured without tents, 532 and 533. The Bars exposed to the sun while the tents were being carried forward. The Microscopes were screened by their "carrying box," 536. One of the men tripped while carrying the forward end of bar B and fell: his end of the Bar rested upon him, and received no injury, 539. The wind being dangerously strong the measurement was discontinued: for the same reason there was no measuring on Monday and Tuesday. In the meantime the men cleared more ground, and finished comparison shed No, 4. The instruments were examined, cleaned, and adjusted where necessary: the Microscopes by Mr. Maclear, the Bars by Captain Henderson, DETAIL OP THE MEASUREMENT OP THE ZWARTLAND BASE—CAPE OP GOOD HOPE. 295 DATE. 1841. Feb. 24 No. of Scries. a.m. 8 54 9 38 10 22 11 7 541 542 543 544 545 11 52 p.m. 40 1 32 546 547 Micro- scopes. N O Q R {'' N O Q R iS o Q R iS UM 1 N O Q R IS UM I N O Q R I N O Q R Therm. 85-4 Apparent Lenglh. feet 52-5 DATE. 1841. Feb. 24 89-8 93-3 99-0 52-5 62-5 52-5 TIME. p.m. 2 53 25 102-0 93-9 95-2 (289 52-5 52-5 52-5 79-75) No. of 548 549 3 47 5 21 a.m. 9 2 560 551 552 9 54 10 46 553 554 11 28 Micro- scopes. N O Q R JS N O Q R JS IM N O Q R iS 1 N O Q R JS ( JM I N O Q R hS i|M [ N O Q R iS IM N O Q R Therm. 94-1 Apparent Length, feet 52-5 91-4 52-5 83-8 77-5 52-5 52-5 80-2 83-9 52-5 52-5 86-4 (293 52-5 47-25) 550. Drove a register picket at the advanced end of this set, carrying a brass pin and dot, marking 29137-25 con- ventiraal feet. The locality is commonly called "the myrtle bush station," and marked with the letter M on the plan of the triangulation of the Base. Prom it both ends of the line become visible on ascending from the Salt River vale. The point appears to be about ]J inch north of the true line: rather it becomes necessary to move the lining Theodolite that quantity to bring its optical axis, the point, and the east end signal into the same vertical. This will be exa- mined further when triangulating the base. 296 VERIFICATION AND EXTENSION OP LA CAILLE'S ARC OP THE MERIDIAN. DATE. 1841. Feb. 25 TIME. p.m. 11 50 1 52 No. of 8erics. 555 556 557 2 37 3 21 558 559 560 26 4 7 a.m. 7 53 561 Micro- scopes. JM 'N O Q R iS iM O Q R {' M N O Q R iS iM "N O Q R l« iM N O Q R iS JM N O Q R 84-6 85-0 Apparent Length. feet 52-5 62-5 87-2 88-8 90-8 82-8 70-8 (297 DATE. 52-5 52-5 1841. Feb. 26 52-5 52-5 52-5 14-75) a.m. 8 48 9 32 10 17 11 5 11 50 p.m. 30 Nn.of Series. 562 •563 564 665 566 1 14 567 568 Micro- scopes. JM N O Q R IS iM N O Q R iS JM N O Q R JM N O Q R iS IM "N O Q R JS iM "N O Q R iS ■|M N O Q R JS 760 82-2 85-8 87-0 90-9 Apparent Length, feet 52-5 52-5 52-5 5 2-5 52-5 90-3 52-5 91-7 (300 52-5 82-25) DETAIL OP THE MEASUREMENT OF THE ZWARTLAND BASE.-CAPE OP GOOD HOPE. 297 DATE. TIME. No. of Series. s Micro- scopes. Tlierra. Apparent Lengtll. DATE. TIME. No. of Series. Micro- scopes. Therm, Apparent Lengtll. 1841. h m o feet 1841. h m o feet Feb. 26 569 A (iM I N Feb. 27 576 A UM 1 N B B C Q C Q p.m. E R p.m. E R 2 20 570 G A B C E ( iM I'N Q R 88-5 52-6 8 577 G A B C E UM Q R 81-4 52-5 3 28 * G JS 82-8 52-5 59 G IS 81-6 52-5 „ 27 a.m. 571 A B C E UM f I Q R 578 A B C E UM u Q R 8 22 672 G A B C E Q R 74-3 52-6 1 51 679 G A B C E IS Q R 82-6 52-5 9 16 573 G A B C E jiM Q R 80-4 52-5 2 38 580 G A B C E IS (|M 1 N Q R 81-7 52-5 9 58 G IS 76-7 52-5 3 29 G |S 81-0 52-5 574 A (IM 1 N O Mar. 1 581 A i|M B B C Q C Q E R a.m. E R 10 43 675 G A B C E |S 1 N Q R 77-9 52-5 8 48 582 « G A B C E IS (IM Q R 87-4 52-5 11 25 G iS 79-3 52-5 9 61 G |S 91-1 52-5 (304 49-75) (308 17-25)1 570. Delayed hy haying to cut throuf fh a mound. Left off to compare Bars. 582. Privates J. George and Day adji isted Bars C and D of this series. February 26. Fine weather. 298 VERIFICATION AND EXTENSION OP LA CAILLE'S AEC OP THE MERIDIAN. 1841. Mar. 1 TIME. No. of Series. a.m. 10 44 11 42 583 584 p.m. 30 1 20 585 586 2 4 2 53 587 588 589 3 40 Micro- scopes. Thcnn. iM ~N O Q R iS JM N O Q R JS JM N O Q R ;|M ' N O Q R JS JM "N O Q R JM N O Q R M N O Q R :S 95-2 Apparent Length, feet 52-5 98-8 102-0 104-8 52-5 DATE. 1841. Mar. 1 TIME. 52-6 102-9 103-2 100-4 (311 52-5 52-5 52-5 52-5 84-75) p.m. 4 24 5 19 No. of Series. 590 691 a.m. 7 41 8 24 592 593 594 '9 44 10 40 11 26 595 596 Micro- scopes. JM ~N O Q R IS JM N O Q R iS Therm. JM O Q R JS JM ~N O Q R IS JM N O Q R JS ■ JM O Q R, JS 97-0 92-9 87-0 Apparent Length. 52-5 52-6 52-5 89-3 99-3 101-4 52-5 52-5 62 5 106-6 (315 52-25) 583. Private Day adjusted B for level, &c., of this series. DETAIL OF THE MEASUREMEITT OF THE ZWARTLAND BASE.— CAPE OP GOOD HOPE. 299 DATE. TIME. Jfo.rf i Micro- Therm. Apparent DATE. TIME. No. of 2 Micro- Therm, Apparent Series, n scopes. Length. Series n scopes. Length. 1841. h m o feet 1841. h m o feet Mar. 2 597 A 1 N Mar. 5 604 A * B B C Q C Q p.m. E R p.m. E R 24 598 G A B C E 1 N Q R 103-4 52-5 6 605 G A B C E 1 N Q R 78-6 52-5 1 5 699 G A B C E JS 1 N Q R 100-0 52-5 46 606 G A B C E Q R 80-7 52-5 1 44 600 G A B C E UM \ N O Q R 94-9 52-5 1 24 607 G A B C E 1 N Q R 81-0 52-5 2 27 601 G A B C E UM Q R 96-6 52-5 2 7 608 G A B C E N Q R 80-1 52-5 3 12 G IS 95 3 52-5 2 52 G is 78-6 52-5 „ 5 a.m. 602 A B C E 1 N Q R 609 » A B C E * I Q R 10 43 603 G A B C E Q R 77-8 52-5 3 42 610 G A B C E Q R 77-7 52-5 11 30 G iS 78-1 (319 52-5 19-75) 4 36 G .^s 75-0 (322 f 52-5 37-25) 597, 598, and 599. Dangerous whirlwinds from the N.W. March 3 and 4. Adjusting Microscopes. Heavy rain on the evening of the 3rd. „ 5. Occupied three hours removing wet from the Bars, which gained admittance through the level windows 1 on Wednesday night. 607. Whirlwinds. 609. Strong wind from S.W. < 300 VERIFICATION AND EXTENSION OF LA CAILLE'S AEC OF THE MERIDIAN. DATE. TIME. No. of Series. 1 Micro- scopes. Therm. Apparent Length. DATE. TIME. No. of Series. Micro- scopes, Therm. Apparent Length. 1841. h m feet 1841. h m o feet Mar. 5 611 A ■ N Mar. 6 618 A J |M ■ N B B C Q C Q p.m. E R p.m. E R 5 16 G iS 72-8 52-5 48 G IS 89-1 52-5 „ 6 a.m. 612 A B C E Q R 619 A B C E UM Q R 8 47 613 G A UM 72-0 52-5 1 32 620 G A IS UM 91-8 52-5 B B C Q C Q E R E R 9 25 614 G A B C E IS Q R 74-5 52-5 2 28 621 G A B C E IS UM Q R 90-0 52-5 10 10 615 G A IS 78-0 52-5 3 16 622 G A IS UM IN O 84-4 52-5 B B C Q C Q E R E R 10 47 G IS 81-5 52-5 5 18 « G |S 82-2 52-5 616 A i|M 1 N „ 11 623 A UM 1 N B B C Q C Q E R a.m. E R 11 31 617 G A B C IS I|M I N Q 83-0 52-5 7 48 624 G A B C IS i|M Q 63-0 52-5 p.m. E R E R 13 G |8 86-8 52-5 8 48 G |S 72-0 52-5 (326 54-75) (330 22-25) 622. Drove a register picket at the end of this set, marking 32917-25 feet: the centre of the dot is ahout one-thii-d of its diameter too easterly. DETAIL OF THE MEASUKEMENT OP THE ZWARTLAND BASE.— CAPE OP GOOD HOPE. 301 DATE. TIME. No. of Series. 1 Micro- scopeB. Therm. Apparent Length. DATE. TIME. No. of Series. 2 Micro- scopes. Therm. Apparent Length. 1841. h m o feet 1841. h m feet Mar. 11 a.m. 625 A B C E j JM t N Mar. 11 p.m. 632 A B C E i|M Q R 9 52 Q |8 72 52-5 3 37 G IS 72-4 52-5 626 A 1 N „ 12 633 A i|M B B a Q C Q E R a.m. E R 10 46 627 a A B C E IS Q R 72-2 52-5 9 14 634 * G A B C E IS i|M ■ N Q R 72-7 52-5 11 31 628 G A B C IS Q 73-8 52-5 9 59 635 G A B C IS ||M 1 N Q 75-9 52-5 p.m. E R E R 13 629 * G A B C E IS j|M t N Q R 76-0 52-5 10 45 636 G A B C E |S ||M Q R 80-0 52-5 1 3 630 G A B C E IS 1|M Q R 76-6 52-5 11 36 p.m. 637 G A B C E IS i|M Q R 85-2 52-5 2 631 G A B C E IS i|M ■ N Q R 75-6 52-5 37 638 G A B C E |S j|M ■ N Q R 90-0 52-5 2 46 G IS 73-9 (333 52-5 89-75) 1 22 G IS 90-1 (337 62-5 57-25) 629 and 632. Dangerous puffs of wine I from the south. 634. Cahn. 302 VERIFICATION AND EXTENSION OF LA CAILLE'S ARC OF THE MERIDIAN. DATE. 1841. Mar. 12 13 TIME. p.m. 2 11 3 4 No. of Series. 639 4 1 4 40 5 23 6 8 a.m. 7 28 640 641 642 643 644 645 Micro- scopes. N O Q R JS iM N O Q R JS |M N O Q R hS JM N O Q R M N O Q R IS iJM I N O Q R |S UM I N O Q R 90-6 86-1 84-4 82-0 80-3 76-3 Apparent Length, feet 52-5 52-5 65-4 (341 52-5 52-5 52-5 52-5 52-5 24-75) 1841. Mar. 13 TIME. a.m. 8 19 9 33 No. of Series. 646 647 648 10 33 11 29 p.m. 13 1 6 1 58 649 650 651 652 Micro- scopes. ,M N o Q R iM N O Q R JS JM N O Q R {' M N O Q R JS JM N O Q R JS JM N O Q R JS JM N O Q R JS Therm. 71-8 78-4 84-4 88-6 Apparent Length. 94- 52-5 525 52-5 52-5 92-4 52-5 96-7 (344 62 5 52- & 92-25) 651. Occasional whirlwinds. DETAIL OF THE MEASUREMENT OF THE ZWARTLAND BASE.— CAPE OF GOOD HOPE. 303 DATE. TIME. . Xo.rf ^ Micro- Therm. Apparent DATE. TIME. No. of i Micro- Therm. Apparent :^erie6. ■" scopes. LengLh, Series. n scopes. Lengtli. 1841. h m feet 1841. h m o feet Mar. 13 653 A 1 N Mar. 15 660 A « B B C Q C Q p.m. E R a.m. E R 2 57 654 G A B C E IS 1 N Q R 91-3 52-5 10 12 661 G A B C E 1 N Q R 80-3 52-5 3 51 655 G A B C E I N Q R 90-7 52-5 11 24 p.m. 662 G A B C E ^8 ■ N Q R 79-4 52-5 4 44 656 G A B C E |M 1 N Q R 89-2 52-5 22 663 G A B C E 1 N Q R 80-6 52-5 5 35 657 * G A B C E Q R 82-8 52-5 1 15 664 * G A B C E ■ N Q R 80-0 52-5 6 19 G J8 76-0 52-5 2 8 G ^8 79-4 52-5 „ 15 658 A 1 N „ 16 665 A 1 N B B C Q C Q a.m. E R a.m. E R 7 34 659 G A B C E J8 u Q R 68-5 52-5 7 5 666 G A B C E ^8 J |M N Q R 62-9 52-5 8 41 G ^8 75-2 52-5 7 45 G JS 69-3 52-5 (348 ■59 -75) (352| 27-25) 653. Level of bar B — 7 divisions in e rror. 654. „ „ -9 do. 655. „ „ — 5 do. 656. „ „ +10-5 do. 657. Could not be brought to level. ] Five series of this Bar are seemingly inclined 40 divisions, or mean =— 27*5 divisions. 664. Obliged to leave off owing to the violence of the wind. 304 VERIFICATION AND EXTENSION OF LA CAILLE'S ARC OF THE MERIDIAN. DATE. TIME. No. of Series. 1 Micro- scopes. Therm. Apparent Lengtli. DATE. TIME. No. of Series. ee Micro- scopes. Therm. Apparent Length. 1841. h m o feet 1841. li m o feet Mar. 16 667, A ■ N Mar. 16 674 A 1|M B B C Q C Q a.m. E R p.m. E R 8 32 668 G A B C E IS Q R 75-2 52-5 2 13 675 G A B C E IS |M N Q R 88-2 52-6 9 34 669 G A IS (|M 78-3 52-5 2 50 676 G A IS i|M I N 91-0 52-5 B B C Q C Q E R E R 10 34 670 G A B C E IS (•JM I N Q R 82-0 52-5 3 20 677 G A B C E IS i|M O Q R 87-2 52-5 11 14 671 G A B C E IS Q R 83-7 52-5 4 678 G A B C E IS 1|M 1 N Q R 85-1 52-5 11 58 672 G A B C |S UM i N Q 86-2 52-5 4 47 679 G A B C IS J|M Q 82-0 52-5 p.m. E R E R 37 G |S 90-0 52-5 5 44 G IS 79 2 52-5 673 A j|M 1 N ., 17 680 A i|M B B C Q C Q E R a.m. E R 1 22 G IS 90-2 52-5 8 57 G |S 77-2 52-5 (355 94-75) (35962-25) 672. -W '■hirlwinds; afterwards calm until No. 678. Calm from No. 680 to 687. DETAIL OP THE MEASUREMENT OP THE ZWARTLAND BASE.— CAPE OP GOOD HOPE. 305 DATE. TIME. Ko. of Series. Micro- scopes. Therm. Apparent Length. DATE. TIME. No. of Series. i Mlcro- scopeB. Therm. Apparent Length, 1841. h m o feet 1841. h m o feet Mar. 17 681 A jiM Mar. 17 688 A UM 1 N B B C Q C Q a.m. E R p.m. E R 9 40 682 G A B C E iS i^M O Q R 82-9 52-5 2 54 689 G A B C E IS UM ( N Q R 91-7 52-5 10 14 683 a A B C E |8 i|M Q R 87-5 52-5 3 32 690 G A B C E IS UM Q R 88-8 52-5 10 46 G iS 90-3 52-5 4 22 G IS 86-0 52-5 684 A UM 1 N „ 18 691 A UM 1 N B ^ B C Q C Q E R a.m. E R 11 28 685 G A B C |8 UM 1 N Q 93-4 52-5 7 14 * 692 G A B C |S UM ■ N Q 65-0 52-5 p.m. E R E R 2 686 G A B C E IS UM ' I Q R 92-8 52-5 7 57 693 G A B C E IS UM ■ N O Q R 74-2 52-5 41 687 G A B C E IS UM ' I Q R 95-4 52-5 8 47 694 G A B C E |S UM 1 N Q R 81'4 52-5 1 27 G IS 97-2 (363 52-5 29-75) 9 62 G IS 88-2 (366 62-5 97-2.5) 688. Drove a register picket at the tej •mination of this series, marking 36382'25 feet. The centre of the dot is rather to the apparent east of the wire. 691. The thermometer was in the con iparison shed close by, and shaded. 306 VERIFICATION AND EXTENSION OP LA CAILLE'S ARC OF THE MERIDIAN. DATE. TIME. No. of Series. CD Micro- scopes. Therm. Apparent Length. DATE. TIME. No. of Series. Micro- scopes. Therm. Apparent Length. 1841. h m o feet 1841. h m feet Mar. 18 695 A 1 N Mar. 18 702 A 1 N B B C Q c Q a.tn. E R p.m. E R 10 58 G ^s 95-0 52-5 5 21 G iS 86-8 52-5 696 A ■ N „ 19 703 A ' N B B C Q C Q E R a.m. E R 11 39 697 » G A B C Q 100-0 52-5 8 22 704 G A B C i N Q 74-3 52-5 p.m. E R E R 023 698 G A B C E ||M 1 N Q R 102-8 52-5 9 34 705 G A B C E JS j JM ■ N Q R 82-2 52-5 2 18 699 G A B C E i JM IN Q R 98-7 52-5 10 20 706 G A B C E IS Q R 86-0 52-5 3 6 700 G A B C E JS 1 N Q R 95-3 52-5 11 14 p.m. 707 G A B C E JS i JM Q R 90-9 52-5 3 53 701 G A B C E |S Q R 91-4 52-5 3 708 G A B C E JS iJM Q R 97-1 52 5 4 34 G iS 89-8 (370 52-6 64-75) 2 10 G JS 97-4 (374 52-5 32-25) Comparing bars between 697 and 698. Hot puffs of wind from the westward. Comparing bars between 707 and 708. DETAIL OF THE MEASUREMENT OF THE ZWARTLAND BASE— CAPE OF GOOD HOPE. 307 DATE. 1841. Mar. 19 20 p.m. 2 50 3 36 4 30 No. cf Series. 709 710 711 712 5 33 a.m. 7 17 8 2 9 5 713 714 715 Micro- scopes. JM N O Q R iS JM N O Q R I N O Q R JS UM I N O Q R iS 'g Q R JM N O Q R Therm. 98-6 Apparent Length, feet 52-5 95-1 89-9 52-5 52-5 83-4 52-5 65-6 69-6 74-1 (377 52-5 52-5 52-5 99-75) DATE. 1841. Mar. 20 TIME. a.m. 9 39 No. of Scries. 716 717 10 24 11 13 p.m. 42 718 719 720 2 3 3 4 14 721 722 Micro- scopes, ■|M N O Q R iS |M N O Q R |M N O Q R |S I N o Q R JS iJM 1 N O Q R i N O Q R JS [ N O Q R Therm. 77-0 52-5 Apparent Length, feet 79-6 52-5 81-8 82-4 83-2 52-5 52-5 80-8 52-5 52-5 78-3 (381 52-5 67-25) 709. Light air from S. W. tlien from N. W. Hot as from an oyen : soutli liorizon hazy. Lightning northward at 1 p.m. 718. Uneven ground. 719. Drove an iron picket for the lining theodolite plummet, and a point-carrier placed over it for counting: position on the top of the rise before descending into Buckle's vale. March 20. The measurement retarded this day by misplaced pickets. „ 21. Microscopes adjusted in the accidental temperature. 308 VERIFICATION AND EXTENSION OF LA CAILLE'S ARC OF THE MERIDIAN. DATE. TIME. No. of Series. n Micro- scopeB. Therm. Apparent Length. DATE. TIME. No. of Series. at P3 Micro- scopes. Therm. Apparent Length. 1841. h m o feet 1841. h m o feet Mar. 22 723 A Mar. 22 730 A B B C Q C Q a.m. E R p.m. E R 8 3 724 G A 73-9 52-5 2 31 731 G A 81-7 52-5 B B C Q C Q E R E R 9 23 725 G A 75-2 52-5 3 13 732 G A ■ N 79-8 52-5 B B C Q C Q E R E R 10 16 726 G A B C E Q R 82-3 52-5 4 5 733 G A B C E IS ilM N Q R 78-4 52-5 11 12 G ^S 81-8 52-5 5 2 « G |8 74-2 52-5 - 727 A B C Q M 25 734 A B C 1 N Q p.m. E R a.m. E R 7 728 G A B C E 1 N Q R 85-4 62-5 8 21 735 G A B C E t N Q R 67-1 52-5 58 729 * G A B C E IS 1 N Q R 84-2 52-5 9 56 736 G A B C E IS Q R 71-7 52-5 1 43 G J8 82-8 52-5 10 49 G |S 75-0 52-5 (385 34-75) (389 02-25) March 22. A strong and dangerous whirlwind at 45™ past noon; first from S.W. hy W., then from the south: lasted about five minutes. 729. Dangerous descent from the preceding series. 733. Drove a register picket at the advanced end of this series, marking 3874475 feet: the centre of the dot is too eastward by about a third part of its diameter. DETAIL OF THE MEASUREMENT OP THE ZWARTLAND BASE.— CAPE OP GOOD HOPE. 309 DATE. TIME. No. of . Micro- Therm. Apparent DATE. TIME. No. of , Micro- Therm, Apparent Series. scopes. Length, Series. n scopes. Length. 1841. h m o feet 1841. h m o feet Mar. 25 a.m. 737 B C E 1 N Q R Mar. 29 a.m. 744 A B C E 1 N Q R 11 37 738 G A B C |8 UM i N Q 76-2 52-5 7 54 745 G A B C iS 1 N Q 62-0 52-5 p.m. E R E R 18 739 G A B C E Q R 74-0 52-5 8 52 746 G A B C E IS Q R 67-9 52-5 G iS 76-9 52-5 10 17 G |8 71-9 52-5 740 A ]|M „ 18 747 A B B C Q C Q E R E R 2 20 741 G A B C E is Q R 73-4 52-5 11 3 748 G A B C E |8 ' I Q R 75-3 52-5 3 12 742 G A B C E 'S Q R 72-6 52-5 11 43 p.m. 749 G A B C E IS Q R 78-4 52-5 3 58 743 G A B C E N Q R 71-3 52-5 025 750 G A B G E |8 (IM ' g Q R 79-9 52-5 4 53 G IS 68-6 (392 52-5 69-75) 1 7 G IS 82-4 (396 52-5 37-25) March 25. Eain came on at the termi nation of series 74 13, which continued throughout the 26th and 27th: the time spent in cleaning and afterwards ad. usting Microscope s in the accidental temperature. At 9 o'clock, p.m., on the 26th, the Barometer reading was 29-5 34 inches. An Officer of the United States Nayy introduced by th e American Consul, came to witness the operation and remained some days. 310 VERIFICATION AND llXTENSION OP LA CAILLE'S ARC OF THE MERIDIAN. 1841. Mar. 29 30 TIME. p.m. 1 49 No. of £ Series, p 2 35 3 25 4 17 751 752 5 4 a.m. 7 19 753 754 755 756 8 20 757 Micro- scopes. Therm. JM N Q R ^8 JM N O Q R ;jM I N ' O Q R I N O Q R JS UM I N O Q R JS I N O Q R h» i N O Q R IS 81-7 80-1 78-1 apparent Length. 76-9 72-6 61-8 feet 52-5 52-5 52-5 (400 52-5 52-5 52-5 1841. Mar. 30 TIME. 52-5 04-75) a.m. 10 1 10 53 No. of E Series. |^ 758 759 11 51 p.m. 43 1 37 760 761 762 763 2 21 3 8 764 Q R hS Q R |S I N O Q R |8 1 N O Q R Apparent Length. iM N O Q R JS |M N O Q R 79-4 84-4 89-5 94-2 89-3 85-8 feet 52-5 62-5 52-5 52-5 52-5 52-5 85-3 (403 52-5 72-25) • DETAIL OF THE MEASUREMENT OF THE ZWARTLAND BASE.— CAPE OF GOOD HOPE. 311 DATE. TIME. No.cf Series Micro- scopes. Tlierm. Apparent Lengih. DATE. TIME. No.o Series r 2 Micro- scopes. Tlierm. Apparent Length. 1841. h m feet 1841. il m feet Mar. 30 765 A April 1 772 A B B V Q C Q. p.m. JiJ R a.m. E R 4 1 766 A B C E 1 N Q R 81-2 52-5 11 38 p.m. 773 G A B C E J8 1 N Q R 71-5 52-5 4 47 767 G A B C E 1 N Q R 78-5 52-5 31 774 G A B C E J8 Q R 70-5 52-5 5 45 G iS 75-0 52-5 1 23 G JS 70-2 52-5 April 1 a.m. 768 A B C E 1 N Q R 775 A B C E 1 N Q R 7 52 769 G A B C E Q R 62-4 52-5 2 7 776 G A B C E IS N Q R 76-1 52-5 9 6 770 G A B C E J8 Q R 67-6 52-5 2 54 777 G A B C E IS Q R 73-4 62-5 10 771 G A B C E 1 N Q R 72-8 52-5 3 35 778 G A B C E IS Q R 74-0 52-5 10 51 G JS 74-3 52-5 4 22 G JS 75-9 52-5 (407 39-75) (411 ( )7-25) 312 VERIFICATION AND EXTENSION OP LA CAILLE'S ARC OF THE MERIDIAN, DATE. TIME. No. of t Micro- Therm. Apparent DATE. TIME. No. of OT Micro- Therm. Apparent Series. a scopes. Length. Series. « scopes. Length. 1841. h m o feet 1841. b m o feet April 1 779 A j |M ■ N April 2 786 A UM B B C Q C Q p.m. E R a.m. E R 5 16 G JS 70-0 52-5 11 44 G JS 77-2 52-5 „ 2 780 A j JM 787 A N B B C Q C Q a.m. E R p.m. E R 7 25 781 G A 60-6 52-5 33 788 G A ■ N O 79-3 52-5 B B C Q C Q E R E R 8 11 782 G A 1 N 63-2 52-5 1 14 789 G A 1 N O 80-9 52-5 B B C Q C Q E R E R 9 8 783 G A B C E j JM Q R 68-5 52-5 1 58 790 G A B C E ||M 1 N O Q R 82-0 52-5 9 47 784 G A "c E ^8 ' I Q R 70-0 52-5 2 35 791 G A B C E ' N Q R 83-1 82-5 10 29 785 G A B C E 1 N Q R 73-0 62-5 3 16 792 G A B C E 1 N o Q R 83-0 52-6 11 6 G JS 75-0 (414 52-5 74-75) 4 25 « G iS 79-9 (418 52-5 42-25) 792. A register picket driven at the i idvanced end of this series, carrying an iron pin, marking 41f i42-25feet. The apparent west edge of the dot is the con ect mark. DETAIL OP THE MEASUREMENT OP THE ZWARTLAND BASE.— CAPE OP GOOD HOPE. 313 DATE. TIME. No. of Series. 1 Micro- scopes. Therm. Apparent Length. DATE. TIME. No. of Series. m Micro- scopes. Therm. Apparent Length. 1841. h m O feet 1841. h m o feet April 2 793 A 1 N April 3 800 A 1 N B B C Q C Q p.m. E R a.m. E R 5 27 « G |S 750 52-5 11 54 G |8 89-1 52-5 » 3 a.m. 794 A B C E 1 N Q R p.m. 801 A B C E 1 N Q R 7 15 795 Q A B C E Q R 60-5 52-5 31 802 G A B C E ■ N Q R 88-1 52-5 8 31 796 G A B C E Q R 68-8 52-5 1 6 803 G A B C E N Q R 90-9 52-5 9 21 797 G A B C E Q R 730 52-5 1 42 804 G A B C E ■ N Q R 91-4 52-5 10 798 G A B C E 1 N Q R 78-1 52-5 2 30 805 G A B C E IS i|M ■ N Q R 90-3 52-5 10 38 799 G A B C E ■ N Q R 81-2 52-5 3 16 806 G A B C E IS j|M ■ N Q R 88-4 52-5 11 16 G IS 84-4 (422 52-5 09-75) 4 6 G IS 82-0 (425 52-5 77-25) 793. T] le Microscope carrying box fel 1 from the hands of the two men -who were moving it forward, by which and Q w ere tilled a little in their cells, ai id their levels slightly deranged. Their other adjustments were not disturbed. 314 VERIFICATION AND EXTENSION OF LA CAILLE'S AKC OP THE MERIDIAN. DATE. TIME. No. of Series. 2 Micro- Bcopes. Therm. j^pparent Length. DATE. TIME. No. of Series, i Micro- scopes. Therm. Apparent Length. 1841. h m feet 1841. h m o feet April 3 807 A April 5 811 A N B a.m. B p.m. C E Q R 9 40 • C IS 31-5 4 48 G iS 79-2 62-5 809 A 1 N Q R iS 808 A B 1 N „ 20 p.m. B C E C E Q R 1 50 G 91-4 52-5 „ 5 5 45 * 809 G A B J8 72-2 52-5 810 A B C E 1 N O Q R IS a.m. C E Q R 2 55 G 92-0 52-5 7 42 G iS 63-0 52-5 811 A 810 A B G 1 N Q 5 B a 82-0 31-5 (428 18-75) E R 67-2 8 50 * G JS 52-5 808. A Strong register picket driren, and a brass pin inserted at the advanced end of this series, marking 42682-25 feet. The centre of the dot is the correct point. 810. A strong register picket driven, and a brass pin inserted at the advanced end of this series, marking 42787-25 feet. The apparent east limb of the dot is the true mark. 811. These three bars were laid on to find, approximately, the position of the east terminal point. Four pickets driven at right angles to each other, carried marks to define the places of lines whose intersection denote the position. April 20. Series 809 and 810 re-measured. 811, consisting of bars A, B, C, reached the platinum stud exactly wherein the puncture was made to define the east terminal point. ERRORS OP ALIGNMENT OP BASE. 315 2. Errors of Alignment When the measurement reached the elevated ground at M (a) where both ends of §5- , T) • • I • Errors of the Base came into view, that point was discovered to be a little north of the true line. Alignment. This circumstance led to an examination of the measured line, for the purpose of applying corrections, if necessary. The examination was eflfected with the 20-inch Theodolite, by means of the signal poles which were stationed in the line for the trian- gulation of its parts, and by placing other poles over picket points which had been left for reference in the event of accident or uncertainty when measuring. From the west terminal point, signals 6194 (5), 9712, and 1 1497 seemed as one pole; hence a right line had been run to the latter point, but that point was 7-02 inches south of the true line. Let I be the measured length. 6 the inclination of the measured length to the true n line : then I — I 2 sin. ^ ~= the projection of the measured length upon the true line. But for inclinations of a few seconds the perpendicular distance p, from the true line, may be substituted for 6, and the projected length will sensibly he I -• The correc- tion (2nd term) for the inclination of 11497 =- 0-000179 inches. Point 17797 was 6-64 inches south of the true line, or 0*38 inch more northerly than the last picket : the correction is insensible. Point 21367 was 6'02 inches south of the true line, or 0*62 inch more northerly than 17797 : the correction is —0000005 inch. Point 23992 was 0-96 inch south of the true line, or 5'06 inches north of the last point : the correction is —0-000406 inch. Point 25987 was 0-09 inch south of the true line, or 0-87 inch north of the last picket : the correction is 0*0000 16 inch. Point 29137 was 11-48 inches north of the true line, or 11*57 inches north of the last: the correction is 000177 inch. The line was sensibly straight from the last point to the east end of the base : the correction is 0000401 inch. The sum of these corrections is -0'002778 inch = 0000023 foot: to which is to be added a similar correction for series No, 20 (see page 257), = -000332. It is difficult in practice to plant points in a right line. Perhaps the best method would be as follows, — viz : to centre a good theodolite at intervals of about one mile, and to shift it until the angles subtended by the terminal signals become 1 80° on each side. In the present instance, nearly one half of the base was directed to a point situated (a) See plate. (b) The numbers represent the distances in feet from the west end. T 316 VERmCATION" AND EXTENSION OP LA CAILLE'S ARC OF THE MERIDIAN. § 5- about six inches south of the true line. The direction then inclined towards it during; a Errors of . . Alignment, run of 2625 feet, and coincided with it through a distance of 1 995 feet. The next length of 3150 feet ran towards a point ITS inches north of the line, and the remaining 13681 feet straight to the east terminal point. No satisfactory explanation can be given of the deviation at M. It may have com- menced two series back when the signal at M was removed, to allow the picket drivers to proceed, and a directing upright could not be placed in advance until the removal of that signal ; in the meantime, the direction rested with the stability of the lining instru- ment. On this supposition, the correction would be 0'052 inch ; but there is no proof, and little probabihty, of the instrument having shifted. The east end signal was not visible on the ascent to M. Level Obser- 3. LeVEL OBSERVATIONS FOR SeCTION OF THE BaSE, AND FOR ITS MeAN HeIGHT vations. ABOVE THE SeA. No register was kept of the varying heights of each series of compensation bars above the surface of the ground, because that method is less accurate perhaps, and certainly is more troublesome, than running a line of levels per se. The later operation was per- formed by Mr, C. P. Smyth, between the 8th of April and 10th of May, 1841, by means of a 14-inch spirit level. Taking intervals of 100 feet, he observed both forward and backward between the terminal points, and the results diflfered by less than one inch ; therefore it has not been thought necessary to publish the numbers for both directions. Captain Henderson, with the same instrument, carried a line of levels to the sea at Saldanha Bay, which he performed between the 24th of May and 28th of June ; starting from a register picket, distant 4000 feet from the west end of the Base, and 31 feet 8 inches less elevated. At Saldanha Bay he jumped two holes in a rock, one six feet below the other, and distant from each other 31 feet 8 inches. The following memorandum is quoted from his field-book : — " The rock is at the south part of the bay, where it begins to narrow southward, and opposite the south end of Schapen Island. From the rock is seen the pointed peaks of Jutten Island, over the low point on the south of Rietberg. The direction of the holes runs into the middle of the bay in Schapen Island. " The lower hole was, according to the high water mark of June 26, below it 9 inches. On the morning of the 27th, the tide was about two inches above the surface of the rock where the lower hole is jumped. At 10|^ hours, a.m., on the morning of the 28th, high water was even with the surface of the rock in which the lower hole is jumped." ERRORS OF ALIGNMENT OF BASE. By the line of levels to Saldanha Bay, the starting picket on the Base is higher than the lower hole in the rock By the line of levels on the Base, the starting picket is lower than the west terminal point ...... Mean level of the Base below the west terminal point Mean height of the compensation-bar tongues above the ground (a) Mean level of the tongues above the lower hole in the rock at Saldanha Bay 317 174-44 feet §5. Level Obser vations. + 31-67 J? 20-48 5» + 3-83 )J 189-46 Assuming the radius of curvature in latitude 33° 15', and Azimuth 71° 28' to be Keductionto . „ the sea level. [7-3208623], the reduction to the lower hole in the rock before mentioned is 0-3875 foot. (a.) Mean height of trestles used on the base Mean height of picket + thickness of triangles Mean height of camel Bar tongues above lower surface of box rt. in- 1-10 ..0 I- 0- 9 0- 3 3-10 = 3-83 feet. 318 LEVEL OBSERVATIONS FOR SECTION OF ZWARTLAND BASE-LINE. (TABLE I.) No. of Stat on. Distance backward andfoiward. Back staff. Forward Staff. Dip. Ilise. No. of Station. Distance backward andforward. Back Staff. Forward Staff. Dip. Rise. . APRIL 8, 1841. 44 feet. 100 inches. 54-31 inches. 57-06 inches. 2-75 inches. feet. inches* inches. inches. inches. 45 57-50 50-79 6-71 * 1 100 14-60 62-70 48-10 46 » 53-12 59-22 6-10 2 » 49-65 61-75 12-10 47 J? 50-28 51-49 1-21 3 >f 51-55 60-10 8-55 48 J? 52-73 48-93 3-80 4 >J 50-90 61-15 10-25 49 ») 61-63 65-11 3-48 5 39 50-95 62-48 11-53 50 JJ 59-33 49-36 9-97 6 >J 61-14 55-70 4-56 51 J> 58-52 54-98 3-54 7 » 50-20 55-60 5-40 52 J) 45-61 54-80 9-19 8 » 36-04 66-50 30-46 53 J? 52-93 55-52 2-59 t9 » 39-42 68-05 28-63 54 99 43-25 55-73 12-48 10 » 41-35 66-10 24-75 55 J) 42-95 60-89 17-94 11 19 38-12 62-08 23-96 56 J> 47-50 57-60 10-10 12 » 43-37 58-45 15-08 57 >J 50-34 65-32 14-98 13 » 27-58 63-35 35 77 58 J9 18-13 66-51 48-38 14 99 45-65 60-75 15-10 59 '9 19-14 63-95 44-81 15 99 35-27 58-40 23-13 60 9? 3-40 85-90 82-50 16 » 53-63 62-90 9-27 61 99 2-80 77-23 74-43 17 99 47-40 58-39 10-99 62 99 32-50 73-22 40-72 18 » 43-06 56-77 13-71 63 9J 36-18 74-78 38-60 19 99 46-58 56-98 10-40 64 99 36-70 70-35 33-65 20 » 42-47 79-72 37-25 65 99 43-93 54-45 10-52 21 >J 50-02 52-75 2-73 66 99 56-94 51-52 5-42 22 J> 70-42 35-98 34-44 67 99 59-50 47-91 11-59 23 » 50- 16 39 00 11-16 68 99 33-73 43-19 9-46 24 3J 49-52 56-76 7-24 69 9? 51-42 65-36 13-94 125 JJ 15-32 59-41 44-09 70 yy 59-95 44-44 15-51 26 J3 55-59 21-65 33-94 71 99 40-10 48 95 8-85 27 >» 66 41 41 12 25-29 72 9 9 61-85 73-72 11-87 28 » 41-95 43-70 1-75 73 99 53-00 54-08 1-08 29 9} 57-27 42-78 14-49 74 yy 78-60 60-38 18-22 30 99 68-39 41-60 26-79 75 99 43-70 40-48 3-22 31 99 66-33 53-12 13-21 76 ?9 29-62 58-39 28-77 32 99 55-02 56-38 1-36 77 99 60-22 75-66 15-44 33 J> 50-84 70-70 19-86 78 99 16-80 57 32 40-52 34 99 46-98 57-56 10-58 1179 ?? 58-18 44-33 13-85 35 J> 49-59 56-06 6-47 1180 99 40-30 62 23 21-93 36 » 57-72 48-22 9-50 81 9' 50 82-00 17-56 64-44 37 )> 58-50 65-03 6-53 82 80-20 63-70 16-50 38 » 55-59 57-88 2-29 **83 100 58-00 .51-20 6-80 39 JJ 47-20 46-74 0-46 84 53-60 50-14 3-46 40 » 63-23 61 35 1-88 85 ?? 56-40 37-00 19-40 §41 » 50-75 61-85 11-10 86 99 73-70 63-10 14-86 35 69 58-84 27-41 APRIL 14, 1841. 87 99 88 >J 31-38 64-76 33-38 42 100 46-40 55-64 9-24 89 99 65-50 57-73 7-77 43 99 50-45 55-52 5-07 90 J> 65-02 66-41 1-39 *i . The back staff on the west terminal point. 1- -6. Fogg y; reading s difficult. t 9- Fog cleari ngoff. ts 5. Near Kotze's swamp. § 41. A picket drivt jn. Sun Dip 1 of the b ack staff readings rward staff readings 1985-73 2307-56 321-83 in ches. II 7 9. Register picket 15802, about 3 feet beyond forwar Dist i station ance from 18 west end. . 8200 fe )f the Salt 2t. Eiver. 0. Crossin g the bed t ** 83. A picket driven at forward station 83. 41 — 83 . Sum oi IT Dip.... Distan "the back „ forw< ce from we staff readings 19f ird staff readings 24S 44 st end 1 3-74 4-77 1-03 inche 6500 feet. 9. LEVEL OBSERVATIONS FOK SECTION OF ZAVARTLAND BASE-LINE. 319 (TABLE 1)— colli. No. of Station. Distance backward andforward. Back staff. Forward Staff. Dip. Rise. No. of Station. Distance hackward and forward. Back Staff. Forward Staff. Dip. Rise. feet. inches • Inches. inches. inches. feet. inches . inches. inches. inches. 91 100 39-00 53-75 14-75 134 100 71 84 34 65 37-19 92 62-87 40-52 22-35 136 Jf 74 26 49 37 24-89 93 68-65 46-33 22-32 136 49 18 52 22 3^04 94 59-75 60-53 0-78 137 66 87 40 80 25-07 95 54-76 59-71 4-95 138 jy 60 80 45 80 15 00 96 61-60 47-17 14-43 139 Jf 52 55 61 38 1-17 *97 69-85 41-48 28-37 140 141 ?J 53 66 30 37 62 45 66 88 0-64 20-49 142 ?J 70 16 46 19 23-97 APRIL 15, 1841. 143 61 22 46 60 14-62 144 72 00 46 21 25-79 98 100 67 71 51 60 16-11 145 60 48 39 00 21-48 99 JJ 54 00 64 48 10-48 146 66 70 35 88 29 82 100 jy 36 82 69 60 32-78 147 51 96 49 72 2-24 101 J) 56 53 52 40 4-13 148 47 17 61 79 4-62 102 jj 60 23 48 24 11-99 149 55 95 51 50 4-45 103 jj 73 82 44 38 29-44 150 54 08 42 88 11-20 104 55 36 44 92 10-44 151 50 05 38 95 11-10 105 39 45 43 80 4-35 152 52 83 62 24 69 106 59 30 47 85 11-45 153 57 32 48 14 9-18 107 jj 68 15 59 74 8-41 154 J J 46 60 54 89 8-29 108 jj 60 73 40 80 19-93 165 JJ 40 16 55 73 15-58 109 jj 65 82 69 65 3-83 156 JJ 48 32 55 13 6-81 110 5j 47 11 40 70 6-41 157 yy 52 53 55 27 2-74 111 5j 47 24 65 26 18-02 tl58 yy 64 •08 64 55 10-47 112 59 80 44 80 15-00 169 )j 44 95 54 18 9-23 113 68 22 66 87 11-35 160 J J 60 -77 48 19 2-68 114 60 21 46 72 13-49 161 61 -24 56 62 6-62 115 64 85 51 39 13-46 162 yy 56 •78 66 07 0-71 116 72 80 51 08 21-72 163 yy 62 46 41 36 11-10 -117 61 85 37 40 24-45 164 ?7 57 •42 45 47 11-95 118 74 65 42 90 31-75 165 ?J 58 •17 53 76 4-41 119 62 98 49 88 13-10 166 yy 79 80 41 60 38-20 120 65 83 17 73 48-10 167 yy 58 45 55 00 1 45 121 42 10 55 25 13-15 168 7? 54 •57 46 32 8-25 122 65 62 51 62 14-00 169 J? 60 95 51 06 9-89 123 66 45 46 60 19-85 170 yy 44 18 60 88 6-70 124 63 42 45 29 18-13 171 jy 63 37 62 90 0-47 125 69 83 52 30 17-63 172 J) 62 65 34 05 28-60 126 64 20 45 20 19-00 173 J) 55 04 40 38 14-66 127 60 96 40 67 20-29 174 J* 55 30 63 50 8-20 128 61 21 50 06 11-15 176 ?j 66 80 74 05 7-26 129 55 70 41 85 13-85 176 ?? 51 60 56 95 4-35 130 59 00 45 27 13-73 177 jj 58 23 68 50 0-27 131 70 69 46 80 23-89 178 J? 57 76 53 77 3-99 132 63 08 47 89 15-19 179 ?J 57 52 52 53 4-99 133 J? 67-30 29-73 37-67 180 ?J 60-90 .50^10 10-80 * 97. A picket driven I It the forward station 97. )um of the back staff readings 182.5-18 inches. „ forward staff readings 676-08 „ lise between 83 and 97 149*10 ,, I distance of 97 from west end 19300 feet. f 158. A picket driven at the forward end of this station. )um of the back staff readings from 97 to 158 — 3627-79 inches, forwflrrl ^tflflT readiiiffs =r:2948'15 ■,■, I lise between 97 and 1 58 = 679'64 „ I Distanceof 158 from west end = SlSUOfect. 320 LEVEL OBSERVATIONS FOR SECTION OF ZWARTLAND BASE-LINE. (TABLE I)— core*. No. of Stat on. Distance backward andforward. Back Staff. Forward Staff. Dip. Else. No. of Station. Distance Ijackwaxd andforward Back staff.. Forward Staff. \ Dip. Rise. APRIL 16, 1841. feet. inches. inches. inches. inxches. 209 50 nn .nK a.A.[\K. 1 Q . rjn 4 t /ti Dt: vt# lo i\} feet. inches. inches. inches. inches. 210 ff 71 40 40 23 31 17 181 100 67 56 50 87 16-69 211 J) 55 86 41 08 14 78 182 JJ 56 53 47 98 8-55 212 JJ 75 04 38 22 36 82 183 }f 60 60 64 80 4-20 213 ?J 67 80 55 00 12 80 184 J) 67 25 58 55 8-70 214 fj 61 81 42 47 19 34 185 J? 44 80 70 00 25-20 215 99 65 16 47 92 17 24 186 fj 45 32 62 63 17-31 216 99 74 10 46 76 27 34 187 9t 38 00 50 80 12-80 217 99 68 30 38 04 30 26 188 J) 42 70 70 08 27-38 218 99 63 68 37 30 26 38 189 }f 48 63 60 77 12-14 219 99 70 11 34 82 35 29 190 )f 54 14 57 38 3-24 220 }? 70 28 31 60 38 68 191 )> 42 55 75 62 33 07 221 99 62 82 42 12 20 70 192 50 37 63 70 13 32-50 222 77 72 59 49 71 - 22 88 193 JJ 37 97 73 74 35-77 223 99 64 71 46 13 18 58 194 JJ 29 77 72 97 43-20 224 99 52 32 53 40 1-08 195 J? 35 92 75 83 39-91 225 99 62 90 48 80 14 10 196 ?? 32 97 66 05 33 08 226 99 60 82 42 23 18 59 197 y} 41 06 65 97 24-91 227 99 59 92 47 82 12 10 198 )» 41 45 69 75 28-30 228 99 60 82 51 77 9 05 199 jj 60 90 33 77 27-13 229 J? 68 49 57 58 10 91 200 jj 54 43 49 41 5-02 230 99 67 02 45 77 21 25 201 J) 34 98 78 72 43-74 231 99 57 90 43 42 14 48 202 J) 47 38 45 00 2 38 232 JJ 64 48 41 36 23 12 203 tt 50 62 49 42 1-20 233 jj 67 83 37 40 30 43 204 ji 74 38 45 07 29-31 234 „ 58 80 46 01 12 79 205 jf 61 52 50 42 11-10 235 99 67 00 42 88 24 12 206 jf 57 63 52 40 5-23 236 99 59 77 46 57 13 20 207 jf 58 83 54 39 4-44 237 99 69 40 49 80 9 60 208 ?' 59 19 43-58 15-61 *238 50 57-62 27-75 29-87 1 238. A mark on the block of masonry carrying the eas t termin a,l point. Sum of back staff readings from No. 158 =4588-12 „ „ forward staff readings Rise 4189-35 448-77 Mark above wir e 4-80 1 Mark below snri ace of brass plug whic ;h Carrie nt 3 the term inal point 6-00 Kise from No 158 to east terminal po 459-57 By station No. 41 No. 83 Dip = Dip = 321-83 441-03 I ) 762-6« No. 97 Kise = 149-10 ) No. 158 Rise = 679-64 \ 1288-31 ] East point Difference in height between the east Rise = ind wesi 459-57 terminal ) point s 525-4 s Difference by the levellings repeated b ackward , but not J rinted Mean = 624-5 9 525-0 2 inches. = 43-9-02 '«'• 1 LEVEL OBSERVATIONS BETWEEN THE ZWAETLAND BASE-LINE, AND THE SEA SALDANHA BAY, CAPE OF GOOD HOPE. Note. — The departure is from a point in the Base-line, 31"* S'"- below the platinum stud, marking the west terminal point of the Base. 322 VERIFICATION AND EXTENSION OP LA CAILLE'S ARC OF THE MERIDIAN. (TABLE II.) Distance. Back Staff. Forward Staff. KEMARKS. Distance. Bacli Staff. Forward Staff. BEMARES. a MAY 24, 1841. $ MAT 25, 1841. feet. ft. inches. ft. inches. feet. ft. inches. ft. inches. 600 2 5-9 4 2-5 Commenced at 600 4 4-5 5 3-2 A. >> 3 8-5 . 3 11-5 4 6-6 3 7-4 picket left on line by Mr. Smyth near Mr. Kotze's house (80). 3 11-2 6 1-4 3 90 1 7-8 600 7 4-6 2 2-6 5 2-3 5 2-8 268 2 10-5 7 2-9 5 2-8 3 9-2 600 2 2-0 6 2-8 4 5-8 4 2-6 yt 3 9-7 8 2-2 5 1-4 3 10-2 400 4 2-6 2 10-6 4 1-7 6 0-4 600 4 6-4 5 7-4 600 2 9-8 6 30 f) 4 6-0 6 1-6 260 1 11-5 9 8-5 )J 2 8-5 5 5-8 600 2 11-6 3 7-4 600 2 11-2 4 11-6 fr 6 1-4 4 7-2 400 3 1-5 4 9-7 600 4 8-8 3 4-6 600 4 3-8 4^ 8-1 400 5 3-9 2 6-6 JJ 2 7-6 5 4-4 600 8 0-4 1 0-0 97 4-6 600 3 6-7 4 11-2 8 0-8 5 8-3 4 4-6 2 6-0 4 2-0 3 6-6 91 4-4 58 11-0 81 1-3 A. 6 0-2 58 11-0 2 70 3 11-3 3 2-4 5 2-4 5 00 6 0-9 22 2-3 600 B. 97 4-6 91 4-4 600 2 2-6 3 11-0 4 1-6 Re-Ievelled the 3 11-2 former portion, com- ?j 3 7-4 3 6-4 mencing at picket left on line by Mr. 600 7 8-5 2 8-5 Smyth near Mr. n MAY 27, 18 41. 363 600 1 9-3 2 5-0 7 7-6 5 0-0 Kotze's house. » 4 2-0 7 6-2 600 2 11-4 5 8-4 B. )} 6 70 6 5-4 yj 3 10-4 4 6-6 » 3 3-1 5 60 }t 5 9-6 3 8-5 » 3 1-3 4 2-5 }j 6 91 2 9-4 » 3 3-7 5 110 fj 5 4-6 3 0-6 jj 3 40 4 2-4 ") 4 11-4 5 9-7 ?? 2 3-4 6 5-8 600 1 9-6 7 1-9 600 2 30 5 5-3 400 2 7-3 6 6-6 460 3 11-7 4 7-0 A. 600 9 5-7 6 1-7 1 0-3 2 0-8 53 11-2 76 2-6 4 9-6 5 7-8 93 6-3 53 11-2 5 5-9 2 10-2 65 7-7 5 0-5 5 1-4 2 6-1 3 2-7 22 3-4 Former levelling. 27 10-6 4 6-7 4 4-6 3 0-4 2 0-3 22 2-3 6 3*0 1 1*2 1-1 Difference. 8 1-8 2 11-2 c. 93 6-3 65 7-7 . LINE OF LEVELS FROM THE ZWARTLAND BASE TO SALDANHA BAY. 323 (TABLE II)— co«f. Distance. feet- 600 600 720 600 460 560 600 600 400 300 320 600 440 600 600 400 400 400 400 330 Forward Staff. BGMABES. 9 MAY 28, 1841. ft* inches. 4-6 6-6 6-6 0-2 0-5 10-4 0-4 9-0 10' 8' 6' 4' 9' 0' 6' 5 2 86 8-4 5 5' 2' 8' 3 9 10 9 10-8 8 10-2 8 8 9 9 70 8-1 15 9-7 54 10-4 ft* inches* 1 6 11 9 9 2 5 1 1 1 11 8 6 5 2 58 11 2 3 2 1 1 3 1 16 9-7 B. Re-levelled the work done yesterday. 86 8-4 58 11-9 27 8-5 c. Moved the camp to Thee Fontein. D. Distance. feet. 600 460 600 600 400 » 400 340 Tj MAT 29, 1841. 8 9 8 8 5 9 10 6 72 17 5-2 3-4 0-0 8-5 1-8 11-5 7-8 0-0 1-4 3-6 3-8 54 11-8 2 11-4 2 10-5 2 6-2 1 0-7 1 4-8 1 0-4 1 0-6 2 8-5 1 8-7 17 3-8 c. Ke-levelled the above portion. D. 360 460 340 200 430 400 500 500 300 300 200 500 400 390 400 500 400 500 400 600 600 400 600 J) j> Back Staff. ft* inclies* 6 8 8 9 8 6 9 10 6 0-6 3-1 0-1 1-5 72 17 4-9 7-4 54 9-5 1 7 9 10 2 7 9 8' 7- 9' 10 6-8 3-4 48 10-2 Forward Staff. inclies. 9-5 11-0 6-0 6-0 7-4 0-4 0-1 7-8 7-2 17 7-4 6 1- 1 6' 10' 3 3 1 17 1-5 EEMAEKS. c. On adding up in pencil there-levelling of Friday's work, I made some mistake, which I did not dis- cover, and hence this third levelling. D. 54 10-4 11-8 9-5 54 10-57 D. 48 10-2 17 1-5 31 8-7 $ JUNE 1, 1841. 2 5 8 11 9 7 6-2 6-4 44 10-7 7 9 9 8 3 9 6 6 6 8 9-7 9-9 4-7 7-1 6-5 1-4 6-8 9-3 5- 6' 8 10' 4 5' 1 0' 7' 3 5 5 1 3 3 1 2 6-1 90 9-5 01 0-6 7-6 5-5 13 2-4 6-4 6-2 0' 11' 1 3 D. 44 10-7 13 2-4 31 8-3 E. 6 6-8 324 VERIFICATION AND EXTENSION OF LA CAILLE'S ARC OP THE MERIDIAN. (TABLE U)—cont. DiEtance. Back Staff. Forward Staff. REMARKS. Distance. Back Staff. Forward Staff. REMARKS. feet. ft. inches. ft. inches. feet. ft. inches. ft' inches. 600 5 8-5 6 7-2 600 7 3-8 5 4-0 F. 400 5 9 9 2 110 400 8 9 4 10-5 400 9 9-6 1 101 600 3 00 3 7-8 600 6 5-6 5 1-4 F. 131 6-6 5 8-1 7 11-2 59 5-8 t9 2 10- 1 4 6-2 131 6-6 59 5-8 4 2-5 5 10-6 6 00 4 4-2 4 35 6 3 6 72 0-8 r. yj 67 9 8 56 4-6 600 5 1-4 6 5-6 )9 400 400 1 10-2 3 2 9 10 5 108 Levelled back again this morning's work. 600 5 20 3 11-2 4 10-2 4 9-2 1 5-2 600 6 6-3 5 8-4 400 5 0-5 5 6-2 G. 600 600 4 31 1 2-4 5 6-3 4 11-0 57 9-8 66 4-6 600 600 3 9-5 4 4-7 3 3-5 4 9-0 400 G. 5 6-2 5 0-5 600 3 70 9 0-3 600 4 10-9 4 1-0 400 600 3 4-4 5 5-3 8 6 6 1-3 4 10 2 6 2-5 5 1-3 6 Levelled the line back of this day, and finding a difference 500 7-8 6 11-0 4 3-3 5 10-2 of 1 foot evidently at 500 2 1-7 7 10-6 4 5-2 4 3 8 the last but one 600 2 5-0 6 8-6 131 1-2 4 53 2 8-7 9-l-8msteadof 8-1-8 400 9-7 6 0-1 59 0-6 >f 7 10 9 5 60 430 5 5-4 7 4-6 9 3-5 600 400 3 6-7 4 5 2 3 0-5 9 1-8 460 2 1-2 72 0-6 600 4-2 8 9-4 600 6 3-2 7 4-6 The line was levelled again. 520 2 7-1 9 1-2 E. 66 9-6 58 2-4 69 0-6 131- 1-2 58 2-4 55 9-6 5 JUNE 2, 1841. 2 4-8 400 7 9-6 3 6-4 E. 500 9 8-6 4 2-6 On re-levelling, I % JUNE 3, 184 1. 400 9 2-8 1 0-3 was aware that a 9 had been put down 500 8 8-1 1 4-0 600 7 1-7 5 2 3 F. 400 600 3 6-4 9 0-8 3 70 2 7-4 instead of a 6. viz.: at the 7th 0, the first levelling. I was. 400 9 0-2 2 11-8 5 1-2 3 7-6 » 6 7-1 6-2 however, determined 5 6-8 7 10-4 j> 6 10-5 71 to do it again this 2 8-5 4 5-7 79 6 70 5 2-6 mornmg. 4 3 4 4 3 6 400 8 5-3 3 79 5 10-3 4 4-0 600 9 10 3 8-1 6 13 6 2-4 3? 4 8-5 4 4-4 5 2 2 4 9-1 57 8-4 )> 3 50 3 10-2 600 3 8-7 4 90 56 2-4 5 00 1 3-1 400 5 1-5 5 7 1 5 8'0 4 5-4 138 0-3 65 11-9 G. 1 60 600 5 10-0 6 81 57 8-4 56 2-4 400 6 11-0 10 0-5 3 11 1 11-6 400 G, 72 0-4 4 11 1 4 0-7 400 6 8-1 5 3 8 600 600 4 8-2 6 1-7 3 11-4 4 4-3 6 2 200 6 1-4 5 0-7 r. 4 03 138 0-3 65 11-9 400 3 9-4 4 0-8 LINE OF LEVELS FROM THE ZWAHTLAND BASE TO SALDANHA BAY. 325 (TABLE II)— CM*. Distance. Back staff. Forward Staff. REMARKS. Distance. Back Staff. Forward Staff. REMARKS. feet. ft. inches. ft. inches. Ij JUNE 5, 1841. 1 60O 600 5 2 8-8 7-7 2 9 3 4 5-2 400 5 2-2 1 3 8 feet. ft. nches. ft. inches. 600 8 4-7 7 7-5 500 4 2-4 2 7-5 H. 400 400 1 6 4-3 6-8 2 11-4 6 4-5 500 600 6 4 4-3 0-3 8 6-9 3 100 Ee-leyelled yester- day's work. 500 2 4-5 2 8-2 600 4 10 7 1 3 9-5 600 5 2-7 6 5-9 400 2 8-9 4 7-4 ?J 5 1-8 5 11 75 8-0 500 5 1-0 5 7-5 JJ 5 6-2 4 5 75 9-2 3(0 4 9-2 4 5-2 43 6-1 600 4 5 6 1-0 w 400 600 3 6 7-3 6-2 5 4-8 4 7-0 42 2-3 T 2 10-8 75 80 72 9-2 1 3-8 600 H. 600 42 2-3 43 61 5 6-8 6 1-0 4 0-5 I. 3 0-1 4 5 61 10 5 7-3 5 2-7 LeTelled the line of this morning back. 600 5? 4 3 7-2 6-9 4 2 1 3 7-3 600 6 91 5 5-8 600 5 5-2 4 5-4 500 2 11-6 2 7-5 200 3 3-2 6 10 7 400 6 6-2 6 7-3 600 3 6-5 5 10-2 400 3 2 1 8-4 400 7 9-3 4 111 60O 7 7-6 8 40 400 3 2-4 7 3-8 400 1 5-4 5 5-0 600 2 0-8 5 00 600 4 94 2 9-3 600 2 8-7 4 110 600 2 8-5 5 6-4 400 5 01 5 80 400 4 00 3 91 400 5 2-3 7 2-7 600 4 2 4 2-7 600 3 3-6 7 11-4 jf 6 8-1 6 7-5 77 8-0 j» 3 61 3 40 600 4 4-6 4 90 74 9-9 600 1 1-2 4 9 4 90 8-3 400 4 11 4 11-5 r;. 400 500 8 2-7 1 5-5 69 5-3 2 10-1 3 110 8 6-9 K. 74 9 9 77 8-0 21 3-0 600 69 2 5-3 10 7 90 8-3 I. 5 5-2 ? JUNE 4, 18 11. 4 3 7-4 7-0 4 2-3 3 8-4 Re-levelled the work. 600 200 5 3 71 6-3 4 7-2 6 3 The ground was high, and the line 500 4 1-4 2 5-7 H. 600 3 7-1 5 8-5 running in the direc- tion of the setting 600 6 1-7 8 2-6 400 7 110 5 8 sun, it was difficult 6C0 3 10-1 3 9 5 400 3 3-8 7 6-4 at times to read off, 600 400 5 2 0-2 9-4 4 0-5 4 80 600 600 2 2 1-5 80 4 11-4 4 11-5 as the object glass could not be screen- ed. I determined, eo;t 4 10 6 5 6-5 400 5 0-6 5 8-6 therefore, to levelthis 3t:0 4 5-8 4 5-5 42 103 400 5 2-5 7 2-8 again on Monday. 400 3 90 5 3-2 41 6-2 600 3 30 7 10-5 600 6 6 4 4-8 I 3 5 3 3 4-5 1 41 600 400 1 8 2-5 3-5 4 91 1 8-2 91 90 70 0-8 41 6 2 42 10-3 500 3 9-5 8 8-6 K. . 21 8-2 Moved the camp to Eland's Fontein. 70 n. Q l\^ n.i\ U O £?■!■ £/ U , 326 VERIFICATION AND EXTENSION OF LA CAILLE'S ARC OF THE MERIDIAN. Distance. Back Staff. Forward Staff. HEMAUKS. Distance, Dack Staff. Forward Staff. BEMABKS. C JUJSTE 7, 1841. feet. ft. inclies. ft. inclies. 340 200 3 5-4 4-6 5 7-2 9 0-2 feet. ft. iuches. ft. inches. 600 0-0 8 3-0 600 2 10-6 5 3-0 I. 400 2 10-4 9 01 4 4-2 4 10 600 3 11-2 4 2-5 j> 3 7-0 3 9-7 >f 4 3-7 9 8-2 600 5 6-9 4 6-6 600 2 10-0 6 9-6 200 3 4-9 6 1-8 400 2 2-3 4 8-9 600 3 5-6 5 2-8 400 3 91 4 7-1 400 7 7-5 5 0-4 600 4 11-6 6 11-1 400 3 2-5 7 4-9 400 3 2-6 2 3-4 600 1 11-2 4 7-7 600 7 7-8 9 11-3 600 2 5-6 4 8-5 ;» 1 6-2 5 8-0 400 4 11-4 5 9-6 '? 3 10-9 6 4-7 400 5 3-4 7 4-2 600 5 6-8 4 5-0 600 3 51 7 11-2 500 6 3-0 4 11-1 600 3 9-1 3 6-2 200 5 5-6 8 10-3 600 1 0-6 5 0-5 90 11-2 200 0-8 10 0-0 400 8 6-4 1 7-5 69 8-4 200 8-3 8 5-9 500 4 2-4 8 9-6 K 400 4 5-4 8 2-0 21 2-8 600 400 5 6-1 6 30 9 0-4 1 2-1 153 5-3 93 2-8 69 8-4 90 11-2 200 Left off at noon, in 200 400 9 10-8 4 1-2 2-7 5 0-5 60 2-5 1 5-8 7 7-3 93 2-8 153 5-3 600 400 400 2 7-7 4 7-8 2 9-6 2 8-6 8 8-3 3 10-0 consequence of the high wind, and the levelling being over the sandhills at Levelled the line back again. 400 5 0-5 4 1-2 400 5 7-4 4 1-6 Eland's Fontein. 200 2-7 9 7-1 26 11-8 17 2-3 400 600 1 1-2 9 0-8 6 5-3 5 8-6 17 2-3 26 11-8 400 200 8 5-9 7 10-3 4 4-1 3-2 9 9-5 200 9 10-1 0-3 ' 200 500 9 7-1 6 1-2 5 00 6 6-5 $ Kain until noon, when the wind became so high as to 600 4 8-8 5 9-0 pre vent using the leyel. 6 6-3 3 10-2 5 90 9 5-8 1 10-6 7 1-5 § Eain all D AT. 600 400 2 3-6 3 20 600 400 400 6 11-5 4 6-0 4 100 4 11-4 3 9-2 2 3-4 i; JUNE 10, If 41. 600 >» 600 400 600 200 340 G 10-0 9 3-8 4 1-7 9 0-8 8 1-7 9 3-5 5 2-5 2 8-8 4 0-4 3 10-2 2 11-2 30 1-6 3 3-0 200 600 400 400 1 4-3 2 6-6 5 1-8 2 103 5 9-0 7 6'7 2 7-4 9 2-3 3 10-5 4 2-8 Ee-levelled Mon- day's work. 27 5-7 17 8-0 153 3-6 93 1-0 60 2-6 9 9-7 17 8-0 27 5-7 153- 3-6 93 1-0 LINE OF LEVELS FROM THE ZWARTLAND BASE TO SALDANHA BAY. 327 (TABLE 11)— eimt. Distance. Back Staff. Forward Staff. BEMABES. Distance. Back Staff. Forward Staff. REMAHKS. ? JUNE 11, 1841. § JUNE 16, 1841. feet. ft. inches. ft. incites. feet. ft. inches. ft. inches. 440 5 80 5 9-5 320 2 6-1 6 8-4 600 2 1-0 2 9-9 500 3 4-4 4 2-1 450 3 7-4 8 11-3 280 5 4-4 6 35 600 6 2-4 9 6-3 240 2 11-2 6 0-3 600 4 8-8 2 11-6 600 2 5-2 5 6-0 400 4 9-2 2 1-4 300 3 11-3 5 10-8 600 6 3-8 7 1-4 340 3 80 4 2-1 400 30 2 11-3 280 2 11-7 4 9-0 400 5 7-1 8 3-1 , 400 4 1-4 6 0-5 600 2 4-5 3 6-4 400 3 4-5 5 7-4 70 2-3 )> 6 11-2 5 0-3 )) 3 4-5 6 2-1 44 8-6 600 4 0-0 5 7-6 JJ 4 10-3 3 5-0 400 3 75 2 7-1 400 1 9-6 6 5-1 25 5-7 600 7 10-1 8 8-7 600 5 2-3 6 31 44 8-6 70 2-3 500 7 6-5 6 7-1 400 2 7-0 6 10 320 2 5-6 6 7-8 Be-levelled this 300 6 10-7 1 5-4 500 3 5-2 4 2-8 morning's work. 400 3 11-5 7 4-2 125 3-5 280 5 2-7 6 3-2 400 4 11-9 9 1-7 101 8-4 240 3 2-6 6 4-6 400 300 6 4-5 2-0 4 1-2 8 3-9 600 300 2 7*4 5 7-0 23 7-1 3 9-5 5 8-4 340 280 3 9-2 4 4-3 101 8-4 125 3-5 3 03 4 11-4 400 4 3-5 6 1-7 jj 3 5-6 5 8-5 71 1-6 300 8 3-9 20 Levelled the line jj 3 4-5 6 4-1 45 6-7 400 4 1-7 6 2-8 back. JJ 4 11-2 3 4-4 400 400 9 0-0 7 3-8 4 11-8 4 1-0 400 1 11-4 5 5-4 25 6-9 300 400 500 1 6-7 5 11-1 6 5-4 6 9-8 2 4-8 7 6-0 45 6-7 71 1-6 600 600 6 2-5 8 7-2 4 11-6 7 9-6 -2;. roNE 17, 18 41. 400 2 6-2 3 8-4 380 3 9-7 6 0-9 600 5 10-1 4 1-2 300 3 2-3 5 10-2 6 0-5 6 11-2 June 12, 13, and 14 400 7 0-2 3 11-1 600 3 7-2 2 2-7 raining. 300 1 10-1 7 5-4 400 400 600 8 0-6 2 9-8 7 3-5 5 5-1 4-0 6 7-6 June 15, moved to Massenberg. 500 400 300 5 8-6 7 2-6 2 0-6 5 11-3 6 0-4 4 8-2 400 600 2 4-4 3 0-8 5 0-6 4 6-0 400 600 4 2-5 4 10-8 6 11-3 6 0-0 Obliged to leave off from the high wind, 11^ a.m. 600 9 5-5 6 2-4 126 4-3 400 5 0-4 6 11-8 450 9 8-0 4 7-6 102 9-1 400 5 4-1 5 4-5 600 440 3 1-3 6 0-1 2 3-1 5 9-8 300 600 400 5 5-0 5 6-8 4 5-7 3 8-6 8 9-3 4 8-6 82 5'6 65 9-4 23 7-2 16 8-2 126 4-3 102 9-1 65 9-4 82 5-6 328 VERIFICATION AND EXTENSION OF LA CAILLE'S AEC OF THE MERIDIAN. (TABLE II)— COB*. Difltance. feet. 380 300 400 300 500 400 300 400 600 400 400 300 600 400 400 600 600 400 » » 400 340 400 500 600 400 400 240 400 600 600 400 » 400 ^0 340 400 500 600 400 » 400 240 Back Staff. Forward Staff. BEMABKS. 1? JUNE 19, 1841. 10-4 9-5 1-9 5-1 8-6 6-6 30 6-4 11-4 11-7 5-6 8-7 11-6 5-4 67 9-9 60 6-2 5-U 0-4 10-0 4-1 9-8 7-2 2' 2' 0' 2- 9-8 4-1 9-5 8-4 76 3-5 5-6 6-3 2-3 1-0 9-0 6-8 ft* inches* 6 5 4 7 6 6 5 7 6 6 11 5 8 4 8 11 4 7 84 6 76 5-3 74 9 5 4 5 11 4 3 2 3 6 5 10 1 4 7 8 3 4 4 4 2 2 4 5 4 1 6 74 10-8 Ee-levelled Thurs- day's work. 84 6-6 67 9-9 16 8-7 76 3-5 74 9-9 1 5-6 Be-levelled this morning's work. 76 5-3 74 10-8 1 6-5 Distance. 200 400 600 400 400 200 400 600 400 400 300 400 500 400 400 400 400 400 » >> }> 400 400 400 300 200 200 200 400 400 Back Staff. Forward Staff. C JUNE 21, 1841. ft. inches . 10 1-2 4 11-6 2 11-2 1 6-3 1 100 21 4-3 ft. inches. 3 4 4 9 1 22 6-9 Obliged to leave off at 11 a.m., in conse- quence of the rain, 22 21 6-9 4-3 1 2-6 $ JUNE 22, 1841. 9 8 •1 2 9 6 4 11 •4 4 3 1 3 6 •2 5 5 3 1 7 4 9 3 7 1 10 3 1 5 21 7 4 22 10 2 10 1 4 6 1 9 8 1 2 11 1 5 8 4 3 8 4 3 11 7 2 3 3 8 7 5 1 9 4 4 3 1 5 6 6 4 1 6 3 7 4 3 11 1 7 5 2 5 7 •7 5 4 9 5 11 3 5 4 5 9 1 4 7 8 5 8 4 3 1 2 6 7 6 3 6 6 2 7 3 2 11 2 6 5 5 2 10 6 6 7 4 3 10 1 7 6 2 3 10 7 4 9 6 3 8 2 4 8 6 3 9 7 4 8 4 3 4 1 4 1 7 6 3 5 3 5 7 8 1 3 1 5 6 8 1 4 5 9 9 1 6 9 4 3 8 8 2 10 8 2 6 7 2 8 2 4 3 5 7- 6 3 9 1 5 0-3 5 1-8 183 11-9 117 53 Ee-levelled yester- day's work. 22 10-2 21 7-4 1 2-8 183 11-9 117 5-3 66 6-6 LINK OP LEVELS FROM THE ZWARTLAND BASE TO SALDANHA BAY. 329 (TABLK lI)—cont. Distance. Back Staff. Forward Staff. REMARKS. Distance. Back Staff. Forward Staff. REMARKS. feet. ft. inches. ft. inches. feet. ft. inches. ft. inches. 400 5 1 8 5 3 Ke-IeTellingofthis 200 3 1-0 9 4-1 » 3 9 7 5 8 2 day's work. 400 5 5-1 6 11-6 400 4 6 6 8 2 4 400 8 1-1 1 9-6 135 11-2 200 7 2 8 3 3 400 8 8-7 2 5-3 98 2-2 10 8 8 10 6 500 400 6 6-4 3-2 9 6-8 9 3-8 »7 1 8 9 6 3 37 9-0 200 4 3 9 9 6 400 2-2 7 3-5 300 6 7 8 3 400 1 5 3 7 6 4 8 2 6 5 3 98 2-2 135 11-2 4 2 2 3 3 2 400 7 3-5 2-2 Re-levelling the If 4 7 1 3 9 4 400 9 3-5 31 line of this morning t9 4 9 2 3 10 4 500 9 6-5 5 5-5 back again. tf 4 10 6 3 10 6 400 2 5-5 8 9-8 }f 7 6 4 3 10 2 400 1 11-6 8 2-5 if 5 8 4 3 1 400 7 0-4 5 5-2 JJ 5 7 5 3 1 2 200 9 4-1 3 1-2 400 7 4 3 6 7 1 400 6 11-8 4 0-5 400 6 5 2 6 1 400 6 6-4 4 6-4 ff 4 3 6 6 8 400 4 10-3 6 4-5 ff 4 7 6 6 11 3 350 5 3-4 6 2-5 ff 5 1 6 5 11 8 300 9 9-1 2 6-4 y> 5 5 4 5 7 6 400 5 3-4 5 7-0 ff 7 5 6 4 4 400 9 2-3 1 20 ff 3 8 4 3 2 180 6 1-6 1 5-7 ff 5 9 4 3 3 400 9 11-4 2 11-0 99 1 8 8 7 2 185 9-7 ff 6 0-4 4 10-1 400 2 4 4 4 5 119 1-5 )J 5 6-1 4 5-4 136 11-0 500 400 300 3 9 2 10 n ii 6 R 5 8 9 8 9 10 3 7 1 400 200 400 400 1 2-3 2 104 4 7-7 5 9-3 8 2-0 7 1'3 99 0-9 66 8-2 3 6-6 5 9-0 37 10-1 \J WW «y J.I./ .L 119 1-5 185 9-7 136 11-0 99 0-9 ? lUNE 25, 1841. 1 5 JUNE 23, 1841. 400 ff 2 5-4 2 6-2 7 6-0 8 4-1 400 5 8-2 5 7-5 400 3 5-3 4 5-6 ff 1 7-1 8 11-5 200 6 11-5 2 9-4 400 0-2 10 1-2 400 8 1-2 1 2-4 300 1 10-0 9 08 ff 4 5-6 6 5-8 400 2 5-4 6 3-0 19 4 10-0 6 0-0 ff 2 6-0 7 3-4 400 2 10-2 9 9-6 ff 5-1 8 11-5 180 1 4-4 6 1-4 400 0-1 9 11-1 400 1 1-2 9 2-1 300 1 2-6 8 7-0 120 5-4 400 5 7-3 5 3-4 300 2-3 9 110 18 4-2 300 2 6-2 9 8-8 240 6-8 9 4-4 350 5 2-0 5 2-5 180 1 23 9 2-7 102 1-2 400 6 3-2 4 8-8 200 4-7 6 11-7 4 6-6 4 0-6 6 6-8 7 0-6 400 18 4-2 120 5-4 -J 330 VERIFICATION AND EXTENSION OF LA CAILLE'S ARC OF THE MERIDIAN. (TABLE II)— comf. 200 180 240 300 300 400 400 300 400 400 200 400 270 260 300 270 400 500 500 300 400 300 470 140 240 100 400 600 480 480 500 400 100 240 140 470 300 400 Back Staff. ft. inches. 120 10-3 Forward Staff. ft* inches. 6 11-7 4-7 9 4-3 1 4-3 9 5-6 7-8 9 9-8 0-8 8 7-3 1 2-0 9 9-5 10 9 2-8 5 6 7 3-1 2 5-1 6 3-4 2 6-7 9 0-1 1 9-7 10 0-8 0-0 8 10-4 1 7-6 8 6-1 3 7-7 7 7-4 2 5-3 18 8-3 REMARKS. Levelled the line of this morning back again. 120 10-3 18 8-3 102 2-0 Tj JUNE 26, 1841. 46 1 2 2-1 9 11-0 9 10-1 6- 9 9 8 7 7 6 6 8 8 6 8 5 3 6 0-6 7-0 7-2 0-5 4-5 5-3 9-0 5-3 6-7 6-6 6-4 6-8 0-1 150 8-8 10-0 4-4 4' 7 0' 4' 3 10-6 9-6 150 8-8 46 1-6 104 7-2 Ee-IeveUing of this morning's work. Distance. feet. 300 500 500 400 270 300 260 270 400 200 416 300 400 400 300 300 Rack Staff. ft. inches. 0-1 7-4 6-7 2-3 5-6 30 2-6 7.5 0-8 9 11-2 2 1-8 7 7 8 9 8 9 9 9 10 152 1-1 Forward Staff. ft* inches; 7-5 2-6 4-0 4-8 1' 5' 1' !■ 4' 9 11 47 4-8 152 11 47 4-8 104 8-3 JtTNE 27, 1841. 9-3 0-6 8-2 10-2 9-6 10-0 25 11-9 9 3 4-5 4 5 6-8 1-1 4 5 5 6 32 10-7 32 10-7 25 11-9 6 10-8 The levelling rod placed on the surface of the rock, over the upper hole jumped in it. 6 ■ =Difference in height between the two holes jumped in the rock, distance between the holes 31"- 8'»- The lower hole is according to the high water mark of yesterday, below it 9 inches. The direction of the two holes runs into the middle of a Bay in Schapen Island. The rock in which the two holes are jumped is at the south part of the Bay where it begins to narrow south- wards, and opposite the south end of " Schapen Island." From the rock is seen the pointed peaks of Jutten Island, over the low point on the south of Riet Bay. Two large stones were placed over the holes jumped in the rook, the holes about two inches deep. The tide this morning was about two inches above the surface of the rock where the lower hole is jumped. LINE OF LEVELS FROM THE ZWARTLAND BASE TO SALDANHA BAY. 331 (TABLE ll)—conf Back Staff. feet. 300 300 400 400 300 416 20 10-1 7-6 8-0 4-3 7-4 33 3-4 Forward Staff. ft, iuchest 2 10-4 2 9-8 6 10-4 5 11-2 21 8-6 3 4 26 4-5 REMARE3. Ee-levelling of this morning's worli:. 33 3-4 26 4-5 6 10-9 I observed the back (last 0) station, and onre-observingfound it 4-7-4 instead of 9-4 as I had entered it. Back Staff. Forward Staff. REMAEKS. C JUNE 28, 1841. The high water mark observed this morning at lOJ a.m., was even with the surface of the rock in which the lower hole is jumped. Collecting the Kesults. Dip. Rise. feet> inches. feet, inches. 22 2-85 6 0-20 1 3-95 27 9-55 21 2-90 54 10-57 9 9-60 31 8-50 60 2-55 72 0-60 23 7-15 1 5-60 25 6-30 2 10-45 16 8-45 1 605 1 2-70 66 7-40 37 9 05 102 1-60 104 7-75 6 10-85 433 4-20 264 10-92 1 Depression of upper hole. 168 6 inches* 5-28 00 Depression of lower hole, or sea level', below ) the starting point on the Base-line. . . ) 174 6-28 Royal Ast. Society's and Imperig,! Standard. Expansion of 6-inch Standard. 332 VERIFICATION AND EXTENSION OF LA CAILLE'S ARC OF THE MERIDIAN. § 6- § 6. Reduction of the Microscope intervals to Temperature 62° Fahrenheit. Of the 4281875 feet, the apparent length of the Base, 40780 feet were measured in terms of the compensation bars, and 2039 in terms of the 6-inch brass standard (page 244) to which the microscopes were referred. By Mr. Baily's report on the Royal Astronomical Society's 5 feet scale (Ast. Soc. Mem., vol. 9, pages 101 and 1 19) the first six inches are less than the mean six inches of the centre yard, by 0"000031 inch. But the centre yard exceeds the Imperial Stand- ard yard, by 0000374 inch, or 0000063 on six inshes. Therefore the first six inches of the Royal Astronomical Society's scale, exceeds six inches of the Imperial Standard by 0-000032 inch, equivalent to 01 305 inch on 2039 feet. No further allusion need be made to the Imperial Standard; for independent of the quantity being small, the Cape six-inch standard will be expressed in terms of the Ordnance Standard, in the calculation of the Cape arc of the meridian. The elaborate discussion of the experiments, carefully conducted by Captain Yolland, Royal Engineers, at Southampton, in the year 1844 — 1846, and published in the account "of the Measurement of the Loch Foyle Base," assign cogent reasons for assuming the expansion of the Ordnance 6-inch brass standard to be 000000982, on unity for one degree of Fahrenheit. The same expansion is adopted for the Cape standard, since the only known difference between them consists in the difference of their volumes ; the recorded depth of the former being 055 inch, whereas the depth of the latter is 035 inch. The comparisons of the intervals between the foci of the outer microscopes with the 6-inch standard were exceedingly difficult to manage, which may be gathered from the registered temperature of the air while measuring the base. As before mentioned, the the thermometer rested upon one of the bars near the middle of each series, screened from the sun by the tents on one side, the canvass of the opposite side clued up, and a thorough draught from end to end. The average temperature of the 88 dayp, while measuring, is 80°-16; the extreme range from 20° to 30° occasionally on the same day : therefore it became necessary to watch for the temperatures in which the preceding comparisons of the standard with the microscopes were made, in order to discover if the wires had shifted; but as this could seldom be hit exactly, such examinations fall short of the precision attainable by means of micrometer microscopes. The attempt to estimate small differences in length, by comparing the images of the dots with the diameters of the wires, is uncertain; it was the practice, therefore, when consecutive comparisons were made under considerable differences in temperature, and on two or three occasions of accident to a microscope, — to adjust the wires to exact bisection. Upon the whole, however, as far as the eye could detect, the wires retained their positions with admirable pertinacity: indeed, they were never known to shift, except from accidental violence. Adjustments for length on six-inch istandard. REDUCTION" OP MICROSCOPE INTERVALS TO 62" FAHRENHEIT. 333 The microscopes were adjusted for length at the following dates, and temperatures § e. of the six-inch standard as indicated by its attached thermometer, — irrespective of the for^ien^r*" occasional examinations when they appeared to be correct. }40.— October 20 M 65-5 N 64-2 69-5 P 73 Q 68-1 R 66-9 S 62-4 „ November 30 M 620 N 66-5 62-8 P 63-8 Q 66 9 R 63-3 s 65-8 „ December 6 p 59-4 >» » 12 O 62-8 Q 650 s 66-0 „ Jamiary 20 M 700 N 69-3 68-8 Q 68-8 R 68 8 S 69-7 be correct. on six-inch Standard. 1840. — January 25 S 65-8 » » 30 M N Q R S 67-4 63-2 69-5 70-7 72-3 66-7 „ March 4 M N Q R S 73-6 73-6 73-6 73-0 73-6 74-1 » » 21 M N Q R S 77-0 790 785 78-4 78-2 76-0 „ 26&27 M 61-4 N 61-6 60-1 Q 61-9 R 600 S 760 On April 21, the day after the east terminal point was fixed, the following com- parisons were made at sunrise. o Microscope S, temperature 63'0, exceeds the standard by about ^ diameter of a dot. „ M, „ 63'5, less by a minute quantity. „ N, „ 635, exactly the length of the standard. „ 0, „ 64'8, less by about i diameter of dot. „ Q, „ 65'2, less by about j- diameter of dot. „ R, ,, 66'5, less by about ^ diameter of dot. As S had been adjusted to the length of the standard in the temperature 76°"0, it was left over the standard until the attached thermometer indicated 76°, when the dots were found exactly bisected. (The diameter of each dot or puncture on the 6-inch standard is 0*00139 inch) The result of this examination is in pretty close accordance vpith the adjustments on the 26th and 27th of March, making allowance for the difference in temperature of the standard on that occasion. 334 VERIFICATION AND EXTENSION OP LA CAILLE'S ARC OF THE MERIDIAN. § 6. The following table exhibits the elements and calculation of the reduction to temper- Calculation of , ^r>n i reduction for atuFC 62", where temperature. Columns 1 and 2, show the intervals between the points on the line, reckoned from the west end, and the number of series in each interval. „ 3, give the number of bars in each series (n). „ 4 — 10, distinguish the microscopes. „ 5, gives the sum of the excess or defect in temperature of the several microscopes, over or under 62° (2 t°). „ 6, gives the resulting correction to 62° in inches, assuming the expansion of the standard to be 0000589 on six inches, for one degree of the thermometer. Reduction = 0-0000589 x n x 1 t°. REDUCTION OF THE SIX-INCH STANDARD TO 62° FAHRENHEIT, FOR THE INSTANTS WHEN THE MICROSCOPES WERE ADJUSTED FOR LENGTH. BASE-LINE. — TABLE III. .9 j S-3 ]1 1.1 Reduction INTERVALS. i: i. MICROSCOPES. 2 t°* =00000589 o o *" X n X S /°. gi + ° Inch _|__ 0- 40 40 6 4 N M p Q R 4 S 33-65 0-079280 40- 43 3 4 i N M R 4S 16-55 -002924 43- 55 12 4 i N M p 4S 22-65 -016009 55- 87 32 5 4 N M p R 4S 27-55 -051926 87- 88 1 5 4 N Q iM R 4S 21-55 •001269 88- 91 3 5 4 N- M p R 4S 27-55 •004868 91-106 15 5 4 N M p Q 4S 28-75 •025401 106-108 2 5 4 N M p R 4S 27-55 ■003245 108 — 166 58 5 4 N M p Q 4 S 28-75 ■098216 166 — 179 179-214 13 35 5 5 iM 4 M N N p p R R 4S 4 S 10-30 Sum lO'SO ■007887 ■291025 ■021233 214—230 16 5 4 M N p R 4 S 5-90 ■005560 230—249 19 5 4 M N Q R 4S 13-40 ■014996 249—250 1 5 4 M N Q R 4S 11 '60 ■000683 250—334 334-357 84 23 5 5 \ M 4 M N N Q Q R R 4S 4 S 11-60 Sum 11-60 ■057392 ■099864 ■015715 357—385 28 5 i M N Q R 4 S 35-55 ■058629 385—402 17 5 4 M N Q R 4 S 33-60 •033644 402—452 50 5 4 M N Q R 4 S 32-75 ■096449 452-550 550-601 98 51 5 5 4M \ M N N Q Q R . R 4S 4 S 32-75 Sum 32-75 ■189040 •393477 •098380 601-688 688-722 87 34 . 5 5 4 M 4M N N Q Q R E 4S 4 S 58-25 Sum 58-25 •298490 •396870 •116652 722-743 21 5 i M N Q R 4S 80-60 •099694 743-810 67 5 4 M N Q R Is 2-30 •009076 810-811 1 3 4M N 4S 4-40 Sum 0^000259 0-225681 REDUCTION OF MICROSCOPE INTERVALS TO 62° FAHRENHEIT. 335 The sum of the values from n x ^ t° x 00000589 is 1-4069 inches = 0-11724 feet, § e. additive to the apparent length of the Base : and the mean of the several microscopes, t^e^M*iro"-°* during the measurement, was equal in length to the six-inch brass standard in the tem- ^c°P|J"t"-^''is perature 67°-9 nearly, — assuming the compensation of the microscopes to be perfect. The mean temperature of the atmosphere under the Base-line tents was 80-2 nearly. § 7. Verification of the Base by Triangulation. § -. For the purpose of verifying the registered number of bars, the Base was divided Sections of into six unequal sections as follows, reckoning from the east terminal point, — viz. : * ^ ^*^^' 6436-5, 7245-0, 5145-0, 6195-0, 8085-0, and 9712-25 feet, numbered consecutively 1, 2, 3, &c. The plate on the left hand page represents the plan of the triangles. The recog- Selection of noisance for selecting the stations occupied ten days, and those which were adopted were p'anofthe the most favourable that could be found. Advancing along the line from the west end, a swell of the ground on the right masks the positions at the desired distance. The descent to the Salt River vale begins at register picket 11497 feet from the west end ; and at 1600 feet the river crosses the line; from thence there is a gradual undulating ascent to picket 29137'25: throughout this interval there is but one commanding rise to the right, — viz. : the north end of the long undulation which forms the east bank of the Salt River vale, upon which stands, near G, the Coggera farm house. From this position, with two exceptions, the line is visible from the west end to picket 29137-25. The first exception is unimportant; the second extends between pickets 14857-25 and 23624-75, and serves the purpose only of connecting the left hand stations. From 29137-25 to the east terminal point, the ground is more favourable. On the left side of the line, the only available distant station is close to the Uyle Kraal farm house, which was occupied chiefly for the purpose of connecting the 4th section with the others. There was another object in view (but secondary to the verification of the register). Probable in the endeavour to select well conditioned triangles ; viz. : to obtain an estimate of the Base. probable error of the measurement of the Base, by comparing the sections with each other; or which amounts to the same thing; — to determine the distance between two points out of the line, from each section of the base. To perform this correctly, optical power equal to that employed for adjusting the dots of the point-carriers on the base, is required for centering the signals and theodolite over the stations : also the outlines of the signals should be well defined, and the line of sight should be free from the disturbance which occurs in the stratum of the atmosphere near the 2 A Base. 336 VERIFICATION AND EXTENSION OP LA CAILLE'S ARC OP THE MERIDIAN. 5 r. ground in dry weather and strong sunshine. Hence, since these circumstances cannot be erro/o/the Commanded, a length determined by triangulation may, a priori, be regarded as not so accurate as one by direct measurement : on the other hand, the former is free from several small errors, particularly from those depending upon temperature and alignment. With respect to the latter it has been shewn (page 315) that the sum of the corrections for the deviation of the register pickets was very small ; but it is not improbable that the deviation of intermediate points, whose positions could not be examined, may have been greater. 2. Particulars relating to Signals and Stations. Signals. The signals which were employed when triangulating the Base were of three kinds, viz. : helioslats, with screens and apertures of about one-tenth of an inch ; cylindrical poles, painted black above and white below ; and white slits. The plan of the white slits was furnished by Captain Henderson; who stated that they had been found to answer well for short distances at the Loch Foyle Base. Each consisted of a triangular frame, four or five feet high, carrying two slips of thin sheet iron painted black, the adjacent edges separated ftom one to three inches, according to the distance of the station. Behind the slit thus formed, a board painted white is fixed at an angle of about 40° with the plane of the frame, for the purpose of reflecting light. A plumb-line bisecting the slit, centers it over the station point. The image of the slit, as seen through a telescope, is a sharply defined white line on a black ground, perfectly free from phaze, and when the atmosphere is favourable the slit is as sharp and distinct as the bisecting wire. The only inconvenience attending this signal (of which there were six on the Zwartland Base) is the adjusting of its plane perpendicular to the line of sight, for each theodolite station, which must be done by an intelligent person, — not always available. Each station out of the line was defined by a picket about three feet long and four inches diameter, driven firmly, and carrying a pin to define the point. Three other pickets were driven to support the theodolite trestle. Station par- East end, 0. A frame-slit signal. Well seen owing to the elevation of the station. .36'382, O. A frame-slit signal when observed from the east end, A and D : a pole when observed from B : an heliostat when observed from M and E. The signal in general flickering : and being somewhat masked by bush when observed from A, the top of the slit only could be seen. A O. A frame-slit signal. Definition good when observed from the east end, and 36382 ; the reverse when observed from M. Signal twice overturned by cattle. E, 0. A frame-slit signal when observed from the east end, 36382, and D: the first series from M an heliostat : from C a pole. Captain Henderson visited this station VERIFICATION OF THE BASE BY TRIANGULATION. 337 when the theodolite was at M, and found the signal 1^ inches excentric towards the §7. west. Being an important point, the theodolite was taken again to M. The early ficuiara.''*'' observations are not so good as the subsequent, partly owing to bush which was cleared away when the latter were made. D, 0. A frame-slit signal, projected on rising ground behind it. Invisible in strong sunshine, but well defined in the evening. M, O. A frame-slit signal when observed from D, 36382, A and B : an heliostat when observed from E : a pole from the other stations. The upper half only of the pole visible from Uyle Kraal. Returned to this station to observe Uyle Kraal, but the pole there, in the meantime, was thrown down by cattle, and the design was given up. B, O. A pole signal when observed from 36382 : a frame-slit from A and M : a pole from the other stations. The signals overturned three times by cattle. Being on low ground the signal was not well seen from M, and there is evidence of the signals first set up, being excentric. A directing pole on the line near M was inadvertently observed for the one on C while at this station ; the signals between B and G could not be seen from the Base-line. C, O. On arriving at this station with the theodolite, the signal was found to be a board, 4 inches in breadth, placed excentric : the distance between the half thick- ness of the board and station point was about two inches, and the distance seemed to coincide with M, C, prolonged. The theodolite was centered over the station point : a reduction is necessary for the angles with C, measured at E, G, and 23992. On leaving, a cylindrical pole was centered over the station point. 23992, O. A frame-slit signal when observed from M : a pole from the other stations. Well observed from C. G, O. When the theodolite was at B, G signal was tilted to one side by cattle. On visiting the station to re-adjust, the signal was found to be a board similar to the one at C : the excentricity 1^ inches in a direction parallel to the Base-line. The board was replaced by a cylindrical pole, centered over the station point. A reduction is necessary for the angle G M C. This station was well observed from C, M, and 9712: disturbed by cattle but re-adjusted, when observing from the west terminal point and K; returned to it to observe 9712 and K. 9712,0. The signals over this and the subsequent stations were poles, and were relatively well observed : returned to it to observe K and 17797. Uyle Kraal, 0. The signal pole was on the high ground, behind and to the west of the farm-house, and distant from it about 200 paces. The buildings cut off the view of the line eastwards of M, likewise of G. While occupying this station the sky was clouded and the signals steady. K 0, and west end O. Nothing worth recording. 17797, 0. This station is not visible from C, G, or the west end. Signal twice over- turned, and not exactly vertical when observed from 9712 ; the lower end was observed. 338 VERIFICATION AND EXTENSION OF LA CAILLE'S ARC OF THE MERIDIAN. Corrections for level and temperature. 3. Corrections for Level and Temperature. For the present purpose, the mean level of each section has been reduced to the level of the east terminal point. The following table exhibits these reductions, also the reduction to 62° of the six-inch brass standard, extracted from table III, page 334 : — BASE-LINE. — TABLE IV. No. of Section. Depression below- east end. Reduction to east end. Reduction to temperature 62°. Sum of Reductions. Measured lengths. Lengths at temper- ature 62°, and at elevation of east end. feet. feet. feet. feet. feet. feet. 1 33-29 + -0102 + -0188 + ^0290 6436- 5 6436-5290 2 33-46 -0116 •0331 •0447 7245- 7245-0447 3 57-42 •0141 •0158 •0299 5145- 5145-0299 4 •0170 •0816 6195- 6195 • 0816 5 97-49 •0376 •0083 •0459 8085- 8085 • 0459 6 66-56 •0309 •0243 (a) •0552 9712-25 9712^2971 3&4 84-90 •0787 •0328 •1115 11340- 11340^1115 5&6 80-61 + -0685 + -0326 + •ion 17797-25 17797 • 3430 Weights of angular mea- Bures, 4. Observed Angles and Corrections for Errors of Observation. The following table gives the observed angles, the number of partial measures upon which each angle depends, the reciprocals of the weights, and the seconds of the angles corrected for calculation. The weight of each angle was calculated by dividing the square of the number of partial measures by twice the sum of the squares of the differences from the mean, assuming the theodolite errors of division to be insensible, an assumption which is not strictly correct. The method pursued when measuring, of stepping the divided circle, eleminates the division errors from the mean result; they ai'e restored in the weight as above calculated ; but that factor cannot justly be represented by the number of measures alone, — where, as in the present instance, the triangulation is carried over flat ground, — the line of sight passing in close proximity to heated sand and bush, causing the signals to undulate so much, except during gloomy and moist weather, or early in the morning and late in the evening, as to materially diminish the precision of the pointing : it is therefore necessary to introduce this element of error. The sum of the reciprocals of the weights of each triangle, having an angle at a central station has been employed for that angle when reducing the sum of the angles at the central station to 360° (b). (a) The sixth section contains 40 series of 6 bars and 15 series of 4 bars, whose lengths exceed the same number of series of bars A, B, C, E, G by -0081 foot, which subtracted from -0552, leaves -0471 for the sum of the reductions. (b) On the meridian triangulation the errors are distributed \>j the laborious, but strict geometric process. VERIFICATION OF THE BASE BY TRIANGULATION. 339 BASE-LINE.— TABLE V. No. of Triangle. NAMES OF STATIONS. Observed Angles. Number of Observations. Eeciprocals of the "Weights. Seconds Corrected. 1 2 3 4 5 6 7 8 9 East end of Base. A 36382 36382 A B A M 36382 M A B B M 36382 M G B East end of Base. D 36382 E D 36382 E M 36382 O / II 42-57-54-13 56-26-44-43 80-35-22-86 21 7 16 1-63 0-84 1-37 // 53-72 44-22 22-06 + 1-42 3-84 00-00 53- 2-40-13 82- 0-18-26 44-57- 1-03 12 8 15 3-53 3-96 1-65 40-25 18-68 1-17 - 0-58 9-14 00-00 47-5630-52 32-38-48-61 99-24-33-67 12 16 15 605 2-56 3-68 35-73 50-11 34-16 - 7-20 11-29 00-00 35-23-31-03 34- 3-49-46 110-3246-99 8 8 15 2-48 6-29 1-54 29-11 44-99 45-90 + 7-48 10-31 00-00 65-35-45-96 68- 2-19-60 46-21-53-42 18 20 12 1-45 1-59 4-08 46-87 19-22 63-91 - 1-02 7-12 00-00 85- 1-51 -57 28-47- 3-49 66-11- 0-76 19 17 14 1-49 1-99 1-62 62-61 5-21 2-18 - 4-18 5-10 00-00 75 -45 -50 -62 47-37-41-29 56-36-25-51 20 19 14 2-85 1-60 1-96 52-08 42-12 25-80 - 2-58 6-41 00-00 84-38-58-14 51 •28- 66- 03 43 •52- 3-01 13 19 14 1-82 1-67 4-33 59-09 56-91 4-00 - 2-82 7-82 00-00 53 -IS- 15 -73 47-13-10-94 79-31-35-08 13 20 16 4-21 1-61 2-48 15-72 10-30 33-98 + 1-75 8-30 00-00 2 B 340 VERIFIC ATIOIir AND EXTENSION OF LA CAILLE'S AKC OP THE MERIDIAN. BASE-LINE —TABLE V-com*. No. of Triangle. NAMES OF STATIONS, Observed Angles. Number of Observations. Eeciprocals of the Weights. Seconds Corrected. 10 11 12 13 14 15 16 17 18 c M E East end of Base. E 36382 M 23992 C M G C G C K 9712 West end of Base. K 9712 G K 9712 K C 6 C 9712 O / It 58-56-11-86 60- 5-66-40 60-^-56-65 19 12 11 1-53 2-79 7-49 ft 11-43 54-06 54-51 + 3-91 11-81 00-00 40-29-26-73 39-2- 1-71 100-28-28-96 15 12 16 1-21 3-01 2-09 26-52 3-68 29-80 - 3-60 0-31 00-00 72-41 51-63 74- 14- 10 50 33- 4- 3-lQ 10 10 22 3-04 2-69 1-74 49-35 8-71 1 94 + 5-23 7-47 00-00 99-36-44-24 35-41-31-61 44- 41 -44- 86 24 17 20 108 1-56 1-44 43-81 31-42 44-77 + 0-61 4-08 00-00 56- 4-35-82 63-30-42-70 60-24-44-69 18 23 12 0-83 0-85 3-62 35-31 42-18 42-51 + 3-21 6-20 00-00 103-14 300 36-69-41 16 39-46- 9-88 24 10 16 1-73 2-12 0-79 4-91 44-11 10-98 - 5-96 4-64 00-00 103-52 51-10 34-11-10-39 41-66-59-81 21 12 20 1-79 1-99 1-17 49-29 10-71 60-00 + 1-30 4-95 00 00 49-22 2208 102-20-43-50 28-16-57-71 5 5 13 2-61 0-24 1-33 19-83 43-34 56-83 + 3-29 4-18 00-00 90- 16 -48 -75 35-13-43-00 64-30-30-39 14 11 17 1-33 3-68 1-89 48-43 42-11 29-46 + 2-14 6-90 00-00 VERIFICATION OF THE BASE BY TRIANGULATION. 341 BASE-LINE.— TABLE V-cod*. No. of Triangle. NAMES OP STATIONS. Observed Angles. 1 ^ J Reciprocals of the Weights. Seconds Corrected. 19 20 21 22 23 24 9712 K 17797 K 17797 West end of Base. 9712 West end of Base, Uyle Kraal. 9712 Uyle Kraal. 17797 G K West end of Base. Uyle Kraal. 9712 M* or // 76-45-50-24 47-12-44-84 56- 1 •30-33 20 22 7 1-74 0-70 1-50 47-96 43-84 28-20 + 5-41 3-94 00-00 86-58-54-86 56- 1-24-51 36-59-39-45 16 7 10 0-81 1-50 2-12 - 1-18 4-43 93-16-28-71 58- 4- 9-22 28-39-22-40 24 14 25 1-36 3-52 1-13 28-84 8-87 22-29 + 33 6-01 00-00 86-43-24-08 25-45-41 -33 67-30-55-54 25 23 11 2-19 1 33 3-96 24-03 41-10 54-87 + 0-95 7-48 00-00 46-58- 9-26 81-42-10-21 51-19-36-31 8 15 14 5-27 1-57 1-49 - 4-22 8-33 50-20-34-32 86-43- 4-73 62-56-20-95 11 5 J 7- • Not measured. 5. Comparison of the several Sections of the Base with the first. The following table exhibits the calculation of the lengths of the sections (excepting the 4th) from the first section as a base, through the chain of triangles to the north of the line, — the best conditioned and the best measured. The undulations of the ground disconnected the chain at the 4th section, but that section has been included with others in a way to verify its length. 342 VERIFICATICiN AND EXTENSION OF LA CAILLE'S ARC BASE-LINE. -TABLE VI. OP THE MERIDIAN. No. of Triangle. NAMES OP STATIONS. Angles. Log Sines. Log Sides. Sides in feet: computed. Sides in feet: measured. 7 8 9 10 12 13 14 23 20 19 15 21 22 24 D 36382 East end of Base. E 36382 D M E 36382 C M E 23992 M C G C M K G C West end of Base. K G 17797 K West end of Base. 9712 K 17797 West end of Base. 9712 K Uyle Kraal. 9712 West end of Base, 17797 9712 Uyle Kraal. M* 9712 Uyle Kraal. 47-37-42-12 56-36-25-80 76-45-52-08 9-8685204 9-9216431 9-9864550 3-8086517 3-8617744 3-9265863 Seetion 1 = 6436-529 84-38-59-09 43-.52- 400 51-28-56-91 9 9981038 9-8407310 9-8934386 3-7692135 3-8219211 47-13-10 30 53-15-15-72 79-31-33-98 9-8656732 9-9037949 9-9927028 3-8600428 3-9489507 7245-073 Section 2 7245-045 58-56-11-43 60- 5-54-06 60-57-54-51 9-9.327761 9-9379602 9-9416727 3-9541348 3-9578473 74-14- 8-'71 72 -41 -49-35 33- 4- 1-94 9-9833500 9-9798876 9-7368922 3-9543849 3-7113895 5145-050 Section 3 5145-030 35-41-31-42 44-41-44 77 99-36-43-81 9-76.59878 9-8471667 9-9938596 3-9578473 4-0390262 4-1857191 60-24-42-51 56- 4-35-31 63-30-42-18 9-9393179 9-9189646 9-9518355 4-1653658 4-1982367 14634-091 51-19-3706 81-42-11-01 46-58-11-93 9-8924978 9-9954305 9-86391.52 4-3011694 4-1696541 56- 1-24-91 86-58-55-08 36-59-40-01 9-9186948 9-9993972 9-7794071 4-2-503565 4-0303664 17797-398 Section 5 and 6 17797-343 76-45-47-96 47-12-43-84 56- 1-28-20 9-9883059 9-8656217 9-9186994 3-9076822 3-9607599 8085-040 Section 5 8085-046 36-59-44-11 103-14- 4-91 39-46-10-98 9-7794186 9-9883093 9-8059788 4-1696506 3-9873201 9712-256 Section 6 9712-297 28-39-22-29 93-16-28-84 58- 4- 8-87 9-6808363 9-9992903 9-9287474 4-3057741 4-2352312 67-30-54-87 86-43-24-03 25-45-41-10 9-9656632 9-9992894 9-6381144 4-2688574 3-9076824 8085-044 Section 5 8085-046 42-56-20-96 86-43- 4-72 50-20-34-32 9-8332882 9-9992871 9-8864215 4-2352312 4-4012301 4-2883645 19425-156 Sections 3/4, '& 5 19425-157 This angle was not measured. VERIFICATION OF THE BASE BY TRIANGULATION. The following results are deduced from the foregoing table : — 343 Measured. Calculated. Differences feet. feet. foot. Section 1 = 6436-529 Base. 1 2 = 7245-045 7245 060 - -015 3 = 5145-030 5145-050 - -020 5&6 = 17797-343 17797-398 - -055 5 = 8085-046 8085-042 + -004 6 = 9712-297 9712-256 + -041 3,4&5 = 19425-157 19425-156 + -001 Comparison of the calculated with the mea- sured Sections. The comparison of sections 3, 4, and 5 are effected by means of a triangle, of which two angles only were measured : but another combination is deduced by calculating the side C — K of the triangle C, G, K (a), from each of the other five sections, as follows: The mean of the five determinations of C— K is 14634-036 feet [4-1653642]; which gives [4-0390246] and [4-3011678] for the logarithms of the sides M— G, and west end of Base — G; of the triangle M, G, west end. With these two sides, and the included angle at G (138°-44'-18"-66), the sum of the sections 3, 4, 5, and 6, is 29137-595, the measured length is 29137-455. 6. Calculation of the side C — K, of the triangle C G K, from the several sections of the Base, excepting the Ath. BASE-LINE.— TABLE VII. No. of Triangle. NAMES OF STATIONS. Angles. Log Sines. Log Sides. C— K. Section. 9 10 13 14 E M 36382 C M B G C M K C G O / // 5315-15-72 47-13-10 30 79-31-33-98 9-9^37949 9-8656732 9-9927028 3-8600411 3-8219194 3-9489490 feet. Section 2 ^ 7245-045 58-56-11-43 60- 5 54-06 60-57-54-51 9-9327761 9-9379602 9-9416727 3-9541331 3-9578456 35-41-31-42 44-41-44 77 99-36-43-81 9-7659878 9-8471667 9-9938596 4-0390245 4-1857174 60-24-42-51 63-30-42-18 56- 4-35-31 9-9393179 9-9518355 9-9189646 4-1982350 4-1653641 14634-034 Calculation of the probable error of the Base. 2 C (a) See the following table. 344 VERIFICATION AND EXTENSION OF LA CAILLE'S ARC OF THE MERIDIAN. BASE-LINE— TABLE VH-con«. *7. Calculation of the probable error of the Base. No. of Triangle. NAMES OP STATIONS. Angles. Log Sines. Log Sides. C— K. Section. 12 13 14 19 15 23 14 15 23 14 c M 23992 G C M K C G K 9712 17797 West end of Base. K 9712 G K West end of Base. C K G K West end of Base. 9712 G K West end of Base. C K G 34 72 74 / 4 41 14 / 1 49 8 94 35 71 9-7368922 9-9798876 9-9833500 3-7113879 3-9.^43833 3-9578457 feet. Section 3 5145-030 35 44 99 41 41 36 31 44 43 42 77 81 9-7659878 9-8471667 9-9938596 4-0390246 4-1857175 60 63 56 24 30 4 42 42 35 61 18 31 9-9393179 9-9518356 9-9189646 4-1982361 4-1663642 14634-037 47 76 56 12 45 1 43 47 28 84 96 20 9-8656217 9-9883059 9-9186994 3-9076825 4-0303667 3-9607602 8085-046 Section 5 36 39 103 59 46 14 44 10 4 11 98 91 9-7794186 9-8059788 9-9883093 3-9873204 4-1696509 46 81 51 58 42 19 11 11 37 93 01 00 9-8639152 9-9954305 9-8924978 4-3011662 4-1982335 63 60 56 30 24 4 42 42 36 18 51 31 9-9518356 9-9393179 9-9189646 4-1857159 4-1653626 14633-983 39 36 103 46 59 14 10 44 4 98 11 91 9-8059788 9-7794186 9-9883093 3-9873220 3-9607618 4 1696525 9712-297 Section 6 46 81 61 ■58 42 19 11 11 37 93 01 06 9-8639152 9-9954305 9-89-24978 4-3011678 4-1982361 63 60 66 30 24 4 42 42 36 18 51 31 9-9518355 9-9393179 9-9189646 4-1857175 4-1653642 14634-037 C — K from Section 1 has already been calculated. (No. 14, page 342). It will be remarked, that the last decimal place of the several values of C — K cannot be correctly taken from tables to seven places only. (Tables of greater depth are not available at the Cape). The result, however, would be little altered by confining the calculation to the nearest hundredth of a foot. It will also be remarked that the frequent repetition of the same triangle C G K might have been dispensed with, by taking the difference of the logarithms. But it is better to spare a little space, than to not exhibit the calculation in the usual form. "^ West End 385,. dofiis aiuoii j'MOj- dcrqs dSjo'i{ Jddd/i '4j ^ %' ^^ Si I ^ ■^ „ ■^ X5« ?$^ ^ TSi S?- S^ ?^ ■^ ^ ^ S.- tw ^" ft:- ^. ?^- ■is K- 'Va §^ t\. ^ ru r-v ^ ^ ^ '^ K ■-^ rv s- r ^ 1- ^ ^ V ^; ^ "X .\ S; 'X.' ?5 5^ ^ ^ -K^; s.^. vg ^. ^, ^ -ss Jl ?c ^ ^ 1 ft -^ 'i:) ~as si- \-. ^1 "si ^ « -5 1 .1 ^ ^ ■^ N ^ U^ -L. 4 ^ i tt f^ .. '-^ m-^ ss •^^^.^.^- =--i*V^, &■ 4 W SI ?>- ^ 5^* I I ^ ia '^ '\^ ^ f 1 s ^ -^- ^ % 1^ a 'N ^ ^ ^ 1 u ^ '^ ^' .^^ CALCULATION OP THE PKOBABLE ERROR OF MEASUREMENT. 345 The weight given to each determination of C — K, is the fraction whose numerator is § ?• the length of the section from which the determination is deduced ; and the denominator the prohaWe" the sum of the sections. Section 4 has been omitted, because it cannot be calculated Se." independently. Section. Calculated lengths. "Weights. Products. Differences. Squares of differences. 1 2 3 5 6 feet. 14634-091 14634-034 14634-037 14633-983 14634-037 -176 •198 •140 -221 -265 •0160 -0067 '0052 -0038 -0098 -057 •000 •003 •051 ■003 -00325 -OOOOO •00001 •00260 •00001 1-000 •0339 -00587 '•00587 X •454936 = -0115 foot = -138 inch. \/ 5'^ - 5 The length of C— K is therefore 14634-034 feet, with a probable error of ±'14 inch, equivalent to '41 inch on the length of the Base. This result is meant to shew that the error of measurement is small, rather than the exact numerical value of the probable error : for a small, yet plausible, alteration in the distribution of the theodolite work errors would alter the numbers. Upon the whole, however, so far as it may be worth consideration, the triangulation of the Zwartland Base contributes to the increase of confidence in compensation bar measurement. The labour of the measurement is another matter : — the trial to the eyes of so many optical adjust- ments, when the summer sun is strong and the heat great, can only be appreciated by experiment. Yet there is a variety in carrying out the details of actual measurement, which relieves, and for which there is no substitute in the comparisons of the measuring bars inter se, and with the standard. Here there is a constant strain of mind and eye in search of accordant results, baffled by ever varying temperature, which disheartens and depresses. But these personal considerations dwindle to nothing, in comparison with the degree of accuracy which Colby's compensation apparatus appears to be capable of affording. 346 VERIFICATION AND EXTENSION OF LA CAILLE'S ARC OP THE MERIDIAN. § *• § 8. Comparisons of the Compensation Bars with the Standard Iron Bars. 1. Particulars relating to the arrangements. The first experiments for obtaining the relative lengths of the compensation and standard bars were made under the zenith-sector tent, in the Observatory grounds, where two ancient pillars of brick masonry stand, which by chance are 10 feet apart. Stones were let into these pillars for carrying the microscopes, but the results from a few experiments proving unsatisfactory, the microscope stones were removed from the pillars, and fixed in the east wall of the telescope room. This room having a southern aspect, and an area of nearly 28 x 23 feet, preserves a pretty uniform temperature ; but a block of masonry disconnected from the boarded floor, for supporting the bars, could not be built up from the foundation underneath, before the arrival of the time for removing the instruments to Zwartland. Immediately after deciding upon the direction of the Base-line; a barn near the west end was hired of the Koekoek farmer, wherein two pillars were built of stone and lime masonry, to carry the Ordnance microscopes. Between this spot and the east end of the line, there was no house or hut of any description, excepting the Coggera farm, distant about three miles, — and Buckle's farm, distant about four miles from Coggera; and neither of these within a convenient distance from the line. Early experience had shown that no ordinary canvass covering would be a suffi- cient protection against rapid temperature changes ; also that the time absorbed in conveying the bars to fixed microscopes, and comparing them there, would seriously retard the measurement of the line. To meet the first as far as practicable, it was Microscopic *^ beamcompass proposed to sink pits and cover them with bush ; and the last by a microscopic beam ana compan- . . son sheds. compass, if it could be made sufficiently stiff" to slide along a smooth surface, without sensible flexure, so that the microscopes might be brought in quick succession over the several bars resting on their camels. Accordingly, the Cape micrometer microscopes A and B were attached to trussed arms, projecting from a trussed plank of well-seasoned pine (saturated with oil), 3 inches thick and 9 inches in depth, having foot pieces at right angles to the plank, which rested upon a quadrilateral frame of pine, of the same thickness and depth of material ; and of dimensions sufficient to enclose the standard iron bar B, and the five compensation bars. The upper surface of the side pieces of the frame, and the lower of the foot pieces, were planed true and smooth, and polished with black lead ; so that by slight force, applied in the proper direction to the ends of the foot pieces, the beam could be slided along. The frame rested upon a ledge cut in the bank of the pit, wherein spare trestles were placed to carry the bars. Over the pit a shed was constructed of bush and canvass, to screen the interior from the sun aqd weather. COMPARISONS OF THE COMPENSATION BARS WITH THE CAPE STANDARD BARS. 347 The first comparisons by the agency of this apparatus were discordant, the chief § s. cause of which was traced to lateral contact of the frame guide-flanches with the foot beam compass pieces ; the flanches were therefore removed : still the residual discrepancies were at son sheds*" times sufficient to create a doubt of the efficiency of the apparatus, until experiments were made under a shed where the microscopes were attached to stone piers, when it was found that a portion of them were due to change of temperature during the com- parisons, although the time required for making the comparisons had been materially diminished. Three pit sheds were constructed for the beam compass (numbered consecutively 1, 2, 3) at 12127, 19897, and 25500 feet, reckoning from the west end of the Base, In the middle of February, stone pillars were erected near the point M (plan of the stone pillars. triangulation, page 335) ; and early in March, at a point rather more than half way between M and the east end of the line (the shed covering like the former, consisting of bush) : hence, including the barn, there were six sheds along the line for comparing bars. On the return of the apparatus to the Royal Observatory, arrangements were made Arrangements for determining, with all practicable accuracy, the relative lengths of the two iron bars at the standards and the five compensation bars. In the telescope room before mentioned, ^^'^^^ "^' and under the microscope stones projecting from the east wall, rather more than 8x4 feet of the boarded floor was cut out, to allow of a solid block of masonry, topped with flag stones, being built up to its level from the foundation without touching it; and upon this firm and independent bearing was placed a strong and well-braced frame of pine-wood, with a sliding board and appliances for the camels. Considering the dimensions and position of the room, a better for the purpose could scarcely be found above ground, excepting the exposure of the east wall to the morning sun : the experiments, however, were made between the 19th of August and 9thi of September, when the action of the sun at the Cape is comparatively weak. 2. Runs of the Cape Micrometer Microscopes A and B, and of the Ordnance Micrometer Microscope. The runs of the microscopes A and B were not altered between the 14th of August, ^nerationof 1840 (the date when they were first used), and the 23rd of February, 1841, when the "^Xii^^ object glasses were moved to bring the runs into closer coincidence with each other. The runs were again altered on the 4th of March, 1841, in shed No. 5, after which the object glasses were not disturbed. The whole of the comparisons between the compensation and standard bars were made with these microscopes, except those in the barn at Koekoek Valei, during the interval between the 14th of October and the 16th of December, 1840, which were made 348 VERIFICATION AND EXTENSION OF LA CAILLE'S ARC OF THE MERIDIAN. Ordnance microscopes. Reference scale. Examination of its divisions — 6 inches. with two microscopes belonging to the compensation bars; one furnished with a micrometer, and the other witfi a fixed wire. The four feet brass scale by Dollond, divided to inches and tenths of inches by lines, was used for converting the revolutions of the several micrometer microscopes into fractions of an inch. The late Mr. Frances Baily compared this scale with the Royal Astronomical Society's, in the year 1839; and found its total length equal to 47*997083 standard inches of that scale. The subdivisions were not examined. The scale was unfortunately placed on the base-line, in the way of a waggon wheel (page 243), which broke the case and curved the scale near its middle, leaving the distance on each side uninjured. Assuming the six inches, from to 6, to be the 8th part of the scale ; it became expedient to examine how far each subdivision could be taken as the 60th part of the six inches, and the relation of this 60th part, or the mean tenth of an inch, to the tenths which had been used for the runs. The first examination was made in shed No. 5, on the 22nd of April, 1841, by comparing each tenth in terms of microscopes A and B, when the results appeared as follows : — Microscope A. — Mean 0-1 inch = 20-0315, temperature 66*59 = 20*0303, temperature 62. „ B — Mean 0*1 inch = 19-9429, temperature 74-98 = 19-9402, temperature 62 / o Tev. Hence in temperature 62, 1 of A = -0049924 inch. 1 of B = -0050150 inch. The second examination was made in the telescope-room of the Royal Observatory, on the 22nd and 23rd of February, 1844, no intentional alteration of the runs having been made in the interim : — reT- o rev. c Microscope A.— Mean 0-1 inch = 19-9681, temperature 76-10 = 19-9651, temperature 62. „ B.— Mean 0-1 inch = 19-8534, temperature 73-18 = 19-8511, temperature 62. 12-0— 12-1 inches. Hence, 1 in temperature 62 of A = -0050087 inch. „ B = -0050375 inch. On the same occasion, Mr. Mann examined the micrometer value of 120— 12*1 inches, as follows : — Microscope A.— 12 • 0— 12 - 1 inch = 20 - 0089, temperature 76 * 98 = 20 ■ 0058, temperature 62. B.— 12 •0-12*1 inch = 19 • 9262, temperature 76 ■ 93 = 19 -9231, temperature 62. Value of the mean 0-1 of the first inch, and of the first two inches. This interval, therefore, exceeds the mean 0*1 inch, by -0002832 = 00564. From the several examinations of the first six inches ; the mean 0*1 of the first inch, and the mean 0*1 of the first two inches are less, respectively, by -0000336 and -0000108 inch, than the mean 0-1 of the first six inches taken as the standard. COMPARISONS OF THE COMPENSATION BARS WITH THE CAPE STANDARD BARS. 349 In shed No. 4, on the 22nd of February, 1841, two fine dots were made on the fj^j lots on the 6-inch brass standard, in the position with respect to the engraving upon it, thus — st^'a'ard dotfl* "Standard at 62° Fahrenheit." The interval between them was measured by Captain Henderson, Mr. Maclear, and Mr. Smyth, and the mean results were in terms of rev- Microscope A, 18-692. „ B, 18-375. On the following day, and after the alteration of the runs, ref. Microscope A, 18 "570. „ B, 18-596. Again, with great care at the Royal Observatory, in February, 1 844 : rev. o rev' A, 18 • 9154, temperature 78 • 63 = 18 ■ 9121 ) B, 18-7966, „ 76-05 = 18-7938 } ^^'^P^'^^'^'-^ 62°. which gave for the length of the interval, in terms of the mean O'l inch, "0946997 inch. These dots were occasionally referred to in the latter part of the operation, for Lines on gold detecting any variation of the runs : but although more delicate, they were not so con- standard. venient nor so generally employed for the same purpose, as two lines which were drawn on each of the gold studs of the 10-feet standard. August, 1840, the scale division was 12-0 — 12'1 inches. Runs of micTOECopes '«'• ° '="• employed in Microscope A, 19-9113, temperature 71-90 = 19-9092 ) the reductions. B, 19-5820, „ 71-95 = 19-5800 I *«'°P^''^"^''« ^^ ' But this division exceeds the mean 0*1 inch by '0002832 ; the run of rev. A therefore becomes 19 ■ 8528. of B „ „ 19-5245. which values have been used in the reductions prior to February 23, 1841. rev. Feb. 23. Microscope B. — Mean of 10 measures over the first inch = 19-6391 „ 20 „ „ first two inches =16-5328 5 „ over 12-0-12-1 = 19-7176 „ 3 „ „ 12-0-12-1 =19-6089 - fev- The mean of these determinations, in terms of the mean 0-1 inch, is 19-5822, By the dots on the 6-inch standard, the run of Microscope A = 18-570 x 19-5822 'Z^.c 18^596 = 19"^^^' reV" rev* which values, viz. : 19*5822 and 19*5548, have been used in the reductions from February 23 to March 4. 350 VERIFICATION AND EXTENSION OF LA CAILLE'S ARC OF THE MERIDIAN. §8. After March 4, the runs deduced from the examination of the mean O'l inch of the Buns of . , . Microscopes first six inches, eflPected on the 22nd and 23rd of April, has been used;— viz. : employed in ^^_ thereiiuctions. __. . „„ «„„„ Microscope A, 20-0303. „ B, 19-9402. On the 13th and 15th of October, 1840, the scale division was 12*0 — 12-1 inches, Run of nucroscope. and the run over it reduced to 62 = 206065. Subtracting 0-0584 for the excess of rev- that division over the mean 0-1 inch, the run becomes 20-5481 ; which value has been used for the comparisons made with the Ordnance microscope, in the barn at Eoekoek Valei, between October 14 and November 30. It is unnecessary to give at full length the details of the partial experiments upon which the foregoing determinations are founded. For arithmetical convenience in the reduction of the comparisons of the bars, the microscope readings were corrected to what they would have been if 20 revolutions of the screw had been exactly equal to O-l inch, or one revolution = -005 inch. 3. Expansion of the Cape 10-feet Iron Bars A and B. Brperiments Previous to the discussion of the Base-line comparisons, it is necessary to refer to in London :on . oi ■ ■ ^ the expansion experiments for determining the expansion of the standards. A and B. Before forwarding the bars from England they were subjected to experiment, under the superintendence of the Astronomer Royal, G. B. Airy, Esq., in a cellar of their makers house, Messrs. Troughton and Simms, — the result of which is embodied in the following extract from a communication tome, from Mr. Airy, dated August 13, 1840: — " By examination of Cape Bar A, the expansion of 10 feet of iron for 1° Fahrenheit appears to be o o inch. From 45 to 59 Fahrenheit 0-000714 „ 59 „ 74 „ 0-000734 „ 74 „ 79 „ 0-000757 „ 97 „ 119 „ 0000798 „ 119 „ 139 „ 0-000864. By examination of Cape Bar B, the expansion of 10-feet of iron for 1" of Fahrenheit appears to be From 44 to 65 Fahrenheit 0000745 „ 65 „ SO „ 0-000732 „ 80 „ 105 „ 0-000741 „ 105 „ 121 „ 0-000817. It is important to observe that the expansion for 1° increases as the temperature rises. COMPARISONS OF THE COMPENSATION BARS WITH TPIE CAPE STANDARD BARS. 351 " In the reduction of the comparisons in which all the temperatures are near 45°, to be reduced to 62°, I have used 0-000730 (the mean of the two results for that part of the scale). This is considerably less than you will usually find in tables of expansion ; but I have no doubt that the tables are wrong, for the following reason. The expan- sions have always been determined by comparing the lengths at 32° and 212° : but if (as appears above) the expansion increases rapidly with the rising temperatures, it is plain that the number so obtained is much too large for temperatures near 59° or 60°. In. in. Taking therefore 0-000730 for the iron, and 0-001257 for the brass (which is the number adopted by Mr. Baily, though for the reason above it may be erroneous, as it was determined by 32° and 212°). I obtain as follows, (all being reduced to 62° Fahrenheit) :— Experiments in London : on tlie expansion of iron l)ars A and B. Cape Bar A Cape Bar B = Simm's Standard = Col. Colby's Bar No. 1 = Col. Colby's Bar No. 2 - = double Astronomical Society's Scale — 0-003 1 2 = do. do. - 0-00361 = do. do. - 000265 do. do. -0-00179 do. do. 0-00150." Relative lengtlis of Cape Stand- ards A and B, Ordnance, and Royal Astro- nomical Society's. The rate of expansion given for the lower recorded (a) temperature of bar B presents a singular anomaly, of which there is no trace in the expansion of bar A. Assuming homogenity in the elementary molecules of the bar, it may have been produced by some accidental influence, which might not recur. The following table gives the mean expansion in relation to the arguments of temperature for both bars, deduced from a mean curve, which equally distributes the minute differences : — BASE-LINE.- -TABLE VIII. Temp, of Bar. Expansion. Temp, of Bar. Expansion. Temp, of Bar. Expansion. temp, of Bar. Expansion. o in. o in. o in. o in. 45 0-000730 59 0-000732 73 0-000737 87 0-000748 46 730 60 732 74 737 88 749 47 730 61 732 75 738 89 750 48 730 62 732 76 739 90 752 49 730 03 733 77 739 91 753 50 730 64 733 78 740 92 754 51 730 65 733 79 741 93 756 52 731 66 734 80 741 94 757 53 731 67 734 81 742 95 759 54 731 68 734 82 743 96 761 53 731 69 735 83 744 97 763 56 731 70 735 84 745 98 765 57 731 71 736 85 746 99 767 58 0-000731 72 0-000736 86 0-000747 100 0-000769 Mean expan- sion deduced from a curve drawn throu^ii Mr. Airy's numbers. (a) Table XV contains the experiments forwarded by the Astronomer Royal. 2 E 352 VERIFICATION AND EXTENSION OF LA CAILLE'S ARC OF THE MERIDIAN. 1 8. The following; table gives the expansions employed in the reduction of the micro- meter measures of the iron standard B, to 62° Fahrenheit, taken during the measurement of the Base-line. It is deduced from the preceding table (Base-line table VIII), by taking the mean of all the expansions corresponding to the given temperature, and 62° inclusive. In the reduction of the comparisons of the standards A and B, made in the telescope room of the Royal Observatory, inter se, the rate of expansion was taken at 0007312 o rev- for 1 of Fahrenheit: the equivalent in terms of the micrometer is 0* 14624. In the reduction of the comparisons of the compensation bars with the standard bars in the telescope room of the Royal Observatory ; the rate of expansion of the standards in. rev. o was taken at 00007316, equivalent to 0'14632 of the micrometer, for 1 Fahrenheit: — BASE-LINE. — TABLE IX. Table for re- flucing to 62° the compari- sons made with standard B, on the Ease-line. EXPANSION. EXPANSION. EXPANSION. 1 Temp, of Bar. Temp, of Bar. Temp, of Bar. EoT olutions: Re^ solutions : Bevolutions :| Inch. "• Id. Inch. '• in. Inch. '■ iD. 1 = -005. 1 = -005. 1 = -005. o o o 53 0- 0007314 14628 66 0-0007330 14660 79 0-0007359 14718 54 •0007314 14628 67 •0007333 14666 80 •0007362 14724 55 •0007315 14630 68 •0007333 14666 81 •0007365 14730 56 •0007316 14633 69 •0007335 14670 82 •0007368 14736 57 •0007317 14634 70 •0007336 14672 83 •0007371 14742 58 •0007318 14636 71 •0007340 14680 84 •0007374 14748 59 •0007320 14640 72 •0007341 14682 85 •0007378 14756 60 •0007320 14640 73 •0007343 14686 86 •0007382 14764 61 •0007320 14640 74 •0007345 14690 87 •0007385 14770 62 •0007320 14640 75 •0007348 14696 88 •0007390 14780 63 •0007325 14650 76 •0007351 14702 89 •0007393 14786 64 •0007327 14654 77 •0007353 14706 90 0-0007398 14796 65 0- 0007328 14656 78 0^ 0007356 14712 Comparisons made on the Base-line. 4. Reduction of the readings of the Standard Bars B and A to 62° Fahrenheit, for comparison with the Compensation Bars. The comparisons of the several bars at the Base-line (and subsequently at the Obser- vatory) were made by myself, Mr, Smyth, and Mr. Maim, excepting a few in the early part of the operation (in the barn at Koekoek Valei), where Captain Henderson took a share. Three partial measures by each micrpscope were registered for a comparison of each bar. The standard was first brouclht under the microscopes, next the compensa- tion bars in succession, then the standards ; and the mean between the two i-eadings of the standard was taken for the comparison with the compensation bars. When several sets of comparisons were taken in succession, the rule to calliper the readings of the compensation bars, by the readings for the standard, was not altered. COMPARISONS OF THE COMPENSATION BARS WITH THE CAPE STANDARD BARS. 353 Base-line table X, presents an abstract of the reduction to 62° Fahrenheit of the s g. readings of the standard B, when compared with the compensation bars (a). The stendarTbar calculations in greater detail would consume too much space. ^ *° *^°' The first and second columns give the date, and the significant number of each comparison : The third gives the sums of the microscope readings, corrected to 20 revolutions of the screw for O'l inch : (b) The fourth gives the mean of the readings of the two attached thermometers (/°), whose bulbs are immersed in olive oil within holes in the bars ; and the fifth gives their differences from 62° : The sixth gives the expansion, in terms of the micrometer corresponding to 62 — 1°, extracted from the last table (Base-line IX) : And the seventh (the sum or difference of the third and sixth) gives the sums of the microscopes reduced to 62°, which are immediately comparable with the readings of the compensation bars, for difference in length. Base-line table XI is similar to X : it gives the reduction to 62° of the standard Keduction of bar A, for the instants of comparison with the compensation bars; which comparisons a to 62°. were all made in the telescope room of the Observatory, after the measurement of Ihe Base. 5. Abstract of the Comparisons of the Compensation Bars, with the Standard B, reduced to 62° Fahrenheit. The trial comparisons in the Koekoek Valei barn, between the standard bar B and the compensation bars, which were made by means of the beam compass, before that mstrument was properly trussed, have not been used in the calculations : nor two sets on December 21 and 22, made in shed No. 1, when microscope A was discovered to be loose: these comparisons, therefore, are not printed. Base-line table XII, exhibits the differences, in terms of the micrometer, between the standard B reduced to temperature 62° and the several compensation bars ; where one revolution of the micrometer equals "005 inch. The numbers do not present the degree of uniformity, which might have been expected to result from the care that was taken in every detail of the experiments. One of the prominent features is the greater accordance among those made in the more uniform temperature in the telescope room of the Observatory, where also the several appliances were more perfect than could be secured in the open plain. Another is the unexpected fact, that several of those (a) Standard B was employed on the Base-line : A was left at the Observatory. (h) The screw heads were turned towards the centre of the bar, .■. a greater reading implies a greater length. 354 VERIFICATION AND EXTENSION OF LA CAILLE'S AEC OF THE MERIDIAN. § 3. made in the barn at Koekoek Valei, where the microscopes were attached to stone pillars, and the temperature more uniform than in the sheds, present such grave anomalies as to render it doubtful if they should be taken into account in the reductions. In general, the comparisons made on the Base-line, by means of the microscopic beam compass, are not so accordant as those with the microscopes attached to stone pillars ; yet it will be seen hereafter, that their means differ from each other by only •000012 inch on 52| feet. The first column of the table gives the dates. The next columns, headed by the distinguishing letters of the compensation bars, exhibit the differences of each from the standard. The eighth column gives the sum of the differences, and the ninth and tenth give the mean temperature of the standard bar and of the air during the time of experiment. (Base-line table XIII, gives a similar abstract of the comparisons of the compen- sation bars, with standard bar A reduced to 62° Fahrenheit, which were made at the Observatory, after the measurement of the Base. No use has been made of this table ardAwiththe jn calculating the length of the Base.) compensation o o / bars. Table XII, shewing the differences giyen by the comparisons of the stand- ard B with the compensation bars. Table XUI, shewing the differences given by the comparisons of the stand- ( Continued at page 359). COMPARISONS OF THE COMPENSATION BARS WITH THE CAPE STANDAEP BARS. 355 P % Q '■I CO W H W H < ffl o M . '^ H (^^ S o fa H !*< O "» 02 o 03 h- 1 P3 <1 Oh o a H O m 1^ tJ 03 W w H O f-i o ■< Pi H CO CQ O H ft EI O u ft oek Valei from these ipancies. piers. piers. earn. earn. earn. iers. iers. , 1840, asured, h bars ader of except d with ■•.:a^j2&B< to u .-s-a,,-?; BSooooo t,g gl'^S oo-a'OTJ'ana go ^.-c ~S " " i g S i g -g ''^ g'a<1^ « 0) o 03 O +J to a It- -o o OJ « 0) 1S3 ^ s|| ■2 si ^^iiisi o°^ i"l»^ g^^^g^i ; a 1 O rH " 2«.S^-E .9 '3 a CO -^ CO CM t-- t^ Tj CD CD CD OS CD t-- oi r- OS oi CD CO a ) 00 00 00 OS c (N ot o o o oo o c o o o o o o o o o o o o c o o o o 6 o O O c?) O -^ l> w s o to in in CD 1-- a5 ^ ,-H r- CO t^ »n c CO CO tP OS ■^ -«* a i 53 CQ ■a 50 iSi CD Tf m Tf a ) (N . t^ CO O) CO CO CO CO CO CO CO c } CO CO CO Ti» CO ■* ■* CO w:) o OS 00 Tj t- t-. TV _, CD o CD i o i O O »rt t~ 00 (N c 3 O Ol *-- ■* 'M eq 5 Tj* 00 --< CO cq "ft a ■* in -* r- 00 r>. 1 nH (M ^ .— ,- (N CN Tj- O t^ 5^ CO '# « 5 CD « OS 00 CO 00 . GO ■* 00 OS —1 to 0* ) CD Tl* CI 00 -^ i H =3 i-H or ifs OS CO — ' c > (N r- »n »n 00 Tl< ^ o o o o o c o o o o 1 ^ '"' &H cq 'cf* CO CD O J-- O C OS tv ^ 00 CT « p- <-< O CM -^ OS 00 "^ .-< r. »n CO M 00 u > S Tt< »n T(* >n ^ c-i a r* CO Tfl ^ O ^-< r- O -H C CT l-H IN 1 r- ^ '"' r-* ^ ■"* ■ u CO tJ* OS CO 00 CO «■ ■* (N CO 00 CO OS . « - t> Tt< t^ ^ . -: -fc; .& rH CO r-t Ol ^ O CO CI in t^ CO o a> IgM — " — ,-^.^-^ — -^ .^^ — , 1 o Pi : o S^ - m O ■ m O ; M CJ C^ i-< C5 CQ g i S o 03 ™ SS : §^ : g 'Jf _ _ 0-00002225 20 O C 6-inch ^ _0^ _ ^0-00002225 + 0-0000069^ 20 V / 20 O, 0-00002915 foot: 20 and putting O, = 10 feet. C 6-inch ^ 0-5 - 0-00002915 foot. Consequently 0-00002915 x 4077-5 microscopes = 0-118858 foot; to be deducted from the approximate length of the Base-line. 358 VERIFICATION AND EXTENSION OF LA CAILLE'S ARC OF THE MERIDIAN. Length of Zwartland Base, in terms of Ordnance Bar O, I/cngth of Zwartland Base, in terms of Ordnance Bar O,. Apparent Length in terms of Compensation Bars 42818-75000 I. Excess of Compensation Bars above Cape Standard B + 131753 II. Defect of Bar B below Ordnance O, - 61252 III. Defect of Cape six-inch Standard, below mean half foot of O, — 0-11886 Page 335 Expansion of Cape six-inch Standard, above 62° + 0-11724 Page 317 Reduction to Level of the Sea Page 315 Correction for Errors of Alignment - 0-38750 - 0-00056 4281906533 The length of the Zwartland Base-line, in terms of the Ordnance Standard O,. at the temperature 62° Fahrenheit, and at the level of the Sea = 42819065 feet. Log. 4-6316371-4. COMPARISONS OF THE COMPENSATION BARS WITH THE CAPE STANDARD BARS. 359 (^Continued from page 354). 6. Abstract of the direct comparisons made in the telescope-room of the Observatory, §8. between the two \0-feet Cape Standard Bars A and B, and calculation of their difference in length. The bars were compared for length in London through the intervention of the Royal Experiments . ^ ^ ° •'in London. Astronomical Society's 5-feet scale (page 351). The experiments for this purpose and for the thermal expansion, are given in extenso after table XIV, at the end of this section, as received from the Astronomer Royal. On the arrival of the bars at the Cape, and before B was removed to Zwartland. Comparisons . ' ' for the differ- 24 comparisons were made in the telescope-room of the Observatory, — the supports ence in length resting upon the boarded floor. After the measurement of the Base, and an interval the Cape, of twelve months from the first, 240 comparisons were made in the same room, — the supports resting upon the isolated pier ; bar A during the interval having remained undisturbed in the room, while B was on active service in the field. A third determination, or second indirect result, is available through the experiments for the relative lengths of both bars and the compensation bars, which were made in the same room, and under similar circumstances with the direct experiments. And here it is necessary to revert to the statement in the fourth article (page 352), No-of Wsec- that three partial measures by jeach microscope were registered for a comparison of each mean reading. bar; in other words, — each dot was bisected three times at each comparison. It should also have been stated, that this rule referred to the experiments at the Base-line, and to only a few in the telescope-room; but for the chief part of those made in this room, five bisections were made. A strict record has not been kept of the positions of individual observers with respect Personal Equation. to individual microscopes, except for the direct comparisons of the standards. In this instance, on the bar dots being brought into focus, Mr. Mann first stationed himself at microscope A, and registered the readings of five bisections, while Mr. Maclear or Mr. Smyth at microscope B did the same; the parties then changed places and repeated the bisections. The bar being replaced by the other, the same course with respect to order was pursued. The personal equations deduced from the experiments were not so accordant as might have been expected ; — a matter of no importance, since they are eHrainated by the method of combining the observations. Table XIV exhibits the direct comparisons and the results, from which it appears by 264 comparisons, that A— B =0-0001189 inch. A— B = 0-0001189 in. 2 O 360 VERIFICATION AND EXTENSION OP LA CAILLE'S ARC OF THE MERIDIAN. By the indirect process of the compensation bars : Compensation Bars — A = 0* 021721 inch. 37 comparisons. Compensation Bars — B = 0-021998 inch. 51 „ Hence A— B = 0-000277 By the experiments in London : Bar A = double Astronomical Society's scale — 0-00312 Bar B = double Astronomical Society's scale — 0-00361 Hence A— B = 0-00049 inch. The result from the compensation bars is comparatively of little value perhaps ; but why the London should differ from the Cape determination, by so much as 000371 inch, is difficult to conjecture. END OP THE DESCRIPTION OF THE MEASUREMENT OF THE BASE. REDUCTION OF STANDARD B TO 62° FAHRENHEIT. 361 BASE-LINE.— TABLE X. Reduction of the readings 9/ the Standard bar B to 62° Fahrt, for the comparisons with the Compensation Bars, made at the Base-line. ■sl .a »- l°- o % .a»i §.2 — - Date. No. a o El S 62°— t U Is Date. No. ai ii 62°— «. 'iB n II |5 "1 |a i o Q, > l« 1840. rev. o o rev. rev. 1841. rev o o re'. rev. Oct. 12 1 2-1511 63-62 - 1-62 -0-2374 1-9137 Jan. 6 263 6-2639 64-20 - 2-20 -0-3224 5-9415 8 2'4508 65'85 3-85 0-5644 1-8864 269 6-2718 65-10 3-10 0-4543 5-8175 13 10 1-6955 66-33 4-33 0-6348 1-0607 270 6-3264 65-30 3-30 0-4837 5-8427 16 2-1102 68-83 6-83 1-0020 1-1082 276 6-2438 66-25 4-25 0-6231 5-6207 23 2-1725 70-72 8-72 1-2801 0-8924 9 277 8-3267 75-90 13-90 2-0436 6-2831 30 2-1111 71-65 9-65 1-4168 0-6943 283 8-3418 75-35 13-35 1-9621 6-3797 14 31 1-4288 63-10 1-10 0-1612 1-2676 284 8-3056 75-15 13-15 1-9325 6-3731 38 1-7899 64-67 '2-67 3913 1-3986 10 285 6-0906 65-20 3-25 0-4763 5-6143 39 1-9165 65-08 3-08 0-4514 1-4651 295 6-3196 67-35 5-35 0-7846 5-5350 46 1-9758 66-88 4-88 0-7157 1-2601 296 6-3040 67-65 5-65 0-8286 5-4754 47 2-5297 70-70 8-70 1-2770 1-2600 302 6-3478 68-60 6-60 0-9681 5-3797 54 2-6951 71-18 9-18 1-3476 1-3475 303 6-0590 75-25 13-25 1-9474 4-1116 15 56 1-4396 63-10 1-10 0-1612 1-2784 314 6-0442 74-10 -12-10 -1-7775 4-2667 63 1-8834 64-38 2-38 0-3488 1-5346 11 315 5-6578 58-45 + 3-55 + 0-5196 6-1774 71 2-0849 65-77 3-77 0-5527 1-5322 321 5-2968 58-05 + 3-95 + 0-5781 5-8749 72 2-1384 66-22 4-22 0-6187 1-5197 322 5-3821 58-00 + 4-00 + 0-5854 5-9675 79 2-0810 67-72 5'-72 0-8389 1-2421 323 4-8598 81-80 -19-80 -2-9173 1-9425 86 2-3467 69-10 7-10 1-0416 1-3051 325 4-9839 81-80 19-80 2-9173 2-0666 29 87 3-9682 66-25 4-25 0-6231 3-3451 327 4-9922 81-80 19-80 2-9173 2-0749 93 4-3955 68-87 6-87 1-0078 3-3877 328 4-9675 81-80 19-80 2-9173 2-0502 30 94 4-0257 65-38 3-38 0-4954 3-5303 330 4-9446 81-80 19-80 2-9173 2-0273 101 3-8281 65-00 3-00 0-4397 3-3884 332 5-0836 81-85 19-85 2-9247 2-1589 Nov. 13 102 4-3848 65-93 3-93 0-5761 3-8087 334 4-9593 81-85 19-85 2-9247 2-0346 108 4-7070 68-05 6-05 0-8873 3-8197 13 341 5-2011 83-50 21-50 3-1704 2-0307 18 109 2-8976 65-15 3-15 0-4617 2-4359 347 5-2166 84-95 22-95 3-3864 1-8302 115 3-1555 67-33 5-33 0-7817 2-3738 348 6-3433 89-30 27-30 4-0376 2-3057 19 116 4-9328 78-15 16-15 2-3760 2-5568 354 6-3005 89-50 27-50 4-0678 2-2327 122 5-1732 79-50 - 17-50 2-5763 2-5969 360 6-4810 89-60 27-60 4-0826 2-3984 30 123 2-5667 61-65 + 0-33 + 0-0512 2-6179 20 361 7-9628 73-30 11-30 1-6597 6-3031 129 2-5783 62-25 _ 0-25 -0-0366 2-5417 367 7-8408 73-20 11-20 1-6449 6-1959 135 2-8334 63-23 1-23 0-1802 2-6532 373 7-8557 73-10 11-10 1-6304 6-2253 136 2-9988 64-77 2-77 0-4060 2-5928 22 374 3-9172 84-85 22-85 3-3717 0-5435 142 31633 66-02 4-02 0-5893 2-5740 380 3-8453 84-70 22-70 3-3492 0-4961 148 3-2013 6708 5-08 0-7450 2-4563 386 3-7656 84-40 22-40 3-3044 0-4612 Dec. 11 149 5-1189 78-50 16-50 2-4281 2-6908 23 387 15-3255 67-75 5-75 0-8433 14-4822 160 4-7853 77-85 15-85 2-3319 2-4534 393 15-2622 67-55 5-55 0-8140 14-4482 13 161 3-4221 71-93 9-93 1-4579 1-9642 399 15-2904 67-50 5-50 0-8066 14-4838 167 3-3561 72-50 10-50 1-5418 1-8143 24 400 16-0801 74-40 12-40 1-8217 14-2584 173 3-6449 72-60 10-60 1-5565 2-0884 406 15-9523 74-35 12-35 1-8145 14-1378 179 3-6835 72-60 10-60 1-5565 2-1270 412 16-1246 74-30 12-30 1-8071 14-3175 15 180 8-6732 77-25 15-25 2-2427 6-4305 25 413 14-2855 64-55 2-55 0-3737 13-9118 186 9-1288 77-45 15-45 2-2724 6-8564 424 14-2956 64-35 - 2-35 -0-3444 13-9512 192 8-6972 77-55 15-55 2-2875 6-4097 26 425 13-4943 59-70 + 2-30 + 0-3367 13-8310 198 8-5183 77-55 15-55 2-2875 6-2308 431 13-5179 59-70 2-30 0-3367 13-8546 199 8-8086 77-40 15-40 2-2650 6-5436 437 13-3170 59-80 + 2-20 + 0-3221 13-6391 205 8-6689 77-10 -15-10 -2-2206 6-4483 27 438 14-0132 64-25 - 2-25 -0-3297 13-6835 16 211 2-1326 60-15 + 1-85 + 0-2708 2-4034 444 14-0452 64-25 2-25 0-3297 13-7155 217 2-1540 62-83 - 0-83 -0-1216 2-0324 450 13-9701 64-50 2-50 0-3664 13-6037 223 2-4898 65-37 3-37 0-4939 1-9959 28 451 12-8962 62-10 - 0-10 -0-0146 12-8816 229 2-9044 68-45 6-45 0-9461 1-9583 457 12-8895 61-95 + 0-05 + 0-0073 12-8968 21 230 12-9990 84-70 22-70 3-3492 9-6498 463 12-8412 61-95 + 0-05 + 0-0073 12-8485 236 13-2914 84-65 22-65 3-3418 9-9496 464 14-7944 78-75 -16-75 -2-4649 12-3295 242 13-3586 84-55 22-55 33271 10-0315 470 15-0022 78-85 16-85 2-4796 12-5226 22 243 2-9709 62-30 0-30 0-0439 2-9270 476 15-0145 78-95 16-95 2-4947 12-5198 249 2-7458 62-00 - 0-00 -0-0000 0-0000 29 482 14-6494 81-75 19-75 2-9100 11-7394 255 2-7614 61-75 + 0-25 + 0-0366 2-7980 488 14-9464 82-10 20-10 2-9623 11-9841 256 3-0916 61-85 0-15 0-0220 3-1136 489 15-1495 82-80 20-80 3-0659 12-0836 - 262 2-9397 61-75 + 0-25 + 0-0366 2-9763 495 15-1694 82-75 -20-75 -3-0590 12-1104 Expansion for 1° = 0-0007316 inch = 0-] 4632 rerolutions. 1 revolution of the Micrometer = -005 inch. 362 VERIFICATION AND EXTENSION OF LA CAILLE'S ARC OF THE MERIDIAN. BASE-LINE —TABLE X. Reduction of the readings of the Standard bar B to 62° Fahrenheit — continued. to -si .9 ^ §1 t3 lo- tn ■si 1 Date. No. as -3 5- ^1 ^ a 62°— t. II ss m O Date. No. 09 U S g s a ^ S3 H 62°— t. -1? a O ^-5 3- '"i |l +J 1841. rev. o rev. rey. 1841. rev. O rev* rev. Jan. 29 496 15-2529 82-75 -20-75 -3-0590 12-1939 Feb. 18 733 10-0154 67-60 - 5-60 -0-8213 9-1941 502 15-2220 82-70 20-70 3-0512 12-1708 734 9-9671 31 503 14-8011 81-30 19-30 2-8433 11-9578 735 9-9557 67-30 5-30 0-7773 9-1784 509 14-8352 81-40 19-40 2-8580 11-9772 22 736 7-3972 70-40 8-40 1-2328 6-1644 515 14-8-236 81-45 19-45 2-8654 11-9582 742 7-7355 72-45 10-45 1-5345 6-2010 Feb. 3 516 15-8973 79-85 17-85 2-6282 13-2691 749 8-1275 75-05 13-05 1-9178 6-2097 522 15-8867 79-75 17-75 2-6135 13-2732 23 750 5-5-268 78-50 16-50 2-4281 3-0987 528 15-8349 79-55 17-55 2-5841 13-2508 756 5-4213 78-25 16-25 2-3910 3-0303 4 529 14-8794 79-00 17-00 2-5021 12-3773 762 5-3589 77-75 15-75 2-3168 3-0421 535 14-8729 79-30 17-30 2-5462 12-3267 24 763 6-0675 82-45 20-45 3-0135 3-0540 545 14-9200 79-75 17-75 2-6135 12-3065 769 6-0058 82-25 20-25 2-9840 3-0218 556 14-9080 79-95 17-95 2-6430 12-2650 25 770 4-0715 70-80 8-80 1-2917 2-7798 7 557 14-0037 75-60 13-60 1-9995 12-0042 776 3-8709 69-50 7-50 1-1004 2-7705 563 14-002-2 75-55 13-60 1-9919 120103 777 4-7848 74-55 12-55 1-8441 2-9407 569 13-9877 75-50 13-50 1-9848 12-0029 783 4-8453 75-15 13-15 1-9325 2-9123 570 14-0161 75-45 ' 13-45 1-9768 12-0393 789 4-8841 75-60 1360 1-9992 2-8849 576 14-1189 75-40 13-40 1-9695 12-1494 26 790 30838 64-50 2-50 0-3664 2-7174 582 14-0274 75-40 - 13-40 - 1-9695 12-0579 796 2-9291 64-00 2-00 0-2931 2-6360 8 583 13-8874 57-35 + 4-65 ■+ 0-6805 14-5679 797 5-6845 81-30 19-30 2-8433 2-8412 589 13-8302 57-15 4-85 07097 14-5399 803 5-7216 81-05 19-05 2-8061 2-9155 590 13-7394 58-80 3-20 0-4685 14-2079 809 5-6371 80-80 -18-80 -2-7689 2-8682 596 13-7978 59-20 2-80 0-4099 14-2077 27 810 3-5998 61-70 + 0-30 + 0-0439 3-6437 602 13-8863 59-55 + 2-45 + 0-3587 14-2450 816 2-6049 61-35 0-65 0-0952 2-7001 11 604 12-8104 77-45 -15-45 -2-2724 10-5380 822 2-5784 61-20 + 0-80 + 0-1171 2-6955 606 12-7634 77-50 15-50 2-2797 10-4837 823 4-4215 73-15 -11-15 - 1-6375 2-7840 608 12-8645 77-50 15-50 2-2797 10-5848 829 4-4463 73-75 11-75 1-7258 2-7205 610 12-8726 77-50 15-50 2-2797 10-5929 835 4-5421 74-15 12-15 1-7848 2-7573 612 12-8756 77-50 15-50 2-2797 10-5959 28 836 5-5016 80-75 18-75 2-7615 2-7401 12 613 U-8555 67-05 5-05 . 0-7406 11-1149 837 5-5050 80-75 18-75 2-7615 2-7435 619 11-7867 66-80 4-80 0-7040 11-0827 843 5-6500 81-55 19-55 2-8805 2-7695 6-25 11-7292 66-50 4-50 0-6599 11-0693 849 5-7629 82-05 20-05 2-9546 2-8083 13 626 11-1854 67-10 5-10 0-7480 10-4374 Mar. 1 850 4-1951 73-55 11-55 1-6965 2-4986 632 11-1323 66-75 4-75 0-6966 10-4357 856 4-1117 73-10 11-10 1-6302 2-4815 638 10-9943 66-40 4-40 0-6452 10-3491 862 4-0904 72-85 10-85 1-5934 2-4970 639 13-3963 85-80 23-80 3-5134 9-8829 2 863 6-5895 88-90 26-90 3-9774 2-6121 645 13-4684 85-85 23-85 3-5207 9-9477 869 6-6519 89-30 27-30 4-0371 2-6148 651 13-4515 85-85 23-85 3-5207 9-9308 875 6-7310 89-85 27-85 4-1201 2-6109 14 652 11-9130 78-50 16-50 2-4281 9-4849 4 876 3-4628 71-40 9-40 1-3800 2-0828 654 11-9204 78-55 16-55 2-4355 9-4849 881 3-3340 71-40 9-40 1-3800 1-9540 656 11-9449 78-70 16-70 2-4576 9-4873 5 882 3-1771 63-80 1-80 0-2638 2-9133 658 11-9740 78-85 16-85 2-4800 9-4940 888 2-9315 63-35 1-35 0-1978 2-7337 660 11-9857 78-95 16-95 2-4947 9 4910 889 5-1128 73-75 11-75 1-7261 3-3867 662 11-9768 79-00 17-00 2-5021 9-4747 895 5-0283 73-45 -11-45 -1-6818 3-3465 663 12-0554 79-15 17-15 2-5241 9-5313 6 898 1-8108 60-70 + 1-30 + 0-1903 2-0011 669 12-1048 79-65 17-65 2-5984 9-5064 904 1-7021 60-60 1-40 2050 1-9071 675 12-0903 79-90 17-90 2-6356 9-4547 910 1-7158 60 80 + 1-20 + 0-1757 1-8915 16 676 12-6778 86-15 24-15 3-5655 9-1123 11 911 8-3436 65-55 - 3-55 -0-5204 7-8232 682 12-8114 85-95 23-95 3-5360 9-2754 917 8 3360 65-70 - 3-70 -0-5423 7-7937 688 12-6870 85-60 23-60 3-4834 9-2036 12 918 6-3189 56-25 + 5-75 + 0-8413 7-1602 17 689 10-2754 69-70 7-70 1-1297 9-1457 924 6-3879 55-90 + 6-10 + 0-8926 7-2805 695 10-3680 70-20 8-20 1-2031 9-1649 17 925 7-1173 ■69-85 - 7-85 -1-1517 5-9656 701 10-3941 70-40 8-40 1-2326 9-1615 931 6-9416 68-75 6-75 09901 5-9515 707 10-3862 71-85 9-85 1-4462 8-9400 932 7-4109 73-15 11-15 1-6375 5-7734 713 10-5048 72-30 10-30 1-5125 8-9923 938 7-5951 74-25 12-25 1-7997 5-7954 714 11-6106 79^85 17-85 2-6282 8-9824 944 7-7344 75-05 13-05 1-9178 5-8166 720 11-6099 79-85 17-85 2-6282 8-9817 18 945 9-3550 87-05 25-05 3-6999 5-6551 18 721 10-1844 68-05 6-05 0-8873 9-2971 951 9-5427 89-05 27-05 3-9996 5-5431 727 10-0861 67-70 - 5-70 -0-8360 9-2501 19 953 5-8639 63-40 - 1-40 -0-2051 5-6588 Expansion for 1° = 0-0007316 inch = 0-14632 revolutions. 1 revolution of tlie Micrometer = -005 inch. EEDUCTION OF STANDAKD B TO 62° FAHKENHEIT. 363 BASE-IilNE.— TABLE X. Reduction of the readings of the Standard bar B to 62° Fahrenheit — continued. Date. No. 03 a § §1 62°— t U F3 ""• ■a Is Date. No. a o 62°— <. .s»- .§1 m 3 t3 0) ^1 « o 1 H §1 1841. rCT- O rev- rev. 1841. rev. o O rev- rev- Mar. 19 959 5-7659 63-35 - 1-35 -0-1978 5-5681 Aug. 25 1142 6-1273 55-53 + 6-47 + 0-9466 7-0739 960 8-6671 83-50 21-50 3-1704 3-4967 1143 6-3003 56-00 6-00 0-8779 7-1782 966 9-0272 86-10 24-10 3-5581 5-4691 1149 6-2844 56 05 5-95 0-8706 7-1550 21 967 6-3948 69-35 7-35 1-0782 5-3166 1150 6-2706 56-05 5-95 0-8706 7-1412 973 6-4898 69-90 7-90 1-1590 5-3308 1156 6-2509 56-10 5-90 0-8633 7-1412 974 8-4499 74-80 12-80 1-8808 6-5691 1157 6-2545 56-20 5-80 0-8487 7-1032 980 8-6746 76-00 14-00 2-0583 6-6163 1163 6-3255 56-30 5-70 0-8340 7-1595 981 9-2176 79-65 17-65 2-5984 6-6192 1164 6-3068 56-35 5-65 0-8267 7-1335 987 9-2260 79-55 17-55 2-5837 6-6423 1170 6-2513 56-50 5-50 0-8084 7-0561 988 8-7845 76-25 14-25 2-0951 6-6894 26 1171 6-2482 54-60 7-40 1-0826 7-3308 994 8-6887 75-70 13-70 2-0139 6-6748 1177 6-2903 54-55 7-45 1-0899 7-3802 995 8-6788 75-70 13-70 2-0139 6-6649 1178 6-2887 54-60 7-40 1-0826 7-3713 23 996 7-7554 67-45 5.45 0-7993 6-9561 1184 6-2890 54-70 7-30 1-0680 7-3570 1002 8-0068 68-85 6-85 1-0049 7-0019 1185 6-3268 54-70 7-30 1-0680 7-3948 24 1003 8-6489 73-15 11-15 1-6375 7-0114 1191 6-2948 54-80 7-20 1-0534 7-3482 1009 8-6724 73-10 -11-10 - 1-6302 7-0422 1192 6-3185 54-90 7-10 1-0387 7-3572 28 1010 6-8259 61-75 + 0-25 + 0-0366 6-8625 1198 6-2997 55-03 6-97 1-0198 7-3195 1016 6-8868 61-85 0-15 0-0220 6-9088 1199 6-3293 54-95 7-05 1-0314 7-3607 1017 6-8611 61-95 + 0-05 + 0-0073 6-8684 1205 6-3073 55-05 6-95 1-0168 7-3241 1018 8-5375 7160 - 9-60 - 1-4095 7-1280 1206 6-3164 55-15 6-85 1-0023 7-3187 1024 8-5903 71-58 9-58 1-4065 7-1838 1212 6-3113 55-30 670 0-9803 7-2916 April 5 1025 8-1758 68-85 6-85 1-0048 7-1710 28 1213 6-2200 56-10 5-90 0-8633 7-0833 1031 8-2020 68-85 6-85 1-0048 7-1972 1219 6-2394 56-15 5-85 0-8560 7-0954 22 1032 4-2286 70-48 8-48 1-2445 2-9841 1220 6-2340 56-20 5-80 0-8487 7-0827 1038 4-3929 70-93 8-93 1-3109 3-0820 1226 6 0588 56-25 I 5-75 0-8413 6-9001 23 1039 3-3805 65-50 3-50 0-5130 2-8675 1226 6-0598 56-25 1045 3-4604 65-71 - 3-71 -0-5438 2-9166 1227 1233 1234 6-1645 6'1853 6-2028 56-35 56-40 56-35 5-65 5-60 5-65 0-8267 0-8194 0-8267 6-9912 7-0047 7-0295 At t le Eoj ral Observ itory: E xpansion : or 1° Tahi enheit 1240 6-2276 56-45 5-55 0-8121 7-0397 = 14632 re volutions. 1241 1247 1248 6-2217 6-2417 6-2121 56-55 56-70 56-95 5-45 5-30 5-05 0-7974 0-7755 0-7389 7-0191 7-0172 6-9510 Aug. 19 1046 6-1627 56-55 + 5-45 + 0-7974 6-9601 1052 6-2115 56-60 5-40 0-7901 7-0016 1254 6-1427 56-95 5-05 0-7389 6-8816 20 1053 5-9603 56-70 5-30 0-7755 6-7358 1255 6-1769 56-95 5-05 0-7389 6-9158 1059 6-0596 56-70 5-30 0-7755 6-8351 1261 6-1721 57-05 4-95 0-7244 6-8965 1060 6-0157 56-75 5-25 0-7682 6-7839 30 1262 6-2953 54-65 7-35 1-0753 7-3706 1066 6-0415 56-95 5-05 0-7389 6-7804 1268 6-2714 54-75 7-25 1-0607 7-3321 1067 6-0691 57-00 5-00 0-7317 6-8008 1269 6-2814 54-70 7-30 1-0680 7-3494 1073 6-0678 57-25 4-75 0-6951 6-7629 1275 6-2592 54-80 7-20 1-0534 7-3126 21 1074 6-1426 56-95 5-05 0-7389 68815 1276 6-2759 54-85 7-15 1-0460 7-3219 1080 61800 56-95 5-05 0-7389 6-9189 1282 6-3161 54-95 7-05 1-0314 7-3475 1081 6-1963 57-05 4-95 0-7244 69207 1283 6-3119 55-00 7-00 1-0241 7-3360 1087 6-2011 57-15 4-85 0-7097 6-9108 1289 6-3148 52-20 6-80 0-9950 7-3098 1088 6-2355 57-30 4-70 0-6878 6-9233 1290 6-2234 55-60 6-40 0-9364 7-1598 1094 6-2417 57-45 4-55 0-6658 6-9075 1296 6-2097 55-65 6-35 0-9291 7-1388 23 1095 5-9128 56-30 5-70 0-8340 6-7468 1297 6-2150 55-65 6-35 0-9291 7-1441 1101 6-0079 56-45 5-55 0-8121 6-8200 1303 6-2204 55-70 6-30 0-9218 7-1422 1102 6-1593 57-55 4-45 0-6512 6-8105 1304 6-2537 55-70 6-30 0-9218 7-1755 1108 6-1663 57-70 4-30 0-6293 6-7956 1310 6-2340 55-90 6-10 0-8926 7-1266 1114 6-2110 57-85 4-15 0-6073 68183 1311 6-2418 5600 6-00 0-8779 7-1197 i5 1115 6-0734 54-80 7-20 1-0534 7-1268 1317 6-2351 56-05 5-95 0-8706 7-1057 1121 6-0588 54-90 7-10 1-0387 7-0975 1318 6-2359 56-05 5-95 0-8706 7-1065 1122 6-0768 54-90 7-10 1-0387 71155 1324 6.2399 56-10 5-90 0-8633 7-1032 1128 6-0959 55-00 7-00 10241 7-1200 Sept. 1 1325 6-0768 55-95 6-05 0-8852 6-9620 1129 6-1017 54-95 705 1-0314 7-1331 1331 6-1002 56-05 5-95 0-8706 6-9708 1135 6-1204 55-15 6-85 1-0022 7-1226 1332 6-1094 56-00 6-00 0-8779 69873 1136 6-1375 55-30 + 6-70 + 0-9802 7-1177 1338 6-1012 56-00 + 6-00 + 0-8779 6-9791 Expansion for 1° = 0-0007316 inch = 0-14632 reTOlutions. 1 revolution of the Micrometer = -005 inch. 2 H 364 VEKIFICATION AND EXTENSION" OP LA CAILLE'S ARC OF THE MERIDIAN. BASE-LINE.— TABLE X. Reduction of the readings of the Standard bar B to 62° Fahrenheit — continued. Date. No. a § t s a 62°— t .9»- 11 t l°- U ^ s° 3 03 Date. No. is .1 e a « 2 in 62°— t 11 1 EC 1841. rev* o o rev- rev. 1841. rev. o o rev. rev. Sept. 1 1339 6-1291 56-05 + 5-95 + 0-8706 6-9997 Sept. 1 1374 6-2773 57-25 + 4-75 + 0-6951 6-9724 1345 6-1765 56-15 5-85 0-8560 7-0325 1380 6-3210 57-35 4-65 06805 7-0015 1346 6-1917 56-15 5-85 0-8560 7-0477 1381 6-3136 57-35 4-65 0-6805 6-9941 1352 6-1915 56-35 5-65 0-8267 7-0182 1387 6 3444 57-50 4-50 0-6585 7-0029 1353 6-2127 56-50 5-50 08048 7-0175 1388 6-3441 57-55 4-45 0-6512 6-9953 1359 6-2374 56-70 5-30 0-7755 7-0129 1394 6-3097 5760 4 40 0-6439 6-9536 1360 6-2895 57-00 5-00 0-7317 70212 2 1395 6-1820 56-45 5-55 0-8121 6-9941 1366 6-2892 57-05 4-95 0-7244 7-0136 1401 6-2153 56-55 5-45 0-7974 7-0127 1367 6-3099 57-20 4-80 0-7024 7-0123 1402 6-2565 56-55 5-45 0-7974 7-0539 1373 6-2918 57-30 + 4-70 + 0-6878 6-9796 1408 6-2623 56 65 + 5-35 +0-7828 7-0451 BASE-LlriE.— TABLE XI. Reduction ofth e readings of the S andard bai - A to 62° Fahrt.-i for the cnmimtisons with the Compensation Bars, made at the Base-line. Sept. 2 1409 6-2797 56-90 + 5-10 + 0-7462 70259 Sept. 4 1542 62011 57-50 + 4-50 + 0-6585 6-8596 1415 6-3182 57-00 5-00 0-7317 7-0499 1548 6-1939 57-60 4-40 0-6439 6-8378 1416 6-3240 57-05 4-95 0-7244 7-0484 1549 6-1943 57 85 4-15 0-6073 6-8016 1422 6-3545 57-30 4-70 0-6878 70423 1555 6-1844 57-95 4-05 0-5927 6-7771 1423 6-3489 57-25 4-75 0-6951 7-0440 1556 6-1816 57-95 4-05 0-5927 6-7743 1429 6-3655 57-45 4-55 0-6658 7-0313 1562 6-1765 58-05 395 0-5781 6-7546 1430 6-3643 57-45 4-55 0-6658 7-0301 1563 6-1650 58-05 3-95 0-5781 6-7431 1436 6-4197 57-55 4-45 0-6512 7-0709 1569 6-1812 58-10 3-90 5708 6-7520 1437 6-4733 58-20 3-80 0-5562 7-0295 1570 61786 58-10 3-90 0-5708 6-7494 1443 6-4750 58-30 3-70 0-5415 7-0165 1576 6-1968 58-25 3-75 0-5489 6-7457 1444 6-4585 58-35 3-65 0-5342 6-9927 7 1577 6-2398 56-55 5-45 0-7974 7-0372 1450 6-4859 58-55 3-45 0-5049 6-9908 1583 6-2286 56-50 5-50 0-8048 7-0334 1451 6.4982 58-50 3-50 0-5123 7-0105 1584 6-2258 56-55 5-45 0-7974 7-0232 1457 6-4991 58-60 3-40 0-4976 6-9967 1590 6-2174 56-65 5-35 0-7828 7-0002 1458 6-4738 58-65 3-35 0-4903 6-9641 1591 6-2174 56-65 5-35 0-7828 7-0002 1464 6-4874 58-65 3-35 0-4903 6-9777 1597 6-2291 56-70 5-30 0-7755 7-0046 3 1465 6-0984 57-15 4-85 0-7097 6-8081 1598 6-2249 56-70 5-30 0-7755 7-0004 1471 6-1058 57-20 4-80 0-7024 6-8082 1604 6-1952 56-80 5-20 0-7609 6-9561 1472 6-1206 57-20 4-80 0-7024 6-8230 1605 6-1997 56-75 5-25 0-7682 6-9679 1478 6-1452 57-30 4-70 0-6878 6-8330 1611 61847 56-80 5-20 0-7609 6-9456 1479 6-1408 57-30 4-70 0-6878 6-8286 1612 6-1769 56-95 5-05 0-7389 6-9158 1485 6-1535 57-40 4-60 0-6732 68267 1618 6-2274 56-95 5-05 0-7389 6-9663 1486 6-1416 57-40 4-60 0-6732 6-8148 1619 6-1857 57-15 4-85 0-7098 6-8955 1492 6-1769 57-60 4-40 0-6439 6 8208 1625 6-1749 57-25 4-75 0-6951 6-8700 1493 6-2034 57-65 4-35 0-6366 6-8400 1626 6-1609 57-30 4-70 0-6878 6-8487 1499 6-2160 57-70 4-30 0-6293 6-8453 1632 6-1811 57-35 4-65 0-6805 6-8616 1500 6-2420 5810 3-90 0-5708 6-8128 1633 6-1831 57-35 4-65 0-6805 6-8636 1506 6-2326 58-15 3-85 0-5635 67961 1639 61977 57-40 4-60 0-6732 6-8709 1507 6-2259 58-10 3-90 0-5708 6-7967 1640 6-2030 57-40 4-60 0-6732 6-8762 1513 6-2407 58-15 3-85 05635 6-8042 1646 6-1548 57-55 4-45 0-6512 6-8060 1514 6-2316 58-20 3-80 0-5562 6-7878 1647 6-1749 57-50 4-50 0-6585 6-8334 1520 6-2224 58-30 3-70 0-5415 6-7639 1653 6-2179 57-60 4-40 0-6439 6-8618 1521 6-2524 58-40 3-60 05269 6-7793 1654 6-2106 57-65 4-35 0-6366 6-8472 1527 6-2643 58-40 3-60 0-5269 6-7912 1660 6-1802 57-80 4-20 0-6146 6-7948 4 1528 6-1735 57-45 4-55 0-6658 6-8393 8 1661 6-3037 57-75 4-25 0-6219 6-9256 1534 6-1909 57-45 4-55 0-6658 6-8567 1667 6-2829 57-85 4-15 0-6073 6-8902 1535 6-2076 57-45 4-55 0-6658 6-8734 1668 6-2741 57-85 4-15 0-6073 6-8814 1541 6-1967 57-45 + 4-55 + 0-6658 6-8625 1674 6-2570 58-05 + 3-95 + 0-5781 6-8351 Expansion for 1° = 0-0007316 inch = 0-14632 revolutions. 1 revolution of the Micrometer = -005 inch. RELATIVE LENGTHS OF THE COMPENSATION BARS AND STANDARD B. 365 BASE-LINE.— TABLE XII. Abstract of the Compan sons of the Compensation Bars i vith the Standard B, reduced to 62° Fahrenheit: made t luring the measurement of the Base-line. Excess op each Compensation Bae above the Standard Bar. TEMPEBAinEES OP DATE. Sums. A B C D E G Bar. Air. 1840. div. div. div. div. div. div. div. o o October 12 - 0-4 103-4 85-1 + 11-9 75-0 + 4-5 279-5 64-8 13 + 9-5 96-4 72-1 - 22-6 38-0 - 20-2 172-2 67-6 73-7 - 7-5 771 68-7 - 7-9 600 - 2-7 187-7 69-8 74-5 + 33-8 106-6 92-7 + 1-7 77-1 + 9-8 321-7 71-2 74-0 14 + 28-4 112-1 111-0 + 7-3 ll-'-l 8-9 344-9 63-9 68-7 - 4-8 105-3 85-8 - 8-9 68-2 + 2-6 248-2 66-0 70-7 + 1-1 97-9 51-7 - 21-6 29-2 - 36-7 121-6 71-0 73-5 15 34-1 121 96-3 + 13-0 79-1 + 7-6 351-0 63-8 68-1 8-8 113-9 76-3 - 27 44-0 - 7-7 232 6 65-1 70-1 38-2 110-2 100-7 - 19-5 40-9 - 24-2 246-3 67-0 71-7 21 74-7 73-6 - 14-4 67-6 - 26-3 167-3 68-4 72-5 30 Mean . . . November 13 + 45-2 116-6 120-4 + 80-6 23-6 + 2-8 388-2 65-2 67-0 66-4 15-71 102-77 86-20 1-41 55-82 - 6-81 255-10 + 31-2 120-5 98-8 102-8 + 13-2 366-5 18 + 25- 1 111-8 112 6 111-8 + 4-5 365-8 66-3 73-7 19 - 03 95 7 98-5 98 2 - 6-6 285-5 78-9 80-7 30 + 36-6 1-27 -9 130- 1 128-7 + 24-3 447-6 62-0 64-6 32-6 112-9 122-6 112-6 32-1 412-7 62-8 66-5 32-2 125-1 111-5 105-9 20 3 395-0 65-4 68-8 Mean . . , December 16 + 38-2 129-5 125 122-9 + 14-0 429-6 66-6 61 "5 68-4 73-9 27-95 117-63 114-14 111-84 14-54 386-10 23-6 105-5 97-4 102-1 4-1 332-7 31-8 104-0 111 104-0 10-9 361-7 64-1 75-6 Mean . . . December 22 20-8 112-2 106-7 104-1 91 352-9 67-0 61-9 76-6 68-7 25-40 107-24 105-03 103-40 8-03 349-10 30-4 123-9 118-9 115-4 21-5 410-1 1841.— Jan. 6 37-7 114-6 105-0 106-2 21-4 384-9 64-7 73-9 35-3 130-0 137-7 129-6 25-7 458-3 65-8 75-6 9 9-4 110-7 109-8 112 9 23-9 366-7 75-7 71-6 10 111 104-3 111 8 110-1 26-7 364-0 66-4 77-9 40-6 133-9 132-9 120-5 27-0 454-9 68-2 86-5 38-8 138 4 141-2 in-4 43 6 473-4 75-3 71-6 47-7 123-3 112-7 122-6 29-9 436-2 74-1 69-1 11 32-4 116-2 112-9 112-5 23-6 397-6 58-3 56-3 13 13-3 ]03 8 93-7 80-4 1-9 293-1 83-5 99-1 30-4 106-2 96-2 77-9 21-8 332-5 84-3 99-1 12-3 112-4 104-6 83-4 - 2-8 309-9 89-4 93-4 Mean . . . January 20 19-7 101-8 108-0 934 16-0 338-9 89-6 73-3 930 75-1 27-62 116-89 114-26 105-87 21-55 386-19 21-6 121-2 107-8 91-5 29-0 371-1 23-6 125-4 106-8 73-8 24 9 354-5 73-2 75-1 22 17-7 109-5 103-7 99-8 21-9 352-6 84-8 84-1 37-3 112-5 115-9 110 1 10-2 386-0 84-6 83-4 366 VERIFICATION AND EXTENSION OF LA CAILLE'S ARC OF THE MERIDIAN. BASE-LINE.— TABLE XII. Abstract of tht Comparisons- of the Compensation Bars with the Standard B, redmed to 62° Fahrenheit: made during the measurement of the Base-line — continued. Excess of each Compensation Bak above the Standard Bab. Tempeeatures op 1 DATE. Sums. A B C E G Bar. Air. 1841. div. div. div. div. div* div. o o January 23 46 8 112 2 124 6 131-9 28 2 443 7 67 7 68 8 22 2 111 3 100 8 121-4 31 7 387 4 67 6 69 6 24 53 8 113 5 115 9 107-2 1 7 392 1 74 4 74 7 25 8 137 7 132 4 107-4 28 8 432 1 74 4 73 4 25 4 9 100 7 113 2 137-9 5 5 362 2 64 6 63 5 18 9 116 8 97 9 133-3 9 1 376 64 4 63 8 26 13 9 132 3 110 4 119-6 33 7 409 9 59 7 65 9 29 7 132 3 129 2 116-0 29 4 436 6 59 8 67 1 27 9 113 5- 125 2 117-9 25 5 391 1 64 3 67 4 19 6 128 4 127 114-6 37 9 427 5 64 4 67 8 28 11 2 129 8 129 2 121-4 23 8 415 4 62 1 61 3 23 5 130 3 133 8 118-7 21 7 428 62 63 9 22 2 123 2 122 3 116-8 38 9 423 4 78 9 82 20 3 105 7 114 5 110-5 21 2 372 2 ■ 79 81 3 29 27 7 131 8 119 2 96-7 17 6 393 81 8 88 5 43 2 131 3 121 108-5 19 4 423 4 82 88 28 4 116 3 120 7 106-5 16 8 388 7 82 8 82 6 31 2 120 9 119 115-6 15 1 401 8 82 8 80 6 31 21 4 116 4 116 7 86-8 3 7 345 81 4 84 22 2 113 7 117 3 105-4 15 2 373 8 81 5 83 3 February 3 22 9 108 6 105 8 116-7 13 4 367 4 79 9 76 6 27 5 102 108 5 118-6 14 1 370 7 79 7 75 5 4 12 3 101 8 101 1 95-5 - 4 3 306 4 79 2 85 21 1 94 4 106 3 102-3 2 6 326 7 79 6 84 5 21 8 95 5 121 2 114-9 21 4 374 8 79 9 83 3 15 1 109 3 102 100-6 11 8 338 8 80 82 5 7 18 4 96 4 117 2 98-8 8 2 339 75 6 78 4 28 2 117 2 119 1 106-4 13 9 384 8 75 6 77 5 22 9 107 103 2 107-5 19 6 360 2 75 5 76 4 20 8 109 5 105 3 103-2 6 1 344 9 75 4 76 3 8 31 1 121 122 6 113-3 24 6 412 6 57 3 57 1 30 5 119 9 119 8 111-2 24 405 4 59 70 4 Mean . . . February 11 35-9 116-4 113-1 108-9 25-7 400-0 59-4 77-5 72-4 77-9 24-25 115-83 115-40 109-92 18-70 384-30 12-9 111-7 103-5 100-7 - 5-2 323-6 12 22 2 114-3 107-2 102-3 - 1-5 344-5 67-0 61-0 30-5 121-1 107 1 108-6 8-5 375-8 66-7 60-2 13 39-3 128-7 119-4 116-6 18-3 422-3 67-0 ^ 36-3 1230 127-8 118-4 10-6 416 1 66-6 8-9 109-6 94-4 113-3 7-4 333-6 85-9 85-8 16-9 99-1 90-0 115-1 3-8 324 9 85-9 85-4 14 20-0 102-8 92 5 103-0 3-4 321-7 79-1 86-1 8-7 106-9 86-6 97-1 2-6 301-9 79-5 85-7 12-9 105-4 87-7 104-4 0-6 311-0 79-8 85-2 16 17-7 92-5 104-8 104-2 3-7 322-9 86-1 81-5 22-4 90-2 108-9 101 1 13-2 335-8 85-8 80-2 17 6-1 105-8 97-2 83-7 - 3-3 289-5 71-2 84-8 23-8 112-1 106-2 89-4 - 3-9 327-6 72-1 85-6 10-6 100-9 88-3 92-7 - 23-4 269-1 79-9 81-0 RELATIVE LENGTHS OP THE COMPENSATION BARS AND STANDARD B. 367 BASE-LINE.— TABLE XII. Abstract of the Comparisons of the Compensation Bars with the Standard B, reduced to 62° Fahrenheit: 1 made during the measurement of the Base-line Excess op each Compensation Bus. above the Standard Bab. Temperatures op DATE. Sums. A B C E G Bar. Air. 1841. div. div. div. div. div. div. o February 18 22-2 104-4 108-2 98-7 6-2 339-7 67-9 64-4 Mean . . . February 22 19-5 112-3 103-6 104-0 8-2 347-6 67-7 71-5 64-7 82-2 19-47 108-28 101-97 103 13 2-89 335-74 18-0 106-9 100-3 89-6 8-3 323-1 16-8 109-0 88-5 80-4 3-6 298-3 73-8 84-3 23 29-8 109-7 105-3 91-3 6-7 342-8 78-4 76-4 25-6 107-8 97-5 97-9 1-7 330-5 78-1 73-5 24 36-9 106-9 113-8 103-6 9-1 370-3 82-4 81-7 25 39-4 116-3 129-4 117-1 26-6 428-8 70-2 56-8 30-8 106-1 109-5 97-7 9-9 354-0 74-8 80-5 34-9 108-3 111-7 98-2 8-0 361-1 75-4 78-1 26 50-4 122-7 128-3 112-3 16-7 430-4 64-3 58-1 27-8 96-8 104-3 96-5 - 4-4 321-0 81-2 80-6 34-4 109-1 112-9 104-9 6-9 368-2 81-0 78-7 27 35-2 120-4 1-23-9 112-3 31-1 422-9 61-6 58-2 34-7 119-5 119-2 108-0 29-0 410-4 61-3 60-1 35-3 115-1 116-7 101-4 17-9 386-4 73-5 78-2 33-6 110-6 115-7 102-3 16-5 378-7 74-0 76-4 28 16-8 105-3 98-8 80-8 11-5 313-2 81-2 88-0 19-5 102-1 99-7 75-3 1-6 298-2 81-9 87-6 March 1 30-0 113-7 114-5 106-5 17-9 382-6 73-4 67-9 31-6 114-3 115-4 108-1 15-6 385-0 730 70-7 2 31-3 107-0 105-8 96-6 2-7 343-4 89-1 93-9 27-6 101-6 105-6 91-5 - 0-7 325-6 89-6 93-4 5 44-5 121-4 131-1 105-8 31-2 444-0 63-6 61-2 33-1 118-5 111-1 104-9 21-0 388-6 73-7 69-2 6 31-9 126-9 1-21-1 104-4 26-4 410-7 60-7 59-8 44-8 122-3 125-4 109-6 32-4 434-5 60-7 62-8 11 38-1 119-8 116-8 111-9 25-4 412-0 65-7 66-3 12 Mean . . . March 17 39-5 1190 124-9 125-4 40-0 448-8 56-1 69-4 53-8 61-6 32-31 112-48 112-86 101-64 15-28 374-57 46-1 125-8 130 118-2 27-6 447-7 37-5 113-7 115-6 109-7 15-8 392-3 73-8 83-2 29-0 107-5 110-3 109-4 5-9 362-1 74-7 80-0 18 28-2 110-4 92-7 84-7 0-5 316-5 88-1 98-8 19 26-6 117-3 117-5 115-7 17-4 394-5 63-4 63-6 25-8 113-4 91-8 82-3 0-2 313-5 84 8 96-6 21 28-4 112-5 105-4 94-3 13-9 354-5 69-7 75-2 25-0 115-2 98-0 85-4 7-6 331-2 75-4 82-2 29-0 107-6 99-1 92-2 3 9 331-8 79-7 80-0 29-7 108-2 106-8 101-9 11-6 358-2 76-0 72-2 23 29-3 115-1 104 98-4 19-4 366-2 68-2 72-0 24 32-5 115-3 105-7 103-4 7-4 364-3 73-2 72-4 28 37-4 119-8 117-6 104-8 23-7 403-3 61-9 63-8 29-3 115-0 109-6 96-2 11-8 361-9 71-6 71-4 April 5 34-3 118-0 112-4 1101 15-7 390-5 68-9 69-3 22 31-0 112-8 .109-9 92-9 16-1 362-7 70-7 73-1 2 I 368 VERIFICATION AND EXTENSION OP LA CAILLE'S ARC OF THE MERIDIAN BASE-LINE.— TABLE XII. ' Abstract of the Comparisons of the Compensation Bars with the Standard B, reduced to 62° Fahrenheit: I made during the measurement of the Base-line — continued. Excess of each Compensation Bae above the Standard Bak. Tempekatubes op DATE. ' Sums. A B c E G Bar. Air. 1841. divr. div. div. div* div. diir. o April 23 Mean . . . 383 121-3 1164 106 6 23^1 405 • 6 656 66-8 31-60 114-65 108^40 100-36 13 04 368 •OS AT THE ROYAL OBSERVATORY, CAPE OE GOOD HOPE. August 19 42-81 129-21 122^72 115-51 29^02 439-27 56^6 58-3 20 34 •11 126 58 126 -43 114 50 28 85 430 •47 56 -7 57 •9 36 •15 123 •54 121 -18 111 •50 26 00 418 37 56 •9 58 •7 38 -49 129 •25 1-22 -74 115 •84 23 08 429 40 57 2 59 •2 21 42 •54 130 39 129 -23 117 •73 25 43 445 32 57 1 58 3 40 •01 126 36 127 58 114 •15 22 51 430 61 57 2 58 9 37 •28 122 90 127 35 111 42 20 78 419 73 57 4 59 1 23 47 -54 134 55 131 35 121 68 36 99 472 01 56 4 67 5 41 -56 127 88 128 30 118 08 25 12 440 94 67 7 59 3 34 •36 125 25 123 03 111 07 22 68 416 39 57 8 59 8 25 45 -18 130 66 129 60 123 40 28 66 457 40 54 9 66 41 •07 132 35 131 43 119 89 30 52 456 26 55 67 1 36 -88 126 32 124 31 114 90 22 25 424 66 55 2 57 3 47 •26 127 62 129 81 115 34 28 52 448 55 55 4 57 6 44 •42 127 14 125 48 119 37 28 20 444 61 56 1 57 1 42 -17 128 91 125 51 119 61 25 36 441 56 56 1 57 3 40 -41 124 30 126 60 116 82 22 34 430 47 56 3 67 7 42 75 127 05 125 96 114 60 25 66 436 02 56 5 67 7 26 43 28 133 38 130 96 119 64 33 27 460 53 54 6 55 7 44 75 134 28 130 78 116 00 26 92 452 73 64 7 56 3 40 89 129 01 128 16 114 66 27 30 440 02 54 8 56 7 41 49 129 60 132 08 117 92 31 89 452 98 54 9 56 9 40 55 128 08 129 27 115 00 25 43 438 33 55 1 67 1 43 81 126 93 128 21 112 87 26 16 437 98 55 3 67 3 28 43 96 128 17 124 48 113 74 25 01 435 36 66 2 56 9 42 45 130 37 128 91 116 46 28 42 446 61 66 4 57 7 32 97 1-24 08 120 77 110 03 24 42 412 27 66 6 67 9 39 •30 121 39 125 82 112 70 22 77 421 98 66 7 68 41 35 126 58 126 69 113 85 25 55 434 02 57 57 5 41 19 125 31 124 72 116 85 36 18 443 25 67 1 57 9 30 39 69 131 54 130 01 117 45 29 76 448 45 54 7 56 8 43 55 128 87 131 56 115 58 27 47 447 03 54 8 56 5 42 97 131 30 126 22 116 11 29 87 446 47 65 66 9 42 26 130 69 129 66 116 13 26 31 445 05 55 1 67 44 44 132 48 133 69 117 24 27 80 455 65 55 7 66 9 44 28 130 18 130 97 117 56 25 33 448 32 55 7 57 4 37 91 129 52 126 23 112 75 24 70 431 11 56 9 57 6 41 70 128 44 128 32 115 74 26 33 440 53 66 1 57 8 41 08 128 62 126 86 112 37 28 16 437 09 56 1 68 September 1 42 54 129 37 127 88 117 69 28 76 446 24 56 1 57 2 41 03 127 61 129- 80 116 27 25 88 440 59 66 57- 7 39 93 129 25 128- 35 115 25 29 86 442 64 56 2 68 • 2 41 34 128-99 124-20 114-22 24-47 433-22 56-5 58-6 1 RELATIVE LENGTHS OF THE COMPENSATION BARS AND STANDARD B. 369 BASE-LINE.— TABLE XII. Abstract of the Comparisons of the Competisation Bars with the Standard B, reduced to 62° Fahrenheit: made at the Royal Observatory, Cape of Good Hope — continued. DATE. 1841. September 1 Mean . . . Excess of each Compensation Bar above the Standard Bak. 41-51 38-35 44-61 43-44 39-33 38-28 44-48 40-00 41-25 div. 130-34 132-05 129-58 128-26 125-33 121-08 127-77 123-73 128-28 128-14 127-71 129-46 128-48 125-01 122-31 128-10 123-75 127-38 div. 115-51 117-24 117 09 116-58 115-33 114-76 116-82 117-03 115-88 G 27-33 28-26 33-52 24-54 30-52 26-52 30-06 25-52 27-16 Sdms. 442-83 443-61 454-25 441-30 435-52 422-95 447-23 430-03 439-95 Temperatuees of Bar. 66-9 67 67 67 57 57-6 56-6 66-7 Air. 58-5 58-4 68-7 59-0 59- 69- 57- 58- 370 VEEIFICATIOlSr AND EXTENSION OF LA CAILLE'S ARC OP THE MERIDIAN. BASE-LINE.— TABLE XIIL Abstract of the Comparisons of the Compensation Bars with i he Cape Standard Bar A, reduced to 62° Fahrenheit: made at the Royal Observatory, Cape of Good Hope. Excess or each Compensation Bae above the Standard Bab. TEMPERATtTRES OF DATE. Sum. A B C E G Bar. Air. 1841. div. div. div. div. div. div. o o September 2 40-10 126 18 124 89 117-08 28 93 437-18 57 58 8 40-66 131 39 128 07 112-49 29 35 441-96 57 2 59 1 42-41 129 08 128 09 116-73 27 00 443-31 57 5 69 3 39-85 127 68 122 87 114-48 26 84 431-72 57 9 69 5 41-12 120 61 121 01 109-55 19 89 412-18 58 4 59 5 38-74 127 93 124 62 111-38 23 20 425-87 58 5 59 5 38-14 121 84 120 80 112-33 28 16 421-27 58 6 59 4 36-89 125 93 126 25 113-85 26 09 429-01 58 7 69 1 3 40-12 128 19 125 23 118-30 25 87 437-71 57 2 58 6 42-54 127 64 124 00 115-56 29 93 439-67 67 3 69 40-98 128 27 127 47 114-31 30 11 441-14 57 4 69 3 40-25 126 65 125 80 113-15 29 86 435-71 57 5 69 4 42-14 123 -78 120 88 112-00 27 30 426-10 67 7 69 6 40-23 128 23 122 88 11405 27 98 433-37 58 2 59 42 -.56 123 99 1-25 16 111-88 25 88 429-47 58 2 69 4 38-89 125 20 123 20 114-41 24 89 426-59 58 3 69 6 40-86 122 92 124 44 111-03 22 32 421-57 58 4 ■59 3 4 44-65 127 94 125 49 113-52 27 03 438-63 57 5 58 9 40-42 126 65 124 55 110-04 26 68 428-34 57 6 69 3 39-57 121 28 122 77 114-08 24 90 422-60 58 59 42-37 125 14 125 55 114-18 25 03 4.32-27 58 1 59 1 44-74 127 50 123 41 116-54 29 84 442-03 58 1 59 3 39-42 125 77 123 37 112-31 27 19 428-06 58 2 59 5 7 41-18 127 77 126 86 118-30 28 05 442-16 66 6 56 9 44-98 129 63 129 42 118-40 34 90 4.57-33 56 7 67 4 43-57 126 45 128 40 112-83 32 15 443-40 66 7 67 6 40-87 128 67 124 40 115-75 31 44 441-13 56 8 57 8 44-22 132 36 129 88 115-41 29 38 451-25 56 8 68 47-71 129 12 124 42 114-70 30 60 446-55 57 68 1 43-31 129 99 125 59 118-67 28 01 445-57 57 3 57 9 42-26 130 85 127 05 117-26 31 60 449-02 57 4 68 2 40-60 128 87 123 68 113-48 25 96 432-65 57 4 58 5 38-70 127 64 123 82 113-25 25 59 429-00 67 5 58 8 40-95 125 28 126 47 110-82 26 39 429-91 57 6 68 9 37-61 125 06 122 41 111-74 25 22 422-04 67 8 59 1 8 38-33 122 56 119 54 112-51 21 27 414-21 57 9 59 3 Means of 37 sets 47-26 123-41 126-73 118-61 23-73 439-64 69-0 59-8 41-33 126-69 124-85 114-18 27-26 434-31 One division of the Micron leter = 0-000 05 inch. 43' 1-31 divisions = 0-021716 inch. Note.— The temperatures above given are to the nearest tenth of a degree only. CALCULATION OF THE RELATIVE LENGTHS OP CAPE STANDARDS A AND B. 371 BASE-LINE.— TABLE XIV. Abstract of Comparisons of the Cape Standards A and B, made at the Royal Observatory, Cape of Good Hope, and Calculation of their difference in length. Sum of Mean of Sum Mean of Expansion in Sum of microscope A— B in Day AND HOUK, 1840. o Tim /» i*f» c ort -n o of readings Therms. (t.) 62°— t. microscope readings microscope readings. for each Bar. reTolutious. reduced to 62° Fahrt. divisions. h m r o diT, Aug. 26, 7-39 a.m. A 4-0187 57-31 + 4-69 +0-6859 4-7046 -1-45 7-46 B 3-9821 56-96 5-04 0-7370 4-7191 5- 8 p.m. 5-15 A B 4-1759 4-0984 57-85 57-57 415 4-43 0-6069 0-6479 4-7828 4-7463 + 3-65 5-47 A 4-2019 57-95 4-05 0-5923 4-7942 + 4-55 5-53 B 4-1272 57-75 4-25 0-6215 4-7487 J7 28, 4-30 A 4-3216 56-97 5-03 0-7356 5-0572 + 3-11 B 4-2686 56 '82 5-18 0-7575 5-0261 }} 29 A 4-3059 57-89 4-11 0-6011 4-9070 + 1-66 9-13 B 4-2685 57-74 4-26 0-6230 4-8915 }? 31 A B 4-4251 4-3665 58-24 58-00 3-76 4-00 0-5499 0-5850 4-9760 4-9515 +2-35 Aug. 1841. 23, 9 -48 a.m. B 6-0102 56-45 5-55 0-8116 6-8218 + 6-29 +2-60 + 3-29 •+0-91 -0-44 10 46 A 6 1096 56 70 5-30 0-7751 6-8847 10 53 B 6 0763 56-65 5-35 0-7824 6-8587 11 3 A 6 1312 56-80 5-20 0-7604 6 -8910 11 9 B 6 1001 56-65 5-35 0-7824 6-8825 11 17 A 6 1.323 56 90 5-10 0-7458 6-8781 2 19 p.m. A 6 1869 57-55 4-45 0-6508 6-8377 + 1-70 + 5-22 +6-49 —0-58 2 25 B 6 1553 57-45 4-55 0-6654 6-8207 2 33 A 6 2221 57-55 4-45 6508 6-8729 2 40 B 6 1572 57-55 4-45 0-6508 6-8080 2 50 A 6 1587 57-60 4-40 0-6435 6-8022 —0-79 2 56 B 6 1593 57-55 4-45 0-6508 6-8101 — \j i tJ Sept. 8, 10 39 a.m. A 6 3675 66-70 10 40 A 6 3G07 6-3641 56-70 5-30 0-7751 7-1392 10 45 B 6 2722 + 3-39 10 45 B .6 2712 6-2717 56-30 5-70 0-8336 7-1053 10 52 A 6 3595 + 3-06 10 53 A 6 3710 6-3653 56-73 5-27 0-7706 7-1359 11 B 6 2540 +5-47 11 1 B 6 2560 6-2.550 56-35 5-65 0-8262 7-0812 11 6 A 6 3374 + 2-78 11 ■ 7 A 6 3539 6-3457 56-78 5-22 0-7633 7-1090 11 13 B 6 2504 +3-04 11 14 B 6 2689 6-2597 56-40 5-60 0-8189 7-0786 11 19 A 6 3410 + 1-63 11 20 A 6 3367 6 3389 56-83 5-17 0-7560 7-0949 11 28 B 6 2824 +0-45 11 -29 B 6 2605 6-2715 56-40 5-60 0-8189 7-0904 11 34 A 6 3621 + 1-72 11 35 A 6 3468 6-3545 56-85 5-15 0-7531 7-1076 11 39 B 6 3026 + 1-02 11 -41 B 6 2835 6 2931 56-50 5-50 0-8043 7-0974 11 -47 A 6 3531 —1-00 11-48 A 6-3389 6-3460 56-93 +5-07 +0-7414 7-0874 2 K 372 VERIFICATION AND EXTENSION OF LA CAILLE'S ARC OF THE MERIDIAN. BASE-LINE.— TABLE XIV. Abstract of Comparisom of the Cape Standards A and B, made at the Royal Observatory, Cape of Good | Hope, and Calculation of their difference in length — continued. 1 1 Sum of deduced Mean of Sum Mean of Ttar Expansion in Sum of microscope A— B in DAT AND Hour, 1841. O of readings Therms. (t.) 62°—*. microscope readings microscope microscope readings. for each Bar. revolutions. reduced to 62° Fahrt. divisions. h m r o o div. Sept. 8, 0-12 p.m. B 6-2964 0-14 B 6-2914 6-2939 56-70 +5-30 +0-7751 7-0690 0-18 A 6-3744 + 1-60 0-19 A 6-3712 6-3728 57-13 4-87 0-7122 7-0850 0-25 B 6-2847 + 4-40 0-26 B 6-2853 6-2850 56-83 5-17 0-7560 7-0410 0-33 A 6-3107 -2-57 0-34 A 6-3101 6-3104 57-18 4-82 0-7049 7-0153 0-38 B 6-2643 +0-34 0-39 B 6-2678 6-2661 56-90 510 0-7458 7-0119 Sept. 9, 10- a.m. A 6-2314 10- 1 A 6-2118 6-2216 57-68 4-32 0-6318 6-8534 10-16 B 6-1980 -1-26 10-17 B 6-2120 6-2060 57-48 4-52 6610 6-8660 10-23 A 6-2855 + 4-79 10-24 A 6-2699 6-2777 57-65 4-35 0-6362 6-9139 10-29 B 6-2290 + 3-16 10-30 B 6-2136 6-2213 57-48 4-52 0-6610 6-8823 10-35 A 6-2492 -1-16 10-36 A 6-2344 6 2418 57-70 4-30 0-6289 6-8707 10-40 B 6-2174 +0-61 10-41 B 6-1956 6-2065 57-50 4-50 0-6581 6-8646 10-46 A 6-3078 +6-35 10-47 A 6-2848 6-2963 57-68 4-32 0-6318 6-9281 10-52 B 6-2096 +6-26 10-53 B 6-2052 6-2074 57-50 4-50 0-6581 6-8655 10-58 A 6-2807 + 2-00 10-59 A 6-2560 6-2684 57-78 4-22 6171 6-8855 11- 4 B 6-2240 +2-31 11- 5 B 6-1934 6-2087 57-53 4-47 .0-6537 6-8624 nil A 6-2711 +0-81 11-12 A 6-2415 6-2563 57-80 4-20 0-6142 6-8705 11-19 B 6-2149 + 1-45 11-20 B 6-2042 6-2096 57-58 4-42 0-6464 6-8560 11-37 A 6-2819 +0-37 11-38 A 6-2528 6-2674 57-95 4-05 0-5923 6-8597 11-43 B 6-1876 + 4-90 11-44 B 6-1907 6-1892 57-75 4-25 0-6215 6-8107 11-48 A 6-2893 +5-73 11-49 A 6-2709 6-2801 57-98 4-02 0-5879 6-8680 0- 1p.m. B 6-2438 +3-14 0- 2 B 6-2098 6-2268 57-83 4-17 0-6098 6 8366 0- 6 A 6-2828 +0-02 0- 7 A 6-2590 6-2709 58-13 3-87 0-5659 6-8368 0-11 B 6-2133 + 3-19 0-12 B 6-2119 6-2126 67-95 4-05 0-5923 6-8049 0-17 A 6-2923 +3-66^ 0-18 A 6-2880 6-2902 58-23 +3-77 +0-5513 6-8415 CALCULATION OF THE RELATIVE LENGTHS OP CAPE STANDARDS A AND B. 373 BASE-LINE.— TABLE XIV. Abstract of Comparisons of the Cape Standards A and B, made at the Royal Observatory, Cape c / Good Hope, and Calculation of their difference in length — continued. 1 Sum of Mean of Sum Mean of Bar Therms. (t.) Expansion in Sum of microscope A— B in Day and Hour, 1841. microscope readings. of readings for each Bar. 62°— «. microscope revolutions. readings reduced to 62° Fahrt. microscope divisions. h m r o o div. Sept. 9, 0-23 p.m. B 6-2316 + 1-96 0-24 B 6-2276 6-2296 57-95 + 4-06 +0-5923 6-8219 0-31 A 6-2793 -0-97 0-32 A 6-2570 6-2682 58-28 3-72 0-5440 6-8122 0-36 B 6-2449 -0-08 0-37 B 6-2258 6-2354 58-05 3-95 0-5776 6-8130 215 A 6-2589 2-16 A 6-2479 6-2534 58-58 3-42 0-5001 6-7535 2-21 B 6-2128 + 1-77 2 22 B 6-2002 6-2065 58-38 3 62 0-6293 6-7358 2-26 A 6-2869 + 3-00 2-28 A 6-2591 6-2730 58-63 3 37 0-4928 6-7658 2-33 B 6-1922 +3-28 2-34 B 6-2152 6-2037 58-38 3-62 0-5293 6-7330 3-17 A 6-2428 3-18 A 6-2302 6 2365 58-70 3-30 0-4826 6-7191 3 23 B 6-1767 +2-63 3-24 B 6-1795 6-1781 58-48 3-52 0-5147 6-6928 3-29 A 6-2405 +0-99 3-30 A 6-2144 6 2275 58-76 3-26 0-4752 6-7027 3-36 B 6-1998 -0-62 3-37 B 6-1797 6-1898 68-45 3-55 0-5191 6-7089 3-43 A 6-2661 +2-88 3-44 A 6-2589 6-2625 58-75 3-25 0-4752 6-7377 3-49 B 6-1866 + 3-61 3-50 B 6-1892 6-1879 68-48 3-52 0-6147 6-7026 3-54 A 6-2379 + 1-59 3-55 A 6-2486 6-2433 58-75 3 25 0-4762 6-7185 4- 2 B 6-1825 +2-69 4- 3 B 6-1878 6-1852 58-53 3-47 0-6074 6-6926 4-14 A 6-2426 +0-38 4-15 A 6-2232 6-2329 58-83 3-17 0-4635 6-6964 4-20 B 6-2007 -0-74 4-21 B 6-2067 6-2037 68-58 3-42 0-6001 6-7038 4-26 A 6-2814 +3-90 4-27 A 6-2830 6-2822 58-85 315 0-4606 6-7428 4-33 B 6-1906 +6-23 4-34 B 6-1905 6-1906 68-65 3-35 0-4899 6-6806 4-39 A 6-2862 + 4-08 4-40 A 6-2586 6-2724 68-93 3-07 0-4489 6-7213 4-44 B 6-2022 +2-60 4-45 B 6-2106 6-2064 68-65 3-35 0-4899 6-6963 4-49 A 6-2.587 + 1-34 4-50 A 6-2687 6-2637 58-95 3-05 0-4460 6-7097 4-54 B 6-2083 +0-80 4-69 B 6-2163 6-2118 58-65 3-35 0-4899 6-7017 Sept. 10, 9*45 a.m. B 6-1726 B 6-1652 6-1689 66-58 +6-42 +0-7926 6-9616 374 VERIFICATION AND EXTENSION OF LA CAILLE'S ARC OP THE MERIDIAN, BASE-LINE. —TABLE XIV. AbstrnM of Comvarisons of the Cape Standards A and B, made at the Royal Observatory, Cape of Good 1 Hope, and Calculation of their difference in length — continued. 1 ^ Sum of Sum of Mean of Sum Mean of Bar Therms. Expansion in microscope A— B in DAT AND Hour, 1841. o deduced microscope of readings for each Bar. 62°— t. microscope revolutions. readings reduced to nicroscope divisions. 1 readings. (t.) 62° Fahrt. Sept. h m 10, 9-51 a.m. A r 6 1348 o div. -2-02 9-63 A 6-1480 6-1414 56-53 +5-47 +0-7999 6-9413 9-58 B 6-1387 + 1-06 9-59 B 6-1375 6-1381 56-58 5-42 0-7926 6-9307 10- 4 A 6-1962 +5-60 10- 6 A B 6-1773 6-1740 6-1868 56-53 5-47 0-7999 6-9867 + 1-40 B 6-1716 6 -1728 56-53 5-47 0-7999 6-9727 10-18 A 6-2428 +5-55 10-20 A B 6-2284 61946 6-2356 56-58 5-42 0-7926 7-0282 t +5-69 10-25 B 6-1628 6-1787 56-58 5-42 0-7926 6-9713 10-30 A 6-2265 + 3-45 10-32 A 6-2056 6-2161 56-60 5-40 0-7897 7-0058 10-37 B 6-1864 +4-06 10-39 B 6-1646 6-1755 56-60 5-40 0-7897 6-9652 10-44 A 6-2392 +4-67 10-45 A 6 2031 6-2212 56-60 6-40 0-7897 7-0109 10-50 B 6-1450 +8-64 10-51 B 6-1245 6-1348 56-60 5-40 0-7897 6-9245 10-55 A 6-2192 + 7-27 10-57 A 6-2104 6-2148 56-65 5 35 0-7824 6 9972 11- 1 B 6-1498 + 7-90 11- 4 B 6-1305 6 1402 56-68 5-32 0-7780 6-9182 11- 8 A 6-1865 +3-71 11-10 A 6-1739 1802 56-70 5-30 0-7761 6-9563 11-15 B 6-1666 + 2-65 11-16 B 6-1428 6 •1647 56-70 5-30 0-7761 6 9-298 11-21 A 6-1950 + 2-32 11-26 A 6-1902 6-1926 56-80 5-20 0-7604 6-9530 11-27 B 6-1667 + 4-37 11-28 B 6-1311 6-1489 56-80 5-20 0-7604 6-9093 11-32 A 6 2104 + 6-80 11-33 A 6-2034 6-2069 56-80 5 -20 0-7604 6-9673 11-38 B 6 1834 + 3-32 11-40 B 6 1640 6-1737 56-80 5-20 0-7604 6-9341 11-45 A 6-2189 + 2-53 11-46 A 6-2082 6-2136 50-90 5 10 0-7458 6-9594 11-50 B 0-1893 +4-00 11-51 B 6-1578 6-1736 56-90 5-10 0-7458 6-9194 11-55 A 6-1721 -0-35 11-67 A 6-1827 6-1774 56-96 5-05 0-7385 6-9159 0-12 p.m. B 6 1917 0-13 B 6 1939 6-1928 57-00 5-00 0-7312 6-9240 017 A 6-2426 +2-77 0-18 A 6-2275 6-2351 57-10 4-90 0-7166 6-9517 0-22 B 6-1663 +6-92 0-24 B 6-1609 6-1586 57-05 +4-95 + 0-7239 6-8825 0-27 A 6-2458 + 6-24 CALCULATION OF THE RELATIVE LENGTHS OF CAPE STANDARDS A AND B. 375 BASE-LINE.— TABLE XIV. Abstract of Comparisons of the Cape Standards A and B, made at the Royal Observatory, Cape of Good 1 Hope, and Calculation of their difference in length — continued. 1 Sam of deduced Mean of Sum Mean of Bar Expansion in Sum of microscope A— B in DAT AHD Hour, 1841. o of readings Therms. (t.) 62°— t microscope readings -nicroscope 0) B IS microscope readings. for each Bar. revolutions. reduced to 62° Fahrt. divisions. h m r o div. Sept. 10, 0-29 p.m. 0-35 A B 6-2196 6 1922 6-2327 57-13 +4-87 +0-7122 6-9449 +4-75 38 B 6- 1694 6-1808 57-10 4-80 0-7166 6-8974 0-43 A 6 2107 +0-32 0-44 A 6-1864 6-1986 57-20 4-80 0-7020 6-9006 2-23 B 6-1470 2-25 B 6- 1555 6 1513 57-60 4-50 0-6581 6 8094 2-29 A 6-1755 + 1-88 2-31 A 6-1734 6-1745 57-53 4-47 0-6537 6-8282 2 35 B 6- 1563 + 1-69 2-36 B 6-1501 6 1532 67-50 4 50 0-6581 6-8113 241 A 6-2109 +3-63 2-42 A 6-2060 6-2085 67-63 4-37 6391 6-8476 2-47 B 6-1399 +4-16 2-49 B 6-1558 6-1479 67-50 4-50 0-6581 6-8060 2 55 A 6-2465 + 6-91 2 56 A 6 2113 6-2289 67-65 4-35 0-6362 6-8651 2-59 B 6 1770 + 4-52 3- B 6 1463 6-1618 57-50 4-50 0-6581 6-8199 3- 5 A 6' 1767 -1-91 3- 6 A 6-1525 6-1646 57-65 4-35 0-6362 6-8008 3-12 B 6-1690 -1-14 313 B 6-1538 6-1614 57-55 4-45 0-6508 6-8122 317 A 6 2397 +4-68 318 A 6-2185 6-2291 57-70 4-30 0-6289 6-8580 3-26 B 6 1727 + 6-49 3-27 B 6- 1405 6 1596 57-60 4-40 0-6435 6-8031 3 32 A 6-22-20 + 3-32 3-34 A 6 2017 6-2119 67-73 4-27 0-6244 6-8363 3-38 B 6 1621 +5-17 3-39 B 6 1200 0-1411 67-60 4-40 0-6436 6-7846 3-43 A 6- 1696 +009 3-45 A 6-1583 6-1640 67-75 4-25 0-6215 6-7855 3-49 B 6-1615 -0-48 3-50 B 6-1408 6-1512 57-63 4-37 0-6391 6-7903 354 A 6-2-262 +4-70 3-55 A 6-2-200 6-2231 57-80 4-20 0-6142 6-8373 4- 2 B 6-1384 + 7-62 4- 3 B 6-1260 6-1322 57-70 4-30 0-6289 6-7611 4- 7 A 6 2396 + 8-50 4- 9 A 6-2242 6-2319 57 80 4-20 6142 6-8461 4-14 B 61620 +6-39 415 B 6-1535 6-1578 67-73 4-27 0-6244 6-7822 4-20 A 6 2221 +3-18 4-21 A 6-2067 6-2144 57-90 4-10 0-S996 6-8140 4-25 B 6-1738 +3-61 4-27 B 6-1478 6-1608 67-78 4-22 0-6171 6-7779 4-31 A 6-2338 +5-18 4-32 A 6-2264 6-2301 57-90 + 4-10 +0-5996 6-8297 2 L 376 VERIFICATION AND EXTENSION OF LA CAILLE'S ARC OP THE MERIDIAN. BASE-LINE.— TABLE XIV. Abstract of Comparisons of the Cape Standards A and B, made at the Boyal Ohservatory, Cape of Oood \ Hope, and Calculation of their difference in length— -continued. 1 i Sum of Mean of Sum Mean of Bar Expansion in Sum of microscope A— B in Day AND HOBR, 1841. s uuu. ut^cii. of readings TPliovmo 62°— t. microscope readings microscope 1 microscope readings. for each Bar. jLiicriiiB. (t.) rCTolutions. reduced to 62° Fahrt. dirisions. h m r o o div. Sept. 10, 4 -37 p.m. B 6 1841 + 4-42 4 38 B 6 1585 6-1713 57-80 +4-20 +0-6142 6-7855 4 43 A 6 2076 +0-93 4 44 A 6 1973 6-2025 57 95 4-05 0-5923 6-7948 Sept. 11, 9 34 a.m. A 6 2762 9 35 A 6 2610 6-2686 55-63 6-37 0-9315 7-2001 9 40 B 6 1607 +3-54 9 41 B 6 1799 6-1703 55-20 6-80 0-9944 7-1647 9 47 A 6 2261 -0-78 9 48 A 6 2305 6-2283 55-65 6-35 0-9286 7-1569 9 53 B 6 1791 -1-43 9 54 B 6 1745 6 1768 55-20 6-80 0-9944 7-1712 10 A 6 2337 -1-20 10 1 A 6 2275 6-2306 55-65 6-35 0-9286 7-1592 10 4 B 6 1681 -1-58 10 5 B 6 2018 6-1850 55-23 6-77 0-9900 7-1750 10 8 A 6 2732 +0-83 10 9 A 6 2450 6-2591 55-68 6-32 0-9242 7 1833 10 14 B 6 1645 + 3-52 10 15 B 6 1574 6 1610 55-25 6-75 0-9871 7-1481 10 21 A 6 2766 +3-22 10 22 A 6 2414 6-2590 55-70 6-30 0-9213 7-1803 10 26 B 6 1599 +3-73 10 27 B 6 1665 6-1632 55-30 6 70 0-9798 7-1430 10 31 A 6 2485 + 1-79 10 32 A 6 2306 6-2396 55-70 6-30 0-9213 7-1609 10 40 B 6 2055 -0-38 10 41 B 6 1733 6-1894 55-33 6-67 0-9753 7-1647 10 45 A 6 2847 +2-64 10 46 A 6 2697 6-2772 55 75 6-25 0-9139 7-1911 10 53 B 6 1612 + 6-84 10 54 B 6 1540 6-1576 55-40 6-60 0-9651 7 1227 10 59 A 6 3038 + 7-26 11 A 6 2823 6-2931 55 83 6-17 0-9022 7-1953 11 4 B 6 1760 + 6-81 11 5 B 6 1570 6-1665 55-43 6-57 0-9607 7-1272 11 8 A 6 2926 + 4-74 11 9 A 6 2726 6-2826 55-90 6-10 0-8920 7-1746 11 14 B 6 1679 +6-65 11 15 B 6 1618 6-1649 55-55 6-45 0-9432 7-1081 11 19 A 6 2757 +5-41 11 20 A 6 2647 6-2702 55-90 6-10 0-8920 7-1622 11 25 B 6 1977 +3-19 1] 26 B 6 1910 6-1944 55-60 6-40 0-9359 7 1303 11 31 A 6 2910 + 3-15 11 32 A 6 2777 6-2844 66-00 6-00 0-8774 7-1618 7 p.m. B 6 1956 0- 8" B 6-2000 6-1978 55-80 +6-20 +0 9066 7-1044 CALCULATION OP THE RELATIVE LENGTHS OF CAPE STANDARDS A AND B. 377 BASE-LINE.— TABLE XIV. Abstract of Comparison » of the Cape Standards A and B, made at the Royal Observatory, Cape of Good | Hope, and Calculation of their difference in length- continued. 1 1 Sum of Mean of Sum Mean of Expansion in Sum of microscope A— B in DAT AND HODR, 1841. S a microscope readings. of readings for each Bar. J3dr Therms. (t.) 62°— t. microscope revolutions. readings reduced to 62° Fahrt. microscope divisions. h m r o div. Sept. 11, 0- 13 p.m. A 6- 3045 + 4-45 014 A 6 2969 6 • 3007 56^20 + 5-80 +0-8482 7-1489 018 B 6 1925 + 5-12 019 B 6 2043 6 • 1984 55^85 6-15 0-8993 7-0977 0-24 A 6 2994 + 2-87 0-25 A 6 2715 6-2855 56^25 5-75 0-8409 7-1264 0-30 B 6 2165 +2-01 31 B 6 2121 6 2143 55 •go 6-10 8920 7-1063 34 A 6 2689 -1-31 35 A 6 2502 6 2596 56 30 5-70 0-8336 7-0932 0-39 B 6 2225 +0-27 0-40 B 6 2037 6 2131 56 00 6-00 0-8774 7 • 0905 2-27 A 6 2339 2-28 A 6 2300 6 2320 56-50 5-50 0-8043 7-0363 2-33 B 6 1718 + 2^64 2-34 B 6 1898 6 •1808 56^33 5 67 8291 7^0099 2-40 A 6 2120 +0-68 2-41 A 6 2127 6 2124 56^50 5-50 0-8043 7-0167 2-45 B 6 1610 + 1-82 2-46 B 6 1778 6 1694 56 33 5-67 0-8291 6-9985 2 51 A 6 2458 +3-31 2-51 A 6 2176 6 2317 50 53 5-47 0-7999 7 •0316 2-55 B 6 1781 +2-97 256 B 6 •1675 6 •1728 56 33 5-67 0-8291 7-0019 3- 3 A 6 2340 +2-71 3- 4 A 6 2299 6-2320 56-55 5-45 0-7970 7-0290 3- 8 B 6 •1500 +5-90 3- 9 B 6 •1375 6 1438 56 •35 5-65 0-8262 6-9700 313 A 6 •2195 +3-48 314 A 6 ■1961 6^2078 56-55 5-45 0-7970 7-0048 3-18 B 6 •1456 + 3-55 3- 19 B 6 •1493 6^1475 56 38 5 62 0-8218 6-9693 3-30 A 6 •2148 +2-79 3-31 A 6 ■2147 6-2148 56 65 5-35 0-7824 6-9972 3-35 B 6 •1662 +2-37 3-36 B 6 •1518 6 1590 56^43 5-57 0-8145 6-9735 3-41 A 6 •2129 + 2-30 3-42 A 6 ■2095 6-2112 56-63 5-37 0-7853 6-9965 3-47 B 6 •1535 + 2-65 3-48 B 6 ■1633 6 • 1684 56^45 5-55 0-8116 6-9700 3-52 A 6 ■2429 + 3-98 3-53 A 6 •2119 6 2274 56^65 5-35 0-7824 7-0098 3-54 B 6 •1311 +5-31 3-55 B 6 •1590 6 1451 56-45 555 0-8116 6-9567 4- 5 A 6 2380 + 4^15 4- 6 A 6 •2082 6-2231 56^70 5-30 0-7751 6-9982 4-10 B 6 •1472 +399 4-11 B 6 ■1608 6^1540 56-50 +5-50 +0-8043 6 • 9583 4-15 A 6-2540 + 4^52 378 VERIFICATION AND EXTENSION OF LA CAILLE'S ARC OF THE MERIDIAN. BASK-LINE.— TABLE XIV. Abstract of Comparisons of the Cape Standards A and B, made at the Royal Observatory, Cape of Good \ Hope, and Calculation of their difference in length — continued. 1 Sum of rlpfliipprl Mean of Sum Mean of Bar Expansion in Sum of microscope A— B in DAT AND HOUK, 1841. o UCU.UUCLI, TY11 0T*tf'\Cfk/'\T'40 of readings Therms. (t.) 62°— t. microscope readings microscope 0) g 12; iniLruaLupc readings. for each Bar. revolutions. reduced to 62° Fahrt. divisions. h m r o o div. Sept. 11, 4 4 16 p.m. 20 A B 6-2118 6 1586 6-2329 56-73 +5-27 +0-7706 7-0035 +3-70 4 21 B 6-16.58 6-1622 56-50 5-50 0-8043 6-9665 4 26 A 6-2.354 +2-88 4 27 A 6-2-285 6-2320 56-78 5-22 0-7633 6-9953 4 31 B 6-1972 ' + 1-55 4 32 B 6 1771 6 1872 56-58 5-42 0-7926 6-9798 4 39 A 6-2490 + 1-36 4- 40 A 6-2-2.57 6-2374 56-83 5-17 0-7560 6-9934 4 44 n 6-188G + 0-91 4 45 B 6 1860 6-1873 56-55 5-45 0-7970 6-9843 4- 49 A 6-2252 -1-94 4 50 A 6-2071 6-2162 56-88 5 12 0-7487 6-9649 4 54 B 6-1787 +0-02 4 55 B 6-1858 6- 1823 56 65 5 35 0-7824 6-9647 Sept. 14, 9 35 a.m. B 6-31-26 9 36 B 6-2865 6-2996 56-08 5-92 0-8657 7-1653 9 41 A 6 -2969 -2-27 9 48 A 6-3007 6-2988 56-23 5 77 0-8438 7-1426 9 51 B 6-3015 -0-71 9 54 B 6-2869 6-2942 56-15 5-85 0-8555 7-1497 9 57 A 6-3386 +2-31 9 58 A 6-3-252 6-3319 56-25 5-75 0-8409 7-1728 10 9 B 6-2685 +6-70 10 10 B 6-2612 6-2649 56-25 5-75 0-8409 7-1058 10 15 A 6-3145 +3-26 10 16 A 6-3099 6-3122 56-35 5-65 0-8262 7-1384 10 24 B 6-2840 + 1-98 10 25 B 6-2713 6-2777 56-25 5-75 0-8409 7-1186 10 32 A 6-3161 + 1-38 10 33 A 6-3197 6-3179 56-43 5-57 0-8145 7-1324 10 46 B 6-2968 +2-07 10 47 B 6 2742 6-2855 56 35 5-65 0-8262 7-1117 10 52 A 6-3149 +0-66 10 53 A 6-3072 6-3111 56-48 5-52 0-8072 7-1183 11 00 B 6-2821 + 3-36 11 1 B 6-2641 6-2731 56-45 5-rj5 0-8116 7-0847 11 • 8 A 6-3500 + 5-80 11 9 A 6-3502 6-3501 66-58 5-42 0-7926 7-1427 11 14 B 6-2873 +4-88 11 15 B 6-2919 6-2896 56-50 5-50 0-8043 7-0939 11 22 A 6-3683 + 4-29 11 23 A 6 3405 6-3-544 56-65 5-35 0-7824 7-1368 11 30 B 6 3128 + 5-37 11 31 B 6-2828 6-2978 56-63 5-37 0-7853 7-0831 11 40 A 6-3268 —0-48 11 41 A 6-3090 6-3179 56-80 + 5-20 + 0-7604 7-0783 11 49 B 6-2939 + 312 CALCULATION OF THE KELATiVK LENGTHS OF CAPE STANDARDS A AND B. 379 BASE-LINE.— TABLE XIV. Abstract of Comparison^ of the Cape- Sta and Calculat ndards A and B, made at the Royal Observatory, Cape of Oood \ Hope, ion of their difference in length — continued. 1 1 Sum of deduced Mean of Sum Mean of "Rflr Expansion in Sum of microscope A— B in Day AND HOUK, 1841. O microscope of readings Therms 62°— t microscope readings microscope 1 readings. for each Bar. (t.) revolutions. reduced to 62° Fahrt. divisions. b m r o div. Sept. 14, 11 -50 a.m. 0-12 p.m. B A 6 6 2591 3694 6-2765 56-73 + 5-27 +0-7706 7-0471 013 A 6 3520 6-3607 56-95 5-05 0-7385 7-0992 0-18 B 6 2931 +7-10 019 B 6 2805 6-2868 56-93 5-07 0-7414 7-0282 0-35 A 6 3596 • +4-08 0-36 A 6 3598 6-3597 57-15 4-85 0-7093 7-0690 0-44 B 6 3106 +2-71 0-45 B 6 2962 6-3034 56-95 5-05 0-7385 7-0419 2-39 A 6 2795 2-40 A 6 2917 6-2856 57-60 4-40 0-6435 6-9291 2-46 B 6 2887 -1-21 2-47 B 6 2716 6-2802 57-48 4-52 0-6610 6-9412 2-53 A 6 2926 -1-72 2-54 A 6 2684 6-2805 57-60 4-40 0-6435 6-9240 2-59 B 6 2682 + 0-44 3- B 6 2547 6-2615 57-50 4-50 0-6581 6-9196 3- 7 A 6 2886 +0-14 3- 8 A 6 2955 6-2921 57-70 4-30 0-6289 6-9210 3-14 B 6 2753 -0 04 3- 15 B 6 2513 6-2633 57-50 4-50 0-6581 6-9214 3-30 A 6 3103 +0-70 3-31 A 6 2887 6-2995 57-70 4-30 0-6289 6-9284 3-40 B 6 2908 + 1-16 3-41 B 6 2558 6-2733 57-60 4-40 0-6435 6-9168 3-47 A 6 2887 -1-78 3-48 A 6 2897 6-2892 57-83 4-17 0-6098 6-8990 3-54 B 6 2680 + 0-83 3-55 B 6 2497 6-2589 57-68 4-32 0-6318 6-8907 4- 2 A 6 3209 +2-90 4- 3 A 6 3192 6-3201 57-90 4-10 0-5996 6-9197 4- 9 B 6 2527 +4-53 4-10 B 6 2531 6-2529 57-75 4-25 0-6215 6-8744 , 4-19 A 6 3040 +0-96 4-20 A 6 2648 6-2844 67-90 4-10 0-5996 6-8840 4-27 B 6 2737 + 0-23 4-28 B 6 2555 6-2646 57-78 4-22 0-6171 6-8817 4-35 A 6 3202 +0-86 4-36 A 6 2846 6-3024 57-98 4-02 0-5879 6-8903 4-44 B 6 2721 +3-06 4-45 B 6 2422 6-2572 57-88 4-12 0-6025 6-8597 Sept. 15, 9 ■36 a.m. B 6 3734 9-37 B 6 3687 6-3711 57-00 5-00 0-7312 7-1023 9-45 A 6 3819 -0-98 9-46 A 6 3699 6-3759 57-10 4-90 0-7166 7-0925 9-53 B 6 3788 -0-18 9-54 B 6 3561 6-3675 57-03 +4-97 +0-7268 7-0943 9-56 A 6-4436 + 4-97 2 M 380 VERIFICATION AND EXTENSION OF LA CAILLE'S ARC OP THE MERIDIAN. BASE-LIN E.— TABLE XIV. Abstract of Comparisons of tie Cape Standards A and B, made at the Royal Observatory, Cape of Good \ Hope, and Calculation of their difference in length — -continued. 1 pq Sum of Mean of Sum Mean of Bar Expansion in Sum of microscope A— B in Day and HOBR, 1841. s QCUUCcU. of readings Therms. (t.) 62°— t. microscope readings microscope microscope readings. for each Bar. revolutions. reduced to 62° Pahrt. divisions. h m r o o div. Sept. 15 9 51 z..m. A 6 4258 6-4347 57-15 +4-85 +0-7093 7-1440 10 2 B 6 3758 + 4-54 10 3 B 6 3677 6-3718 57 03 4-97 0-7268 7-0986 10 6 A 6 4212 + 2-32 10 7 A 6 4038 6-4125 57-15 4-85 0-7093 7-1218 10 11 B 6 3706 +3-49 10 12 B 6 3553 6-3630 57-05 4-95 0-7239 7-0869 10 16 A 6 4071 + 1-74 10 17 A 6 3974 6-4023 57-20 4-80 0-7020 7-1043 10 21 B 6 3557 +3-08 10 22 B 6 3523 6-3540 57-08 4-92 0-7195 7 0735 10 26 A 6 4152 +3-35 10 27 A 6 4093 6-4123 57-25 4-75 0-6947 7-1070 10 31 B 6 3652 +2-21 10 32 B 6 3713 6-3683 57-10 4-90 0-7166 7-0849 10 36 A 6 3915 + 0-74 10 37 A 6 4125 6-4020 57-28 4-72 0-6903 7-0923 10 42 B 6 3932 + 0-60 10 43 B 6 3753 6-3843 67-20 4-80 0-7020 7-0863 10 48 A 6 4221 -0-08 10 49 A 6 4034 6-4128 57-40 4-60 0-6727 7-0855 10 53 B 6 3780 + 1-19 10 54 B 6 3652 6-3716 57-20 4-80 0-7020 7-0736 10 58 A 6 4040 -0-46 10 59 A 6 3886 6-3963 57-40 4-60 0-6727 7-0690 11 6 B 6 3990 +0-99 11 7 B 6 3737 6-3864 57-40 4-60 0-6727 7-0591 11 13 A 6 4277 + 1-59 11 14 A 6 4060 6-4169 57-50 4-50 0-6581 7-0750 11 20 B 6 3805 + 2-38 11 21 B 6 3764 6-3785 57-40 4-60 0-6727 7 0512 11 33 A 6 4126 +1-09 11 34 A 6 4245 6-4186 57-60 4-40 0-6435 7-0621 11 38 B 6 4047 + 1-14 11 39 B 6 3950 6-3999 57-55 4-45 0-6508 7-0507 11 45 A 6 4765 +4-63 11 46 A 6 4597 6-4681 57-70 4-30 0-6289 7-0970 5 p.m. B 6 4009 6 B 6 4029 6-4019 57-70 4-30 0-6289 7-0308 11 A 6 4038 -2-30 12 A 6 3921 6-3980 57-83 4-17 0-6098 7-0078 16 B 6 3735 + 1-30 17 B 6 3731 6-3733 57-75 4-25 0- 6-215 6-9948 21 A 6 4264 +2-79 22 A 6 4197 6-4231 57-90 4-10 0-5996 7-0227 26 B 6 3845 +2-44 27 B 6 3925 6-3885 57-83 4-17 0-6098 6-9983 31 A 6 4101 -0-42 0-32 A 6-4022 6-4062 57-98 +4-02 +0-5879 6-9941 CAT-CULATION OP THE RELATIVE LENGTHS OP CAPE STAJSTDAEDS A AND B. 381 BASE-LINE.— TABLE XIV. Abstract of Comparisons of the Cape Standards A and JS, rmde at the Royal Observatory, Cape of Good \ Hope, and Calculation of their difference in length— -continued. 1 Sum of deduced Mean of Sum Mean of Bar Expansion in Sum of microscope A— B in Day AND HOUK, 1841. o s microscope readings. of readings for each Bar. Therms. (t.) 62°— t. microscope revolutions. readings reduced to 62° Fahrt. microscope divisions. h m r o o djv. Sept. 15, 36 p.m. B 6 4015 -0-24 37 B 6 3864 6-3940 57-88 +4-12 +0-6025 6-9965 40 A 6 4424 +1-44 41 A 6 4093 6-4259 58-00 4-00 0-5850 7-0109 2 42 B 6 3652 2 43 B 6 3602 6-3627 58-33 3-67 0-5366 6-8993 2 48 A 6 3521 -2-52 2 49 A 6 3521 6-3521 58-43 3-57 0-5220 6-8741 2 54 B 6 3492 -0-08 2 55 B 6 3478 6-3485 58-40 3-60 0-5264 6-8749 3 1 A 6 3451 -1-97 3 2 A 6 3416 6-3434 58-50 3-50 0-5118 6-8552 3 6 B 6 3191 + 1-23 3 7 B 6 3139 6-3165 58-40 3-60 0-5264 6-8429 3 10 A 6 3462 + 0-90 3 11 A 6 3339 6-3401 58-50 3-50 0-5118 6-8519 3 14 B 6 3205 + 1-79 3 15 B 6 3035 6-3120 58-43 3-57 0-5220 6-8340 3 27 A 6 3764 +3-40 3 28 A 6 3593 6-3679 58-58 3-42 0-5001 6-8680 3 32 B 6 3426 +2-09 3 33 B 6 39,9:?, 6-3324 58-48 3-52 0-5147 6-8471 3 40 A 6 3132 -4-57 3 41 A 6 3185 6-3159 58-68 3-32 0-4855 6-8014 3 44 B 6 3128 -1-51 3 45 B 6 2965 6-3047 58-50 3-50 0-5118 6-8165 3 50 A 6 3436 +1-39 3 51 A 6 3373 6-3405 58-65 3-35 0-4899 6-8304 3 56 B 6 3131 +0-31 3 57 B 6 3266 6-3199 58-53 3-47 0-5074 6-8273 4 A 6 3527 +0-10 4 1 A 6 3387 6-3457 58-70 3-30 0-4826 6-8283 4 11 B 6 3382 +0-84 4 12 B 6 3159 6-3271 58-63 3-37 0-4928 6-8199 4 17 A 6 4034 +4-45 4-18 A 6-3749 6-3892 58-75 +3-25 + 0-4752 6-8644 382 VERIFICATION AND EXTENSION OF LA CAILLE'S ARC OF THE MERIDIAN. ABSTRACT OE DAILY EESTILTS DERIVED FROM TABLE XIV. DATE. No. of results. Sum of A-B. Mean daily Talue of A— B. Equivalent in inches. 1840. diT. div. August 26 10 19-70 1-970 -0000985 28 5 15-55 3-110 •0001555 29 4 6-20 1-550 -0000775 31 5 11-75 2-350 -0001175 1841. August 23 10 24-69 2-469 -0001234 September 8 14 25-33 1-809 -0000905 9 39 87-35 2-240 •0001120 10 49 183-86 3-752 •0001876 11 51 138-96 2-724 -0001362 14 34 66-67 1-961 -0000981 15 43 47-82 1-144 •0000572 Therefore by the comparisons made in 1840, before the measurement of the Base, A— B = 2-2167 = -0001108 inch. dlv- And in 1841, after the measurement of the Base, A— B = 2-3945 = -0001197 inch. The relative number of comparisons, however, are very unequal : but both materially disagree with the result of the comparisons made in London, before the Bars were forwarded to the Cape, see page 350. EXPERIMENTS IN LONDON, IN THE YEAR 1839, UITDISE THE SUPEEINTENDENCE OE THE ASTUONOMEE ROYAL, ASCERTAINING THE THERMETIC EXPANSION OF THE CAPE 10-feet IRON BARS A and B, AND THEIR LENGTHS IN RELATION ORDNANCE 10-FEET IRON BARS O. and 0«; ROYAL ASTRONOMICAL SOCIETY'S 5-FEET BRASS TUBULAR SCALE; and to Mr. SIMM'S 5-FEET BRASS TUBULAR SCALE. 384 VERIFICATION AND EXTENSION OP LA CAILLE'S ARC OP THE MERIDIAN. Reductions of the Observations for ascertaining the values of the Micrometer Screws ; used in measuring the Expansion of the Cape Bars, and their lengths in relation to other Bars. Observations made 1839, April 10, by Mi-. Main. Western Microscope. Eastern Microscope. Division on Simms' Scale. Micrometer Readings. Mic. intervals corresponding to 0-1 iuoli. Value of If. Division on Simms' Scale. Micrometer Readings. Mic. intervals corresponding to 0-1 inch. Value of v. in. 30 2-9 2-8 r 95 105 115 039 016 000 r 9-977 9-984 in. in. 3-0 2-9 2-8 r 90 100 110 100 161 163 r 10-061 10-002 in. 2-8 2-7 2-6 89 99 109 917 989 989 10-072 10-000 2-8 2-7 2-6 90 100 110 154 205 215 10-051 10-010 2-6 2-5 2-4 90 100 110 068 109 105 10-041 9-996 2-6 2-5 2-4 90 100 110 221 272 295 10-051 10 023 2-4 2-3 2-2 90 100 110 107 139 164 10-032 10-025 2-4 2-3 2-2 90 100 110 257 305 293 10-048 9-988 2-2 2-1 20 90 100 110 085 127 146 10-042 10-019 2-2 2-1 2-0 90 100 110 331 336 323 10-005 9-987 20 1-9 1-8 90 100 110 087 134 171 10-047 10-037 2-0 1-9 1-8 90 100 110 310 349 300 10-039 9-951 1-8 1-7 1-6 90 100 110 072 132 150 10-060 10 018 1-8 1-7 1-6 90 100 110 625 661 644 10-036 9-983 1-6 1-5 1-4 89 100 110 979 037 026 10-058 9-989 1-6 1-5 1-4 90 100 110 100 127 088 10-027 9-961 1-4 1-3 1-2 89 100 110 903 002 015 10-039 10-013 1-4 1-3 1-2 90 100 110 045 061 048 10-016 9-987 1-2 11 1-0 89 99 109 917 961 972 10 044 10-011 1-2 1-1 1-0 90 100 110 070 089 086 10-019 9-997 Sum 2-0 = 200-504 0-00997486 2-0 = 200-242 0-00998791 Tl 1840, Au 16 eqiu gust 8 valent f or W revolutio in = W X 0- = (E+W) in. = 0-0099813 in. = 0-01 X ( ns of western + ] 00997486 + E X In. X 0-00998138 + ( 8 {(E+W) + ^ j) revolutions in. 0-00998791 in E-W) X 0-( ^ (E -W) 531^ ^ HW+ ' 1531 of east )00006 ern: 32 (Signed) G. B. AiRT. I;XPERIMENTS MADE IN LONDON, IN THE YEAR 1839. 385 Reduction of the Observations for ascertaining the values of the Micrometer Screws ; used in comparing the lengths of the Cape Bars with those of other Bars. Dai, 1839. April 25 Western Miceoscope. Division on R. A. See. Scale. April 29 Sum . . . 12-0 11-9 12-0 11-9 120 11-9 12-0 11-9 12-0 11-9 12-0 11-9 120 11-9 12-0 11-9 12-0 11-9 12-0 11-9 Micrometer Readings. Mic. intervals corresponding, to O'l inch. 120 11-9 12-0 11-9 120 11-9 95-435 105-353 95-478 105-400 95-485 105-410 95-483 105-410 95-492 105-423 95-490 105-417 95-683 105-667 95-682 105-662 95-695 105-672 95-697 105-670 95-691 105-670 95-690 105-668 95-699 105-672 r 9-918 9-922 9-925 9-927 9-931 9-927 9-984 9-980 9-977 9-973 9-979 9-978 9-973 1-3 = 129-394 0-0100468 = 1' Eastebn Mickoscofe. Division on E. A. Soc. Scale. 12-0 11-9 12-0 11-9 12-0 11-9 120 11-9 12-0 11-9 12-0 11-9 120 11-9 12-0 11-9 12-0 11-9 12-0 11-9 12-0 11-9 120 11-9 Micrometer 94-403 104-348 94-450 104-348 94-443 104-322 94-424 104-310 94-429 104-300 94-431 104-307 95-229 105 239 95-239 105-241 95-238 105-235 95-233 105-236 95-238 105-238 95-233 105-232 Mic. intervals corresponding to 0-1 inch. 9-945 9-898 9-879 9-886 9-871 9-876 10-010 10-002 9-997 10-003 10-000 9-999 1-2 = 119-366 0-0100531 = 1"^ 386 VERIFICATION AND EXTENSION OF LA CAILLE'S ABC OF THE MERIDIAN. Reduction of the Observations made in 1839, April 8, for ascertaining the Thermetic Expansion of Cape Bar B. To 6'' SO™, the Micrometer Observations were made by Mr. Main and Mr. W. Simms, the Thermometers being read by Mr. Simms and Mr. Maun: afterwards the whole was done by Mr. Simms and Mr. W. Simms. Thermometers. MiCEOMETERS. TIME. W. E. Mean. Diff. Mean. ■w. E. E+W —180°. E-W. Diff. E+W. Diff. E-W. h m O O o o r r r r r I r 4-20 129-3 132-3 130-8 1-95 060 2-20 2-7 3-05 3-6 3-2 3-2 2-35 2-4 2-0 2-0 3-25 10-6 2-85 1-4 1-65 6-45 1-4 1-0 4-3 1-05 0-6 3-1 0-7 98-040 98-746 16-786 0-214 0-158 0-249 0-249 0-295 0-301 0-250 0-248 0-170 0-205 0-149 0-182 0-210 0-818 0189 0111 0-101 0-460 0-082 0-079 0-340 0-074 0-055 0-226 0-041 4-30 127-3 130-4 128-85 98-022 98-550 16-572 4-40 127-1 129-4 128-25 97-878 98-536 16-414 6 W =45-320 4-45 125-0 127-1 126 05 97-690 98-475 16-165 6E =49-186 6=728-15 5- 122-6 124-1 123 35 97-603 98-313 15-916 5-10 119-8 120-8 120-3 97-482 98-139 15-621 5-20 116-3 117-1 116-7 97-398 97-922 15-320 5-30 113-3 113-7 113-5 97-269 97-801 15-070 5-40 110-2 110-4 110-3 97-068 97-754 14-822 5-50 108-0 107-9 107-95 96-973 97-679 14-652 6=627-20 6- 105-7 105-4 105-55 96 853 97-594 14-447 6W = 40-894 6-10 103-7 103-4 103-55 96-770 97-528 14-298 6 E =45-347 6-20 101-3 101-8 101-55 96-657 97-459 14-116 6-30 98-6 980 98-3 96-573 97-333 13-906 7-30 88-3 87-1 87-7 96-134 96-954 13-088 7-40 85-4 84-3 84-85 95-987 96-912 12-899 7-50 84-0 82-9 83-45 95-915 96-873 1-2-788 7 W = 40-507 7=560-05 8- 82-3 81-3 81-8 95-854 96-833 12-687 7 E =47-393 8-50 760 74-7 75-35 95-587 96-640 12-227 9- 74-5 73-4 73-95 95-527 96-618 12-145 9-10 73-6 72-3 72-95 95-503 96-563 12-066 9-50 69-0 68-3 68-65 95-345 96-381 11-726 10- 67-8 67-4 67-6 95-312 96-340 11-652 10-10 67-2 66-8 670 95-441 96-156 11-597 6W = 32-199 6=392-85 10-50 64-0 63-8 63-9 95-298 96-073 11-371 6E =36-758 11- 11- 63-2 62-6 63-2 62-4 63-2 62-5 95-412 95-391 95-918 95-890 11-330 11-281 0-7 18-75 0-049 1-407 Diff. E+W 19-40 44-2 43-3 43-75 94-724 95 150 9-874 for 1°. Mean of 6 Mean of 6 Mean of 7 Mean of 6 1 121-36 104'53 80-01 65-48 43-75 16-83 2452 14-53 21-73 97-553 96-816 95-787 95-367 94-724 98-198 97-558 96-770 96126 95-150 15-751 14-374 12-557 11-493 9-874 0-645 0-742 0-983 0-759 0-426 1-377 1-817 1-064 1-619 -0-097 -0-241 +0-224 +0-333 rey- 0-0818 0-0741 0-0732 0-0745 The effect of E— W is insensible. Hence, froi n 121° Fahrenl Id- leit to 105°, the expansion of the Bar for 1° Fahrenheit = 0-000817 *» 105 80, „ „ „ =0-000740 j» 80 65, „ „ „ = 0-000731 j» 65 44, „ „ „ =0-000744 1840, August 8. (Signed) G. B. Aibt. EXPERIMENTS MADE IN LONDON, IN THE YEAR 1839. 387 Reduction of the Observations made on 1839, April ^, for ascertaining the Thermetic Expansion of Cape Bar A. To 3' 5™, the Observations were made under Mr. Main's direction: after that under Mr. Simms's direction. TIME. Thekmometbrs. MiCEOMBTERS. W. E. Mean. Diflf. W. E. E+W E-W Diff. Diff. Mean. —190°. E+W E-W. h m C o o o r f r r r 0-15 139-5 141-7 140-6 -0-55 +5-20 5-65 5-4 5-35 5-05 2-75 2-10 305 4-4 2-35 1-95 1-8 1-95 1-8 1-75 1-85 6-6 1-5 1-3 1-2 4-5 1-15 1-0 3-15 1-15 0-85 3-15 0-5 0-8 2-0 0-6 0-4 2-7 99-985 97-703 7-688 2=277-10 0-25 140-0 142-3 141-15 99-818 97-772 7-590 0-098 2 W = 19-683 0-35 135-3 136-6 135-95 99-865 97-210 7-075 0-515 2 E = 14-982 0-45 130-0 130-6 130-3 99-562 97-031 6-593 0-482 0-55 1250 124-8 124-9 99 449 96-710 6-159 0-434 6=710-65 1- 5 119-4 119-7 119-55 99-202 96-514 5-716 0-443 0-441 0-247 6 W = 54-944 1-15 1150 114-0 114-5 99-035 96-240 5-275 6 E =38-629 1-25 112-1 111-4 111-75 98-915 96-113 5-028 1-35 109-5 109-8 109-65 98-781 96-021 4-802 0-226 1-45 106-9 1063 106-6 98-541 96-050 4-591 0-211 1-55 102-7 101-7 102-2 98-416 95-868 4-284 0-307 2- 5 100-3 99-4 99-85 98-313 95-791 4-104 0-180 2-15 98-3 97-5 97-9 98-229 95-732 3-961 0-143 9=868-50 2-25 96-6 95 6 96-1 98-170 95-661 3-831 0-130 0-163 0-150 9W = 73-452 2-35 94-5 93-8 94-15 98-058 95-610 3-668 9E =51-157 2-45 92-9 91-8 92-35 97-970 95-548 3-518 2-55 91-0 90-2 90-6 97-912 95-485 3-397 0-121 3- 5 89-1 88-4 88-75 97-843 95-412 3-255 0-142 3-55 82-4 81-9 82-15 97-648 95-082 2-730 0-525 0-107 4- 81-1 80-2 80-65 97-589 95-034 2-623 4- 5 79-8 78-9 79-35 97-537 94-952 2-519 0-104 0-073 0-335 0-076 0'074 0-245 0-060 0-045 0-244 0-045 0-051 0-149 0-047 0-046 0-212 4-10 76-5 77-8 78-15 97-497 94-949 2-446 10=739-85 4-50 74-0 73-3 7365 97-272 94-839 2-1 n 10W=72-845 5- 72-8 72-2 72-5 97-230 94-805 2-035 lOE =48-563 5-10 71-8 71-2 71-5 97-182 94-779 1-961 5-50 68-1 68-6 68-35 97003 94-713 1-716 6- 67-4 67-0 67-2 96-950 94-706 1-656 6-10 66-4 66'3 66-35 96-937 94-674 1-611 6-50 63-4 63-0 63-2 96-789 94-578 1-367 7- 62-9 62-5 62-7 96-771 94-551 1-322 7-10 62-0 61-8 61-9 96-786 94-485 1-271 7-50 60-0 59-8 59-9 96731 94-391 1-122 9W = 59-990 9=532-85 8- 59-4 59-2 59-3 96-691 94-384 1-075 9E =39-512 8-10 59-0 58-8 58-9 96-653 94-376 1-029 8-50 56-2 55-8 56-2 55-5 56-2 55-65 96-553 96-515 94-264 94-254 0-817 0-769 9- 0-55 0-55 10-25 0-048 0-039 0-699 Diff. E+W 9-10 55-2 55-0 55-1 96-501 94-229 0-730 for 1°. 21-10 45-0 44-7 44-85 96-453 93-578 0-031 Mean of 2 Mean of 6 Mean of 9 Mean of 10 Mean of 9 1 138-55 118-44 96-5 73-98 59-21 44-85 20-11 21-94 22-52 14-77 14-36 99-842 99-157 98-161 97-284 96-666 96-453 97-491 96-438 95-684 94-856 94-390 93-578 7-333 5-595 3-845 2-140 1-056 0-031 -2-351 -2-719 -2 477 -2-428 -2-276 -2-875 1-738 1-750 1-705 1-084 1025 +0-368 -0-242 -0-049 -0-152 +0-599 rev. 0-0864 0-0798 0-0757 0-0734 0-0714 From 13 9° Fahrenheit in- to 119°, the expansion of the Bar for 1° Fahrenheit = 0-000863 „ 11 9 97, „ „ „ =0-000797 „ 9 7 74, „ „ „ = 0-000756 7 4 59, „ „ „ =0-000733 5 9 45, „ „ „ =0-000713 1840, All gust 8. (Signed) G. B. Airy. 2 O This stands -468 in the original. 388 VERIFICATION AND EXTENSION OP LA CAILLE'S ARC OP THE MERIDIAN. 1^^ ICOCDOOOOtTJCOO to rt 050t*CO-^005t^'^p-Hi^(N .nHOO^ 00 05 ^«3OQ0C»'-l00-«#t^'^00;C> Trill raeasui Standi tempei CNn-.(NCN(M(N(NfiO n (M Oi-i.-IC003(NOC0O(NOC0 - (N(N{M(M(N(NGO(N>OC0t^C0;0 Correc tion fo excess ( Standai c^aicoco»0"^»o^ CO 0:1 I^IO-^COCN^CNOOOCNIOOO rJOCD^05 CO T)t (M«5Tll-*(NlOi~CT00-*^«5 's +S CClCOJ>00(Nt^C0O5 1 + >o Oi ■*OtOT)lt~COtt>-*QOrHCOt~ OOiX'QOQ0050D005 CO t^ a5i-i05005CMO'-tOCOr^^ i^T 000000<-'0 5 oooooooo 9 9 oooooooooooo - 6 1^ . H-^ f^s; t^CO-^COO^-HO* f^°o; CO -f OCOi-HOOCO^-* ■Tj<005rHOOW5^-*^COCOOaoa005'Xl +1 iX)GOi^CXJCMl>.CQa> +2 >o C-j -^-^OSt-hio*^^ 0DCDrH»0>Ot^^CDrHCD{NOC0(NI^ QO^QOQOO^GOOO^ to »~ 050SOi-<050SO CT)05(N(NOO'^^^OC0C0^i-Hr-H ^ 1 ^ 666666f^6 ^ 1 6 6 6 6 A i^ 6 6 « 6 6 i^ i^ r^ t^ rt Ai .^ r^ .^ A A rt A i ©OOOOt^tMXO to 05 01 "O 00 CO CO 10 00 t- CD (N 00 rH CO « CM CO >0 t- 1 OCO>0»0'^'— it^OO OS Tf n-. 05 03 00 rt CO >0 CO 1> i-i -Tfl CO t- '^ XO CD (M (N >0 H OWr-lr-l>OI>»0-^ OD OS a0GOp'7lO51>-rH O5p>53'*{NC0i-Hi-l00pc0C0>O»O(N . »bTt<>b»0'^-^«« O) 00 05050005005 000505050503050500030505050305 OJOiOSOOSOSOsOS 05 a> 05030005005 030303050505050505050505050505 i-H rH ft ;S t^iOT^coco-^coca t~00t^(NrHC050OO— H^>Oa)O;Dt^CDt-.O!N00(M00TIO ^'^CNC0t^CD>O'-i ODOOCOOCN»ca)i-H*^CDi-HOGq>OQOt^Tl<{Nooa)t^rHlca0^t^OO»o ^ 00 OT t^J:^ CO rH Tf »0 ^>^>a)<»^-Hpaioo5CN0505po^lX)^^ao^-a)05(^^oC5aicD^r^05G5 Tt<»OTi<'^»o»ocbcb OOOOOOOiOdiOSOO-^OOOOOOOr^r^OOOOOO O5O5050i05O5O50i 0000000500503000000000000000000 PP i-Hi— II— (i-Ht— 1(— 1 r-t 1— li— lrHr-1r-lr-o »c to »c 00 >0»0»0>C »0 00 »oco Q »p»0.^CDCDOC0O'0>O*~OTt< Z 6iOooooa)obi>.j>- ih At ^^>b6-*mT(id5m(Nc6d5 02 H M rHC»|i— fi-Hi— CO CO ■" ,— *— V ,_.^., /—*— > ,— *— N (4 f5 »o »o »o »o >o »o CO »0 »0 »0 »^ CO »o *^ r* »o t^ t^ g ■^>o^*(«■^cpGp9 f^ CO i-H (N W5 CO 0^0 CD {N»0»p CO eft CO*^ 1 o Sl!!ll?!2?I2?2^!^'^ j^ 65 6 i>- t>- CD <^ ^ 6d do (» (f^CNO) 63 do b S -511 ^ ■* Sj «5 o r~t-^ 1 4^ »O»OC0C0'«J CO CpTHO 03 « 1>-T^CD CO r-( 03-* S3 o 23i22f2^£23'^ 1-* 65 t^ ^.. (i> Aicqdb do <» (Nwdo 05 03 (nco w ■^^niTji^^-*}!^ ■* Tjl V3 ■* Tt< ■* >0 >0 ■* T)< Tf «5 «5 ^ i* ^ 53 S (i5 »^ 05 rfi (N CO (N CO S o b- 65 05 ^ A (N CN Cfl Tf ■* Tji •O >0 >0 io S S ^' ■^»0(M-^Tjpocpw7^o«cp^T|.2§m 1 (N(Nl?-«>OOrHrH •= tM !N CT (N m «> mOOO-HrnA^CTCTCTCT t§ ■= 00 of oT oT ^- lO* » (M (M a ra t-i ^ s r = ~ J <1 00050 9000000«5 "OIOIOIOXJUOIOXS EXPERIMENTS MADE IN LONDON, IN THE TEAR 1839. 389 n CO t~ o »o 00 o w >o W5 o CO CO o lo t~ CO CO OS CD :S OS Til -* fN r^ OJ >o O CD O CO I-H 00 OS 00 »o o rt CO CO a. 5^ o o 1— 1 O i-H CO OS .—1 IN CO lOS o o 1^ r~ to CO t^ 00 IN CO o 00 »~ »^ o o o o o o ^ o 05 Ol o CD t~ OS 00 lO »o CD Til o ^ o CO I— 1 1— t CO -* OS 00 CD 00 CO ?» CO (N o o o O rH O OS o o o 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 • 9 O (Mt^r^C00005C)C0G0t^O-* t^ CD ^ I-H O CD W5 X5 00 CO 00 r-< Od I^ 1 00 ut o ^ 00 - ■* IM OOCN^iO(N ■OOKOCOOCOtII-* OS OS 00 OS t~ C£ op 1— t .— CO o> 0>OS00030SOSCSOSCSCSOSO)OSOSGSCSOSOSOSCSOS OS OS OS OS OS OS rtCC'00»OCDCOT)^CO>0>0^i-IOOr- 00 Tt O CD - HrtooooinHcoeqiM O 00 CO rt ,-1 (^ CO 00 l~ «3 lO j>oscot->oOooccp 1 O rt tP CC -" 'Z "■• " ~-^ ■ ^**^QOoocoo5ai^^(»'o■^■^■^■^"^wcooiOOdioSoioSo5ob»ococ^^^QbOi^O'^cN(7l05a:lO^ CsOiOOOOOO SOOOOOOOOO-lrtOOOOrHr^rH^rnOOOO o o O s " )s! ^ '="•'■' ii « ■ ojosooooooooooooooooooododooooooooo o o 2 '-"-'"•':=; ±; i ^^^^^^^^ I-H " " >o 00 iM v:i >o »o ■10 IN >o >o >o »o lO »o CO t^ CD oo i~ T(< »~ »^ CN CO CO CO CO CM W3 r-l «5 •T" (M CI 0 CO CO aH^ r-l rH CO «5 Til lO CO s *>- t* t^ CO r-H» , 1- 00 -tjl CD r- ■^ V3 -* X5 CO S 1> CO CO CO CO o oo ~ a — 1~ 00 00 i-l IN 00 2 OS 0 Til Tjl ij Til ^ ^ ■* >0 XO ^ Tjl rl< Tl< ^ • Tfl Tt" W3 X5 T)H Ti< Tf >0 « ■* ■* ■* CO '^ >0 CO »^ W5 CO (N 1^ 1^ l^ CD >0 00 OS t^ CO >o CO U5 00 CO IM OS Til CO ■* 05 05 O CO CO 00 00 1^ t* 1:^ ^- t^ t^ O >-H^ 00 00 (N IN oo OS OS 0 Tf Tjl Tjl ^ T|< ^ •to >o >0 "* Tt ■* -* ■^ -* t ^ "O X5 Tl< t-a>aio\ (N 00 •* >o O IN >0 op (M (N 1^ 00 >0 lO T)l Tf o o 1— I r— 1 o* 0^ t: t: «0 lO Tf Til « ■* CO ^ OS (N -^ CD CO CO 00 r- 1~- r-< O CO 1* 0 •<* ■* ■* ^ ^ ^ T)l O i-H 1^ >0>OTl< 00 00 l-l IN 00 Tt< T)l >0 >0 Tf en 00 lO >0 Til Til 11 ^ tK o >o >o «5 (N o CO (N CO CO CO CO CO CO o o 6 o o r-^ fH rl rH IN IN IN (N at n ■* 9 1— ( CO CO r-l -Cf •* -cl< CO (N 00 9 Til Til -^ >b t— 1 >o CO (X> PH At «5 ■o ■o Ki lO ■^ >o «5 c _ 390 VERIFICATION AND EXTENSION OF LA CAILLE'S ARC OF THE MERIDIAN. — I CM r-i (N (N o o o o t^ Q) a O O CJ S *^ cutB CD O CO CD '-^ *^ O "O o o I— « o o I— < o O 00 O O OJ o rt O rt o o o f— I lo I— I CD J> l~ ■* >o C^ Oi O^ Oi rt o o o o o o o 05 o CO O CO (N J^ —I 1^ o O 1-1 o ^ ai'To ^^2 !3 +2 00 (N 05 en ^ o c 5; 2 r1 O O o o o o O O o OOti-^ OOf-icNCNQOOOOasc^COOiOi-HCCi^- .-lOI>- OSOiOipOOOOiaiOSOSOr-Hr-Hr-ip ,1hAO OOO'-H'-Hr^'^OOOO'— 'f-l'-lr^'-l OSCil— (l-Hl— (l-HCNr-l pppOpppPP OOr— li— irHi— li-Hi— * 1— (I— li— ii— — lOsOicooi'X' COO^OOi— lOOCDCDOCNCO>OCD(N'^ OC003i-iC0^i-H^-00Oi— iCOW3-^"*CO C30F-l>O«C^r-IC000 ■^CDOGOOO-— iCNOi 00OiCQCN^>O»O00 J>-0005Q0(^^o:lCD■-^oc^^ COCOOipJ'-HMC0C0F-i»0Tto ^ >o m o a a -2 a a o CO tH o o «~- O H o ■o l^) (N ^ CM (n t^ v:) !>. O 1^1 1— I o 1-1 00 00 CO 1-1 (>» 00 *C W3 tP 5 00 lO >o ■^ >o ■^ t^ OS l-H o 1—1 00 CO 00 (M (N 00 OJ CO CO CD CO 00 » CO 00 W W J>- CD lO >0 T)< T)< o ^ CO Oi o 6 >a 'a OJ >p !N O O r^ O) >o >o '^ CO !*■ "^ »— t ^ I— I 1—1 00 OJ 00 lO «o ^ "^ "^ 1> i i> >o uo ■* Iz; pq OO ^ FQ H P5 CO CO OC53 J fQ W cc co d"0 J J fQ M co co cTcTo 2 J O O O O'd'o OCTo a Tf o 6 o IN 6 CO th >o O 6 6 6 Ai CO 05 (N lO >0 —1 n o (N CO (N CO 1— 1 1-1 (M CO IN CO CO (N §5 p< £ o >o o CO ■* WO O CT> W3 >o xo Tfl O o r-i IXI 00 (M <-> en O 05 o 9 9 9 oo ^ »^ (^ p— t Oi im o o a, o f-^ ■* OS >^ (N j^ P-H I-H o a. o 9 9 o o r-t 50 -^ m o CO c< >n o 03 o I— I O rH o o 9 o OiO>OCOCOCOOt^TtiCOC005(M»COCOCD(N-^OSTj< OC0OO)O-*00t~OOOOCTa5Q05OC0(N »OC0OO^O5050S>Ci^i-ICNCQOC005(N»00'-ICO'^OOCO(N V^CC>^0>0C}CC!r-irH05*^CDOO-^OCOC£3t-Oi^ («^-^>p(»9l~*9*Oi>OTCN'^>0'y3COr-^cpTj<(>IiyHtN odooDOO'^O'^OOOOOsdsOSOSOOOOOO O0i05OOOOOOOOO0S0S0503OOOOOO 50 9 ©"d d'do'd'*^ JWMffl ^ o o cq CO 6 6 i-f o Cff W5 CO 1^ o o CO >01 CO CO CO 2 P 392 VERiriCATION" AND EXTENSIOJf OF LA CAILLE'S AKO OF THE MERIDIAN. Ledger of Results in Comparison of Bars. S A — continued. Ast. — continued. Dat and Hodb, 1839. True measure at Standard temperature. Dat and Hock, 1839. True measure at Standard temperature. Dat and Houe, 1839. True measure at Standard temperature. h m April 8, 2 „ 9, 7-40 „ 8, 20 „ 9, 21 Mean . . „ 25, 0- 6 1-30 2-20 . 2-47 „ 26, 0- 0-35 1-42 2-36 23-30 „ 27, 0-20 1- 1-45 Mean . . -02295 •02248 •02278 -02310 h m April 29, 0-41 0-59 Mean . . •02019 •0-2021 b m April 27, 0-35 112 1-59 Mean . . •02349 •02342 •02313 •02009 •02334 •02283 B •02107 -0-2089 •02087 •02143 -02095 -02090 -020(10 -02013 •02034 •02037 •02086 •02071 0. April 8, 2 „ 9, 7-30 Mean . . „ 26, 1-22 2-30 23-15 „ 27, 0-10 0-55 1-29 Mean . . „ 29, 0-30 0-50 1- 3 Mean.. •02180 •02206 April 25, 0^ 1-25 2^10 3- 6 23-53 „ 26, 15 Mean . . „ 28, 23-15 23-26 23-40 Mean . . •02160 •02210 •0^2241 •02197 -02210 •02175 •02193 •01963 •01986 •01959 •01982 •01942 •01946 •02199 •02108 •0-2138 -02187 •0-2071 01963 A -01968 -01980 •01996 •02144 •01981 0. April 8, 20 „ 9, 21 Mean. . „ 24, 23-50 „ 25, 1-15 2- 4 3- 23-45 „ 26, 0-7 Mean . . „ 29, 0-20 •02216 •02283 Ast. April 26, 1-51 2-45 23-47 „ 27, 0-25 1- 6 1-53 Mean . . „ 28, 23^20 23 34 23-48 Mean . . •02135 •02199 •02164 •02115 •02131 •02153 •02250 April 24, 23-20 23-33 „ 25, 0-29 1-45 2-35 3-28 23-35 „ 26, 1- 2-10 2-55 23- 5 23-59 •02386 •02291 •02383 •02347 •0-2362 •02360 -02375 •02303 •02317 •02286 •02345 •02252 -02019 •01994 •02074 •02023 •01958 •02055 •02150 •02142 •02153 •02166 -02021 •01989 •02154 EXPERIMENTS MADE EST LONDON, IN THE YEAR 1839. 393 Abstract of Ledger. 1839. B. A. Ast. Oi April Sand 9 April 25, 26, 27 April 28 and 29 Correction of April \ 8 and 9 J Correction of April 1 28and29 j •02283 •02071 •02193 •01963 •01981 •02250 •02021 •02009 •02334 •00212 -•00230 •00229 - -00018 + •00012 Adopted Cohrections. April 8 and 9 = — -00221 April 28 and 29 = + -00011. Corrected Numbers. •02199 •02144 •02150 •02154 + •00055 -•00004 4.... 12.... S •02062 •02071 B 2.... ^01972 6.... -01963 3.... -01992 A 2.... -02029 6.... -02021 Mean •02069 3.... -02020 Mean -01973 Mean -02022 Ast. -02334 O, 6.... -02199 3.... -02155 Mean • 02184 O. 6.... ^02150 3..,. •0-2165 Mean • 02155 Therefore, S = Ast. — -00265 (Simms's Standard) B = Ast. - •00361 (Cape Bar B) A = Ast. — • 00312 (Cape Bar A) O, = Ast. — • 00150 (Ordnance Bar [2]) O, = Ast. — • 00179 (Ordnance Bar [1] ) 1840, August 13. (Signed) G. B. Airy. OPEEATIONS FOR THE VERIFICATION AND EXTENSION OF THE ABBE DE LA CAILLE'S ARC OF THE MERIDIAN, AT THE CAPE OF GOOD HOPE. PART IV. TRIANGULATIOISr OF THE ARC. § 1. Character of the Country. Coimnencing at Cape Hanglip, and running nearly due north, a sand-stone topped § i. range of mountains, of different elevations under 5700 feet, extends to the north end of fte^'country! the Cedar Mountains (a distance of about 140 miles), where high table land begins, and is continued to the east end of the Kamies Bergen, — the mountains which marked the former north-west boundary of the colony. On the west side of False Bay, a range commences at Cape Point, extends from thence to Table Mountain, a distance of 28 miles : then an interruption of some thirty miles occurs, wherein lie the Cape Downs and a few hills. The next 150 miles north- ward is partly occupied by the isolated masses, Paarden Berg, Riebeek's Kasteel, Piket Berg, (the Zwartland Plain) and Heerenlogement's Berg. From Heerenlogement's Berg to the Kamies Bergen the surface is mostly an undulating desert, more or less covered with bush and granite boulders. The head lands that here and there fringe the sea shore between Blaauwberg (near the Cape Downs) and the Kamies Bergen are com- paratively low, excepting in the neighbourhood of Saldanha Bay. 396 VERIFICATION AND EXTENSION OF LA CAILLE'S ARC OF THE MERIDIAN. § 1- Character of the Country. Scenery. Cultivation. Eivers. Granite and gneiss, topped with sand-stone, is the distinguishing feature of the several masses south of the Kamies Bergen. A few hills are entirely of granite, as Kapoc Berg and the elevations about Groenekloof. The Kamies Bergen commence at the north-west edge of the Bokkeveld table land, run westward, then north-westward, bordering the sea shore, and enclosing the Kopper Bergen in their course. The most productive of the latter are at the commencement of the bend, near an elevation named Vogel Klip. Strictly the name " Kamies " is confined to about 30 miles of the transverse run : the broad girdle of isolated masses composing the continuation, bear local names mostly of Hottentot origin. The Kamies Bergen and their continuation bound on the south and west sides, the remarkably flat elevated table land, named the " Bushman Flat," the area of which, ex- cluding the undulating portion adjacent to the Karree Berg and Orange River, may be taken at 6000 square miles, and the mean height of its surface above the sea at 3200 feet. It consists almost entirely of granite and gneiss. Parts of its surface are frosted with quartz ; but in general there is a sufficient covering of sand to afford a nidus for grass and stunted bush, which spring up luxuriantly after thunder rains. On viewing, from the Bushman Flat, the quartz table-shaped tops of the mountains fringing its west border, they convey the impression of being the wreck of disintegration, — the hardy remnants of similar table lands. Excepting the mountain scenery, and the impress of civilization about the few villages and missionary institutions, there is little to please the eye of the traveller between Cape Town and the Orange River. The outlines of the mountains are suffi- ciently varied to continually interest, — and it is impossible to regard without emotion, the changing hues of the landscape, when the rays of the rising or setting sun glide along their crests. The sandy downs of the open country between Cape Town and Groenekloof, between Piket Berg and Heerenlogement's Berg, are relieved to a certain extent, by the intermediate blotches of pot-clay, more or less arable, and here and there an oasis as Lang Valei. From Heerenlogement's Berg to the Kamies Bergen the open country is dreary. Of the pot-clay blotches, Koeberg and Zwartland in particular, produce excellent corn, said to be unrivalled. The vineyards, orchards, and gardens are mainly confined to the immediate proximity of the mountains and ravmes, where evaporation is less and water more abundant than in the open country. But the most remarkable instance of fertility occurs in the occasionally overflowed banks of the Olifant's River, at a place named Friedensdal, in the desert north of Heerenlogement's Berg, where the circumstances are similar to the overflowing of the Nile. The wheat planted in the soil thus watered, returns 120-fold. Of the several rivers between Cape Town and the Bushman Flat, all are either dry or mere lagoons, except three, during the summer season : the exceptions are the Liesbeek, the Berg, and the Olifant's Rivers. The first, compared with the other two, CHARACTER OF THE COUNTRY. 397 is small : it springs from the south face of Table Mountain and empties into Table Bay, § i- north-west of the Observatory. The Berg River springs from the mountains between the Country. Hottentot's Holland and French Hoek, passes northward through Drakenstein and near Rivers. the Paarl : receives the collection of the " 24 Rivers," intersects Zwartland in its westward course, and enters the sea near the south end of St, Helena Bay. Before entering Zwartland, it has received the west face drainage of above 70 miles of mountain range, and by comparison with the mean height of the Base-line, the fall between Piket Berg and its mouth (a distance of some 35 miles) may be estimated at 140 feet, or less than 4 feet per mile: hence the body of water is large at all seasons, and its depth in parts considerable. Proceeding from the mountains near Winterberg, the Olifant's River takes a northerly course, in the vale on the west side of the Cedar Bergen, receives the Doom' River and other tributaries, bends westward near Freidensdal, and after a few windings opens into the sea, in about latitude 31° 40'. (The latitude was not observed). Between Freidensdal and the sea the fall is small, and the depth in parts from 15 to 20 or more feet. Like most of the South African rivers, the mouth is blocked by a sand bar, under- neath the surface of which the water finds its way through the sand into the sea, except during floods, when an open channel is cut by the force of the torrent. There is no bridge over this river, nor over the Berg River below the Paarl ; but there is a floating "pont" over the latter, near the entrance to Zwartland. 2. Description of the Theodolites, and method of using them. The Fuller Theodolite. — The instrument by means of which the chief portion of the 20-inch angles were measured, was lent to the Lords Commissioners of the Admiralty, by the Theodoute. Royal Astronomical Society, for service at the Cape, — apparently the first it had been employed in (a). In general construction it is on the plan adopted by Ramsden, for his large Theo- dolites. The horizontal circle is about 20 inches in diameter, and the telescope about 30 inches in focal length. A second telescope, of shorter length but nearly of equal power, was fixed, at my suggestion, to the frame underneath the divided circle, in the vertical axis prolonged, having a small range of motion in Azimuth for the purpose of adjusting it to a mark. The spirit level of the horizontal axis hangs from projecting cocks fixed to the axis, — and attached to one end of the latter there is a small circle (provided with a short spirit level) intended for measuring diflferences of elevation to the accuracy of one minute. Three equidistant microscopes are fixed to horizontal arms projecting from a ring (a). It IB named the Fuller Theodolite in the observing books, in consequence of having been presented to the Society by the late J. Fuller, Esq.., M.P. It was made by Mr. Thos. Jones. 398 VERIFICATION AND EXTENSION OP LA CAILLE'S ARC OP THE MERIDIAN. 4 1- -'0-inch Theodolite. Method of using the 20-inch Theodohte. which works on the vertical axis, — the outer ends of the arms resting upon a flat ring, along which they are moveable by sliding, and to which one of them is clamped when measuring: this ring serves the purpose of a "repeating table," admitting of an angle being measured on any arc of the divided circle. The register head of each micrometer screw is divided into 120 parts, marked in succession from to 60, to 60 ; the divisions of the circle are to every tenth minute, and 5 revolutions of the screw carry the cross wire over one interval, therefore one part of the micrometer equals one second, — the error for " runs " being taken into account. By this arrangement of the micrometer divisions, mistakes of a minute are likely to occur if the excentricity and division errors are considerable. The quality of the divisions, and the infirm connexion between the biting pieces and block of the tangent screw clamp, were not such as might have been expected from an instrument of its appearance. Against the infirmity of the latter, no other remedy than extreme care was available at the Cape. The division errors were eliminated by measur- ing each angle on consecutive arcs of the circle without omitting a division, a system not rigorously pursued when triangulating the sections of the Base, but strictly adhered to on the general triangulation. The method pursued in measuring an angle was as follows : the " runs " of the micrometer screws were determined in the accidental temperature, in three equidistant positions of the circle (0°, 120°, 240°, in succession under microscope A) to supply the proportional correction to be applied to each partial measure. The microscope arm having been clamped to the flat ring, and the lower or " tell tale" telescope pointed to a defined object ; the upper telescope was directed to the left hand signal, and the three microscopes were read : the telescope was then directed to the right hand signal, and the microscopes read, after examining the " tell tale " telescope bisec- tion. The upper telescope was again pointed to the left, and to the right hand signal as before, and the mean of the two measures was regarded as one partial measure, or in field phrase, a " couplet." Next, the microscope arm was undamped from the flat ring and slided along it, until the advanced reading of the last measure appeared as near in the focus of microscope A as could be managed with facility: the arm was then clamped, and another " couplet" measured as before ; and so on stepping the circle without omitting a division, until as many " couplets " were measured for the determination of the angle (seldom less than thirty for a primary angle, and sometimes as many as eighty) as were believed to be necessary. If any discrepancy appeared between the first and second measures of a "couplet," the measure was repeated : and generally the telescope was moved from the left to the right hand signal, alternately direct in the order of increasing readings, and back through the supplement of the angle : also one half of the measures were taken with the perforated pivot to the right hand, the telescope was then lifted from its bearings and reversed, DESCRIPTION OF THE THEODOLITES. 399 and the other half were taken with the perforated pivot to the left hand. Thus the § i- 1 . , . , T • 1 n ,. r ■ ^■ ■, Method of advantages of the repeating circle were obtained, free from some of its disadvantages, using the though at a great sacrifice of labour, time, and expense. Theodolite. Care was taken to keep the flat ring clean, to prevent stickage between it and the microscope arms, so as to allow the latter to quickly assume the resting position : and here it may be proper to observe, that greater confidence with respect to the constancy of the relative positions of the microscopes would have been obtained, if the microscope pillars had sprung from a circle attached to the arms, or if the ends of the arms had been joined by arcs of a circle. Upon the whole, however, there is reason to expect that the angles measured with this instrument by the method just described, are perfectly free from division errors; and that the errors from want of firmness in the clamping, and' from any cause which has not « a constant tendency in one direction, are so distributed by the large number of repeti- tions, as to be nearly insensible in the mean also. The supporting trestle was massive and well braced. The Beaufort Theodolite. — From an early period of the triangulation, the econo- The Beaufort mical advantage of working two theodolites simultaneously at adjacent stations became repeating obvious, particularly where heliostat signals are used; because the reflector can be placed exactly in line, at the distance of a few feet from a station, by means of the theodolite centered over the station point. Having solicited Sir Francis Beaufort's attention to this circumstance, he searched, but without success, for a second theodolite of the requisite power : then rather than any thing should be wanting that would facilitate the operation ; with his characteristic liberality and public spirit, he at once forwarded to the Cape his own pet theodolite by Reichenbach and Ertel, an instrument of comparatively small dimensions, but of consi- derable power and exquisite workmanship. The horizontal circle is about 8 J inches in diameter, divided to. every tenth minute, Description of and by each of four verniers to 10 seconds; but three seconds maybe estimated with Thefdol^r* facility, owing to the divisions being sharp and fine, and the plane of the verniers coin- ciding with the plane of the divided circle. The upper telescope is about 13| inches in length (a little longer than the lower) : the pivots of its axis are of polished steel, and the axis carries at one end a small altitude circle, counterpoised at the other end by an arm provided with a tangent screw for motion in altitude. The vernier of the vertical circle is screwed to the frame, near one of the Y bearings, hence when the azimuth axis is adjusted for verticality, the zero of the altitude circle is constant, and one level serves for the adjustments in altitude and azimuth. This (the axis) level rides on the pivots (prolonged) of the horizontal axis. The makers supplied one mounted and one spare tube, the scale of each cut in the 400 VERIFICATION AND EXTENSION OF LA CAILLE'S ARC OP THE MERIDIAN. § 1- Description of the Beaufort TheodoUte. Method of working the Beaufort Theodolite. DoUond's repeating circle. glass. Two others were added in London, with ivory scales. The divisions of the spare tube have not been examined, — the values of the other are as follows : Munich, mounted, M. \"'9. London, mounted, A. 3 '3. B. 8-0. A has always been employed at the Cape. Three discs of brass, each having a conical hole to receive the conical end of a foot screw ; and three strong pins projecting from its lower surface, for the purpose of being pressed firmly into the wooden top of the supporting trestle, — secure the frame of the instrument against horizontal shift on its bearings. After a few preliminary essays the instrument came into systematic use in March, 1844. With few exceptions, the plan pursued when measuring was by repetition, the verniers being read at the beginning and end of every tenth. The lower or " tell tale " telescope having been adjusted to one of the signals, or to some well-defined mark, was watched from time to time ; and if any shift became visible, it was rectified by moving the whole instrument (save the tripod) by means of the proper tangent screw, which transferred the quantity shifted to the following bisection of the right hand signal. The mean of every tenth repetition being regarded as one partial result, the required number of such results depended upon the importance of the angle, and the atmospheric circumstances during the time when measuring. The value of the latter may be gathered from the fact of five results obtained during first-rate definition, giving a probable error of 0"'05 and weight 360 (a) ; whereas during bad definition and lateral refraction, 16 results gave a probable error of 0""3, and weight 11 {b). In moving the object glass, it was passed forward over the angle direct, and over the supplement of the angle backward, in alternate order, which amounts to measuring the angle and its supplement : and if the difference between the elevation of the signals was considerable, the Y bearings were reversed 180° in Azimuth for one half of the partial measures. Notwithstanding the excellence of the object glass, its small dimensions, compared with that of the 20-inch instrument, was felt when dealing with distant opake signals during sunshine ; forasmuch as the phase of the signal was not always visible : but with respect to heliostat signals, the light through a 4-inch diaphragm aperture, distant 80 miles, appeared as a small star in the telescope and was successfully observed ! (c). The compactness and portability of instruments of this description particularly suit them for a mountainous country. Repeating Instrument, by Dollond. — This instrument is described in the 1st volume of the memoirs of the Royal Astronomical Society, page 55. It was used on the trian- gulation for measuring zenith distances. (aj Simon's Berg, Nov. 19, 1845. (b) Kapoc Berg, Feb. 12, 1846. (c) Kamies Sector Berg— Keibiskow. STATION POINT SIGNALS. 401 3. Signals. The solar reflectors or heliostats which were employed on the survey, were con- § i. structed in a homely way, on the principles of an altitude and azimuth instrument, the reflector swinging toilet-glass fashion in a frame, which frame moved freely in azimuth. The centre of the reflector is supposed to coincide in all positions with the azimuth axis prolonged, and the degree of accuracy aimed at in centering the azimuth axis over the station point, is the same as in centering a theodolite. The reflector is a piece of silvered plate-glass, 7 inches square, fixed within a teak- wood border, by means of corner pieces of tin plate, care having been taken to select plane and parallel surface glass. Stiff" cartridge paper is pasted round the border, leaving a circular disc of reflecting surface, 6 inches in diameter. The frame is formed from a piece of steel bar, 16 inches long, 0"5 inch broad, and 0*2 inch thick. Four inches of each end are turned up at right angles, and the centre of the base is perforated to receive a square-necked screw, 2 inches in length, which passes through a teakwood tail piece and the cylinder of hard wood that forms the azimuth axis. The lower end of the screw receives a nut screw, with a loop (in one piece) for the suspension of a plumb- line. An equilateral wooden tripod, furnished with foot screws for levelling it, has a socket in its centre to receive the cylinder or azimuth axis. The azimuth axis prolonged should intersect the horizontal axis of the reflector, in the centre of the reflecting disc. Opposite to this intersection, a hole of about O'l inch in diameter, is made in the tin plate that protects the back or silvered face of the glass : and at the intersection a little of the amalgam is scraped off", for a purpose that will be mentioned presently. Each heliostat is provided with a small level, to be placed upon the reflecting surface (when turned up) for the purpose of adjusting the cross axis parrallel to the horizon. The light is reflected towards the required point by means of a hole in a screen, set up at the distance of from 10 to 15 yards in front of the heliostat. A 2-inch aperture is sufficient in the Cape climate for 30 miles, 3 inches for 40 or 50 miles, 4 inches for 70 or 80 miles, &c. The method of proceeding is as follows : at the station where the theodolite is being worked, a heliostat is placed on a convenient spot near the instrument, and screens with wide apertures are set up in the lines of the distant stations, for the purpose of directing and telegraphing (a). On the signalman reaching a distant station, if the point has not already been defined. Adjustment of he drills a hole in the rock, fills it with lead, drives a brass pin into the centre of the lead, (a) The following wiU show the system of telegraphing: — Attention to your heliostat, or " flashing up " a light Flashes of 3 seconds duration and 3 seconds shade, in alternate order. Tour %ht not wanted again to-day 3 minutes light, 3 minutes shade, &c., until answered. Leave your station 10 minutes light, 10 minutes shade, 10 minutes light, until answered. 402 VERIFICATION AND EXTENSION OF LA CAILLE'S ARC OF THE MERIDIAN. § "• and smooth off the top. Having; adjusted his heliostat over the brass pin, he turns up Adjustment of '^ o j • p i i i i the Heliostat. the surface of the reflector and places any convenient object in front, looks along the reflector towards the theodolite station, and notes a point on the object, apparently of the same height, by v^hich he is guided in " flashing " until he is answered by a steady light to enable him to fix his screen. This is effected by placing the reflector vertical, and looking through the small hole in the centre ; while his second shifts the screen according to his directions, until the light from the theodolite station appears exactly in the middle of the circular aperture, — in which position the screen is firmly fixed. He then throws on his light, and if the theodolite light disappears his adjustments are correct, otherwise he re-examines them. A slight tap on the tail-piece and reflector bed, at intervals of about 40 seconds, keeps the screen aperture sensibly in the centre of the ellipfc section of the reflected rays cast upon the screen. If it should be remarked that unnecessary details have been here given regarding steps so simple and obvious ; the excuse rests with the many prolonged disappointments on the Cape survey, which altogether amounted to a considerable item of expense, and led to the inducement being held out of a higher rate of pay to leading signal men ; — personal antecedents in this service having proved deceptive. Opake Beyond distances of 20 miles, opake signals were seldom used. The station points Signals. were preserved by stone piles of dry masonry, in the form of truncated cones, 12 feet in diameter at the base, 2 feet at the top, and 14 feet high ; the axis coinciding with station point. Great care was taken in building them, that they might be employed instead of heliostats, if signal men should be scarce, or the tenure of the stations difficult. Four of this class, over primary points, were partially referred to. § 2. Historic Abstract of the Progress, of the Triangulation. S2 After the heliostat drill in September, 1841, signalmen were despatched to Kapoc Year 1841. Berg and Riebeek's Kasteel, and the Fuller theodolite was stationed at the Observatory to commence the triangulation, by measuring the angle between these stations : but the Riebeek's Kasteel light was seldom seen, notwithstanding incessant " flashing up " for some days ; it was therefore deemed expedient to concentrate the whole party in Zwart- land, and to commence the operation at the Base, where any cause of failure could be quickly investigated, and the qualifications of the parties become better known. The angles at the terminal points of the Base were finished on the 4th of December, when the instrument was removed to K. F. Centre Berg, and from thence to Kapoc Berg on the 21st. Riebeek's Kasteel was occupied from the 1 5th of February to the 3rd of April, Year 1842. 1842 : Drie Fontein on the plain from the 8th to the 11th of April: Zwartberg, inZwart- land, from April 15 to May 2 : Klip Fontein (the locality of the north end of La Caille's arc) from May 5 to June 3 : and Piket Berg from June 5 to June 21. HISTORIC ABSTRACT OF THE PROGRESS OP THE TRIANGULATION. 403 From the date of the occupation of Riebeek's Kasteel, the triangulation went on with § 2. ... . Year 1842. viffor : the individuals of the party had fallen into their proper niches ; the middle of Working . ,-. •,• 1 • -,. party of the wmter was now approaching, — the occasional rain and snow storm interruptions being 25th Regt. amply compensated by the intermediate splendid definition of the signals, — when on the 18th of June a letter arrived from the Deputy Quartermaster-General, written by direc- tion of His Excellency the Commander-in-Chief, requesting the detachment of the 25th Regiment to be forwarded to Cape Town without delay, as the Regiment was under orders for India. The removal of this detachment reduced the survey party to Serjeant Hemming, and five men Royal Sappers and Miners. With this force the several heliostats could not be efficiently managed ; but being desirous of finishing the triangulation of the northern portion of La Caille's arc, the instrument was removed to Patrys Berg, near St. Helena Bay, — Mr. Smyth engaging to work the heliostats on two distant stations in quick succession. The measurement of the angles at this station was commenced on the 30th of June and finished on the 1 1 th of July (though not according to the indepen- dent system previously followed) ; and the remnant of the late party returned to the Observatory with the instruments. With respect to La Caille's arc, it may be proper to explain in this place (though Terminal alluded to before, in Part I) that the northern extremity is close up in a corner formed by CaUieVarcare a north-westerly bend of Piket Berg, which precludes the possibility of connecting it with mountain! a station northward of Patrys Berg. Only one angle of the triangle formed by Klip Fontein, Eland's Berg, and Patrys Berg can be measured, — viz., the angle at Patrys Berg, and the elevations eastward of Piket Berg are completely shut out by the latter. Table Mountain presents a similar obstruction in the direction of Cape Point, The re-measurement of La. Caille's arc, therefore, must from necessity stand by itself \\ as a verification of his measure so far as it went, and no further. Consequently, j| the expression " verification and extension of La Caille's arc of the meridian" is not I strictly correct; moreover, the new and longer arc between Cape Point and the ,! Bushman Flat, is in the meridian described by the optical axis of the 10-feet transit || instrument of the Royal Observatory, some 3| miles east of the meridian of La Caille's Observatory. Having obtained permission on the 10th of August, 1841, from the trustees of Dirk year i84i. Gysbert Kotze, to erect a pillar on the Blaauwberg estate, on a hill south-west merXn^^'^ of his dwelling house, in the meridian of the transit room of the Royal Observatory, a p'^'*''- party was told off for this service shortly after the return from the measurement of the Base. The pillar is a truncated pyramid 14 feet high, constructed of stone and lime masonry, cased with Roman cement. By observation of the consecutive transits of circumpolar stars in the winter season made with the 10-feet transit instrument, the azimuth of the centre of the pillar is 179° 59'-57", reckoning from the south round by the west; and by triangulation its distance is 68415 feet, or nearly 13 miles north of the transit instrument, c 404 VERIFICATION AND EXTENSION OF LA CAILLE'S ARC OF THE MERIDIAN. § 2. On the 1st of August, 1842, the Fuller theodolite was centered over the Observatory Year 1842, . . r>- i i , August. roof station, for the purpose of measuring the angle between Kapoc Berg and Riebeeks Kasteel (postponed the year before for the reason given, page 402), and for comparing both with the Blaauw Berg pillar; on the 17th it was centered on the roof of the Rogge Bay Guard House, over the position occupied by the axis of Bradley's sector in the year 1838; on the 23rd of August it was employed at a base-line on the Parade, Cape Town, to determine the height of Table Mountain ; and on the 24th it was remo- ved to the station on King's Battery, situated about half way up the north face of Devil's Berg. CiviUans em- As no soldiers could now be spared from the duties of the garrison, it became neces- ployed in con- . ^ „..,. iii a ■ junction with sary to Organise and instruct the necessary number ot civilians to be added to oerjeant Hemming and the four remaining Sappers. On the 28th of August the wreck in Table Bay of the Abercrombie Robinson, a vessel of 1500 tons, threw several persons out of employment, who having no local ties were ready for a bush life, and gladly accepted service on the survey. While organizing the party, the theodolite was engaged on King's Battery Station (a). Zwart Kop, south stationssouth of Simon's Town, was occupied from the 15th to the 28th of November, and Cape Point Observatory, from the 28th to the 30th, From Cape Point the instrument was taken to the Naval Yard, Simon's Town, to fix the position of a granite block let into the ground in front of the Naval Storekeeper's dwelling, where altitudes are usually taken by the Naval OflBcers for rating their chronometers (b). On the occasion, a copper bolt was let into a large rock, and referred, by leveling, to the midwater point of the self-registering tide-gauge. The arrangements were now commenced for continuing the triangulation northward from Piket Berg, which included the transport of Bradley's Sector from the Observatory Assistance to Heerenlogcment's Berg and the Kamies Bergen. Rear-Admiral the Hon'ble Jocelyn Admiral Percy, the Naval Commander-in-Chief, who had hitherto evinced a lively interest in the operation, was pleased to grant the use of H.M. Ketch the Arrow, to convey the instru- ments and stores to Donkin's Bay, with directions to the officers to aflPord every assistance in their power. Accordingly, Captain Robinson brought the Arrow round to Table Bay for the cargo, with which I embarked, and left for Donkin's Bay on the 26th of December. Stationsnorth On the Same day, the survey party in charge of Serjeant Hemming (including a working Obse^atory. ing party of masons and labourers to be left at the termini of the Base) started for Eland's Berg. Tear 1843. After a fruitless attempt at Donkin's Bay, the Sector, &c., were safely landed at the mouth of the Berg River, where wagons were obtained for conveying them to Eland's Berg. Shortly after reaching this station I was joined by Mr. Mann, accompanied by (a). The same station point employed when connecting the positions of Sir John Herschel and La Cailie with the Eoyal Obserratory, see Part I. (b). This would be a good position for a 20 or 30-inch transit instrument. HISTORIC ABSTRACT OF THE PROGRESS OF THE TRIANGULATION. 405 Dr. Wallich, the Superintendent of the Honourable East India Company's Botanic Garden, § 2. at Calcutta, and by Serjeant Hemming with the signal party. Eland's Berg was occupied, on this occasion from January 9 to February 2, and Lambert's Hoek Berg from February 9 to March 2; in the meantime, Serjeant Hemming was encamped at Heerenlogement's Berg with the sector and stores. On leaving Lambert's Hoek for the Cedar Mountains, the most splendid Comet (as Great Comet of March yet) of the present century burst forth in all its brilliancy. It is impossible to describe 1843. the imposing grandeur of the tail as it shot up above the crests of the mountains, illumin- ating the heavens by its splendour, as we threaded the ravines descending to the Olifant's River on the evening of March 4 : — the head was masked by the mountains. On the 5th, we pushed on to the saddle (Ronde Gat) at the entrance to the Cfedar Mountain masses, and attempted that evening to obtain a position through the agency of Dollond's theodolite, but failed. After this we were threading our way for several days in the Langkloof ravine of the Cedar Mountains, and when we reached the culminating top of Sneeuwkop on the 20th, the comet had become too faint for observation with our instru- mental means. The Cedar Mountains terminate the range which extends northward from Cape Cedar Hanglip to about the parallel of 31°"60', where high table land becomes the distinguish- ""'' ing feature on to the Orange River. Four culminating elevations, named Sneeuw Kop, Sneeuw Berg, Tafel Berg, and Joachim's Neus, are nearly of equal height. From the top of either of these a complete view of the horizon is intercepted by the others. The most commanding, particularly with respect to clear sweep, is Sneeuw Kop : from it there is an uninterrupted view from the west round by the north to nearly south ; and through the wide gap between Tafel Berg and Joachim's Neus, Table Mountain, near Cape Town, is visible, distant about 112 miles. To the northward, the Kamies Bergen, distant 140 miles, are distinctly seen. The vegetation in the ravines is luxuriant. The Cedar trees (juniper species) occupy a zone between three to nearly five thousand feet elevation above the sea. A cross section of one of these trees, indicated (according to Dr. Wallich, who had the section made) that it was 121 years old. The wood is rather brittle, of a light colour, and the aroma so strong as to impregnate the air with its fragrance. Above the Cedar tree zone or girdle the vegetation becomes stunted, and the tops of the elevations are naked sandstone. The labour attending the occupation of the Cedar Berg station was amply repaid by its bold, interesting scenery, irrespective of its importance to the triangulation. The resources were mainly obtained from the Wupperthal Missionary Institution (situated in the vale, on the north-east side of the mountains) through the friendly influence of the Rev. F. G. Schroder, acting in the absence of the superintendent. On the 4th of April the instruments were removed from the Sneeuw Kop station, by a circuitous path down the east slope to Ezel's Bank ; thence through Wupperthal to Clanwilliam, where the party encamped at the hospitable residence of John Ryneveld, Esq., 406 VERIFICATION AND EXTENSION OP LA CAILLE'S AEC OP THE MERIDIAN. §2. Year 1843. March and April. Heerenloge- ment's Berg. June. Sappers re- called: imme- diate compli- ance imprac- ticable. Representa- tion to Commander- in-Chief. the Civil Commissioner, — a gentleman to whose kind and energetic assistance, both pri- vately and through the influence of his office, the survey vpas greatly indebted during the lengthened period of the operations in his extensive district. On the 13th April, the party reached Heerenlogement's Berg, an isolated elevation of some celebrity, owing to its position on the path to Namaqualand, but more to a small fountain at its base, the influence of which is recorded on the rocky sides of a shallow cave close by (a), by names ranging from Governor Van der Stell, year 1701, La Vaillant, and other less distinguished personages, down to the wagon driver who tried to spell his name, and displayed his ambition to let posterity know it. The operations contemplated at Heerenlogement's Berg included the erection of the Zenith Sector, on or close to the theodolite point on the summit of the mountain ; but sufficient room for so large an instrument, with its tent tripod and guy ropes, was not available there, — moreover, the steep declivities to the north-east and south-west could not be regarded with indifference : therefore the sector was placed on a flat rock, 496 feet to the north-westward of the theodolite, and 74 feet less elevated. The sector and the theodoHte observations occupied the interval between the 17th of April and the 13th of June; but for reasons which will appear hereafter, it became necessary to revisit the station with the theodolite, when returning from the northward. On the 28th of April (while engaged at the Heerenlogement's Berg station) I re- ceived a letter from the Deputy Quarter-Master General of the Garrison, requesting me to order Serjeant Hemming and the four men, Royal Sappers and Miners, to Cape Town, with the least possible delay. Private Powel at the time was 50 miles to the north-east of Heerenlogement's Berg, and Private George 30 miles S.S.W. on heliostat stations : Lance-Corporal Stone and Private Ward were about 100 miles to the southward, engaged erecting the pyramids at the Base-line. Immediate compliance with this unexpected recal would have seriously delayed the operation ; and Serjeant Hemming, who had charge of the stores and accounts, could not well, if at all, be replaced by his equal. Accordingly, a strong repre- sentation was forwarded; through the Deputy Quarter-Master General, to His Excellency Sir George Napier, the Commander-in-Chief, — and His Excellency, for the reasons assigned, was pleased to " sanction the retention of the soldiers for the present." It may be well, while on this subject, to remark that the system of going into winter quarters (if this led to the communication, and [ know of no other reason) which may be necessary in a different climate, does not apply to the Cape ; and with respect to Astro- nomical and Geodetic work, one observation in the winter is equal to three in the summer season. Impressed with these facts, and with the danger of an organised and instructed survey party being broken up at a critical moment, the future arrangements contemplated the employment of civilians only. (a). There is no water between Uitkom and Heerenlogement's Berg, nor between the latter and the Olifant's Eirer. HISTORIC ABSTRACT OF THE PROGRESS OP THE TRIANGULATION. 407 On the 3rd of June, Dr. Wallich and Mr, Mann left Heerenlogement's Berg for § 2. Cape Town, the latter having been relieved by Mr. Smyth. Dr. Wallich had amused himself by gathering specimens of the plants in our path, thus benefiting science while in search of health. He had lived with us on the Cedar Mountain station, — indeed accompanied us wherever we went, enlivening otherwise dull or anxious moments by his animated intellectual conversation ; the necessity for his departure, therefore, was a matter of deep regret. Having crossed the Olifant's River with the assistance of the Ebenezer Missionary Institution boats, Mr. Smyth was placed in charge of the Fuller theodolite, and estab- lished on the Louis Fontein station on the 25th of June, — while I pushed on with the Louis zenith sector to the Kamies Bergen, the ascent to which I reached on the 1st of July. The theodolite had hitherto been worked by myself, or conjointly with Mr. Mann. The Kamies Berg granite masses stand out prominently in front when advancing The Kamies northward across the Hardevelt. The highest mass, which is named "Welcome," juts ^^^^^' out like the corner of a gigantic fortress, — the curtain running eastward, and screening another range from which it is separated by a vale or amphitheatre named Ezels Kloof. Passing the base of "Welcome" on the west, a circuitous ascending route leads to the Lily Fontein Missionary Institution, situated at the west end of an open plateau sur- rounded by mountain tops, at an elevation of near 5000 feet above the level of the sea. The Lily Fontein range forms the north wall of the amphitheatre ; thence stretching eastward some 20 miles, it becomes confounded with, or lost in the high table land of the Onder Bokkeveld. From its prominent points, a complete view is commanded from the west, round by the north to the south-east; "Welcome" and its curtain cuts off the south and south-west. While ascending by the circuitous path before-mentioned, we encountered one of the most severe snow storms within my experience. With the kind permission of the Rev. Mr. Jackson, the Superintendent, we established our head-quarters at the Lily Fontein Institution, while the several mountain tops were examined for a station which would be suitable for the sector, and visible from Louis Fontein. After a tedious scouring survey of ten days' duration along the tops, one was found which answered the conditions pretty well, distant about five miles S.E. by E. from the institution, and in the line of a small saddle in the "Welcome" curtain, through which the Louis Fontein station is visible. The part of this mountain range selected, having no local name, has been desienated the " Kamies-Sector Berg." It is a flat-topped mass of naked granite, Kamies- IP • J A r- 1 Sector Berg situated towards the north-east end of the amphitheatre before mentioned. A tew loose station. blocks are sprinkled about the top, besides two groups, one at the south-east corner, the other at the south-west,— the former about 20 feet high, the latter less elevated. Certain particulars relating to these groups are given with the observed angles. The zenith distance observations were begun on the 26th of July, and finished on the July- 13th of August. The determination of the azimuthal error of a meridian mark, estab- 408 VERIFICATION AND EXTENSION OP LA CAILLE'S ARC OP THE MERIDIAN. §2. Tear 1843. Beturn with Bradley's Sector to the Observatory in October. Mr. Smyth's operations. Serjeant Hemming allowed to remain on the snrvey. Boyal Sappers and Miners: dates of their leaving the survey. Year 1844. Acknowledg- ment of the services of Serjeant Hemming. lished on a rock of the " Welcome " curtain by means of the 30-inch transit, for the purpose of checking the azimuths brought down by calculation from- the Observatory : and a small triangulation to the Missionary Institution, together with preparations for departure, consumed another fortnight. Snow (rather a novelty to Cape low-landers), attended with sharp frost, covered the ground during a large portion of the time. On my way back from Kamies-Sector Berg with the zenith sector, I was met at the Olifant's River by Mr. Smyth, for the purpose of arranging future operations. On the 23rd of October I arrived at the Observatory, and on the 25th the sector was erected in the sector-room, — ten months from the date of my departure in H.M. Ketch Arrow. While employed as I have described, Mr. Smyth had been pretty active. He occu- pied Louis Fontein from June 25 to July 16; Elands Hoogte from July 26 to August 1; Bokkeveld's Berg from August 14 to September 8 ; and Klip Rug from September 19 to September 28 ; and when we met at the Olifants River, his wagon was on its way to the Kamies-Sector Berg. A look-out was now kept for civilians to supply the place of the Sappers, the dates of whose departure from the survey it may be well to trace at once. On the 5th of December I applied to His Excellency the Commander-in-Chief (^Sir George Napier) for permission to retain Serjeant Hemming and Lance-Corporal Stone for a time after the retirement of the privates, — a concession His Excellency was pleased to grant. On the 27th of December, Private Ward was returned to the Commanding Royal Engineer. On the 2 1 st of February, 1844, Privates James George and Walter Powell were returned. On the 30th of March, 1844, Serjeant Hemming retired; and on the 30th of November, 1844, Lance- Corporal Stone also. Serjeant Hemming had served the term in the Corps of Royal Sappers and Miners that entitled him to ask for his discharge. About the same time I was informed by the Honourable John Montagu, the Colonial Secretary, that having heard of Mr. Hemming'* superior qualifications and excellent conduct, he wished to secure his services to the Colonial Government by a permanent appointment, which would have a rising salary, commencing with £120 per annum. On the 26th of March I addressed the following letter (in reply) to the Deputy Quarter- Master General : — " Royal Observatory, Cape of Good Hope, 26th March, 1844. " Sir,— With reference to your letter of last December, signifying that His Excel- lency the Commander-in-Chief was pleased to sanction Serjeant Hemming and Corporal Stone, Royal Sappers and Miners, remaining on the survey,— I have the honour to state that I have made arrangements for supplying Serjeant Hemming's place, and that I am ready to return him immediately, or on the 3 1st instant. " I cannot part with Serjeant Hemming, without expressing the most sincere regard HISTORIC ABSTRACT OP THE PROGRESS OF THE TRIANGULATION. 409 and esteem for a man, whose uniform temper and strict morality in every sense of the § 2. word, had a most beneficial influence on the survey party, — while his rigid regularity, probity, and industry, enabled me to conduct the operation with comparative facility in the department of accounts and stores. " As a civilian, I hope I shall not be considered to have done any thing incompatible with the regulations of the military service, in bearing testimony to the excellent conduct of Serjeant Hemming, and in acknowledging, on the part of the survey, how ably he performed his duties. "I have, &c., "Thos. Maclear. "To Colonel Cloete, K.H., &c., &c., Deputy Quarter-Master General." Thus terminated the connexion between the survey and the Royal Sappers and Miners, to whom generally my acknowledgments are due for uniform respect, and attention in complying with my wishes. The zenith distance observations at the Royal Observatory made with the sector, zenith dist- together with a multiplicity of other engagements there, consumed the interval between t^n^s°ame* my return on the 2Srd of October, 1843, and the 30th of June, 1844. From the EoyaiObser- Observatory I removed with the sector to Zwart Kop, south of Simon's Town, where Kop,aiidCap» the zenith distance observations were commenced on the 25th of July and terminated on the 3rd of October, having been protracted by unfavourable weather, particularly by the eflfect of a gale which endangered the integrity of the instrument. From Zwart Kop the sector was removed to Cape Point, — a naked windy locality, where it became imperative to abandon the hitherto canvas tent-covering, surrounded by a bush fence, in favour of a wooden building keyed to the rock. A conical-shaped canvas tent, 30 feet in diameter at the base, and 20 feet high, presents a surface which no ordinary system of rope-stays can control in windy weather, irrespective of tlie changes of tension in the ropes and canvas, depending upon the diurnal changes of atmospheric moisture ; and it may not be out of place to mention, as the result of experience with respect to theodolite protec- tion, that a properly constructed wooden building, composed of moveable pieces, is infinitely superior to any framework covered with canvas. The zenith distance observations were begun on the 16th of November, 1844, and Teari844— 5. finished on the 15th of January, 1845. On the 17th the instrument was dismantled, and on the 23rd it was erected in the sector-room of the Royal Observatory. To the assistance derived from the Naval Yard, Simon's Town, by command of the Assistance Honourable Jocelyn Percy, the Commander-in-Chief; to the cheerful and friendly thrNav^T*- co-operation of Captain Charles Eden, Lieut. Wainwright, and the several ofl5cers on tabUshment. the station, the successful occupation of Zwart Kop and Cape Point Stations with Bradley's Sector is indebted. The instrument was carried over the rugged declivities by marines ; a party of sailors were encamped at Zwart Kop to erect the protecting 410 VERIFICATION AND EXTENSION OF LA CAILLE'S ARC OF THE MERIDIAN. §*■ ^ fence; the services of Lieutenant Hornby were granted, to whose daring intrepidity may be mainly attributed the rescue of the sector from imminent danger during the gale, in the night of the 21st of August, Zenith dist- On the 24th of January, 1845, the day following the erection of the sector at the tions at the Observatory, the zenith distance observation of the stars observed at Zwart Kop and Cape Point was commenced. Between this date and July 8, Cape Point was visited twice and Zwart Kop once with the Beaufort theodolite, for the purpose of measuring horizontal angles at these stations, and for leveling from each down to the sea (the Zwart Kop leveling was carried to the Simon's Bay tide-gauge). The intermediate time was spent at the Observatory, observing zenith distances and measuring angles with the Beaufort theodolite, excepting three days spent on King's Battery Station with that instrument. Mr. Mann. Mr. Mann was engaged from July 19 to September 26, scouring the country between Winter Hoek and the Zonder End Mountains, to ascertain the practicability, or the contrary, of forming large triangles between the former and Cape L'Agulhas. His report being unfavourable, the scheme was given up. Mr. Smyth, While thcsc Several services were being performed, Mr. Smyth who, in October, ] 843, had been met on his way to the Kamies-Sector Berg, occupied that station with the Fuller theodolite, from October 21 to November 10. Returning southward, he visited Elands Berg from the 1st to the 9th of December, for the purpose of connecting the Cedar Berg with the adjacent stations. He next occupied as follows : Piket Berg from December 26, 1843, to February 22, 1844, having been delayed there by the masking difficulties of the eastward masses ; Kapitein's Kloof Station from April 22 to May 25 ; Winter Hoek's Berg from July 9 to October 10 (a difficult snow-capped mountain in the winter season) ; Sneeuw Kop, near Hottentot's Holland, from Novem- ber 22, 1844, to July 21, 1845 ; from the latter he returned to the Observatory, pre- paratory to leaving the Cape, to fill the chair of Practical Astronomy in the University of Edinburgh, and the office of Royal Astronomer of Scotland, which had become vacant by the decease of the late Mr. Henderson. At this period the prospective operations needed for completing the survey, were the side triangulation along the southern shore, from Cape Point to Cape L'Agulhas ; and northward the triangulation from Kamies-Sector Berg to a point in the Bushman Flat, including observations there for latitude ; the distance between the starting points being about 300 miles. To facilitate the immediate accomplishment of the former, Mr. Smyth agreed to delay his departure for a short time, and took charge of the Observatory. Side triangu- On the 24th of July, Mr, Mann started for Sneeuw Kop to bring away the Fuller L'Aguihas*^^ theodolite and equipments from that mountain, which he accomplished by the 31st; then bending his way eastward, he reached the base of the high Zonder End Mountain (north- east of Caledon), on the 6th of August, and its summit on the 8th, with the instrument and stores, the natural difficulties of the ascent being increased in consequence of the depth of snow on the mountain. HISTOKIC ABSTRACT OF THE PROGRESS OP THE TRIANGULATION, 411 While Mr. Mann proceeded to his station, I moved to Cape L'Agulhas per horse § 2. wagon, equipped with the Beaufort theodolite, to work the stations on the headlands July, August, along the shore, — between which the comparative goodness of the roads admitted of pretty quick traveling. The following dates give the times spent at each of the stations, the intermediate intervals having been taken up in traveling, climbing, &c. ; but it should be stated that few angles were required at each : — Cape L'Agulhas, occupied from August 3 to August 5. Danger Point, „ „ August 12 to August 22. Mudge Point, „ „ August 27 to August 21. Babylon's Toren, „ „ September 9 to September 14. When stationed on Danger Point, a violent gale occurred in the night of the 20th Violent gaie of August. The guy ropes of the theodolite tent broke, and the frame was carried over the precipice, and smashed. The custom on the survey, of dismounting the theodolite in the eveniog, packing it in its box, and building a wall round the box in the absence of a convenient nook or cave, saved the instrument on this occasion, as it saved the Fuller theodolite at the Devil's Berg Styiioo, on the 28th of September, 1842. Mr. Mann, who was stationed at the summit of the Zonder End Mountain, 5300 feet high, and 45 miles inland from Danger Point, states his inability to describe the violence of the snow storm, and the searching severity of the cold during its continuance that night, although the registered temperature by the thermometer was only 22°. The comparative despatch and mutua' advantage, arising from the nearly simultane- ous working of the two theodolites on the same triangles, became evident on this small triangulation ; but the difficulties in the way of forming a just estimate of the relative precision of dissimilar instruments, with respect to optical power and construction, are obvious. That two instruments, as near as possible alike, are needed for important and expensive triangulations — as a matter of prudence and economy — is proved by the acci- dent that happened to the large theodolite of the Irish survey, and to the large theodolite of the Indian survey. The cost of a second instrument is soon absorbed in the cost of the obstruction, irrespective of the advantage of being able to employ two instruments when opportunity offers. Mr. Mann finished his observations at the Zonder End on the 15th of September, and proceeded to Kegel Berg Station on the east side of False Bay ; in the mean time I returned to the Observatory to relieve Mr, Smyth, where I remained until the 24th, when, perceiving that he bad no immediate prospect of a passage to England (a), I left for the Tyger Berg Station with the Beaufort theodolite, to connect the Simon's Town Naval Yard, and other places of local interest, with the triangulation. Having learned from James Searight, Esq. (a merchant in Cape Town), that he had recently purchased the property of the late Mrs. de Wet, and was making alterations in (a) Mr. Smyth sailed for England in the Citi/ of Poonah, merchant vessel, on the 22nd of October. E 412 VERIFICATION AND EXTENSION OF LA CAILLE'S ARC OF THE MERIDIAN §2. Year 1845. November. Site of La CajUe's Observatory excavated. the store that covered the supposed site of La Caille's Observatory, which presented an opportunity for examining if any trace of the Observatory existed ; accordingly, on the' 1st of November I had the floor excavated, the result of which it may be proper to record. The soil immediately under the surface consisted of sand, remnants of mortar, and broken bricks. At the depth of 2J feet, a pavement was encountered, of the kind termed "pitching," — apparently the ancient pavement of the yard ; and a portion of a narrow wall, running parallel to the outer wall (the north-west wall) of the yard; also a square-shaped block of rough masonry of between 2 and 3 feet square, horizontal section; both built of stone, cemented with pot-clay. Nothing else was discovered, excepting a letter in the Dutch language, dated July 24, 1783, addressed to Mrs. de Wet. The result of this investigation proves the fact that no trace of La Caille's Observatory remains ; for it can be proved by the diagrams of the property, that the north-west wall of the store was the boundary of the yard or court on that side, in the year 1752, — and the block just described is not only nearer to the wall than the dimensions of the Observatory would permit, but its structure and area are inconsistent with the account given by La Caille (Mem. de L'Academie, 1751, p. 398). At the south-east side of the yard, sunk even with the pavement and serving a domestic purpose, I found a dressed block of gneiss, somewhat resembling dark-grey limestone in colour, which may have been the top stone of the pillar " M " of " une espace de marbre de Bengale" (Mem. de L'Academie, 1751, p. 399). Mr. Searight kindly allowed me to reniove this block. Although much has been recorded in the first part of this work, to prove the locality of La Caille's Cape Town Observatory, it may not be superfluous to collect the leading facts in this place. 1. La Caille lodged in the house No. 2, Strand -street, then the property and the residence of M. Bestbier ; and the Observatory was placed on the north-west side of the yard or court of that house. 2. From M. Bestbier the property passed to Arend de Waal, and from the latter to Mr. de Wet, who, about the year 1 798, erected a store on the north-west side of the yard, which store included the site of the Observatory. The widow of Mr. de Wet occupied the house in the year 1838, when the observations were made there with Bradley's Sector, and continued to occupy it until her death in the year 1845, when it was pur- chased by James Searight, Esq., the present proprietor. 3. The store extends from the dwelling house along the north-west side of the yard, the whole way to its termination in the Fishmarket. Mr. Searight removed the interior partition walls and an outside gallery above in the year 1845; also a number of cottages at the lower end of the yard, formerly tenanted by fishermen, and on their site he has built stores to contain merchandise. HISTOEIC ABSTRACT OF THE PROGRESS OP THE TRIANGULATION. 413 4. The street extending from the north entrance to Government Gardens, to the § 2. ° . . Year 1845. opening upon the sea beach east of the Fishmarket, was named Heerenstraat in La Caille's time, subsequently Heerengracht as far as Strand-street, and Justice-street from thence to the beach. The south-east side of Justice-street, in La Caille's time, contained the workshops of the Dutch East India Company, afterwards the stores of the British Royal Navy, until the Naval Station was shifted to Simon's Bay. Upon these buildings La Caille saw the corner of the opposite street projected, when he was stationed on Riebeek's Kasteel (Mem. de L'Academie, 1751, p. 429), I had now the misfortune to lose the services of Mr. Mann. He had charge of the ninessof Observatory while I was engaged on Simon's Berg, from the 15th to the 25th of Nov- ember. On the 18th of that month he fell from horseback and sustained an injury of the head, from the effects of which he had so far recovered by the 1 1th of December as to undertake light duty, — but he soon relapsed and left the Observatory for change of air. On the 17th of March, 1846, his medical attendant reported no improvement, and re- commended the trial of a colder climate. On the 29th of March he sailed for England, on sick leave, in the Agincourt, merchant ship. The loss of both assistants within a month of each other, and the rumour of a proposal to place the Magnetical and Meteorological service in charge of the Astronomer, pre- vented immediate arrangements being made for bringing the survey to a conclusion. On the 19th of December I applied to Rear- Admiral the Honourable Jocelyn Percy, the December. Commander-in-Chief, for the services of Hubert Campion, Esq. (a young gentleman ^gage™^""' belonging to the flag-ship, who had passed the examination for mate, and had paid con- siderable attention to scientific subjects), which were readily granted, and Mr. Campion joined the Observatory. Between the 9th and 28th of January I was engaged with the Beaufort theodolite on Year i846. the roof of the Observatory, and on the roof of the store over the supposed site of La Caille's Observatory. In the month of February, Mr. George Montagu joined me in a February. trip to Kapoc Berg with the Beaufort theodolite, preparatory to engaging that young gentleman for service on the survey. The intention to plant the north termination of the arc in the Bushman Flat required serious consideration, for the arrangements must comprehend the utmost possible despatch in the execution of the work, because of the sterile character of that locality, and its distance from resources of every. description; and if the health of the director of the survey should fail, a competent person should be ready to supply his place. In the latter particular, the ability and sound judgment of Mr. Mann left nothing further to be desired ;, but his malady continued without any improvement, and it became necessary to look elsewhere. On the 10th of March, Rear- Admiral Dacres, the new Commander-in-Chief, acceded March. to the continuance of Mr. Campion's services, subject to the approval of the Lords 414 VERIFICATION AND EXTENSION OF LA CAILLE'S ARC OF THE MERIDIAN. S 2 Year 1846. March. April. Mr. George Montagu engaged. June. Arrival of Mr. Childe. Transfer of the Magneti- cal and Mete- orological Observatory to the Astronomical Department. August. September. Arrival of Mr. SmaUey. Departure for the Kamies Berg. October. November. Fail in the attempt to reach Boschluis. Commissioners of the Admiialty. Oa the 27tli of March, Captain (now Colonel) Wilmot, Royal Artillery, joined the staff of His Excellency Sir Peregrine Maitland, on the frontier (a Caffre war having broken out), leaving the superintendence of the Magnetic Observatory in my hands, — and on the 29th, as before mentioned, Mr. Mann sailed for England. My course was now pretty clear : since November the survey party had been reduced to a few individuals for carrying on casual work, and to form the nucleus of a fresh survey party. On the 6th of April Mr. George Montagu was engaged, aud con- jointly with Mr. Campion, placed in charge of the Fuller theodolite, for the purpose of obtaining a thorough command of that instrument, and to experiment for its division errors. In the month of June, the Rev. George Frederick Childe, M.A., who had received the appointment of 2nd Assistant to the Asl ronomer, arrived from England, and was placed in charge of the Astronomical work, while arrangements were begun for collecting and organizing the signal party ; also the Magnetical and Meteorological Observatory was officially joined to the Royal Observatory, — Captain Wilmot kindly permitting Serjeant Weir and two gunners to remain, until the arrival of an assistant for that department. On the 10th of August, Messrs. Campion and Montagu set out for Patrys Berg with the Fuller theodolite and a signal paviy. On the 8th of September, George Robarts Smalley, M.A., arrived from England as 3rd Assistant to the Astronomer for the Mag- netical and Meteorological work, and on the 28th I started with Bradley's sector and the Beaufort theodolite for the Kamies Bergen, which I reached on the 17th of October. By previous arrangement, Messrs. Campion and Montagu left the Fuller theodolite at the Bokkeveld Station, and joined me at Lily Fontein on the 20th of October, for the purpose of a simultaneous reconnoissance of the Busbman Flat. We started with horses and a guide on the 23rd, and by rapid traveling reached Pella, on the Orange River, on the 28th. Two days were spent on the Pella mountain, endeavouring to discover the most elevated part of this singular flat, by means of the nearly horizontal rays of the rising and setting sun. Returning, we bore away to the westward, in the direction of the Copper Mines, and climbed the most commanding elevations on the west and south-west border, and arrived again at Lily Fontein on ihe lOfh of November. The result of this examination was not so satisfactory as could be wished ; it proved the impracticability of seeing a point in the flat, distant some 60 or 70 miles north of the Kamies-Sector Berg, from stations east and west of the latter. Messrs. Campion and Montagu left for their station on the 1 1th, and on the 12th I set out with the Rev. John A. Bailie, Superintendent of the Lily Fontein Missionary Institution, and a guide, hoping to penetrate the flat on the eastward side ; but owing to intense heat and want of water we were unable to get beyond a spot named Nourbys, where we bivouacked. From this place the top of Keibiskow (a high mountain, distant 70 miles S.E.) was discovered at sunrise ; and on the 18th a signal party set out to HISTORIC ABSTRACT OF THE PROGRESS OF THE TRIANGULATION. 415 occupy it. On the 19tli, I proceeded to Roodewal Bay, to select a station in that neigh- § 2. bourhood, and on my return I occupied the Kamies-Sector Berg station with the Beau- fort theodolite. On the morning of December I, the Keibiskow heliostat light, which for some days December. had been anxiously looked for, made its appearance, — distant nearly 80 miles; the image, as seen in the telescope of the Beaufort theodolite, appeared to be about equal in brilliancy to a star of the 4th or 5th magnitude. Having measured the angle between it and the Bokkeveld's Berg light, I started on the 7th to establish a signal party at Boschluis, in the Bushman Flat, taking the eastward route, and entering at " Koegoed Flats." While traveling on the 11th, under a burning sun and clear sky, the cattle sinking from thirst and heat, we experienced the imagery of the desert in perfection. Stunted bushes, at Mirage in the the distance of a few yards, were magnified into wide-spreading trees in violent agitation; Fiat. the tantalizing deceptive sheet of blue water kept in advance of us a couple of miles, while the view was shut out in other directions by the impenetrable turmoil of the air. Towards sunset the mirage disappeared as the heat moderated, then our guide acknow- ledged that he did not know where we were, and that we ought to have been at Boschluis two hours before. We therefore stopped, and giving the cattle the supply of water intended for the station, we waited until moonrise, and then retreated on the trace of our wagon wheels to " Kobus," where we obtained a scanty supply of water by digging in the sand. Leaving the party at this place, I rode some 60 miles on the 13th, in a fruitless search for the place we wanted. On the 14th, I rode back to Koegoed Flats, where I obtained a guide who was more successful. I have dwelt on this occurrence, to convey some idea of working the Bushman Flat in the summer season. The following fortnight was spent in part on Kamies-Sector Berg, measuring angles, and in part at the Lily Fontein encampment, sending off supplies and making up accounts. On the 1st of January, I set out for the Boschluis station, with the Beaufort theo- Yeari847. dolite, where I arrived on the 5th, barely in time to rescue the leading signalman (oj, ™"*''y- who was sinking from the effect of intense heat and exposure to the sun. The angle between the Keibiskow and Kamies-Sector Berg station detained me there until the 11th, for the top of Keibiskow could only be seen during the maximum refraction. Shortly after daybreak, the culminating top of the mountain gradually ascended above the horizon ; at sunrise, the heliostat light entered the telescope like a diffused, orange- Effect of coloured nebula, which gradually contracted to a brilliant point, equal to a star of the KriMskow""" 5th magnitude. At 7 o'clock on the morning of the 8th, the top assumed the figure of a ^'^ht. cocked hat, the light elongated vertically, then separated into a string of beads, each a perfect round image, — the vertical bisecting spider line representing the string. The cocked hat and string of lights above it were apparently separated from the mountain by (a). Adam Cairns. F 416 VERIFICATION AND EXTENSION OF LA CAILLE'S ARC OF THE MERIDIAN. §2- Tear 1847. February. March. Proceedings of Messrs. Campion and Montagu. April. Kemoval of the zenith sector and head-guarters to the Bush- man Flat. a band of the sky. This continued about half an hour, then the definition became indifferent, and towards 8 o'clock the top descended, as usual, below the horizon. The heat at this station, from the 5th to the 11th, was in general from 100° to 105° towards 2 o'clock, p.m., in the shelter of a wagon, shaded from the direct and reflected rays of the sun, — and in the night as low as 50° near the ground. The interval between the 1 7th and 28th was spent in writing, examining accounts, &c., on Kamies-Sector Berg, — the movemeuts of Messrs. Campion and Montagu being known by the heliostat telegraph signals. On the 29th, a signal party was despatched to Vogel Klip, near the copper mines, — and on the 30th, I set out with the Beaufort theodolite and leveling apparatus for Roodewal Bay, where I was joined by Mr. Montagu on the 21st of February, who had left Mr. Campion moving with the Fuller theodolite to Louis Fontein. Shortly after the commencement of operations at Roodewal, the thunder clouds to the north and east, which were expected to appear at a later date, materially retarded the work, by masking the heliostat lights. On the 5th of March, I left for Kamies-Sector Berg, where I was engaged from the 14th to the 21st, measuring the several angles round from Louis Fontein to Vogel Klip, — and on Ezel's Kop from the 23rd to the 30th. The simultaneous operations of Messrs. Campion and Montagu, from the date of our journey into the Bushman Flat (in November) were as follows : they occupied the Bokkeveld's Berg station from the 20th to the 30th of November, and Keibiskow from the 15th of December to the 26th of January. Returning by Bokkeveld Berg, they mounted the instrument again there, for the purpose of clearing up a discre- pancy between the angles connected with the Klip Rug heliostat, and a pile built over the Klip Rug station-point. Next, they occupied Louis Fontein, from the 2nd of March to the 17th of April; on the 23rd, they joined me at the Doom River, near the north base of the Kamies Berg. To accomplish the safe conveyance of the sector through the rocky kloofs of the Kamies Berg, it was preconcerted to unite our resources, and to enter the Bushman Flat together. The usual route by Peter's Kloof had been examined, and abandoned in favour of one more direct to the east, provision being made for carrying the sector on men's shoulders through a rugged defile. This was accomplished on the 24th, and on the 28th we reached Riet Fontein, situated on the south border of the flat. Riet Fontein is an oasis in the desert, where there is a garden containing grapes, figs, and vegetables in profusion. The owner, Gert Beukes, a half-caste, then some 70 years old, had married a Hottentot girl only a few days before our arrival, — whose bridal ornaments chiefly consisted in face patches of black and red paint. His sons by the partner of his youth, with their wives and children, were shifting for themselves some 30 miles off in the desert. The limits of Gert's domain were undefined : he patronized a few Bushmen, and as his locality was beyond the boundary of the colony, he enjoyed something more than HISTORIC ABSTRACT OF THE PROGRESS OP THE TRIANGULATION. 417 old baronial independence. But a few months before our visit, the exigencies of a § 2- CafFre war had demanded aid from the ex-boundary squatters, which was effected by declaring the true boundary to be a right line drawn from Koegoed Flats to the mouth of the Orange River. This, in conjunction with the general distrust regarding the true object of our operations as land-measurers and beacon-builders on a large scale, touched Gert on a tender point ; and his misery became complete on the production of a Govern- ment order to force the assistance from his ample stock, — which, by the offer of an amicable adjustment, he previously refused to furnish. After thinking over the matter for a night he agreed to supply our immediate wants, also to forward wagon loads of water to our station, for a stipulated sum per cask ; and amicable relations for the future were smoothed by presenting him with a pig of lead. This apparently trifling affair is recorded, for upon Gert Beukes greatly depended the means for occupying the north station. On the 30th, we left Riet Fontein, and reached Koe Berg late on the 1st of May; May. from thence Mr. Campion returned to Riet Fontein, to convey the Fuller theodolite to Vogel Klip, — Mr. Montagu remaining with me. The operations at Koe Berg, and the search for a commanding swell whereon to plant the north station, consumed several days. On the 1 4th, the sector was removed to the selected locality, and the men commenced to sink a pit 30 feet in diameter and six feet deep. By some inexplicable misunderstanding, the Kamies-Sector Berg light was not directed to this station until the 22nd. Between this date and the 14th of June, the greater June, part of the theodolite work was effected. On the 18th of June, the zenith distance observations were commenced. On the 23rd, Mr. Campion arrived with the Fuller theodolite, on his way to Boschluis, from whence he returned on the 1st of July. It now becomes necessary to mention the illness that deprived me of the pleasure of completing the survey in person. The repeated alternate exposure to the burning summer heat of the Bushman Flat, and the pinching cold of the Kamies Berg, combined with great personal exertion in climbing, and indiscreet indulgence in water after long privation, brought on a rheumatic affection in the latter part of March, from which I was slowly recovering, until I had occasion, now in the middle of winter, to sit up every night in the sector-tent, exposed to a freezing temperature. An aggravated relapse ensued on the 22nd of June. Still I persevered with the sector work until the 28th, when finding I could hold out no longer, the continuation of the operations were deputed to Mr. Montagu, and on the 1st of July, I left the station, accompanied by Mr. Campion. Mr. Montao-u finished the sector work on the 11th, and the observations for azimuth j^iy, on the 17th; and it appears he left the station the day following. The stations on the Bushman Flat were exceedingly difficult to maintain, owing to the scarcity of water. Estimating distance by bullock wagon traveling, the Boschluis station is 40 miles, and the north station 20 miles, from the requisite supply for a party. 418 VERIFICATION AND EXTENSION OP LA CAILLE'S ARC OP THE MERIDIAN. § 2. No rain falls upon the Flat unaccompanied by thunder : then hollows in rocks are filled, July. and if the fall has been plentiful, the Kamies Berg farmers migrate with their flocks, to reap the advantage of the pasturage that quickly springs up. Such a contingency hap- pened while I was engaged at the Roodewal Station in March. Returning from the Bushman Flat, Mr. Montagu occupied the Kamies-Sector Berg station until the 6th of September, with the Beaufort theodolite. On his way southward from thence he communicated with Mr. Campion, and passed on to the Cedar Mountain station, to connect Kapitein's Kloof with Heerenlogement's Berg, and Klip Rug with Winter Berg. Mr. Campion occupied Heerenlogement's Berg with the Fuller theodolite from the 8th to the 20th of October ; then left for the Observatory, which he reached on the 6th of November. On the 8th, he joined the flag-ship. The services of this accomplished young officer since then, show the error of the notion entertained by many, that scientific pursuits unfit men for the executive depart- ment of the Royal Navy, Year 1848. Mr. Moutagu rcaclied Kapoc Berg on the 3rd of January, where he filled up the round of angles. From Kapoc Berg he moved to the Blaauw Berg azimuth pillar, and from the latter he returned to the Observatory on the 8th of April; on the 10th, he retired from the sui-vey. Shortly after, he received the appointment of 2nd Assistant Surveyor-General, — and at a subsequent date, the appointment of Surveyor-General of British Caffraria. Lastly, Bradley's Sector was erected again at the Observatory in the month of May. The observation of zenith distances commenced on the 1st of June and terminated on the 2nd of September. On the 1st of May, 1850, Captain Brown, of H.M. Steamer Geyser, kindly under- took the charge of conveying the sector to England. § 3. Observed Horizontal Angles. Preliminary Explanations. It was the general practice on the survey, when measuring angles, to call out the § s. reading of each microscope or vernier to an amanuensis, who repeated the numbers aloud recording the while recording them in the field-book ; and during the evening or other leisure moments mea°t°re!^ the observer computed and applied the corrections for micrometer runs, and calculated the means. Twenty-four field-books contain the Fuller theodolite measures, and the Beaufort Field-books theodolite work occupies two. These books were afterwards transcribed at the Observa- thereTF*^ tory into five pretty thick folio volumes, where the whole of the arithmetic was repeated, and carefully compared with the field-books. Exclusive of these books, there are others, which contain zenith distance measures for time and relative heights. The printing of such a mass of figures would incur an unwarrantable expense, and Reasons for few persons would take the trouble to consult them ; therefore, after due consideration, it Tn det"u.^"^ has been decided to print the mean results only, first placing in evidence the details of one angle by each instrument, which may be taken as the general type of the whole. The weight annexed to each angle observed with the Beaufort theodolite is the reci- Weights of procal of the square of the probable error (P), derived from the formula : Saufort theodolite. P = /2.t X 0-454936 V? — n where 2.e is the sum of the squares of the differences from the mean of each partial result, — 10 repetitions being taken for the unit; 0'454936 = 2 p^, derived from ths theory of probabilities {p = ■476936). The weight annexed to the final determination of an angle is the sum of the weights of the separate determinations. When an angle has been derived from the sum or difference of other angles, the weight (W) annexed : With respect to the Fuller theodolite, the errors depending upon the state of the j-^ner atmosphere and the eye, are mixed up with instrumental errors of a different order to *^° "''**' errors of observation. The precision of the partial measures have therefore been regarded as equal, and the weight annexed to each angle is the sum of the partial means from which it is derived. Thus, unfortunately, there is a want of homogeneity in the method of estimating the weights, exclusive of the element introduced by the inequality between the dimensions and optical power of the two instruments. In the latter particular, perhaps, ample justice is conceded to the Fuller theodolite, by regarding a partial mean or two measures, as equivalent to ten measures with the other. G 420 VERIFICATION AND EXTENSION OP LA CAILLE'S ARC OP THE MERIDIAN. § 3. It became necessary, on a few occasions, to infringe the general rule of centering the Reduction to ■" so the center. theodolite over the trigonometric or angle point ; but great care was taken to prevent the possibility of doubt regarding the elements for calculating the reduction to the center. In each instance, the angle of direction (y) commences by pointing the telescope to the angle point (C), from which the object glass moves towards the right hand in the order of increasing readings, to the direction of the consecutive distant stations. Instead of the ordinary notation + 7, representing the observed angle, and the angular distance of C, from one of the stations, the notation -y -y^ y^, &c., has been introduced, and the reduction for each station, in other words the angle at each distant station, subtended between the excentric position of the theodolite and C, has been computed separately, and tabulated in consecutive order. By this arrangement, the correction to any observed angle is obtained by algebraically subtracting the reduction for the left hand station, from the reduction for the right hand station, y for the left station is always less than y^ for the right. The calculation of the reduction : r sine y D sine 1" is given with all necessary detail in a tabular form with the observed angles; where r, the distance between the theodolite and angle point, and D, the distance between the angle point and distant station, are expressed in feet. OBSERVED HORIZONTAL ANGLES. 421 Angle at Kamies- Sector Berg, West Hock Station ; between Keibiskow and Bohheveld Berg : measured with the Beaufort Theodolite. ■gi Pointer. Verniers. Mean. Angle. 1846. Vol. 23, p. 21. A D B C 23°-32'. o / r // T // // / II „ „ $ 1st Dbc. Measured forward, Y right. h m A.M., 9- Middling definition. 2 8 2-5 9-24 Do. 1 10 235 20 13 8 10 27 235 20 14-5 1-20 1-20 9-46 Do. Northerly wind, perhaps 10 110 40 28 24 26 32 470 40 28-0 1-35 1-28 10- 9 Not so good. 1 point E. of N. Hot 10 346 44 50 48 52 706 48-5 2-05 1-53 10-35 Worse. temperature : about 10 221 20 60 50 56 64 941 20 57-5 0-90 1-35 11- "Worse. 85°. 10 96 40 1 20 12 26 28 1176 41 21-5 2-40 1-58 11-21 Same as last. J 10 332 1 38 34 42 48 1412 1 40-5 1-90 1-63 P.M., 4-48 Bad definition and bad signaling at Bokkeveld 10 207 20 2 8 8 10 20 1647 22 11-5 310 1-84 5-11 Definition improving. 1 10 82 40 2 22 20 30 32 1882 42 26-0 1-45 1-79 5-32 Fair definition. Wind west, next S.W., and lastly south; this af- ternoon very hot, therm. 90°. 10 318 2 40 45 45 56 2118 2 46-5 2-05 1-82 5-52 Good do. 10 193 20 3 12 8 8 22 2353 23 12-5 2-60 1-90 6-14 Do. do. 10 68 40 3 40 28 42 40 2588 43 37-5 2-50 1-95 6-33 Very good do. 10 304 3 50 58 58 60 2824 3 56-5 1-90 1-95 6-48 Excellent do., points. . 10 179 20 4 18 8 16 28 3059 24 17-5 2-10 1-96 Sum of squares of errors = 4-5708 Probable error of 10 measures = 0-42 „ 130 „ =0-1155 Wpif^jit — ' — 7,'>-0^ weignt- ^.^^ggy- '0"^ Vol. 23, p. 21. % 3rd Dec. Measured backward, Y left. A,M., 8-46 Definition in the morning not good, towards 179 20 4 20 8 12 30 3059 24 17-5 9- 7 llh it became much worse. 10 304 3 62 58 60 70 2824 4 2-5 1-50 1-50 9-30 10 68 40 3 48 34 46 50 2588 43 44-5 1-80 1-65 9-47 10 193 20 3 26 16 22 40 2353 23 26-0 1-85 1-72 10- 6 10 318 2 58 58 62 70 2118 3 2-0 2-40 1-89 10-26 10 82 40 2 58 44 60 60 1882 42 55-5 0-65 1-80 10-46 10 207 20 2 20 12 26 30 1647 22 22-0 3-35 1-93 11- 8 10 332 1 58 58 58 62 1412 1 59-5 2-25 1-97 9 4th Dec. 332 1 50 50 50 60 1412 1 52-5 A.M., 8-10 Plashing to the Keibiskow station, from sunrise 10 96 40 1 22 26 18 26 1176 41 23-0 2-95 2-09 8-32 until 8i> 47" ; signal light first returned at 10 221 20 58 54 58 62 941 20 58-0 2-50 2-14 8-55 8 47"'. 10 346 40 44 44 48 706 44-0 1-40 2-07 9-15 10 110 40 22 22 18 28 470 40 22-5 2-15 2-07 9-33 10 235 20 6 2 16 235 20 6-0 1-65 2-04 9-45 IT Sum of the squares of the errors = 6-04 Probable error of 10 measures = 0-48 „ 130 „ =0-1327 10 359 50 9 46 50 52 54 359 59 50-5 1-55 2-00 Weight = , — 56-77 (-1327) -> 1-96 X 75-02 = 147-039 2-00 X 56-97 = 113-940 . ^ Weight = 131-99) 260-979 = ° ' 1-98 Resulting angle from 260 meas. = 23-32-1-98 Weight = 131-99 §3. Kamies - Sector Berg Station. \ 422 VERIFICATION AND EXTENSION OE LA CAILLE'S AKC OF THE MERIDIAN. § 3. Eiebeek's Kasteel Station. Angle at Riebeeh's Kasteel, Trigonometric Station; between Kapoc Berg Signal Rock and east end of Base-line heliostats: measured with the Fuller Theodolite. o o Pointei Microscopes. Buns. Mean. Angle. 1842. o o 2 Kbmakks. A B C +1-15 33°^50'. o / / // II ,/ II o / // // % Feb. 17 Vol.4 322 2 38 - 1-8 42-0 29-0 + -97 322 28|24'04 57-91 ) p. 52 356 1 3 9 - 2-0 40-0 24-6 1-08 356 1921-95 322 2< ) 8 - 2-0 39-8 26-0 •96 322 28|22-23 \ 57-09| 356 1( ) 9 - 5-5 37-8 20-0 1-07 356 19 18-50 00 27 I 356 1( ) 8 37-2 75-0 51-5 1-02 356 18 55-59 47 06 30 9 31-0 64-6 29-0 1-12 30 9 42-65 356 1( ) 8 37-2 72-2 47-2 102 356 18|53-22 46-39 30 9 29-0 62-5 24-0 Ml 30 9 39-61 p. 62 f 356 K ) 8 56-0 95-5 72-3 106 356 19 15-66 55-22 54-15 -50-70 Repeated on the 19th -j 30 356 IC 9 55-6 )8 56'0 95-2 97-8 58-3 73-8 1'18 1-06 30 10 10-88 356 19 16-93 ( 30 9 55-2 96-3 58-2 1-18 3010 11-08 p.52 30 9 12-8 52-0 1-0 1-08 30 3 23-01 60'64) Runs. 64 24-0 45-4 1-4 •05 64 3 23-65 ABC — 0-5 —13-4 — 4-8 30 9 12-0 49-8 3-2 1^08 30 3 22-75 V 60^33 60^02 1 64 230 45-0 0-2 •04 64 |22-77 + 0-0 + 0-0 + 5-4 -41-8 -30-0 -47-5 64 14-8 41-5 - 2-0 •03 64 0|18^13 50^87 ) \ 52^08 +39-2 +33-8 +49-8 97 50 1 12-4 31-0 -16-8 •13 97 5 1 9-00 —23-0 —51-8 — 6-4 64 15-0 39-2 - 4-2 ■03 64 116-70 +28-0 +52-6 + 0-0 97 50 73-2 92-0 44-4 •13 97 5 1 1000 53^30 1 p. 53 — 0-5 —13-4 + 0-6 97 50 1 17-2 23-4 -25-0 •13 97 5 1 5-33 . - 2-6 + 3-8 + 2-3 + 50 + 0-8 - 6'4 131 40 97 50 131 40 2 19-5 76-2 1 79-8 17-0 80'4 77-0 -29-0 32-8 31-4 •24 ■13 •24 1314 97 5 1314 2 2-74 1 3-26 2 2-97 5741 / \ 58-56 59-71 \ + 1-9 — 8-8 — 3-5 lo-^-r-is 131 40 2 23-2 16-0 -34-0 •24 131 4 2 1-97 60-28) 9 165 30 2 85-5 65-4 34-8 •35 165 3 3 2-25 131 40 2 14-0 3-0 -51-5 •24 1314 1 48-74 V 60-93 61-58 I 165 30 2 74'5 52-4 23-0 •35 165 3 2 50-32 165 30 3 42-2 14-5 - 1-8 ■36 165 3 3 8-99 -, 199 20 4 36-0 6-2 - 1-2 •49 199 2 4 14-16 65-17 165 30 3 43-6 16'0 - 3-2 •36 165 3 3 8-49 199 20 4 37-0 8-4 1-2 •49 199 2 i 16-02 67-53 p. 62 c 165 30 3 38-0 88-2 34-2 •45 165 3 3 53-92 62-95 Repeated on the 19th J 199 20 4 44-0 94-0 23-6 •56 199 2 1 54-43 60^51 1 165 30 3 41-8 92-0 33-0 •45 165 3 3 56-05 * Bad division. ( 199 20 4 46-0 *94-2 22-0 •56 199 2' i 54-63 58-58 199 20 4 50-0 21-5 28-2 •52 199 2< 1 33-75 56-71 ) V 57-94 233 10 5 39-5 19-5 30-5 •63 233 1. 5 30-46 199 20 4 50-0 22-4 30-5 •52 199 -2' t 34^82 233 10 5 41-2 20-0 33'5 ■63 233 1. ) 32-20 57-38 i p. 54 233 10 5 28-0 31-0 42-4 ■64 i 233 1. ! 34^44 -^ 267 6 25-0 34-5 39-8 ■75 i 267 6 33-85 59-41 / y6M7 233 10 5 28'0 27-2 41-4 •64 : 233 U ) 32-84 267 6 28-0 36'0 41-0 •76 i 267 6 35-76 32-92 \ 267 6 38-4 58'2 67-0 •79 S 267 6 55-32 -. 300 50 7 24-0 64'5 62-5 •90 . 300 5' ^ 51-23 55-91 / \ 56-69 57^28l 267 6 39'0 57-8 65-2 •79 i 267 6 54^79 300 50 7 26-0 66-0 61-5 ■f -90 . 300 5' r 52^07 \ OBSEKVED HORIZONTAL ANGLES. 423 Angle at RiebeeKs Kasteel, Trigonometric Station ; between Kapoc Berg Signal Rock and east end of Base-line \ Jieliostats: measured with the Fuller Theodolite 1 Pointer. Microscopes. Euns. Mean. Angle. 1842. il Behasks. / A B C + l'-15. 33°-50'. / 11 1, II « o , II // 9 Feb. 18 Vol.4 300 50 7 30-0 68-6 63-5 + -91 300 57 54^94 62-82) > 62-49 62-15 I A.M. p. 54 334 40 8 43-8 73-2 53-2 1-03 334 48 57^76 300 50 7 29-5 69-8 64-2 •91 300 57 55-41 334 40 8 44-5 73-5 51-6 1-03 334 48 57-56 p. 57 334 40 8 43-8 79-8 52-3 1-03 334 48 59-66 63-36) \ 62^65 61^95 I 56-27) V 57-05 57-84 j 56-41 ) U6-81 57-21 j 56-38) U6-96 57-55 I 8 30 9 41-0 81-0 63-6 1-15 8 39 63-02 334 40 8 44-2 79-0 53-4 1-03 334 48 59-90 8 30 9 9 40-5 42-0 79-8 88-5 61-8 71-2 1-15 1-16 8 8 39 39 61-85 68-39 8 30 42 30 53-0 86-8 53-8 •13 42 31 4-66 8 30 9 43-0 88-0 72-2 1-16 8 39 68-89 42 30 55-0 57-0 88-8 89-4 56-0 41-0 -13 •12 42 42 31 31 6-73 2-59 42 30 76 20 1 55-8 84-0 36-5 -23 76 21 59-00 42 30 57-6 90-0 41-6 12 42 31 3-19 76 20 1 1 56-0 49-2 86-0 72-2 38-5 24-5 •23 •21 76 76 22 21 0-40 48-84 76 20 110 10 2 54-2 64-0 16-5 •32 110 12 45-22 76 20 I 49-0 72-2 23-2 ■21 76 21 48-34 110 10 2 55-0 64-2 17 5 •32 110 12 45-89 p.58 110 10 2 55-0 570 16-5 •31 110 12 43-14 59-45) y 61-13 62-82 \ 56-58) V 55-17 53 78 1 63-96) V 65-22 66-49 I 57-97) V 56-54 55-10 1 58-67) \ 59-28 144 3 53-0 55-3 18-2 •42 144 3 42-59 110 10 2 53-5 55-5 14-5 •31 110 12 41-48 144 3 3 54-6 57-2 58-0 40-6 19-0 5-8 •43 •41 144 144 3 3 44-30 34-94 144 177 50 4 52-2 31-6 9-2 •52 177 54 31-52 144 3 57-8 42-0 8-0 •41 144 3 36-34 177 50 4 4 51-2 50-5 30-8 30-0 6-8 120 •52 •52 177 177 54 54 30-12 31-35 177 50 211 40 5 51-0 29 4 23-6 •64 211 45 35-31 177 50 4 48-8 28-8 14-2 •52 177 54 3112 211 40 5 5 51-5 68-0 32-0 62-0 27-4 14-0 •64 •67 211 211 45 45 37-61 48-67 211 40 245 30 6 71-2 39-2 27-2 •77 245 36 46 64 211 40 5 57-2 42-2 61-0 •68 211 45 54-15 p. 59 245 30 6 6 38-4 29-4 49-2 44-0 57-8 48-0 •78 •77 245 245 36 36 49-25 41-24 245 30 279 20 7 20-2 52-1 44--8 •88 279 27 39-91 245 30 6 22-5 40-2 46-4 •76 245 36 37-13 59-87J 279 20 7 15-2 50-2 43-0 •87 279 27 37-00 279 20 7 13-0 48-5 34-3 •87 279 27 32-80 65-49) \ 64-42 313 10 8 15-3 56-1 40-5 •99 313 18 38-29 279 20 7 13-0 45-5 33-6 •86 279 27 31-56 63-36 f 313 10 8 14-0 49-8 380 •99 313 18 34-92 313 10 8 5-2 41-5 36-0 •97 313 18 28-54 56-67) 347 9 5-4 45-0 22-0 V08 347 9 25-21 V 57-39 313 10 8 5-0 42-0 36-0 •97 313 18 28-64 58-11 \ 347 9 6-0 45-0 26-0 + 1^08 347 9 26-75 §3- Biebeeki Kasteel Station. H 424 VERIFICATION AND EXTENSION OF LA CAILLE'S ARC OF THE MERIDIAN. § 3. Kiebeek's Kasteel Station. Angle at Riebeeh's Kasteel, Trigonometric Station ; between Kapoc Bere Signal Rock and east end of Base-line heliostats: measured with the Fuller Theodolite. 1842. 9 Feb. 18 Vol.4 p.59 p. 60 T? Feb. 15 Bgmabes. p.61 p. 62 p. 63 Excellent definition. Pointer. 347 21 347 21 54 88 54 88 88 122 88 122 122 156 122 156 156 190 156 190 190 224 190 224 224 257 224 257 257 291 257 291 291 325 291 325 50 1 40 2 Microscopes. 225 259 225 259 259 293 259 293 12-2 15-8 130 13-0 12-6 33-2 11-0 31-0 35-4 49-4 35-0 47-8 47-0 105-6 113-2 104-2 104-5 45-0 108-5 43-8 46-0 46-2 45-0 430 93-5 92-0 88-6 29-0 31-8 24-0 32-5 20-0 23-5 10-0 22-7 9-0 10-0 8-3 8-2 7-5 34-8 51-0 36-2 51-2 33-0 16-8 27-0 13-5 53-0 51-0 53-6 46-4 60-0 70-2 58-6 68-8 70-3 74-5 72-0 74-0 61-4 116-8 128-0 119-6 112-0 39-0 115-5 40-4 34-0 23-0 30-6 21-0 67-6 66-2 64-0 7-0 15-4 18-8 18-0 18-0 22-2 33-5 24-0 35-8 46-2 44-2 41-6 44-8 55-2 50-2 56-8 50-0 18-4 35-8 22-0 35-2 37-0 32-0 36-4 30-0 16-0 - 9-0 17-3 - 7-4 7-0 2-5 8-2 2-0 -17-0 51-4 48-6 53-0 55-6 4-2 61-8 4-8 0-5 2-8 1-6 3-2 57-0 63-8 57-0 4-5 32-2 30-0 33-0 29-6 34-0 36-7 33-4 37-4 43-8 39-3 39-4 38-0 - 2-2 -14-2 - 0-5 -15-0 35-0 35-0 34-8 32-6 Runs. +1-15, + 1-10 •06 1-10 •06 -06 ■17 •06 •17 •19 •31 •19 •31 •29 •40 •30 •41 •40 •52 •41 •52 •51 •62 122 88 122 122 156 122 156 156 190 •51 (156 •62 190 Mean. 347 21 347 21 21 54 21 54 54 88 54 88 •60 •72 •59 •72 •74 •85 •74 •85 •86 •97 •86 •97 1^09 •98 1-09 1-09 ■06 1-09 •06 •06 •17 •05 + ^17 9 51 51 51 42 51 42 42 33 42 33 33 24 33 24 24 15 24 15 15 6 15 6 6 57 6 57 57 48 57 48 48 39 48 39 39 30 39 30 30 21 30 293 21 190 224 190 224 224 257 224 257 257 291 257 291 291 325 291 325 225 259 225 259 259 293 259 35-17 32^99 35^43 29-86 29^59 31-64 29-03 30-97 37-76 42-44 38-59 41-58 30-76 31-67 36-90 32-68 3M0 29^92 35-68 30-19 27-34 •24-62 26 24 2302 13-30 14-72 10 46 14-22 27-21 25^12 28-57 23-38 27-43 27-70 27-56 -28-37 34-31 31-69 30-71 31-19 30^36 29-06 31-92 28-79 28-86 29-37 27-98 27-27 Angle. 33°-50'. 57-82 54-43 62-05 1 61-94 64-68 I 62-99 - 56-13 . 62-00 ■ 63^84 60-91 , 55-78 58-82 1 54^51 1 • 58^35 • 56^66 •28 ] •781 57^03 61^42 ) > 62^59 63^76 I 57-91 i 54-81 I 57-38 i 56-87 - 56-36 . 60-55 - 58^93 ► 57^79 . 59'90l OBSERVED HORIZONTAL ANGLES. 425 Angle at RiebeeKs Kasteel, Trigonometric Station; between Kapt c Bere Signal B.ock and east end of Base-line heliostats: measured with, the Fuller Theodolite fl Pointer. Microscopes. Runs. Mean. Angle. 1842. II Remarks. / A B C +1-15 33°-50'. o / // // ,1 ,/ o / « a Tj Feb. 19 Vol.4 293 20 1 9-0 33-5 25-8 + -16 293 21 22-93 54-66) K 57-83 60-98 I 58-38) 158-86 59-35 I 58-01 ) Uo-11 62-21 1 p. 63 327 10 1 580 89-6 84-4 ■26 327 12 17-59 293 20 1 9-0 32-0 24-4 •16 293 21 21-96 327 10 2 2 6-0 0-8 33-6 46-0 28-4 30-0 -27 •28 327 327 12 12 22-94 25-88 327 10 1 3 1-0 47-2 23-4 •39 1 3 24-26 327 10 2 20 46-0 30-8 -28 327 12 26-55 p. 64 1 3 2 1-5 52-8 50-0 103-3 250 77-4 -40 -38 1 1 3 3 25-90 18-21 1 Beautiful definition. 34 50 4 5-2 40-8 1-2 •49 34 54 16-22 1 2 50-8 102-4 76-3 -38 1 3 16-88 34 50 4 7-6 45-0 3-2 •49 34 54 1909 34 50 4 18-0 41-0 -14-3 •49 34 54 15-39 57-81 ) 158-60 59-39 I 68 40 5 13-8 460 -22-0 ■60 68 45 13-20 34 50 4 12-8 41-2 -15-8 •48 34 54 13-21 68 40 5 13-5 45-6 -23-1 •60 68 45 12-60 68 40 5 15-2 43-7 -24-0 •60 68 45 12-23 53-80) 155-94 58-08 I 102 30 6 16-0 32-0 -32-0 •70 102 36 603 68 40 5 11-6 43-5 -26-2 •59 68 45 10-22 102 30 6 18-8 34-5 -30-5 •70 102 36 8-30 ■ 102 30 5 66-8 74-6 18-4 •68 102 35 53-95 50-12) > 51-78 53-43 I 136 20 6 52-0 58-4 19-5 •77 136 26 44 07 102 30 5 64-5 75-2 18-0 •68 102 35 53-25 136 20 6 55-0 62-2 20-5 •78 136 26 46 68 p. 65 136 20 6 61-0 57-0 5-2 •77 136 26 41-84 51-16) L 53-97 Good definition. 170 10 7 55-0 36-4 5-0 •87 170 17 33-00 Calm. 136 20 6 59-0 51-8 40 •76 136 26 3903 56-77 j 63-22) 170 10 7 7 560 61-0 39-0 42-0 98 18-5 ■87 ■88 170 170 17 17 35-80 41-38 170 10 204 8 66-4 420 22-4 1^00 204 8 44-60 (. 62-24 170 10 7 630 43-8 230 ■89 170 17 44-16 61-25 \ 204 8 8 65-2 61-0 42-3 33-0 25-7 31-2 1^01 VOO 204 204 8 8 45-41 42-73 55-38) 204 237 50 9 47-8 31-2 32-0 1^11 237 59 38-11 V- 54-92 204 8 61-0 35-6 34-5 1^00 204 8 44-70 54-48 \ 237 50 9 9 48-0 47-8 330 33-0 33-2 48-5 1^11 M2 237 237 59 59 39-18 44-22 60-64) 237 50 271 50 44-8 38-8 50-7 •09 271 50 44-86 V 61-27 237 50 9 500 38-0 51-0 1^12 237 59 47-45 61-91 \ 271 50 47-6 44'2 560 ■09 271 50 49-36 p. 66 271 50 41-0 55-2 58-2 •10 271 50 51-57 59-97) Good definition. Calm. 305 271 40 50 1 34-5 37-8 66-5 51-2 53-0 56-5 •21 •09 305 271 41 50 51-54 48-59 U2-19 64-40 \ 305 40 1 38-0 66-5 53-8 •22 305 41 52-99 305 40 1 42-5 76-0 54-5 •23 305 41 57-90 59-74) 339 30 2 36-4 830 52-5 •34 339 32 57-64 y 60-68 305 40 1 43-4 76-2 56-1 •23 305 41 58-80 61-62 \ 339 30 2 38-0 86-0 56-2 + ^35 339 32 60-42 §3. Riebeek'f Kasteel Station, 426 VERIFICATION AND EXTENSION OF LA CAILLE'S AKC OF THE MERIDIAN. § 3- Riebeek's Kasteel Station. Angle at Riebeek's Kasteel, Trigonometric Station; between Kapoc Berg Signal Rock and east end of Base-line heliostats : measured with the Fuller Theodolite. o o Pointer. Microscopes. Runs. Mean. Angle. 1842. Hemarks. A B C +1-15. 33°-50'. o , / // „ „ II o / II » 1? Feb. 19 Vol.4 339 30 2 38-4 87-2 58-6 + -35 339 33 \-15 60-54 ) \ 58-16 55-78 I p. 66 13 20 3 40-2 88-8 56-5 •46 13 24 2-29 339 30 2 40-0 91-4 61-0 -35 339 33 4^48 13 20 3 37-0 86-2 56-2 •46 13 24 0-26 Light north air. 13 20 3 36-8 90-0 46-2 ■46 13 23 58-13 6305) V 64-69 66-33 I Runs, FEBErAKY 22. 47 10 4 49-0 97-8 35-0 •58 47 15 1-18 ABC 13 20 3 34-5 88-5 44-2 •45 13 23 56-18 —49-0 —53-9 —55-4 47 10 i 49-0 100-0 36-8 •58 47 15 2-5] +44-5 +44-4 +55-5 — p. 67 — 7-8 —58-6 —32-0 47 10 i 53-5 100-0 26-8 -58 47 15 0-68 47-12 + 1-7 +60-8 +31-2 81 5 48-5 79-8 13-1 -67 81 5 47-80 - 1-4 -57-5 -13-3 47 10 i 50-0 98-8 27-1 •58 47 14 59-21 50-73 47-15 + 5-9 +59-8 + 8-5 81 47 81 . 10 . 5 49-2 i 50-5 5 45-2 83-0 100-8 81-6 15-6 28-0 13-7 •67 •58 •67 81 47 81 5 14 5 49-94 60-35 47-50 ■ 48-34 —4-5—9-5+0-1 A3 I.'5-9— =4-6 — 6-1+2-2— 0-8 B 3/ 4-7 — =1-6 +4-5+2-3-4-8 C 3/ 2-0-=0-74 81 114 . 50 ( 3 40-5 3 41-9 69-2 62-2 4-0 3-4 •65 •76 81 114 5 56 38-55 36-59 58-04) Uo-48 62-92 i 53-0o) \ 55-18 57-36 I —6-1-5-0—5-5 81 . 5 39-3 69-8 1-5 •65 81 5 37-52 h „ 26 p. 79 !«■«-- 1-84 9 Runs. 114 50 ( 3 44-3 5 57-8 66-2 53-5 8-5 2-4 + ^77 114 114 56 56 40-44 38-85 114 50 ( + 1-44 •95 101>30"',A.M. ABC 148 40- r 53-0 41-8 - 2-5 1-08 148 47 31-85 - 7-1 -51-.5 - 0-4 114 50 ( 3 57-0 55-0 2-0 •96 114 56 38-96 + 4-7 -t-40-9 + 1-0 148 40* r 57-2 47-0 1-5 1^09 148 47 36-32 —49-0 -28-2 -40-7 +44-4 +32-5 +42-2 r 66-9 43-8 17-0 1^11 148 47 43-68 54-56 ) 148 40' -13-5 -31-0 - 5-4 182 30 f i 58-0 32-5 20-5 1^24 182 38 38-24 + 18-1 +31-8 + 1-8 148 182 40' 30 f r 67-0 i 60-8 43-9 37-0 17-2 25-7 Ml 1-25 148 182 47 38 43-81 42-42 \ 56-59 58-61 \ - 2-4 -10-6 + 0-6 _ 4-6 + 4-3 + 1-5 + 4-6 + 0-8 — 3-6 182 30 S i 60-5 34-0 38-3 + 1-26 182 38 45-53 56-50 ) 216 30 ( )- 2-1 -29-0 -22-7 — -04 216 29 42-03 — 2-4 — 5-5 — 1-5 ?^ = l-04 182 216 30 f 30 ( ! 55-0 )- 2-0 312 -32-2 39-0 -22-1 + 1-25 - -04 182 216 38 29 42-98 41-19 \ 57-36 58-21 1 — si-ao", P.M. 9 216 30 ( ) 49-5 29-4 ' 51-0 + -10 216 30 43-40 57-94) V 58-42 Last = 1-84 250 20 43-5 27-8 52-0 •24 250 21 41-34 216 30 ' ) 49-0 I 45-0 28-7 26-9 50-6 52-7 •10 + ^24 216 250 30 21 42-87 41-77 Mean — 1-44 250 20 58-901 ' 54 Couplets = 33°-50'-58"-524. a 20th February.— In general cloudy, with m isty horizon,— non e of the heliostats now visible at the same time. Cape Town seen twice, Kapoc Berg once, east en d of Base for an h 3ur. N.W. wind and dense fOg in the afternoon. T? 26th February.— Violent wind from E. b y S. came on, on Thursday night and continued until 9 o'clock yesterday morning, then died away; but toward s 4 o'clock it ret urned, last night and this morning it may be called a strong gale. Yesterday and last night t le canvas and inst rument were removed for security, but time being valuable, an attempt to observe was made at 10 danger. i" 30"° this mornin g. Bad images, the instrument not free from OBSERVED HORIZONTAL ANGLES. 427 1. Cape L'Agulhas Station. The only distinguishing feature of Cape L'Agulhas — the extreme southern termination § s. of the African Continent — is an oblong limestone hill of trifling elevation, partly covered L'Agulhas with bush. Properly speaking, it consists of three hills vi^hich appear as one from the southward. The west end, which is the most elevated part, is 455 feet above the level of the sea, and commands the seaward sweep from Gunner's Quoin, round by the south and east to Struys Point. Owing to the Umestone at this part being covered with a deep stratum of indurated sand, our usual method of defining a station, by a cylinder of lead inserted in stone carry- ing a brass stud, could not be effected ; therefore an oak picket, 3^ feet in length, was driven home, and a pin inserted to mark the point. (It may be proper to mention in this place, that on the occasion of an official visit to L'Agulhas in the autumn of 1848, for the purpose of examining the tower of the light- house then recently erected, and superintending certain hydrographical operations con- nected with the establishment of that light ; advantage was taken of the opportunity, to determine the position of the burner with respect to the trigonometric point. The horizontal distance was found to be 4372 feet, and the azimuth of the burner from the trigonometric point 358°'59''15", reckoning from the south point round by the west, or l°-0'-45" east of south.) The Beaufort theodolite was centered over the angle point. NAMES OP STATIONS AND SIGNALS. AnSes Obseiva- Weights. No. of )bserva tiODS. BETWEEN Danger Point, heliostat... and Referring cleft 51-58-25-695 50 11-07 Referring cleft and Zondereinde, heliostat. 5- 3-59-454 60 84-08 Referring cleft and Pot Berg, hehostat. . . . 60-46- 4-425 30 10145- Zondereinde, heliostat and Pot Berg, hehostat. . . . 55-42- 3-944 31 7-60 From the above are deduced : Between Danger Point. . . and Zondereinde 57' 225-150 9-78 Zondereinde .... and Pot Berg 55-42- 4-880 91-01 The above angles were measured on the 3rd and 5th of August, 1845, by Mr. Maclear. 2. Danger Point Station. Danger Point is a bold Umestone promontory, from the southern extremity of which Danger Point a tongue of low land projects in a S.S.W. direction, to the distance perhaps of five miles. Dyer's' Island is separated from the east edge of this tongue of land by a narrow passage, and on the west side of the promontory there is a stalactite cavern, the entrance to which is close to the beach. 428 VERIFICATION AND EXTENSION OP LA CAILLE'S ARC OF THE MERIDIAN, § 3. The exposed position of the promontory, by projecting into the southern ocean, sub station-Ccon- jects it to the full force of winds and storms. Lind's wind-gauge, on the 20th of August, indicated a pressure of 15 pounds on the square foot, and occasional puiFs jerked out the water. The station is on the highest or southern end of the promontory, at an elevation of about 1100 feet above the sea, and is marked and protected in the usual way. The Beaufort theodolite was centered over the angle point. Observed observl- Weights. NAMES OF STATIONS AND SIGNALS. Angles tions. Cape Point, hehostat and Sneeuw Kop, pile 41-36-44-41 80 12-60 Mudge Point, pile and Referring niche 21-29-44-93 41 1 1-48 Kogel Berg, pile and Referring niche 25'36'3r64 20 Referring niche and ZwartBerg(Caledon),pile 36'36'50'37 90 1273 „ and Babylon's Toren, pile . 7-46-53-49 30 0-84 „ and Zondereinde, heliostat . 59-52- 6-41 85 40-86 Sneeuw Kop, pile and Zondereinde, heliostat . 67-22-36-08 90 18-71 „ pile and Referring niche 7-30-29-48 40 14-20 Zwart Berg (Caledon), pile and L'Agulhas, heliostat. . . 100- 4-20-01 80 18-50 „ „ „ pile and Zondereinde, heliostat . 23-15-14-51 50 7-97 Zondereinde, heliostat... . and L'Agulhas, heliostat. . . 76-49- 6-23 80 4-34 The Cape Point heliostat was placed close to the base of the pile on the north side, .-. the reduction to the center of the pile is + 5"-ll. From the above are deduced : Cape Point and Sneeuw Kop 41-36-49-52 12-60 Mudge Point and Babylon's Toren 29-16-38-42 0-52 Sneeuw Kop and Zondereinde 67-22-36-01 29-24 Zondereinde and L'Agulhas 7649- 5-82 9-90 Zwart Berg (Caledon) and Zondereinde 23-15-14-29 1150 ... and L'Agulhas 100-4-20-11 21-30 The above angles were measured between the 12th and 22nd of August, 1845, by Mr. Maclear. 3. Mudge Point Station. Mudge Point Mudge Point headland is similar in character and general outline to Danger Point. Station. » -i i i i i i • , A pile had been built on its southern end (which is the highest) for observation from the adjacent stations, which pile was not disturbed when the Beaufort theodolite was taken to it, owing to the weakness of the party, and to the station being secondary. As the theodolite tent was not available, the instrument was placed under the shelter of the pile. OBSERVED HORIZONTAL ANGLES. 429 Calculation of the reduction to the center of the pile. y, the angle of direction, is reckoned from the center of the pile towards the right ^^^^J^?"*^' hand, in the order of increasing readings. Two excentric stations were occupied. ' Mudge Point con- STATIONS. T r Log. r'. sine, y Log Distance. Log Reduction. Reduction. Kogel Beig. . , . Sneeuw Kop . . . Danger Point . . Cape Point Sneeuw Kop . . . o / 70-52 102-51 259- 6 218-20 283- 1 feet 10-02 10-02 10 02 8-00 8-00 6-29062 6-30428 G- 30737 6-01008 6-20621 4-99839 5-14889 4-99581 5-30072 5-14889 1-29223 1-15539 1-31156 0-70936 1-05732 It + 19-60 + 14-30 -20-49 - 5-12 -11-41 The reduction for the left hand station, algebraically subtracted from the reduction for the right hand station, gives the reduction to the pile's center. NAMES OP STATIONS AND SIGNALS. Observed Angle. Reduction. Angle reduced to pile. No. of Observa- tions. Weight. BETWEEN Cape Point, pile, & Sneeuw Kop, pile Kogel Berg, pile, & Sneeuw Kop, pile Sneeuw Kop, pile, & Referring niche . Referring niche, & Danger Point . . .•. Sneeuw Kop & Danger Point . . O 1 II 64-40-55-69 31-58-24-28 40-15-16-44 115-59- 2-70 75-43-46-26 - 6-29 - 5-30 -34-79 O ' " 64-40-49-40 31-58-18-98 75-43-11-47 50 30 30 60 190-73 4-89 30-16 4-60 3-99 The angle between Sneeuw Kop and Danger Point is not required. The above angles were measured on the 27th, 28th, and 31st of August, 1845, by Mr. Maclear. 4. Babylon's Token Station. On emerging eastward from the Houw Hoek pass, the Tower of Babel mountain ^^^y^°g°'«^.^^ stands prominent on the right. It is the west end mass of the irregular range which extends eastward to Breda's Dorp. The Bot River runs close to its base on the west towards the sea, and a valley separates it from the Mudge Point range. The station is on the highest part of the mountain. The Beaufort theodolite was centered over the angle point. NAME8 OF STATIONS AND SIGNALS. BETWEEN Observed Horizontal Angles. No. of Observa- Weight*, tious. Zwart Berg (Caledon), pile and Zondereinde, hehostat. 9-10-44-45 10 „ „ „ and Gunner's Quoin, helios. 93-10-53-23 10 „ and Danger Point, pile .. . 113- 0-31 -46 46 9-21 430 VERIFICATION AND EXTENSION OF LA CAILLE'S ARC OF THE MERIDIAN. |3. Zondereinde, heliostat. ... and Gunner's Quoin, helios. 84' 0-12-51 70 2-00 Toren station and Danger Point, pile .. . 103-49-49-46 40 168-11 Danger Point, pile and Mudge Point, pile... . 73-23-41-81 40 5-67 Mudge Point, pile and Kogel Berg, pile 47-15-11-32 40 19-40 Kogel Berg, pile and Sneeuw Kop, pile 33- 7-55-43 60 19-40 Table Mountain, pile and „ „ „ 22-18-39-51 40" 5-62 King's Battery and „ „ „ 20-35-45-65 10 Sneeuw Kop, pile and Zondereinde, heliostat. 102-23-28-62 60 82*31 „ „ and ZwartBerg(Caledon),pile 93-12-41-93 40 7-03 The angles were measured between the 8th and 15th of September, 1845, by Mr. Maclear. The party was driven twice from the Station by stormy weather, and for several days it was fog-bound. 5. Zondereinde Berg Station. Zondereinde The Station is On the highest point of the range of mountains, bordering the left bank Berg Station. . . „ . of the River " Zondereinde," at an elevation of 5330 feet above the level of the sea. The point is defined in the usual way, by a brass pin hammered into a cylinder of lead in a hole jumped in a rock, over which a pile 14 feet high, 14 feet diameter at the base, and 4 feet diameter at the top, was built on the completion of the observations. The nearest direction of ascent to the station, from the base of the range, is from the farm of H. Roux. The Fuller theodolite was centered over the angle point. Observed No. of No. of HAMES or STATIONS AND siGNALE(. Horizontal Observa- Partial Angles. tions. Measures. BETWEEN O , ,, Pot Berg, pile and L'Agulhas, hehostat. . . 52-36-44-72 100 50 L'Agulhas, heliostat and Danger Point, heliostat 46-8-41-88 120 60 Danger Point, heliostat. .. and ZwartBerg(Caledon),pile 30-11-49-34 48 24 „ „ „ and Babylon's Toren, helios. 24- 5- 7-00 80 40 „ „ „ and Sneeuw Kop, H.H., pile 55-24*46-57 96 48 ■ Sneeuw Kop, H. H., pile, and Pot Berg, pile 205*49-49-43 40 20 Gunner's Quoin, heliostat. and Danger Point, heliostat 21- 3-52-99 40 20 Babylon's Toren, pile and Sneeuw Kop, H.H., pile 31-19-38-57 40 20 The above angles were measured between August 13 and September 14, 1845, by Mr. Mann. Occasional interruptions by snow storms : the cold was intense. )J J) 3) ;> j> J) 3) >) 3) !3 33 33 33 33 33 OBSERVED HOEIZONTAL ANGLES. 431 6. Sneeuw Kop, near Hottentot's Holland, The station is upon the dome-shaped top of the most elevated mountain, of the range § 3. near Stellenbosch. In the field-books it is designated Sneeuw Kop, H.H., to distinguish nearHotten- it from Sneeuw Kop of the Cedar mountains. There is no entry in the field-book relating to the method of marking the station point ; but there is no reason for doubting that it accorded with the general system, — viz. : a brass pin driven into a cylinder of lead let into a stone. The Fuller theodolite was centered over the angle point. HAMES OF STATIONS AND SIGNALS. Observed No. of Partial Angles. Measures. -j^^^^^^ BETWEEN Q , II Cape Point, heliostat and Zwart Kop, heliostat. . 14- 6-27-039 160 80 and Table Mountain, pile. . 45-55-29-813 160 80 and King's Battery, heliost. 48-22-41-201 160 80 and Royal Observatory, hel. 51- 0-26*285 160 80 and Rogge Bay Station, hel. 5 1 • 1 5 • 1 9 • 1 93 1 60 80 and Tyger Berg, heUostat. . 66-25-39-245 80 40 Zwart Kop, heliostat and Table Mountain, pile. . 31-48-59-959 16 8 and King's Battery, heliost. 34- 16" 12-6 13 160 80 and Royal Observatory, hel. 36-54- 1-207 160 80 Noah's Arc, heliostat and Tyger Berg, heliostat. . 48-25-57-511 60 30 Naval Yard, heliostat and Kapoc Berg, heliostat. 70- 5-42-286 60 30 Table Mountain, pile.... and Rogge Bay Station, hel. 5-19-50-155 16 8 and Green Point, light-house 6-59-18-240 8 4 and Mouille Point, Ught-house 7-33- 1-600 8 4 and Kapoc Berg, heliostat . 43-4-41-466 160 80 King's Battery, heliostat .. and Kapoc Berg, heliostat . 40-37-29-671 160 80 Rogge Bay Station, helios. and „ „ „ 37-44-52-464 160 80 Royal Observatory, helios. and „ „ „ 37-59-44-548 160 80 „ and Blaauw Berg, heliostat. 20-52-39-389 16 8 Blaauw Berg, heliostat. . . and Kapoc Berg, hehostat. 17- 7- 4*608 72 36 Kapoc Berg, heliostat and Riebeek's Kasteel, pile. 28-14-9*960 10 5 and Winter Berg, heliostat. 46-56 49-491 160 80 Riebeek's Kasteel, pile. . . and Winter Berg, heliostat. 18-42-42-930 8 4 • Winter Berg, pile and Zondereinde, heliostat. 84- 6-25-048 160 80 Zondereinde, heliostat. . . . and Danger Point, heliostat 57-12"50-525 160 80 and Kogel Berg, heliostat.. 110-5-54-200 74 37 Caledon, Zwart Berg, pile, and „ „ pile 92-19-46-249 40 20 Danger Point, heliostat. .. and Cape Point, heliostat. . 82-43'45-752 160 80 Mudge Point, pile and Kogel Berg, pile ..... 43-6- 6-465 40 20 Babylon'sToren, pile.... and „ „ „ 63-48-57-055 40 20 K 33 33 33 J3 432 VERIFICATION AND EXTENSION OP LA CAILLE'S ARC OF THE MERIDIAN. .§3. Sneeuw Kop, near Hotten- tot's Holland — (continued). Kogel Berg Station. Kogel Berg, heliostat and Cape Point, heliostat. . 29-50-4 1-237 80 40 andNoah's Arc, heliostat.. 47-50-21-122 80 40 „ „ pile and Roman Rock, light-ship 49- 9- 7770 8 4 The above angles were measured between November 2, 1844, and July 21, 1845, by Mr. Smyth. 7. Kogel Berg Station. The station is upon the top of the highest mountain, of the range that bounds False Bay on the east side. The angle point is marked by a hole in a rock filled with lead, and a brass pin in the center. On account of the form of the mass of rock, and the position of the plug in it which marks the angle point, the theodolite could not be centered exactly over the point ; there- fore the observations made on this mountain require a reduction to the center ; and the following are the necessary elements : Distance of theodolite from angle point (brass pin) 6'0 inches. o / // Reading for the line passing through the theodolite and angle point 0- O'O. Reading of the theodolite for the Sneeuw Kop pile 7'35-0. After the observations, a pile was erected over the point, 14 feet in height, 14 feet base, and 4 feet in diameter at the top. Calculation of the reduction to the angle point on Kogel Berg. 01340. r ^ 0'5 foot. log;. , = log;, r" ^ 5' ^ sine I" ^ Angle of direction (-y) measured from the center towards the right. Sneeuw Kop Zondereinde Caledon, Zwart Berg Babylon's Toren Miidge Point Danger Point Cape Point Zwart Koj) Dockyaril, Clock Tower. . . Noah's Arc Admiralty House Roman Rock, light-ship . . . Table Mountain, pile King's Battery Royal Observatory Tyger Berg 7-35 63-27 70 33 90-38 112-31 116-36 234-55 255 48 260 53 261-11 261-23 ■263-14 289-31 292-43 296- 1 311-39 Log. r" sine y. 4-13387 4-96500 4-98788 5-01337 4-97896 4-96481 92632 99992 00788 00S24 00847 01036 98770 97833 96700 88685 Log distance. 4-88766 5-47550 5-26630 5-10299 4-99839 5 ■29703 5-10689 5-115-29 5-14375 5-11948 514512 5-11704 5-2-2972 5-2-2-281 5-21646 5-21649 Log reduction. 9-24621 9-48950 9-72168 9-91038 9-98057 9-66778 9-81943 9-84463 9-86413 9 88876 9-86335 9-89332 9-75798 9-75552 9-75054 9-67036 Reduction. +0-176 + 0-309 +0 527 +0-814 +0-956 +0-465 -0-660 -0-767 -0-731 -0-774 -0 730 -0-782 -0-573 -0-570 -0-563 -0 468 OBSERVED HOEIZONTAL ANGLES. 433 The reduction for the left hand station, alp-ebraically subtracted from the reduction for § 3- • 1 1 1 • ■ 1 1 - , -, ■ KogelBerg the right hand station, gives the reduction to the angle point. station-Ccon- tinued). Horizontal angles observed at Kogel Berg, reduced to the angle point. FULLER THEODOLITE. NAMES OF STATIONS AND SIGNALS. Oliservea Hori- zontal Angles. Redction to center. Angles reduced to Station point. No. of Observa- tions. No. of Partial Means. BE Sneeuw Kop, H.H,, pile j» >» )? Mudge Point, pile Cape Point, pile w >» » » »1 )» Zwart Kop, pile » }> )) »» »» j» n ij *) Noah's Arc, center Roman Rock rWEEN . and Zondereinde, pile and Mudge Point, pile Ola 55-51-46-632 104-55-35-468 83- 3-15-089 109- 0-55-894 62 58-23-481 143-17-24-308 20-53-24-264 54-36.30-178 57-47-.58-202 55-50-35-890 5- 4-33-500 5-34-35-600 5- 6-10-850 40-13-16-677 , 50-27-43-300 26-17-29-650 78- 3-52-049 74-52-23-128 71-33-41-976 55-56-23-589 70-47-42-775 72-29-44-480 4-33-30-480 17-33-59-910 5-26-57-840 16-40-33-520 11-54-36-710 0-20-39-380 54-57-17-170 36-54-32-320 -1- 0-133 + 0-780 -1- 0-638 -H 0-289 -1- 0-351 - 1-723 -0-107 + 0-087 -1- 0-090 -1- 0-299 -f 0-040 + 0-040 -\- 0-040 -1- 0-204 -1-0-310 -t- 0-210 -1- 0-749 + 0-746 -f- 0-739 + 0-644 - 0-600 - 1-560 -t- 0-090 -t- 0-200 O 1 It 55-51-46-765 104-55-36-248 83- 3-15-727 109- 0-56' 183 62-58-23-832 143-17-22'585 20-53-24-157 54-36-30-265 57-47-58-292 55-50-36-189 5- 4-33-540 5-34-35-640 5- 6-10-890 40-13-16-881 50-27-43-610 26-17-29-860 78- 3-52-798 74-52-23-874 71-33-42-715 55-56-24-233 70-47-42-175 72-29-42-920 54-17-17- 26 36-54-32- 52 20 80 40 40 40 80 100 102 80 100 6 3 3 80 3 5 100 80 80 100 20 4 4 4 4 4 8 2 4 10 40 20 20 20 40 50 51 40 50 3 40 3 50 40 40 50 10 2 2 2 2 2 4 2 and Babylon's Toren, pile andDanger Point, pile and Zwart Berg (Caledon),pile . and Zwart Kop, pile .. and „ „ „ and Table Mountain, pile and King's Battery, heliostat. . and Tyger Berg, heliostat and Naval Yard Clock Tower. and Admiralty House, center. andMartello Tower, center... and Royal Observatory, helios. ..and Tyger Berg, pile .and Table Mountain .. and Sneeuw Kop, PLII., pile... .and „ „ It and „ „ „ ..and . . and Zwart Kop pile Table Mountain, pile King's Battery, heliostat ... Royal Observatory, heliostf Tyger Berg, heliostat Cape Hanglip, pile Mudge Point, pile Table Mountain, pile Green Point Light-house.... Table Mountain, pile Mouille Point Light-house. Robben Island Church Tow Captain Owen's, pile » ** VI Zwart Kop, pile and Green Point Light-house. ..and Tyger Berg, pile .. and Mouille Point Light-house .. andTveer Bere. Dile 3rand „ „ „ .. and Cape Point, pile and Table Mountain, pile . . and King's Battery, heliostat.. The angles at this station were measured between the 1st and 28th of October, 1845, by Mr. Mann. 8. Cape Point Station. The land formino; the west horn of False Bay has been likened to a boot. Viewed Cape Point . . Station. from the southward, the remarkable and well-known precipice of hard sand-stone, like the vertical section of a pyramid, is the leading feature towards the toe of the boot. On the top of the precipice, elevated 800 feet above the level of the sea, stands a small conical pile of weather beaten stones, said to be the mark of one of Captain Owen's stations (a bottle containing a pistol bullet was found in a crevice near the top of the pile). From this point the ridge slants north-westward to a saddle, which is less elevated by 112 feet (elevation 688). The theodolite and the sector station are on this saddle, exactly parallel to each other, — the latter to the west of the former, and distant from 434 VERIFICATION AND EXTENSION OP LA CAILLE'S ARC OF THE MERIDIAN. §3. Cape Point Statiou-feon. tinued). Owen's pile 690 feet. The meridian of the Royal Observatory passes close to this locality, and the Observatory might be seen from it if the trees on the eastward slant of Wynberg hill were not in the way. The angle point is marked by a brass pin inserted in a plug of lead, let into a hole drilled in a rock, and was left covered by a pile of stones, 12 feet in diameter at the base, 2 feet in diameter at the top, and 12 feet high, — built with great care in the form of a truncated cone, in order that the axis of the cone should be a normal to the station point, — the plan, indeed, pursued with the piles generally throughout the survey. The several operations performed at this station were carried on at convenient times with reference to each other, and to the signal parties on the neighbouring stations. It was first visited on the 28th, 29th, and 30th of November, 1842, with the Fuller theodolite; next with the Zenith sector and the Beaufort theodolite, in December and January 1844 — 45 ; again for a few days in each month of March, May, and June, 1845, with the Beaufort theodolite and levelling apparatus. The Fuller theodolite was centered over the angle point. NAMES OF STATIONS AND SIGNALS. King's Battery, pile and Simon's Berg, heliostat. „ „ „ and Hanglip, pile „ „ „ and Hanglip, knob King's Block House, niche and King's Battery The Beaufort theodolite was centered over Table Mountain, pile. . . King's Battery, heliostat Blaauw Berg, heliostat . Tyger Berg, heliostat . . Sneeuw Kop, heliostat . and Sneeuw Kop, heliostat. and and and and Kogel Berg, pile J) „ „ and Mudge Point, heliostat ,) „ „ and Danger Point, heliostat Subtense of 28 feet at Owen's pile The above angles were measured by Mr. Maclear. Observed Horizontal Angles. O I It 40- 8- 5-82 97-33-40-73 97-19-42'13 0- 4 •43-82 the angle point. 60-26-14-98 57- 8- 0-04 53-33- 9-38 43- 9-38-88 17-28-57-46 42-22-27-79 55-39-34-47 2-19-43-08 No. of Measures. No. of Partial Means. 90 74 6 24 44 120 116 100 50 60 190 3 45 37 3 12 Weights. 179-7 49'42 100-52 79-49 15-89 3-96 65-24 Zwart Kop Station. 9. ZwART Kop Station. Zwart Kop is one of the sand-stone elevations of the range which forms the west side boundary of False Bay, and the third reckoning from Simon's Town. It is separated by Klaver Valei from signal-hill on the north, and by another ravine from Miller's Point on the south side. OBSERVED HORIZONTAL ANGLES. 435 This elevation was selected for a sector station, in preference to Miller's Point, because § 3- „ \ _ ^ Zwart Kop it seems to be nearly in the center of gravity (meridian-wise) of the ridge. station-Ccoc. The theodolite station is on the most elevated part, which consists of a narrow ledge of sand-stone blocks, topping a precipice towards False Bay. The Cape Point station is masked by Miller's Point, — a matter of little consequence, owing to its contiguity. As the ledge of rocks did not afford one-fifth part of the breadth needed for the tripod of the sector-tent, besides the danger of being on the brink of a precipice ; a spot was selected for the sector, nearly 92 feet less elevated, 404 feet to the west, and 169"86 feet to the south of the theodolite point, determined by a triangle, one side of which (303 '396 feet) was carefully measured There is no commodious or fitting spot on the parallel of the theodolite station, — and though the selected site is partially sheltered on the east and west sides by ridges of rock, and during the sector observations there was a high ring fence of bush round the tent, yet the instrument narrowly escaped destruction during a gale. As at Cape Point, this station was occupied several times ; first with the Fuller theo- dolite, afterwards with the Beaufort theodolite, zenith sector, and levelling apparatus. The Fuller theodolite centered over the angular ■point. — November, 1842. Observed -^ . No. of NAMES OF STATIONS AND SIGNALS. Horizontal ,, ■ Partial Angles. Measures. ^^^^^ BETWEEN O , „ King's Battery, pile and Blaauw Berg, heliostat. 2-57- 7-44 46 23 „ „ heliostat. .. and Royal Observatory, hel. 4-20-29-91 86 43 pile and Simon's Berg, pile. ... 47- 0-29-13 110 55 and Hanglip, white spot. .. 115-15-4509 12 6 and North hump of Hanglip 115- 7-18-52 8 4 A hole plugged with lead, in the vertical face of ' a rock, the southern- <(and King's Battery ^111 •58- 072 12 6 most of a mass near the sector-station. Tand A hole plugged with lead "^ The same hole \ ™ *^" "P?''' T'f^^K 26'18-41-67 16 8 \ oi a large rock to the i ' north of the latter . . j > The Beaufort theodolite was centered over the angular point. — June, 1845. Weights. Table Mountain, pile and Kogel Berg, pile 96-31 • 2-90 20 andSneeuwKop,H.H.,hel. 79-15-11-06 60 19-73 King's Battery, pile and Winter Hoek, heliostat. 28-14-13-23 1 1 „ „ heliostat. . . and Blaauw Berg, hehostat. 2-57* 9*00 3 andSneeuwKop,H.H.,hel. 67-32-22-05 150 15-23 L 1) jj )) 436 VERIFICATION AND EXTENSION OF LA CAILLE'S ARC OP THE MERIDIAN. IwartKo King's Block House, niche and Royal Observatory, hel. 4-27- 9-63 6 station-fcon- „ „ „ and King's Battery, heliostat 0- 6-40-92 30 3-26 tinned ) CD t/ ' Royal Observatory, heliost. and Kogel Berg, pile 87-27-44-55 50 24*09 „ and Sneeuw Kop, H.H., hel. 63-11-52-28 100 43-91 Blaauw Berg, heliostat ... and „ „ „ „ 64-35-14-33 90 80-68 Sneeuw Kop, pile and Kogel Berg, pile 24- 15-53-49 20 Sector Station(by the north) and Sneeuw Kop 179-33-14-90 4 Sector Station and King's Block House, niche 111-54-11-70 3 The small triangle, for the purpose of ascertaining the relative positions of the sector and theodolite stations. AT SECTOR STATION : Theodolite Station and South end of Base, pole 88-33-49-60 5 AT SOUTH END OF BASE : Sector Station. . . and Theodolite Station 56-17-25-05 5 AT THEODOLITE STATION : South end of Base, pole. . and Sector Station 35- 8-43-35 5 The angles at this station were measured by Mr. Maclear. 10. Naval Yard, Simon's Town. Naval Yard, As sextant observations for rating chronometers are usually made at the west end of the Naval Yard, a block of granite was bedded in masonry, in the hollow opposite to the residence of the Naval Storekeeper, in December, 1 842, — the upper surface nearly even with the ground. The horizontal distance between its center and the clock-tower is 156 feet, and reckoning from the south round by the west, the azimuth of the tower at thestoneis338°-2'-ll". Two angles were measured at this stone with the Fuller theodolite, for the purpose of fixing its position ; but one of the points was given up afterwards in favour of another more elevated. They were as follows : No. of ' Measures. Partial Means. ^ZTenBe?""^""!^"'^ ^^'^" ^"^' '''"^''*- 1 45-31-13-38 52 26 Between the same chimney and Sneeuw Kop, heliostat.. 48-45-40-32 46 23 11. RoGGE Bay Guard House Station, Cape Town. fiogge Bay The Station is on the flat roof, which, like the general roofing in Cape Town, is of station, Cape brick, covered with a thick coat of lime. For the present purpose additional firmness was given to it by posts resting upon the floor underneath. When closing the opening made in it in the year 1838, a copper tube was inserted, to allow of a plummet being suspended over the granite block left to mark the position of Bradley's sector : there- fore, the theodolite could be centered exactly over the position of the spindle. OBSERVED HORIZONTAL ANGLES. 437 The angles were measured with the Fuller theodoHte in October, 1841, and August, § 3. 1842, — an observer being stationed at each microscope. Since then the building has Guard House been taken down ; but the stone sunk in the ground remains, covered at present with a tinned). mound of earth. NAMES OF STATIONS AND SIGNALS. BETWEEN Observed Horizontal Angles. No. of Measures. No. of Partial Means. 16-54-38-53 152 74 33-33-34-96 108 54 67-37-54-63 68 32 16-38-56-83 88 44 91-46-5277 44 21 0-29-52-26 3 0- 1- 0-88 23 35-31-3876 60 29 Station. Kapoc Berg Signal-rock, h. and Blaauw Berg, pillar . . . „ „ „ „ and Riebeek's Kasteel, hel. Blaauw Berg, pillar and Simon's Berg, heliostat „ „ „ and Riebeek's Kasteel, hel. „ „ „ and Royal Obs., lantern-ball „ „ „ and Dassen Berg Rock, ? La Caille's Kapoc Berg Signal-rock, h. and Cylindrical Rock, ex- centric, heliostat. . . Royal Observ., lantern-ball and King's Battery, pole . . The above angles were measured by Mr. Maclear. 12. La Caille's Observatory Station. The position on the roof of the store, over the site of the east corner of La Caille's l^ CaiUe's Observatory, was found by stretching a rope from the corner of the street, and describing observatory an arc with the radius 118"8 feet (111^ French. Mem. de 1' Academic, 1751, page 429) ; then shifting a small theodolite, armed with a magnetic needle for zero along the arc, until the corner bore 43°-30' from the south (73°— 29°-30). Here the Beaufort theo- dolite was centered, but on the Kapoc Berg and Riebeek's Kasteel heliostat lights appearing, a blacksmith's chimney and a vessel at anchor in the bay were in line with Riebeek's Kasteel ; it became necessary, therefore, to shift the theodolite to a position 124 feet from the corner of the street (a). At this position the observations were carried on during the short intervals between the volumes of smoke from the chimneys, and the thundering of the forge hammers, — the smith refusing to enter into any treaty for indul- gence ; and when the principal angles were measured, the exact position of the theodohte, with reference to the corner of the street and the point where it ought to have been placed, were ascertained by triangulating over the roofs of the buildings ; also the data were obtained for reducing the angles observed at the former to the latter. At the first station : o i « Reading for the Tyger Berg, pile 0' 0' 3 „ True Point 38-28- (a) The north-west wall of the store is contiguous to a blacksmith's forge, along which there are four foige chimneys and two others. 438 VERIFICATION AND EXTENSION OF LA CAILLE'S ARC OF THE MERIDIAN. 5«. Ia Caille's Cape Town Obserratory Station-Ccon- Umud). At the true point, 118"8 feet from the corner of the street : Reading for the Tyger Berg, pile 0* 0' 3 „ Corner of the Street 43' 3-58 „ „ Rogge Bay Guard House Station 2-32-30 The plan of the buildings, plate I, is sufficient for general information, and supercedes any necessity for recording in print a number of measurements which were made on the present occasion. Calculation of the reduction from the first theodolite position, to the position 11 8*8 feet from the corner of the street. r = 5" 192 feet. log. r" = log. sine 1" = 6-02976. ■y, the angle of direction is reckoned from the true point towards the right, in the order of increasing readings of the instrument. Sneeuw Kop Kapoc Berg Blaauw Berg Riebeek's Kasteel . Tyger Berg Simon's Berg Royal Observatory King's Battery . . . 1-31 255-10 272- 8 •288-43 3-21-32 339-40 3-35 38-51 Log. r" sine y. 4-45248 6-01504 6-02946 6-00616 5-8-2359 5-57069 4-82-564 5-8-27-22 Log distance. 5-24368 5-26291 4-81828 5-38593 4-74787 5-17154 4-2.3462 4-13241 Log reduction. 9-20880 0-75213 1-21118 0-6-2023 1-07572 0-39915 0-59102 1-69481 Reduction. + 16 - 5-65 -16-26 - 4-17 -11-91 - 2-51 + 3-90 + 49-52 NAMES OF STATIONS AND SIGNALS. Angles observed at r 24 feet from the corner of the street. Reduction. Angles observed at. or reduced to, 118-8feetfromthe comer of thestreet. No. of Observa- tions. Weights. BE Blaauw Berg, pillar rWEEN . and Riebeek's Kasteel, heliost. andTyger Berg, pile and Dassen Berg, rock ? . and Royal Obser., lantern-ball and „ ., „ ,; and King's Battery, pile . and Blaauw Berg, pillar andSneeuw Kop, pile 16-34-54-19 0-27-11-75 42- 2-39-60 16-57-36-78 106-21-26-63 33-32-30-39 50-57-14-88 35-17-12-78 0- 6-44- 72-16- 3-60 27-55-43-63 49-24-31-50 + 12-09 + 15-81 -10-61 + 5-81 + 1-48 + 1-K6 + 45-02 o / * 16-35- 6-28 49-24- 4-52 42- 2-55-41 42- 2-55-03 77-20-42-63 16-57-26-17 106-21-32-44 33-32-31-87 50-57-16-54 35-17-5b-40 35-17-50-30 60 60 10 10 40 20 60 52 HO 20 20 20 J 10 4 4 15-17 10-30 1-00 5-30 27-84 16-69 ?) » n )J »» V Tyger Berg, pile Kapoc Berg, heliostat )i » »> It !) >' Riebeek's Kasteel, heliostat Koyal Observat., lantern-bal „ )» J) !) Dassen Berg, rock Lion's Rump, signal-staff:.. and Riebeek's Kasteel, heliost. andSimon's Berg, pile land King's Battery, pole and „ „ „ and Summit of Dassen Berg. . . .and Kapoc Berg, heliostat and Station House, chimney... and King's Battery, pole Station House, chimney The angles were measured between the 9th and 28th of January, 1846, by Mr. Maclear. OBSERVED HORIZONTAL ANGLES. 439 13. Cape Town Parade, Base-line. With the view of estabhshing a permanent length, in a convenient position, for testing § s. surveyors chains and other local purposes, two guns (24-pounders) were sunk in the Parade, parade ground, and built in with masonry, in November, 1837, — ^their muzzles even with the surface, and surrounded by a circle of nearly flat brick work. The position of the west gun is between the north end of the Commercial Exchange building and the Custom House ; that of the east gun is near the small entrance gate next to the Castle, and the line between them runs parallel to the north enclosing wall, a few yards south of the avenue of trees on that side. The muzzle of each gun is plugged with lead, in the centre of which a brass pin is driven home to define the terminal point. The line was measured on the 2nd of December, 1837, with trussed deal rods, each 20 feet long, resting on trestles, and found to be 1049*209 feet in the mean temperature 89°'9, during measurement, or reduced to the temperature 70°, — 1049*279 feet, from which "018 foot should be subtracted owing to a slight inclination of the ground. On the 23rd of August, 1842, the Fuller theodolite was employed at the terminal points, to measure the horizontal angles between the line and a conspicuous tooth-shaped rock on the top of Table Mountain ; and two days after, Dollond's repeating instrument was employed to measure the zenith distance of the rock, both as follows : — at the east terminal point : Horizontal angle between the rock on Table Mountain and west termmal pomt 120-51-9-73, 48 measures or 24 partial means. Zenith distance of the rock 7°6-10-54-4, 40 repetitions. at the west terminal point : Horizontal angle between the east terminal point and the rock on Table Mountain, 55-4'0- 13-57, 52 measures or 26 partial means. Zenith distance of the rock 76-4'2-4'2-16, 40 repetitions. The zenith distances are corrected for the height of the trestle (3 feet 1 1 inches) above the muzzles of the guns. 14. Royal Observatory. The top of the lantern is the only part of the roof that commands the sweep of the Royal horizon, but it is totally unfitted for supporting a theodolite. The selected trigonometric Observatory. or angle point, is the centre of the strong iron bolt which passes through the zenith shutter, over the 10-feet transit instrument, with a ring at its lower end to receive the 440 VERIFICATION AND EXTENSION OF LA CAILLE'S ARC OF THE MERIDIAN. 1^3. ^^ hook of the pulleys for raising the instrument from its bearings. The upper end of the Obserratory bolt appears outside, and its centre may be regarded, in practice, as coinciding with the zenith of the instrument. To keep the shutter in firm contact with the cheek pieces of the meridian opening, it was loaded with several pigs of lead, and planks were placed, stage fashion, to isolate three observers (one for each microscope), to avoid any disturbance which might be occasioned by moving round the instrument. The several obstructions in the direction of distant stations are a dome on each wing of the building, the lantern, and the elevation of the east and west wings above the roof of the transit room. These necessitated the occupation of excentric stations. August, 1842. — The Fuller theodolite centered over a point on the shutter, 5 J inches due north of the angle bolt. r = 5A inches, log. — ^, = 4-97530 = log. r". ^ ^ sme 1" ^ (^) y, the angle of direction, measured from the angle point round by the right. STATIONS. r Log. r'. sine, y Log Distance. Log Beduction. Reduction. Kapoc Berg ..., Blaauw Berg, pillar Riebeek's Kasteel O 1 II 172-35-50 180- 0- 207- 6-56 4-08535 4-63381 5-27715 5-37893 8-80820 9-25488 // +0-064 -0-180 (^) The Beaufort theodolite placed on the adjacent west parapet. — June, 1845. r = 12-74 feet. log. r" = 6-41960. Sneeuw Kop . Zwart Kop . . . Kapoc Berg . Blaauw Berg. 14-37-53 5-82203 5-19913 0-62290 94-31-43 6-41824 5-02695 1-39129 263-35-10 6-41687 5-27715 1-13972 270-59-43 6-41953 4-83516 1-68437 + 4-197 + 24-620 -13-795 -38-404 (^) On the shutter due south of station bolt. — June, 1845. r = 1-467 feet. log. r" = 5-48086. Sneeuw Kop . 103 -38 -50 6-46843 6-19913 0-26930 + 1-859 OBSERVED HORIZONTAL ANGLES. 441 (*) On west wing sky-light frame. — September, 1846. r = 17-717 feet. log. r" = 6-5628153. Sneeuw Kop . Kogel Berg. . Zwart Kop . . . BlaauwBers. 16-34- 8 44- 9- 6 96-27-48 272-56- 4 6 01792 5-19913 6-40577 5-21646 6-56005 5-02695 6-56226 4-83516 0-81879 1-18931 1-53310 1-72709 Eoyal Observatory — (continued) + 6-589 + 15-464 + 34-127 -53-345 (^) On the north-east chimney of west wing. — July, 1857. r = 42-627 feet. log. r" = 6-9441075. Zwart Kop . . . Blaauw Berg . Tyger Berg . . Simon's Berg . 23-14-48 199-43- 1 246-47-17 278-44-38 6-5403641 6-4722187 6-9136391 6-9390305 5-0269456 4 8351480 4-6507367 5-1241745 1-5134185 1-6370707 2-2629024 1-8148560 + 32-615 - 43-358 -183-190 - 65-291 The reduction for the left hand station, algebraically subtracted from the reduction for the right hand station, gives the reduction to the center, — viz. : to the bolt angle point in the zenith of the transit instrument. NAMES OF STATIONS AND SIGNALS. m Observed Angles at excentric station. Reduction to angle point. Horizontal Angles at angle point. ■3-1 o > o ^.2 (')Kapoc Berg, heliostat.. T» *t 5) Blaauw Berg, pillar Kapoc Berg, heliostat.. OKapoo Berg, heliostat.. »» )' )j „ „ cylind. roG Blaauw Berg, pillar Sneeuw Kop, heliostat. (') Blaauw Berg, pillar..... (') Sneeuw Kop. pile... . and Blaauw Berg, pillar and Eiebeek's Kasteel, heliost. ■ and „ „ „ . and Cylindrical Eock, exc. lieL . and Blaauw Berg, pillar F F B B B B B B B B B B B B o / n 7-24-10-313 34-30- 7-043 27- 5-56-350 0- 0-48-378 7-24-33-494 111- 2-43-542 0- 0-34-120 103-38- 9054 79-53-49-570 103-38'49-650 27-34-59-275 176-28-16-000 52-18-42-180 49- 4-16-580 79- 1-37-470 104-30- 9-480 n - 0-064 - 0-244 - 0-180 - 24-609 + 17-992 + 42-601 + 20-423 + 1-860 + 8-875 - 87-470 + 18-660 -139-830 - 21-930 + 97-910 o / f 7-24-10-25 34-30- 6-80 27- 5-56-17 7-24- 8-88 111- 3- 1-53 103-38-51-65 79-54- 9-99 103-38-51-51 27-35- 8-15 176-26-48-53 52-19- 0-84 49- 1-56-75 79- 1-15-54 104-31-47-39 153 183 105 16 40 120 212 70 110 10 40 10 41 40 70 149 59-00 90-00 51-00 9-34 12-64 35-94 19-21 •23-81 and Sneeuw Kop, heliostat k. and Signal Eock, heliostat . and Sneeuw Kop, heliostat . and Zwart Kop, heliostat . and Sneeuw Kop, heliostat Kogel Berg, pile C) Blaauw Berg, pillar.... Simon's Berg, pUe . and Zwart Kop, pile 9-33 13-44 and Simon's Berer. nile 10-20 . and Zwart Kop, heliostat 19-90 By observation with the 10-feet transit instrument, the azimuth of the Blaauw Berg pillar's center is 1 79°-59'-57", and from the triangulation its distance appears to be 68415 feet. 15. King's Battery Station. The theodolite was centered over this angle point in the year 1837, when connecting King'sBattery Sir John Herschel's position at Field Haussen, with the Royal Observatory, and with La Caille's Observatory in Cape Town, (part I, page 121). It is near the center of the 442 VERIFICATION AND EXTENSION OF LA CAILLE'S ARC OF THE MERIDIAN. Ifn 'sBatter P^^^^o™ ^^ t^e battery, on the east face of Devil's Berg, at an elevation of about 1415 feet station-fcon- above the level of the sea. tmued). The instrument was centered over the angle point. FULLER THEODOMTB. — SEPTEMBER, OCTOBER, NOVEMBER, 1842. Observed No. of p.^jai NAMES OF STATIONS AND SIGNALS. AnD-1ps Mpasiires J-liH-ll No. of , ,, Partial Angles. Measures. ^^^^^_ BETWEEN Blaauw Berg, pillar , and Riebeek's Kasteel, hel. 21-59 37-41 77 36 and Simon's Berg, pile. fa; ^7Ml-32-36 112 56 andZwart Kop,heliostat.. 173- 4-48-28 104 51 Kapoc Berg, heliostat.... and Riebeek's Kasteel, hel. 32-58-17-03 172 60 and Blaauw Berg, pillar... 10-58-40-20 248 122 Signal Rock, heliostat . . . . and Kapoc Bg.,cyl.rk.exc.h. 0- 0-50-55 8 Lion's Rump, signal-staff. . and Royal Obs., lantern-ball 103-38- 9-86 8 4 Rogge Bay Guard House, and „ „ „ 92-10-6-05 62 31 RoyalObserv., lantern-ball and Sir J. Herschel's, obelisk 112-39-47-87 10 5 Robben Isld., church-tower and Royal Obs., lantern-ball 77-13- 4-13 16 Simon's Berg, pile and Cape Point, hehostat. . -98-11-10-17 76 38 „ „ „ and Cape Hanglip, culm.pt. 65-41-38-27 16 8 BEAUFORT THEODOLITE. — JULY, 1845. Weights. Kapoc Berg, heliostat . . . . and Sneeuw Kop, heliostat. 105-51-55-78 113 29-48 Sneeuw Kop, heliostat . . . and Cape Point, pile 74-29-25-54 120 78-63 and Zwart Kop, pile 78-11-29-71 220 22 00 Blaauw Berg, pillar and Sneeuw Kop, heliostat. 94*53-17-00 50 259-10 „ „ and Simon's Berg, pile. .. . .71-11-29-45 30 0-42 and Tyger Berg, pile 43-45-41-45 20 2-00 Sneeuw Kop, heliostat. .. . and Sir J. Herschel's, obelisk 65-30-44-98 10 and Kogel Berg, pile 26-54-14-28 10 24-52 Tyger Berg, pile and Sneeuw Kop, pile 51- 7-35-93 20 2-00 „ and Muizen Berg, pile 127-30-33-58 10 0-50 Simon's Berg, pile and Cape Point, pile =98-11-13-20 10 0-50 and Zwart Kop, pile 101-53-16-49 40 12-95 and Muizen Berg, pile 100-4-45-95 10 0-50 Kogel Berg, pile and Cape Point, pile 47-35- 9-63 40 9-62 and Zwart Kop, pile 51-17 12-58 40 19-36 Cape Hanglip, pile and Cape Point, pile 32-29-21-33 20 2-00 Cape Point, pile and Cape Point, sect.-station 0-1-11-30 5 and Zwart Kop, pile 342-1-53 20 2-00 Zwart Kop, pile and Blaauw Berg, pillar. . . 186-55-14-35 20 2-00 The above angles were measured by Mr. Maclear. (a) Doubtful, owing to the pile at Simon's Berg having fallen within 7 feet of the base. The loose stones were cleared away before measuring the angles with Cape Point and Hanglip. OBSERVED HORIZONTAL ANGLES. 443 16. Tyger Berg Station. The station is on the middle rise, which is the highest part of Tyger Berg. It was § s. occupied for the purpose of fixing the position of the Naval Yard, Simon's Town (which sution. ^'^^ is masked by Muizen Berg, from the Observatory and King's Battery), and partly for local purposes. The Beaufort theodolite was centered over the angle point. — September, October, 1845. Observed „ , „ NAMES OF STATIONS AND SIGNALS. Horizontal 1,/ ■■ Angles. Measiires. WeightB. BETWEEN Sneeuw Kop, pile and Cape Point, pile 70-24 •47-40 81 12-40 „ „ and Naval Yard, clock-tower 82-28-56-90 20 „ „ and Naval Yard Station, hel. 82-31-50-19 50 324-45 „ „ and Admiralty House, hel. 82-48-28-30 30 „ and Noah's Arc Rock, hel. 79-16-37-38 50 11-25 „ „ and Table Mountain, pile. . 111-10-59-83 50 19-06 „ „ and Zwart Kop, pile 77-31-19-55 90 7-36 „ „ and King's Battery, signal. 110-49-26-50 40 1870 „ „ and Royal Obs., lantern-ball 109-56-39-97 40 14-02 „ „ and Royal Observatory, hel. 109-57-57-82 50 35-95 Kogel Berg, heliostat and Cape Point, pile 42-37-31-04 41 12-07 and Zwart Kop, pile 49-44- 1-18 35 1589-50 Zwart Kop, pile and Table Mountain, pile. . 33-39-40-43 40 5-68 Naval Yard, clock-tower. . and King's Battery, heUost. 28-20-29-33 20 „ „ and Royal Obs., lantern-ball 27-27-40-73 10 Naval Yard, trig, stat, hel. and „ „ „ 27-24-47-42 6 „ „ and PinnacleofWesl. Chapel 0-11-42-48 12 Royal Observ., lantern-ball and Blaauw Berg, pillar. . . 90- 8-37-11 50 3-21 Royal Observatory, heliost. and „ „ „ 90- 7-22-58 50 20-34 King's Battery, heliostat. . and Lion's Rump, signal-st. 17-47-41-15 20 „ „ „ and Robben Is., church-tower 53-49-18-88 20 and Blaauw Berg, pillar... 89-15-49-73 30 23-76 Table Mountain, pile and Robben Is.,church-tower 53-27-49-09 40 14-09 Robben Isld., church-tower and Blaauw Berg, pillar. . . 35-26-30-40 30 202-91 Blaauw Berg, pillar and Sneeuw Kop, pile 159-54-42-91 30 3-02 Chimney on west side of Eerste River Bridge. . and Centre archway of Bridge 0- 2'33-44 4 „ „ and King's Battery, heliostat 86-39-21-33 20 „ „ and Zwart Kop, pile 53-21-13*45 20 „ „ „ and Col. Michel's house on Montagu Road 87-32-20-46 30 9-07 Simon's Berg, pile and Stellenbosch (an helios- tat, placed on eleva- tion above the town : town invisible 18-46-34-75 10 Stellenbosch, heliostat. . . . and King's Battery, heliostat 118-45-38-50 1 Measured by Mr. Maclear. M 444 VERIFICATION AND EXTENSION OP LA CAILLE'S ARC OF THE MERIDIAN. §3. Blaauw Berg Station. 17. Blaauw Berg, Azimuth Pillar Station. The position of the pillar is on the undulation, immediately to the east of the mountain named Blaauw Berg, distant nearly 13 miles north from the Royal Observatory. The pillar was built to serve as a permanent meridian mark for the 10-feet transit instru- ment ; also for ascertaining the azimuths, by direct angular measurement of the trigono- metric points, that are visible from the Observatory. When observed from elevated distant stations, an heliostat was placed in line close to the pillar ; and when angles were measured at the pillar, the theodolite was placed near to its south front, and require a reduction to the center. Beaufort theodolite. — March, April, 1848. r = 20-35 feet. log. r" = 6-62310. y, or angle of direction, measured from the pillar towards the right. STATIOJfS. r Log. i" sine y. Log distance. Log reduction. Reduction. Riebeek's Kasteel Sneeuw Kop Tyger Berg Kogel Berg / // 35-50-08 123-20-59 137-58-08 143-50-51 177-55-12 178-49-52 181-16-38 184-57-46 189-53-49 193-18-22 198-36-49 347-17-30 6-39060 6-54496 6-44887 6-39390 5-18294 4-93272 4-97121 5-56016 5-85831 5-98508 6-12714 5-96550 5-26150 5-27082 4-71313 5-33431 5-34327 4-83516 4-87322 4-91245 4-81828 4-81954 5-09202 1-12910 1-27414 1-73574 1-05959 9-83967 0-09756 0-68694 0-94586 1-16680 1-30760 0-87348 + 13-46 + 18-80 +54-42 + 11-47 + 0-69 + 1-25 - 4-86 - 8-83 -14-68 -20-30 - 7-47 Royal Observatory Muizen Berg King's Battery Table Mountain, pile La Caille's Observatory Lion's Rump, signal-staff . . Kapoc Berg, cylindrical rock NAMES OF STATIONS AOT) SIGNALS. Horizontal Angles observed at excentric Station. Reduction to pillar. Horizontal Angles reduced to pillars center. No. of Observa- tions. WEIQBTS. ] Sneeuw Kop, pile )) ») J) )i " )» *Tyger Berg, pile Cape Point, pEe Royal Observatory, helio " » ». jj » ,i »» >5 »> La Caille's Observatory.. JETWEEN .... and Royal Observatory / // 55-28-52-60 20-29-51-65 54-34-11 -18 61 ■36-47-72 40-51-44-13 0-54-40-32 168-27-38-10 2-26-45'76 11- 3-57-14 14-28-30-73 6- 7-64-39 43-56-52-05 5-18-57-08 - 17-55 - 7-33 - 18-11 - 23-66 - 53-17 + 0-56 - 8-72 - 10-08 -15-93 - 6-11 - 5-62 O / ff 55-28-35-05 20-29-44-32 54-33-53-07 61-36-24-06 40-50-50-96 0-54-40-86 168-27-29'38 11- 3-47-06 14-28-14-80 6- 7-48-28 5-18-21-46 110 10 60 10 10 80 10 30 100 100 60 50 20 21-74 35-07 59-48 2-97 6-19 30-85 14-74 6-75 and Cape Point, heliostat and King's Battery, pole .... and Royal Observatory, helios. and „ „ „ Stat and Kapoc Berg, cyKndrl. rock and Muizen Berg, pile and Table Mountain, pile and La Caille's Observatory... and King's Battery and Signal-pole on the top of and Lions' Rump, signal-staff. The above angles were measured by Mr. Montagu. * This angle was re-measured by Mr. Maclear in August 1857. OBSERVED HORIZONTAL ANGLES. r = 5-354 feet. log. r" = 6-04310. 445 STATIONS. y Log. r". sine, y Log Distance. Log Reduction. Reduction. Sneeuw Kop Tva-er Bere: O I II 116-51- 131-29- 172-19-56 174-29-20 178-27-24 5-99356 5-91768 5-16835 5-02554 4-47338 5-27082 4-71315 4-83514 5-24238 4-87322 0-72274 1-20452 0-33321 9-78316 9-60016 // + 5-28 + 16-01 + 2-15 + 0-61 + 0-40 Royal Observatory Zwart Kop King's Battery §3. BlaauwBerg Station-Ccon- timted). The reduction for the left hand station, subtracted from the reduction for the right hand station, gives the reduction to the pillar. NAMES OF STATIONS AND SIGNALS. Observed Hori- zontal Angles. Reduction to pillar. Angles reduced to pillar. No. of Observa- tions. Weights. BETWEEN Sneeuw Kon. mle and Zwart Kod heliostat f II 57-38-20-20 40-50-55-86 II - 4-67 — 13-86 O / i/ 57-3B-15-53 40-50-42-00 70 80 15-36 6-91 Tyger Berg, pile and Royal Observat, heliostat. The above angles were measured by Mr. Maclear. 18. Simon's Berg Station. The circumstances of this station are not what were intended. When the Fuller theo- Simon's Berg dolite was on Riebeek's Kasteel, a signalman was sent with an heliostat to the singular shaped knob on the west or lowest end of Simon's Berg ; but on reaching the place he fancied that the theodolite tent could not be secured on the knob, he therefore chose a spot on the saddle between it and the next peak, within command of Riebeek's Kasteel, — but, unfortunately, not of Kapoc Berg. Hence, for observing Kapoc Berg, it became neces- sary to either adopt an excentric point or to re- visit Riebeek's Kasteel. He was mistaken in the belief that the theodolite could not be securely placed on the knob. As the Observatory lantern interposed between the angular point, over the transit instrument and Simon's Berg, the Observatory heliostat was placed 10-242 feet to the north of the point; therefore, the correction 15" '63 has been subtracted from the theo- dolite readings for the heliostat, to reduce them to the angular point. For the reduction to the center, where stations were compared with Kapoc Berg, r = 15-708 feet. log. sine V ^ 6-51052 446 VEKIFICATION AND EXTENSION OP LA CAILLE'S AKC OF THE MERIDIAN. §3. Simon's Berg Station-Cco«- tinued). STATIONS. r Log. r^. sine, y Log. distance. Log. reduction. Beduction. Table Mountain o / // 202-48-22 204 -22 -29 206- 4-50 263-22-40 300-28-28 6-09892 6-12616 6-15361 6-50761 6-44695 5-17897 5-15259 5-12417 5-36124 5-27628 0-91995 0-97357 1-02944 1-15637 1-16967 - 8-32 - 9-41 -10-70 -14-33 -14-78 King's Battery Royal Observatory KapoeBerg Riebeek's Kasteel The reduction for the left hand station, subtracted from the reduction for the right hand station, gives the reduction to the angle point. BEAUFORT THEODOLITE. NOVEMBER, 1845. NAMES or STATIONS AND SIGNALS. Observed Hori- zontal Angles at excentric station. Reduction. Horizontal Angles observed at, or reduced to, trigo- nometric point. No. of Observa- tions. Weights. BETWEEN Cape Point, heliostat and Table Mountain, pile .. .. „ and King's Battery, heliostat. Zwart Kon, dUc and o / n 59- 0-12-03 57-18- 7-30 60-34-18-49 37- 5-46-74 a - 4-92 - 3-63 - 6-02 - 0-45 o 1 a 40- 6-46-83 41-40-49-30 31- 6-19-69 32-48-19-52 29-32-17-13 1-41-59-41 59- 0- 7-11 94-23-48-77 3- 0- 0-48 3-51-27-68 13-20- 9-66 57-18- 3-67 16-36-12-41 60-34-12-47 91-23-46-35 81- 3-41-89 37- 5-46-29 222-13-22-31 28-19-16-52 34-33-15-40 19-31- 2-68 50 80 50 100 50 40 80 50 80 10 20 153 18 80 40 20 90 60 10 10 20 4-81 103-88 360-35 80-29 17-15 74-53 7-05 18-50 . 12-73 8-38 9-71 8-21 7-55 2-71 >. H » and Eoyal Observatory, hel.... » .) » and Table Mountain, pile King's Battery, heliostat and Royal Observatory, heL... " i> „ and Kapoc Berg, heliostat Royal Observatory, heliostat and Riebeek's Kasteel, pUe.... .. .. „ and Rogge Bay, Guard-hs.,hel. " >i „ and Lion's Rump, signal-staff. 11 n „ and Tyger Berg, pUe » >. „ and Kapoc Berg, heliostat Table Mountain, pile and Tyger Berg, pile and Kapoc Berg, heliostat RoggeBay,Guard-house,hel. and Riebeek's Kasteel, pUe.... Tyger Berg, pile and Kapoc Berg, heliostat and „ „ „ Riebeek's Kasteel, pile and Cape Point, heliostat.' Naval Yard Clock and Royal Observatory, helios. Muizen Berg, heliostat and Tyger Berg, pile... . >. J. » and King's Battery, heliostat. The above angles were measured by Mr. Maclear. Kapoc Berg Station. 19. Kapoc Berg Station. The circumstances of this important station require to be particularly described. Of the two rocks mentioned by La Caille in his journal, page 173, the larger was supposed to be the one to which he referred his angles, and the mistake was not dis- covered until after the terminal points of the Base had been connected with it ; nothing, however, has been lost by the occurrence. The mistaken rock is a huge oblong mass of granite, of considerable elevation on the north-east side, separated into two unequal parts H^ — "- OBSERVED HORIZONTAL ANGLES. 447 by a rent, the smaller part towards the north. " La place de ce signal est une grosse § s- " roche appuyee d'une plus petite vers le nord. The smaller part was supposed to be station-(eoK- the " plus petite vers le nord ;" accordingly an angle point was established at a conve- signai-rock. nient part of the surface of the larger block, in the following manner : having chiselled out a square foot to a sufficient depth, a hole was drilled in the bottom of the hollow to receive a plug of lead, with a brass pin or stud in its center, and a piece of granite was nicely fitted to fill up the hollow, — yet sufficiently fi-ee for removal when necessary. This brass pin defines the Kapoc Berg angle point of the modern triangulation, and the rock has been named the signal rock in the field-books, and throughout the discussions. Figure 1 of the plate to the left, represents the signal rock as viewed from the west, I'late to the also the small stage which was keyed to it for supporting the heliostat, and subsequently the Beaufort theodolite. Ota Bearing 78'57'14 towards the right from Riebeek's Kasteel trigonometric point, and LaCaiUe's distant 127"73 feet (from center to center), stands the rock to which La Caille reduced his angles. It is a granite block of greater height than thickness, situated on the southern brow of the hill, from whence the ground declines rapidly. The face towards the south is flat, that towards the north is somewhat rounded, and upon its top rests a portion of a small block, which may have been entire in La Caille's time. At the height of about two feet above the ground on the north side, the horizontal section is an irregular pentagon : the south face 10 feet, the east 3, the north-east 10, the north-west 5, and the west 6 feet. Figure 2 represents its appearance as viewed from the south, and figure 3 as viewed from the direction of Riebeek's Kasteel, at the distance of 40 feet ; also the " une plus petite vers le nord " of La Caille. In the field-books, La Caille's rock is termed the cylindrical rock, though the resemblance to that figure is rather remote. A theodolite, with proper protection against sun and wind, could not be placed upon the top of this rock, without incur- ring a large and unjustifiable expense. La Caille did not attempt to place his quadrant upon it; but at various distances, between 11 and 13|^ feet to the north-west, on the ground below. The engineering needed for estabhshing a large instrument on the signal rock is Signai-rock. relatively trifling ; but the south-east gales were in season during the first occupation of the station, and the danger of accident from their force — an accident that might put a stop to the survey for a time — was by no means improbable. The Fuller theodolite, therefore, occupied an excentric position on the ground, where its tent received partial shelter from the rock.; but when Kapoc Berg was visited with the Beaufort theodolite, (an instrument capable of being quickly removed on the approach of danger) it was occa- sionally centered over the angle point on the rock. 448 VERIFICATION AND EXTENSION OP LA CAILLE'S ARC OF THE MERIDIAN. §3. Kapoc Berg Station-(con- tinued). The distance between the center of the cylindric or La Caille's rock, and the angle point on the signal rock, — also the angle at the trigonometric or angle point between the line joining them, and the trigonometric point on Riebeek's Kasteel and other stations, have been determined with great care ; therefore, the angles observed at the one can be reduced to the other with facility and precision. For this reason, the only angles mea- sured close to La Caille's rock were between Riebeek's Kasteel and his Observatory, and between Riebeek's Kasteel and Rogge Bay Station, — and for no other purpose than to prove that the elements for reduction are correct. Reduction of Angles observed at the Kapoc Berg Signal Rock, excentric Station, to the Angle Point on that Rock. r = 31-269 feet. log. . ^ „ = log. /' = 6- ^ sme I" ^ 809539L (y) the angle of direction, measured from the angle point towards the right. STATIONS. 7 Log. r". sine y. Log. distance. Log. reduction. Reduction. O t II 27-35-19 36-44-32 56-52-53 69-17-59 69-20-15 73- 49 -40 75-40-25 90-30-54 96-54-24 127-40-20 143-11- 6 200-15-44 205-34-49 236-32-24 239- 6-44 241-25-35 241-26-44 241-27-27 246- 8-29 6-4752325 6-6863970 6-7325453 6-7806561 6-7806642 6-7920043 6-7958189 6-8095216 6-8063761 6 '7080009 6-5871360 6 3490131 6-4447969 6-7308470 6-7430391 6-7531227 6-7532133 6-753-2625 6-7707448 4-9584945 5-3731858 4-7369159 5-4206552 5-4203170 5-4266080 5-4171664 4- 8794881 6-19866-26 6 4074004 6-1328128 5-3612429 6-4578565 6-2771466 6-2883707 5-2628136 5-3004387 5-2631265 6 1560447 1-5167380 1-2132112 1 9956294 1-3599009 1-3603466 1-3653963 1-3786525 1-9300335 1-6078136 1-3006006 1-4543222 0-9977702 0-9869401 1-4537004 1-4646084 1-4903091 1-4527746 1-4901360 1-6147001 // -h 32- 865 4-16-338 -f 99 -000 + 22-903 +22-927 +23-195 + 23-914 +85-120 + 40-533 + 19-980 +28-466 - 9-949 - 9-704 -28-425 -28-488 -30-925 -28-364 -30-913 -41-181 West end of Base Klip Fontein, granary „ „ sector station. Piket Berg Kapitein's Kloof East end of Base Zwart Berg Winter Hoek Riebeek's Kasteel Simon's Berg Sneel^^Y Kop, H.H Royal Observatory King's Block -house Battery. Rogge Bay, Guard-house. . . Table Mountain, pile. .... La Caille's Observatory. . . . Robben Island, church-tower The reduction for the left hand station, algebraically subtracted from the reduction for the right hand station, gives the reduction to the center. Thus the reduction to the center for the angle Riebeek's Kasteel — Royal Observatory = + 28-'''466 - 28"-425 = -56"-891. OBSERVED HORIZONTAL ANGLES. 449 Horizontal Angles observed at Kapoc Berg Signal Station. NAMES OF SIGNALS AND STATIONS. BETWEEN Groote Berg, heliostat... and East end of Base, hel.... West end of Base, pole, and „ „ „ „ East end of Base, heliost. and Riebeek's Kasteel, hel... Patrys Berg, heliostat... and Zwart Berg, heliostat.... „ ,, „ and Piket Berg, heliostat „ „ „ and Kapitein's Kloof, hel KlipEontein, sect.st.,hel. and Granary Station, hel — „ „ ,, hel. and Riebeek's Kasteel, hel... „ „ grany.st.,h. and „ „ „ Piket Berg, heliostat.... and „ „ „ Kapitein's ICloof and „ „ ,, „ „ and Winter Berg, heliostat... Zwart Berg, heliostat.... and Riebeek's Kasteel, hel... „ „ pile and „ „ pile.. ,) »> H and „ „ ,, (Mean) Winter Berg, heliostat.. and Riebeek's Kasteel, pile... " » ») 3.na „ „ „ (Mean) Winter Berg, heliostat.. and Sneeuw Kop, heliostat... „ ana „ „ „ „ and „ ,, „ ,, anu „ „ „ „ and „ ,, „ „ and „ „ „ Riebeek's Kasteel, hel.. pile.. Simon's Berg, heliostat )» ?» )j Sneeuw Kop, pile Dassen Berg, rock Tyger Berg, pile Royal Observatory, hel. Mouille Pnt. Ught-h., hel. Table Mountain, pile King's Block-h. Bat., hel. (Mean) and Royal Observatory, hel.. andRoggeBay, heliostat and King's Block-h. Bat., hi. and Simon's Berg, heliostat.. and Table Mountain, pile and Sneeuw Kop, H.H., hel. and Dassen Berg, rock and La Caille's Observ., hel. and Royal Observatory, hel. and King's Block-h. Bat.,hel. and Royal Observatory, hel. and Blaauw Berg, pillar and „ „ „ and Table Mountain, pile and Mouille Pnt. light-h., hel. and (Supplement) and Winter Berg, heliostat... and „ „ and La Caille's Observ., hel,. and Robben Isld., chu. tower and Patrys Berg, heliostat... and Table Mountain, pile and Block House, niche 5^ •£2 Horizontal Angles observed at excentric position. Reduction to center. 55-34-592 37-61-002 40-12-077 ' 9-51'397 ■ 5- 9-300 55-5 1-440 ' 2-16-768 50-51-420 '53- 7-178 21-25-917 ■30-40-500 '59-56-500 16-42-065 16-42-090 15-30-46-247 77-54-27-020 41- 36' 33- 21-18-356 14-18-622 '54-38-303 ' 4-37-700 15-38-830 '23-43-380 ■11-43-240 •16-40-680 30-60-730 4-54-16-690 4 155 2' ■ 0-41-300 41-44-900 17-46-680 20-59-760 3-12-570 +52-255 13-880 56-650 + 24-195 + 6'860 + 7-580 + 0-026 + 5-539 5-563 + 5-271 + 4-550 - 3-934 -12-067 -12-067 + 8-486 —29-684 -56-891 -59-391 -56-954 -52-790 — 56-830 -38-170 — 6-660 — 4-150 -18-780 + 0-060 — 2-550 -12-840 +44-700 + 0-120 Angles observed at, or reduced to, the center. 62-56-26-847 33-37-47-122 52-39-15-427 60-10-15-592 37- 5-16-160 38-55-59-020 0- 2-16-794 73-50-56-959 73-53-12-741 69-21-31-188 67-30-45-050 51-59-52-566 46-16-29-998 46-16-30-023 46-16-30-730 (46-16-30-220) 15-30-54-733 15-30-54-770 (15-30-54-737) 77-53-57-336 77-53-58-010 77-53-56-720 77-53-56-660 77-53-57-040 77-53-57-370 (77-53-57-470 93-20-21-465 98-13-19-231 95-53-41-349 57- 3-44-910 98-14-42-000 62-23- 5-210 58-22-36-200 41-11-36-580 36-16-36-530 33-30-41-950 30-57-21-430 30-48-41-730 8-36-51-050 4-54-16-750 5-55-36-220 354- 4-24-050 251- 8-41-930 245-13- 6-410 0- 0-38-750 4-41-32-060 155-18-31-380 2-20-59-880 0- 3-12-570 o > 34 58 49 81 130 160 23 49 19 41 11 100 40 50 20 225 30 255 50 80 loo 100 100 100 530 41 43 38 100 70 100 30 60 100 110 ^0 30 10 145 190 100 160 50 100 10 20 70 Weights and Partial Means. 34-00 58-00 49-00 81-00 32-25 10-98 23-00 49-00 19-00 41-00 100-70 40-00 13-80 20-30 39-36 3-08 22-84 6-68 3-46 5-93 15-65 57-68) 41-00 43-00 38-00 6-45 12-88 31-57 4-05 14-12 14-96 43-72 42-10 32-43 43-71 216-30 14-53 58-65 2-86 29-28 33-46 §3. Kapoc Berg Station-fcon- tinued). On the 5th of February, 1842, the Fuller theodolite was placed near La Caille's rock, for the purpose of measuring the angle between Riebeek's Kasteel trigonometric point and the Rogge Bay Station. §3. ICapoc Berg Station-Ccon- tinuerl ). 450 VERIFICATION AND EXTENSION OP LA CAILLE'S ARC OF THE MERIDIAN. r = 12-563 feet, r" = log. 6-41352. y, for Riebeek's Kasteel = 210-13-41, and for Rogge Bay 308-31 -00. . • . the reduction to La Caille's rock = - 1 1 -077 - 9-6 1 = - 1 -467. Observed angle (46 measures, or 21 partial means) = 98-17-18-591. Angle reduced to La Caille's rock = 98-17-17-124. On the 6th of February, 1846, the Beaufort theodolite was placed near La Caille's rock, for the purpose of measuring the angle between Riebeek's Kasteel trigonometric point and La Caille's Observatory. 13-879 feet. sine 1" 6-45678. y, for Riebeek's Kasteel = 211-45-15 : for La Caille' Observatory, 310-4-38 Hence, reduction to rock = - 1 1-957 - 1 1°-098 = - 0-859. Observed angle between Riebeek's Kasteel and La Caille's Observatory (100 repeti- tions, weight 22-84) = 98-19-22-67. Angle reduced to La Caille's rock = 98-19-21-81. The angles measured by means of the Fuller theodolite were effected by Mr. Maclear and Mr. Mann, conjointly; those with the Beaufort theodolite, in February, 1846, by Mr. Maclear, — and in 1847, by Mr. Montagu. Reduction of Angles from Signal Rock to La Caille s Rock, Kapoc Berg. r = 127-729 feet. log. . ^ „ = log. r" = ^ sme 1" ^ 7-4207136. y = angle of direction, measured from La Caille's rock towards the right. Rogge Bay Guard-house La Caille's Observatory Patrys Berg. Klip Fontein, granary „ „ sector station Zwart Berg Riebeek's Kasteel, trigonom. point Simon's Berg, excentric station . . East end of Base West end of Base 19-16-05 19-18-07 174 -30 -00 207- 9-33 207-11-49 234-46-16 281- 2-46 338- 6-31 228 -23 -31 194-45-44 Log. r* sine y. 6-9392119 6-9399461 6-3943416 7-0801201 7-0806778 7-3328581 7-4125921 6-9922458 7-2944437 6-8269271 Log distance. 2625308 2626271 3734216 4208540 4205180 1987691 13-27371 3510113 4-8799741 4-7378979 Log reduction. 6766811 6770367 0209200 6592661 6601598 1340890 2798550 6412345 4144696 0890292 Eeduction. 47-499 47-568 10-492 45-633 45-726 -136-172 -190-482 - 43-776 -259-699 -122-752 The reduction for the left hand station, algebraically subtracted from the reduction for the right hand station, gives the reduction to La Caille's rock. OBSERVED HORIZONTAL ANGLES. 451 20. East end of Base. The Fuller theodolite centered over the terminal point NAMES OP STATIONS AND SIGNALS. BETWEEN Zwart Berg, heliostat. . . . ?j ?? ?) Drie Fontein, heliostat. . . Kapoc Berg, signal-rock. , and Drie Fontein, heliostat. and Riebeek's Kasteel, hel. and K. F. Contre Berg, hel. and Kapoc Berg, signal-rck. and West end of Base .... „ „ „ and Groote Berg, heliostat. K. F. Contre Berg, heliost. and West end of Base .... Riebeek's Kasteel, heliostat and Kapoc Berg, signal-rck. Groote Berg, heliostat .... and Zwart Berg, heUostat, . Heliostat signals on Riebeek's Kasteel, Zwart Berg, Drie Fontein, Groote Berg, and part of the time on Kapoc Berg ; an upright having a slit, over the west terminal point, and a pole over K. F. Contre Berg. Generally bad definition. Measured by Mr. Maclear. srminal point. Observed ^.y - Horizontal ivrfo^;,?! Angles. Measures. No. of Partial Means. §3. East end of Base. 8°6-3'5-55-155 119 44 74-18-35-656 65 30 63- 7-21-434 96 34 81-12-28-241 37 9 44-53-24-986 127 40 66-57-32-989 86 22 62-58-29-910 60 28 93-29-48-396 91 39 125-14- 6-700 15 3 21. West end of Base. The Fuller theodolite centered over the terminal point. Obseived Horizontal Angles. NAMES OP STATIONS AND SIGNALS. BETWEEN No. of Measures. West end of No. of Partial Means. East end of Base and K. F. Contre Berg 77-32-12-824 135 53 and Kapoc Berg, signal-rck. 101-28-48-550 89 42 K. F. Contre Berg and „ „ „ 23-56-37-953 11 3 An heliostat signal over east terminal point, a 6-inch diameter cylindrical pole on Kapoc Berg, and on K. F. Contre Berg. Generally bad definition. Measured by Mr. Maclear. 22. Klip Fontein, Contre Berg Station. This station is upon a swell, near a farm-house. The Fuller theodolite centered over the angle point. NAMES OP STATIONS AND SIGNALS. Observed Horizontal Angles. BETWEEN West end of Base and East end of Base. East end of Base and Drie Fontein .... No. of Measures. Klip Fontein, Contre Berg Station. No. of Partial Means. 39-29-18-196 94 46 66-11- 0-071 90 44 Zwart Berg and Riebeek's Kasteel 52-51 • 7-657 70 35 Heliostat signals over east end of Base, Drie Fontein, and Riebeek's Kasteel stations an upright with slit over west end of Base. The east end heliostat badly served. Measured by Mr. Maclear. §3. Riebeek s Kasteel Station. 452 VERIFICATION AND EXTENSION OE LA CAILLE'S ARC OF THE MERIDIAN. 23. RiEBEEKS Kasteel Station. The station is on the second peak, or crest, reckoning from the north. The highest part of this crest consists of a sandstone crag, divided into blocks by fissures, more or less close. The eastward face of the crest is a perpendicular precipice. La Caille's pile of stones stands on the small southernmost block, close to the edge of the precipice, — partly shel- tered by Protea bush, growing out of the crevices of the rocks. The position of the pile with respect to the edge of the precipice, is an important element in the discussion of the ancient with the modern determination of the distance between this pile and his rock on Kapoc Berg. The area of the pile-rock not being large enough for the theodolite tent, and in other respects undesirable, the rock next to it was preferred for the modern trigonometric or angular point, leaving La Caille's pile undisturbed. The Fuller theodolite was accordingly centered over the brass pin, marking the angle point for all angles measured on Riebeek's Kasteel, which is the Riebeek's Kasteel trigo- nometric or angle point of the modern triangulation, as the signal rock is of Kapoc Berg; and no other reference will be made to La Caille's pile than the reduction to it, for the purpose of verifying his angles, in which reduction we must assume that the axis of his quadrant coincided with the center of the pile. The reductions are as follows : — Reduction to La Caille's pile on Riebeek's Kasteel, of Angles observed at the trigonometric or angle point. r = 18 feet. log. . ^ „ = log. r" = log. 6-5696976. ^ sme 1" ^ ^ (y) = angle of direction, measured from center of pile towards the right. STATIONS. 7 Log. r". sine, y Log. distance. Log. reduction. Eeduction. Rogge Bay Guard house La Caille's Observatory Kapoc Berg, La Caille's rock. „ „ signal rock East end of Base O / // 111-10-10 111-11- 9 159-20-12 159-23-22 193-14-20 235-25-55 235-29- 1 235-29-40 6-5393541 6-5393060 6-1173200 6-1162576 5-9295551 6-4853363 6-4856059 6-4856624 5-3858028 5-3859624 5-1327918 5-13-28519 5-0340561 5-4163458 5-4161869 5-4157577 1-1535513 1- 1533436 0-9845282 0-9834057 0-8954990 1-0689905 1-0694190 1-0699047 + 14-241 + 14-234 + 9-650 + 9-625 - 7-861 -11-722 -11-733 -11-746 Klip Fontein, fire „ granary „ „ Bradley's sector The reduction for the left hand station, algebraically subtracted from the reduction for the right hand station, gives the reduction to La Caille's pile. OBSERVED HORIZONTAL ANGLES. 453 Horizontal Angles observed at Riebeelis Kasteel angle point, with the Fuller theodolite. § 3. Riebeek's Observed „ „ No. of Kasteel NAMES or STATIONS AND SIGNALS. Horizontal J:°- °' Partial Station-fco^- Angles. Measures. ^^^^^^ ,.^^^^^^^_ BETWEEN Royal Observatory, heliost. and KapocBerg,signal-rock 52- 9-37-840 103 48 » » „ and Klip Font, sector-stat. 128'15-53-583 6 3 King's Battery, heliostat. . and KapocBerg,signal-rock 51- 8- 7-278 96 48 Rogge Bay, sector-stat, hel. and „ „ „ „ 48-13-12-813 108 46 Lion's Rump, signal-staff, and „ „ „ „ 46-49-50-330 16 8 *Robben Isld., church-tower and „ „ LaCaille'srk. 39-39-16-276 20 10 Kapoc Berg, signal-rock . . and East end of Base, hel. . 33-50-58-524 112 54 and Klip Fon., granary Stat 76- 5-39-295 52 26 and Klip Fon., sector station 76- 6-18-263 74 35 and Zwart Berg, heliostat . 76-53-24-494 102 51 and Piket Berg, heliostat. . 80-32-39-364 55 27 and Groote Berg, heliostat. 25- 5-36760 31 14 „ exc. St and Kapoc Berg,signal-rock 0- 2-31-210 25 LaC's.r.,exc.st and „ „ „ 0- 0-28-237 25 Kapoc B., La Caille'3rock,h. and East end of Base, hel. 33-54- 7-203 18 9 East end of Base, heliostat and Zwart Berg, heliostat.. 43-2-26-661 98 49 Simon's Berg, heliostat. .. and Kapoc Berg, signal-r.,h. 85-50-32-384 72 36 Winter Berg, heliostat... . and „ „ „ „ 181-50-19-245 20 10 Klip Fontein, granary, hel. and KlipFon., sector station 0- 0-38-090 8 Heliostat signals were used at the several station points. The above angles were measured by Mr. Maclear and Mr. Mann, between the 15th of February and 3rd of April, 1842. 24. Drie Fontein Station. The station is upon a sandy undulation, towards the Riebeek's Kasteel side of Zwart- Dne Fontein land plane. A stone, carrying a lead plug and brass pin, was sunk in the ground, and ^*^°"' secured by ramming others firmly round it. The brass pin marks the angle point, over which the Fuller theodolite was centered. Heliostat signals were employed at the observed stations. Much inconvenience was experienced from the showers of sand, carried by strong wind at times into the theodolite tent while measuring. Observed „ „ No. of NAMES OP STATIONS AND SIGNALS. Horizontal Mpasiiirps! Partial Angles. measures, jje^ns. BETWEEN Klip Font., Contre Berg, h. and East end of Base, hel . . 50-41 -39-632 73 36 East end of Base, heliostat. and Zwart Kop, heliostat. . 48-43-36-350 78 35 Measured by Mr. Maclear, between the 8th and 11th of April, 1842. * Reduction to Signal-rock +3'-10"-48. 454 VERIFICATION AND EXTENSION OF LA CAILLE'S ARC OF THE MERIDIAN. 25. ZwART Berg Station. Zwart B Zwart Berg is an oblong mountain running meridian-wise nearly, and commencing Station. close to the left bank of the Berg River. The station is on the southernmost (which is the most elevated) of the three connected masses of which the ridge is composed. As the surface consists of loose slate, a large stone was bored, and firmly bedded to receive the lead and brass pin which defines the angle point. The Fuller theodolite was centered over the point. Heliostat signals were employed at the observed stations. NAMES OF STATIONS AND SIGNALS. BETWEEN Riebeek's Kasteel, heliostat and KapocBerg,signal-rock ,, „ „ and East end of Base, hel. . Drie Fontein, heliostat. . . . and „ „ „ „ Kapoc Berg, signal-rock . . and Patrys Berg, heliostat . Patrys Berg, heliostat. . . . and Klip Font., sector-stat.. ,, „ „ and Piket Berg, hehostat. . Riebeek's Kasteel, heliostat and Patrys Berg, heliostat . Klip Fontein, granary, hel. and Klip Font., sector-stat. Measured by Mr. Maclear and Mr. Smylh, between the 15th of April and 2nd of May, 1842. 26. Klip Fontein, the Locality of the North end of La Caille's Arc. Klip Fontein, An elaborate account of the investirations, which were undertaken for the purpose of the locality of , _ . . . . . . . the north end discoveriup- the positiou of the p-ranary at this locality wherein La Caille made his sector of La Caille's . . & ^ J Arc. observations, is given in the first part of the present work ; with a plan of the buildings Plate II. then extant, and of the foundations of others of ancient date. Pig. 9. The Fuller theodolite was centered over the point on the corn floor, which marks the Fig. 13. position of the axis of Bradley's sector in the year 1839; also over a point within the foundation supposed to be that of La Caille's granary, or sector station, in the year 1752. The latter point is defined by a stone sunk in the ground and bedded in masonry, carrying a lead plug and brass pin. By La Caille's account, his signal fire (which was also the position of his quadrant) was 36 toises exactly west of his sector : hence there is no difficulty in reducing angles measured at the granary station to his signal fire, when the azimuths of Riebeek's Kasteel and Kapoc Berg are known, nor of Bradley's sector station to the granary station, when the angles of direction and the distance between them have been measured. Observed Horizontal Angles. No. of Measures. No. of Partial Means. 56-50- 8-849 114 57 62-38-59-932 94 46 44-40-29-042 64 32 78-49- 2-386 79 38 42-55- 4-186 75 37 51-8- 7-380 73 36 135-39-11-515 6 2 0- 1- 4-780 16 OBSERVED HORIZONTAL ANGLES. 455 Farm yard obstructions intervened between the sector and granary stations, but the § s. small corn floor to the west commanded both. Here a point was taken up, from which tS^io^aiity of the distance to both and the inchided angle were measured,— they were as follows : to TiTcm^s the sector point 151-296 feet, to the granary point 269-970 feet, and the included t^ed).^"""'' angle 73-23-1-7. .-. the distance between the sector and granary points is 269-099 feet, which was checked by a rough measure over the intervening obstructions. The angle between Zwart Berg and Patrys Berg is the only important one measured at the sector point. r = 269-099 feet. W. -— - = 7' ^ sinel" 7443369. The angles of direction (y) measured from the granary point round, in the order of increasing readings. STATIONS. 7 Log. r" sine. y. Log Distance. Log Eeduction. Reduction. Zwart Berg Patrys Berg / // 189-27-43-7 283-2113-2 6-9602277 7-7324332 5-1569282 5-1537117 1-8032995 2-5787215 / // -1- 3-576 -6-19-082 At the sector point the mean of 54 measures, or 27 partial means, gave for the angle between Zwart Berg and Patrys Berg 93-53-29-43 Reduction —5-15-51 Angle reduced to the granary angle point 93-48-13-92 By ah approximate calculation, the azimuth of Riebeek's Kasteel is 335-20-57-68, and of Kapoc Berg signal-rock point 5-22-13-74, — reckoning from the south point round by the west. The reduction from the trigonometric point on Riebeek's Kasteel to La Caille's pile, there (page 452) is — ir'-73, and from Kapoc Berg signal-rock point to cylindric rock centre (page 450) is — 45'''-63. Applying these corrections to, and sub- tracting 90° from the azimuths, the angles of direction (-y) are found. 7- = 36 toises x 6-3945925. log r" = 7-6765405. STATIONS. 7 Log. r" sine y. Log, Distance. Log. Eeduction. Reduction. Riebeek's Kasteel. Kapoc Berg O I II 245-20-45-95 275-21-28-11 7-6350299 7-6746389 5-4163458 5-4208079 2-2186841 2-2538310 / II -2-45-457 -2-59-404 456 VERIFICATION AND EXTENSION OE LA CAILLE'S ARC OF THE MERIDIAN. §3. Klip Pontein, the locality of the north end of La CaiUe s Arc — (conti- nued ), . ■. the reduction to the signal fire =— 6'13"95. The mean of 72 measures, or 36 partial means, of the angle at the granary angle point, between Riebeek's Kasteel and Kapoc Berg, is 30' 1 "IB' 188, and the reductions to La Caille's pile on the one, and to his rock on the other, are +ll"-73 and — 45"'63. (La Caille's stations on Riebeek's Kasteel and Kapoc Berg are to the left of the modern points, as viewed from Klip Fontein). Consequently, Observed angle at granary point 30"1*16'19 Reduction to signal fire — 13'95 Reduction to his points, as above — 33'90 Angle at La Caille's signal fire, between his Riebeek's Kasteel and Kapoc Berg stations 30"0'28*34 Referring to the Memoirs of the Academy of Sciences, year 1751, page 432. La Caille's numbers for calculation are 29"59"56. Adding 2-7 for spherical excess, his observed angle becomes 29-59'58-7, differing by 29-6 from the above result. The difference is discussed in another part of this work, in conjunction with the other angles and sides of this triangle, where there is evident proof of La Caille's sector position having been within a building still existing and inhabited, 25 yards to the north-west of the assumed granary point. . o / # Returning to the angles observed at the granary, — the mean of 80 measures, or 40 partial means, of the angle between Zwart Berg and Patrys Berg, is 93-48-12-99 The angle between these stations, observed at the sector point, reduced to the granary point (27 partial means) 93-48-13-92 Mean (Weight 67). . . . 93-48-13-37 The above angles were measured by Mr. Maclear and Mr. Smyth, between May 5 and June 3, 1842. Heliostat signals were employed at the several stations. 27. PiKET Berg Station. Piket Berg Station. The point was taken up by a signalman, who was sent from Kapoc Berg with an heliostat, and instructions to select the highest part of the range. The conditions were not strictly carried out, but the station commands an important elevation to the north- west, which it masks from the highest point. On the other hand, the latter masks an important elevation to the south-east, — therefore it became necessary to occupy both. OBSERVED HORIZONTAL ANGLES. 457 The Fuller theodolite centered over the terminal point. §3. Piket Berg Observed -jj - No. of Station-(con- NAMES OP STATIONS AND SIGNALS. Horizontal Measures Partial tinuedj. Angles. ■ Means. BETWEEN o / // Riebeek's Kasteel, heliost. and Kapoc Berg, heliostat. 30- 5-58-070 49 24 „ „ „ and Patrys Berg, heliostat. 9M0-50-140 8 4 (Kapoc Berg, heliostat and „ „ „ 61- 4-47-512 67 33| ( „ „ „ and „ „ „ 61- 4-47-851 120 6OJ Zwart Berg, hehostat and „ „ „ 88" 2-37-852 80 37 f Patrys Berg, heliostat and Eland's Berg, heliostat. 83-57-34-188 104 52| 1 „ „ „ and „ „ „ 83-57-35-328 120 60J I Eland's Berg, heliostat... and Lambert's HoekBerg,h. 52-20-34-365 53 27 ") ( „ „ „ and „ „ „ „ 52-20-32-636 120 60J „ „ andHeerenlogement'sB.,h. 26-57-12-804 40 20 „ „ „ and Ceder Berg, heliostat. . 81-58-18-009 120 60 Heerenlogement's Berg, h. and „ „ „ 55' 1- 4-432 120 60 Lambert's Hoek Berg, hel. and „ „ „ 29-37-44-749 40 20 Ceder Berg, hehostat and Zwart Berg, pile 106- 1-26-885 40 20 „ „ „ and Kapoc Berg, heliostat. 132-59-20-370 Lambert's Hoek Berg, hel. and Kapoc Berg, heliostat. 162-37- 3-276 40 20 Kapoc Berg, heliostat and Eland's Berg, heliostat. 145- 2-24-810 40 20 Eland's Berg, heliostat ... and Niche B 116-30-17-007 24 12 „ „ „ and a remarkable Rock .. . 112-47-36-550 8 4 The observations for including Tafel Berg and West End in the triangulation are not published, because neither of them are visible from the Ceder Berg station. The above angles were measured by Mr. Maclear and Mr. Smyth, between June 5 and 21, 1842 ; December 26, 1843, to February 22, 1844. 28. Kapitein's Kloof Station. This is the second station on Piket Berg, before alluded to, taken up because it com- Kapitein's mands Winter Berg, which is visible from the Ceder Mountain station, and shuts out ^^'°°^ station. Winter Berg from the first station on Piket Berg. The name of the adjacent pass (Kapitein's Kloof) is given to it for distinction. The Fuller theodolite centered over the terminal point. Obseived -jj f No. of NAMES OF STATIONS AND SIGNALS. Horizontal Mooo'iiroB Partial Angles. Measures. ^^^^^ BETWEEN Riebeek's Kasteel, hehost.. and Kapoc Berg, hehostat. 30-55-38-791 160 80 Kapoc Berg, heliostat. ... and Patrys Bei-g, heliostat. 62-23-20-631 160 80 458 VERIFICATION AND EXTENSION OF LA CAILLE'S ARC OP THE MERIDIAN. Ka it i ' Kapoc Berg, heliostat and Donkin's Bay, heliostat 149-57-45-470 Kloof Station -{continued). 4 2* 4 2* 120 60 160 80 160 80 160 80 Patrys Berg, heliostat and „ „ „ 87-34-35-100 „ „ „ and Heerenlogement'sB.,h. 106'10*19'919 Heerenlogement's Berg, h. and Ceder Berg, pile 54" 2"38*846 Ceder Berg, pile and Winter Berg, heliostat. 74-42-47-233 Winter Berg, hehostat. . . . and Riebeek's Kasteel, hel. 31"45'16'584 The angles were measured by Mr. Smyth, between April 22 and May 25, 1844. Heliostat signals over the several station points except the Ceder Berg, where the excentric pile was observed. Reduction from the Ceder Berg pile to the angle point of that station, for the angle with Winter Berg = — 15"'67 ; for Heerenlogement's Berg = +15""67 (see Ceder Berg station. No. 33); hence these angles become 74-4'3-2-903 and 54-2-23-176. 29. Winter Berg Station. Winter Berg This is One of the remarkable commanding masses of the eastern range. " The ground round the station was very uneven : one foot of the theodolite trestle rested on the station rock (of no great size), one on an iron picket, and one on a block of stone put into a hole to bring up to the level. North winds were frequent and violent. The cold was very great during the first half of the time, when the tents were generally coated with snow." The Fuller theodolite centered over the angle point. Observed ^ - No. of NAMES OP STATIONS AND SIGNALS. Horizontal Ti, ' Partial Angles. Measures. ^^^^^_ BETWEEN • O / // Kapitein's Kloof, heliostat . and Ceder Berg, pile 52'1511'068 160 80 Ceder Berg, pile and Sneeuw Kop,H.H.,hel. 187-15-52-545 160 80 Sneeuw Kop, H.H., hel. . and Kapoc Berg, heliostat. 55' 9-32-323 160 80 Kapoc Berg, heliostat and Kapitein's Kloof, hehos. 65-19-23769 160 80 „ „ „ and Zwart Berg, heliostat. . 36' 18* 1*114 16 8 Riebeek's Kasteel, pile. . . and Ceder Berg, pile 133-48-58-529 40 20 Royal Observatory, heliost. and Riebeek's Kasteel, pile. ]3"15"25'241 24 12 The angles were measured by Mr. Smyth, between July 9 and October 10, 1844. Reduction from the Ceder Berg pile to the angle point, for the angle with Kapitein's Kloof, Sneeuw Kop, H.H., and Riebeek's Kasteel = 9"'073 ; hence these angles become 52-15-1-995, 187-16 1-618, and 133-48-49-456. (See Ceder Berg Station, No. 33.) * Angle (y) at theodolite station between Kapoc Berg and a temporary station that commands Donkin's Bay, 124°'43', Distance 21-67 feet. OBSERVED HORIZONTAL ANGLES. 459 30. Patrys Berg Station. Patrys Berg is the comparatively low whale-backed granite mountain, at the south § 3- end of St. Helena Bay. The trigonometric point is on a flat block of granite, even with station, the common surface, and is defined as usual by a cylinder of lead and brass pin. At the first visit in June, 1842, the angles were measured under unfavorable circum- stances, owing to the detachment of soldiers having been re-called for military duty, and the signal stations, therefore, could not be occupied simultaneously. When visited in August, 1 846, Messrs. Campion and Montagu had instructions to measure each angle separately, as usual : also combined, viz., bisecting the several signals in succession, then shifting the microscopes a given number of degrees, and so on round the circle. The results from the latter method proved so discordant that no use has been made of them : while the experiment confirms the necessity of stepping the divisions of the Fuller theo- dolite without a break. The discordant measures are not printed. The Fuller theodolite centered over the angle point. Observed j^ - No. of Horizontal Measures I"^'***! Angles. Measures, ^^^j^^^ NAMES "or STATIONS AND SIGNALS. Horizontal Measures -P^''*'*^ BETWEEN Kapoc Berg, heliostat and Referring hole 134- 16-4 177 74 36 Eland's Berg, heliostat ... and Piket Berg, heliostat. . 44 48-35-40 81 40 Kapitein's Kloof, pile. . . . and Kapoc Berg, hehostat.. 78-40"51-71 116 51 Piket Berg, heliostat and Zwart Berg, hehostat. . 40-49-18-04 79 36 Referring hole and La Caille's Granary,hel. 141-24-41-48 74 34 Referring hole and Zwart Berg, hehostat.. 184-42-3M4 82 41 Zwart Berg, heliostat. . . . and Kapoc Berg, hehostat.. 41- 0-47-99 152 60 The " referring hole " is a natural aperture in a gigantic group of rocks near St. Helena Bay, through which the sky is seen. The measures in 1842 by Mr. Maclear, those in 1846 by Messrs. Campion and Montagu. 31. Eland's Berg Station. Eland's Berg is a flat-topped hill, or table land, situated near the north end of St. Eland's Berg Helena Bay. The Verloren Valei outlet to the sea passes close to its northern precipitous end. Owing to the flatness of the top, and the thick bush that covers it, a spot could not fee found which would command an uninterrupted view of the sea and of the inland stations. From the station selected near its northern extremity, the sea is visible at the mouth of the Berg River, and northward in the direction of Lambert's Cove and Donkin's Bay. The point is near the centre of a blotch of naked sandstone rock, which is even with the surface of the ground, and is marked in the usual way by a cylinder of lead and brass pin. Q Eland's Berg Station-(con- tinuedj. 460 VERIFICATION AND EXTENSION OF LA CAILLE'S ARC OF THE MERIDIAN. The Fuller theodolite centered over the angle point. Observed -^^ ^f No. of KAMES OF STATIONS AHD SIGNALS. Horizontal Measures I''irtial Angles. , ■ Means. BETWEEN O / /' Heerenlogement's Berg, h. and Lambert's Hoek Bg., h. 58-41-16-91 124 62 „ „ and Referring hole 84-14-11-85 124 61 „ „ and „ niche 84-14-27-17 80 40 „ „ and Ceder Berg, heliostat. . 63-43-19-27 160 80 Lambert's Bay, heliostat. . and Heerenlogement's B.,h. 37'29'22"02 16 8 Lambert's Hoek Berg, hel. and Piket Berg, heliostat. . 67-45-33-27 106 53 „ „ and Referring hole 25-32-54-63 100 50 Piket Berg, hehostat and Patrys Berg, heliostat. 5ri3-56'02 66 33 Referring niche and „ „ „ 93-26-18-66 62 31 and Piket Berg, heliostat. . 42-12-21-99 130 64 and „ „ „ 42-12-21-23 80 40 hole and „ „ „ 42-12-40-12 128 64 and Referring niche 0- 0-16-74 96 48 Ceder Berg, heliostat and Piket Berg, hehostat. . 62-43-29-58 160 80 and Referring niche 20-31- 9-01 80 40 The measures between January 9 and February 2, 1843, by Mr. Maclear and Mr. Mann, — those of subsequent date by Mr. Smyth. Lambert's Hoek Berg Station. 32. Lambert's Hoek Behg Station. The fertile Lang Valei, stretching eastward from the sea-shore through a sandy desert, is suddenly brought to a close by two whale-shaped, ridge-topped, elevations of sandstone, at a corner named Alexander's Hoek. From the summit of the north-eastern of the two, the view to the eastward is magnificent : in the vale below, the Olifant's River pursues its northerly course, nearly insulating the little town of Clanwilliam. Beyond, the gigantic masses of the Ceder Bergen extend across with imposing grandeur. The station is on the north-eastern (Lambert's Berg), marked as usual by a cylinder of lead carrying a brass pin, inserted in a rock. The Fuller theodolite centered over the angle point. NAMES OF STATIONS AND SIGNALS. BETWEEN Observed Horizontal Angles. Eland's Berg, heliostat. . . and Heerenlogement's B.,h. 65"47' 8'49 „ „ „ and Referring niche 155"40"40'21 Heerenlogement's Berg, h. and „ „ 89'53'31'84 „ „ „ and Joachim's Neus, top. . . 149-10-44-23 No. of Measures. 141 160 127 7 No. of Partial Means. 70 80 63 OBSEKVED HORIZONTAL ANGLES. Klip Rug Kop, peak and Referring niche 24-56-59'80 6 Lambert's Cove, heliostat. and „ „ 124-16-39-75 40 Piket Berg, heliostat and Eland's Berg, heliostat. 59-53-53-75 122 and Referring niche 144-25-25-80 66 *Clanwilliam, heliostat. . . . and ,, „ 25-53-54-27 4 Referring niche and Peak on Ceder Berg. . 37-24-42-80 6 The angles at this station were measured by Mr. Maclear and Mr. Mann. 461 §3. Lambert's 20 Hoek Berg Station-fcon- bO tinued). 30 33. Ceder Berg Station. The station is upon the highest part of Sneeuw Kop, in the center of a sort of dish ceder Berg or cup, nine feet in diameter, hollowed out of the rock by the action of the weather, and ^***"'°- is marked by a brass pin in the center of a cylinder of lead, let into a hole drilled in the rock. The Fuller theodolite centered over the terminal point. Observed ^ , No. of NAMES OF STATIONS AND SIGNALS. Horizontal t.^ Partial Angles. Measures. jjg^ns. BETWEEN Q , ^^ Kapoc Berg, heliostat .... and Eland's Berg, heliostat. 60-52-41-45 17 8 Donkin's Bay, heliostat. .. and Heerenlogement's B.,h. 8'52"45'83 10 5 „ „ i, and Referring hole 24-29-39-05 7 4 Eland's Berg, heliostat. .. and Heerenlogement's B.,h. 35-39-29-94 160 80 „ „ „ and Donkin's Bay, heliostat 26-46-41-69 20 10 Heerenlogement's Berg, h. and Referring hole 15'36-53-92 60 30 „ „ and Klip Rug, heliostat. .. 66-43-28-36 101 50 Lambert's Hoek Berg, pile and Referring hole 45-33-15-04 32 16 Piket Berg, hehostat and Eland's Berg, heliostat. 35'18-16-03 68 34 „ „ „ and Donkin's Bay, hehostat 62- 5' 2"46 5 3 „ „ and Heerenlogement's B.,h. 70-57-46-15 22 10 The " referring hole " is a natural opening in a distant group of rocks. The Beaufort theodolite centered over the angle point. Weights. Winter Berg, heliostat... . and Kapitein's Kloof, pile.. 53' 2-1M8 400 59-36 Kapitein's Kloof, pile and Heerenlogement's B.,h. 73-31-44-90 800 4371 Klip Rug, heliostat and Winter Berg, heliostat. 166-42-35-28 400 29-89 „ „ kop .....and ., „ „ 165-17-23-49 160 7-48 The light was given from the Civil Commissioner's house, situated at the south end of the tovra. 462 VERIFICATION AND EXTENSION OP LA CAILLE'S ARC OF THE MERIDIAN. 5 3- On leaving the station in the beginning of April, 1843, a signal pile of dry stones was station-Cco«. built with care, in the form of a truncated cone, on the south side of the station point, in tinned). • i • ij i. order that it might be used if, from the severity of the wmter, the station could not be held by a signalman, thus leaving the station point open for an heliostat, if practicable. ft. In. Circumference of top of pile 19'7^ „ „ base of pile 38'OJ Nearest distance between base of pile and station point U'lf o / Theodolite reading for center of pile, derived from the reading for both edges = 189"0 „ „ „ Lambert's Hoek Berg, pile = 330-5 Hence y, or angle of direction, for Lambert's Hoek = 14r5 r = 17-184 feet. log. " = 6-5495241. Combining the several angles with y for Lambert's Hoek Berg, we obtain : — ■y for Winter Berg = 44-27'25. Reduction from piletostationpomt 9*073 + Kapitein's Kloof. = 97-29-36. „ „ „ „ 15-670+ Piket Berg = 100-3-35. „ „ „ „ 15-428 + Eland's Berg = 135-21-51. „ „ „ „ 9-882 + Heerenlogement's Berg = 171' 1-21. „ „ „ „ 2-415 + Klip Rug = 237-44-50. „ „ „ „ 11-034- The reduction to be subtracted from the theodolite reading (at these stations) for the bisection of the pile, to obtain the reading for the station point. The angles at the Ceder Berg, measured with the Fuller theodolite, were effected by Mr. Maclear and Mr. Mann, — those with the Beaufort theodolite by Mr. Montagu. 34. Heerenlogement's Berg Station. Heerenloge- ment's Berg Station. Heerenlogement's Berg, or Gentleman's-hotel Mountain, is an isolated mountain on the path to the north-west frontier. At about half of its height from the base the mountain is divided by a ravine, running S.E. and N.W., into two crests of rugged sandstone, where the process of disintegration, aided by the south-east wind (a), has channeled out the softer material, leaving the harder in the form of long walls in the direction of the current. The crest to the north- ward being the higher of the two, was selected for the trigonometric station. The point is marked by a cylinder of lead, having a brass pin in its center, over which the Fuller theodolite was centered in April and May, 1843, and October, 1847. (a) The dry south-east wind acts more powerfully upon sand-stone, than the moist north-wester. 1 OBSERVED HORIZONTAL ANGLES. 463 Observed Horizontal Angles at Heerenlogemeni s Berg. § 3. Heerenloge- Obseived y, . No. of merit's Berg NAMES OF STATIONS AND SIGNALS. Horizontal ■,/ Partial Station-fcon- Angles. Measures. -^^^^^^ tinned). BETWEEN Bokkeveld's Berg, heliostat and Klip Rug, heliostat. . . 41-56-13"84 80 40 and Ceder Berg, pile (red.) 105-56-45-06 54 27 Eland's Berg, heliostat and Donkin's Bay, heliostat 68-54-34*83 20 10 „ „ „ and Louis Fontein, heliostat 123-34-58-35 80 40 Eland's Hoogte, heliostat. and Bokkeveld's Berg, hel. 37-51 •30-32 100 50 Klip Rug, heliostat and Ceder Berg, hehostat. . 64- 0-29-81 60 30 and „ „ pile (red.) 64- 0-29-17 20 10 ,, „ kop and „ „ heliostat.. 63-39-50-97 6 3 and „ „ „ 63-39-53-22 20 10 Lambert's Hoek Berg, hel. and Eland's Berg, hehostat 55-31-38-25 128 50 Louis Fontein, heliostat. .. and Cedefr Berg, pile (red.) 155-47-44-52 100 50 and Bokkeveld's Berg, hel. 49-50-57-68 80 40 Piket Berg, pile and Heerenl. B., sector stat. 137-45-55-43 8 4 Referring niche (i) and Ceder Berg, pile (red.) 9- 8- 1-39 4 2 „ Q) and „ „ „ „ 9- 8- 9-26 4 » O and „ „ „ „ 7- 4-49-05 56 28 „ (^) and Piket Berg, heliostat. . 61- 6- 8-22 18 9 Ceder Berg, pile (reduced) and Joachim's Neus 9-54-36-21 36 18 Ceder Berg, heliostat and Kapitein's Kloof, pile.. 52-26- 6-12 80 40 and Piket Berg, pile 54-1-20-07 60 30 Sector Station, Heerenl. B. and Ceder Berg, heliostat... 168-12-44-50 16 8 Ceder Berg, heliostat and Eland's Berg, hehostat. 80-37-16-28 82 40 „ pile (reduced) and „ „ „ 80-37-18-03 80 40 Subtense of 20 feet across the sector station point, from which point the line to the theodolite station point is perpendicular to the 20 feet 2-17- 7-78 20 10 The angles measured at this station, in 1843, v^^ere by Mr. Mann and Mr. Maclear, those of subsequent date by Mr. Campion. The observations for latitude, vrith Bradley's sector, were made by Mr. Maclear. The observations with the 30-inch transit by Mr. Mann. 35. Klip Rug Station. The station is on the top of a low clayey hill, and the lead plug is in a very hard blue KUp Rug round stone, about three feet in diameter, sunk into the ground and well rammed in on all sides. The stand of the instrument rested on hard clay. Note. — When the Ceder Berg pj'fc was observed at any station, the correction from page 462 was applied, as there indicated, to reduce to the Ceder Berg trigonometric point. R 464 VERIFICATION AND EXTENSION OF LA CAILLE'S ARC OF THE MERIDIAN. 13- A pile, 10 feet in diameter at the base and 10 feet high, was built over the point after station-(con- removing the instrument. tinuedj. There is a remarkable group of rocks on the east end of the hill, named in the books " Klip Rug Knob." The Fuller theodolite centered over the angle point. Observed jj » No. of NAME8 OF STATIONS AND SIGNALS. Horizontal nT„„^,„„„ Partial Angles. Measures. -^^^^^ BETWEEN O ; II Heerenlogement's Berg, h. and Bokkeveld's Berg, hel. 80'10'11'19 160 80 „ „ and Conical Hantam Berg. 157-19-42-09 16 8 Referg.n.,inCederBergen and Bokkeveld's Berg, hel. 102-49-32-91 80 40 „ and Heerenlogement's B.,h. 22-39-21-30 80 40 Ceder Berg, pile (reduced) and Referring niche 26'36'51"94 40 20 „ heliost and „ „ 26-36-52-34 40 20 „ „ and Heerenlogement's-B.,h. 49-16-13-29 160 80 The angles at this station were measured by Mr. Smyth, between September 19 and 28, 1843. 36. Bokkeveld's Berg Station. Bokkeveld's The Station is on the top of a table mountain, the lead cylinder in a mass of very Berg Station. , . , . . . ^ brittle ironstone, of small size ; two feet of the stand of the instrument rested on the ground, and the third on an iron picket driven through the iron stone. The referring niche was in the Hantam Berg. A pile, 20 feet high and 15 feet in diameter at the base, was erected over the station point after the observations were made. The Fuller theodolite centered over the angle point. Observed -j^ „ No. of NAMES OF STATIONS AND SIGNALS. Horizontal nT Partial Angles. Measures. ^^^^^ BETWEEN Eland's Hoogte, heliostat and Referring niche 19°3-56-5"7-79 80 40 „ „ „ and Kamies-Sec.B.,W.R.,h. 51- 6-41-33 160 80 Heerenlogement's Berg, h. and Eland's Hoogte, heliost. 65- 6-27-68 160 80 „ „ „ and Louis Fontein, heliostat 76- 9-45-71 160 80 Kamies-SectorB.,W.R.,h. and Referring niche 142-50-16'60 80 40 „ „ „ „ and „ „ 142-50-17-21 80 40 „ „ and Keibiskow, heliostat. . . 89-48-55-92 160 80 Keibiskow (supplemty.), h. and Kamies-Sec.B.,W.R.,h. 270-1 1- 2-29 40 20 Keibiskow, heliostat and Referring niche 53- 1- 19-73 132 60 and Klip Rug, pile 96-4- 5-70 24 12 „ „ and „ „ heliostat... 96-4-6-52 60 30 „ „ and „ „ kop 94-13-43-68 20 10 Klip Rug, heliostat and Heerenlogement's B.,h. 57-53-47-50 160 80 60 80 80 40 80 40 16 8 80 40 24 12 OBSERVED HORIZONTAL ANGLES. 465 Louis Fontein, heliostat. .. and Kamies-Sec.B.,W.R.,h. 40- 3-24-21 160 80 §3 Referring niche and Louis Fontein, heliostat 177" 6"19"03 80 40 Berg station and KHp Rug, heliostat. . . 43- 2-46-33 80 40 -f-'"'-^'')- and „ „ kop 41-12-19-94 „ „ and Heerenlogement'sB.,h. 100-56-33-09 „ „ and Conical Hantam Berg.. 6'57°36'65 The term Kamies Berg here means the elevation, generally termed Kamies-Sector Berg. The Kamies Bergen consist of several elevations which have separate names, as "Welcome," " Ezels Kop," &c. The angles at this station were measured by Mr. Smyth, and by Messrs. Campion and Montagu. 37. Louis Fontein Station. On the left hand side of the road leading from the Olifant's River to the Kamies Louis Fontein Bergen, over the Hardevelt, there is a whale-backed granite hill, with a farm-house at its base, named Louis Fontein. The station is on the top of the hill, in the middle of a large fiat granite rock, marked as usual by a cyUnder of lead, carrying a brass pin, let into the rock. The Fuller theodolite centered over the terminal point. Observed -j^ „ No. of NAMBS OP STATIONS AND SIGNALS. Horizontal Moaoiii-co Partial Angles. Measures. ^^^^^_ BETWEEN Bokkeveld's Berg, heliostat and Heerenlogement"sB.,h. 53-59-39-01 160 80 Ezel's Kop, heliostat and (a) Kamies-Sect. Berg, West Rock, heliost. 4-29-14-66 180 80 and Referring niche 2-1 1- 6-98 40 20 Kamies-Sector Berg, (red. to West Rock), heliost. and Bokkeveld's Berg, hel. 87-43- 1'86 160 80 Kamies-Sector B.,w!R.,h. and Kamies-S.B.,theod.,h. 0- 2-20-39 200 100 Referring niche and Heerenlogement's B.,h. 144- 0-49-05 160 80 and Bokkeveld's Berg, hel. 90- 1- 9-38 160 80 and Kamies-Sect. B., theod. (red. toW.R.), hel. 2-18- 8-13 80 40 and Kamies-Sec.B.,W.R.,h. 2-18- 8-32 86 41 Roodewal, heliostat and „ „ „ „ „ 54-59-15-86 172 80 Kamies-Sector B.,W.R.,h. and Roodewal, heliostat. . . 305- 0-43-78 80 40 Roodewal, heUostat and Ezel's Kop, hehostat. . 50-30- 177 120 60 and Referring niche 52-41- 9-29 62 31 The referring niche is a natural cleft in a group of rocks on the top of " Welcome," Kamies Berg. The angles at this station were measured by Mr. Smyth, and by Messrs. Campion and Montagu. (a) The west rock station wiU be described, with the other particulars of the Kamies Berg (Sector Berg) station. 466 VEI^IFICATION AND EXTENSION OF LA CAILLE'S ARC OF THE MERIDIAN. 38. Eland's Hoogte Station. Iiand's Eland's Hoogte is a low smooth hill in the Hardevelt, with small patches of granite Hoogte here and there. The plug marking the station point is in one of these patches. The Fuller theodolite centered over the angle point. Observed No of ^°' °^ NAMES OF STATIONS AND SIGNALS. Horizontal Measures Partial Angles. ■ Means. BETWEEN O / II Bokkeveld's Berg, heliostat and Heerenlogement'sB.,h. 77- 2-14-81 160 80 and Referring niche 43-14- 9'62 40 20 Kamies-Sector Berg, theod. (reducedtoW.R.), hel. and „ „ 140-35-55-54 40 20 Kamies-Sector Berg, theod. (reducedtoW.R.), hel. and Bokkeveld's Berg, hel. 97-21-48-93 160 80 Referring niche and Heerenlogement'sB.,h. 33-48" 4-80 80 40 The referring niche was a cleft in the Bokkeveld Berg, it was seldom well-defined. The angles at this station were measured by Mr. Smyth in July, 1843. 39. RooDEWAL Bay Station. KoodewaiBay About 4rr milcs north of the mouth of the Zout Riviere, and within three miles of the btation. -^ ' sea-shore, there is a conical-shaped mound of granite, naked at the top, which top is 621 feet above the sea level. Roodewal Bay is about nine or ten miles to the north ; further to the north, the remarkable stone (Hondeklip) that gives the name to the small inlet, Hondeklip Bay, is visible. The land all about is a sandy desert, in parts covered with stunted bush. A little brackish water can be obtained by digging in the sand near the beach, but in greater quantity about 4^ miles to the north-west, where a small habitation has been built. The station is upon the naked granite topping of the conical-shaped rise, and is marked, as usual, by a cylinder of lead inserted in the rock. The Beaufort theodolite was centered over the angle point. Observed j^ „ NAMES '"of stations AND SIGNALS. Horizontal ^ ' Weights. Angles. ■ftleasures_ between o , J, Kamies-Sector Berg, hel. and Louis Fontein, heliostat 64" 7'56'176 128 7'65 „ and „ „ „ 64- 7-55-360 118 16-75 Louis Fontein, heliostat. . . and Kamies-Sector B., hel. 295-52- 3-225 100 7-58 and „ „ „ „ 295-52- 3-980 30 3-14 (Mean = 64- 7-55'900 35-12) OBSERVED HORIZONTAL ANGLES. 467 Louis Fontein, heliostat.. . and Vogel Klip, heliostat. . 248-10-42-560 100 20-95 §3. , EoodewalBay and „ „ „ 248-10-42795 100 272 station-fcoK- and „ „ „ 248-10-42-688 40 33-52 "™"^^' (Mean =248-10-42-650 57-19) Vogel Klip, heliostat and Kamies-Sector B., hel. 47-41-20-660 100 11-48 „ „ and „ „ „ „ 47-41-22-565 100 28-65 and „ „ „ „ 47-41-20-260 100 31-68 (Mean = 47-41-21-240 71-81) Vogel Klip, heliostat and Ezel's Kop, heliostat. . 46-39-28-235 100 8-53 and „ „ „ 46-39-28-180 100 6-74 (Mean = 46-39-28-210 15-27) Ezel's Kop, heliostat and Kamies-Sector B., hel. 1- 1-53-080 100 6*02 and „ „ „ „ 1- 1-53-180 100 41-47 and „ „ „ „ 1- 1-53-050 40 18-91 (Mean = 1- 1-53-130 66-40) Ezel's Kop, heliostat and Louis Fontein, heliostat 65- 9-49-715 100 22-54 and „ „ „ 65- 9-48-780 100 3-66 (Mean = 65- 9-49-580 26-20) Very bad definition, and very bad signalling throughout the time (February 12 to March 4). One half of the measures were made with the axis reversed ; also the teles- cope was moved alternately direct and backward, which amounts to the same as measuring the supplement of the angle, and the angle itself Dense thunder clouds often capped the stations. By combining the angles in every possible way, we obtain the following : — Ezel's Kop and Louis Fontein 65- 9-49-28 82-7 Kamies-Sector Berg and „ „ 64-7-56-08 95-9 Vogel Klip and Kamies-Sector Berg. . 47-41-21-25 120-1 and Ezel's Kop 46-39-28-05 84-2 Ezel's Kop and Kamies-Sector Berg. . 1- 1-53-20 102-7 Louis Fontein and Vogel Klip 248-10-42-67 99-7 The angles at this station were measured by Mr. Maclear. 40. Ezel's Kop Station. Ezel's Kop is one of the granite peaks of the Kamies Bergen, and the nearest to the Ezel's Kop south of the Lily Fontein Missionary Institution. It was occupied conventionally, being the only one which could be recognised from Vogel Klip, among the confusion of tops, while on the preliminary expedition in search of stations; and retained lest Kamies-Sector Berg should be masked from any of the Bushman Flat stations. It is not essential to the arc of the meridian. §3. Ezel's Kop Station-(eon- tinned). 468 VERIFICATION AND EXTENSION OP LA CAILLE'S ARC OF THE MERIDIAN. The Beaufort theodolite was centered over the angle point. Observed No of NAMES OP STATIONS AND SIGNALS. Horizontal Measures W^^Stts. Angles. BETWEEN O , ,1 Roodewal, heliostat and Vogel KHp, heliostat. . 91 -51 •34-47 100 16-02 Vogel Klip, hehostat. and Louis Fontein, heliostat 203-48- 8-50 130 19-29 Louis Fontein, heliostat.. . and Roodewal, heliostat. . . 64-20-17-32 100 24-58 Vogel Klip, heliostat and Referring niche 190-16-50-57 100 24-78 Referring niche and Vogel Klip, heliostat. . 169-43- 9-75 20 At first, the Louis Fontein and Roodewal stations were frequently fog bound, which led to the employment of the referring niche, — afterwards the weather improved. The angles at this station were measured by Mr. Maclear, between the 23rd and 30th of March, 1847. Kamies- Sector Berg Station. 41. Kamies-Sector Berg Station. This station has been described at page 407. On detecting the outline of Louis Fontein Berg, through a gap in the " Welcome Curtain," the signalman who was left to flash an heliostat light along its top, inadvertently took up a position which is masked from Bokkeveld's Berg by the south-east group of rocks, and from Roodewal Bay by the opposite one. From this position he directed a steady light on being answered from Louis Fontein, which Mr. Smyth, who was on the look-out there, connected with the Bokkeveld station. The point thus inadvertently taken up is termed the " theodolite " station in the field-books, but more correctly since, the " azimuth point ;" the operations performed there were as follows : DoUond's repeating theodolite having been centered over the point, and made to bisect a meridian mark, viz. : a disc 14 inches in diameter, painted on the nearly vertical face of a rock to the south, in the " Welcome " range, distant about seven miles ; the 30-inch transit instrument, resting upon a block of granite of about two tons weight, was placed 26 feet 3 inches south of the repeating instrument, and by means of the latter as a collimator, the optical axis was brought to coincide with the line joining the " azimuth point " and meridian disc. The transit instrument served for determining the error in azimuth of the disc by astronomical observation. The angle between the disc and the Louis Fontein station point was measured after wards with the Fuller theodolite, and found to be 10-34-44-96 ; and between the disc and the " west rock " station point (to be mentioned presently) 306-54-32, reckoning from that station in the order of increasing readings through north, east, to south. No other angles were measured at " point azimuth," nor light reflected from it, except to Louis Fontein and Eland's Hoogte, and if the light had been given from the " west rock " angle OBSERVED HORIZONTAL ANGLES. 469 point, the angles at Louis Fontein would have been greater by 2'19''44 and 2-17-42 Kamies- respectively. A square building of dry stone, 12 x 12 feet inside area, the walls 3 feet station-Ccon- thick and 8 feet high, was erected (but not roofed), wherein pendulum experiments '""" were intended to be made : " azimuth point " is in the middle of the floor of this building, marked by a cylinder of lead let into the rock, with a brass pin inserted in its center. The second station is that of the zenith sector, the spindle of which was 21 feet 3 inches west of " azimuth point," and 5|- inches more southerly. The third is the " west rock," or real theodolite station. This rock is the southernmost and the larger of two huge granite blocks, resting near together, — the chief of the group that interrupted the line of sight between " azimuth point " and Roodewal Bay. The angle point, marked as usual, is in the middle, at the bottom of a natural channel which runs across the rock, and is distant 210 feet from "azimuth point," — and the angular distance be- tween the latter and Bokkeveld's Berg station, viz.: the angle of direction (y) is 74"38"4b. The Fuller and the Beaufort theodolites were consecutively centered over the " west rock " point, and the heliostat lights to the several distant stations (with the exceptions before specified) were shewn from it ; it should, therefore, be regarded as the Kamies- Sector Berg trigonometric or angle point, although for a particular purpose it may be necessary to refer the angles to " azimuth point." The follovdng table exhibits the calcu- lation of the reductions : — Calculation of the reductions from the "West Mock" angle point to "Azimuth point." (2\ feet 3 inches east, and 5|- inches north of the Zenith Sector spindle). r ==210 feet. log. . ^ „ = log. r" = 7-6366444. ^ sme 1" ^ (-y), the angle of direction is reckoned from "azimuth point" towards the right. STATIONS. r Log. r" sine y. Log, Distance. Log. Reduction. Reduction, Boschluis Keibiskow .Bokkeveld's Berg. .. Eland's Hoogte Meridian Disc Louis Fontein Roodewal VoQ-el Klin 1 II 0-18 -55 51- 6-39 74-38-40 106-10-27 116- 4-14 126-52-32 187-45-29 273-41-10 321-57-20 327-10- 4 5-3772129 7-5278260 7-6208571 7-6191053 7-5900433 7-5397022 6-7669468 7-6357450 7-4264172 7-3707886 5-4763866 5-6231340 5-5861267 5-4810443 5-3953179 5-3546493 5-3634221 5-4000914 5-4170639 9-9008263 1-9046920 2-0347304 2-1380610 2-1443843 1-4122975 2-2723229 2-0263258 1-9537247 + "0-796 + 80-296 + 108-325 -t- 137 -424 + 139-439 - 25-840 -187-208 -106-249 - 89-893 Koe Berg North Sector Station, Bushman Flat. . . . The total reduction for any angle is found by subtracting, algebraically, the reduction for the left hand station from the reduction for the right hand station. The angle of direction (y) for the left hand station is always less than for the right. 470 VERIFICATION AND EXTENSION OP LA CAILLE'S ARC OF THE MERIDIAN. § 3. The following table exhibits the observed angles at the West Rock station, and the Sector Berg same reduced to the Azimuth point : also the two angles observed at the latter : — Station-Ceon- tinued.) NAMES OP SIGNALS AND STATIONS. u "J Horizontal Angles observed at the "West Rock Station. Reduction to Point Azimuth. Horizontal Angles observed at, or reduced to, Point Azimuth. No. of Observa- tions. Weights and Partial Means. BEI Keibiskow, heliostat Bokkeveld's Berg, heliost »i »» « ,» )» »» Eland's Hoogte, heliostat Louis Fontein, heliostat. Eoodewal, heliostat Vogel Klip, heliostat Koe Berg, heliostat Boschluis heliostat WEEN and Bokkeveld's Berg, hel. and Louis Fontein, heliost. and Eland's Hoogte, hel.... B F F F F B B B B B B B B B P F F F / // 23-32- 1-98 52-13-51-85 31-31-47-12 41-25-31-18 9-53-45-18 60-52-57-67 85-55-40-91 48-16-11-61 53-28-54-50 213-11-21-42 38-21-37-52 50-47-44-32 50- 7- 4-90 25- 7- 1-40 116- 4-13-87 74-38-39-63 + 28-03 + 31-11 + 29-10 -165-28 -161-37 + 80-96 + 97-32 +326-65 + 107-05 + 79-50 o / « 23-32-30-01 52-14-22-96 31-32-16-22 60-50-12-39 85-52-59-54 48-17-32-57 53-30-31-82 213-16-48-07 38-23-24-57 50-49- 3-82 306-54-39-20 10-34-44-96 260 160 140 160 160 400 312 150 600 200 100 378 5 5 8 8 4 160 131-99 80-00 70-00 80-00 80-00 120-13 189-32 16-20 102-42 30-96 15-36 49-29 4-00 4-00 2-00 80-00 and „ „ and Eoodewal, heliostat.... and Vogel Klip, heliostat.. and Koe Berg, heliostat.... and North End, heliostat... and Louis Fontein, heliost. and Boschluis, heliostat... and Keibiskow, heliostat... and Institution Berg, pile.. . and Vogel Klip, heliostat.. . and Meridian disc Ezel's Kop, heliostat Institution Berg, pile Azimuth point West Rock Station and Bokkeveld's Berg, hel. and Louis Fontein, heliost. . and „ „ „ Meridian disc The observations at this station were made by the following persons : those with the Fuller theodolite by Mr. Smyth. The greater part of those with the Beaufort theodolite by Mr. Maclear, the remainder by Mr. Montagu. The observations for latitude, with Bradley's seetor, by Mr, Maclear. The observations for azimuth by Mr. Maclear. 42. Keibiskow Station. Keibiskow Station. Keibiskow is the remarkable conical-shaped high mountain, which is conspicuous for a long distance from all directions on the north-west frontier. It is nearly 80 miles south-eastward from the Kamies-Sector Berg, and the only elevation, within that distance, that commands a view of the Bushman Flat to the north, and of the Bokkeveld's Berg to the southward, — strictly speaking, it commands only the eastern part of the flat. " The station point is covered by a four feet pile, which is surrounded by a stone house, five feet six inches in height. Leaden plugs, each carrying a brass pin, and secured by a small pile, are laid down for the direction of Kamies Berg, Boschluis, and Bokkeveld's Berg. The position of the station would not allow of a plug being fixed for Klip Rug." * The north station is the theodolite point in the Bushman Flat, close to the Zenith Sector station there, OBSERVED PIORIZONTAL ANGLES. 471 The Fuller theodolite was centered OA'er the station point. § 3. ^ Keibiskow Observed jj^ ^^ No. of Station-fpon- NAMES or STATIONS AND SIGNALS. Horizontal Measures ^^^^^^ tinned ). Angles. Means. BETWEEN Bokkeveld's Berg, heliostat and Kamies-Sector B., hel. 6°6-3'9-14-81 158 62 Kamies-Sector Berg, hel.. and Boschluis, heliostat. .. 45'12"25"49 68 34 Boschluis, heliostat and Bokkeveld's Berg, hel. 248- 8-16-98 100 50 Klip Rug, heliostat and „ „ „ 48-46-11-18 86 40 „ „ kop and „ „ „ 50-16-10-05 20 10 Hantam Berg and Klip Rug 44- 0-58-60 1 Spion Berg and „ „ 64-21- 7-90 1 The observations at this station were made by Messrs. Campion and Montagu, between December 15, 1846, and January 26, 1847. 43. VoGEL Klip Station. Vogel Klip is one of the granite elevations of the range, extending north-westward vogei Kiip from the Kamies Berg, situated in the neighbourhood of the most valuable of the copper mines. The Roodewal station is visible through a narrow cleft, or kloof, in the mountains, about 10 miles to south; in the opposite direction, mountains prevent a view of the Bushman Flat further to the north than the line to Koe Berg prolonged. The top is naked granite, and the point is masked, as usual, by a cylinder of lead and brass pin ; also " leaden plugs, each carrying a brass pin and covered with piles six feet in height, are laid down for the direction of all the stations observed from the point, viz. : Koe Berg, North End, Kamies-Sector Berg, and Roodewal. After the measure- ment of the angles, a stone pile, 15 feet in height, twelve feet at the Base and three and a half at the top, was erected over the station point." The Fuller theodolite was centered over the station point. Observed f, „ No. of NAMES OF STATIONS AND SIGNALS. Horizontal Mpa'siirea Partial Angles. jjiv-asuico. jieans. BETWEEN O / * North End Station, helios. and Kamies-Sector B., hel. 70-14-25-17 120 60 „ „ „ „ and Ezel's Kop, pile 75- 8-25-87 20 10 Ezel's Kop, pile and Roodewal, heliostat. . . 41 •29- 8-36 20 10 Kamies-Sector Berg, hel... and „ „ 46-23- 9-92 80 40 „ „ and Ezel's Kop, pile 4-54- 3-62 30 15 Koe Berg, heliostat and Kamies-Sector B., hel. 7M7- 6-58 80 40 „ „ „ and North End Station, hel. 1- 2-40-95 120 60 „ „ „ and Ezel's Kop, pile 76-1 1- 7-32 20 10 Roodewal, heliostat and North End Station, hel. 243-22-25-32 120 60 472 VERIFICATION AND EXTENSION OF LA CAILLE'S ARC OF THE MERIDIAN. 44. BoscHLuis Station, Bushman Flat. §3- . The position of this station is on the most westerly part of the Bushman Flat, from station, Bush- whence the top of Keibiskow is visible above the horizon, during: the hours of maximum man Flat. ^ . refraction. It is upon a gentle swell, about 12 miles distant from an extensive salt pan, or rather series of salt pans, which are fed by a fountain of brackish water that issues from the ground, and bears the name, in Dutch, of a disagreeable insect. The soil at the station is deep brown sand, covered with tufts of " Bushman grass," which is said to grow luxuriantly after thunder showers. Making due allowance for this relief to the eye, it is difficult to conceive anything more dreary or depressing to the spirits than the monotonous aspect of this desert flat, — without water, shelter, or resource of any description. The station was occupied from the 5th to the 12th of January, 1847, with the Beaufort theodolite, and from the 26th to the 29th of June, with the Fuller theodolite. During the former, the thermometer sheltered from the sun by a wagon, was rarely below 100° in the middle of the day, sometimes 105°. The station point is marked by a wooden picket, carrying a brass pin, which was left covered with a mound of sand. Beaufort Observed jj » NAMES OF STATIONS AND SIGNALS. Or Fuller Horizontal Mpasures ^^isbts. Theodolite. Angles. measures. BETWEEN Keibiskow, heliostat and Kamies-Sector B.,hel. B °84' d'l2-94 200 59-4 Kamies-Sector Berg, hel. and Koe Berg, heliostat. . F 56-40'51-88 60 30-0 Koe Berg, heliostat and Kamies-Sector B., hel. F 303-19-10-48 20 10-0 The measures with the Beaufort theodolite by Mr. Maclear, those with the Fuller theodolite by Mr. Campion. 45. KoE Berg Station, Bushman Flat. Koe Berg ^^^ Station is on a low mountain, apparently composed of quartz, — the middle and manFTaf"^*"' *^^ highest of an irregular group, situated in a gentle depression of the flat, and distant north-easterly about 25 miles from Riet Fontein. It was taken up from necessity, in order to connect Boschluis with the north station. The Beaufort theodolite was centered over the station point. Obseived ij „ NAMES OF STATIONS AND SIGNALS. Horizontal HI Weights. Angles. Measures. BETWEEN Kamies-Sector Berg, hel... and Vogel Klip, heliostat. . 60-2'6-55"66 200 75-26 Vogel Klip, heliostat and Kamies-Sector B., hel. 299-33- 4-63 200 40-29 Kamies-Sector Berg, hel... and Vogel Klip, heliostat. . 60-26-58-38 56 5-62 „ „ and Ezel's Kop, pile 3-38-22-55 20 OBSERVED HORIZONTAL ANGLES. 473 Ezel's Kop, pile and Vogel Klip, heliostat. . 56-48-34-45 10 § 3. Vogel Klip, heliostat and North End, pole 189-14-54-83 40 26-41 station,Bush- *North End, pole and Boschluis, heliostat. . . 25-20-23-62 30 6-08 T^mtin^. *Boschluis, heliostat and Kamies-Sector B., hel. 84-57-46-23 50 50-85 North end of a small Base and South end of small Base 36-20-31-20 10 South do. do. and Kamies-Sector B., hel. 82-37-43-45 10 The above angles were measured by Mr. Maclear, excepting the two marked with an asterisk, which were measured by Mr. Montagu. 46. North End Station, Bushman Flat. This station is the north termination of the Arc : it is on a gentle swell of the Flat, North End distant about 4*8 miles east of Koe Berg. The angle at Koe Berg, between it and man Fiat. Kamies-Sector Berg, "West Rock" station, is 110-18-9-9; the angle at the north end, between Kamies-Sector Berg, "West Rock" station, and Koe Berg, is 64-29-12. The soil is loose limestone covered with sand, resting on granite, — the common base of this extensive plain. As there was no bush to be had for constructing a ring fence round the sector-tent, a circular pit, 30 feet in diameter, was cut through the limestone to the depth of about six feet, into which the lower part of the tent tripod was sunk, and there firmly jammed. The distance between the spindle (vertical axis) of the sector and the theodolite point was 35 feet 4 inches, the former east of, and on the parallel of the latter. The Beaufort theodolite was centered over the angle point. Observed -^^ ^^ NAMES OF STATIONS AND SIGNALS. Horizontal Measures ^^^8^*^- Angles. BETWEEN O / // Kamies-SectorB.,W.R.,h. and Vogel Klip, heliostat.. 56-16-53-40 500 223-83 Vogel Klip, heliostat and Kamies-Sec.B.,W.R.,h. 303-43-6-60 500 371-49 Kamies-Sector B., W.R.,h. and Ezel's Kop, pile 3-15-53-88 50 8-39 Ezel's Kop, pile and Vogel Klip, pile 53- 0-59-32 70 14-69 Vogel Klip, heliostat and Koe Berg, pole 8-12-18-58 60 109-20 Of the operations at this station : the above angles were measured by Mr. Maclear, Mr. Montagu made a few observations for azimuth, with the 30-inch transit instrument. A large portion of the observations for latitude, with Bradley's sector, were made by Mr. Maclear and Mr. Montagu conjointly, the remainder were made by Mr. Montagu alone. ABSTRACT HORIZONTAL ANGLES OBSERVED THE SEVERAL STATIONS, CORRECTED (WHERE NECESSARY) SO AS TO SATISFY THE RELATIONS SUBSISTING AMONG THE INDEPENDENT MEASURES. Note. — The Angles which are numbered ate those actually employed in the formation of the equations of Condition. The numeration commences at the Base-line. u 476 VERIFICATION AND EXTENSION OP LA CAILLE'S ARC OF THE MERIDIAN. §4. West end of Base. East end of STATION. West end of Base. East end of Base. 21 Kapoc Berg. Klip Pontein, Centre Berg. Kapoc Berg. Klip Fontein, Centre Berg. 20 OBSEBTED STATION POINTS. East end and Kapoc Berg „ „ and K. F. Centre Berg. . . For other Angles measured at this Station, see page 451. 19 22 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 Kapoc Berg and West end Drie Fontein and K. F. Centre Berg. . Riebeek's Kasteel and Kapoc Berg West end and K. F. Centre Berg. . Zwart Berg and Drie Fontein ,, „ and Riebeek's Kasteel .. . Por other Angles measured at this Station, see page 451. 101-28-48-56 77-32-12-82 44-53-24-99 63- 7-21 -43 93-29-48-40 62- 58 -29 -91 86-35-55-16 74-18-35-66 East end and Kapitein's Kloof and Patrys Berg and „ „ and Piket Berg. and Riebeek's Kasteel and „ „ and „ „ and „ „ and Sneeuw Kep and „ „ and West end and Winter Berg and Zwart Berg and Patrys Berg and King's Battery and Winter Berg and Riebeek's Kasteel and „ „ and Simon's Berg and „ „ and Royal Observatory .... and „ „ and Table Mountain and Bradley's Sector and La Caille's Granary. . . and J) jj ,, and Riebeek's Kasteel Winter Berg Zwart Berg Kapitein's Kloof Riebeek's Kasteel Simon's Berg King's Battery Royal Observatory .... Rogge Bay King's Battery Royal Observatory .... East end Sneeuw Kep Riebeek's Kasteel Piket Berg Table Mountain Riebeek's Kasteel Table Mountain Sneeuw Kep La Caille's Observatory Royal Observatory .... Table Mountain Winter Berg La Caille's Observatory Riebeek's Kasteel Bradley's Sector. For other Angles measured at this Station, see page 449. East end and Drie Fontein . West end and East end For other Angles measured at this Station see page 451. 52 •39- 15- 51 59-52- 60 10-16- 38 55-59- 69 21-31- 57 3-45- 95 53-41 • 93 20•23• 98 13-19- 33 .30 •39- 30 57-20- 33 37-47- 77 53-57- 46 16-30- 37 5-15- 2 20-59- 15 30-55- 98 14-41 • 62 23- 2- 41 11-35- 36 16-37- 4 54-18- 251 8-41- 0-39- 73 60-56- 73 53- 13- 2-16- -42 •57 -09 •05 -06 -96 -99 -15 -23 -75 •91 •12 •41 •70 •73 •54 •17 -53 -24 •39 -19 •38 -68 -82 •78 •19 •41 66^11- ©•07 39 ■29^ 18^20 Weight divided by 10. 42 5^3 4 10 8 1 4 1 6^8 5^9 4^3 4.7 4-2 5^8 7^5 6^0 3^2 3 3 1 3 1 1 4 5 2 5 3 3 9 1 1 1 1 74J 4-4 4^6 h S ABSTRACT OF THE HORIZONTAL ANGLES, 477 STATION. 1^ OBSERTED STATION POINTS. ANGLES. Weight divided by 10. Drie Fontein. 24 25 26 East end and Zwart T^pvo* / // 48^43^36-35 50-41 •3963 3-5 3-6 K. F. Contra Berg and East end Riebeek's Kas- teel. 23 27 28 29 30 31 32 33 Kaooc Berff and East end. 33-50-58-30 80-32-39-36 43- 2-26-42 51- 8- 7-28 52- 9-37-84 48-13-12-81 85-50-32-38 76-53-24-72 76- 6-18-13 76- 5-39-47 0- 0-38^66 7-9 2-7 7-5 4-8 4-8 4-6 3-6 7-7 4-1 3-25 2-3 „ „ and Piket Berg East end and Zwart Bero- King's Batteiy and Kapoc Berg Royal Observatory and „ „ Rogge Bay and „ Simon's Berg and „ „ Kapoc Berg and Zwart Berg „ „ and Bradley's Sector Station „ ,, and La Caille's Granary. . . . La Caille's Granary . . . and Bradley's Sector Station For other Angles measured at this Station, see page 453. Zwart Berg. 25 34 35 36 37 38 Kapoc Berg and Patrys Berg 78-49- 2-39 44-40-29-04 51- 8- 7-38 56-50- 8-85 62-38-59-93 3-8 3-2 3-6 5-7 4-6 Drie Fontein and East end Patrys Berg and Piket Berg Riebeek's Kasteel and Kapoc Berg J J ,, and East end Por other Angles measured at this Station, see page 454. Patrys Berg. 30 39 40 41 42 Filand'^ Berp* and Piket Berp* 44-48-35-40 40-49-18-04 41- 0-47-77 78 -40- 51 -71 4-0 3 6 7-9 5-1 T*ilfpf Tipro" and Zwart Bero* Zxvart TJpro* . . . and Kanoc Berei* Kapitein's Kloof and „ „ For other Angles measured at this Station, see page 459. Piket Berg. 27 43 44 45 46 47 48 49 TTflnnp Rprcr and T'atrvs TJprc 61- 4-47-83 83-57-3508 52-20-33-03 55- 1- 4-58 26-57-13-26 30- 5-58-55 88- 2-38-53 145- 2-22-91 81-58-17-84 29-37-44-81 162-37- 406 106- 1-28-55 132-59-19-25 14-0 13-0 12-6 7-5 5-0 3-9 6-1 7-0 7-6 5-9 Patrys Berg and Eland's Berg Eland's Berg and Lambert's Hoek Berg. . Heerenlogement's Berg and Ceder Berg Eland's Berg and Heerenlogement's Berg Riebeek's Kasteel and Kapoc Berg Zwart Berg and Patrys Berg Kapoc Berg and Eland's Berg Eland's Berg and Ceder Berg Lambert's Hoek Berg. . and Ceder Berg „ „ „ and Kapoc Berg Ceder Berg and Zwart Berg and Kanoc Bere* §4. l)rie Fontein. Riebeek'i Kasteel. Zwart Berg, Patrys Berg. Piket Berg. 478 VERIFICATION AND EXTENSION OF LA CAILLE'S ARC OF THE MERIDIAN. § i Piket Berg—; (continued). Kapitein's Kloot Eland's Berg. Lambert's Hoek Berg. Ceder Berg. STATION. ■Si 1 I 1 1 OBSEEVED STATION POINTS. ] ANGLES. 1 Weight divided by 10. The following Angles were omitted at page 457 for the reasons there assigned; but they are introduced here, as they enter into the combinations from which the preceding are deduced. Piket Berg— (continued). 27 Eland's Bero- and Tafel Ber" o / » 135-30-48-28 83-10-15-70 95-12- 1-32 53-32-31-15 G5-34-16-97 79-26-47-79 140-31-35-43 128-29-49-21 67-25- 2-74 37-19- 3-45 4-0 6-0 6-0 6-0 4-0 6-0 2-0 2-0 6-0 2-0 Lambert's Hoek Berg. . and „ „ „ „ „ and Western Point „ „ and Western Point Tafel Berg and Kapoc Berg „ „ and Pah-ys Berg. Western Point and „ ,, „ „ and Kapoc Ber? „ „ and RJebeek's ;^asteel For other Angles measured at this Station, see page 457. Kapitein's Kloof. 28 50 51 52 53 Kanof' Bero" . and Patrvs Berer 62-23-20-32 74-43- 2-58 54- 2-22-86 62-40-54-74 31-45-16-27 30-55-38-47 106-10-19-50 9-5 9-5 9-5 4-75 9-5 9-5 7-6 Ceder Berg and Winter Berg TTppTprjlrtn-prnpnt's Rerpr and Ceder Berc'. W^intpp Bero* and Kaooc Berff. ... - „ „ and Riebeek's Kasteel Riebeek's Kasteel and Kapoc Berg. Patrys Berg and Heerenlogemenf s Berg. For other Angles measured at this Station, see page 457. Eknd's Berg. 31 54 55 56 57 Ceder Bertr and Piket Bero^ 62-43-30-27 58-41-16-52 63-43-19-48 51-13-56-10 67-45-33-23 11-1 9-3 10-5 5-8 8-6 Heerenlogement's Berg, and Lambert's Hoek Berg. . „ „ and Ceder Berg Piket Berg and Patiys Berg Lambert's Hoek Berg. . and Piket Berg. For other Angles measured at this Station, see page 460. Lambert's Hoek Berg. 32 58 59 Eland's Berg and Heerenlogement's Berg. Piket Berg and Eland's Berg 65-47- 8-45 59-53-53-79 10-5 8-2 For other Angles measured at this Station, see page 460. Ceder Bei^. 33 60 61 62 63 Kapitein's Kloof and Heerenlogement's Berg. Piket Berg and Eland's Berg „ „ and Heerenlogement's Berg. Winter Bero- and Kapitein's Kloof. 73-31 ^i-g? 35-18-16-07 70-57-46-03 53- 2-11-23 166-42-35-38 35-39-29-96 66-43-28-42 5-8 4-3 3-4 7-25 4-7 8-8 6-4 Klip Ruw and Winter Berg Eland's Berg. and Heerenlogement's Berg. Heerenlogement's Berg, and Klip Rug For other Angles measured at this Station, see page 461. ABSTRACT OF THE HORIZONTAL ANGLES. 479 STATION. 1^ OBSERVED STATION POINTS. ANGLES. Weight divided by 10. Heerenloge- ment's Berg. 34 64 65 66 67 68 69 70 71 72 73 CederBerg and Eland's Berg ), „ and Kapitein's Kloof „ „ and Piket Berg Eland's Hoogte and Bokkeveld's Berg Louis Fontein and „ „ Lambert's Hoek Berg. . and Eland's Berg Eland's Berg and Louis Fontein Bokkeveld's Berg and Klip Rug O / ft 80-37-17-26 52-26- 6-12 54- 1-2007 37-51-30-32 49-50-58-75 55-31-38-25 123-34-58-55 41-56-14-81 64- 0-30-63 9-3 4-0 3-0 50 7-1 5-0 5 5 7-0 7-0 Klip Rug and Ceder Berg For other Angles measured at this Station, see page 463. Bokkeveld's Berg. 36 Heerenlogement's Berg, and Louis Fontein „ „ and Eland's Hoogte Louis Fontein and Kamies Berg Kamies-Sector Berg. . . and Keibiskow Louis Fontein and Kamies-Sector Berg. . . Klip Rug and Heerenlogement's Berg. Eland's Hoogte and Kamies-Sector Berg . . . Keibiskow and KHd Rue* 76- 9-45-54 65- 6-28-41 40- 3-24-30 89-48-56-78 40- 3-24-30 57-53-47-19 51 6-41-43 96- 4. 6 19 10-0 10-0 10-7 13-4 10-7 100 10-7 6-6 For other Angles measured at this Station, see page 464. Klip Rug. 35 Ceder Berg and Heerenlogemenf s Berg. Heerenlogement's Berg, and Bokkeveld's Berg For other Angles measured at this Station, see page 464. 49-16-13-36 80-10-11-32 10-0 10-0 Eland's Hoogte. 38 74 75 76 77 78 79 Bokkeveld's Berg and Heerenlogement's Berg. Kamies-Sector Berg. . . and Bokkeveld's Berg For other Angles measured at this Station, see page 466. 77- 2-14-75 97-21-48-60 9-3 9-0 Louis Fontein. 37 Bokkeveld's Berg and Heerenlogement's Berg. Kamies-Sector Berg. . . and Bokkeveld's Berg Roode Wal and Ezel's Kop „ „ and Kamies-Sector Berg. . . Ezel's Kop and „ „ „ For other Angles measured at this Station, see page 465. 53-59-39-22 87-43- 1-61 50-30- 1-76 54-59-16-63 4-29-14-87 120 120 7-2 14-2 9-6 Keibiskow. 42 80 81 Bokkeveld's Berg and Kamies-Sector Berg. . . Kamies-Sector Berg. . . and Boschluis Boschluis and Bokkeveld's Berg ) Supplementary Angle ) Klip Rug and Bokkeveld's Berg For other Angles measured at this Station, see page 471. 66-39-15-48 45-12-26-71 248- 8-17-81 48-46-11 18 8-2 6-2 7-2 4-0 §4. Heerenloge- ment's Berg. Bokkeveld's Berg. KHp Rug. Eland's Hoogte. LouisFontein. Keibiskow. 480 ATERIPICATION AND EXTENSION OF LA CAILLE'S ARC OF THE MERIDIAN. §4. Eoode Wal. Ezel's Kop. Togel KUp. Kamies- Sector Berg. Koe Berg. STATIOir. +3 6 OBSEEVED STATION POINTS. ANGLES. Weight divided by 10. Roode Wal. 39 82 83 84 85 86 Kamies-Sector Berg. . . and Louis Fontein Voffel Klio and Ezel's Kon O 1 If 64- 7-56- 08 46-39-28-05 47-41-21-25 65- 9-49-28 1- 1-53-20 248-10-42-67 9-6 8-4 12-0 8-3 10-3 10-0 „ „ and Kamies-Sector Berg. . . Ezel's Kop and Louis Fontein „ „ and Kamies-Sector Berg . . . Louis Fontein and Vogel Klip 1 Supplementary Angle ) Ezel's Kop. 40 Louis Fontein and Roode Wal 64-20-17-25 91-51-34-35 203-48- 8-40 3-34 2-68 2-9 Roode Wal and Voerel KHd Vogel Klip and Louis Fontein 1 Supplementary Angle ) For other Angles measured at this Station, see page 468. Vogel Klip. 43 87 88 89 90 Ezel's KoD and Roode W^al 41-29- 7-83 46-23- 9-82 71-17- 6-15 70-14-25-00 75- 8-27-00 4-54- 1-99 1- 2-41-15 7611- 8-15 243-22-25-17 2-2 4-8 7-7 9-1 3-6 4-0 8-9 3-4 6-0 Kamies-Sector Berg. .. and „ „ Koe Berg and Kamies-Sector Berg. . . North end Station and „ „ „ „ „ ,, and Ezel's Kop Kamies-Sector Berg. . . and „ „ Koe Berg and North end Station „ „ and Ezel's Kop Roode Wal and North end Station . . . . ) Supplementary Angle J Kamies-Sector Berg. 41 91 92 93 94 95 96 97 98 99 Bokkeveld's Berg and Eland's Hoogte and Louis Fontein 31-31-46-71 52-13-51 45 50-47-43-66 38-21-35-41 23-32- 1-73 60-52-57-40 86-55-40-74 53-28-54-50 48-16- 9-61 41-25-31-63 9-53-44-82 11-0 8-0 4-93 1-54 13-2 12-0 18-9 10-24 1-62 11-7 11-7 Boschluis and Keibiskow Koe Berer and Boschluis , . Keibiskow and Bokkeveld's Berg Louis Fontein and Roode Wal Roode Wal and Vogel Klip Vogel Klip and North end Station „ „ and Koe Berg Bokkeveld's Berg and Meridian Mark Eland's Hoogte and „ „ Tor other Angles measured at this Station, see page 470. Koe Berg. 46 100 101 102 Boschluis and Kamies-Sector Berg. . . Kamies-Sector Berg . . . and Vogel Klip 84-57-46-23 60-26-55-66 170-45- 5-17 5-09 11-66 2-64 North end Station and „ „ For other Angles measured at this Station see page 472. ABSTRACT OF THE HORIZONTAL ANGLES 481 STATION. ^1 OBSBKVED StATION POINTS. ANGLES. Weight divided hy 10. North end Station. 46 103 104 Kamies Berg and Vogel Klip O / // 56-16-53-40 8-12-18-58 59-5 10-92 Vogel Klip and Koe Berg Tor other Angles measured at this Station, see page 473. Boschluis. 44 105 106 Kamies-Sector Berg. . . and Koe Berg Keibiskow and Kamies-Sector Berg. . . Tor other Angles measured at this Station, see page 472. 56-40-51-29 84- 012-94 4-0 5-94 8-2 2-25 9-8 7-5 Rogge Bay. 11 107 108 Kapoc Berg and Riebeek's Kasteel 33-33-35-14 50-58-58-02 16-54-38-53 16-38-56-61 Riebeek's Kasteel and Simon's Berg Kapoc Berg and Blaauw Berg Blaauw Berg and Riebeek's Kasteel Eor other Angles measured at this Station, see page 437. Royal Obser- vatory. 14 109 110 111 112 113 114 Blaauw Berg and Sneeuw Kop 103-38-51-57 34-30- 6-59 86-25-25-01 111- 3- 1-66 104-31-47-08 79-54-10-43 79- 1-14-92 5-5 12 7 1-6 5-3 2-6 2-5 2-0 Kapoc Berg and Riebeek's Kasteel „ „ and Simon's Berg „ ,, and Sneeuw Kop Simon's Berg and Zwart Berg Sneeuw Kop and „ „ Blaauw Berg and Simon's Berg For other Angles measured at this Station, see page 441. Blaauw Berg, Meridia,TiMark. 17 115 116 117 118 Sneeuw Kop and King's Battery „ „ and Cape Point „ „ and Royal Observatory „ „ and Zwart Kop Cape Point and Royal Observatory Royal Observatory and King's Battery For other Angles measured at this Station, see page 444. 61-36-22-89 54-33-53-43 55 -28 -34- 51 57-38-15-53 0-54-41-08 6- 7-48-38 1-9 5-2 4-5 1-54 7-4 1-7 Simon's Berg. 18 119 120 121 122 123 124 125 Cape Point and King's Battery Kapoc Berg and Riebeek's Kasteel 41-40-49-30 37- 5'45-63 59- 2 68 57-18- 3-07 91-23-47-49 31- 619-73 32-48-19-34 94-23-48-70 3- 0- 1-21 13-20- 8-23 1-41-59-61 81- 3-40-47 222-13-22-39 10-4 1-36 0-76 1-37 1-57 40-9 14-2 2-25 1-27 7-5 0-27 King's Battery and Kapoc Berg Royal Observatory and „ „ Rogge Bay and Riebeek's Kasteel Zwart Kop and King's Battery „ „ and Royal Observatory Royal Observatory and Riebeek's Kasteel „ „ and Tyger Berg King's Battery and Royal Observatory Tyger Berg and Riebeek's Kasteel Riebeek's Kasteel and Cape Point For other Angles measured at this Station, see page 446. §4- North end Station. Boschluis. Eogge Bay. Royal Observatory. Blaauw Berg, Meridian Mark. Simon's Berg. 482 VERIFICATION AND EXTENSION OP LA CAILLE'S ARC OP THE MERIDIAN. § 4. King's Battery. Sneeuw Kop, H.H. Winter Berg. STATION. +3^ OBSBKTED STATION POINTS. ANGLES Weight divided by 10. King's Battery. 15 126 127 128 129 130 131 132 133 Kapoc Berg and Riebeek's Kasteel „ „ and Simon's Berg „ „ and Sneeuw Kop Blaauw Berg and „ „ Simon's Berg and Zwart Kop o / // 32-58-17-12 82-10-10-20 105-51-56-65 94-53-16-71 101-53-15-53 98-11-10-78 74-29-24-33 78-11-29 08 26-54-14-87 71-11-32-49 173- 4-48-02 21 -59- 37- 18 43-45-41-11 47-35- 9-46 51-1714-21 3-42- 4-75 10-58-39 94 51- 7-35-60 8-8 1-6 14-4 30-0 4-03 3-9 1-9 3-3 3-5 6-7 6-4 7-6 0-4 1-8 3-1 3-4 17-2 0-4 „ „ and Cape Point Sneeuw Kop and „ „ „ „ and Zwart Kop „ „ and Kogel Berg Blaauw Berg and Simon's Berg „ „ and Zwart Kop „ „ and Riebeek's Kasteel and Tvsrer Bere* Kogel Berg and Cape Point „ „ and Zwart Kop Cape Point and „ „ TCanop Bero- . . , and Blaauw Berer Tyger Berg and Sneeuw Kop Per other Angles measured at this Station, see page 442. Sneeuw Kop, H.H. 6 134 135 136 137 138 139 140 141 Cape Point and King's Battery „ „ and Blaauw Berg Kapoc Berg and Winter Berg Xino-'s Batterv .... and Kaooc BerfT 48 22-40-77 71-53- 6-36 46-56-49-07 40-37-30-22 37 59-42-13 20-52-37-50 34-16-13-77 36-54- 1-86 51-15-18-86 51- 0-28-86 45-55-29-66 89- 0-10-99 14- 6-27-00 66-25-38-81 82-43-45-27 29-50-41-18 47-50 21-70 48-25-68-29 37-44-52-13 67- 12-50 04 110- 5-54-13 84- 6-24-63 43- 4-41-33 16-9 2-9 10-5 14-2 14-2 3-5 12-0 12-0 13-0 16-9 13-0 19-8 12-0 5-3 11-9 6-3 4-0 3-0 13-0 11-9 6-1 10-5 13-0 Royal Observatory. . . . and ,, „ „ „ and Blaauw Berg Zwart Kop and King's Battery „ „ and Royal Observatory CaDe Point and Rofrere Bay „ „ and Royal Observatory „ „ and Table Mountain „ „ and Zwart Kop » „ . and Tyger Berg Danger Point and Cape Point Kogel Berg and „ „ „ and Noah's Arc Noah's Arc and Tyger Berg Rogge Bay and Kapoc Berg Zonder Einde Berg and Danger Point and KoQi-el Bero- Winter Berg and Zonder Einde Bero-. . . . Table Mountain and Kapoc Berg For other Angles measured at this Station, see page 431. Winter Berg. 29 142 143 144 Kapoc Berg and Kapitein's Kloof Kapitein's Kloof and Ceder Berg 65-19-23-84 52-15- 207 55- 9-32-39 187-16' 1-70 10-7 10-7 10-7 10-7 Sneeuw Kop and Kapoc Berg Ceder Berg and Sneeuw Kop For other Angles measured at this Station, see page 458. ABSTRACT OF THE HOKIZONTAL ANGLES. 483 STATION. "Si O 'ti 'CO 1^ OBSEKVED STATION POINTS. ANGLES. Weight divided hy 10. Zwart Kop. 9 14-5 146 147 148 149 150 151 152 King's Battery and Simon's Berg o / // 47- 0-29-13 67-32-2200 64-35-14-39 63-1] -52-22 42-39-39-33 4-20-29-78 2-37- 7-61 87-27-44-72 24-15-52-30 72-15-11-00 96-31- 3-50 5-5 5-5 11-1 6-8 3-0 6-7 3-6 2-4 2-0 2-0 1-0 !> „ and Siieeuw Kop BLiauw Borg and „ „ Royal Observatory and „ „ „ ,, and Simon's Berg King's Battery and Royal Observatory jj J, and BLiiiuw Berg Royal Observatory. . . . and Ko^el Berg Sneeuw Kop and ,f „ Table Mountain and S)ieeuw Kop „ „ and Kogel Berg For otlier Angles measured at tliis Btation, see page 435. Cape Point. 8 Blaauw Berg and Sneeuw Kop King's Battery^ and Simon's Bero- 53-33- 9-38 40- 8- 5-82 37- 8- 0-04 10-0 4-5 4-9 „ „ and Sneeuw Kop For ottier Anglos measured at this Station, see page 434. Kogel Berg. 7 Sneeuw Kop and Mudge Point Mudge Point and Zwart Kop Cape Point and „ „ „ „ and Table Mountain „ „ and King's Battery Zwart Kop and Tyer Bern- 104-33 36-91 143-17-23-25 20-53-23-53 64-36-30-42 57-47-38-89 55-50-35-90 40-13-17-00 78- 3-52-95 74-52-24-48 71-33-42-84 56 36-23-94 4-0 4-0 50 3-1 4-0 5-0 4-0 50 4-0 4-0 5-0 „ „ and Royal Observatory Table Mountain and Sneeuw Kop King's Battery and „ „ Royal Observatory. . . . and „ „ Tyger Berg and „ „ For other Anglos measured at this Station, see page 433. Zonder Einde Berg. 5 4 Cape L'Agulhas and Danger Point Danger Point and Sneeuw Kop „ „ and Babylon's Toren Babylon's Toren and Sneeuw Kop Pot Berg and Cape L'Agulhas 46- 8-41-22 35-24-46-03 24- 5- 7-08 31-19-38-95 52-36 44-32 205-49-48-43 7-2 7-3 5-4 4-2 6-2 3-9 Sneeuw Kon . . . a,nd Pot Bero" For otlior Angles measured at this Station, see page 430. Babylon's Toren. Kogel Berg and Sneeuw Kop Sneeuw Kop and Zonder Einde Berg. . . . Zonder Einde Berg. . . . and Danger Point Danger Point and Mudge Point Mudge Point and Kogel Berg For other Angles measured at this Station, see page 429. 33- 7-31-00 102-23-28-62 103-49-47-25 73-23-41-81 47-15-11-32 1-9 8-2 16-8 0-6 1-9 §4. Zwart Kop. Cape Point. Kogel Berg. Zonder Einde Berg. Babylons's Toren. 484 VERIFICATION AND EXTENSION OF LA CAILLE'S ARC OP THE MERIDIAN. §4. Tyger Berg. STATION. 1^ OBSEBVED STATION POINTS, ANGLES. "Weight divided by 10. Tyger Berg. 16 Sneeuw Kop and Cape Point „ „ and Naval Yard, clock tower „ „ and Naval Ya:rd Station „ „ and Table Mountain „ „ and Zwart Kop „ „ and King's Battery „ „ and Royal Observatory Kogel Berg and Cape Point „ „ and Zwart Kop Zwart Kop and Table Mountain Naval Yard, clock tower and King's Battery Royal Observatory and Blaauw Berg King's Battery and Robben Isld., ch. tower and Blaauw Berer , 70-24-47-40 82-28-57-15 82-31-50-20 in-10-58-92 77-31'19-09 110 -49 ■26- 73 109 -57 •57- 15- 42-37-30-61 49-44- 2-30 33-39-39-83 28-20-29-58 90- 7-21-06 63-49-21-09 89-15'51-48 53-27-48-90 35-26-30-39 159-54-41-79 1-24 32-4 1-91 0-74 1-87 3 60 1-21 159-0 0-57 2-03 2-38 1-41 20-3 O-30 Table Mountain and Robben Isld., ch. tower Robben Isld., ch. tower and Blaauw Berg Blaauw Berg and Sneeuw Kop ) Supplementary Angle j Por other Angles measured at this Station, see page 443. For La Caille's Observatory Station, see page 437. For the Cape Town Parade Station, see page 439. For the Klip Fontein Station, see page 454. For the L'Agulhas Station, see page 427. For the Danger Point Station, see page 427. For the Mudge Point Station, see page 428. For the Naval Yard Station, see page 436. INVESTIGATION OF THE COMECTIONS APPLIED TO THE NUMBERED ANGLES PRECEDING SECTION, so AS TO SATISFY THE GEOMETRICAL RELATIONS SUBSISTING AMONG THE DIFFERENT PARTS OF THE SYSTEM OF TRIANGLES. 486 VERIFICATION AND EXTENSION OP LA CAILLE'S ARC OP THE MERIDIAN. § ^- § 5. Investigation of the Corrections to be applied to the numbered Angles in THE preceding SeCTION, SO AS TO SATISFY THE GEOMETRICAL RELATIONS SUB- SISTING AMONG THE DIFFERENT PARTS OF THE SYSTEM OF TrIANGLES. The trianguktion of the Arc of the Meridian admits of being divided into two inde- pendent portions or figures, — viz., the series south of the side Heerenlogement's Berg, Ceder Berg ; and that north of tlie side Heerenlogement's Berg, Klip Rug. These two portions are separately discussed ; and as the several steps of the process are alike in each case, they are distinguished for convenience by the same symbols (A), (B), (C), &c. In the formation of the equations of condition, the numerical values of the angles are increased by indeterminate corrections a;,, X2, x^, ... &c., (which are distinguished from each other, by having the same numeral suffixed as that annexed to the angle in the pre- ceding section), and it is our object to determine these corrections so as to satisfy all the relations of the figure, as well as the condition that the sum of their squares shall be a minimum. The equations are separated into three classes, viz. : (A) Those depending on the condition that the sum of the angles of a geodetical triangle is equal to 1 80°, + the spherical excess ; (B) Those deduced from the relations subsisting among the observed angles at a station ; and (C) The equations arising from the geometrical relations of the figure. The formations of these equations is given in detail ; those of the class (A) perhaps require no further explanation here. The second class (B) are of an equally simple form, and are obtained by equating to 360°, the sum of the angles measured round the horizon at a station point ; or in cases wl lere an angle is made up by the sums or differences of two independent sets of angles, by equating the value given by one set to that given by the other. The third class (C) (called side equations by Bessel) are obtained in the fol- lowing manner. When in a system of triangles, the second has a side a in common with the first ; the third a side b in common with the second, and so on to the last, which has a side m in common with the first ; — if we form the identical equation : a b c m — X - X - X . . m a b " J and for the ratios —,-.... we substitute the ratios of the sines of the opposite angles ma (each angle being diminished by \ of the spherical excess of the triangle to which it belongs) an equation is obtained among the angles of the system. The readiest way of treating this class of equations is by logarithms. INVESTIGATION OF THE CORRECTIONS TO THE ANGLES. 487 For supposing a " side equation," to be represented by the following expression, § s. , sin. A,, sin. A3, sin. A5. sin. A2. sin. A4. sin. Ag. let the angles Aj, Aj, A3, . . . ., respectively receive a small increment ar,, x^, Xg,..,., then taking the logarithms of both sides, and remembering that the eifect of a small increase of x seconds in an angle (A), upon the logarithm of the sine of the angle is = M cotan. Ax sin. 1" very nearly, (M being the modulus) we obtain the equation = log. sine A^ + log. sine A3 + log. sine A5 — ^log. sine Aj, + log. sine A^ + log. sine Ag\ + m cot A, a;, + m cot A3 aSj + m cot A^ x^ — Cm cot Aj x^ + m cot A^ x^ + in cot Ag xA where m = M sine 1", or log. m = 1-32336 if we refer the co-efficients to the seventh decimal place of logarithms. In the calculation of the side equations, the eighth decimal place of the logarithms of the sines of the angles is given, but this is not correct in all cases. Tables exceeding seven places were not available when the computations were in progress. The equations of condition thus obtained are abstracted and exhibited in detail in the group (D), for each division of the triangulation separately ; and the succeeding steps, having reference to the determination of the numerical values of the corrections, may be shortly described as follows. Each equation 1, 2, 3, ... . is multiplied by an undetermined factor f\,fi,fi, • • ■ • then collecting and adding together the factors by which the like errors are multi- plied, with their respective signs and numerical co-efficients, and equating the sum to the same error multiplied by its weight, the system of equations, marked (E) ig obtained ; and by reduction, the values of x^, X2, x^,. . . . in terms of the factors fi, fi, fs,.... are deduced, as given in the group (F). The next step is to substitute these expressions for ar,, ajj, x^,.... in the equations of condition, and by this process we obtain a system of equations (G) from which we can ehminate the unknown quantitiesyi,/2j/3 The equations (G) for the second division of the work are given in full, as they involve only nineteen unknown quantities ; but in the first division they amount to 68, and occupy too great an area of paper to admit of being explicitly arranged. The next group (H) exhibits the logarithms of the values of/,,/2,/3, which are obtained by ehmination from the equations (G). Finally, substituting these values in the equations (F), the corrections Xi, x^, x^,. . . .are obtained. The preceding method of investigating the corrections is in accordance with that of Gauss and Bessel, as explained by Rosenberger, in Nos. 121, 122, of the Astronomische Nachrichten; and by Mr, Galloway, in the 15th volume of the Memoirs of the Royal Astronomical Society. 488 VEKIPICATIOlir AND EXTENSION OP LA CAILLE'S ARC OE THE MERIDIAN. U) Formation of the Eqimtions of Condition. south of the Side Ceder Berg— Heerenloge- ment's Berg. 0) • It STATION POINTS. ANGLES. EQUATIONS OP CONDITION. 1 KapocBerg East end of Base West end of Base Sum 180° + £. O / 1/ > 33-37-47-12+a;3„ V 44-53-24-99+a;3 yl01-28-48-55 + a;, 0=0"-119 + a;, + a;3+a;j„ 180- 0- 0-66 180- 0- 0-541 2 Riebeek's Kasteel East end of Base Kapoc Berg 33-50-58-30+a'^r , 93-29-48-40+a;, 52-39-15-42+a;5 0=0"-188 + a5, + a!,+a;„ Sum , . . 180° + £. 180- 0- 2-12 180- 0- 1-932 3 K. F. Contre Berg East end of Base West end of Base Sum 180° + £. V 39-29-18-20+a;24 X 62-58-29-91 +a!6 x77-32-12-82+£c. 0=0"-338 + a;, + x, + a;,, 180- 0- 0-93 180- 0- 0-592 4 Drie Fontein > 50-41-39-63+a;,6 > 63- 7-21-43 + a;, V 66-11- 0-07 + a;^ 0=0"-053 + aj,+a!^+a;^ East end of Base K. F. Contre Berg Sum 180°+£. 180- 0- 1-13 180- 0- 1-077 5 Zwart Berg East end of Base Drie Fontein / 44-40-29-04+a;35 v 86-35-55- 16 + a;, K 48-43-36-35+a;„ 0=-0"-973+x, + a;^ + a;3, Simi 180° + £. 180- 0- 0-55 180- 0- 1-523 /T~> 6 7 Riebeek's Kasteel Zwarfr Berg East end of Base Sum 180° +£. 43 2-26-42+a;« 62-38-59-93+a;3, . 74-18-35-66+a;, 0=-0!'-033+x^+x^+x^ 180- 0- 2-01 180- 0- 2-043 Kapoc Berg 46-16-30-70+a;« 56-50- 8-85+a;„ 76-53-24-72+a;„+a>,„ 0= 0" • 609 + !K» + «„ + a;^ + a," /7> Zwart Berg Riebeek's Kasteel Sum 180° +£. 180- 0- 4-27 180- 0- 3-661 INVESTIGATION OF THE CORRECTIONS TO THE ANGLES. 489 Formation of the Equations of Condition. ?! STATION POINTS. ANGLES. EQUATIONS OF CONDITION. 8 Piket Berg Kapoc Berg Riebeek's Kasteel Simi 180°+£. f II 30- 5-58-55+a!48 / 69-21 -31 -Oe+aj^ 80-32-39-36+a,-,, j 0= 0"- 956 +ic,3+ 35.3 +a!,3 • 180- 0- 8-97 180- 0- 8-014 9 Patrvs Bersr 41- 0-47-77 + aj« 78-49- 2-39+a;3, 60-10-16-09+a!„ 0=-l"-394+aj„+x3.+x,, Zwart Berg Kapoc Berg Sum 180° +£. 180- 0- 6-25 180- 0- 7-644 10 Patrys Berg 40'49-18-04+a;« 88- 2-38-53+a;,3 .51- 8- 7-38+a;3e 0=-V-2QQ+x^+x,,+x^ Piket Berg Zwart Berg Sum 180° + £. 180- 0- 3-95 180- 0- 6-246 11 Patrvs Berff 81-50- 5-81+a;4„+a;„ 37- 5-15-73+x,,— a;,3+a;22 61- 4-47-83+a;„ 0=0"-387+a!„-a;„+a;,,+a!,„+ar„+a;„ Kapoc Berg. Piket Berg Sum 180° +£. 180- 0- 9-37 180- 0- 8-983 12 13 Eland's Berg Piket Berg Patrys Berg Sum 180° +£. 51-13-56-10+a:„ 83-57-35-08+a;„ 44-48-35-40+a;3, 0=0"-959+ar3,+ar,,+x„ 180- 0- 6-58 180- 0- 5-621 Lambert's Hoek Eland's Berg Piket Berg Sum 180°+£. 59-53-53-79+a!59 67-45-33-23+a!54+a!56-a;« 52-20-3303 + a;« 0= -4"-277 + *45+a'„-««-f ««+a:5, 180- 0- 0-05 180- 0- 4-327 14 Heerenlogement's Berg. Eland's Berg Lambert's Hoek Sum 180°+ £. 55-31 -38-25+a;69 58-41-16-52+x« 65-47- 8-45+»5, 0=-0"-824+a5„+ar,3+ir«, 180- 0- 3-22 180- 0- 4-044 §5. (A) Xriangulation south of the side Ceder Berg — Heerenloge- ment's Berg. ^ 490 VERIFICATION AND EXTENSION OP LA CAILLE'S ARC OF THE MERIDIAN. §5. (A) Triangulation south of the side Ceder Berg — Heerenloge- ment's Berg. O Formation of the Equations of Condition. o a* STATION POIMTS. ANGLES. EQUATIONS OP CONDITION. 15 Heerenlogement's Berg. Eland's Berg Piket Berg Sum l80° + £. O f II 26-35-57-19+a;64— xee 126-26-49-75+a;a4+a!5e 26-57-13-26+a;„ 0= -^'•Q&)+x„^x^ + x^+x^-x^ 180- 0- 0-20 180- 0- 4-160 16 Ceder Berg Piket Berg Eland's Berg 35-18- 16-07 + Je6. 81-58-17-84+a;«+a!47 62-43-30-27+a;« 0=-3"-600+a:,, + x„+x^+x„ Sum 180° + £. 180- 0- 4-18 180- 0- 7-780 17 Ceder Berg Piket Berg Heerenlogement's Berg. Sum 70-67-46'03+a?6= 55- 1- 4-58+a;« 54- 1-20-07 + a!,, 0=-0"-88n+ar,,+x,,+a;„ 180- 0-10-68 180- 0-11-666 180° + £. 18 19 20 Kapitein's Kloof Patrys Berg KaDOc Berff 62-23-20-32+a;™ 78-40-5l-71 + a:« 38-55-59-05 + a;,, 0=l"-920 + a>„ + a!„ + a:«, Sum , 180° + £. 180- 0-11-08 180- 0- 9-160 Winter Berg Kapitein's Kloof KapocBerg Sum 180° +£. 65-19-23-84+a;,« 62-40-54-74+a;,3 51-59-52-57+«,<, 0=-l"-277+a!„+x,,+a!,„ 180- 0-11-15 180- 0-12-427 Ceder Berg Kapitein's Kloof. Winter Berg Sum 180° + e. 53- 2-ll-23 + a;e3 74-43- 2-58+a;,, 52-15- 2-07+a;„3 0=4"-320+x,,+x,3 + x„3 ■ 180- 0-15-88 180- 0-11-560 21 Heerenlogement's Berg. Kapitein's Kloof. Ceder Berg Sum 180° +£. 52-26- 6-12+a;a5 54- 2-22-86+a;« 73-31 -44-97+a;«, 0=2"-317+ir,,+x„+x„. 180- 0-13-95 180- 0-11-633 INVESTIGATION OF THE CORRECTIONS TO THE ANGLES. 491 Formation of the Eqmtions of Condition. II STATION POINTS. ANGLES. EQUATIONS OP CONDITION. 22 Rogge Bay Kaooc Bere* O / ir 33-33-35-14+a;,„ y 98-l.s-iP-9aj.„, 0=l"-367 + x„ + a^,, + a.,„ Riebeek's Kasteel Sum 180° + E. 48- 13-12-81+a;35 ISO- ISO- 0- 7-18 0- 5-813 23 Simon's Berg 91- 50- 37- 23-47-49+ir,53 58'58-02 + a;,„3 = - 1" - 541 - r,, + a;,3 + fl5,„, + .T,,3 Rogge Bay Riebeek's Kasteel Sum 180° + E. 180- 180 0- 5-08 0- 6-621 24 25 Simon's Berg KaDoc Berer 37- 57- 85- 5-45-63+a;,2„ 3-45-96+a;„ 50 -32 -38+ a;,. 0= -2"- 072 + aj„ + a;33 + «;,,„ Riebeek's Kasteel Sum 180° + £. 180- 180- 0- 3-97 0- 6-042 Royal Observatory. . . . Kapoc Berg 34- 93 52- 30- 6-59+a;„„ 20-23-15+a!,6 9-37-84+a;3, 0=l"-520+fl5„ + a;3, + a;„„ Riebeek's Kasteel Sum 180° + £. 180 180 0- 7-58 0- 6-060 26 Simon's Berg Royal Observatory KapocBerg Sum 180° + E. 57 86 36 18- 3-07 + a;,22 25-25-01+a;„, 16-37-19+a;,s-a;„ 0= -0"-669-J^, + a5,, + x,„+a;,^ 180 180 0- 5-27 0- 5-939 27 King's Battery Kapoc Berg Riebeek's Kasteel Sum 32 95 51 58-17-12+a;„6 53-41-99+a;,5 8- 7-28+a;3o = 0"194 + a;„ + a,3„ + a;,^ 180 180 • 0- 6-39 • 0- 6-196 180°+£. 28 Simon's Berg King's Battery Kapoc Berg Sum 180° +£. 59 0- 2-68 + a;,5, 82-10-10-20+!B,„ 38-49-56-03+a!,5-a-„ 0=2" -451 -a;,, + <»,, + 05,,, + a;,,, 180- 0- 8-91 180- 0- 6-459 §5. (A) Triangulation south of the Bide Ceder Berg— Heerenloge- ment's Berg. Al 492 VERIFICATION AND EXTENSION OP LA CAILLE'S ARC OP THE MERIDIAN. § 5. (A) Triangulation south of the side Ceder Berg— Heerenloge- ment's Berg. n r r r Formation of the Equations of "Jondition. STATION POINTS. ANGLES. EQUATIONS or CONDITION. 29 Sneeuw Kop Royal Observatory. . . . Kapoc Berg 37-59-42-13 + ic.3, 111- 3- l-66 + a^„, 30-57-20-9l + a;„ 0=-l"-900 + x„ + ^„, + ^,^^ Sum 180°+f. 180- 0- 4-70 180- 0- 6-600 30 31 32 33 Sneeuw Kop King's Battery Kapoc Berg 40-37-30-22 + a!.37 105-51-56-65 + a;„3 33-30-39-75 + a:„ 0=-0"-G48 + ^, + ^„, + x.„ 0=l"-930 + ^„ + jr„, + r,„ Sum 180° + £. 180- 0- 6 62 180- 0- 7-268 Sneeuw Kop Kapoc Berg 46-56-49-07 + a;,36 77 -53 -57 -41+ a;,, 55- 9-32-39 + a!,« Winter Berg Sum 180° + £. 180- 0-18-87 180- 016-934 Zwart Kop Royal Observatory. . . . Sneeuw Kop Sum 180° + £. 63-ll-52-22+a;ue 79-54-10-43 + a;,H 36-54- l-86 + a;,„ 0=0"-597 + a!„, + x,„ + x„. 180- 0- 4-51 180- 0- 3-913 Zwart Kop King's Battery Sneeuw Kop Sum 180° + £. 67-32-22-00 + ifu6 78-ll-29-08+a!,33 34-16- ]3-77 + !c,„ 0=l"-029 + z,33 + ^,„ + a;„, 180- 0- 4-85 180- 0- 3-821 34 Zwart Kop Royal Observatory .... Simon's Berg Sum 42-39-59-35 + a!H9 104-3I-47-08 + a!„3 32-48- 19-34+a!„, 0=2'-532 + :.„3 + x,, + ;.,. 180- 0- 5-77 180- 0- 3-238 180° + E, 35 Zwart Kop King's Battery Simon's Berg Sum X 47- 0-2913 + a;,« 101-53-15-63+a;,3„ 31- 6-19-73+a!„, 0=l"-094+x„, + a;.3„ + :r,„ 180- 0- 4-39 180- 0- 3-296 180° + e. INVESTIGATION OF THE COERECTIONS TO THE ANGLES. 493 ForToation of the Equations of Condition, si. STATION POINTS. ANGLES. EQUATIONS OP CONDITION. 36 Cape Point King's Battery Simon's Berg o / // 40- 8- 5-82 + a!,„ 98-ll-10-78+a;,3, 41-40-49-30 + x-,,, 0=I"-030 + x„ + x,3, + x,,, Sum 180° + £. 180- 0- 5-90 180- 0- 4-870 37 38 Cape Point 57- 8- 0-04 + a!,52 74-29-24-33 + !r,3, 48-22-40-77 + a;,3, 0=-0"-354 + x.3, + ^,3. + x„, King's Battery Sneeuw Kop Sum 180° + £. 180- 0- 5-14 180- 0- 5-494 Meridian Mark Royal Observatory .... Sneeuw Kop Sum 180° + £. 55-28-34-51+a;,,, 103-38-51-67 + a;,„, 20-52-37-50 + a!,33 0=l"-097+^™ + x.„ + a;„, 180- 0- 3-58 180- 0- 2-483 39 Meridian Mark King's Battery Sneeuw Kop Sum , 180^ + E. 61-36-22-89 + a;„5 94-53-16-71+a!,jg 23-30-25-69-a;,3^+a;,3, 0=2"-296 + x,, + x.,-x„. + x,3, 180- 0- 5-19 180- 0- 2 894 40 41 Meridian Mark Zwart Kop Sneeuw Kop Sum 180° + £. 67-38-15-53 + aJu8 64-35-14-39+a;,„ 57-46-39-36 + aj,3c,+a;„, 0=2"-777+a-„^+x,3, + x„, + x„, 180- 0- 9-28 180- 0- 6-503 Meridian Mark Cape Point Sneeuw Kop Sum 180° + £. 54-33-53-43 + a;„e X 53-33- 9-38 + a5,,o 71-53- 6-38 + a;,35 0=l"-257 + x„, + x,3,+x,,„ 180- 0- 9-17 180- 0- 7-913 § 5- (A) Triangulation south of the side Ceder Berg — Heerenloge- ment's Berg. 494 VERIFICATION AND EXTENSION OP LA CAILLE'S ARC OF THE MERIDIAN. (B) Triangulation south of the side Ceder Berg — Heerenloge- ment's Berg. Formation of the EqiuOions of Condition. Kapoc Berg Station. The Angle Patrys Berg and Royal Obsei-vatory is made up as follows :- Patrys Berg and Kapitein'sK. 38 • 55 • 59 • 05 + a;,, Kapitein'sK. and Winter Berg 51 • 59 • 52 • 57 + «,„ Winter Berg and Sneeuw Kop 77 • 53 • 57 • 41 + x^ Sneeuw Kop and Royal Obser. 30 • 57 • 20 • 91 + a;.. Sum 199-47- 9-94 Patrys Berg and Zwart Berg. 60-10-16-09 + a!,i Zwart Berg . and Riebeek's K. 46 • 16 • 30 • 70 + ar^j Riebeek's K. and Royal Obser. 93 • 20 • 23 • 15 + «,« Sum.. 199-47- 9-94 Hence we have: (42): 0=a;,„— a!„ + ar„— a!,5+a;,g+a;,,— as^. Angle : Riebeek's Kasteel and Sneeuw Kop. Riebeek's K. and King's Batr. 95 • 53 • 41 • 99 + x.^ Sneeuw Kop and „ „ 33-30-39-75+a!,j DiSerence 62-23- 2-24 Riebeek's K. and Royal Obser. 93 • 20 • 23 • 15 + as.j Sneeuw Kop and „ „ 30 -57 -20 -91+ a;,, Difference 62-23- 2-24 Hence we have: (43): 0=a;,5— a;,^— a!,g + a:,<| Simon's Bekg Station. Angle : King's Battery and Royal Observatory. King's Batr. and Kapoc Berg. 69- 0- 2'68+a;,j, Royal Obser. and „ „ 57-18' 3-07 H-a:,,^ Difference. 1-41 •59-61 Zwart Kop. . and King's Batr. 31 • 6 • 19 • 73 + x^ „ „ and Royal Obser. 32-48-19-34+a!„ Difference . 1-41-59-61 Hence: (44): 0=x,,^—x,^ + x,,—3 King's Battery Station. Angle : Cape Point and Zwart Kop. O / // Simon's Berg and Zwart Kop. . 101 • 53 • 15 • 53 + a;,, „ „ and Cape Point. 98-ll-10-78 + x,j Difference . 3-42- 4-75 Sneeuw Kop and Cape Point. 74'29"24*33+a;,3s „ „ and Zwart Kop.. 78-ll-29-08+a:,3, Difference . 3-42- 4-75 Hence: (45): 0=x^^-x,,,+x,,,-x,^ Angle : Simon's Berg and Sneeuw Kop. O / // Kapoc Berg, and Simon'sBerg 82 • 10 • 10 • 20 + a;,; „ „ and Sneeuw Kop 105 -51 "56 '65+ a;,. Difference 23-41 •46-45 Simon'sBerg and Zwart Kop. . 101 - 53 • 15 • 53 + x^o Sneeuw Kop and „ „ 78-ll-29-08+a!,33 Difference 23-41-46-45 Hence: (46): 0=a:,„-a-„3+a-,3„-a;,3 INVESTIGATION OF THE CORRECTIONS TO THE ANGLES. 495 Formation of the Eq^mtions of Condition. Sneeuw Kop Station. Angle : King's Battery and Royal Observatory. o / // Royal Obser. and Kapoc Berg. 37 • 59 • 42 • 13 + Xu^ King's Batr. and „ „ 40-37-30-22 + a;,3, Difference . 2-37-48-09 Zwart Kop. . and King's Batr. 34 • 16 • 13 • 77 + x,,,, „ ,, and Royal Obser. 36'54' 1-86 + 05,4, Difference . 2-37-48-09 Hence: (47) 0=x,^-x,^ + x,,,- 13s T "^140 "^Hl Angle : Cape Point and Blaauw Berg Meridian Mark . Cape Point and King's Battery 48 •22* 40 '77 + 05134 Zwart Kop and Royal Observatory. . . 36 •54- 186 + 35,4, Royal Observatory and Blaauvr Berg. 20 -52 -37 -50 + 05,39 Sum 106- 9-20-13 Zwart Kop and King's Battery 34- 16- 13 • 77 + x^ Difference 71-53- 6-36 Cape Point and Blaauw Berg 71 •53" 6'36 + a!,35 Hence: (48) 0=a!,34-a5,35+a!,3,-a!,4„+a;,4, Royal Observatory Station. Angle : Simon's Berg and Sneeuw Kop Kapoc Berg, and Simon'sBerg 86 • 25 • 25 • 01 + as,,, „ „ and Sneeuw Kop 111- 3" l'66 + a5„2 Difference 24-37-36-65 Simon'sBerg and Zwart Kop. . 104 • 31 • 47 • 08 + a5„ Sneeuw Kop and „ „ 79'54"10"43 + ar„ Difierence 24-37-36-65 Hence: (49) 0=a;„i— a;„5,+a;„3— a;,, Zwart Kop Station. Angle : Simon's Berg and Sneeuw Kop. O / // King's Batr. and Simon'sBerg 47- 0-29*13 + a;,45 „ „ and Sneeuw Kop 67-32-22-00 + a:,4e Difference 20-31 •52-87 Royal Obser. and Sneeuw Kop 63-ll-52-22+a;,48 „ „ and Simon'sBerg 42-39-59-35+a!,43 Difference 20-31-52-87 Hence: (50): 0=ix,^^—x,^^+x^^-x^^ §5. (B) Triangulation south of the side Ceder Berg — Heerenloge- ment's Berg. Bl 496 VERIFICATION AND EXTENSION OP LA CAILLE'S ARC OP THE MERIDIAN. §5. (C) Triangulation south of the side Ceder Berg — Heerenloge- ment's Berg. Formation of the Equations of Condition. In the quadrilateral EZRC we have the following : C R Z R E R X X =1 Z R E R C R Therefore : Sin. CZR. Sin. ZER. Sin. ECR. = 1 Sin. ZCR. Sin. EZR. Sin. CER. W.-West end ol- Base. E. . .East end of Base. Z...Zwart Berg. E. . .Riebeek's Kasteel. D...Drie Fontein. K...K.F.ContreBerg. C.Kapoc Berg. CALCULATION. CZR ZER ECR ZCR EZR CER ANGLES. 56-50- 8-85 74-18-35-66 52 SQ- 15-42 46-16-30-70 62-38-59-93 93-29-48-40 ANGLES — Jc. 1-220 0-681 0-643 1-220 0-681 0-643 56-50- 7-630 74-18-34-979 52-39-14 777 Sum. . 46-16-29-480 62-38-59-249 93-29-47-757 LOG. SINES. 9-9227788-8 9-9835080-0 9 -9003604 -3 9-8066473-1 9-8589363-6 9-9485180-7 9-9991907-5 9-8066451-8 CO-EPFICIENTS OP THE CORRECTIONS. 13-760 x„ 5-914 X, 16-066 X, 20-139 jcjs 10-891 X,, - 1-287 X, (51) : 0=21-3 + 1 •287rB,+5-914a;, + 16-066a!,-20-139a),, + 13-760a;„-10-891a!3. In the figure above we have -. WE EC CR ZR ZE DE KE -=1 EC CR ZR ZE DE KE WE Consequently : Sin. WCE. Sin. ERC. Sin. CZR. Sin. ZER. Sin. EDZ. Sin. EKD. Sin. EWK. =1 Sin. EWC. Sin. CER. Sin. ZCR. Sin. ERZ. Sin. EZD. Sin. EDK. Sin. WKE. mVESTIGATION OP THE CORRECTIOlSrS TO THE ANGLES. 497 Formation of the Equations of Condition. CALCULATIOJiT. ANGLES. 1- ANGLES— Je. LOG. SINES. CO-EFFICIENTS OF THE CORRECTIONS. WCE 33-37-47-12 0-180 33-37-46-940 9- 7433712-1 31-656 x^ ERC 33-50-58-30 0-643 33 50-57-657 9-74-58639-0 31-394 x^ CZR 56-50- 8-85 1-220 56-50- 7-630 9-9227788-8 13-760 x^ ZER 74-18-35-66 0-681 74-18-34-979 9-9835080-0 6-914 x. EDZ 48 43-36-35 0-508 48-43-35-842 9-8759698-2 18-480 x^ EKD 66-n 0-07 0-359 66-10-59-711 9-9613459-4 9-294 x^ EWK EWC 77-32-12-82 101-28-48-56 0-197 0-180 77-32-12-623 Sum: . 101-28-48-370 9-9896433-1 4:- 654 X, - 4-270 X, 9-2224810-6 9-9912233-5 CER 93-29-48-40 0-643 93-29-47-767 9-9991907-5 - 1-287 X, ZCR 46-16-30-70 1-220 4616-29-480 9-8589363-6 20-139 X,, ERZ 43 2-26-42 0-681 43- 2-25-739 9-8341121-3 22 547 ^29 EZD 44-40-29-04 0-508 44-40-28-532 9-8470044-2 21-295 X,, EDK 50-41 -39-63 0-359 50-41-39-271 9-8886156-6 17-237 x^ WKE 39-29-18-20 0-197 39-29-18-003 Sum . ." 9-8034032-0 25-553 x« 9-2224857-7 ' (52^ ): 0=47-1-4-2 7.6»,— 4-e 54«,-l-287a;5-5 -914x^-31 -655k „ + 20- 139x^,-9 -294x,3 + 20-55 30.^-18- i80a;^ + 17-237a:,,- -31-394a;„+22- 547r»,,+21 -295a;3,-13-760a!„ In the figure PCRZ we ha-ve P 1 CROP c z X < -1 C P c z C R Conseq iiently : / 5* I Si Sii n. CPR. Sin. C a. CRP. Sin. C ZP. Sin PZ. Sin CRZ. -1 CZR. p A \\ P...PiketBerg, \\ C.KapooBerg. M K...Eieteek's Kasteel. R CALCULATI ON. ANGLES. J- ANGLES — Je. 4 LOG. SINES. CO-EFFICIENTS OF THE CORRECTIONS. CPR 30-'5-58-55 2 -'671 30- 5-55-879 9-7002652-7 36-324 x^. CZP 129-57- 9-77 1-302 129-57- 8-468 9-8845567-6 -17-638 (x^ + x,s) 4-904 \x„ + x,,<^ CRZ 76-53-24-72 1-2-20 76-63-23-500 Sum. . 9-9886303-6 9 -5733523 -8 §5. (C) Triangulation south of the side Ceder Berg — Heerenloge- ment's Berg. 498 VERIFICATION AND EXTENSION OP LA CAILLE'S ARC OF THE MERIDIAN. §5. (C) Triangulation soutli of the side Ceder Berg — Heerenloge- ment's Berg. CRP CPZ CZR Formation of the Equations of Condition. CALCULATION — continued. ANGLES. J^- 80-32-39-36 26-57-50-70 56-50- 8-85 2-671 1-302 1-220 ANGLES — Je. 80-32-36-689 26-57-49-398 50-50- 7-630 Sum. . LOG. SINES. 9-9940577-8 9-6565066-3 9-9227788-8 9-5733432-9 CO-EFFICIENTS OF THE COBKECTIONS. 3 - 507 ajjj 41-389 (x,^ 13-760 X.,., (53): 0=90-9-|-4-904a;„-3-507a;,, + 4-904a;^-17-638a53-17-638«,,-13-760a;„ + 41-389a;« + 36-324a;,3-41-389ir,, In the figure PP,CZ -(ve have : Z C Z P Z P, X X =1 Z P Z P[ z c Consequently : Sin. ZPC. Sin. ZP,P. Sin. ZCP,. Sin. ZCP. Sin. ZPP,. Sin. ZP,C. P...PiketBerg. P|. . .Patry s Berg. C.Kapoc Berg. Z...Zwart Berg. CALCULATION. ZPC ZP,P ZCP, ZCP ZPP, ZP,C ANGLES. 26-57-50-70 40-49-18-04 60-10-16-09 23- 5- 0-36 88- 2-38-53 41- 0-47-77 J- 1-302 1-749 2-548 1-302 1-749 2-548 ANGLES — Je. 26-57-49-398 40-49-16-291 60-10-13-542 23- 88- 41- Sum. . 4-59-058 2-36-781 0-45-222 Sum. . LOG. SINES. 9-6565066-3 9-8153788-3 9-9382739-6 9-4101594-1 9-5933584-8 9-9997467-8 9-8170524-3 9 -4101576 9 CO-EFFICIENTS OP THE CORRECTIONS. 41-389 (x,, 24-374 ^a;,, 12-073 X, — aUa) 49-404 (x,,-x^) 0-723 ^x^ ' 24-210 Xii (54): 0=17-2 + 12-073a;„-49-404a;,3+49-404a!,,+24-374a;„-24-210»,,-41-389«,3+40-666a;^ INVESTIGATION OP THE CORRECTIONS TO THE ANGLES. 499 Formation of the Equations of Condition. From the quadrilateral EHLP we obtain : EL E P EH -=1 E P E H E L E Therefore : Sin. EPL. Sin. EHP. Sin. ELH. Sin. ELP. Sin. EPH. Sin. EHL. -=1 E... Eland's Berg. H...Heerenlogement'8 Berg. L... Lambert's Hoek Berg. P...Piket Berg. CALCULATION. EPL EHP ELH ELP EPH EHL ANGLES. i^- / II 52- 20- 33- 03 1-442 26-35-57-19 1-387 65-47- 8-45 1-348 59-53-53-79 1-442 26-57-13-26 1-387 55-31-38-25 1-348 ANGLES — Je. 52-20-31-588 26-35-55-803 65-47- 7-102 Sum. . 59-53-52-348 26-57-11-873 55-31-36-902 Sum. . LOG. SINES. 9-8985457-0 9-6510267-8 9-9600019-9 9-5095744-7 9-9370828-2 9-6563512-8 9-9161338-6 9-5095679-6 CO-EFFICIENTS OF THE CORRECTIONS. 16-249 a;« 42-048 (x,,-x^) 9-469 V, ^ 12-207 X,, 41-406 x„ 14-456 a;™ (55):0=65-H-16-249a;„-41-406a!„+9-469a;^-12-207a!5s-(-42-048a;64-42-048a5,e-14-456a!ei In the quadrilateral EHCP we have : PH P E PC X X =1 P E PC PH Therefore : Sin. PEH. Sin. PCE. Sin. PHC. -=1 Sin. PHE. Sin. PEC. Sin. PCH. E... Eland's Berg. H. . .Heerenlogement's Berg, C.Ceder Berg. P...PiketBerg. d :c)" Triangulation south of the side Ceder Berg — Heerenloge- ment's Berg. 500 VERIFICATION AND EXTENSION OP LA CAILLE'S ARC OP THE MERIDIAN. § 5. (C) Triangulation south of the side Ceder Berg — Heerenloge- tnent's Berg. Formation of the Equations of Condition. CALCULATION. PEH PCE PHC PHE PEC PCH ANGLES. 126-26-49-75 35-18-16-07 54- 1-20-07 26-35-5719 62-43-30-27 70-57-46-03 1-387 2-593 3-856 1-387 2-593 3-855 ANGLES — §£. 126-26-48-363 35-18-13-477 54- 1-16-215 Sum. . 26-35-55-803 62-43-27-677 70-57-42-175 Sum. . LOG. SINES. 9-9054770-3 9-7618609-3 9-9080742-2 9-5754121-8 9-6510267-8 9-9488099-5 9-9755700-2 9-5754067-5 CO-EFFICIENTS OF THE COBHECTIONS. -15-550 (x,. 29-733 X, 15-286 «„, + Xi^ 42-048 (ir6.-iC66) 10-856 x^ 7-266 a!„. (66): 0=54-3-26-4065,-15-550a;5,+29-733a;„-7-266a;,,-42-048a!,,+67-334«e<, From the annexed figure we obtain : HC KG KW KG, G,P, PP, PE PH X -X X X X X X =1 KG KW KG, C,P, PP, PE PH HC H...Heerenlogement's Berg. C. ..Ceder Berg. W... Winter Berg. C,...Capoc Berg. P,...Patry8 Berg. E... Eland's Berg. P...PiketBerg. K...Kapitein's Kloof. Sin. HKG. Sin. KWC. Sin. KG,W. Sin. C,P,K. Sin. P,PC,. Sin. PEP,. Sin. PHE. Sin. HCP, Sin. CHK. Sin. KCW. Sin. KWC,. Sin. G,KP,. Sin. P,C,P. Sin. PP,E. Sin. PEH. Sin. HPC. =1 INVESTIGATION OF THE CORRECTIONS TO THE ANGLES. 501 Formation of the Equations of Condition. CALCULATION. ANGLES. he. ANGLES— Je. LOG. SINES. CO-EFFICIENTS OF THE CORRECTIONS. HKC KWC KC,W C,P,K, •?&^: PHE HCP CHK KCW KWC, C,KP, PEH HPC 54- '2-22-86 52-15- 2-07 51-59-52-67 78-40-51-71 61- 4-47-83 51-13-56-10 26-35-57-19 70-67-46-03 52-26- 6-12 53- 2-11-23 65-19-23-84 62-23-20-32 37- 5-15-73 44-48-35-40 126-26-49-76 55' 1- 4-58 3-'878 3-853 4-142 3-053 2-994 1-874 1-387 3-855 3-878 3-853 4-142 3-063 2-994 1-874 1-387 3-855 5°4- 2 -18 -982 52-14-58-217 5] -59-48-428 78-40-48-667 61- 4-44-836 51 13-54-226 26-36-65-803 70-67-42-175 Sum. . 52-26- 2-242 53- 2- 7-377 66-19-19-698 62- 23 17 -267 37- 5-12-736 44- 48 -33 -526 126-26-48-363 65- 1- 0-725 Sum. . 9-9081700-8 9-8980031-5 9-8965130-8 9-9914683-6 9-9421511-2 9-8919190-8 9-6510267-8 9-9766700-2 15-276 X,, 16-303 a5,„ 16-452 ar,„ 4-216 a;« 11-633 x^ 16-910 ar„ 42-048 (Xet—Xm) 7-266 xe, 16-195 X,, 15-846 ar,3 9-674 »,„ 11-013 x^ 27-863 (asn— ajia + acss) 21-196 x^ —15-560 (x^+Xse) 14-734 x^ ^ 9-1548216-7 9-8990820-9 9-9025606-0 9-9684060-0 9-9474864-9 9-7803354-7 9-8480348-0 9-9064770-3 9-9134640-2 9-1548265-0 (57): =48-3-16-452r,„+27-853!r„-27-853a!„+27-863»^+21-196a;3,-4-216a;„-ll-633a;,3 + 14-734«4e + ll-013a;«,-16-276x„-16-550a;34-15-550iC56-16-910iB„-7-266a!« + 15 - 846a!6,-42 - 048a;64 + 16 - 195a;e5 + 42 - 048a;66 + 9 • 674a;,«- 1 6 - 303aj„3 Thert Si Si In the quadrila RR, R C fore: n. RCR,. Sin. n. RR,C. Sin. teral CRNR, we have : R C RN < X =1 RN RR, RNC. Sin. RR,N. ^ R C.Kapoc Berg. Ti 'Riphpplr's 'KflRfppI RCN. 8 =1 R in. RNR,. I N N... Simon's Berg. E,...RoggeBay. § 5. (C) Triangulation south of the side Ceder Berg— Heerenloge- ment's Berg. 502 VERIFICATION AND EXTENSION OP LA CAILLE'S ARC OF THE MERIDIAN. §5. (C) Triangulation south of the side Ceder Berg — Heerenloge- uient's Berg. RCRj RNC RR,N RR|C RCN RNR, Formation of the Equations of Condition. CALCULATION. ANGLES. 98-13-19-23 37- 5-45G3 50-58-5802 33-33-3514 57- 3-45-96 91-23-47-49 l^- 1-938 2 -014 2-207 1-938 2-014 2-207 ANGLES— Je. 98-13-17-292 37- 5-43-616 50-58-55-813 Sum. . 33-33-33-202 57- 3-43-946 91-23-45-283 Sum. . LOG. SINES. 9-9955135-1 9-7804214-6 9-8903930-8 9-6663280-5 9-7425669-4 9-9238972-3 9-9998711-0 9-6663352-7 CO-EFFICIENTS OF THE CORRECTIONS. - 3-042 x„ 27-845 x,^ 17-061 x,„. 31-739 a;,o7 13-641 x„ — 0-513 x,„ (58): 0=72-2+13-641«„-|-3-042a;„-|-31-739a!,„-17-061a!,„,-27-845a;.^-0-513x„ In the quadrilateral CRNO we have : C N CO C R X X =1 CO C R C N Therefore : Sin. CON. Sin. CRO. Sin. CNR. -=1 Sin. CNO. Sin. COR. Sin. CRN. CALCULATION. C...KapocBerg. E...Riebeek's Kasteel. ]\J N... Simon's Berg. O... Royal Obserratory. CON CRO CNR CNO COR CRN ANGLES. J^- O / // 86-25-25-01 1-980 52- 9-37-84 2 020 37- 5-45-63 2-014 57-18- 3-07 1-980 34-30- 6-59 2 020 85-50-32-38 2 014 ANGLES— Je. 86-25-23030 52- 9-35-820 37- 5-43-616 Sum. . 57-18- 1-090 34-30- 4-570 85-50-30-366 Sum. . LOG. SINES. 9-9991531-1 9-8974766-1 9-7804214-6 9-6770511 8 9-9-250611-3 9-7531420-1 9-9988552-7 9-6770584-1 CO-EFFICIENTS OF THE CORRECTIONS. 1-316 a;,,, 16-356 ajj, 27-845 x,^ 13-517 fl5,2j 30-634 a;„„ 1-531 a;,. (59): 0=72-3-16-356a!3. + l-531x,3+30-634jB„„-l-316:»„.-27-845a-,^ + 13-517a;,, INVESTIGATION OF THE CORRECTIONS TO THE ANGLES. 503 Formation of the Equations of CondiUon. In the quadrilateral CRNB we have : C N C B C R •X- -=1 C B C R C N Therefore : Sin. CBN. Sin. CRB. Sin. CNR. -=1 , Sin. CNB. Sin. CBR. Sin. CRN. C.Kapoc Berg. ■NT l{...Riebeek's Kasteel. N.. .Simon's Berg. E.. .King's Battery. CALCULATION. CBN CRB CNR CNB CBR CRN ANGLES. 82-10-10-20 51- 8- 7-28 37' 5-45-63 59- 0- 2-68 32-58-17-12 85-50-32-38 ^e. 2-153 2-065 2-014 2-153 2-065 2-014 ANGLES — Jt. 82-10- 8-047 51-8- 5-215 37- 5-43-616 Sum. . 59- 0- 0-627 32-58-15-055 85-50-30-366 Sum. . LOG. SINES. 9-9959308-1 9-8913278-7 9-7804214-6 9-6676801-4 9 -9330662 -9 9-7357682-8 9-9988552-7 9-6676898-4 CO-EFFICIENTS OF THE CORRECTIONS. 2-896 X,. 16-968 x^, 27-845 X,, 12-651 £c,„ 32-459 x,^ 1-531 a;,, (60):0=97-0-16-968a!3„+l-531a!33-27-845a3,^+12-651a;.,,+32-459aj„e-2-896a5,, In the figure CNBSC, we have : BC, BS BC BN X X X =1 BS BC BN BCi Therefore : Sin. BSC,. Sin. BCS. Sin. BNC. Sin. BC,N. =1 Sin. BC,S. Sin, BSC. Sin. BCN. Sin. BNC,. C...Kapoo Berg. N... Simon's Berg. S...Sneeuw Kop. C,...Cape Point. B... King's Battery. Dl § 5. (C) Triangulation south of the side Ceder Berg — Heerenloge- ment's Berg. 504 VERIFICATION AND EXTENSION OP LA CAILLE'S ARC OP THE MERIDIAN. Ti-iiingulation south of the sidy Ct'd-:^r IVrs- Heerenloge- inent'i Tier" Formation of the Equations of Condition. CALCULATION. BSC, BCS BNC BC,N BC,S BSC BCN BNC, ANGLES. 48-22-40-77 33-30-39-75 59- 0- 2-68 40- 8- 5-82 57- 8- 0-04 40-37-30-22 38-49-56-03 41-40-49-30 1-831 2-423 2-153 1-623 1-8.31 2-423 2-153 1-623 ANGLES — §£. 48-22-38-939 33 30-37-3-27 59- 0- 0-627 40- 8- 4-197 Sum. . 57- 7-58-209 40 -37 --27 -797 38-49-53-877 41-40-47-677 Sum. . LOG. SINES. 9-8736327-8 9-7420082-4 9-9.330662-9 9-8092795-9 9-3579869-0 9-9242435-9 9-81.36459-1 9-7972910-7 9-8-228010-6 9-3579816-3 CO-EPFICIENTS OF THE CORRECTIONS. 18-709 a!,34 31-799 a;,, 12-651 a;,„ 24-974 a;„, 13-604 X,,, 24-544 a;,3, 26-158 (x,,—x») 23-648 «,,„ (61): 0=52-7+26-158„-26-158ir,5 + 31-799a!,3-23-648a;„^ + 12-6.51a;,„ + 18-709a;,^-24-544a;,3^ +24-974a;,,,-13-604x„. In the figure CNOSB -we have : CN CB CS CO -X- =1 CB CS CO CN Therefore : Sin. CBN Sin. CSB. Sin. COS. Sin. CNO. Sin. CNB. Sin. CBS. Sin. CSO. Sin. CON. CALCULATION. -A C.Kapoe Berg. N.. .Simon's Berg S...Sneeuw Kop. O... Royal Observatory. B... King's Battery. ANGLES. J- ANGLES — Jt£. LOG. SINES, CO-EFFICIENTS OF CORRECTIONS. THE CBN CSB COS CNO 82-io-10-20 40-37-30 22 111- 3- 1-66 57-18- 3-07 2-1.53 2-423 2-200 1-980 8°2-i0- 8-047 40-37-27-797 111- 2-59-460 57-18- 1-090 Sum . . 9-99,59308-1 9 81364.59-1 9-9700065-3 9-9250611-3 2-896 a;,„ 24-544 a;,„ - 8-103 a;„, 13-517 x,^ 9-7046443-8 INTESTIGATION OF THE CORRECTIONS TO THE ANGLES. 505 Formation of the Equations of Condition. CALCULATION — continued. CNB CBS CSO CON ANGLES. 59- 0- 2-68 105-51-56-65 37-59-4213 86-25-25-01 2-153 2-423 2-200 1-980 ANGLES — \e. 59- 0- 0-527 105 -51 -54 -227 37-59-39-930 86-25-23-030 Sum. . LOG. SINES. 9-9330662-9 9-9831336-6 9-7892879-1 9-9991531-1 9-7046409-7 CO-EFFICIENTS OF THE CORRECTIONS. 12-651 a;,,, — 5-984 a)|28 26-955 a;,3, 1-316 cc,„ (62): 0=34-l-l-316a;,„-8-103a;,„-12-651a;,„ + 13-517a;,,, + 2-896a;,„+5-984a;„ + 24-544a;,^-26-955a;„. In the figure ONZSB we have : ZO ZN ZB ZS X X X = 1 ZN ZB ZS ZO Therefore : Sin. ZNO. Sin. ZBN. Sin. ZSB. Sin. ZOS. -=1 Sin. ZON. Sin. ZNB. Sin. ZBS. Sin. ZSO. CALCULATION. O...Eoyal Obseryatory, N... Simon's Berg. S...Sneeuw Kop. Z...Zwart Kop. B... King's Battery. ZNO ZBN ZSB ZOS ZON ZNB ZBS ZSO ANGLES. 32-48-19-34 101-53-15-53 34-16-13 77 79-54-10-43 104-31-47-08 31- 6-19-73 78-11-2908 36-54- 1-86 i- 1-079 1-099 1-274 1-304 1-079 1-099 1-274 1-304 ANGLES — Je. 32-48-18-261 101 -53 -14 -431 34-16-l'2-496 79-54- 9-126 Sum. . 104-31-46 001 31- 6-18-631 78-11-27-806 36-54- 0-556 Sum. . LOG. SINES. 9-7338250-6 9-9905850-3 9-7505819-9 9-9932205-5 9-4682126-3 9-9858838-0 9-7131634-1 9- 9907097 9-7784568-5 9-4682137-6 CO-EFFICIENTS OF THE CORRECTIONS. 32-665 X,, - 4-432 X,, 30-900 X,, 3-750 a;,, — 5-457 iTii 34-896 X,, 4-402 X,, 28-043 a:,. (63): 0=ll-3-5-457«„-3-750x„,+34-896a!,^-32-665.r„,-t-4-432ic,3„-h4-402a:,, -30-900a:,„-t-28-043a-,,, § 5. (C) Trianij'uhition south of tlie side Ceder Bcrs— Heerenlogc- ment's Ber;.'. 506 VERIFICATION AND EXTENSION OF LA CAILLE'S ARC OP THE MERIDIAN. it n. (C) Triangulation sout}i of the side Ceder Bersj — Heerenloge- luent's Berj;. formation of the Equations of Condition. In the figure CNBSZ we have : BZ BN BC BS BN BC BS BZ Therefore : Sin. BNZ. Sin. BCN. Sin. BSC. Sin. BZS. =1 Sin. BZN. Sin. BNC. Sin. BCS. Sin. BSZ. CALCULATION. C.Kapoc Berg. N... Simon's Berg. S-.-Sneeuw Kop. Z...Zwart Kop. B... King's Battery. BNZ BCN BSC BZS BZNj BNC BCS BSZ ANGLES. i^- o / // — 31- 6-19-73 l-b99 38-49-56-03 2-153 40-37-30-22 2-423 67-32-22-00 1-274 47- 0-29-13 1-099 59- 0- 2-68 2-153 33-30-39-75 2-423 34-16-13-77 1-274 ANGLES— Jf. 31- 6-18-631 38-49-53-877 40-37-27-797 67-32-20-726 Sum. . 47- 0-28-031 59- 0- 0-527 33-30-37-327 34-16-12-496 Sum. . LOG. SINES. 9-7131634-1 9-7972910-7 9-8136459-1 9-9657379-5 9-2898383-4 9-8641824-6 9-9330662-8 9-7420082-4 9-7505819-9 9 -2898389 -7 CO-EFFICIENTS OF THE COHRECTIONS. 34-896 x,» 26-158 (x,,-x„) 24-544 ^x,^ ' 8-704 ;c,„ 19-629 xu 12-651 X,, 31-799 X,, 30-900 X,, (64) : 0=6 - 3 + 26 - 158a;„-26 - \^x,, + 31 - 799a;,3 + 12 • 651a;,,,- 34 • 896(»i,4- 24 - 544a;,3 + 30 - 900a;,„ + 19 - 629a;,,,-8 • 704i;,,e In the quadrilatei-al MBZS we have : S M SB S Z X X =1 SB 8 Z S M Therefore : Sin, SBM. Sin. SZB. Sin. SMZ. -=1 Sin. SMB. Sin. SBZ. Sin. SZM. M.. .Meridian Mark, Blaauw Berg. S...Sneeuw Kop. S Z...ZwartKop. B... King's Battery. INVESTIGATION OF THE CORRECTIONS TO THE ANGLES. 507 SBM SZB SMZ SMB SBZ SZM Formation of the Eqitations of Condition. CALCULATION. ANGLES. 94-53-16-71 67-32-22-00 57-38-15-53 61-36-22-89 78-1] •29-08 64-35-14-39 J^- 0-965 1-274 2-168 0-965 1-274 2-168 ANGLES — §£. 94-53-15-745 67-32-20-726 57-38-13-362 Sum. . 61-36-21-925 78-11-27-806 64-35-12-222 Sum. . LOG. SINES. 9-9984178-5 9-9667379-5 9-9266891-9 9-8908449-9 9-9443341-2 9-9907097-0 9-9558012-2 9-8908450-4 CO-EFFICIENTS OF THE CORRECTIONS. - 1-801 OSia, 8-704 «!« 13-344 X,,, 11-382 a?i, 4-402 a!,3 10-004 a!„ (65):0=0-5 + ll-382a!„5-13-344x„,+l-801a!,^+4-402a;,33-8-704a;,«+10-004a!„ In the figure MOZS we have ; S M SO S Z X X =1 SO S Z S M Therefore : Sin. SOM. Sin. 8Z0. Sin. SMZ. -=1 Sin. SMO. Sin. SOZ. Sin. SZM. § 5. (C) Triangulation south of the side Ceder Berg— Heerenloge- ment's Berii. M... Meridian Mark, Blaauw Berg, S...Sneeuw Kop. Z...Zwart Kop. O.. .Eoyal Observatory. CALCULATION. SOM 8Z0 SMZ ANGLES. 103-38-51-57 63-11-52-22 57- 38- 15-53 0-828 1-304 2-168 ANGLES— |e. 103 -38 -50 -742 63- 11 •50-916 57-38-13-362 Sum. . LOG. SINES. 9-9875617-3 9-9506403-1 9-9266891-9 9-8648912-3 CO-EFFICIENTS OF THE CORRECTIONS. — 5-112 as,o9 10-637 jThs 13-344 £c„3 El 508 VERIFICATION" AND EXTENSION OF LA CAILLE'S ARC OF THE MERrDIAN". §5. (C) Triangalation south of the side Ceder Berg — Heerenloge- ment's Berg. 8M0 SOZ SZM Formation of the Equations of Condition. CALCULATION — continued. ANGLES. ie. 65 -28 -34 -51 79-54-10-43 64-35-14-39 0-828 1-304 2-168 ANGLES — Ic. 55-28- 33-682 79-54- 9-126 64-35-12-222 Sum. . LOG. SINES. 9-9158687-6 9-9932205-5 9-9558012-2 9-8648905-3 CO-EFFICIENTS OF THE CORHBCTIONS. 14-484 Xm 3-750 «,„ 10-004 «,„ (66): 0=7-0-5-112a;.„5-3-750a;„,-14-484a;,„ + 13-344a!,„-10-004a!,„ + 10-637a;„ In the quadrilateral MBCS we have ; S M S C SB -=1 S C SB S M Therefore : Sin. SCM. Sin. SBC. Sin. SMB. -=1 Sin. SMC. Sin. SCB. Sin. 8BM. C CALCULATION. M... Meridian Mark, BlaauwBerg, S...Sneeuw Kop. C.Cape Point. B... King's Battery. SCM SBC SMB SMC SCB SBM ANGLES. 53-33- 9-38 74-29-24-33 61-36-22-89 54-33-53-43 57- 8- 0-04 94-53-16-71 I 2-638 1-831 0-965 2-638 1-831 0-965 ANGLES — Je. 53-33- 6-742 74-29-22-499 61-36-21-925 Sum. . 54-33-50-792 57- 7-58-209 94-53-15-745 Sum. . LOG. SINES. 9-9054693-9 9-9838886-0 9-9443341-2 9-8336921-1 9-9110322-9 9-9242435-9 9-9984178-5 9-8336937-3 CO-EFFICIENTS OF THE CORRECTIONS, 15-651 Xis 6-843 a;,3 11-382 a;,, 14-983 ar„6 13-604 X,,, - 1-801 »,„ (67) : 0=16- 2-11 •382„,+ 14- 983a;,„-l ■ 801a;,,,-6 ■ 843£c„,-15- 551x.,,+ 13- 604a!„ ESrVESTIGATION OF THE CORRECTIONS TO THE ANGLES. 509 Formation of the Equations of Condition. From the annexed figure we obtain : CB CS CW CK CP, CP CR — X- CS CW CK CP, CP CR CB P...PiketBerg. P,...Patrys Berg. C.KapocBerg. B.. .King's Battery. S...Sneeuw Kop. W.. Winter Berg. K...Kapitein's Kloof. E...Riebeek's Kasteel. Sin. CSB. Sin. CWS. Sin. CKW. Sin. CP,K. Sin. CPP,. Sin. CRP. Sin. CBR. Sin. CBS. Sin. CSW. Sin. CWK. Sin. CKP,. Sin. CP,P. Sin. CPR. Sin. CRB. CALCULATION. §5. (C) Triangulatioii south of the side Ceder Berg — Heerenloge- ment's Berg. -=1 CSB CWS CKW CP.K CPP, CRP CBR CBS CSW CWK CKP, CP.P CPR CRB ANGLES. h^- 40 -37 -30 -22 2 -'423 55- 9-32-39 5-646 62-40-54-74 4-142 78-40-51-71 3 053 61- 4-47-83 2-994 80 •32- 39 -36 2-671 32' 58- 17- 12 2-066 105 -51 -SB -65 2-423 46-56 4907 6-646 6519 23-84 4-142 62-2:3-20-32 3 053 81-50- 5-81 2-994 30- 5-58-55 2-671 51- 8- 7-28 2-065 ANGLES — Je. 40-37-27-797 55- 9-26-745 62-40-50-598 78-40-48-657 61- 4-44-836 80-32-36-689 32 58-15-055 Sum . . 105 -51 -54 -227 46-56-43-425 65 -19 19 -698 62-23-17-267 81-50- 2-816 30- 5-55-879 51- 8- 5-215 Sum. . LOG. SINES. 9-8136459-1 9-9141976-2 9-9486392-6 9 -9914683 -6 9-9421511-2 9-9940577-8 9-7357682-8 9-3399283-3 9-9831336-6 9-8637411-5 9-9584060-0 9-9474864-9 9-9955742-4 9-7002652-7 9-8913278-6 9-3399346-7 CO-EFFICIENTS OF THE CORRECTIONS. 24-544 14-657 10-876 4-215 11-633 3-607 32-459 - 5-984 19-672 9-674 11-013 3-021 36-324 16-968 ^128 •"us X (68): 0=63-4-3-507x,3+16-968iC3„ + 3-021ic,„-i-3021a;,.-4-216.r„-ll-633j!,3+36-324x,. + 11 ■ 013a!,„- 10 - %lQx,-'i2 ■ 4.^9a!„,- 6 - 984a!,,, + 19 - 672;c.35-24 • 5Ux,,, + 9 • 674»„,-14- 657a;,, 510 VERIFICATION AND EXTENSION OF LA CAILLE'S ARC OP THE MERIDIAN. (D) Triangulation south of the side Ceder Berg — Heerenloge- nient's Berg. Abstract of the Equations of Condition. (1) 0= 0- (2) 0= 0- (3) 0= 0- (4) 0= 0- (5) 0=- -0- (6) 0=- -0- (7) 0= (8) 0= 0- (9) 0=- -1- (10) 0=- -1- (11) 0= 0- (12) 0= 0- (13) 0=- -4- (14) 0=- -0-/ (15) 0=- -3- (16) 0=- -3 (17) 0=- -0- (18) 0= 1- (19) 0=- -1- (20) 0= 4- (21) 0= 2- (22) 0= 1- (23) 0=- -1- (24) 0=- -2- (25) 0= 1- (26) 0=- -0- (27) 0= 0- (28) 0= 2- (29) 0=- -1- (30) 0=- -0- (31) 0= 1- (32) 0= 0- (33) 0= 1- (34) 0= 2- (35) 0= 1- (36) 0= 1- (37) 0=- -0- (38) 0= 1- 3m+x^+xe+x^ OSii + x^+x^g+x^g 973 + 05^ + 0525 + 0535 033+a!g+D;^g+x^ em+x^^+x^+x^g+x^ 956 + 0513 + 0528 + 05^ 394+a;ii+a!34+a!4i 296 +a;3g+ 05^0 +05^5 387+Xii-a;i3+a;22+a;4o+a^4i + ^« 959 + 0533 + 05^4 + a!5.^ 277+054s+a!54-a;5s+a!5g+ ^55 824 + a55s+0558 + «69 960 + 05^ + X54+055g + 0J64-Xg6 &M+x^+x^^+x^+Xg^ 886+x^+xes+Xgg Q20+x^^+x^+x^ 277+ario+a;53+Xi42 320+ 0551 +ar6j+Xi43 317 + *52 + «60 + ^65 367 +a;iy+ 0532 + a;io^ 541-a-32+a;33+a5io8+z,23 072 + ari4 + 0533 + 05120 520+a;ig+a;3i+o5„o 669-ari4+»i6+05in + iri2s 194+o5is+a;3o+fl5j2g 451 -0514 +05i5+a;i21 + J",27 900+a;ig+arii2+*i38 648+a;i8+o5i28+a;i3^ 936 + 0521 + a!i3g+ 05144 597+o!ii4+a5i4i+aTi,3 = 1 -029 + 05133 +Xi4„ + '146 = 2-532+a;ii3 + £»i25+a5i4g 094 + a:i24 +35130 +05145 030+a!iig+a;i3i +05151 354 + 05132 +a!i,4+Xl52 Od7+x^og+x^„+x "117 139 INVESTIGATION OF THE COREECTIONS TO THE ANGLES. 511 Abstract of the Equations of Condition. (39) (40) (41) (42) (43) (44) (45) (46) (47) (48) (51) ~ • ~ Jo + ^^115+ ^'jop ^lu + ■^IM 2 • 777 + a-jjg + ajjjg + a-j^j + x^^^ 1 • 257 + a?ng+!Ci,5 +07150 ^130 ""^ISl +'''l3C '^133 ^1. X,. 1 ' ■''140 ■^lil — ^134 '''135 + ^139 — ""im"^^ * (49) (50) L ^iiaT'Ti ■^14/i "^ 146 ■ (52) : (53) = (54) = (55) = (56) : (57) : (58) : (59) = (60) : (61) (62) : (63) ■ (64) = I (65) = I (66) : 1(67) : ! (68) : = 21-3 + l-287«5 + 5-914^s + 16 0662'g-20-139^„„ + 13-760:(^„-10-891x,B 47-l-4-276iBi-4-654iCj-l-287«5-5'914a;B-31-65oa!,,o + 20-139j2„-9-294x53 + 25 • 553a;2^-18 • 480a;25 + 17 • 237xs,g-31 • 394a;„. + 22 ■ 547a;„g+ 21 • 295a;35- 13 • 7605^3- = 90-9+4-904£C27-3-507ar5g + 4-904a„g-17-638x3^-17-638a;3g-13-760£C3j+41-389r43 + 36'324a;^-41-389«^ 17-2+12'073*ii-49'404rj3+49-404iC22+24'374x^„-24-210x^i-4]-389a;^3 + 40-666r^g = 65-l+16-249a-^j-41-406x^^+9-469.rj3-12 207a:ag+42-048rg,-42'048.T6g-14-456x, = 54 • 3-26 ■ 406a:,,- 15 ■ 550^:,. + 29 • 7332^., - 7 • 20i7a-.,- 42 • 048a^., + 57 • 334x, fig ''66 4-215x^,-11 -eSSa-^, 15-550a'j,-]5-550xjg-16-910T5j-7'266a-g„ 48 ■ 3-16 • 452^10 + 27 • 853a'i,-27 ■ 853a-,3 + 27 • 853a;„„ + 21 • 196X3^ + ]4-734a;^g + ll-013a;5„-15-276a-3„-15-550a'j,-]5-550xjg-.>. ^.^.^^ + 15 • 846x83-42 • 048xg, + 16 • 195xg5 + 42 • 048xgg + 9 • 674x1^2 - 16 • 303x„3 72-2 + 13-641a'i^+3-042xi^ + 31-739a:i„-17-061a-,0B-27845xi„o-0-513xj„3 72-3-16-356x3i+l-531a;33 + 30'634xiio-l-316xiji-27-845xi„„ + 13-617Xj„„ 97 • 0- 16 • 968a:3o + 1 • 531x33-27 ■ 845a:j„o + 12 ' 651r j.^ + 32 • 459xi„g - 2 ■ 896x,„^ 52 • 7 +26 • 158.z:i^-26- 158a;ij + 31 • 799xjg-23 • 648x„g + 12 ■ eola'iji + 18 ■ 7G9x„^ -24 • 544ar. 3. + 24 974Zi5, - 13 ■ 604xi5„ -12-651a;i,i +13-517»i„2+2-896a-,„j +5-984xj "137 34-l-l-316a:iii— 8-103iCii2- + 24 • 544*137 -26 • 955a;i38 ll-3-5-467x„3-3-75Oa;i,4+34-896xi24-32-665a;i2g+4-432a,30+4-402a-,33 -30 • 900x140 + 28 • 043xi4i 6-3+26-158a!i4-26- 158x15 + 31 ■799a-i3 + 12-661a!i2,-34-896i24-24-544i37 + 30 ■ 900.ri4o + 19 • 629x,45 -8 ■ 704a;,4g ■ 5 + 11 • 382xii5 - 13 344xii8 + 1 • BOlxi^g + 4 • 402x133 -8 • 704x,46 + 10 • 004x14^ 7-0-5-112xiog-3-750xi,4 + 14-484x117 +13- 344xii8-10004xi47 + 10-637x143 16-2-11 382x115 +14-983x,i5-l-801xi29-5-843xi32-15-551xi.5o+13-604x|,2 63-4-3-507x28 + 16-908x3o + 3-021x4o + 3021x4,-4'215x4j-ll -633x43 + 36-324x48 + ll-013x5o-10-876xg3-32-459x,2e-5-984xi2g+19-672x,3e-24-544xi37 +9-674x,42-14 657x,44 (D) Triangul.'ition south of the side Ceder Berg — ITeei'enloge- racnt's Berg. Equations (49) and (50) are placed to the right to gain room. F 1 512 VERIFICATION AKD EXTENSION OP LA CAILLE'S ARC OP THE MERIDIAN. §5. (E) Triangulation r^e Corrections x„ a;^ (multiplied by the weights J in terms of the factors f„f- south of the side Ceder Berg- Heerenloge- ment's Berg. 4- o- 2x, =/, - 4-276/g, 3 ^2 =/3- 4-654/, 4- 0x3 =/ 3- 4^4 =/4 3- 9 a;, =/+ l-287/,-l-287/, 2- 8^6 =/3 4- 4«^7 =/5 3- 3^8 =/6 + 5-914/,-5-914/, 4 9^9 =/ +16-066/, 10- 1 ^10 =/i9+/42-16-452/„ 8- 1 '^ii =/ +/i+/42 + 12-073/4+27-853/„ 1- 1 ^12 — /18+/68 4- 1 ^13 =/8 -/i-49-404/,-27-853/„ 1- 74 cB,, =/,-/,-/3 + 13-641/3+26-158/, + 26-158/4 6 8 ^,5 =/7+/28+/43-26-158/,-26-158/, 5- 9 '''le = /5+/26~"/42~/43 4 3 a-,, =/,+3-042/8 4 7 ^,8 =/3o-/3 + 31-799/e, + 31-799/, 4 2 ^\^ = /29+/42+/3 5 8 ^20 =/i -31-655/, 7 ^ "^21 = /3I +/2 6 ^22 =/7 +/„-/4,-20-139/,+20-139/, + 49-404/4+27-853A 4 4a;,3 =/ -9-294/, 4 6 0^,4=/ +25-653/, 3 5 ^25 =/5 -18-480/, 3 6 x,e=/4 +17-237/, 7 9 aj,, =/, +/-31-394/, + 4-904/3 2 • 7 a.,, =/-3-607/3-3-507/, 7 • 5 x,s=fe +/ + 22-647/, + 4-904/3 4 8 3^30 =/,7-16- 968/0 + 16 -968/, 4 8 ^31 =/5-16-356/g 4 D 3!g2 ^ /, — /23 3 • 6 X33 =/3+/„ + l-531/c, + l-531/(, 3 • 8^.3, =/ -17-638/3 3 • 2 0^35=/ +21-295/, 3 • 6a:36=/.o-17-638/3 5 ■ 7 X37 =/ +13-760/,-13-760/,-13-760/3 4 6«-38=/6-10-891/, INVESTIGATION OF THE CORRECTIONS TO THE ANGLES. 513 The Corrections a;,, Xj (multiplied by the weights) in terms of the factors /„ fa. 4- a^ag : 3- 6 x^Q : 7- 9X,^: 5- 1 x^2 -- 14- Xi3 : 13- 0^44 12- 6 X45 : 7- 5 a;46 5- Ox„ 3- 9 a^s 6- 1 SCi^ 9- 5 aJjo 9- 5 a^ji 9- 5 aj52 4-75 ^53 11- 1 »54 9- 3^,6 10- 5 aise 5- 8x5, 10- 5 aJgs 8- 2 0=59 5- 8 ago 4- 3 Xgi 3- 4 a;62 7-25 x,3 9- 3 a!64 4- ajfis 3- Wee 5- »69 8- 2 a!jQ7 2-25 a!io3 5- 5 a;io9 12- 7 a^iio 1- 6 aj,ii 5- 3 a;ii2 2- 6 ajjia 2- 5 atiH 1- 9 a;„s /,3 + 21-196/„ /io+/ii+24-374/,,+3-021^ /9 +/u-24-210/,,+3-021/e, /,8-4-215/„-4-215/e, :/„ + 41 • 389/,3-41 • 389/,4-ll • 633/„- 11 • 633^6, ■ /12 :/,3+16-249^ ^/i6+/i7 + 14-734/„ :/5+/,6-41 -406/55 :/8+36-324/53 + 36-324/e8 :/,o-41- 389/53 + 40 -666/5, :/8+ll-013/5, + ll-013/e8 ■ J20 :/,-15-276/5, :/9-10- 876/3 = /3 +/6 +/6-26 - 406/e-15 • 550/, = ~/l3+/4 = /3+/5-15-550/5e-15-550/5, :/2-16-910/, :/h+9-469/55 = /3-12-207/5 '- J21 :/6+29-733/e :/,-7- 266/6-7 -266/57 = /o + 15-846/, = /5 + 42-048/55-42-048/6-42-048/7 = /, + 16-195/, = -/5+/r-42-048/55+57-334/5e+42-048/„ = /,-14- 456/55 = /, + 31 -739/3 = /3-17-061/53 = /8~5- 112/3 = /5+30-634/59 = /6-/49-l -316/9-1 -316/, = /29+/9-8-103/, = /34-/49-5- 457/3 = /32+/49-3 -750/3-3-750/6 = /9 + 11-382/5-11-382/, §5. (E) Triangulation south of the side Ceder Berg — Heerenloge- ment's Berg. 514 VERIFICATION AND EXTENSION OP LA CAILLE'S AEC OP THE MERIDIAN. § 5- (E) Triangulation south of the side Ceder Berg — Heerenloge- ment's Berg. The Corrections Xi, x^ (multiplied by the weights) in terms of the factors /„ f. 5- 2 x„g: 4- 5 »,„: 1-54 a!ii8 10- 4 a;i,9 1*36 a;i2o 0-75 a:,2i 1-37 a;,22 1-57 a;i23 40- 9 a, 14- 2 8- 8 1- 6 14- 4 30 4 3 1 3 16 *^19B '^I'jn — Xjjg •03 3^130 = ^^124 ''125 '''12G ' ^127 ^128 ' ''^129 ^130 9 iEjgj: y 21132 ■ " ^133 9 a!i34 9 3^135 10- 5 aJi35 14- 2 x,3j 14* 2 ir,3g 3- 5 a;i3g: 12- X,,,. 12- X,^y 10- 7 a;i42 10- 7 ^H3 10- 7 x„, 5- 5 a;i45 5- 5 37,45 11- 1 a;,47 6- 8 a-148 30" a;, 49 10- X,,,. 4- 5 X,5i: 4' 9 a;,52: /4, + 14-983/e, /3,-14- 484/^5 /4„-13-344^ + 13-344/„5 /3S-23- 648/6, /24-27 • 845/58-27 • 845/9-27 • 845/„ /28+/44 + 12-651/eo+12-651/e,-12-651/2 + 12'651/4 /26-/44 + 13-517/9 + 13-517/2 /23-O -513/8 /35 +/44 + 34 ■ 896/33-34 ■ 896/4 /34-/44-32-665/3 A + 32-459/eo-32-459/8 A-2-896/o + 2-896/2 /3„ + 5-984/,2-5-984/8 /39 + l-801/e5-l-801/, /35-/45 + 4-432/3 J Si +/45 /37-/5-5 -843/7 /33+/45 + 4-402/3 + 4-402/,, /37-/39+/48+18'709/, J 39 +/41 ~Ms A + 19 -672/^ /30-/4,-24-544/3,+24-644/2-24-544/e4-24-544/^ ./29+/7— /62 fss +/40 +/8 /33-/;7 -/48-30 ■ 900/3+30 • 900/64 ^32 +/4D +/? +/48 +/63 /9 + 9G74/„+9-674/3 /o-16-303/„ /,- 14 -657/8 /35+/o + W-629/e4 /33-/0-8' 704/4-8 -704/, /40 + 10 004/5-10- 004/6 /32+/0 + 10 637/33 ^4-/60 /4,- 15 -551/3, /33 + 24-974/, /3,-13 C04/3, + 13-604/, INVESTIGATION OF THE CORRECTIONS TO THE ANGLES. The Corrections a;,, Xi......in terms of the factors /„ /,., 515 14 — ■■17 "IS ^19 ^20 '"21 ^2i ""is ■'^26 : : : : : : : : 0' 0- 0- 0- 0- 0- 0- 0- 0- 0- 0' 0' 0' 0' 0- 0- 0- 0- •2381/,-! -0181/5, ■1887/3-0-8780/,, ■2500/, 2941/ 2564/ + - 3299/, -0 • 3299/, 3571/ 2273/ 3333/ + l-9713/,-l-9713/, 2041/ + 3-2788/, 0990/9 + 0-0990/2-1 •6289/„ 1235/ + 0-1235/,-0-1235/, + l-4905/4H-3-4387/„ -9091/8+0-9091/, • 2439/-0- 2439/, -12 • 0497/,-6- 7934/, ■5747/4-0-5747/e-0-5747/8 + 7-8395/8 + 15-0330/6, + 15-0330/, •1471/,+0' 1471/^ + 0- 1471/3-3-8467/6,-3-8467/6, -1695/5+0-1695/6-0-1695/,-0-1695/3 •2326/,+0-7074/, •2128/3o-0-2128/3+6-7657/, + 6-7657/6, - 2381/9 + • 2381/, + • 238I/3 •1724/-5-4577/, •1333/, + 0-1333/, -1667/ + 0-1667/,-0-1667/,-3-3565/, + 3-3565/, + 8'2340/4+4-6422/, •2273/-2-1122/, •2174/ + 5-5549/, ■2857/-5-2800/, •2778/ +4- 7882/, ■1266/, + 0-1266/-3-9739/, + 0-6207/, ■ 3704/-1 - 2989/3-1 • 2989/66 1333/6+0-1333/+3-0064/,+0-6538/, 2083/,7-3 • 5351/0 + 3 • 5351/3 2083/5-3-4075/9 2174/„-0-2174/3 2778/3 + 0-2778/,4+0-4252/9+0-4252/6o 2632/-4- 6415/3 3125/ + 6 -6549/, 2778/0-4-8993/3 1754/+2-4140/,-2-4140/,-2-4140/3 2174/-2-3676/, §5. (F) Triangulation south of the side Ceder Berg — Heerenloge- ment's Berg. G 1 516 VERIFICATION AND EXTENSION OF LA CAILLE'S ARC OF THE MERIDIAN. §5. Triangulation The Corrections x„ x, in terms of the factors f„f south of the side Ceder Berg— Heerenloge- ment's Berg. ^39 = X,, = 2500/12 + 5-2990/57 2778/,o+0-2778/i,+6-7707/4+0-8392/e8 X41 = 1266/9H-0-1266/i,-3-0646/54 + 0-3824/j8 ^42 = 1961/,8-0 • 8265/„-0 • 8265/8 ^A3= 0714/,i+2-9563/3-2-9563/4-0-8309/57-0-8309/e8 X,, = 0769/, ^45 = 0794/3 + 1-2896/5 x^^ = 1333/6 + • 1333/7 + 1 • 9645/, X,, = 2000/5 +0- 2000/e-8 -2812/5 ^48 = 2564/+9-3140/3 + 9-3140/8 3^49 = 1639/0-6-7851/3+6-6667/4 =^50= 1053/3 + 1 • 1593/7 + 1 • 1593/3 ^51 = 1053/„ 0552 = 1053/1-1-6080/7 ^53 = 2105/9-2-2897/3 ^54= 0901/3+0-0901/5+0-0901/6-2-3790/53-1-4009/7 a^ss =-< M075/3 + 0-1075/, ^56= 0952/3+0-0952/5-1-4809/53-1-4809/57 X,,= 1724/,-2- 9155/7 «58 = O952/4+O-9OI8/55 x,, = -1220/3-1-4886/5 a^eo = -1724/, Xgi = 2326/e + 6-9147/6 a'ea = 2941/7-2-1370/6-2-1370/7 ajjj = -1379/0 + 2-1856/7 3^64 = 1075/5+4-5214/5-4-5214/56-4-5214/57 «65 = 2500/1+4-0488/7 «66 =-< 3-3333/5+0-3333/i7-14-0160/5 + 19-1113/56 + 14-0160/7 a^sg = 2000/4-2-8912/5 «107= -1220/, + 3- 8707/3 a'i08= 4444/3-7 -5828/3 ^m= -1818/33-0-9295/6 a;„o= 0787/5 + 2-4122/0 «iii- 6250/6-0-6250/9-0-8226/g-0-8226/6, «I12= 1887/0+0-1887/9-1-5289/, ajii3= 3846/34-0 - 3846/40-2 • O988/3 «'m= 4000/2 + • 4000/0-1 - 4998/3- 1 • 4998/6 x,,,= 0-5263/3g + 5-9903/e5-5-9903/67 INVESTIGATION OF THE CORRECTIONS TO THE ANGLES. 517 The Corrections Xi, x^ in terms of the factors f^f^. 'lie- ■"119 ■ *120 — '■126 ■ "ISO" ■-isi" ''132- ''133- "W ■'138- ^U9- "140- "ui- ''142- '-143- ■•147" •-ug- '■149- '•152- 0-1923/„ + 2-8814/e, 0- 2222/3,-3 •2186/ee • 6494/,o - 8 • 6646/e5 + 8 • 6646/66 0-0962/36-2- 2739/61 0- 7353/4-20- 4740/,8-20 • 4740/3-20-4740/60 1 • 3333/8 + 1 ■ 3333/44 + 16- 8680/0 -M6 • 8680/1 - 16 • 8680/, + 16 • 868O/4 0-7299/6-0-7299/44+9-8664/9+9-8664/6, 0-6369/3-0-3268/8 0-0244/35+0-0244/44+0-8532/63-0-8532/64 0-0704/34+0'0704/44-2-3003/63 - 1136/, + 3 • 6885/0-3 • 6885/68 • 6250/8-1 • 8IOO/0 + 1 • 8100/, 0-0694/3o+0-4166/,-0-4156/68 ■ 0333/33 +0- 0600/,-0 • 0600/, 0-2481/35-0-2481/4, + l-0997/3 0-2564/36 + 0-2564/45 - 5263/7-0 • 5263/45-3 - 0754/, 0-3030/3+0-3030/45+1-3340/63 + 1-3340/g 0-0592/3,-0-0592/3+0-0592/48 + l-1070/6, 0-3448/3+0-3448/1-0-3448/48 0-0952/31 + 1-8736/68 0-0704/„-0-0704/4,-l-7285/6i + l-7285/62-l-7285/4-l-7285/8 0-0704/g + 0-0704/,-l-8980/6, 0-2857/38+0-2857/40+0-2857/8 0-0833/33-0-0833/47-0-0833/8-2-5750/63+2-5750/4 • 0833/2 -I- ■ 0833/0 + " 0833/7 + • 0833/8 + 2 - 3369/3 0-0935/9+0-9042/„+0-9042/68 0-0935/0-1-5237/7 0-0935/31-1-3698/8 0- I8I8/5 +0 • I8I8/0 + 3-5689/4 0- 1818/3-0- 1818/„-l -5826/4-1 - 5826/^ 0-0901/0+0-9012/5-0-9012/66 0-1471/2+0-1471/o+l-5643/66 : 0-3333/34-0-3333/0 : 0- 1000/1-1 -5551/, 0-2222/36+5-5497/1 0-2041/3,-2- 7763/1 +2- 7763/7 §6. (F) Triangulation south of the side Ceder Berg — Heerenloge- ment's Berg. 518 VERIFICATION AND EXTENSION OP LA CAILLE'S ARC OF THE MERIDIAN. § 5. Tnangulation south of the side Ceder Berg— Heerenloge- ment's Berg. Final Equations for determining the values of the factors fi, f^.. (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) (13) (14) (15) (16) (17) (18) (19) (20) (21) (22) (23) (24) (25) (26) (27) (28) (29) (30) (31) (32) r-l-900 + :-0-648 + : 1-936 + : 0-597 + + 6605/, -6 -4758/5, 5871/+ •1266/+3-6087/,-4-3038/2+ -6207/3 7632/ + 4- 6769/, 7992/+2-6760/, 8255/ + 1-3749/, 6840/ + - 1333/- - 3963/, + 1 • 0351/, + - 6538/3 1266/+ -1333/+ -6020/+ •1667/,--1667/,--9425/i--0250/, - 1395/3 + 8 • 2340/4 + 4 - 6422/, 8707/- ■ 2439/, + 8 - OI5I/3-1 2 - 0497/,-6 • 7934/, + 8 - 0151/, 5133/+ -2501/,-'1235/,-4-6415/3-l-5741/,+3-4387/,+ -3824/, 7195/0+ -2778/,-ll-6844/3 + 13-4374/,+ -8392/8 1667/- ■ 2439/ + • 2501/ + - 2778/o + 1 ■ 0099/, - • 2902/,-3 • 3565/, 3565/, + 2 - 9663/3 + 22 - 5240/4 + 14 - 0434/, + - 3907/8 4993/,+2-3835/, 4942/3- • 1075/4 + 1853/5 + • 0901/6- • 1990/5-3 - 8599/e-2- 8818/, 1075/3+ -4027/4-1-9894/5 1853/,3 + - 8261/5 + - 2901/6- - 3333/, + 10 • 2562/5-27 • 4926/6-21 • 4192/, 0901/3+ -2901/5+ -6560/6+ ■1333/,-8-2812/5+4-5357/6+ -5636/, 3333/5+ -]333/,6+ -7607/,-14-0160/5 + 16-9743/6 + 13-8435/, = 0-119 + = 0-188 + = 0-338 + = 0-053+ = -0-973 + =:_0-033 + = 0-609+ -1 = 0-956 + = -1-394 + = -1-296+ = 0-387 + +3 = 0-959 + = -4-277 + = -0-824- = -3-960 + = -3-600 + = -0-886- = +1-920 + 1-2105/8+ -9091/,+ -3328/,+ -3328/8 = - 1 • 277 + - 4030/,9 + - 0990/,- • 7247/,- 1 - 3855/68 = 4 - 3-20 + • 3367/o + ■ 6619/, = 2-317+ -5277/, +2- 4408/, = 1-367+ -5720/,- -2174/3 + 4-5781/8 = _ 1 . 541 - - 2174/, + 1 - 5765/,3 + • 2778/,4-7 - 9096/8 + ' 4252/9 + • 4252/o = -2 • 072 + • 2778/3+1 ■ 5878/4- • 5747/6- - 5747/8-12 • 6345/8-20 - 0488/9-20 • 0488/o + 15 -0330/, + 15 -0330/4 = 1 - 520 + - 4565/5 + • 1695/6- ' 1695/2- ' 1695/3- - 9953/9 = _0-669- -5747/4+ -1695/5+2-0991/6+ -5747/8- -1695/,- -1695/43- -7299/4 --6-250/49-7-8395/8+9-0438/9-15-0330/,+90438/6,-15-0330/4 = • 194 + - 4690/, + - 1471/8 + • 1471/3 + • 1534/„-3 • 8467/,-3 - 8467/4- • 1534/68 = 2-451--5747y^4+ -5747/6+ ■]471/,+2-6801/8+ -1471/3 + 1-3333/44-7-8395/8 + 15-0580/„-2-0117/,-15 0580/,-2-0117/64 4972/9 + • 2381/, + • 2381/3 + • 0704/, + - 1887/9-3 - 4269/, 3526/3o--2128/43--0704/4,+5-0372/,+2-1441/6,+5-0372/64-2-1441/68 3220/, + -1333/,+ -5037/8 6304/,+ -0833/40+ -0833/,+ -0833/8+ -4000/9+ -1471/o+ -8371/3 0645/6 INVESTIGATION OF THE CORRECTIONS TO THE ANGLES. 519 Final Equations for determining the values of the factors /„ f^. (33) = 1 • 029 + • 668I/33 + • 3030/,5- • 0833/„- • 0833/,,- • I8I8/50-I • 2410/63 + • 9924/e, -•2486/5 2-532+ -7883/34- -0704/4- •3846/9- •3333/o-4-3991/3 l-094+^4543/5+-0244/4-^2481/5+-1818/„+l-9529/3+2^7157/4 1 • 030 + • 5748/36 + • 2564/5 + 3 ■ 2758/, -0-3o4+ •7896/37- •0592/0- ■5^263/5+ •059-2/8-l-6693/e,--2991/, 1 • 097 + • 6897/s + • 2857/o + - 2857/3-4 • 1481/6 2-298--0592/7+-9636/o+-3448/,--4040/8-l-1070/,+6-0503/5-6-0503/7 2-777+ -0833/32+ -2857/8 + 1 -1085/0+ -0833/7+ -3690/8 + 2-3369/3-7-7634/, +7-7634/6 1 -257+ -3448/9+ -6371/,- -3448/^ + 1 -3263/7 • 000- • 1667/- • 1235/- • 2902/, + • 9091/8 + • 0990/,9- ■ I695/5- • 1695/6 + •2381/9-^1335/3, + 1^8392/2+ -4076/3+3-3565/,-3-3565/2-9-7245/4 -9-7098/7 - 000- • 1695/,- - 1695/6 + • 1471/, + • 1471/, + • 238I/9- • 2128/o + • 4076/2 + ■7675/3-10-6124/,-10-6124/64 • 000- • 7299/6 + 1 - 3333/8 - " 0704/4 + - 0244/^ + 2 - I58O/4-9 - 8664/9 + 16 - 868O/0 + 10-8680/,--26-7344/2 + 3-1535/3 + 16^0148/64 ■ 000 + • 3030/33- • 2481/5 + • 2564/6- • 5-263/7 + 1 ' ^^SS/g + ■ 2343/3 + 1 • 3340/5 + 3-0754/7 0-000+ -0704/9- -0704/0+ -0833/2- -0833/3+ -0833/0+ -3074/7+ -1666/8 + l-7285/,-3-6265/2 + 4-9119/63+l-7285/68 0-000+ -0833/32- -0833/3+ -0592/7+ -2857/8- -4040/9+ -3690/0- -3448/, + -1666/7+ •8563/48 + l-1070/6,+4-9119/63-2-5750/64 0-000- -6250/6+ -1887/9+ -4000/2- -3846/34 + 1-5983/9+ -8226/9- -7063/2 + -6990/63-1-4998/6 0-000+ -1471/2- -I8I8/3- -3333/4+ -I8I8/35+ -8440/0+5-1515/4 + 1-5826/5 + 1-5643/6 21 - 3 + 3-6087/- - 3963/- - 9425/-3 - 3565/, + 3 - 3565/2 + 191 - 3593/,-112 - 8969/2 -33 - 2171/3-1 65 - 826/54-93 - 4890/7 47-1-6-4758/-4-3038/ + 4-6769/+2-6760/ + 1-3749/+1-0351/--0250/ +3-3565/,-3-3565/42-112-8969/, + 970-038/52+28-4720/3 + 165-828/4 + 93-4889/7 (53) = 90-9+-6207/+-6538/6-l-1395/ + S-0151/-4-6415/9-ll-6844/,o+2^9563/„ -33 • 2171/, + 28 • 4720/2 + 953 - 807/3-398 - 276/4-34-3910/7 + 308 • 487/8 (54) = 17-2+8-2340/-12-0497/-l-5741/+13-4374/,o+22-524/,-9-7245/42-165-826/, + 166-828/2-398-276/3+1652-768/4+640-871/7+45-5878/68 (34) (35) (36) (37) (38) (39) (40) (41) (42) (43) (44) (45) (47) (48) (49) (50) (51) (52) §5. (G) Triangnlation south of the side Ceder Berg — Heerenloge- ment's Berg; H 1 •520 VERIFICATION AND EXTENSION OP LA CAILLE'S ARC OF THE MERIDIAN. § 5. (G) Triangultition south of the side Ceder Berg— Heerenloge- meiit's Berg. Final Equations for determining the values of the factors /„ f^. (55) = 65-l--1990/,3-l-9894/,4 + 10-2562/,5-8-2812/i6-14-0160/i, + 1211-8076/55 -993- 704^-779 -^Se/;, (66) = 54'3-3-8-599/,3-27-4926/,5+4-5357/,6 + 16-9743/„-993-704/5g + 1592-809/56 + 1069-2.53/5, (57) = 48-3 + 4'6422/7-6'7934/3 + 3-4387/9 + ]4-04.34/n + 2-3835/i2-2-8818/,3-21-4192/,5 + 0-.5636/;„ + 13-8435/;,+ •3328/,8- •7247/,.,+ ■6619/20 + 2-4408/2, -9-7098/42 -93 - 489/, + 93 - 4889/^-34 - 39IO/53 + 640 - 871/4-779 • 456/55+1069-253/6 + lG.55-721/, + 34-6633/8 72-2+4-5781/2-7-9096/3-12-634.5/24-7-839.5/6-7-839.5/28+931-571/58 + 570 ■ O85/9 + 570 ■ O8.5/0 + 205 • 065/, + 205 - 065/^4 72-3+ -4252/3-20-0488/4- •9953/25 + 9-0438/26-9-8664/44+ -8220/49+570- 085/53 +834-810/9 + 570-7.36/o + 134-4467/2 97 • + - 42.52/3-20 - 0488/4 + - 1534/j + 15 ■ OSSO/j + 16 - 868/44 + 570 - 08-5/8 +570-736/9+969-089/o+213-403/6,-218-6448/3 + 213-403/64-]79-7086/9 52-7 + 15-033/4-15-033/e-3-8467/,-2-0117/8+5-0372/3o+3-2758/3e-l-6693/3, -l-1070/9-10-6124/43 + 16-868/44 + l-7285/4,+ l-1070/48+205-065/53 + 213 - 403/o + 1215 • 670/, - 255 - 8267/62 + 964 - 821/64-37 - 7694/;, + 42 • 4238/8 34-1+9-0438/6-15-058/8-3-4269/9 + 2-1441/30-26-7344/44-3-6265/47--7063/49 + 134 - 4467/9-218 - 6448/o-255 - 8268/6, + 461 • 559/2-255 - 8268/64-44-9105/68 11-3+-8371/2-1-2410/3-4-3991/34 + 1-9629/5+2-3369/40 + 3-1535/44+-2343/45 + 4-9119/, + 4-9119/8+ •5990/49+277-838/3-109 3425/64+5-8723/65 + 5-6236/66 (64) = 6-3 + 15-0330/4-15-0330/26-3-8467/,-2-0117/23+5-0372/30+ -9924/33+2-7157/35 -10-6124/3 + 16-0148/44--8465/4,-2-575q/48+5-1515/o+205-065/53 + 213-403/o+964-821/6,-255-8268/62-109-3425/63 + 1157-994/;4 + 13-7759/5 + 42-4238/8 (65) = 0-5--2486/33+6-0503/9-7-7634/40 + 1-3340/45 + 1-5826/50+5-8723/63+13-7759/64 +212-567/5-124-6323/66-68-28S6/6, (66) = 7-0+-0645/32-4-1481/38 + 7-7634/4o-l-4998/49+l-5643/o+5-6236/63-124-6323/5 + 198-2644/66 (67) = 16-2--2991/3,-6-0503/39 + l-3263/4,+3-0754/45-37-7694/6,-68-2866/65 + 191-3811/6, (68) = 63 -4 + 8-0151/+ -3824/9+ -8392/0+ •3907/,+ -3328/8-1 •3855/,9-- 1534/, -2-1441/39+ •5037/3, + l-7285/4, + 308-487/53+45-5878/54+34-6633/, -179-7086/60+42-4238/6,-44-9105/62 + 42-4238/64+687-689/68 (58) (59) (60) (61) (62) (63) INVESTIGATION OF THE CORRECTIONS TO THE ANGLES. 521 Logarithmic values of the factors /„ f /, = -9-91973 /„ = +0-63399 /jg = +9-73324 /42 = +0-48046 fbd ■=. -8-65860 /j = +9-73787 /,3 = +0-34098 /30 = +0-44371 ^43 = -0^48244 fbl = +9-01991 /3 = -8-55543 /„ = +0-14173 /3, = -0-84156 /44 = -1^12461 f&i = +8-70141 /^ = +9-19335 /,g = -0-58308 /32 = +0-79432 /45 = + 0^ 70377 fm = +9-05931 f, = +0-11034 /ig = +0-28088 /33 = -0-95223 /47 = -1^ 29596 fw = -9-43077 /g = -8-68068 /,o = -1-11516 /34 = -0-90025 ^48 = +0-25766 fu = -9-28526 /, = -8-52901 /,. = -0-68797 /ss = +0-23345 ^49 = -0-69224 Jm = -0-06224 /j = -9-65029 /22 = -0-38805 /3G = -0-46948 ^0 = -0-84230 Jm = +9-50777 /g = +0-75540 /,3 = +9-96247 /3, = +0-46471 A = -9-36458 fu = +9-10193 /j(, = +0-69891 /2, = +8-99238 /33 = -9-95431 /52 = -8-8^-?'>l fm = -9-22879 /u = -0-64617 /25 = -0-38589 /gg = -0-56894 Js3 = + 8-85937 fee := -8-06324 /i2 = -0-38389 A = -0-245-27 /40 = -0-56165 /m = -7-60160 fsi = -9-59077 /,3 = +0-88983 /2j = -9-63679 /^i = +0-26098 /55 = -8 •3-2853 f(& = -9-31187 /,4 = +0-60339 /2s = -0-15540 Resulting- v a^Mf* of the corrections X„ X,. x, = --"l303 ^20 = +-"2191 '"39 — --"O6O3 Xss — + •3627 3^116= -'7723 "'las = -l-"2731 x^ = +-0515 '^21 = --5225 «40 = --0403 0O59 = + •9783 a?„j= —-1628 3^136 = -1-0451 x^ = --2078 '"22 = _.2405 ^41 = + -0939 ^60 = ~ •8405 a;,i8= — -9980 3^137 = +^0615 x^ = +-0459 ^"23 = +-1758 3742 = --6680 a-61 = + •1949 a;„9=+-1549 a'i38 = +-8369 X, = +-0858 ^24 = --3767 '^43 = --0071 a;62 = + •2812 a!i2o= +2^2145 <^m = -•7814 x^ = --0128 ^26 = +-7188 ^44 = -■1861 Xs3 = -1 •5688 37121= -2-0581 35140 = +^2463 », = +-2930 ^^26 = --2746 X4S = + -5886 3^64 = + •0991 a!i22=-1^8141 =^141 = -•6284 arg = --3414 a'27 = +-3736 ^46 = + •6827 ^65 ^ •7950 3^123= +-5677 a'U2 = +•0878 X, = -6474 3528 = +-0408 «47 = +1-4769 aJeo = — •0778 a:i24=--1166 35143 = -1^3784 ar,„= +-3178 "^29 = --1632 ^48 == -1- 3-271 Xea = + •8640 a'i25=--3621 3^144 = -•3684 a!„= +-1370 ^30 = +-1380 ^49 ^ + -3020 ^107^= •1036 a;i26=--2874 »145 = -•5019 ar,2= --7326 a^si = --8973 *B0 ^= -•6197 a'l08= + •0263 fl5i27= -^7070 35l46 = -•2963 a;i3= +-3303 ^32 = --7307 3^51 = -1-3728 <>'109= — •1628 35128= --2016 ^147 = -•4690 a!i,= --3587 *33 = +-2162 0752 = -•6818 a'iio= + •0853 05,29= --1102 s'hs = -•1252 ■%= --0446 '''34 = +1-1629 ^^63 = + -8714 a;i„=+2 •8325 a'i3o=--4756 35149 = -•3310 «,5= --7079 ^^35 = --0390 ^M = +1-2461 ^112= + •9376 05,31= +-5404 35l50 = +•7885 a!i,= — -5328 *36 = +1-0344 a'55 = --4028 fl5ll3=-l •8390 a;,32= +-0373 a'lsi = -1-7254 xi^= +-7880 3^37 = --5791 *56 = +1-0611 a'ii4= + •0564 3=133= -'9790 35l52 = +•0350 !r,9= +-1254 aJas = +-5377 «57 = -•7225 a'ii5= — •6306 07134= +-2819 §6. (H) Triangiilation south of the side Ceder Berg— Heerenloge- raent's Berg. 522 VERIFICATION AND EXTENSION OF LA CAILLE'S AEC OP THE MERIDIAN. -6. (A) Triangulation north of the side Heeren- logement's Berg— Bok- keveld's Berg. Formation of ike Eq,Bi K R K V K C KB, K B KK, K L lY^ V C. ..Vogel Klip. ..Koe Berg. ...Boschluis. \ / \ > ^B B...BokkeTeld'3 Berg. \ / \ ^^ K,...Klip Rug. L... Louis Fontein. E...EoodeWal. \/ L ki K...Kamies-Sector Berg. Sin. KRL. Sin. KVR. Sin. KCV. Sin. KB|C Sin. KBB,. Sin. KK,B. Sin. KLK,. =1 Sin. KLR. Sin. KRV. Sin. KVC. Sin. KGB, Sin. KB,B. Sin. KBK,. Sin. KK,L CALCULATION. ANGLES. J- ANGLES— §£. LOG. SINES. CO-EFFICIENTS OF THE CORRECTIONS. KRL 6°4-'7-6608 ^'•864 64- '7-52-216 9 9541437-2 10-210 X^ KVR 46-23- 9-82 4-102 46-23- 5-718 9-8597327-4 20-061 x,^ KGV 60-26-55-56 3-413 60-26-52- 147 9-9394727-8 11-938 X,,, KB,G 56-40-51-29 3-684 56-40-47-606 9-9220060-4 13-841 X,,, KBB, 45-12-26-71 7-685 45-12-19-025 9 8510354-5 20-905 (Bh KK.B 89-48-56-78 5-095 89-48-51-685 9-9999977-0 0-068 «,3 KLK, 87-43- 1-61 5-964 87-42-55-646 Sum. . 9-9996546-5 0-840 «„ 9-526043Q-8 INVESTIGATION OF THE CORRECTIONS TO THE ANGLES. 527 KLR KRV KVC KCB, KB.B KBK, KK,L Formation of the Equations of Condition. CALCULATION — continued. ANGLES. 64-5916-63 47-41-21-25 71-17- 6-15 84-57-46-23 84- 0-12-94 66-39-15-48 40- 3-24-30 i^- 864 102 413 684 685 095 964 ANGLES — ^£. 54-59-12-766 47-41-17-148 71- 17- 2-737 84 -57 -42 -546 84- 0- 5-265 66-39-10-385 40- 3-18-336 Sum. . LOG. SINES. 9-9132948-3 9-8689330-8 9-9764055-9 9-9983188-1 9-9976155-5 9-9628998-5 9-8085646-7 9-5260323-8 CO-EFFICIENTS OF THE CORRECTIONS. 14-751 Xn 19-167 x^ 7-133 X,, 1-856 o;,^ 9-088 x,„ 25-044 X,, § 5. (C) Triangulation north of the side Heeren- logenient's Berg — Bok- keveld's Berg. (18): 0=107-0-25-044a!„+0-068«,3+0-840a:„-14-751a:,,-9-088x,„+20-905«„ + 10-210a!,, -19-167ir,,+22-061» -7-133a;^-l-856a;j„„+ll-938a!„^+13-841x„3-2-212a;,„ In the quadrilateral CSKV we have : V S V C V K X X =1 V C VK V S Therefore : Sin. VCS. Sin. VKC. Sin. V8K. -=1 Sin. VSC. Sin. VCK. Sin. VKS. C...KoeBerg. S.... North-end Sector Station. K...Kamies-Sector Berg. V...VogeI KUp. VCS VKC V8K ANGLES. 170-45- 5-17 48-16- 9-61 56- 16 -53 -40 0-003 3-413 3-820 CALCULATION. ANGLES — Je. 170-45- 5-107 48-16- 6-197 56-16-49-580 Sum. . LOG. SINES. 9 -2060648 -2 9-8728965-7 9-9200004-1 8 •9989618-0 CO-EFFICIENTS OF THE CORRECTIONS. -129-340 Xm 18-780 Xss 14-053 X.,, K 1 528 VERIFICATION AND EXTENSION OP LA CAILLE'S ARC OF THE MERIDIAN. §5. Triangulation north of the side Heeren- logement's Berg — Bok- keveld's Berg. (D) Formation of the Equations of Condition. CALCULATION — Continued. vsc VCK VK8 ANGLES. ^^■ 8 -12 -is -58 60-26-55-56 53-28-54-50 6-063 3-413 3-820 ANGLES — Je. 8-12-18-517 60-26-52-147 53-28-50-680 Sum. . LOG. SINES. 9- 1544781 -5 9-9394727-8 9-9050706-6 8-9990215-9 CO-EPEICIENTS OF THE COKRECTIONS. 146-023 a;,„4 11-938 a;,„, 15-591 X,, (19) : 597 • 9 + 15 - 591a!, - 18 • 780a;,, + 11 • 938a:„, + 129 ■ 340a!,„,- 14 ■ 053.*,„3 + 146 - 023a!„ Abstract of Equations of Condition. (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) (13) (14) (15) (16) (17) = (18) = - 909 + a;eg + 0370 +^75 — 0-533+a;72 + a'77 + X92 — • 592 + a!j7 + as,! + x^^ 2-319 + a;7o— fl37i+a!72 + a:75 + a59i — 1 ■ 294 + 0573 + OJgQ 4" OJgs 0-255 + a!8i + a;g3 + o:jo5 1 - 877+ 0594 +a;ioo + 05105 — 1-483 + a;79 + 0782 + 0795 -0 • 497 +a;84+aj8g + 0597 -2-387 + fl578+0582-a;83+a;84 + a;85 -0-822 +0583 + 0788 + 0587 1-080 + 0589 +3-99 + 05,01 1-440 + 0590 + 0198 + 05,03 4-7iU + a589 OTgo+rjoj +a5l04 - 000 + 0592 + a;93 + 0J94 + ajgg + 0595 + x„ + x^ 25-2-27-090o5o7 + 17-763o:o8+4-847o;74+2-720x75-15-302a!7o+0-840a;77+34-321% —16-315x92 20-9+17-3570578-14-751x79- 10-117a!85-0-683j586-23-812iB87 + 20'061a;88 + 11-728x95-1-499x97 107-0-25-044x72+0-068x73+0-840x,7-14-751x79-9-088x8o+20-905x8i + 10-210x82 -19-167x84+20061x88-7-133x89-l-856xioo +11-938x101 +13-841x,o5 — Z' ZL2XinR (19) = 597-9 + 15-591x98-18-780x99 + ll-938o5ioi+129-340xio2-14-053xio3 + 146-023x INVESTIGATION OF THE CORRECTIONS TO THE ANGLES. 529 The Corrections a;,, Kj (multiplied hy the weights) in terms of the factors f\,fi. 5'0a;67 = 10-0x70 = 10 -00:7, = 10-70:72 = 13- 4x73 = 9- 3a;-, = 9 -Oar. 74 75 — 12-0a;76 = 12-0x77 = '"2X78 ^ 14-2x73 = 8-2xso = 6 -2x81 = y * D^g2 = 8-4x83 = 12-0x84 = 3-34x85 - 2-68a;86 = 2-2xg7 = 4-8x88 = 7-7X89 = y- IXgQ = 11-OXgi = 8' 0x92 = 4-93x93 = 1-54x94 = 13-2x95 = 12-0x93 = 18-9x97 = 10-24x98 = 1-62x99 = 5-09x,„9 = ll-56x[9i = 2-64xi„2 = 59-5x,„3 = 10-92x,„4 = 4- 0xi95 = 0*y4a7inR ^ /3-27-090/,e /, + 17 -763/13 /1+/4 /2+/4-25-044/,8 /5+-0680/,8 /3+4-847A /4+2-720/,3 /,-15-302/,e /2+-840/.3+-840/,8 /o+17-357/i7 /8-14-751/„-14-751/,8 /-9- 088^8 /3+20-905/.8 /8+/io+10-210/,8 ~l/lO+/ll /9+/io-19-167/,8 /o-10-117/,7 /n- -683/7 /, -23 -812/7 /+20-061/7+20-061/8 /i2+/i4-7- 133/8 /3~'/4 /4 + 34-32I/6 /+/5-16-315/6 / +/5 /7+/15 ■/s+Zs /+/5+ 11 -728/7 /9+/5-I -499/7 /3 + 15 -591/9 /12+/5-18-780/9 /-I -856/8 /2 + 11 -938/8 + 11 -938/9 /4 + 129 -34/9 /3-14-053/9 /4 + 146 -023/9 / + 13 -841/8 /-2- 212/8 §5, (E) Triangulation north of the side Heeren- logement'B Berg — Bok- keveld's Berg 530 VERIFICATION AND EXTENSION OP LA CAILLE'S ARC OF THE MERIDIAN. § 5- (F) Triangulation The Corrections a;,, Xj... ...in terms 0/ the factors /„ f 2 north of the side Heeren- logement's Berg— Bok- keveld's Berg. *6Y = •2OOO/3-S-4I8O/6 •1408/,+2-5018/,6 -1000/+ -1000/4 %i = •1000/3- -1000/4 a'72 = • 0935/ + - 0935/4-2 • 34O6/18 <^13 = 0746/ + -0051/8 ^u = 1075/ + -5212/6 a'75 = 1111/ + -3022/6 «'76 = 0833/-1 -2752/6 a:„ = 0833/+ -0700/6+ -0700/8 ^78 = 1389/0+2-4107/, ="79 = 0704/-1 -0388/7-1-0388/8 3580 = 1220/-1- 1084/8 »81 = 1613/ + 3-3718/8 2^82 = • 1042/+ -1042/0+1-0635/8 ^'ss = ■ -■1190/0+ -1190/, =^84 = ' 0833/ + • 0833/0-1 - 5973/8 2^85 = • 2994/0-3-0289/, a'86 = 3731/1- -2549/, aj„ = 4.545/,-10-8236/n *88 =^ 2083/+4- 1795/, + 4- 1795/8 "'sg = 1299/,+ -1299/4- -9264/8 ""m = 1099/3- -1099/4 Xg, = 0909/ + 3- 1201/6 a;g2 = 1250/ + • 1250/5-2-0394/6 i'^gs = 2028/ + -2028/5 Xg4 = • 6494/+ -6494/5 a'gs = 0758/ + -0758/5 3^96 = 0833/ +• 0833/5 +-9773/, ^97 = 0529/+ -0529/5—0793/, a;98 = 0977/3 + 1 •5-226/9 2^99 = 6I73/2 + • 6I73/5- 11 - 5930/9 3=100 = 1965/- -3647/8 aJioi = ■ 0865/, + 1 • 0327/8 + 1 • 0327/^ 'Pl02 = 3788/4 + 48-9924/9 *103 = OI68/3- -2362/9 ^104 =^ 0916/4 + 13-3720/9 *'l05 = 2500/ +3- 4603/8 «;,„«= -1684/6- •3725/,8 INVESTIGATION OF THE COERECTIONS TO THE ANGLES. 531 — — TO ■* Tt< O ■* TO O CO ^ TO n TO o i-< (N ^ - N 00 ^ ■* v> 00 s o o o lO OS o c^ TO oi G^ 1— 1 G^ TO (N OS 00 Dl ' • • ? I 1 I + + + + 1 + ! +■ + + id C^J in o 1— 1 t- o CO O 00 *< • • • - • • + \ 1 • + • >* + Oi OS + • to Tj< 00 TO ■^ w 00 OS o 00 CN TO »n to o TfH O s + 1 1 TO • S^l »n 4- • o 00 00 ■* TO aa TO in -»*< o O M Oi TO w l^ CO o; TO in r- o •* 00 o K Oi OS o =>* to O o CO a oc in l-H - s t' Ci V l< > I + 1 C^ TO 00 o TO 00 "* -^ Oi 00 TO o TO 1 s • • + O 4- 'l • • CO 1 "P • *o TO OS (M O? . '^^ + ^ • Q m Q to TO CO CO lO O ^ + o + 1 + TO TO >n CO t^ ^ + T* • 1 o '^ ^ CO ^ • TO + 9 + • + T (N • ^ CO ■* ^ IN m + o + + ■ o> TO (?» OS -rji lO t^ TO r- J-- (N o o o Q (N OS O OS II t^ 00 OS s Ol in iO CO (N c^ 00 -* -<* V o w o CT l-H 1— t ■^ o r-H in + 1 1 + 1 + + 1 1 1 1 + + + ■uoi;?nbg;jo 'Ojn .-< (N TO ■* lO «> J>. 00 OS O l-H TO ■* Ui CO t^ 00 § 5. CG) Triangulation north of the side Heeren- logement's Berg — Bok- keveld's Berg. L 1 532 VERIFICATION AND EXTENSION OF LA CAILLE'S ARC OF THE MERIDIAN. § 5. (H) Triangulation north of the side Heeren- logement's Berg— Bok- keveld's Berg. Logarithmic values of the factors /„ /j /i = -9-83415 /„ = +0-29597 /j = +0-07799 /,2 = +9-98163 /s = -9-49998 /,3 = -1-01692 /^ = -0-83042 /i, = -0-91518 /, = +0-53446 /,5 = -0- 14139 /e = +0-38554 /,e = -7 95484 /^ = +9-48006 /„ = +8-85597 /, = +0-73175 /,, = -9-6-2610 /s = +0-53825 /i9 = -7-92630 /,(, = +0-32969 Resulting values of the corrections a;,, x^ X,, = - -0147 x,s = - -7476 x^ = - -1187 ajgg = - -5523 xn = - -7450 o^go = - -2386 «„ = + -6451 Kg, = - -6432 X72 = + -4687 xg2 = - -0051 a;,3 = + -2532 fljgj = + -2119 a-74 = - -0387 x^^ = - -7032 arvB = - -7545 X,, = + -1546 sc^g = - -0453 arge = + -4039 a;„ = + -0695 a^gy = + -1038 a;^, = + -4698 xgg = -1-0287 a;„ = + -7442 «gg = - -1653 osgo = + -8863 x,oo= + -2136 ojg, = -1-0336 a!,oi= - -3624 a^jj = + -3349 trio2= -3-5298 ajgg = - -0190 K,o3= - -1727 a-8, = +1-1410 ^104= - -8664 X,, = + -4222 a!,g5= -1-3874 x,^ = + -7193 a;,o5= + -5666 a:„ = + -1217 ^ SECTION VI. CALCULATION OF THE PRINCIPAL TRIANGLES. Note. — The triangles 1 to 24 and 42 to 64 inclusive, are comprised in the first system of equations for the investigation of the corrections of the angles, and the triangles 27 to 41 inclusive, are employed in the second system. The numerical values of the two series of corrections will be found at pages 521 and 532. The corrections to the angles of the triangles 25 and 26 (which could not be included in the investi- gation), have been obtained by dividing the error of each triangle into parts proportional to the reciprocals of the weights of the angles. 534 TERIFICATIOJf AN^D EXTENSION" OF LA CAILLE'S ARC OP THE MERIDIAN". § 6- SAME8 OF STATIONS. Nos. of ; the i ANGLES. Angles. J Corrections to the Angles. Cor- rections -if- Seconds of Reduced Angles. LOG BIKES. LOG DISTANCES. EEFERENCB8. A 1.— Measured Base = 42819'065 Feet. . .Log. 4-6316371. Kapoc Berg East End of Base 20 3 1 33-37-47-12 44-53-24-99 101-28-48-55 +-21 9 --208 --130 + -039 - -388 - -311 47-159 24-602 48-239 9-7433719 9-8486509 9-9912234 4-7369161 4-8794886 "West End of Base Sum. 180+f. Error 180- 0- 0-66 180- 0- 0-541 --119 - -660 0-000 Feet. 54565-24 75768-48 +0-119 A 2.— East End of Base to Kapoc Berg = 75768-48 Feet. . .Log. 4-8794886. (From A 1.) Biebeek's Kasteel 27 5 9 33-50-58-30 93-29-48-40 52-39-15-42 + -374 + 086 —-648 — -270 — -558 — 1-292 58-030 47-842 14-128 9-7458651 9-9991907 9-9003594 5-1328142 5-0339829 See A 7. See A 6. Kapoc Berg Sum 180+e. Error 180- 0- 2-12 180- 0- 1-932 — -188 —2-120 0-000 Feet. 135773-25 108139-13 +0-188 A 3.— Measured Base = 42819-065 Feet. . .Log. 4-6316371. K.F. ContreBerg East End of Base 24 6 2 39-29-18-20 62-58-29-91 77-32-12-82 --377 --013 + -052 - -574 - -210 - -146 17-626 29-700 12-674 9-8034023 9-9497840 9-9896433 4-7780188 4-8178781 "West End of Base Sum 180+£. Error 180- 0- 930 180- 0- 0-592 —-338 - -930 0-000 Feet. 59981-71 65747-33 +0-338 A 4.— East End of Base to K. F. Contre Berg = 65747-33 Feet. . .Log. 4-8178781. (From A 3.) Drie Eontein 26 4 23 50-41-39-63 63- 7-21-43 66-11- 0-07 --275 + ■046 + -176 — -634 — -313 — -183 38-996 21-117 59-887 9-8886151 9-9503528 9-9613461 4-8796158 4-8906091 East End of Base K. F. Contre Berg Sum 180+£. Error 180- 0- 1-130 180- 0- 1-077 --053 -1-130 000 Feet. 75790-68 77733-66 +0053 A 5.— East End of Base to Drie Fontein = 77733-66 Feet. . .Log. 4-8906091. (From A 4.) Zwart Berg East End of Base 3.5 7 25 44-40-29-04 86-35-55-16 48-43-36-35 --039 + -293 + -719 - -546 - -215 + -211 28-494 54-945 36-561 9-8470043 9-9992343 9-8759712 5-0428391 4-9195760 Sum 180+e. Error 180- 0- 0550 180- 0- 1-523 +•973 -0-550 0-000 Feet. 110366-97 83095-21 -0-973 CALCULATION OF THE PRINCIPAL TRIANGLES. 535 NAMES OP STATIONS. Nos. of the Angles. § M ■^ ho ANGLES. S S 3 Cor- rections -if. Seconds of Reduced Angles. LOG SINES. LOG DISTANCES. KEFEBENCES. A 6.— East End of Base to Zwart Berg = 83095-21 Feet. . .Log. 4-9195760. (From a 5.) Eiebeek's Kasteel Zwart Berg East End of Base 29 38 8 43- 2-2b'-42 62-38-59-93 74-18-35'66 — -163 + -538 - -342 - -844 - -143 -1-023 25-576 59-787 34-637 9-8341118 9-9485187 9-9835078 5-0339829 5-0689720 See A 2. Sum 180+£. Error 180- 0- 2-010 180- 0- 2-043 + -033 —2-010 0-000 Feet. 108139-13 117211-97 - -033 A 7.— Zwart Berg to Riebeek's Kasteel = 117211-97 Feet. . .Log. 5-0689720. (From a 6.) 22 37 27 + 29 46-16-30-70 56-50- 8-85 76-53-24-72 - -240 - -579 + -210 -1-460 -1-799 -1-011 29-240 7-051 23-709 9-8589359 See A 2. Eiebeek's Kasteel Sum 180+E. Error 9-9885305 5-1985666 180- 0- 4-270 180- 0- 3-661 — -609 -4-270 0-000 . Eeet. 135773-25 157967-09 +0-609 A 8.— Zwart Berg to Kapoc Berg = 157967-09 Feet. . .Log. 6-1985666. (From a 7.) Piket Berg Zwart Berg Kapoc Berg 49-43 34+36 13-22 26-57-50-70 129-67- 9-77 23- 4-60-36 + -309 + 2-197 + -571 — -993 + -895 - -732 49-707 10 665 59-628 9-6565079 9-8845529 9-5933613 5-4266116 5-1354200 See A 9. Slim 180+E. Error 180- 0- 0-830 180- 0- 3-907 +3-077 - -830 0000 Feet. 267061-72 136690-35 -3-077 A 9.— Kapoc Berg to Riebeek's Kasteel = 1.35773-25 Feet. . .Log. 5-1328142. (From a's 2 & 7.) Piket Berg Kapoc Berg 48 13 28 30- 5-58-55 69-21-31-06 80-32-39-36 -1-327 + -330 + -041 —3-998 -2-341 -2-631 54-552 . 9-7002604 28-719 9-971 lS.r MERIDIONAL DISTANCES OF THE SECTOR STATIONS. 560 VERIFICATION AND EXTENSION OP LA CAILLE'S AUG OF THE MERIDIAN. At the Royal Observatory, the azimuth of the Meridian Mark from the south point round „ , , by the west ... ... ... ... ... ... 179-59-57-000 Angle, Meridian Mark, Observatory, Sneeuwkop „ Kapoc Berg, Observatory, Sneeuwkop „ Kapoc Berg, Observatory, Eiebeek's Kasteel ... „ Sneeuwkop, Observatory, Zwart Kop ... 103-38-51-417 ... HI- 3- 2-598 34-30- 6-675 79-54-10-486 Azimuth of Sneeuwkop „ Kapoc Berg ... „ Eiebeek's Kasteel „ Zwart Kop ... ... 283-38-48-417 ... 172-35-45-819 ... 207- 5-52-494 3-32-58-903 I. Royal Observatory, Heerenlogement's Berg, Kamies Sector Berg, North End. STATIONS AND NODES. NOS.O.THKANO..S.] ™-" j i'- Seconds of Reduced Angles. LOG SINES. 1 „,„^°™„ . DISTANCES. 1 DISTANCES IN FEET. No. 1.— Eiebeek's Kasteel to Royal Observatory = 239295 • 22 Feet . . . Log. 5 • 3789340. ( a 46, p. 543.) "11 28+31 20-11-64-28 27- 5-52-49 132-42-16-34 - 4-37 4-37 4-37, 59-91 48-12 U-97 9-5381937 9-6584823 9-8662137 5-3789340 5-4992226 5-7069540 315662-12 +509276-82 Royal Observatory Eiebeek's Kasteel 180+E. 180- 0-13-11 — 13-11 0-00 No. 2.— Piket Berg to n,, (315662- 12-253359 -59) = 62302-53 Feet, (a 9, p. 535.) "7 (43+44+46+47+48) 56-54-3603 20-12- 4-28 102-53-2006 — 0-12 0-12 0-13 35-91 4-16 19-93 9-9231475 9-5382181 9-9889175 4-7945057 4-4095763 4-8602757 25678-89 -72489-60 «11 Piket Berg 180+£. 180- 0- 0-37 - 0-37 0-00 No. 3.— Ceder Berg to tij (226171 -64 +25678 -89) = 251850-53 Feet. ( a's 18 & 19, p. 537.) «15 62 52- 7-52-69 56-54-36-03 70-57-46-31 - 5-01 5-01 5-01 47-68 31-02 41-30 9-8972997 9-9231408 9-9755694 5-4011429 5-4269840 5-4794126 267290-80 +301587-01 "7 Ceder Bere 180+£. 180- 0-15-03 — 15-03 0-00 No. 4.— Heerenlogement's Berg to n,, (267290 • 80-228991 • 32) = 38299 • 48 Feet, (a 19, p. 537.) Pi «i5 89-59-60-00 52- 7-52-69 37-52- 7-48 - 0-05 0-06 0-06 59-95 52-63 7-42 0-0000000 9-8973078 9-7880654 4-5831929 4-4805007 4-3712583 30234-35 23510-31 Heerenlogement's Berg... 180+£. 180- 0- 0-17 - 0-17 00 No. 5.— Heerenlogement's Berg to Wi^ (267290-80-228991 -32) = 38-299 -48 Feet, (a 19, p. 537.) «13 21-5521-83 52- 7-52 69 105-56-46-18 — 23 0-23 0-24 21-60 52-46 4594 95721217 9-89731)75 9-9829586 4-5831929 49083787 4 9940298 80980-17 —98634-73 "15 Heerenlogement's Berg. . 180+£. 180- 0- 0-70 — 0-70 j O'OO CALCULATION OF THE MERIDIONAL DISTANCES, &c. 561 STATIONS AND NODES. NOS. OP THE ANGLES. 8PHEEICAL ANGLES. ie. Seconds of Reduced Angles. LOG SINES. LOG DISTANCES. DISTANCES IN FEET. No. a— Bokkeveld Berg to w,, (322890 • 82 + 80980 ■ 17) = 403870-99 Feet, (a 26, p. 539.) "l9 70-1-72 41-51-47-95 21-55-21-83 116-13- 9-56 - 6-45 6-45 6-44 4l"-50 9-8243424 1 T-qa Q-R7onflQO 5-60B2427 5-3539895 5 7347524 225938-13 -f54294U-75 "13 BokkeyeldBerg 180+E. 3-12 9-9528521 180- 0-19-34 -19-34 000 No. 7.— Kamies-Sector Berg to m,9 (385649-91-225938-13) = 159711-78 Feet, (a 28, p. 539.) P2 «19 89-.59-6n00 41-51-47-95 48- 8-15-05 - 1-00 1 5900 1-00 1 46-95 1-00 14-05 0-OOOOOno 5-2033369 9-8243553 .'i-n27fi9')i 1 06584-02 118944-60 Kamies-Sector Berg 180+E. 9-8720078 5-0753447 180- 0- 3-00 - 3-00 0-00 No. 8.— Kamies-Sector Berg to w,g (385649-91-225938-13) = 159711-78 Feet, (a 28, p. 539.) "22 93-f94-f95-|-99-98 30 39-43-14 41-51-47-95 107-28-36-44 - 2-51 2-51 2-51 40-63 45-44 33-93 9-7075377 9-8243516 9-9794766 5.2033369 5-3201508 5-4752758 209002-16 -t-298727-92 "l9 Kamies-Sector Berg 180-fe. 180- 0- 7-53 - 7-53 0-00 No. 9.— North End to n^ (261277-19-209002-16) = 52275-03 Feet, (a 39, p. 541.) Pa "22 89-59-6000 30-39-43-14 59-20-17-14 — 0-10 0-09 0-09 - 0-28 59-90 43-05 17-05 0-00 00000000 9.7075463 9-9345951 4-7182942 4-425S405 4-6528893 26658-79 44966-52 North End 180-l-E. 180- 0- 0-28 Distances between the Perpendiculars from the Stations: No. 1. Royal Observatory to n,, „ 2. n^ „ M„ „ 4. n,5 „pi . -1- 509276-82 feet . - 72489-60 „ . 4- 301587-01 „ . -- 23510-31 „ Royal Observatory to Heerenlogement's Berg No. 6. n,3 to 7!i9 „ 5. ni3 „ "15 „ 4. n,5 „ pi „ 7. Big „ Pi 714863-92 + 542940-75 feet — 98634-73 „ . + 23510-31 „ . -1- 118944-60 „ Heer No. 8. ,. 7. „ 9. Kam enlogement's Berg to K n,9 to Kja "is .! P2 "22 )> Pa ies-Sector Berg to Nor .amies-Sector Be bhEnd ... rg " 586760-93 . -f- 298727-92 feet — 118944-60 „ . -1- 44966-52 „ 224749-84 562 VERIFICATION AND EXTENSION OF LA CAILLE'S ARC OF THE MERIDLAN. § 7. II. Royal Observatory, Heerenlogement's Berg, Kamies-Sector Berg, North End. STATIONS AND NODES. NOS. OF THE ANGLES. SPHEEICAL ANGLES. i£. Seconds of Reduced Angles. liOG SINES, LOO DISTANCES. DISTANCES IN FEET. No. 10.— Riebeek's Kasteel to Royal Observatory = 239295 -22 Feet. .Log. 5-3789340. (a 46, p. 543.) n^ 31 ■00-44-35-52 27- 5-52-49 52- 9-36-94 — 1-65 1-65 1-65 33-87 50-84 35-29 9-9923211 9-6584935 9-8974758 5-3789340 50451064 5-2840887 110944-71 + 192348-45 Eoyal Observatory Riebeek's Kasteel 180+£. 180- 0- 4-95 - 4-95 0-00 No. 1 1.— Kapoc Berg to n, (135773-25-110944-71) = 24828-54 Feet, (a 2, p. 534.) "4 22 32-58-54-21 100-44-35-52 46-16-30-46 - 0-06 0-06 0-07 54-15 35-46 30-39 9-7358952 9-9923204 9-8589382 4-3949512 4-6513764 4-5179942 44810-15 +32960-53 "2 Kapoc Berg 180+£. 180- 0- 0-19 - 0-19 000 No. 12.— Zwart Berg to n, (157967 -09-44810 -15) = 113156-94 Feet, (a 7, p. 535.) "5 34 68-12- 3-98 32-58-54-21 78-49- 3-55 - 0-58 0-58 0-58 3.40 53-63 2-97 9-9677781 9-7358935 9-9916754 5-0536812 4-8217966 5-0775785 66343-23 + 119557-96 "4 ■■ ■ Zwart Berg 180+f. 180- 0- 1-74 - 1-74 0-00 No. 13.— Patrys Berg to n, (208827-67-66343-23) = 142484-44 Feet. ( a's 10 & 11, pp. 535, 536.) ". 40 70-58-41-10 6812- 3-98 40-49-18-00 - 1-03 1-03 102 40-07 2-95 16-98 9-9756121 9-9677778 9-8153805 5-1537674 5-1459331 4.9935358 139937-17 + 98522-59 "5 Patrys Berg 180+E. 180- 0- 3-08 — 3-08 0-00 No. 14.— Piket Berg to n^ (162693-99-139937-17) = 22756-82 Feet, (a's 11 & 12, p. -536.) "lO 44 25- 3-44-28 70-58-41-10 83-57 34-89 - 0-09 009 0-09 44-19 41-01 34-80 9-6269592 9-9756128 9-9975821 4-3571116 4-7057652 4-7277345 50788-48 +53423-77 "8 Pitet Berg 180+E. 180- 0- 0-27 - 0-27 0-00 No. 15.— Eland's Berg to «,„ (147057-91-50788-48) = 96269-43 Feet, (a 13, p. 536.) «.2 54 92-12-45-03 25- 3-44-28 62-43-31-52 - 0-28 0-28 0-27 44.75 44.00 31-25 9-9996761 9-6269583 9-9488139 4-9834S84 4-6107706 4-9326262 40810-38 +85630-06 "lO Eland's Berg 180+£. 180- 0- 0-83 - 0-83 0-00 CALCULATION OP THE MERIDIONAL DISTANCES, &c. 563 STAtlONS AND NODES. NOS. OF THE ANGLES. SPHBHICAL ANGLES. i^- Seconds Eeduced Angles. LOG SINES. LOG DISTANCES. DISTANCES IN FEET. No. 16.— Eland's Berg to n,, = 40810-38 Feet. . .Log. 4-6107706. (No. 15, p. 562.) «14 56 28-29-25-23 87-47-14'97 63-43-20-54 - 0-25 0-25 0-24 24-98 14-72 20-30 9-6785270 4-6107706 9-9996761 4-9319197 9-9526272 4-8848708 85490 86 + 76713-32 n,2 Eland's Berg 180+£. 180- 0- 0-74 - 0-74 0-00 No. 17.— Heerenl.'s : Berg to «u (148873 • 79-85490 • 86) = 63382 • 93 Feet. ( a 's 15 & 16, pp. 536, 537.) Pi "li 89-59-60-00 28-29-25-23 61-30-35-17 - 0-14 0-13 0-13 59-86 25-10 35-04 0-0000000 9-6785275 9-9439385 4-8019723 4-4804998 4-7459108 30234-39 +55707-13 Heerenlogement's Berg... 180+E. 180- 0- 0-40 — 0-40 0-00 No. 18.— Heerenl.'s Berg to «u (148873 ■ 79-85490-86) = 63382 ■ 93 Feet. ( A 's 15 & 16, pp. 536, 537.) j «16 27-55-37-75 0-27 37-48 24-96 57-66 9-6705681 9-6785270 9-9206912 4-8019723 ' 4-8099312 fiisss-io n„ 28-29-25-23 123-34-57-83 0-27 0-27 Heerenlogement's Berg... 180+e. 50520954 + 112744-51 180- 0- 0-81 - 0-81 0-00 No. 19.— Lewis Fontein to n,, (387566-90-64.555-19) = 323011-71 Feet, (a 27, p. 539.) "18 76 98- 4-52-51 27-55-37-75 53-59-39-17 - 3-14 3-14 3-15 49-37 34-61 3602 9-9956667 9-6705567 9-9079209 5-5092183 5-1841083 5-4214725 152794-70 +263920-12 «16 Lewis Fonteio 180+6. 180- 0- 9-43 - 9-43 000 No. 20.— Bokkeveld Berg to «,, (305086-50-152794-70) = 152291-80 Feet, (a 27, p. 539.) "19 »ia 72 41-51-47-95 98- 4-52-51 40- 3-24-77 - 1-74 1-75 1-74 46-21 50-76 23-03 9-8243534 9-9956663 9-8085765 5-1826765 5-3539894 5-1668996 225938-07 + 146858-68 Bokkeyeld Berg 180+e. 180- 0- 5-23 - 5-23 0-00 No. 21.— Kamies-Sector Berg to n,, (385649-91-225938-07) =^ 159711-84 Feet, (a 28, p. 539.) Pi 89-59-60-00 41-51-47-95 48- 8-15-05 - 1-00 59-00 1-00 , 46-95 1-00 i 14-05 0-0000000 5-2033371 9-8243552 5-0276923 106584-07 118944-65 "19 Kamies-Seetor Berg 180+£. 9-8720078 5-0753449 180- 0- 3-00 — 3-00 0-00 No. 22.— Kamies-Sector Berg to n,, (385649-91-225938-07) = 159711-84 Feet, (a 28, p. 539.) | »21 93+95 63-48-30-61 41-51-47-95 74-19-45-76 — 1-44 1-44 1-44 29-17 46-51 44-32 9-9.'529478 9-8243541 9-983.5489 5-2033371 ; 5-0747434 11878003 »19 Kamies-Sector Berg 180+f. 5-2339382 +171371-34 180- 0- 4-32 - 4-32 0-00 § 7- 1 T 564 VERIFICATION AND EXTENSION OP LA CAILLE'S ARC OF THE MERIDIAN. § 7. STATIONS AND NODES. NOS. OF THB ANGLES. SPHERICAI, ANGLES. i'- Seconds of Reduced Angles. LOG SINES. LOG DISTANCES. DISTAKOES IN FEET. No. 23.— Boschluis to w^, (299714-62-118780-03) = 180934-59 Feet, (a 32, p. 540.) "m 105 59-30-46-22 63-48-30-61 56-40-49-90 — 2-24 2-24 2-25 43-98 28-37 47-65 9-9353749 9-9529469 9-9220061 5-2575216 5-2750936 5-2441528 188405-52 +175449-76 "a Boschluis 180+e. 180- 0- 6-73 - 6-73 0-00 No. 24.— Koeberg to n,, (188405 • 52- 180718 • 75) = 1686 • 77 Feet. ( a 33, p. 540.) «23 102 — 100 — 101 95- 8-53-78 59-30-46-22 25-20-20-00 - 0-00 0-00 0-00 53-78 46-22 20-00 9-9982445 9-9353777 9-6314147 3-2270559 3-1641891 2-8602261 1459-45 - 724-81 "24 Koeberg 180+E. 180- 0- 0-00 - 0-00 0-00 No, 25.— North-End Sect. Stat, to n^ (25307 -32 +1459 -45) =26766 -77 Feet. ( a 40&41, pp.541 &542.) «»■ 90- 0- 0-00 84-51- 6-22 5- 8-53-80 - 0-00 0-01 0-01 0-00 6-21 53-79 0-0000000 9-9982444 8-9529546 4-4275960 4-4258404 S-3805506 26658-78 — 2401-88 North-End Sect. Station 180+e. 180- 0- 0-02 - 0-02 0-00 Collecting the results vre have : No. 10. Eoyal Observatory to Bj „ 11. Wj .. rl^ „ 12. n^ „ W5 „ 13. 7I5 „ 7!8 n 14. nj „ M,o „ 15. M,„ „ n,2 „ 16. «,j „ 7/,4 „ 17. «„ „ ;)i . + 192348-45 feet + 32960-53 „ . + 119557-96 „ + 98522-59 „ . + 53423-77 „ + 85630-06 „ . + 76713-32 „ . + 55707-13 „ Royal Observatory to perpendicular from Heerenlogement's Berg = 714863-81 No. 17. Tin top, - 55707-13 feet .. 18. n^^ „ 71,6 + 112744-51 „ ., 19- "16 ., "la + 263920-12 „ .. 20. Bis „ n,9 + 146858-68 „ ., 21. 7!,g „j>, + 118944-65 „ Between perpendiculars from Heerenlogemt's B. and Kamies-Sec. B. = 586760-83 No- 21. ni9 topa - 118944-65 feet » 22. n,g „ jij, + 171371-34 ,, " 23. Bji „ n^ + 175449-76 „ >. 24. nj3 „ n^ ... ... _ 724-8I „ .. 25. Baa „ p^ _ 2401-88 „ Betvi 'een perpendiculars fron 1 Kamies-Sec. B. andNortli End Sec. St. = 224749-76 CALCULATION" OF THE MERIDIONAL DISTANCES, Sec. 565 III. Royal Observatory, Heerenlogement's Berg, Kamies-Sector Berg, North End. STATIONS AND NODES. NOS. OF TRB ANGLES. SPHERICAL ANGLES. if- Seconds of Reduced Angles. LOG SINES. LOO DISTANCES. DISTANCES IN FEET. No. 26.— Sneeuw Kop to Royal Observatory = 158172 -51 Feet. .Log. 5-1991310. (a 52, p. 544.) »i 138 38-21-34-31 103'38-48-42 37-59-42-97 - 1-90 1-90 1-90 32-41 46-52 41-07 9-7928026 9-9875638 9-7892910 5-1991310 5-3938922 5-1956194 247680-74 + 156898-73 Eoyal Observatory Sneeuwkop 180+e. 180- 0- 5-70 - 5-70 0-00 No. 27.— Kapoc Berg to n, (286987 •28-247680- 74) = 39306-54 Feet. (a's52,53,54, p. 544.) »3 21 63-44-29-05 38-21-34-31 77-53-56-89 - 0-08 0-08 0-09 28-97 34-23 56-80 9-9526986 9-7928074 9-9902411 4-5944648 4-4345736 4-6320073 27200-29 +42855-57 n, " 180+E. 180- 0- 0-25 — 0-25 0-00 No. 28.— Winter Berg to % (255508 -12-27200 -29) = 228307-83 Feet, (a 22, p. 638.) % 142 50-56-19-94 63-44-29-05 65-19-23-93 - 4-31 4-31 4-30 15-63 24-74 19-63 9-8901196 9-9526942 9-9584059 5-3585208 5-4210954 5-4268071 263691-04 +267181-96 "3 Winter Berg 180+£. 180- 0-12-92 -12-92 0-00 No. 29-— Kapitein's Kloof to n, (263691-04-226609-48) =37081-56 Feet, (a 22, p. 538.)- »6 51 54-20-39-15 50-56-19-94 74-43- 1-21 - 0-10 0-10 0-10 39-05 19-84 1-11 9-9098412 9-8901268 9-9843633 4-5691580 4-5494436 4-6436801 35435-91 —44023-05 «» Kapitein's Kloof. 180+c. 180- 0- 0-.30 - 0-30 0-00 No. 30. Ceder Berg to n^ (224249 • 12 + 35435 - 91) - 259685 • 03 Feet. ( a 23, p. 538.) "15 60 52- 7-52-45 54-20-39-15 73-31-44-13 - 5-25 5-24 5-24 47-20 33-91 38-89 9-8972989 9-9098334 9-9817986 5-4144469 5-4269814 5-4989466 267289-20 +315461-67 »6 ■ ■ ■■ Ceder Berg 180+e. 180- 0-15-73 -15-73 0-00 No. 31.— Heerenlogement's Berg to rii, (267289 - 20-228991 - 32) = 38297 - 88 Feet. ( a 19, p. 537.) Pi "u ■ 89-59-60-00 52- 7-52-45 37-52- 7-72 - 0-05 0-06 0-06 59-95 52-39 7-66 0-0000000 9-8973074 9-7880661 4-5831747 4-4804821 4-3712408 30233-06 -23509-36 Heerenlogement's Berg. . 180+E. 180- 0- 0-17 — 0-17 0-00 § 7- 566 VERIFICATION AND EXTENSION OF LA CAILLE'S ARC OP THE MERIDIAN. § >■ STATIONS AND NODES. NOS. OF THE ANOLBS. SPHEEIOAL ANGLES. *£• Seconds of Reduced Angles. LOO SINES. LOG DISTANCES. DISTANCES IN EEET. No. 32.— Heerenlogement's Berg to n,, (267289 • 20-228991 • 32) = 38297 ■ 88 Feet. ( A 19, p. 537.) ( "13 21-55-22-07 52- 7-52-45 105-56-46-18 - 0-23 0-23 0-24 21-84 52-22 45-94 9-5721230 9-8973072 9-9829586 4-5831747 4-9083589 4-9940103 80976-48 -98630-30 "15 Heerenlogement's Berg. . 180+e. 180- 0- 0-70 - 0-70 0-00 No. 33.— Bokkeveld Berg to «i3 (322890 • 82 + 80976 • 48) = 403867 • 30 Feet. ( A 26, p. 539.) j "19 70+72 41-51-47-71 21-55-22-07 116-13- 9-56 - 6-45 6-45 6-44 41-26 1 9-8243418 15-62 ! 9-5720905 5-6062387 5-3539874 5-7347490 225937-03 +542936-50 "13 Bokkeveld Berg 180+e. 3-12 9-9528521 180- 0-19-34 -19-34 0-00 No. 34.— Kamies-Sector Berg to n,, (385649 -91 -225937 -03) = 159712-88 Feet, (a 28, p. 539.) | Kamies-Sector Berg 180+t. 89-59-60-00 41-51-47-71 48- 8-15-29 — 1-00 1-00 1-00 59-00 46-71 14-29 0-0000000 9-8243546 9-8720082 5-2033399 5-0276945 5-0753481 106584-61 118945-54 180- 0- 3-00 - 3-00 0-00 No. 35.— Kamies-Sector Berg to n,, (385649 -91 -225937 -03) = 159712-88 Feet, (a 28, p. 539.) | "22 93+94+95+99-98 30-39-43-38 41-51-47-71 107-28-3fr44 - 2-51 2-51 2-51 40-87 45-20 33-93 9-7075385 9-8243511 9-9794766 5-2033399 5-3201525 5-4752780 209002-98 +298729-45 "19 Kamies-Sector Berg 180+£. 180- 0- 7-53 — 7-53 0-00 No. 36.— North End Sector Station to w^^ (261277 •19--209002- 98) = 52274-21 Feet, (a 39, p. 541.) Pa "a 89-59-60-00 30-39-43-38 59-20-16-90 - 0-10 0-09 0-09 59-90 43-29 16-81 00000000 9-7075471 9-9345948 4-7182874 4-4258345 4-6528822 26658-42 +44965-78 North End Sector Station 180-l-e. 180- -0-28 - 0-28 000 Collecting the results, we hare: No. 26. Koyal Observatory to 7!, i> 27. », „ «3 ... » 28. ' «3 „ Tig » 29. «6 „ rig » 30. M, „ n,5 „ 31. ni5 „ p. + 156898-73 feet + 42855-57 „ + 267181-96 „ - 44023-05 „ + 315461-67 „ — 23509-36 „ Eoyal Observati „ 31. «, „ 32. rii „ 33. n, „ 34. «,i Distance betwee „ 34. n, „ 35. Ttii „ 36. % Distance betwee )ry to perpendicular frc .. Pi ) )i "15 » "19 » Pa n perpendiculars from ) »P2 ( » Mjj ! » Pa n perpendiculars from m Heerenlogemi Kamies-Sector B Heerenlogement jnt's Berg erg and N s Berg a orth-End nd KamiE Sector Stati s-Sector Be = 714865-52 + 23509-36 feet - 98630-30 „ + 542936-50 „ + 118945-54 „ on = 586761-10 — 118945-54 feet + 298729-45 „ + 44965-78 „ rg = 224749-69 CALCULATION OF THE MERIDIOlSrAL DISTANCES, &c. 567 IV. Heerenlogement's Berg, Kamies-Sector Berg, North End. STATIONS AND NODES. NOS. OF THE ANGLES. SPHEBIOAL ANGLES. it. Seconds of Reduced Angles. LOG SINES. LOG DISTANCES. DISTANCES IN FEET. No. 37.— Bokkeveld Berg to n,, (322890 • 82 + 80976 • 48) = 403867 • 30 Feet. (From No. 33, p. 566.) n„ 70+72+73 (-180°) 132- 2-39-83 21-55-2207 26- 2- 6-60 - 2-84 2-83 2-83 36-99 19-24 3-77 9-8707756 9-5721094 9-6423759 5-6062387 5-3075725 5-3778390 203035-75 +238692-64 »13 ■ Bokkeveld Berg. 180+e. 180- 0- 8-50 - 8-50 0-00 No. 38.— Keibiscoe to n„ (167709 -38 + 203035 -75) = 370745-13 Feet, (a 31, p. 540.) "20 80 65-23-47-82 47-57-20-17 66-39-16-37 - 8-12 8-12 8-12 39-70 12-05 8-25 9-9586571 9-8707548 9-9628979 5-5690755 5-4811732 5-5733163 302812-08 +374383-19 »17 Keibiscoe 180+e. 180- 0-24-36 -24-36 0-00 No. 39.— Kamies Berg Sec. Stat, to n^ (420039 • 71-302812 • 08) =- 117227 • 63 Feet. ( a 31, p. 540.) Pa 89-59-60-00 65-23-47-82 24-36-13-41 — 0-41 0-41 0-41 59-59 47-41 13-00 0-0000000 9-9586645 9-6194462 5-0690300 5-0276945 4-6884762 106584-61 48806-34 »2o" Kamies-Sector Berg 180+£. 180- 0- 1-23 - 1-23 000 No. 40.— Kamies-Sector Berg to n^ (420039 -71 -302812 -08) = 117227-63 Feet, (a 31, p. 540.) 125 93+94 25-27- 0-47 65-23-47-82 89- 9-18-58 — 2-29 2-29 2-29 58-18 45-53 16-29 9-6331808 9-9586627 9-9999527 5-0690300 5-3945119 5-4358019 248034-40 +272773-33 Kjo Kamies-Sector Berg 180+E. 180- 0- 6-87 - 6-87 0-00 No. 41.— Koe Berg to n,, (251416-13-248034-40) = 3381-73 Feet, (a 33, p. 540.) "a (180°)+101-102 84-51- 5-97 25-27- 0-47 69-41-53-56 - 0-00 0-00 0-00 5-97 0-47 53-56 9-9982444 9-6331910 9-9721464 3-5291389 3-1640855 3-5030409 1459-10 +3184-49 «J5 Koeberg 180+£. 180- 0- 0-00 - 0-00 0-00 No. 43.— North-End Sect. Stat, to n^ (25307 -32 +1459 -10) =26766 -42 Feet. (A40&41,pp.541&542.) Pa 90- 0- 0-00 84-51- 5-97 5- 8-54-05 - 0-00 0-01 0-01 0-00 5-96 54-04 0-0000000 9-9982444 8-9529604 4-4275903 4-4258347 3-3805507 26658-44 -2401-88 W23 . North End Sector Station 180+E. 180- 0- 0-02 ~ 0-02 0-00 1 V § 7- 568 VERIFICATION AND EXTENSION OP LA CAILLE'S ARC OF THE MERIDIAN. §7. Collecting the results, we have: No. 31. re,5 „ p, „ 32. r!,3 „ His „ 37. ni3 „ n„ „ 38. n„ „ Wjo „ 39. na, „ p. ... + 23509-36 feet — 98630-30 „ -1- 238692-64 „ ... + 374383-19 „ ... + 48806-34 „ Between perpendiculars from Heerenlogement's Berg and Kamies-Sector Berg : „ 39. nao „ p, ... — - „ 40. Hao » "i!5 ••■ ■-• ••• "• -■- + „ 41. "23 ., K25 •-• -•■ --- ■-- --- + ., 42. 7123 .. Ps -- - = 586761-23 48806-34 feet 272773-33 „ 3184-49 „ 2401-88 „ Between perpendiculars from Kamies-Sector Berg and North-End Sector Station : = 224749-60 V. Royal Observatory, Zwart Kop. STATIONS AHD NODES. NOS. OF THE ANGLES. SPHERICAL ANGLES. *'- Seconds of Reduced Angles. LOG SINES. LOG DISTANCES. DISTANCES IN EEET. No. 43.— Zwart Kop to Royal Observatory = 106401 • 13 Feet . . Log. 5 • 0269462. ( a 55, p. 544.) Pi Royal Obserratory Zwart Kop 180-l-e. 89-59-60-00 3-32-58-90 86-27- 1-27 - 006 0-06 0-05 59-94 58-84 1-22 0-0000000 8-7917885 9-9991660 5-0269462 3-8187347 5-0261122 6587-71 106196-99 180- 0- 0-17 - 0-17 0-00 No. 44.— -Royal Observatory to Simon's Berg = 133099-24 Feet. .Log. 5-1241756. (a 47, p. 543.) "26 125 46-12-57-71 100-58-46-39 32-48-18-98 — 1-03 1-02 1-03 66-68 45-37 17-95 9-8585074 9-9919771 9-7338240 5-1241756 5-2576453 4-9994922 180986-12 99883-14 Koyal Observatory Simon's Berg 180+e. 180- 0- 3-08 - 3-08 0-00 No. 45.— Zwart Kop to n^ (190110-86-180986-12) = 9124-74 Feet. ( a 's 57 and 58, p. 545.) Pi "w 89-50-60-00 46-12-57-71 43-47; 2-30 - 0-01 0-00 0-00 59-99 57-71 2-30 0-0000000 9-8585094 9-8400693 3-9602205 3-8187299 3-8002898 6587-64 6313-79 Zwart Kop 180-|-£. 180- 0- 0-01 - 0-01 0-00 No. 44. Royal Observatory to n26 » 45. Tijs „ pt . -f 99883-14 feet . + 6313-79 „ Distance Eoyal Observatory to perpendicular from Zwart Kc By No. 4 p = 106196-93 13 106196-99 Mean 106196-96 CALCULATION OF THE MERIDIONAL DISTANCES, &c. 569 VI. Royal Observatory, Cape Point.— Calculation of the distance Observatory, Cape Point. STATIONS AND NODES. NOS. OP THE ANGLES. SPHBHICAL ANGLES. *£■ Seconds Reduced Angles. LOG SINES. LOG DISTANCES. DISTANCES IN FEET. No. 46.— Royal Observatory to Sneeuwkop = 158172-51 Feet. .Log. 5-1991310. (a 52, p. 544.) | Cape Point Eoyal Observatory Sneeuwkop 180+£. 135-139 53-57-46-983 75- 1-50-135 51- 0-28-368 -1-S29 1-829 1-828 45-154 48-306 26-540 9-9077512 9-9850048 9-8905478 5-1991310 5-2763846 5-1819276 188966-39* 152029-41 180- -5-486 -5-486 0000 No. 47.— Royal Observatory to Simon's Berg = 133099-24 Feet. .Log. 5-1241756. (a 47, p. 543.) | Cape Point Royal Observatory Simon's Berg 180+£. 119-124+125 36-57-51-035 99-39-24-855 43-22-48-820 -1-570 1-570 1-570 49-465 23-285 47-250 9-7790981 9-9938026 9-8368501 5-1241756 5-3388801 5-1819276 218212-75"' 152029-41 180- 0-4-710 -4-710 0-000 From No. 47.— Angle Cape Point, Royal Observatory, Simon's Berg ... „ Simon's Berg, Royal Observatory, Sneeuwkop 99-39-24-855 24-37-34-755 .•. „ Sneeuwkop, Eoyal Observatory, Cape Point From No. 46.— „ 75- 1-50-100 75- 1-50-135 Mean 75- 1-50117 ... 283-38-48-417 ... 358-40-38-534 No. 48.— Royal Observatory to Cape Point = 152029-41 Feet. .Log. 5-1819276. (Nos. 46 and 47.) Pi Royal Observatory Cape Point 89-59-60-00 1-19-21-47 88-40-38-66 — 0-05 0-04 0-04 59-95 21-43 38-62 0-0000000 8-3632737 9-9998843 5-1819276 3-5452013 5-1818119 3509-15 151988-92 180+£. 180- 0- 0-13 - 0-13 j 0-00 No. 49.— Royal Observatory to Sneeuwkop = 158172-52 Feet. .Log. 5-1991310. (a 52, p. 544.) j "n 135-139 62-38-25-66 76-21-11-58 51- 0-28-37 - 1-87 1-87 1-87 23-79 9-71 26-50 9-9002786 9-9875620 9-8905478 5-1991310 5-2864144 5-1894002 193381-25 154667-90 Royal Observatory Sneeuwkop 180+£. 180- 0- 5-61 - 5-61 0-00 No. 50.— Cape Point to n^ (193381-25-188966-39) = 4414-86 Feet, (a 60, p. 545.) | Pi «27 90- 0- 0-00 52-38-25-66 37-21-34-34 — 0-00 0-00 0-00 000 25-66 34-34 0-0000000 9-9002816 9-7830561 3-6449169 3-5451985 3-4279730 3509-12 2679-00 180+j. . 180- 0- 0-00 - 0-00 0-00 From No. 49. Royal Observatory to n„ „ 50. n„ „ Ms . = + 154667-90 fe - 2679-00 et 1 Dis tance of perpendiculars from Royal Ob servatory and Cap 3 Point = 151988-90 § 7. (»). A 60, p. 545 C"). A 59, p. 545. 570 VERIFICATION AND EXTENSION OF LA CAILLE'S ARC OP THE MERIDIAN. §7- Calculation of the Reduction to Parallels. Heerenlogement's Berg. From No. i. y = 30234'35 feet. „ 31. „ 30233-06 „ Latitude = 31°-58'-10". Log. i/» 8-9609824 „ tan. lat 9-7952737 Mean 30233-70 8-7562561 „ 2 Normal.. 7-6220752 Eeduction = 13-620 ... 1-1341809 Kamies-Sector Berg. From No. 1. y = 106584-02 feet. „ 21. „ 106584-07 „ ., 34. „ 106584-61 „ „ 39. „ 106584-61 „ Latitude = 30°-21'-21". Log. J^" 0-0553868 „ tan. lat 9-7676462 9-8230330 „ 2 Normal.. 76220391 Mean 106584-33 Eeduction = 158-852 ... 2-2009939 North-End Sector Station From No. 9. y = 26658-79 feet. „ 25. „ 26658-78 „ „ 36. „ 26658-42 „ „ 42. „ 26658-44 „ . Latitude = 29°-44'-17". Lbg.y' 8-8516752 „ tan. lat 9-7568418 8-6085170 „ 2 Normal.. 7-6220256 feet Mean 26658-61 Eeduction = 9-694 ... 0-9864914 Zwart Kop. Latitude = 34°-13'-34". From No. 43. i^ = 6587-71 feet. Log. !/= 7-6374650 „ 45. „ 6587-64 „ „ tan. lat 9-8326786 Mean 6687-68 7-4701436 „ 2 Normal.. 7-6221278 feet ■ ■ Eeduction = 0-705 ... 9-8480158 Cape Point. Lat From No. 48. y = 3509-15 feet. „ 50. „ 3509-12 „ itude = 34°-21'-7". Jjoe.v' 7-0904000 „ tan. lat 9-8347277 Mean 3509-135 6-9251277 „ 2 Normal. 7-6221305 feet ■ ■ Eeduction = 0-201 ... 9-3029972 CALCULATION OF THE MERIDIONAL DISTANCES, &c. 571. § 7- Abstract of Results for the Meridional Distances of the perpendiculars from the Theodolite Points. ARC. RBFKKENCE. Distances of the Perpendiculars. MEAH8. Eoyal Observatory to Heerenlogement's Berg page. 561 564 566 feet. 714863-92) 714863-81 ) 714865-52 feet. 714864-69 Heerenlogement's Berg to Kamies Sector Berg.... 561 564 566 568 586760-93 586760-83 586761-10 586761-23 586761-02 Ramies Sector Berg to North End 561 564 566 568 224749-84 224749-76 224749-69 224749-60 224749-72 Royal Observatory to Zwart Kop 568 568 106196-99 106196-93 106196-96 Royal Observatory to Cape Point 569 569 151988-92 151988-90 151988-91 From the above we derive the distances of the perpendiculars and parallels of each Theodolite Point from the North-End, as follows : AKC. Distances of the Perpendiculars. Reduction to Parallels. Distances of the Parallels. North End to Kamies Sector Berg.... „ „ Heerenlogement's Berg „ „ Eoyal Observatory „ „ Zvrart Kop „ „ Cape Point feet. 224749-72 811510-74 1526375-43 1632572-39 1678364-34 ft. ft. ft. +9-694-158-852=-U9-16 +9-694- 13-620=- 3-93 +9-694 =+ 9-69 + 9 694— 705=+ 899 +9-694- 0-201 = + 9-49 feet. 224600-56 811506-81 1526385-12 1632581-88 1678373-83 1 X 572 VERIFICATION AND EXTENSION OP LA CAILLE'S ARC OF THE MERIDIAN. § '• Calculation of the Reduction from the Zenith Sector Point to the West Rock Theodolite Station Point on the Kamies Berg. At "Point Azimuth." Angle between Meridian Mark and Louis Fontein (pagea 468 and 470) By transit instrument observations, error of Meridian Mark, S.W. Angle between Louis Fontein and West Rook theodolite point (pages 469 and 470) Azimuth of the West Eock theodolite point ... Distance between "Point Azimuth" and West Eock point = 210 feet (Elevation above the sea 5144 feet,) reduced to the level of the sea 209-948 feet.... ... ... (Log.) Azimuth of West Eock theodolite point 63° 40' 7"-62. . . . ... ... ... (Log. sine) (Log. cosine) West Eock theodolite point, west of Point Azimuth ... Meridian difference, West Eock, south Sector point 5 J inches south of parallel of "Point Azimuth " ... Distance on the Meridian between sector point and West Eock point Meridional radius of curvature x sine 1" 188-165 feet ... . 93-1245 feet ... , 0-4583 feet. 92-6662 feet. ... (Log.) (ar. CO. Log.) Sector point North of West Eock theodolite point, difference in latitude O'-Q 1 7 10-34-44-96 1-86 53- 5-20-80 63-40- 7-62 2-3221118 9-9524267 9-6469520 2-2745385 1-9690638 1-9669213 7-9955823 9-9625036 Calculation of the Reduction from the Zenith Sector Point to the Theodolite Point on Heerenlogement's Berg. Azimuth of Piketberg on the horizon of the theodolite point Angle between Piketberg and the sector point (page 463) Azimuth of sector point on the horizon of the theodolite point . Subtense of 20 feet bisected by sector point (page 463). 10 feet. Angle at theodolite point 2°-17'-7"-8 (page 463). l°-8'-33''-9. Distance of sector point from theodolite point 501-319 feet Depression of sector point below theodolite point 8°-26'-40". Horizontal distance 495-884 feet. Differenceof elevation 73-618 feet. ... Height above the sea 2384 feet. Horizontal distance reduced to the level of the s Azimuth of sector point on horizon of theodolite point 139°-36'-17"-06. Perpendicular distance west 321-325 feet. Meridian difference, sector north of theodolite point 377-619 feet. Meridional radius of curvature x sine 1", arth. co. Sector point north of theodolite point, difference in lat. = 3"-737 1-50-21-63 137-45-55-43 ... 139-36-17-06 - (Log.) (Log. cotan.) (Log. cosine) (Log. sine) 1-0000000 1-7001138 2-7001138 9-9952660 9-1668750 (Log.) (Log.) 2-6953798 1-8669888 495-828 feet ... (Log. sine) (Log. cosine.) ... (Log.) 2-6953310 9-8116131 9-8817223 2-5069441 ... (Log.) ... (Log.) 2-5770533 7-9954737 (Log.) 0-5725270 CALCULATION OF THE MERIDIONAL DISTANCES, &c. 573 Calculation of the Reduction from the Zenith Sector Point to the Theodolite Point on Zwart Kop. Pages 435 and 436. — Base of the small triangle 303'396 feet. Elevation above the sea 1939'26 feet. Base reduced to the level of the sea 303-382 feet. § 7- Theodolite Point Sector Point South End of Base... OBSERVED ANGLES. 35- 8-43-35 88-33-49-60 56-17-25-05 —200 44 50 26 LOG. SINES. 9-7601627 9-9998636 9-9200516 LOG. SIDES. 2-4819898 2-7216907 2-6418787 SIDES IN FEET. (303-382) 526-85 438-41 Azimuth of Sneeuwkop on horizon of theodolite point (from general table) Angle No. 146, page 143, corrected ... Azimuth of King's Battery station point Angle between sector point and King's Battery station point, page 436 ... Azimuth of sector point on horizon of theodolite point ... Theodolite point to sector point 438-41 feet. ... 67°-12'-20"-66 Perpendicular distance of sector, west 404-17 feet Meridional distance of sector south 169-85 feet Meridional radius of curvature X sine 1°. Meridional difference of latitude, or reduction = l''-6803 (Log.) (Log. sine) (Log. cosine) (Ar. CO. log.) 246-45-34-98 67-32-21-70 179-13-13-28 112- 0-52-62 67-12-20'66 2-6418787 9-9646848 9-5881857 2-6065635 2-2300644 7-9953169 0-2253813 574 VERIFICATION AND EXTENSION OP LA CAILLE'S ARC OF THE MERIDIAN. § T- Tablk containing the logarithms of the radius of Curvature of the Earth in the Meridian, perpendicular to the Meridian, and in a vertical plane inclined 45° to the Meridian, — also the log. (2 r- sin. 1") for calculating spherical excess. The axes of the earth employed in these calculations are: a=20923713 feet and 4=20853810 feet. LATITUDE. 29 40 50 30 31 32 10 20 30 40 50 10 20 30 40 50 10 20 30 40 50 33 10 20 30 40 50 34 10 20 30 40 50 EADIDS OP CUKVATUBE IN THE MERIDIAN. Log. p. 7-3187975 88084 88193 88303 88413 88524 88635 88746 88857 88969 89082 89195 89308 89422 89535 89649 89764 89878 89992 90108 90223 90339 90455 90572 90689 90806 90923 91040 91158 91277 91395 91513 Diff. 109 109 110 110 111 111 HI 111 112 113 113 113 114 113 114 115 114 114 116 115 116 116 117 117 117 117 117 118 119 118 lis EADIUS OF CnRVAIURE PERP. TO MERIDIAN. Log. V. 7-3209939 09975 10012 10050 10087 10123 10160 10197 10235 10272 10310 10347 10384 10422 10460 10498 10536 10574 10613 10651 10690 10728 10767 10806 10845 10884 10923 10962 11001 11041 11080 11120 Diff. 36 37 38 37 36 37 37 38 37 38 37 37 38 38 38 38 38 39 38 39 38 39 39 39 39 39 39 39 40 39 40 EADIUS OF CURVATURE IN AZIMUTH 45°. Log. r. 73198944 199016 199089 199163 199237 199311 199385 199459 199533 199608 199683 199758 199833 199909 199985 200061 200137 200213 200290 200367 200444 200521 200599 200677 200755 200833 200912 200990 201069 201148 201227 201306 Diff. 72 73 74 74 74 74 74 74 75 75 75 75 76 76 76 76 76 77 77 77 77 78 78 78 78 79 78 79 79 79 79 FOE COMPUTING SPHERICAL EXCESS. Log. 1 2 r» sin. 1" 0-3736063 5919 5773 5625 5477 5329 5181 5033 4884 4735 4585 4435 4285 4134 3982 3829 3677 3524 3371 3217 3063 2908 2753 2597 2441 2285 2128 1971 1813 1655 1497 1339 Diff. 144 .146 148 148 148 148 148 149 149 150 ISO 150 151 152 153 152 153 153 154 154 155 1.55 156 156 156 157 157 158 158 158 158 SECTION VIII. §8. ABSTRACT OF THE AZIMUTHS, LOG. DISTANCES, LATITUDES, AND LONGITUDES, ALSO A GENERAL TABLE OF THE LATITUDES AND LONGITUDES, AND RADII OF CURVATURE OF EACH POINT. In the first column (A), is given the name of the Station at which the calculation originates ; the second column (B), gives the name of the Station whose required Latitude and Longitude are contained in columns 8 and 9. Column 3, contains numbers for reference. „ 4, exhibits the mode of forming the azimuth (a) of the Station (B), as measured on the horizon of the Station (A). The bracketted numbers in this column refer to the angles so particularized in pages 476 — 484, corrected respectively by the application of the quantities in pages 521 and 532. „ 5, contains the value of (a) thus obtained, the log. distance of the two stations, and the arc 8. „ 6, contains the values of | (a' + ^—oi) and | (a' + f+w), also the small correction ^. „ 7, contains the Azimuth (a) of the Station (A) as measured on the horizon of the Station (B), also the difference in Longitude and the difference in Latitude. The former being reckoned from the Meridian of the Royal Observatory, — when to the East. The formulae employed in these calculations are given at the end of this Section. 1 Y 576 VERIFICATION AND EXTENSION OP LA CAILLE'S ARC OF THE MERIDIAN. § 8- fN t^ eo tn CJl lO o OJ -<** ^ CD B o o .(£) »n CO CD in g ^ o 00 9 «£> »o C30 "?* 9 00 -7* 00 ** 6 i;"- w CS b ^ 00 b r- /'- l-H 5 Th (N tH (N "* 1^ Tt* ■^ ■^ o Tj* il^ »h b b ,1h b ■if b b » (?» - 00 •as to CO o CO IN w a Q o t^ o OS CO o OS o r^ O O CO 00 ^- <£> U3 00 t- IN 00 9 00 " k> ii b b 00 b b CO b b 00 b b b b b boo ''-^(=>C> bob c^ b b a ° O [ ur> 1 (N 1 1 *^ 1 1 O j *^ 1 00 00 1 (N 1 1 1 52 3 fi CO 1 CO 1 1 1 1 1 -H 1 CN 1 CO 1 1 1 CN ^^ -coo 00 « »c — t^ ii:5 O »0 Tj« r-. O (D -H O i-H eo CD w (N CO CO CJS CN CO -^ CO 00 CTS (N OS >j 3 T en o o 00 OS o 00 OS c^ o o o (N OS O OS Tj< O CO OS o 00 CD O OS 00 Tf CO iO .-H IN ■* - -4 1 + + + ^ -Tf o o CO -H O r* t* o OS O o TjH OS O •P ■* 9 CO «;- O Tj« p O irs OS o CO OS O CD CO O ,1h -^ CO .^ 'l (N — I JC^ (N *| OS OS 'i §^ + b 00 _L Oi t^ j_ (N b *i CN -tr 1 b ^ 'l b b 'i CO 7^ I b Ah V a ^ 6 b 00 CO b t^ b b fci b OS b CN b b o Ah t-. r-* At b b Ph a a H ^a"a CO ■* 7" ^ r- « ■■ ' -- KJt^-W CO CO ID CD CD H O Tf OS CO ■. CO g O CO CN l-H — m OS C O CO CD CN r-- O CO CO CD CO O CN O O O CT i--»^ Tjl OS (N >!f CO IN x^ «a O Wl>. CO »-- — ■- r-i OS »0 r- iO t^ 00 CO CO — CO -^ o " iO c» 1-* CO (M CO . « h b 00 b b b b b Ah b b b b 6 OJ b b S o t^ t-- o o 00 if3 O Tt< 00 w § (N c< (N CO eo a 3 i » a N -•'■^ ^-\ o §■ d /-N OS to d ^-N d 00 d '^ 6 /-^ Q fa o !zi2 ;2i;: !2i2 ^o !2;2; "i^ taS ^g ssr sc 6^ ac 1 Ph ac S bC- so aff o So 1 + 1 + ^+ 1 + o 1 + 1+ ^ IS' « + B a a Q "b « s « 1 H S ^ p :>i ^ H •aanajajaa rt w CO ■>* o to t^ 00 o> o _, Eh 9 JOJ -0^ ^ o O . !25 o i! o P5 ■J, 1 s tA § 'in b c3 !4 t ^ c_ s & ) i 4^ p s o H w O •s pq jn 'a o a 1 s eg a t 1 I 1 p; 1 a 1 > ■» ^ tH o O 1 r = := ' :^ = c < = = 5 H .Q o 02 o 1 a CALCULATION OF THE GEODETICAL LATITUDES, LONGITUDES, &c. 577 O) (N ^^ ^^" •0 b- ^^ tn ■^ OS un OS CO — in CI -1< -* OS OC 9 00 to in 00 00 in 00 to in. 9 to TO r* 00 '^ CO « ■* to C4 CO b b b ih "-• 6 6 1-1 CO -^ b b ,1) b b in b CO CI 6 6 . c 6 1 b b 6 b 1 1 b b b b b to c c cs 00 . tc o- to 04 00 to 00 to CO to to OS n Cf. b (N t^ b in ih t* r» OS b b b (N b TO »n CO -^ Ol tf" , T Th . 7^ ™ ■"• (N ■^ — in ■<* CN (N CN (N in r-, »n '^ rt* »n Cl CO T** . rp T*< rH in ih "^ -^ !N «a ^- S "* 00 09 b i> th CO OS « 00 CO r^H ■* b b ■^ b r» OS CO ^ in •?*< b -^ b (N ■— 1 •^ .Ih .ll TO Tt-cOT- CO C4 CO tM Ol OJ — CT CT TT CO CO CO 1— < CO CO _ CO CO CO IN CO (O o o 6 6- 6 »h 6 i^ oi b b 'if b b OS b b Tti b b in b b (N b i^ c> c> b b b bob "* a «■ to 1 *^ 1 (N 1 *^ 1 J^ 1 <>• I CO 1 in 1 ■ M CT 1 o» « c^ CT 1 -H 1 I ^ 1 ^ 1 w 1 CO 1 CO 1 ! O 00 OH IT in OS ■<* ■* OS ■rh t- 00 W5 -^ CO to (M CO in Oi '^ Tj in 00 C<1 OS CO in 1ft t>. to d OS r-4 in OS eo i O (N — -* ° s -^ (O ■* CN 00 Th to t^ 00 to CO to ^ to !>. TO Cl to I999 n t^ »n OS CO CO Tj* l> ^- 00 tjH 9 CO CO t-- ec ■^ (N OS ■* TP t^ CI - .-( to b i-H r^ b; rH CO TO (N 01 cq ■<^ (N (N T! (N (N eo CO r— CI ■T ^ CT CM CO . "iP ^ c^ (N CO rH C^ CO CO M CO COCJ CO ift CO CO t^ CD >h th 6 QC «b © »n t-' »h b ^ in b in in b OS in b -^ ih b in in b , CO i^ 00 t- m c in in in m r- ^ CO c^ eo CO CO '"' 1-— \ OS as to ^-\ »n /-^ 00 o- -^ ^ 0) ^(2 Tjl in —1 tN 2$ tc w-^ '^Q IN «■(? "•? cja 1 I 1 c (N ^? i It s ^T E d 1 8 a T a 1- ■as 1 + IT E c tfc 1 It E c * 1 ^1 1 •^8 tfa '^ 1 IT 1 + + 1 5 M « •^ in ec t^ OC OS C ^^ (N CO ■* •n a d « IN CI .0 > pc 1 Q P- •* ■ pq ^ ■» ,i r- . b 1 ^ „ 1 ^ .. - £ * £ 1 " i OS PC CS b c E C 3 s i i/ S ^ M __ ■H>^ 578 VEEIFiCATION AND EXTENSION OF LA CAILLE'S ARC OF THE MERIDIAN. §8. t-^ 1— t o CO CO OS ^ in to o _ w to (M 4^ r» CD o to o t^ to ^ t^ O cq t^ o «p o 9 to 00 * r- cq CO r- in b ^ o tC b co ITS (N ■* (N CO 3 *" *^ o •^ M b ^ ih b b P^ b S?i ■? o» c^ CO o ° 6 1 b 1 b 1 b 1 b 1 b 1 o t b I b b b Oi 00 o »o ^ t- Oa r* o to t>. to in 00 o o OS CO o *^- H J^ CO CD (N C3 I-- CO p 1 00 m b b b ■^ b ^ b St m CO eo CO CO CO CO CO CO CO CO CD ro o O i-< *o l^ O Tf< rH CO O) OS CO CO in OS t-- OS rH O O O CO O CD CO 2S S ^ '^ S *=■ m r- 1— ' 00 CO in OS 00 CM *-- 00 00 I^- t^ ^ CO P rH CT G4 -^ ^H (N CO IN o o -^ b 6 iob (N b b b b b OS b o bob ^C)f=> t^ c> a bob ;- 6 b JH o 1 1 — ' 1 1 (N [ 1 CO 1 I to 1 1 *^ 1 1 CO 1 ■^ 1 o I 1 1 1 1 1 1 1 1 1 1 1 rH 1 CI CM (N ts /^/-^ CO O CO t- 00 o *^ 1:* CO to M CO OS CT 00 -- O 't CO ■* 00 CN t- -^J* (N 00 O in o 00 (N OO OS 9 3 3 CO F-< l-H i-H ■^ rH W CO o CO CN — 00 CD CN in 00 o CO Tfi 4_ eo - T^ ^ i1h O »h th Ti< 6 t^ Tl< 00 b b -^ r- t^ b oc b *-- 4ft r* b b J ^^ «o . Tf ip ^ (N w CO T* "? "? T" 04 in r- CO Tjl r- ■'t 3 TfH urs U!S lb « « eb b -^ IN b b / - b b b b b in b ■^ -^ Hn-W o .-H rH CO CO CO CO CO to t- r* t^ i>- t^ t- t^ t>. 'A O tH (N r^ r^ in O Tt* O -rji o o rH 00 1^ O CO OS 00 r-f t- c» g 00 (D rH o to »n CR eo o rH CO »fO OS t^ CO t- (N OS t^ OS OS *-- r^ T(< O O t^ (N O O to CO ^ 1 n * »p ^ o CO O TJH r- 00 p-H O CD CO -* ■* (N OS «* p O rH OS CO IN (N CO ■«* o 7^ ■* ?* •^ ^ Oi '-' S "^ «> s « ■* Ii: « i 2 0= ^- 2 b (N 2o ^ . (N T* Tf 2 •» 6gi b ;* b b«b ^ to OJ CO t^ rH (M 00 1^ (M rH OS in r- O rH 00 CO IN , r- O b — H o r- •* t^ OS o oa o 00 c» K - O ^ Tj< Tf Til -Kt m 00 -1 rH W T** T** T** rH rH (N (N CO CO Tf Tjt TT o CO eo o CO ^ m CO CO H4 s as ib o A* o b to Ti< 6 b uo b bob bob bob 1^ b b bob t^ ia a bob O 00 en o -* o is^ 1? 0^ §Y 1 s^ S ''^ Hi 5 o - o — o S P r-l P p — p P CO P CO 2 *V ewO *Y *v *v ttl *Y * <» *v *v 3 -B 1 -«£ ~B 1 -8 1 -8 1 "a -B + > ""a -8 + -8 + 1 -33U9I3J3J[ CO *^ 00 OS o ^ IN CO ^ tn to Hi JOJ -Oil « (N G^ (N CO CO CO CO CO CO CO Q Q> Hi fl fH ■ r^ s Q kl Q O a cu t P3 &. D 1 ■s g. ) \ i 1 C ) c \ 1 t ■> > 1 1 3 pq 1 CO 1 1 1 14 1 1 I CO a 1 J O •a c s ! !z| T o H^ ■s 5 s r E 5 ti R g" M H 5 HI s o o ^ :§ ^ 1 M M 1 CALCULATION OF THE GEODETICAL LATITUDES, LONGITUDES, &c. 579 o I o I o I o I § 8. CO 6 t^ to to o w « Oi r* o lO o> «o 03 o o o T^ ^ O -* (N 00 (M Th to CO 00 CO m Tt< O ITU OS 6 w 6 Tt« ^ ^ tH to rH Tt* -^ ^ ■^ »p o 00 TO OS ir iO to 00 -H -rf r- N CO O tH "ft OS CD »0 C^ (O CO {£) -ij* CO 00 t* fi^ .-t r t>. to CO o in t^ ^ cq ^ ►^ t^ rf »n C. to O O OS o o — o o *^ I I CO -^ r^ r-t »rs o 6 2 I rH CT to to 00 ^ iD "t -^ i-i !>. CM CO r" oi 6 o OS I O 00 t-- Tj< O (N - Ttl l-l 00 ~ ^ -^ (O th o oi ip Ti< TfH r- o f-H .-. TO ^ o o (N I I O TO ■-• 00 OO — p Tt( ^ « (N CT o o o O to TO 00 TO in Til i'^ to ^ o o ^ I I Oi -^ r-l in 00 <— CO Tf< ^ OS CT (N T* . ^ r- O 00 "!* ?^ 00 6 6 o to C4 to to cq o to ^ o in OS to J> I— o T|« 4> O T ^ ' 4t< TO Ah CT rh r* TO ■^ OS (N CO *o o O CO . p t* in Tft 00 (N (N 00 O m —I o OS -ii* j_ TO ITS ■;** "? in in 00 00 i-» TO O ^ ■^*< o ' + O (N i^ . 00 O CO 00 O 6 CM 'i TO ^ i— 00 ^ o ift TO O ih — 4_ TO ip I 00 o in O OS 41^ r- r-. TO r- O »n o "i 00 ^ 01 TO ■^ *^ OS OS r* o (N t-- O -^ CO ■[ 00 -* 00 to o o 00 to o W to OS tH (N O T*" 9* *? 00 O j_ CO -^ n 00 00 O Tt< (N OS in z: i>- X; r TO ?^ to O r-t TO tH ■* to 00 O Ofl 00 t-- 00 S 6 . ot'P ui t^ Oi OS -^ O CN 00 -^Jf 00 >-« 00 TO t-- to c^ TO ^- TO to ■^ "^ 6 00 fH 00 N 00 -^ tN ^ to to 00 in ^ ,- Tj« Ti< TO TO -^ ih 6 OS TO Cfl Tp rH CT CT ih o r- i-i 50 ■-< ■-< d 03 OS ^ S i> O "* 00 p — Tf o o Tjl — -«H CT TO TO to th O to — (N T** 2 "? Ol —' «5 r-i cq Ol .^ in o lO f^ TO 'f' -- (M !>. (N (N . o t>- un OS tn to » o o « CO O o »n «3 00 o S3 g * ^ o 9 OS 00 r^ OS OS 00 o * w 4h r-l OS ^ b j^- OS b r- r* g o o ip r^ U5 ■^ o ip lO TT CO *■ I> ii 00 b ^ trs b b to -* o K I—" 'St ?* ■^ ■^ s ° 6 6 1 6 1 b 1 b o b 1 b 1 b 1 b 6 1 TO OS 00 CO Tf ^ "^ 00 ■^ tn cn f^ w 00 -^ »o CO t^ t^ o CO jt^ ^ « tp t'. Oi 00 00 9 CN CO 00 CO " ^ OS r^ ^ o ^ ■^ OS lb t r)< 00 r^ CM CT ip *<^ ^ at 00 00 nH ih b b ^4 OD lb C4 -TS ^ trt CT c^ tp (N ■P ?« -* (7) ^ CT CT « N CO 5*1 ,1h CO S2 CO CO CO CO CO CO CO CO CO CO CO to iM so O ^D O ifS Ol rt T^H to (LD (M OS CD CO t^ CO CO O CO CO CO o r^ t^ n* OS CO CO in to CO t^ i>. !>. CO CO 1-1 r- in O Ui Oi ■>* O tN O CO CT O F- CO 00 CO CO o I-H CO 00 — CO i:^ CO CO 00 v2. «» r- o CO « M rH (£> cn o ¥* T* *P CO 00 O ■"4* t* o CO ^ CD --H OS .-H cq OS CO in OS 00 9^9 1 o r* 00 Ah OS W oi OS »b (N 00 00 ^i. -^ r^ lb t- b CO b b "b eq b r- CO "^ ^ -^ ^ 00 o to CO ^ iri C^ CO M w CO •;* M ^ (N r-. »n CM CO O CO tN CO (M Tjt ^ ^ . v^ ■? CO CO « O 01 —' 6 >- W ^- CO CO CT is b j^- b 1 1 1 I 1 1 - CO o to 00 ^ <£> (N 50 . (N 1— 1 CO CO (N OS Sa> « aa 00 (N J^- -* Cs lO OS lO OS 00 Tt* to o to Tf t^ CO O 00 t^ 00 o ^ CO OS 00 CO ■* (N CO « «o sS" 4n CO .li CO g -* w i:; « « s "^ IS? 4« "* ,li ?^5 ^ S «> sg? CO to tJ< f-i (M « ■<# OS ih (N w w .— ^ (N •<* CT r- O W3 r- J^ lO CO in CO -t (N O -H ^ int^ •* iO »- (M irt T*. -^ r* T" *" O CO CO -^ -^ ^ CM w cp CO .;-. CO CO nH -tj* -^ tN Tji -^ T(f TO CO H s rP « 6 ^ »b o t^ o b «3 lb b -^ « b ^ in b OS w 6 ■^ o b b lb o OT lb b b lb b O U3 00 o CO *^ o CO 00 CO C4 1 I-H (N « CO (N I-H ""• CO H 1 O _^" ^ w 1-- «? t>. t^ 00* S o" »o u? W o CT in w w to CO CD g ■< d /^ d -'-N d -^ 0*0 d d /-N 3^ d^ d/^ 3 1? 3 Q § o »5 ^^ ^5 |2i? !2i ^g l^iS !^S SziS Jzi i+ o ' o ^ 1 + S o i + ay o 1 o ' fl ^— ' g 1 + -- CO "^^ to ^ CO -* ■^ ^~ "^ TO IT c ""■ 10 00 IT) CO CO s z> to >o in to OS "-Sj ir 00 r^ Oi »p Oi p OI ?> IN ? ^^ ? ^ cn i OS t-H M Cfl 05 (N to (X tr* 00 iO (N U) "^ to to f to »o to XT »p 6 6 2 00 to CO 6 TO 00 6 00 CC 6 00 7** CO ■<^ ""• to ■? »o ?» tN (N (N 6 1 6 J 6 1 6 1 6 1 6 1 6 6 c __l 6 6 o^ to (N 00 (N to CO ■^ "to 1? to TO CO CO to Tft (N (N (N ^ ■^ - "T* , "T* V "?* p-t ■?* ■?• (N TO "? li i^^ 60 6 il| CO 6 r^ •?» Ol (-« tp CO . 00 CO t* (N 00 TO OS CO 00 «^ tN OS 00 "* 00 CO to (N t>. 00 kn O) CO (N — — en P3 « to ' TT OS (N (M 1^ to 00 c (Ji CO to CO '^ to (N to to C t^ OS tp ?> (N IN r-* OS to •rV IN V !>. r 00 Tf 00 ^ tN ^- tp p N to o> to o w tb CO O l>- 215 o> 1^ 6 6 -^ 60 Tt< 00 (>1 CO OS 00 '^ cq »^ rji r- Tp IN 6 00 OS IN TO J>- 6 OS r- r^ OS ifo -^ (N O , 1-^ ■^ y 7** « •?* «3 »p to CT i-H (N cq »o ■* 00 to ■eo ■^ (N OS '^ to ir- TO TO 00 (N '' to CD to TO 00 to CO (N O O OS ^00 CO io G4 t-^ (N ■* -* (N CO t^ TO TO 00 >* Ttt Tf TO tN 00 C^ l>- CO to O] cq CO -< + 6 (N + iO rH '1 "^ CO '1 m lb *t lO ■* + lb lb '1 TO t- 1 -^ -^ 1 6 6 1 OS CO 1 6 TO + CO IN 1 -* CO ■* •p »p W CO 1 tp , 1 tp 1 CO -^ CO TO 1 TO TO 1 TO (N I tp Tt< 1 1 1 i^ OD 6 ih 6 6 i^- P3 r^ CO ^- OS r^ (N r^ to 00 ^ ^ TO 00 TO ■^ l> tJO 6 io 6 -^ 00 00 ■* -* Ti* Tj* C4 (N CO CO TO TO -* Tf ■* ■* Ol (N t^ ifl »o r- ^ so to to CO IN (N cq 00 iO tN IN '^C OS TO OS TO to CO Oi ri CS lO - Cft 00 TO TO -<* lb CD TO ci 00 «5 -* -^ l-H *o »ft ^ -b 6 CT lb ^ TO lb b CD 10 6 t^ 10 6 00 r* to (N OJ ■^ CO ir -^ 00 OS (N J I>- 6 d a S 1^ tfc bo a + E 1 1 g'S) B 1 c * T I s IS + 1 + tfcj "a "8 'e^a -B^S (N CO -^ to CO r* 00 01 i-i 1 1 6 w 5 i •g M §8. 582 VERIFICATION AND EXTENSION OF LA CAILLE'S ARC OF THE MERIDIAN. §s. O ^ ^ t^ t* CO CO CO H< oo c4 o o X OS in l^ r^ •* 8 CO •^ ¥» >n C£> T* CD CD T* * (o 00 CO t» b b in H CO tn ■? »n S -- 6 - i>- CO o CO o 00 OS - OS *^ «> t- (N 00 t» 01 9 Oi ?» "^ b (N b !>. t- b ^_ b OS b 9^ ©1 ^ cq Tj* ^ '\ -^ ^ b ^ « 1^ ^ b b b b b 13 (N « ■N CO (N (N »o T** ^r ^ 2 b b b b b b b b b St .s e § CO CO CO CO CO CO CO (N C4 CM CO CO O CO OS ^ (M t^ -^ (N (N »C t^ 00 -H T*l '^ 00 CO rH t^ CO CD CD OS (N o »n ^ Ci CO lO in T(* o t^ ■* r^ •* OS 00 rH Tf CO in in 00 00 rH OS CM l>- — CO ■* ^ CL ■a p t^ ?< O OS (N Tf 7H l^ oi 00 <7^ 00 t;^ p r- Tf( 1^ OJ CN ^ i>. ip CO OS CM ^ p 00 t* I^ CM 1 Q ^ ^ un ot 6i ^ CM b r* 60 b .^ lb OS b Tf OD t^ 0^ Oi Ah ^ b ■^ -^ r- b GM r* b .^ Ah 1 2 -B gS CO ^ cq •^ CO ffi -^ ^ ura . CO •P ■? -^ rH rH tt CO w tn CO cp _ ip Cfl . n CM rH C>1 ^ 00 en ^- b CO 00 b b cq b b t^ b b ■< T^ 1 1 ^ 1 1 1 1 "^ I (N CO 1 CM 1 ■* I CO 1 1 S « CO 1 1 1 1 1 CO 1 1 1 eo 1 (N CO 1 1 1 CO 1 't't' t-« i-i »o O ^ CO ^ »0 r-t *^ Oi ■* rH OS t-- ira in OS Jt- W CD eo rH ^ CO O) CM rH -* 00 I-* CD r» 1 3 3 03 CO CO CO (N ^ W5 OJ rH t^ rH CO OS OS -H Tf -< CO -^ •* CO t>. Tjl OS CO — CO 00 00 1 + + + * O 00 o O O O tp t^ p ip T(t p p r^ p ip CO p ^ P ip CM p CO IN p CM p p •p oj a> b 'i .^ Th "l Oi ^ '\ b lb *i b 00 '1 ■ii< b '1 b w _L ip Ti< -r 00 b '1 b 00 '1 b I?* '1 ■* b j_ ^ C4 1 T* ^ ' -^ CO 1 ip ^ 1 U5 1 T|« ip 1 CO CO 1 ^ T** ' ■^ b lb « b ^ b b b b •* b b b b CM -^ ■^ b >Ih -^ h .^ Ol b b tc tb lb b b b ^ CM b b b b '^H:^ . CO OS CM rH CM i> •» *^ CO CO «-* t- I--. OS ■* (M iO r- ^ 00 CO CO CO Tt< CTi t^ 00 rH Tf CO — CO 00 in CM CO CO ■* b 2 °o ?^i5 ^2b "= ?S « ?3is :i? r'^? 5=1? ?i^ ?i2 _ CO 00 CO (N CT r^ sp e?> t^ 00 OS *^ 00 OS •ft 00 OS (N t^ rH rH CO T|-> —• . !>■ t^ t^ t>. r^ r~ r- ( »^ -«* 00 CO »* 1 1 . t-- . r* • GO . 00 . 00 - 00 f^ K ^^^ d ^% ^-^ 6 /^ d /^ 0^-^ d oiZ' '*-' dC> 1^ GO o Hi Pe4 O :^K ^K |Zi 1 ^£ !2iK fl 1 !zi ^-\- IZi 1 J2; + 00 O + 1 + of*. iT T '^ i So 5 00 il 5 00 5 9 s ^J a i^ "a t + a ?* i -a -a ■90a3J9J3a CO r^ 00 Ui __, (M m ^ lO CO JOJ -Oil t>. t- t^ r^ 00 00 00 00 00 00 00 1 1 o s t « m PQ M bb to 1 2 u 02 1 1 is 1 75 1 c c u 1 CO 1 ] 1 ( 1 t ) 1 ) 2 ,14 5 e s 1 ^ M ^ iS ts s 1 i bb !z; &3 O 1 s 0! C ■ " ' i 1 in 1 E i s J 1 1 1 1 pi it 1 3 ! 1 1 1 CALCULATION OP THE GEODETICAL LATITUDES, LONGITUDES, &c. 583 ■ 1^ O ^ r» O eo ■rji r» OS f^ 4it .1* (N w -^ - I to (N OS O O '^ ^ O O 'Sf CO -■ to CO ^ ^ CO « IN CO o b OS O tH CO 00 CD i-H O i>- *ft b b . CO OS OS O ■^ CO CO ■ ^ r-i O O (N (N 'l b b eo CO o »o OS in (N t- O 'r' CO ^^ 1^ to . to IN GO 00 !>• OS - T* ^ . "P f T** Ti« iQ •-> CO in b CO ^ . t'° — • to r- (N CO CO r^ »h b !>. -n* m m i-< -^ CO S CO t* o ^ CN W O tH (N IN OS (M 7- IN CO bob ■^ 00 O -- rji 00 OS to . 00 v" in t|< to ^ CO CO §8. O /-N d '^^ o IZiS !ziS IZi fl'"^ a p t£^ tC a o » W n \4 I !3 oa O 584 VERIFICATION AND EXTENSION OP LA CAILLE'S AUG OF THE MERIDIAN. §8. g a % o o H o O tJ 5 fi CI 6 I CO O o ^ I I PI O CO CO o a» ,1. -^ b l-H CO »o -f o o 2 I •i) 6 b t-- ITS t-- (N M Ol OS O O OS I Tt* CT CO CO CO « CO -^ 00 b b (M I in t^ Tt* r-i tJI ^ — b (N iO W (M m CO o) 00 O 7H -^ w b eo # 00 61 F^ 61 b b 2 I r* t^ »n «3 O OS CT -^ W .-4 -^ cq ^ CO CO C4 C4 CO OS b b to OS o OS o o (M CO 1 + ITS lb CO O tN (N O 00 CO O *o in ^ b b b ^ 00 ^ OS 00 p OS O *i O Tjf I A. ^ eo Tj< o « ■* O b 60 w 00 b b o «o —' CO 00 p (N O j, b OS CO tC OS OS to to I .-. tp -r b TO CO 10 «5 O CI OS £^ CO « "b *P o '?' rH »ra t>. coSb *P -2 «3 b CO 00 b Tt< b '-' In. *^ -^ U5 O CS W5 i-H .p«cp to CO (N Tf ^ (N 00 in b -^ r-t CO CO OS CO "p ?- 1** O 00 (N CO 00 rH T^ CO . CO CO CO ■-< CT - ■^ CO ' CO ? CT 6 (N oc F-( lb |1n 00 6 ■* tH ^ ^ 6 Tl< CO « T] ■* in CT IM CT _T c 7 6 6 6 6 1 6 I 6 I 6 __l 6 1 6 6 6 ec OS r>. <£ QC o !>. 00 o o 00 CO CT ts. OS CD OS '?' ^' CO •^ « 9 p in CT t^ 0. 9 t^ o- •X) 6 6 o m ^ •ij* 6 ih CT d 6 "? c- w CO in CO in in in in m O" Ai 00 u> 00 00 in 03 1^ Ail ^ lb ^~ ■V in CT 00 CT CT in in in •^ ■it -^ w ■^ CO T(< Tl* ■^ ■^ ■^ CO 00 00 c K CO CO CO CO CO CO CO CO CO CO CO CO j>- CO ^ O Ol (N o- 00 lO CO t* lO CO rH in OS o O 00 o CD r* o 00 OS 00 CT »n t^ CO »n CT CT to m in '^fi i> in CD -ji 00 ^ ^ «£ eo t* p 00 en OS CO 00 00 CT «3 Tf< r* 00 ^ p CT r-f t- t^ CT U) CO H 00 Tti r^ »p CO r- CO -t a ^ p ■_, 00 00 h s i—t 6 w O CT. i-i 6 OS OS 4*1 ii^ « OS 6 6 CT in Tt* CT « CT ■^ 6 CT 4t< »— 00 ^ - CO 00 in Ttt r^ -^ Tft ff- CO Oi o 00 i>. o OS o in CT o l-H O CO 00 CO r-f ■* OS o OS CT O in i> i>- in ^ O IN o p w o 00 t—t 9 00 r 9 ':'PP OS CD O in p p CT O O ^-■^ 9 r* 9* o in 7* 9 in CT p 999 p f1< 6 ' a (N _1_ id ~ 6 o + "^ •^f CO CO CO ^ 6 CT 00 -^ 4_ in CT T^ 6 CT *| *-* 6 ' 6 6 ih 6 6 CO CO -^ "? "P (W =P r^ ^ CO CT ^ r* *P ^ -* 1 in ^ »n CT r^ ■* •^ .-1 CO i» -^ p_i (M 6 ^ CT CT M in OS 00 CO 6 ■^ 00 in 6 6 6 6 6 CO t^ in CD DC W (M ■^ 1— 1 CO TJ4 T** -^ ■?* ■?■ in CO CT CT •? . - CO CT CT CO TT Til w i 0» Oi ■it* O 00 00 CT CT CD ^» CO Tf< •^ « u? eb 6 6 6 6 6 d do 00 ■^ -* (0 CO o O " ""* 00 00 Ti< -* »n in CO CO Tj. ^ ^ Tt< CO CO 00 00 00 00 at -* iO 00 CO u> O CO QOr- CT in CT *^ 00 OS c> OS T*< CO OS t^ ■ CO 00 0S CT O o p r-H !>, 1^ OS o CO CD in CO CO in in i> CO' OS in CO ^ ^ 00 CO OS OS OS 00 gS2 y O T* CN CO ■* CD 6 6 2m N . co°o ip CO S « CT g CO gg? « o r* 6 °£ OS ingo T' o ^ S2 rt* ^ 00 CO 1% ?s? t1< (N BO 1-4 Tt< CO 6 r- m -ij* OS tHCO 00 o t^ in O O CT ^« O CO CD O O co" 6 OS ^ 6 OS P-H 00 6 i-i CT CT ?»■?'■?' ■* r-l (N — " T*'9r' t^ ■^ 00 i-< CO CO CO CT O O 00 >o 6 6 >h o tb -^ 6 r* 4f 6 ■^ ^ 6 in ih 6 00 in 6 6 w o m in o CT O O OS T*< 6 Tji r» in 6 *^ en »o in <> t^ 00 in t^ r- in 94 CO y'^ 1 bo -/"> *''*^ ^/-\ »/-\ ,r^ s .--N /-N << »0 lO toai r^ •^ 2 + 00 i a 1 1 tOco CT to ^ rod wS -^ 26 2t-: ^ < 1 + U3 .K50 r-T < oT + a> Q 1^ to 1 O GO iz; «- If o i 8 00 < bo i 1 1 1' "^ OS SI II Is -a 1 o a -8 + -8 + 8>_^ 7^ °o 1° + 83 1 It -a 1 i Cm "Si's a a C8 S + + CO CO CS v_^ a s + 1 c ^ CT 00 Tt in CO !>. 00 01 o c o o t-l — r- 1— c r-t '"' rt ^^ '"' S3 *s 1 35 I p a c ) a 1 i a" l -g ) -*- 5 1 1 PC ) "b 1 1 ) i "3) 1 b ;- 1 ) 1 1 1 ■» 1 1 P3 a. i ■ n: 1 ) 1 C 1 i CD > E- ) ■4 3 i b f 1 * S3 1 < -t- c ^ 1 i e s "S> 1 P- 0] c u a cS c CO ■& a IS w 586 VERIFICATION AND EXTENSION OF LA CAILLE'S ARC OP THE MERIDIAN. § 8. H a n o o 1^ hi H 33 JOJ 'ON O H 02 OS t^ CO ^ r-. CT CO to CO CO Tt* ^ CO » I I ■^ CO *>• T" ?* ?* CN b 00 ■nf (N (M 2 I OS CO '- cp TO OS OJ — j-t ■* »-r ?* b b 2 I CM OS O d:i Ti; o b (d in 00 '— Tf in p ■^ b "i O — 00 00 CO -^ I CO Tf I b tJ* CO «5 r-( cp N p O) -^ 'l ih ti< (N in b b CO CO w A* tN 00 OS b TO I pH I O O TO « ^ p »« OS Jl. TO b -^ ; + to t- TO U3 (N 00 g2§ o o o CO CO -^ Tf in A CO «0 «5 (N ^ cq w t^ CO o o o »n (O t^ o (M O 00 Tf en 1^ (N OS ^ CO CO ^ t^ ..# CO *^ -.a* CO O Tj* 00 -«* O TO .-< — M 42-21 95849 14-55 9-14 28618 31-43 CO t- OS CO Tf Tf 4-16 94677 14-31 24-57 22740 27-42 44-37 49785 51-39 37-32 49907 51-47 9- 8 45503 46-48 55-59 34652 36-27 T" to . 5i m eo CN lO O m Tji o 2«o F- »0 O CO -- -fl. o 00 in o *>. to o 00 w o ^ U5 O ^ o o 00 « + ^1 ^1 "8 + ^1 ,2 b '8 + •o ^ to < * + in + + 11 o + -•2 g-a « + as g-a "a I o t3 a "3 CO n B B IS P3 •a a> •§ •i M n .a S i w § g* .ill pi? n bo g IS n g Eh ■i 1^ W o W n CALCULATION OF THE GEODETICAL LATITUDES, LONGITUDES, &c. 587 CO S TO ^"^ ■^ 00 00 ^^ ^^m to ^^" ^^ ■■^ in ^"" TO ir •7^ 9* ■^ P ?* CM IN (N ^ ■^ C4 1^ CT c^ CM do ^ cr 1—4 T* "7* (N 5 -* TO 7 T _7 6 b b b b Ji b I 7 7 7 1^ ,!-( ,L« ^ TO OS b ^ TO OS tn cq »n . ^ rH •— ' >— » ■— -* rH •? "?■ k T^ k TO 4* -^ 'ij' ^ ■^ ■^ Tf ■i*< 4f ^ eo 03 TO TO TO TO TO TO TO TO TO TO TO TO 00 OS CT CO OS CO TO i>- 00 TO -til r- TO OS 00 eo 00 . in OS in OS a TO to - ip 00 ^* 00 t^ CO TO a TO to p TO ■ « ih TO »J^ -i** lb 00 ^- Tff t^ r- ^ to Ol ■^ 00 »b to t^ b b TO lb r- Tt< TO b b 00 r- . CO ■^ b b t* b -^ c- b 4i< b b lb rH ■* CO -71 I-H TO « TO -.Jt f-t TO CI CN ™ TO IN (N TO ?< TO TO ^ rH . 6 6 r- 6 6 ^ b 00 b b 4-1 b b b b b b CO b b ■^ b b TO b b "^ b b boo •^ 1 1 ^ 1 1 CN 1 1 s OS (N CO 00 rH TO OS CO CO 6> '1 TO OT "1 TO ^ 1 b ^ lb + to b TO b b OS b "1 dc lb + IN b b b b r- + 3" + Tj< «5 I TO 1 Ol Tl* 1 ■* Tj< (M (N f TO Tf TO 1 (N TO W CO 00 tra TO «o M TO to (b lb TO t^ ^-. (N b ^ OS dc b lb b b t^ ^ ^_, TO TO r-< . T* TO in r-4 't 10 TP (N in CO Tl^ Tf "^ r- TO do 01 TO TO to i) OS OS b b OS OS rH IN do do b b r^ r* b b (N (N lb lb CO CO (N - r^ ^ - 00 00 -^11 (N t^ n* « U3 rj* OS TO «5 W Tt* OS ^ TO TO t^ l>- »p CT ^- to in 00 ^- ■? i> TO p (M -* Tf TO OS (N TO IN TO TO OS in 1?- ■37- 150 •20- sk^ (?: 2« His •^^ -^ ip TO r^ r-l lO in ? dc CM IN in b (N (N ■it ir b in ??i TO b TO (N CO b TO . "^ ■* ^ (M (N ■* CO « rH C^ r* 00 OS ei . ■^ ir in b ia b iO (N CO w (N O) o- to OS cs in (N IN CT c CJ '"' *"" 0- TO ^~v /-\ (N oi /'^ ^ ^ /^ /-^ ^,,_^ OS tN OS EN ^^-N /-^ ^--^ /— N ^^^ n2 CO r-t TO ^ *>■ 1-1 S"s c?i a* O) OS OS 00 OS c C in c^ CD 1? ^ »n 00 2» CO 00 |g ^1 1! ^< < o-< ^1 1 1 < 1 c o < c < 6< d < 6 i J '^ 1 §• &. D 1 a PC 1 E s ^ S b 1 r - # a 3 ) t- a 1 ■ fee 4d M *< I ) T ■» -§ :g b J D pi: 1 i §8. 2 B 588 VERIFICATION AND EXTENSION OP LA CAILLE'S ARC OF THE MERIDIAN. §8. ^ to to »o n ^ o Tj< 9 p ' m r* « g ■^ 3 o OS m •A O ° CT ^ CI iJ 1 1 1 1" o fH » 9 CO " i 6 Co 1— « CO I-* w - cq W (» 5 (M ■? « ■ O tH "^ -* % CO CO CO s 5 ■• - i^ OS OS in r- O ■<*< CO 10 in <» 00 r^ w O 00 p ■^ p CT g ■ Ah i^ 00 CO t^ CO 00 OS i> . -egS (N CO 91 OJ 7H tP in 7H -^jt ^ ■ ^ -^ M 00 ^ CO en OS M to ^ ^1 ?* "?■ T^ CO r-* CO CO CO (N ■ OS eo u3 . . ~B -« T* . i-< ■iP . Sw/V— ' 00 OS w « ^ > fe d u o K P IS ;zi ^ ^ |Zi !zi P p p 00 O OS o lirj — t^ »0 ifS rt •TZ o» noHOSiioo » '^ s s J. 00 - ;; (N ; o to - woo ■* j; « - * * 1 1 1 + + 1 III 1 ■aOTJJns oqj QAOqB paAJS&qo JosfqOJOjqSraH o o s " = o ^ _ - 6 - " 9 . o ■ m o oj 6 " O »n o 6 eg = 6 " •rooplBAJMqo 03 (M ED (N ^ to CO to IN O 00 o o o 00 .^ !0 (N CM to ^ to o eg eg fe JO ON S EH la IN 01*01 r- 1-1 (N t^ 00 Ht o t^ (N w to OS irt 00 r^ to lO F- CM t- eg i> c^ i>- o CD in CO in «5 (N F- (N »f5 CO ^ ^ C33 (N -- C^ Ol . CO *^ t^ 00 00 00 00 00 CO OS rt o ^ OS ^«i o iO Tf ■* W Tf « to rt ri rt a m *" c*i cId " s CO OS W -^ OS OS OS OS OJ o 5 II II 03 00 II II w bb w WW : PS a (D ; d n '~-.?o C OS 1^ ST l-H 1 :d fcolP o m cS : Mo. pq , ^% 1" S5 O o i: b ,1^11 £ II § >~ wco 11 TJ e*ft o< T3 P«&4 ^ > s w E^ WH f§ MB CD 6 N M ^oj -Oil -- (N CO tf in to r<. 00 juatniu^fltti R p p w R p p p p o asa g a ^.^. s a a s E a a s a a a -■ p,cs p. o C8 ji PnOi ^ p. ei C3 d p. p< W ^ iXi o Pt 00 eo to "^ to t^ °= tf t^ 00 r^ v: ;o CO CO CO CO CO to CO ■* so W to t^ OS OS OS (N »0 O »n t>. OS 00 o » ^ rH ^ (N CN 01 (N r- CO i 3*; ^ d *>■ fe ^ (U o '"[Zi |2i R "A !zi !zi OBSERVED ZENITH DISTANCES OF STATIONS. 593 S S bo m o o a, + 1 1 O 6 9 6 O ^ w w mo; laj a 44 » -u p- ni ^ CO rff to « (M tN (M Q m M a sB CS « ft HW) o * -s CO 5 2 3 . 00 J^- CO Oi '-' 1— 1 o o ^ (M (M ifS o o* o •Q -* to in 1^ 00 00 CO CO CO o CM CO O O 05 o C3i o OS OT OS O O OS 00 00 ^ ^ 6 o> o o> Kwa WW wws WW WW wwww P3 a; 00 pq to O " -a II CO L 00 o O a. m2 <-- M "^ WWW P3 P^ to ,i4 OS bed M CO ^11 O s "* ft 2^ bB aE s a cS d - O O •* a a. s -«.ft; r^ rH ,-H CT . 2-3 s fH =8 II !^ § 9- IS be o O O oc i« (N „ «3 .. 1 1 »n Ol " (N " eo o (M ^ -H ,-« r- -i O CO O CO oo as t^ to ^ -^ CO CO (D TT CN OS o CO o tr w WW ^ : ^ 0) "lo o* ^s. bow "Sfe! ^ II 1 ca N H t^ 00 •-' ^ Q o B a a a C3 C p. p. hWHW H«-l« j> in CO CO o o O rt d c5 i? P P + o 1^ ffO C3S 00 c:s CO ■* CO OS Id ^ 00 Ph (?J I>- (£> 00 O CO CO CO m - Tf ^ 00 "3) r-( r-. (M r-l ^ » C^ is 594 VERIFICATION AND EXTENSION OP LA CAILLE'S ARC OF THE MERIDIAN. § 9- rH CO CO ^ in CD i-i fr- ^ CO •az ^t^ CO.CO.»Tf.. ee O (N + + + + 1 1 1 - 1 1 1 •BODJJTIS OtlJ lO W3 W 1/5 o o w o OAOqu paAiBBqo ioafqOJoaqSiaH •8aoijiiA.iflBqo *^.COt~- a ^ '.Jt Ik Tf -^r-t (NrHCM aO "t ^ CO -* ^^ OtO-^ r-OJ — OS »C (s- -^ CO CO '-' bO CO — in n td n O O O — o — o O N '^ OS Oi Ol OJ 00 00 00 II II OS o o> S S W HM waw WWffl bb : ^: ^ w g ■So fc [^ e-c
  • C) CJ 0) CN 04 G4 -1) ^ o i n _ 3 a d fs JO 1-5 1-3 h, H, 1-3 PH ^ 00 to 00 --' un ■^ ■^ CO *az ^CT, CO-. -H_- (M„_ (N , (N > •<**«-.. (Kj uoijaauoo 1 1 1 1 1 1 + •ooBjjng 9TO a pafq0J0?tlSi3H ■^CT- G^^- CT"- CT^" Ot C4 -* (N •* * * ■enopDAjaBqo too CO—CT (NOUS (NOO o o Tt- 00 ooooga N JO OS ^^ ^(NrH — C^^ ^(Min .— (N i > s ^ t^ wotifo (Ot^Tji eD-*o CO (N ^ OS CD CO 00 ^ ««Ot^ OC0(N Tt! W-t C0(Nif3 (Mm'** --iCOCO CO CO CO CO S ^ 00 OJ O (N CO TS ,_( CO (N N CO 1=1 !» S5 (N C^ '-* Ol O ■* to S S -h o 3 o II 11 m CO Ol II II tr WW WWW i Si. § C/2 ft w w w 00 ?0 00 11 II 813 w d O .5 -* tn 00 61)'^ bd « Sh Eib« .•IN PP ID Ei)CO i-i w 1 III 1 II fell 5 II s o a> CO a § 1 « Sll 1^ ^ pq P^ 11 r '33U0Ji3J3^ 1^ CO OS o ^ CO JOJ -Oil CO CO CO -^ -* ^ ■* 'pa^oxduia p p ft p ft' ft p g a a as^ |"aa aaa Sg aS a aaa ft o3 «■ « o rt p* c3 C3 PHft d cS Ph H 00 T*. ;r OS O O !^-* J> 05 rj< o -^ -^ o> fr- ^ to (O (Dt^OO t>. I> OS 00 00 00 r- !>. I— — »0 CO CO ■* cq • — 1— « 1— !—(.—• ,— If—ll— 1 ^-<|— If— ( CO r-4 (—1 H -« S^ ^ =c =2 •^ fe-S 03 fl -H p< p. p< p< s i2 § 3 <)<)<)<< s>? H^ OBSERVED ZENITH DISTANCES OP STATIONS. 595 s s i. 02 i eO rH (O ^ 6^ ^ 1 1 ( 1 1 o o o 6 o> Ol lO fH - n w w ■a t^ H •« M :S 3 W ^ W !25 n M M o l>- CO « W CO pq tt 00 o CO OTf S" 2 O r- — cm c O CO h 4- M H o o Pi ^ 00 00 r- -^ »^ C» CO «5 <0 O O CT (N 6 O O O p O O »h O «3 to CO Tj* i? m 00 CO ip CO O OS 00 Oi 05 00 00 00 CO taw c3 N O o wwrncq s s s a o3 rf c3 ^ IC5 «5 lO O bo a w ID o 1^ 1^ 03 lO ip p cq IN o »p »p iO CT « (N www pq 0) Oh rv nnn s g s I T3 -^ I I I un in in « IN (?) o o o o lo lb ■? T" "?* www •3.2^ bp-S o o o o PPCQpq s a a t- Tf -* IS bo a Om S II 02 o ** T' 9 .^ CO "* I I I Ip p p (N o 6 o 5 ti-S* a""' - CD . CO to ■* o .1- ^ ^ 1 1 1 1 1 1 1 1 o o O 6 o 6 Ip « o CT o o 6 (N (M ;:; tN Ol OS ^ - CT G Oi p p ,1h yS r^ CO o w li 3 Tip; W W n 2=0 a p< w bo M ^■R W isw t^ w lO CO if3 O 00 Ol o to o so CO flfl « R m mw M P3 a C3 ' .a B Is *^ o o a i CO CO »0 CO « t-^ '^ CO I^ '^ o w p p p p W CO (?1 w 1 1 1 1 o 6 = : = M O o o O to CO I>- 00 to CO Ol to p PAR Wpq a s a s a i « « 2 C 596 VERIFICATION AND EXTENSION OF LA CAILLE'S ARC OF THE MERIDIAN. §9- < CO S N P m > CO a O •az 0} aO1}33UO0 •OBBjjnB on? eAOqu p3Aj99qo ?oafqOJo?qSi3H ■suoi^uAjasqo JO 'ON ^ s O N •aonaj^aa loj -OH "pa^oidnia inaraiuJBni ^ + -E3 •az ?Mfqojo»q^3H ■HDOpBAJasqo ■aouaaajsa tnanniJTSnx oop^»ep■»*(^^coc> 00 to OS Tjt I I I I I I I ^ ^ »o o o m o oooooooo .M ? "5 (u cu'3 g § Sra* E f- t-H ►..* «D cu fl ^- , ? es ta o g .g >, c y M fqpqpqpqcqfanmM M S OiOi^^OifJiOidOt at -f- Cl II ho m i> in CO w CO V 'J' co >-< to — I +1 +1 o p i> o o o OJ o poppp po PP iraOi^iOO OO O^C "^ T** *P T* T* ^ ' - "^ copjf^mcb ^->^ coto CO ^ — o* »o "^ do Ai bp'&xj P<3 T: 01 m ni (-1 Si *^ fcr O '"O a .<3 « =4 F ,=« :-: ? 13 ^ .° a a. 2 PMP5«Mfq ma pq OS O) O) OS OS OS c + O CO tn *n b o b a: WK O^ « g o a Mm mpq H 3 . OS ' + II « 1. "^ O ' ^11 -.3 e &'^ £.^ O M fafq o O P3 + P p 00 io p w o . T . T" "P OS OS i o w pppp ppppo P P P 9999 0>^(N0 r^f^OSCTOS coi>^^ ici "?cco4*( eocoeoco ei 00 Tti Tj^ to ^ « (N ■<*• .* ."t (N -pppppopioo .. 't'J^WcO'-Heo (N Oit— 'i-HOJ oc*ioo COtTiOJOO OsOSOiO* WW bo u u . P5 a b M 03 o pacq a a OS oa ^g^ '^< "* ^* 00 (N t(< o^ w cb j>- OS I I I M p p p p p 66066 p G p O

    t^ 00 e( ►-3 s + 'o C9 o t-- p p 00 CO p Tf Tt* CO "^ to i I I I I I I p p p p p p 6 6 6 6 6 6 000000 rM >> OJ nj ^ bog EUD S fcj g' 6d3 m MP5WP3MM ifi io 10 »n »o o 1^ o 9^ -^ i . CO s ■* O si, E-l «3 CD wa & - O.S _ "^ fl cb pqcq W a C8 CO ^" ^ CD gco ra CO a> ir a 03 _ CO cd O) O C o " e cs Wpq .9 a ■5 60 a c« .£3 n o bc a 03 ^ CO 00 p 00 00 w m p o p 00 w -fjH 01 w I II III »n o 6i 6 CT (N pppppooo 6666666 6' o o c 6 ppopppoo w6666666 T** T* . . . "p 'p «^ ibrt< — ioo-^o ^ T* T* . T* ^ 'P T* aocR6666cnos oooooscTicnoooooo P5 W 60 03 o s « „ -"§■§ . .- . '^ ^ a bot-'oJ^E; ■° S g S S M'O S aa 60 cs <1 aa C8 fi, a s s s a & Pi (£4 P< P4 O '-''-' O O ^ r-t aa 598 VERIFICATION AND EXTENSION OF LA CAILLE'S ARC OF THE MERIDIAN. § 9- The following fonnulse have been employed in the calculation of the co-efficient of refraction, and the altitudes of the points observed : Let h and h' be the heights of the two stations above the surface of the sphere. z and z* the reciprocal zenith distances. s the distance of the projections of the two stations on the sphere, c the angle subtended by s at the center of the earth. m the co-efficient of refraction. V the meau of the normals at the two points. then h'—h = s cot. {z + mc—lc) (1+ -^ Y z + /- 180° \ and m^ =.(>- The calculation of m from 10 sets of reciprocal zenith distances is contained in the following table : 4 19 9 29 20 27 7 38 39 22 40 28 32 46 49 47 50 52 57 62 East End of Base.. EapocBerg East End of Base... Eiebeek's Kasteel.. Kapoc Berg Eiebeek's ICasteel., East End of Base.. Zwart Berg Zwart Berg.. Kapoc Berg.. Zwart Berg Eiebeek's Kasteel.. Eiebeek's Kasteel.. Piket Berg Eland's Berg.. Piket Berg Eland's Berg Lambert's Hoek Berg..., TKUE ZEHITH DIST. Coder Berg Heerenlogement's Berg.. 89- 8-29-1 91- 2-170 88 37- 3-2 91-38-19-8 89-29- 51 90-50-11-6 8911- 6-7 91- 0-33-6 90-12-41-8 90- 9-32-1 89-23'26-9 90-53- 5-7 90-21-30-4 9014-23-6 89-18- 0-4 91- 2- 4-1 88-53-27-2 91-25-11-4 91-15-33-4 89-16-59-6 68 82 84 48 44 44 48 48 86 52 20 38 32 48 8 12 21 12 LOO. 2+2- DISTANCE. -180°. 4-87949 646-1 503398 923-0 513281 1156-7 4-91958 700-3 5-19857 1333-9 5-06897 992-6 5-40374 2154-0 5-16749 1204-5 5-12895 1118-6 5-35982 19530 746-2 1065-0 1337-1 818-3 1555-7 1154-3 2495-1 1448-3 1325-3 2255-2 The mean value of m from the above is -0712. Adopting this value of m, and putting h'—h=zs cot. (z -/») ( 1 + h+h' \ 2v /■ we have /= 0-4288 V sin. 1' The following table gives the log. of/, the argument being the mean lat. of the two points ; Lat. 30° Log./= 7-62567 31 7-62565 32 7-62563 33 7-62561 34 7-62558 35 7-62556. -0671 -0667 -0675 -0721 -0713 ■0700 •0684 -0842 -0780 -0670 CALCULATION OF THE DIFPEEENCES OF ALTITUDE. 599 The weight of each separate result is assumed to be directly proportional to the number of observations, and inversely as the distance of the stations. § 9- 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 West End of Base., East End of Base-. KlipEontein, ContreBerg Eapoc Berg.. Riebeek's Kasteel . Zwart Berg.. Klip Fontein, Sect. Stat. Piket Berg POINT OBSERVED. Eland's Berg.. East End of Base Kapoc Berg. Klip Fontein,Contre Berg Kapoc Berg Groote Zwart Berg Contre Berg Eock Zwart Berg Baviaan's Berg Riebeek's Kasteel Winter Berg Drie Fontein West End of Base Klip Fontein.Contre Berg West End of Base Riebeek's Kasteel Drie Fontein Zwart Berg East End of Base East End of Base Riebeek's Kasteel Klip Fontein, Sector Stat. Zwart Berg Winter Berg Patrys Berg Kapitein's Kloof Sneeuw Kop Kapoc Berg. Zwart Berg East End of Base Royal Observatory Klip Fontein, Granary... Piket Berg Winter Berg Rogge Bay Baviaan's Berg Rock. Contre Berg Rock Drie Fontein East End of Base Kapoc Berg Riebeek's Kasteel Patrys Berg Zwart Berg.. Patrys Berg Zwart Berg Kapoc Berg Riebeek's Kasteel Eland's Berg Heerenlogement's Berg... Piket Berg Lambert's Hoek Berg.... TETJE ZEN. MSTAMOE 89-59-50-3 88-42-22-5 89-42- 7-1 89- 8-29-1 89-38-55-6 89- 9-120 89-1 1- 6-7 89- 9-16-0 8837- 3-2 88-21-28-6 89-38-34-4 90- 6-30-5 89-46-52-5 90-26-53-0 88-50-24-4 89-52-38'9 86-46-45-9 90-22-30-1 91- 2-17'0 89-29- 51 90-33-21-7 90- 9-32-1 89- 6-14-4 90-25-27-6 89-53-28-6 89-36-11-9 90-50-11-6 90-53- 5-7 91-38-19-8 91- 0-48-8 90-54-21-5 90-21-30-4 88-31- 4-0 91- 0-14-7 90-46-37-1 90-53- 3-6 90-29-16-1 91- 0-33-6 90-12-41-8 89'23-26-9 89-58-32-9 89-41-33-6 90-53' i-9 90-41-50-7 93-36- 1-0 90-14-23'6 91- 2- 4-0 89-30- 5-1 89']8- 0-4 88-53-27-2 LOG. DISTANCE (.). 4-63164 4-73692 4-77802 4-87949 4-94425 4-90078 4-91958 4-98209 503398 5-30190 4-89061 4-63164 4-81788 4-77802 5-04733 4-87962 5-15760 4-81788 4-87949 5-13281 5-42032 5-19857 5-40740 5-37319 5-41717 5-45786 5-13281 5-06897 5-03398 5-37893 5-41573 5-40374 5-11349 5-38576 5-04757 5-06470 5-04284 4-91958 5-19857 5-06897 5-15390 5-15613 5-21137 5-13542 5-42661 5-40374 5-16749 5-17282 5-16749 5-12895 /s. 3- 0-8 3-50-4 4-13-3 5-200 6-11-4 5-36-0 5-50-9 6-45-2 7-36-6 14-6-3 5-28-3 3- 0-8 4-37-6 4-13-2 7-50-9 5-20-0 10- 7-0 4-37-6 5-20-0 9-33-3 18-31-5 11- 7-1 17-58-9 16-37-2 18-23-5 20-11-9 9-33-3 8-15-0 7-36-6 16-50-5 18-19-8 17-49-9 9- 8-4 17- 6-5 7-51-2 8-10-1 7-46-1 5-50-9 11- 7-1 8-15-0 11-27-0 9-36-8 18-47-8 17-49-9 10-21-0 10-28-7 IO-21'O 9-28-3 z-f.s 89-56-49-5 88-38-32-0 89-37-54-0 89- 3- 9-0 «9-32-44-0 89- 3-36-0 89- 5-160 89- 2-31-0 88-29-27-0 88- 7-22-0 89-33- 6-0 90- 3-30-0 89-42-15-0 90-22-40-0 88-42-33-5 89-47-19-0 89-36-39-0 90-17-52-5 90-56-57-0 89-19-32-0 90-14-50-0 89-58-25-0 88-48-15-5 90- 8-50-0 89-35- 5-0 89-16- 0-0 90-40-38-0 90-44-51-0 91-30-43-0 90-43-58-0 90-36- 2-0 90- 3-40-5 88-21-56-0 90-43- 80 90-38-46-0 90-44-53-5 90-21-30-0 90-54-43-0 90- 1-35-0 89-15-12-0 89-48-31-0 89-31-29-5 90-41-35^ 90-32-14-0 90-17-13-0 89-56-34-0 90-51-430 8919-360 89- 7-39-0 88-43-59-0 h'-h. feet 39-5 1293-0 386-0 1253-0 698-0 1306-0 1323 1605-0 2849-0 6569-0 608-0 - 43-6 339-5 - 395-5 2513-0 279-6 976-0 - 342-0 -1255-0 1598-0 -11360 73-0 5334-0 - 607-0 1894-0 3673-0 -1605-0 -1529-0 -2854-0 -3061-0 -2730-0 - 271-0 3706-5 -3050-0 -1258-0 -1516-0 - 690-0 -1323-0 - 73-0 1527-5 476-0 1188-0 -1968-0 -1281-0 -1337-5 253-0 -22120 1750-0 2240-0 29760 150 160 70 130 50 50 75 35 110 20 65 130 85 65 30 75 25 50 150 70 30 75 10 10 2 45 25 60 10 10 20 20 20 15 15 40 80 40 60 40 10 40 20 15 20 50 10 10 10 600 VERIFICATION AND EXTENSION OF LA CAILLE'S ARC OF THE MERIDIAN. §9- 51 52 53 54 55 56 57 58 59 60 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 97 98 99 100 101 102 103 104 105 106 107 108 Lambert's Hoek Berg.. Ceder Berg., POINT OBSBBVED. Heerenlogement's Berg.. Kamies Sector Berg.. Eoode Wal.. Koeberg.. Ezel's Kop North End.. Eoyal Observatory.. King's Battery.. Heerenlogement's Berg.. Eland's Berg Piket Berg Klip Eug, kop Lambert's Hoek Berg... Piket Berg Heerenlogement's Berg. Winter Berg Kapitein's Kloof. KUp Eug. Ceder Berg Piket Berg Bokkeveld Berg Klip Eug Ezels Kop Louis Eontein Bokkeveld Berg Vogel Klip Koe Berg North End Boschluis Keibiskow Eoode Wal Kamies Sector Berg Ezels Kop Vogel Klip Louis Eontein Kamies Sector Berg Vogel Klip Ezel's Kop Vogel Klip , Louis Fontein Eoode Wal Kamies Sector Berg Ezels Kop Vogel Klip Sneeuwkop KogelBerg Zwart Kop Tyger Berg. King's Battery Muizen Berg Simon's Berg Lion's Eump Cape Hanglip, knob.... Meridian Mark Zwart Kop Cape Point Cape Hanglip Kogel Berg Sneeuwkop Simon's Berg Tyger Berg Meridian Mark Eoyal Observatory Kapoc Berg TKUE ZEN. DISTANCE 2. 90-39-45-1 91-25-11-4 91-27-52-0 90-17-30-3 91-27-44-0 91- 9- 7-9 91.15-33-4 90-14-46-6 91- 0-310 90-51-23'6 89-16-59'6 90-12-48-2 90-1813-0 90- I-350 88-58-296 91- 2-50'8 90-48-14-5 90-28-33-1 90-34-48-0 90-37-52-6 90-43-36-2 90-33-40-4 91-23-53-4 89- 6-48-4 88-53- 3-2 89-38-27-2 89-53-41-3 90- 0- 1-1 90- 6- 0-6 89-56-49-1 90-33-38-4 91- 9-13-4 91-34-43-2 89-57-45-6 89-55- 8-8 90- 4-46-6 88-18-59-8 88-45-55-9 89- 3-34-2 88-22-48-4 82-10-27-1 88-33-33'l 88-53'30-8 87-19-16'4 89-48- 6-7 89'45-47'2 89-46-36-2 90-27-54-0 90-13-10-3 89-15- 9-7 88-52- 4-6 89-31-13-8 90- 7-23-7 90-50-43-I 97-50-54-8 90-12-10-4 LOO. DISTANCE 5-14445 5-12895 5-19683 5-49786 507375 5-35444 5-35982 5-43709 5-35073 5-43396 5-35982 5-42183 5-50905 5-44340 4-30150 5-39510 5-58619 5-36346 5-40039 5-41710 5-47671 5-62329 5-35426 U 3 5-35426 3 5-31479 2 5-49343 3 5-38228 2 5-40039 2 5-29688 2 5-41995 1 5-35534 1 5-38523 1 5-31479 8 5-41710 9 5-43814 9 5-34853 18 5-19913 12 5-21646 4 5-02695 14 4-65074 16 3-99477 8 4-78272 14 5-12418 4 4-36538 6 5-27743 4-83515 I 5-00158 1 5-16613 1 5-27715 I 5-22282 1 5-21674 1 5-15260 1 4-73720 1 4-87322 1 3-99477 1 5-28837 9-48-9 9-28-3 11- 4-4 22- 8-9 8--20-5 15-55-1 16- 7-0 19-15-3 15-47-0 19- 7-0 16- 7-0 18-35-7 22-43-6 19-.32-3 1-24-6 17-29-0 27- 8-8 16-15-3 17-41-8 18-23-5 21' 5-8 29-34-0 15-54-8 15-54-8 14-31-9 21-55-5 16-58-5 17-41-8 13-56-7 18-30-8 z—f.s. 90-29-560 91-15-43-0 90-16-48-0 89-55-21-0 91-19-23-5 90-53-13-0 90-59-26-0 89-55-31-0 90-44-44-0 90-32-17-0 89- 0-53-0 89-54-12-5 89-55-29-0 89-42- 3-0 88-57- 50 90-45-22-0 90-21- 6-0 90-12-18-0 90-17- 6-0 90-19-29-0 90-22-30-0 90- 4- 6-0 91- 7-59-0 88-50-54-0 88-38-31-0 89-16-32-0 89 36-43-0 89-42-19-0 89-52- 4-0 89-38-18-0 15-57-2 90-17-41-0 17- 5-4 90-52- 8-0 14-31-9 91-20-11-0 18-23-5 19-18-3 15-42-3 11- 7-9 11-35-1 7-29-3 3- 8-9 0-41-7 4-16-0 9-22-0 1-37-9 13-19-8 4-48-9 7- 3-8 10-19-0 13-19-3 11-45-3 11-35-5 10- 0-0 3-50-6 5-15-4 0-41-7 13-40-3 h'-h. feet -1214-0 -2964-0 - 769-0 4260 -2737-0 -.3501-0 -3959-0 357-0 -2918-0 -2551-0 3938-0 445-0 424-0 1449-0 366-5 -3278-0 -2367-0 - 826-0 -1251-0 -1481-0 -1962-0 - 501-0 -4471-0 4545-0 4894-0 3938-0 1633-0 1293-0 457-0 1660-0 -1166-0 -3682-0 4816-0 89-39-22-0 15680 89-35-50-5 1927-0 89-49- 4-0 710-0 88- 7-52-0 5161-0 88-34-2 rO 4102-0 88-56- 5-0 1979-0 88-19-39-5 1306-0 82- 9-45-0 1360-0 88-29-17-0 1600-0 88-44- 9-0 2937-0 87-17-38-5 1096-0 89-34-47-0 1389-0 89-40-58-0 379-0 89-39-32-0 597-5 90-17-35-0 - 750-0 89-59-51-0 8-0 89- 3-24-0 2750-0 88-40-29-0 3811-0 89-21-14-0 1602-5 90- 3-33-0 - 56-4 90-45-28-0 - 988-0 97-50-13-0 -1360-0 89-58-30-0 85-0 10 10 10 5 15 15 15 5 7 5 7 5 4 5 40 8 1 7 5 4 2 I 1 2 2 1 2 1 1 1 1 1 1 4 5 6 16 10 5 45 230 20 15 25 5 1-5 1 1 1 1 1 2-5 2 15 1 CALCULATION OF THE DIFFERENCES OF ALTITUDE. 601 109 110 113 114 115 116 117 118 119 120 121 122 123 124 123 126 127 128 129 130 131 132 133 134 135 137 138 139 140 141 142 143 144 US 146 147 149 150 151 152 Tyger Berg.. Zwart Kop., Cape Point.. Danger Point.. Batela Toren.. POINT OBSERVED. Cape L'AguLhas Bast End of Cape Town Parade, Base-line West End of Cape Town Parade, Base-line Sneeuwkop Kegel Berg Zwart Kop Table Mountain, pile.. King's Battery Eoyal Obseryatory.... Meridian Mark Eoyal Obseryatory.... Sneeuwkop Table Mountain, pUe King's Battery ;... Kegel Berg Cape Hanglip, knob.. Muizenberg , Sneeuwkop Meridian Mark King's Battery Tyger Berg Table Mountain, pile. Kogel Berg Zonder-Einde Berg... Cape I/'Agulhas Babels Toren Zwart Berg, Caledon. Gunners Quoin Zwart Kop Kogel Berg Mudge Point Sneeuwkop Zonder-Einde Berg.. Gunner's Quoin Danger Point Sneeuwkop Zwart Berg, Caledon. Mudge Point Kogel Berg Pot Berg Danger Point Rock on Table Mountain Bock on Table Mountain TRUE ZEN. DISTANCE Z. 88-33-48-5 89-13-34-6 89-53-13-7 88- 8- 7-5 90- 0-43-7 91 •44-5 -5 91- 6'37-8 91-10-36-5 89- 9-15-7 89-10-35-6 90-26'26-3 89-12-23-2 90'22-52-8 90-30-10-6 88-50-25-3 90-1926-0 89-53-14-0 89-59-55-2 88-59-33-7 88-35-13-1 89-14'34-9 90-25-48-2 88-35-36-2 89-14-141 90-10-50-2 90- 9-57-1 89-20-45-5 89'51-41-0 89-15-46-2 89-45-59-7 91- 7-52-9 91-39-16-2 89-37-25-4 90-17-33-7 92-37-22-5 90- 1-25-5 89-54'16-2 90- 3-30-7 76-10-54'4 76-42-422 LOG. DISTANCE 5-13736 5-21648 5-15051 4-80851 4-73720 4-65074 4-71314 5-02695 5-24171 4-97692 5-00158 5-11529 5-09150 4-66111 5-27638 5-34327 5-16613 5-26443 5-15072 5-10689 5-38007 5-31427 5-00360 5-17672 4-95471 5-48977 5-29702 4-99582 5-37097 5-28989 5-25093 5-00360 5-14684 4-89600 4-70367 5-10302 5-36737 5-31427 4-15496 4-17182 f.S. 9-39-3 11-35-1 9-57-2 4-31-7 3-50-6 3- 8-9 3-38-6 7-29-3 12-16-7 6-40-4 7- 3-8 9-10-6 8-41-3 3-13-5 13-17-9 15-30-8 10-19-0 12-56-3 9-57-4 9- 0-1 16-53-1 14-30-6 7- 5-8 10-34-3 6-20-4 21-44-2 13-56-7 6-58-2 16-32-1 13-43-1 12-32-5 7- 5-8 9-52-1 5-32-3 3-33-4 8-55-3 16-23-9 14-30-6 1- 0-3 1- 2-7 Z—f.s. 88-24- 9-0 89- 1-59-5 89 43-16-5 88- 3-360 89-56-53-0 91-41- 3-0 91- 2-59-0 91- 3- 7-0 88-56-59-0 89- 3-55-0 90-19-22-5 89- 3-13-0 90-14-11-5 90-26-57-0 88-37- 7-0 90- 3-55-0 89-42-55-0 89-46-59-0 88-49-36-0 88-26-13-0 88-57-42-0 90-11-18-0 88-28-30-0 89- 3-40-0 90- 4-30-0 89-48-13-0 89- 6-49-0 89-44-43-0 88-59-14-0 89-32-17-0 90-55-20-0 91-32-10-0 89-27-33-0 90-12- 1-0 92-33-49-0 89-52-30-0 89-37-52-0 89-49- 0-0 76- 9-54-1 76-41-39-5 hl-h.. 3826-0 2778-0 688-0 2179-5 49-5 -1314-0 - 947-0 -1954-0 3198-5 1547-0 - 566-0 2154-0 - 510-0 - 359-0 4557-0 - 251-0 728-5 696-0 2898-0 3490-0 4348-0 - 678-0 2684-0 2462-0 - 118-0 1059-0 3066-0 440-0 4153-0 1572-0 -2869-0 -2704'0 1324-0 - 275-0 -2263-0 277-0 1500-0 660-0 35190 3513-0 §9. 1 1 1 2 2-5 3 3 1 2 3 1-5 1 1 3 1 1-5 1 1 2 1 1 1 1-5 1 1-5 0-5 1 1-5 0-5 2 1 1-5 3 2 3 2 1 1 The altitudes above the sea level of the following stations have been obtained by leveUing with the spirit-level, as follows : Zwart Kop =2031 feet Cape L'Agulhas 455 .. Cape Point 688 „ West End of Base 206 „ East End of Base 250 „ RoodeWal 622 „ Royal Observatory (station over transit circle) 51 „ 602 VERIFICATION AND EXTENSION OF LA CAILLE'S ARC OF THE MERIDIAN. §9- (1). By means of the altitudes of the West End, East End, and Royal Observatory, we may obtain the altitudes of Kapoc Berg, Eiebeek's Kasteel, and Zwart Berg, as follows : Assume the altitude of Kapoc Berg = 1502+t. Riebeek's Easteel = 3101 -j-y. Zwart Berg = 1574-|-z. Then the observations at the several stations furnish the following equations : WEIGHTS. From No. 2 x +1502—1293—206 =0 or a; +3 =0 16 4 X +1502-1253—250 =0 a: —1 =0 13 7 z +1574-1323—250 =0 z +1 =0 7-5 9 y +3101—2849—250 =0 y +2 = 11 19 X +1502 — 1255—250 =0 x —3 =0 15 20 x—y+1502— 3101+1598 =0 x—y—l =0 7 22 x-0+1502-1574+73 =0 x-z+l =0 7-5 27 j;—3/+1502— 3101 + 1605 =0 x—y-\-6 =0 4-5 28 J/— 2+3101-1574— 1529 =0 y—z—2 =0 2-5 29. y +3101—2854—250 =0 y — 3 = 6 30 y +3101-3061-51 =0 y —11 =0 1 38 z +1574—1323-250 =0 z +1 = 8 39 a;—z+1502— 1574+73 =0 ar-z+I =0 4 40 y—z +3101— 1574— 1527-5 = y— 2-0-5 = 6 Solving these by the method of least squares, having regard to the weights, we have the final equations : 791-5a;— 69-25y— 72-25Z+68-8 = 69-25^- 269-5y+ 42-252-20-0 = 72-25x+42-25y— 234-75Z-78-5 = 0. from these there results : x=—0-i\,y= -0-17, 2= -0-14. Applying these corrections, we have : Height of Kapoc Berg = 1501-6 feet above the sea level „ Riebeek's Kasteel = 3100-8 „ „ „ Zwart Berg = 1573-9 „ „ (2). In like manner if we assume height of Klip Eontein Sector Station = (380+x), Patrys Berg ^ Piket Berg = (2837 +z) we obtain, after reducing, the following system of equations : WEIGHTS. From No. 21 x +14-4 = 3 31 X +9-2 = 1 41 x—y— 8-0 = 4 42 X - 5-9 = 1 24 .y -30-6 = 1 43 y—z— 0-5 = 4 32 z +7-2 = 2 44 z —17-9 = 2 45 2 — 2-1 = 1-5 46 2 -10-8 = 2 These give 27x-16y +4-9 =0 — 16x+33y— 162+17-4 =0 -16y+30-252- 10-73 = whence we have x = —0-76, y = -097, z = —0-16. Consequently : Height of Klip Fontein Sector Station = 379-2 feet above the sea level. „ Patrys Berg = 863-0 „ „ „ Piket Berg = 2836-8 „ ^ (864+y), CALCULATION OF THE DIFFERENCES OP ALTITUDE. 603 Ceder B2gi"(6"37S)"''T^a7w7^avet-^' H^^renlogemenfs Berg= (2382+.). Lambert's Hoek Berg = (3598 +y,) Final equations : From No. 47.... ....w + 0-2 = ■WEIGHTS. 5 48.... 49.... ...,w -{-28-2 — 50.... ....W—1/+ 30 = .?!.... ....x—y— 2-0 = 52.... ....w—y— 9-0 = 53.... ....y - 7-8 = 55.... ....y—z— 20 = 1-5 5fi.... ....2 - 0-8 = 1-5 57.... ....ar-2+ 4-0 = 1-5 62.... ....a;-2 -17-0 = 0-7 63.... ....X — 9-8 = 0-5. 29»— X— 2y +20-2 = — w-\-i-99x— t/—2-74z+ 3-22 = — 2w— j;+6-25^— 2-252- 4-3 = — 2-74.J; — 2-25j>+7-242+ 203 = whence, w = —0-74, j: = — 1-20, y = -00, z = — -74 so that the height of Eland's Berg = 624-3 feet above the sea level. )> „ 'Heerenlogement's Berg. = 2380-8 „ „ >> » Lambert's Hoek Berg... = 3598 „ „ ■> )■ Ceder Berg =6336-3 North E^ni-J^Se^fH^fSaTn^''""^"^' """"''' ^''^ = ^"*'+"'^' ^''^'' ^°^ = ^''''+''^' ^oeberg = (3887 +j,), ■WEIGHTS. From No. 66 w—x— 1-5 = 40 69 V—W+ 2 =0 7 70 «>—y+ 6 =0 5 79 w—y— 36 =0 1 71 W—Z+ 53 =0 4 85 to— 2— 34 =0 4 74 w + 51 =0 1 75 w — 23 =0 2 76 X — 4 =0 2 84 X + 74 =0 1 77 V —240 =0 1 not used. 80 v—y— 24 =0 1 81 x—y— 35 =0 1 82 v—x— 26 =0 1 86 x—z- 25 =0 5 87 v—z =0 6 whence there results — 87k— 49t»— X— y— 362+ 48 = — 49W+1712M;— 1600x— 26^— 32z4-2679 = — t> — 1600m! + 1632x— y— 252— 2976 = — V— 26m)— x+2Sy — 55 = — 36!J— 32w— 25x +932+ 321 = From these we obtain, v = —4-65, w = —2-58, x = — 0"81, y = —0-63, z = —6-36 and consequently the height of Vogel Klip = 4315-3 feet above the sea level. „ „ Kamies-Sector Berg = 5141-4 „ „ „ Ezel's Kop = 5511-2 „ „ „ Koeberg = 3886-4 „ „ „ North End =3603-6 ,, 2 E §9. 604 VERIFICATION AND EXTENSION OF LA CAILLE'S ARC OF THE MERIDIAN. S 9. The heights thus obtained, together with the levelled heights, famish data for the level of the other points observed. The following table gives the separate and mean results for each station. calculation of the altitudes above the sea NAME OF STATION. West End of Base.. East End of Base... Kapoc Berg Kiebeek's Kasteel... Zwart Berg Klip Fontein, Centre Bg. Drie Fontein.. Groote Zwart Berg.. Contre BergEock.... Baviaan's Berg.. Winter Berg Klip Fontein PatrysBerg. PiketBerg Eland's Berg Lambert's Hoek Berg... Ceder Berg. Heerenlogement's Berg. Kapitein's Kloof. Klip Bug Station.. Klip Eug, kop Kamies-Sector Berg.. Ezel's Kop EoodeWal VogelKlip Koe Berg North End Bokkeveld Berg Louis Fontein.. Boschluis Keibiskow Eoyal Observatory.. Zwart Kop Cape Point ® . Altitude ^ above the sea 4 Mean. '^ 2 level. ^ feet. 206 250 1502 3101 1574 .s 592 7 ^ 13 589-5 8-5 14 601-5 588 6-5 , 3 1 593 17 598 2-5 18 592 5 J 11 858 6-5-) 16 873 7-5^ 870 37 884 4 J 5 948 6 36 1556 1585 1-5. 1563 8 35 1855 1843 3-51 1-5. 1851 10 6819 2 ■) 23 6836 1 [ 6818 33 6807 2 J 379 863 2837 624 3598 6336 2381 25 59 3396 3418 2 > 7 .■ 3412 60 65 3785 3830 n 3807 54 4024 5141 5511 622 4315 3886 3604 64 68 2805 2774 t] 2799 67 1863 8 ■) 78 (2255*) [ 1859 an 1829 1 1 72 3179 73 4640 51 2031 688 levelled levelled page 602 page 602 page 603 page 603 » levelled page 603 •mirage mirage levelled NAME OF STATION. King's Battery.. Tyger Berg. Sneeuwkop.. Kogel Berg.. Simon's Berg Meridian Mark.. Table Mountain, pile.. Lion's Eump.. Muizenberg... Hanglip, knob . Danger Point... Mudge Point Gunner's Quoin Zwart Berg, Caledon.. Zonder Einde Berg.... Babel's Toren.... Cape L'Agulhas., Pot Berg a s Altitude above the sea Ifevel. 92 107 99 100 108 113 115 116 91 105 88 109 103 89 110 102 94 104 98 117 106 114 120 129 95 93 124 97 123 140 150 132 138 137 143 139 146 135 142 134 145 131 141 133 149 1411 1411 1433-5 1438 1417 1343 1361-5 1366 1357 1354-6 6212 5183 5222 4158 4135 4161 2988 3013-6 430 410 423 3536-5 3546 3566 1651 1639 1440 1488 1058 1115 1133 1086 (972) 1177 1566 1618 1008 1012 3606 5474 5463 Mean 20 u O-6'l 1 I 1 \ 0-6 I-5J U u feet. 1411 1367 5211 4152 2990 430 3549 1147 1650 1448 1126 1600 1010 3600 6460 8810 465 1955 see below see below see below see below levelled At the Zwart Kop, Cape Point, and Babels Toren Stations an assumed zenith point was employed in the calculation of the observations made at those localities ; the resulting heights of the points observed are therefore relative only. At Zwart Kop, by comparing the known and computed heights of the Observatory, Sneeuwkop, Kegel Berg, and King's Battery Stations, the mean error of the computed heights is found to be + 33 feet. Hence we have, height of Table Mountain = 3645, Hanglip, knob = 1488, and of Muizenberg = 1639 feet. In like manner at Cape Point the mean error of the computed heights of Sneeuwkop, Meridian Mark, King's Battery, Tyger Berg, and Kogel Berg ^ + 20 feet, consequently the height of Table Mountain = 3566. At Babels Toren the absolute heights are obtained by referring the computed values to the known points Sneeuwkop and Kogel Berg. SECTION X. DETERMINATIOIS^ OF THE AZIMUTH OF THE MERIDIAN DISC AT KAMIES-SECTOR BERG, AND COMPARISON OF THE ASTRONOMICAL AND GEODETICAL AZIMUTHS OF LOUIS FONTEIN. The following observations were made with a 30-inch transit instrument by Jones, placed upon a block of granite, and at a distance of 26 feet 3 inches to the south of the " azimuth point," — as described at page 468. The disc, which is 14 inches in diameter, is to the south of the station ; and its distance from the west rock was found to be 40799 "1 feet, by means of a small triangulation effected with DoUond's repeating circle, and derived from a base of 4200 feet measured with the 100 feet steel chain. Hence the distance of the disc from the transit instrument is 40866 feet, and the angle subtended by it at the latter point is 5" • 88. The observations consist of consecutive transits of five circumpolar stars above and below the pole ; the central wire of the transit instrument being made either to bisect the disc, or its deviation to the true east or west of the center, estimated in terms of the diameter of the disc. In the following table, the 4th column contains the observed time of transit of the star corrected for errors of collimation and level, and reduced to the central wire of the system. The 5th column gives the deviations of the central wire to the true east or west of the center of the disc ; and column 6 the corresponding corrections to be applied to the times of transit, in order to reduce them to the vertical plane passing through that point. These corrections are obtained by multiplying the numbers in column 5 by the following factors respectively, — a Trianguli, 0-672 /3 Trianguli, 0-465 y Apodis, 1-472 a Trianguli, S.P., 1-069 fi Trianguli, 8.P., 0-861 y Apodis, S.P., 1-868 j3 Apodis, 1 289 (i Ar^us, 0-687. /3 Apodis, S.P., 1-685 /3 Argus, S.P., 1-084. 606 VERIFICATION AND EXTENSION OF LA CAILLE'S ARC OF THE MERIDIAN. § 10. Determination of the Azimuth of the Meridian Disc at Kamies-Sector Berg. Date. 1843.' Stak. Observed tronflit corrected for collimation and level, and reduced to middle wire. Middle ivire east or weflt of center of diao, interma of diameter of disc. Correc- tion to transit. '6 -of |i Upper transit minus lotrer transit. Sum. Divisor. Error in Azimuth of the Disc. h ID 8 s s s s # Aug. 27 West a Trianguli, S.P... 4-33- 8-72 West 0-50 +0-53 9-25 +3-15 -1-32 + 1-79 |.49 28 J) a Trianguli 1633-12-40 12-40 + 1-83 0-591 +3-10 >> East a Trianguli, S.P... 4-3313-97 East 0-23 -0-25 13-72 0-47 J» 0-79 29 ,j a Trianguli 16-33-15-51 15-51 0-30 ff 0-51 it West a Trianguli, S.P... 433-1681 West 0-18 +0-19 17-00 + 2-31 -1-53 +2-29 — 1-23 0-82 n 1-39 30 ») a Trianguli 16-33-19-31 19-31 0-78 »> 1-32 }J East a Trianguli, S.P... 4-33-20-70 West 0-13 +014 20-84 0-76 J* 1-29 31 ,j a Trianguli 16-33-2313 23-13 1-06 )» 1-79 " West a Trianguli, S.P... 4-33-24'36 24-36 Sept. 5 East a Trianguli 16-33-40-09 West 0-05 —0-03 40-06 -1-04 + 1-74 -1-70 +2-48 -1-09 +2-97 -0-68 )» West a Trianguli, S.P... 4-33-4121 East 0-10 -0-il 41-10 0-70 ti 1-18 6 iJ a Trianguli 16-33-42-84 42-84 0-04 j> 0-07 „ »» a Trianguli, S.P... 4-33-44-38 West 0-15 +0-16 44-54 0-78 » 1-32 7 East a Trianguli 16-33'46-82 East 0-30 +0-20 47-02 1-39 ti 2-35 „ ») a Trianguli, S.P... 4-33-48-11 4811 1-88 ft 3-18 8 »» a Trianguli 16-33-51-08 51-08 2-29 J} 3-87 " >j a Trianguli, S.P .. 4-33-51-71 West 0-05 +0-05 51-76 9 West a Trianguli, S.P... 4-33-55-84 East 0-24 -0-26 55-58 + 1-84 +0-18 +3-42 -1-24 +3-73 10 '» a Trianguli 16-33o7-59 West 0-25 -0.17 57-42 2-02 n 3-42 „ J» a Trianguli, S.P... 4-33-57-24 57-24 3-60 »• 6-09 11 a Trianguli 16-34- 0-66 60-66 2-18 )) 3-69 „ >» a Trianguli, S.P... 4-34- 1-63 West 0-25 +0-27 61-90 2-49 )) 4-21 12 East a Trianguli 16-34- 5-63 65-63 13 East a Trianguli 16-34- 9-58 West 0-15 -o-io 9-48 -0-36 +2-75 -0-79 )y J> a Trianguli, S.P... 4-34- 9-73 West 0-10 +011 9-84 2-39 »» 4-04 14 J» a Trianguli 16-34-12-59 12-59 + 1-96 ji 3-32 it »J o Trianguli, S.P... 4-34-13-49 East 0-10 -0-11 13-38 Mean.. +2-470 Sept. 7 East ;8 Trianguli 15-43- 1'45 East 0-28 +0-13 1-58 -1-06 +2-47 -1-14 „ 3J ;8 Trianguli, S.P.. 3-43- 2-64 2-64 +1-41 0*450 +3-13 8 )1 /3 Trianguli 15-43 5-11 .5-11 1-33 ji 2-96 JJ » P Trianguli, S.P.. 3-43- 6-21 West 0-05 +0-04 6-25 )» 9 West IS Trianguli, S.P.. 3-43' 9-93 East 0-24 -0-21 9-72 + 202 — 0-20 +2-81 -1-37 10 J» ;3 Trianguli 15-43-11-86 West 0-25 -0-12 11-74 1-82 ti 4-04 »> )• /3 Trianguli, S.P.. 3-43-11.94 11-94 2-61 5-80 11 >> /3 Trianguli 15-43-14-75 14-75 1-44 ft 3-20 » J' P Trianguli, S.P.. 3-43-16-12 16-12 13 East (3 Trianguli 15-43 23-82 West 0-12 -0-06 23-76 -0-03 +3-05 —0-95 +2-82 J» » j3 Trianguli, S.P.. 3-43-23-79 23-79 3-02 6-71 14 „ (3 Trianguli 15-43-26-96 West 0-25 -0-12 26-84 2-10 4-67 » » /3 Trianguli, SP.. 3-43-27-88 East 0-10 -0-09 27-79 + 1-87 4-16 15 jj j3 Trianguli 15-43-30-49 „ 0-25 +0-12 30-61 Mean.. +4-334 Aug. 29 East y Apodis 16-10-46-96 46-96 „ West y Apodis, S.P 4-10-48-87 West 0-18 +0-34 49-21 — 2-25 +2-00 -0-25 1-134 -0-22 30 West y Apodis 16-10-51-21 51-21 + 1-66 +2-39 + 1-46 +2-11 J) East y Apodis, S.P. 4-10-51-31 West 0-13 +0-24 51-55 -0-34 +2-73 -0-97 t) 31 East y Apodis 1610-54-28 54-28 + 1-76 + 1-55 »j West y Apodis, S.P 4-10-55-25 55-25 ASTRONOMICAL OBSERVATIONS FOR AZIMUTH, AT KAMIES-SECTOR BERG. 607 Determination of the Azimuth of the Meridian Disc at Kamies-Sector Berg — continued. § JO. Date, 1843. Sept. 5 »♦ 6 )» 7 8 9 10 11 12 13 ', 14 Sept. 5 6 7 8 9 10 11 13 13 14 East West East West East Star. East West East West East 7 Apodis y Apodis, S.i".. y Apodis y Apodis, S.P., 7 Apodis 7 Apodis, S.P. 7 Apndis 7 Apodis, S.P. y Apodis, S.P, 7 Apodis 7 Apodis 7 Apodis, S.P. 7 Apodis , 7 Apodis 7 Apodis, S.P. 7 Apodis Aug. 30 East 31 West n Sept. 4 5 East West 6 »> »» 7 91 East if 8 »> )» ObsBrvod traiuit corrected for colllmatlon and level, and rodnced to middle wire. 16-11-11-90 4-11-12-25 16-11-14-16 4-11-15-33 16-11-18-50 411-18-78 1611'23-33 4- U •23-43 4'll'26-48 16-11-29-11 16-11-31-96 4- 11 -3209 16-11-3780 16-1 1-41 -80 4-U-40-50 16-11-44-59 Middle wire east or west of center of disc, In terms of diameter of disc. West 0-05 East 0-10 West 0-15 East 0-28 West 0'05 East 0'24 West 0-25 West 0-25 West 014 West O'lO West 0-25 Correc- tion to transit. -0-07 —0-19 +0-28 -I-0-41 +0-09 —0-45 -0-37 +0-47 -0-21 +0'19 —0-37 j3 Apodis /3 Apodis, S.P. /3 Apodis P Apodis, S.P., /3 Apodis /3 Apodis, S.P.. /3 Apodis /3 Apodis, S.P., j3 Apodis, S.P., P Apodis )3 Apodis, S.P.- ;3 Apodis /3 Apodis, S.P.. /3 Apodis /3 Apodis, S.P.. /3 Apodis /S Apodis, S.P. /3 Argus, S.P.. /3 Argus /3 Argus, S.P.. /3 Argus j3 Argus ;3 Argus, S.P., S Argus P Argus, S.P. ;8 Argus /3 Argus, S.P. /3 Argus ;3 Argus, S.P. 16-22 4-22 16-22 4-22 16-22 4-22 16-22 4-22 26-12 25-80 27-93 29-46 ■32-29 32-68 37-02 •37-09 4-22-40-89 16-22-43-35 4-22-42-17 16-22-45-72 4-22-46-35 16-22-5607 4-22-54-64 16-22-58-71 4-22-58-40 West 0-05 East 0-10 West 0-15 East 0-30 West 0-05 East 0-24 West 0-25 West 0-25 West 0-14 „ 0-10 „ 0-25 East 0-10 —0-06 —0-17 +0-25 +0-39 +0-08 —0-40 —0-32 +0-42 -0-18 + 0-17 —0-32 -0-17 ■"i n-83 12-06 14-16 15-61 18-91 18-78 23-33 23-52 26-03 28-74 31-96 32-56 37-80 41-59 40-69 44-22 Upper transit minus lower transit. -023 +2-10 -1-45 +3-30 +0-13 +4-55 -0-19 + 1-14> -0-60 +5-24 +0-90 +3-53 Sum. + 1-87 0-65 1-85 3-43 4-68 4-36 4-64 +4-43 Divisor. 1-134 0-567 1-134 Mean., 26-06 25-63 27-93 29-71 32-68 32-68 37-02 37-17 40-49 43-03 42-17 45-72 46-77 55-89 5481 5S-39 58-29 21-12-31-11 9-12-33-40 21-12-34-97 912-37-04 9-12-50-68 21-12-52-38 9-12-54-15 21-12-55-54 9-12-56-78 21-12-59-75 9-12-61-69 21-12-63-35 East 0-10 East 0-10 East 0-15 East 0-10 East 0-08 West 0-05 +007 — O-ll +0-10 +0-07 +0-06 +0-05 31-11 33-40 34-97 37-04 50-75 52-27 54-25 55-54 56-85 59-75 61-75 63-40 +0-43 +2-30 -1-78 +2-97 0-00 +4-34 -0-15 +2-.M +0-86 +3-55 -1-05 + 1-08 +3-58 + 0-10 +2-73 0-52 1-19 2-97 4-34 4-19 3-40 4-41 2-50 4-66 +3-68 1-010 Mean.. +2-29 —1-57 +2-07 -1-52 +1-98 -1-29 + 1-31 -2-90 +2-00 —1-65 Error in Azimuth of tlie Disc. +1-65 0-57 1-63 3-02 4-13 3-84 2-01 4-09 3-90 +2-288 +2-70 0-51 1-18 2-94 4-30 4-15 3-37 4-37 2-48 4-61 3-64 +3-114 +0-72 0-6016 +0-50 » +0-46 n +0-69 )» +0-02 ,> -1-59 »» -0 90 ,» +0-35 » + 1-20 +0-83 +0-76 + 1-15 +0-03 —2-64 — 1-50 +0-58 (a) _is.62 applied for rate, and +0'05 for motion in E.A. a F 608 VERIFICATION AND EXTENSION OF LA CAILLE'S ARC OF THE MERIDIAN. § 10. Determination of the Azimuth of the Meridian Disc at Kamies-Sector Berg — continued. 1 Bate .-. S^ ■ 1843. 1^ Sept. 9 West ») »j 10 )» )» jj 11 )j 1) » 12 East 13 ft „ J» 14 » »» »j 15 West Star. ;3 Argus, S.P. /3 Argus /3 Argus, S.P. j3 Argus P Argus, S.P. |3 Argus P Argus, S.P. ;8 Argus /3 Argus, S.P. /3 Argus j3 Argus, S.P. /3 Argus /3 Argus, S.P. Obsorved transit corrected for coUIinatiofl' tCild ' level, and. reduced to middle wire. , 13- 7-23 13- 7 67 13-10-14 13-11-45 13-13-86 13-15'92 13-17-83 13-20-69 13-21'35 13-24-67 13-25-79 13-27-76 13-2863 Middle wire east or weflt of center Ofdiaeinterms'Of diatneter of disc. East 0-05 West 0-12 East 0-10 Correc- tion to transit. +0-03 -0-08 +0-07 a 3 tea 7-23 7-70 10-14 U-45 13-86 15-84 17-83 20-69 21-35 24-67 25-79 27-83 28-63 Upper transit minus lower transit. +0-47 -2-44 +1-31 —2-41 +1-98 -1-99 +2-86, -0-66 +3-32 -1-12 +2-04 — 0-80 Sum. — 1-97 -1-13 -1-10 —043 — O-OI +0-87 +2-20 +2-66 +2-20 +0-92 + 1-24 Divisor. 0-6016 Mean.. Error in Azimuth of disc. -3-27 —1-88 — 183 -0-71 —0-02 + 1-45 +3-66 +4-42 +3-66 + 1-53 +2-06 +0-499 Collecting the results given by the several stars, we have for the deviation of the disc to the west of the south point : , No. of results. By a Triangiili 2-470 19 /STrianguli 4-334 8 y Apodis 2-288 13 j3 Apodis ..3-114 11 /3 Argus......... 0-499.. 19 The mean of the whole is 2-'22, and reckoning from the south point round by the west, the azimuth of the disc is0°-0'-2'-22. Comparison of the Astronomical and Geodetical Azimuths of Louis Fontein. Angle, Meridian Disc^Azimuth Point — Louis Fontein (p. 470) 10-34-44'96 Azimuth of the Meridian Disc o- 0- 2-22 Azimuth of Louis Fontein at "Azimuth Point" 10-34-47-18 Angle, West Rock — ^Louis Fontein— Azimuth Point (p.469).... -2-19-44 Convergence of the Meridians of West Bock and Azimuth Point .'...'.'.'.. + l-09 Astronomical Azimuth of Louis Fontein at West Rock 10-32-28-83 Geodetical Azimuth of Louis Fontein at West Rock (p. 582, No. 78) .......io-32-2r46 Difference 7-37 COMPARISON OF THE LATITUDES AND MERIDIONAL DISTANCES, &c. 609 § 10. Table of the Final Results of the Observed Latitudes, the Calculated Latitudes, and the Distances of the Parallels of the Sector Stations. Stations. North End Kamies Sector Berg Heerenlogement's Berg.., Royal Observatory Zwart Kop Cape Point Astronomical Latitudes. 29-44-17-69 30-21 ■29-06 31-58- 9-03 33-56- 320 34-13-32-12 34-21- 6-26 Geodetical Latitudes. 29-44-17-32 30-21-20-70 31-58- 9-64 33-56- 3-20 34-13-33-80 34-21- 6-81 Diff. -0-37 -8-36 +0-61 + 1-68 +0-55 Distance of the Parallels. Length of the Meridian Arc calculated with the geodetical latitudes. feet 224600-6 811506-8 1526385-1 1632581-4 1678373-8 feet 224600-7 811506-7 15263850 1632581-5 1678374-1 Diff. +0-1 —0-1 —0-1 +0-1 +0-3 The astronomical latitudes are derived from the amplitudes observed with Bradley's Zenith Sector (vol. ii, page 437), taking the latitude of the Eoyal Observatory, 33°-56'-3"-20. The geodetical latitudes are computed with Airy's elements (page 589). The 5th column gives the distance between tlie parallels of the Stations calculated by the method of " nodes " (page 571). In the 6th column are given, for the purpose of comparison, the same distances calculated with the geodetical latitudes, from Bessel's formula, viz.: S = a (1— n)' (1+n) iimp — m^ sin. ^ cos. 2 \ +n!j sin. 2 cos. i\ — m, sin. 3 cos. 6 X V a — i a + b' where is the difference of the latitudes ; 2 X the sum of the latitudes ; n = 35 , - ^ ny I = 1 + £n« ; m,=3n + —n^ ; ntj =—«.' ; m^ =—n'. 4 ' 8 8 24 With Airy's elements, viz. : o = 209237 13 feet, and 6 = 20853810 feet, we find n = 0-0016732203 ; m = 1 -0000062993 ; m, = 0-00501969 ; nij = 00000052494 ; m, s= 0-0000000068; and log. a (l-«)' (1+n) = 7-31991026. Hence we may put : S = A 0' — B sin. cos. 2 X + C sin. 2

    ns-^--contimied. 2. Kapoc Berg Station. Angle, reduced to La Caille's Kock, between Eiebeek's Kasteel and La Caille's Obser- vatory, p. 450 The reduction of Eiebeek's Kasteel Angle Point to La Caille's file, p. 45 2 — 98-19-21'81 9-65 98-19-12'16 weight 22-84 Angle reduced to La Caille's Bock, between Eiebeek's Kasteel and Eogge Bay, p. 450 98-17-17-12 The reduction, Eogge Bay to La Caille's Observatory ... + 2- 8-26 j, „ Eiebeek's Kasteel AngleE0inttoLaCaille'sPile,p. 452 — 9-65 8-19-15'73 weight 10-5 Angle measured at Signal Eock between Eiebeek's Kasteel and Eogge Bay, A 42 p. 542 98-13- 1 8-70 The reduction. Signal Eock to La Caille's Eock, p. 450 + 3-57'98 „ „ Eogge Bay to La Caille's Observatory -j- 2- 8-18 „ „ Eiebeek's Kasteel Angle Poiot to La CaiUe's Pile, p. 452 — 9-63 98-19'15-23 weight 21-5 Angle measured at Signal Eock between Eiebeek's Kasteel and La Caille's ObservatiDry, p. 476 and A 44 p. 542 ... ... 9815-20-99 The reduction. Signal Eock to La Caille's Eock, p. 450 + 3'58'05 „ „ Eiebeek's Kasteel Angle Point to La Caille's Pile, p. 462 — 9-63 98- 19- 9-41 weight' 4 The mean of these four results gives for the Angle at La CaiUe's Eock between La Caille's Pile, Eiebeek's Kasteel, and La Caille's Observatory 98-19-13-73 weight 58-8 'i Angle measured at Signal Eock between West End of Base and East End of Base ^ Alp- 534 33-37-47-34 Eeduction, Signal Eock to La Caille's Eock, p. 450 ... — 2-16-95 Angle, WestEndof Base— La Caille's Eock, Kapoc Berg -East End of Base = 33-35-30-39 weight Angle measured at Signal Eock between East end of Base and Eiebeek's Kasteel A 2 p. 534 52-39-14'77 Eeduction, Signal Eock to La CaiUe's Eock, p. 450 + 1- 9-22 „ Eiebeek'sKasteel Angle Point to La Caille's Pile, p. 452 ... + 9-63 58 Angle, East end of Base— La Caille's Eock, Kapoc Berg— La Caille's Pile, Eiebeek's Kasteel .. = 62-40-33-62 weight 49 Anele measured at Signal Eock between Klip Eontein Granary and Eiebeek's Kasteel, ^ p. 476 ... - 73-53-13-19 Eeduction, Signal Eock to La Caille's Eock, p. 450 — 2-24-85 „ Eiebeek's Kasteel Angle Point to La Caille's Pile, p. 452 ... + 9-63 „ Klip Eontein Granary to Signal Eire, p. 455 + 2-59-40 Angle, Klip Eontein Signal Fire— La Caille's Eock, Kapoc Berg- La Caille's Pile, Eiebeek's Kasteel ... = 73-53-57-37 weight 35 § 11- Kapoc Berg Station. Eeduction of measured angles to La Caille's Rock. 614 VERIFICATION AND EXTENSION OP LA CAILLE'S ARC OF THE MERIDIAN. S 11. Elebeek'sKas- teel Station. Reduction to La Caille's Pile. Beduction of the measured angles to the assumed Stations — concluded. 3. Riebeek's Kasteel Station. Angle between Eogge Bay and Kapoc Berg Signal Bock, A 42, p. 542 48*13-12'08 Beduction, Angle Point to La Caille's Pile, p. 488 — 4-62 „ SignalBockKaipocBergtoLaCaille'sEock, p. 450... ... — 3'10-48 „ Eogge Bay to La Caille's Observatory — 59-90 Angle, La CaiUe's Observatory— La Caille's Pile— La Caille's Eock, Kapoc Berg ... = 48' 8-57'08 weight 46 Angle between Kapoc Berg and East end of Base, A 2 p. 534 Reduction, Angle Point to La Caille's Pile, p. 452 „ Signal Bock, Kapoc Berg, to La Caille's Eock, p. 450 Angle, La Caille's Rock, Kapoc Berg— La Caille's Pile— East end of Base 33'50-58-67 — 17-49 + 3-10-48 = 33-53-51-66 weight 79 Angle between Kapoc Berg and the Granary Klip Eontdn, p. 477 76-5-39-47 Reduction, Angle Point to La Caille's Pile, p. 452 — 21-36 „ Signal Rock, Kapoc Berg, to La Caille's Eock, p. 450 ... + 3-10-48 „ Granary to Signal Fire, Klip Fontein, p. 455 — 2-45-46 Angle, La Caille's Eock, Kapoc Berg— La Caille's PUe— Signal Fire, KUp Fontein ... = 76- 5-43-13 weight 32-5 4. East End of Base. Angle between Kapoc Berg and West end of Base, A 1. p. 534 Beduction, Signal Eock, Kapoc Berg, to La Caille's Eock, p. 450 Angle, La Caille's Eock, Eapoc Berg— East End of Base— West End of Base ... o / # 44-S3-24-78 + 4-19-70 , = 44-67-44-48 weight 40 Angle between Eiebeek's Kasteel and Kapoc Berg, A 2. p. 534 ... ... 93-29-48-49 Beduction, Signal Eock, Kapoc Berg, to La Caille's Eock, p. 450 ... — 4-19-70 „ Eiebeek's Kasteel Angle Point to La Caille's Pile, p. 452 ... + 7-86 Angle, La Caille's Pile, Eiebeek's Kasteel — East end of Base— La CaiUe's Eock, Kapoc Berg = 93-25-36-65 weight 39 5. West End of Base. ..*>«i:/;(*' Angle between East end and Kapoc Berg, a !• p. -534 Beduction, Signal Eock, Kapoc Berg, to La Caille's Eock, p. 450 .. 101-28-48-42 ,.. — 2- 2-75 Angle, East end of Base— West end of Base— La Caille's Eock, Eapoc Berg = 40l'26-45-67 weight 42 CALCULATION OF THE MODERN TEIANGULATION OF THE ASSUMED STATIONS. 615 STATIONS. Prop. of Error. 13 OS a> • -a S H o t3 bo U CU H Log. Sines. Log. Distances. Distances in feet. La Caille's Distances. M 03 A 1.— Measured Base = 42819-065 Feet. Log. 4-6316371. fca Caille's Rock, Kapoc I Berg ^lastEndof Base..^ West End of Base Sum 180°+e Error 33-3'5-30-39 44-57-44-48 101-26-45-67 180- 0- 0-54 180- 0- 0-54 0-00 58 40 42 0-00 0-00 0-00 —0-18 —0-18 -0-18 30-2 44-3 45-5 9-7429380 9-8491991 9-9912758 4-7378982 4-8799749 54688-8 75853-4 A 2.— La Caille's Eock, Kapoc Berg, to East End of Base = 75853-4 Pieet. Log. 4-8799749. (From a 1.) La Caille's Pile, Rie- beeU's Kasteel East end of Base La Caille's Bock, Kapoc Berg. Siun J I80°+£...... i Error 33-53-51-66 93-26-36-65 52-40-33-62 79 39 49 0-00 0-00 0-00 -0-64 -0-66 -0-64 51-0 36-0 33-0 180- 0- 1-93 180- 0- 1-93 0-00 9-7464076 9-9992228 9-9004861 S-1327901 6-0340534 135765-7 108156-7 135810-3 + 44-( A 3.— La CaiUe'a Pile, Eiebeek's Kasteel, to La Caille's Eock, Kapoc Berg = 135765-7 Feet. Log. 5-1327901. (From A 2.) La Caille's Observatory La Caille's Eock, Kapoc Berg La Caille's Pile, Eie- beek's Kasteel Sum.... 180°+« Error. 33-31-54-96 98-19-13-73 48- 8-57-08 57-7 58-8 46 +0-01 +0-01 +0-02 -1-94 -1-93 -1-94 63-0 11-8 65-2 180- 0- 5-77 180- 0- 5-81 -0-04 9-7422487 9-9954051 9-8720855 5-3859465 5-2626269 243190-4 183074-1 243283-6 183148-8 + 93-2 + 74-7 A 4.— La Caille's Pile, Eiebeek's Kasteel, to La Caille's Eock, Kapoc Berg = 135765-7 Feet. Log. 5-1327901. (From A 2.) Signal Pirej Klip Fon- teln..... i^ CsPC? Eock, Kapoc Befg... ■La Caille's Pile, Eie- beek's Kasteeli......... Sum 18P°+£., Error.. 30- 0-28-34 73-53-57-37 76- 5-43-13 ISO- 0- 8-84 180- 0- 8-12 +0-72 36 -0-23 -2-71 25-4 35 -0-24 -2-71 54-4 32-5 -0-25 -2-70 40-2 9-6990626 9-9826201 9-,9870821 5-4163476 5-4208096 260824-0 263517-6 261000'4 263654-8 +176-4 +137-2 § n. Calculation of the Modern Triangulation of La Caille's Arc in terms of the Modern Base. 2 H 616 VERIFICATION AND EXTENSION OP LA CAILLE'S ARC OP THE MERIDIAN. Companeon of the Ancient and Modern Angles. True site of Ija Caille's Granary. Calculation of La Caille's Triangles in terms of Mo- dem Base. Of the four Stations which define La Caille's two large triangles, the centers of Riebeek's Kasteel and Kapoc Berg (which are common to both triangles) are known to the requisite degree of accuracy, and the Southern or Cape Town Station may be regarded as known within the range of two feet. The sum of the angles of this triangle by La Caille's measure was less than 180° + the spherical excess by 24" '8, or exclusive of the excess by 19", which 19" he distributed in proportion to the magnitude of the angles. The sum of the angles of his north triangle was less than 180° + the spherical excess by 16" '2 or excluding the excess by 8", which he distributed in like manner. The following comparison shows the difierences between the Modem and La Caille's deter- mination of the angles, the former corrected for calculation to the nearest tenth of a second, the latter corrected by himself: — MODERN. CapeTown 33-31-53 Kapoc Berg 98-19-11-8 Riebeek's Kasteel. . 48- 8- 55 -2 Klip Fontein 30- 0-25-4 Kapoc Berg 73-53-54-4 Riebeek's Kasteel.. 76- 5-40'2 LA CAILLE. DIFFEREKCE. 33-31-45-0 98-19-14-0 48- 9- 1-0 29-59-56-0 73'55' 70 76- 4-57-0 + 8-0 - 2-2 - 6-8 + 29-4 - 72 6 -i- 43-2 The differences on the south triangle are less than the recorded errors above mentioned. The differences on the north triangle prove that the true site of the Granary at Klip Fontein was northward and westward of the assumed site, and very close to, but more likely within the dwelling-house numbered 2 on the plan of the Klip Fontein locality. (See plate II of parti). Jasper Thiark's house. Partition walls divide this building into three apartments,— viz. : kitchen, bedchamber, and stable, in sequence order from the north end. Calculation of the sides of La Caille's triangles as given above, in terms of the Modern Base, and comparison of their lengths with the lengths recorded by him. (The French toise = 6*3945925 English feet). Kapoc Berg to Riebeek's Kasteel = 135765-7 Peet. Log. S-132790I. CapeTown Kapoc Berg Riebeek's Kasteel., Klip Fontein Kapoc Berg Riebeek's Kasteel., Angles. 33-31'45'0 98-19-14-0 48- 9- 1-0 29-59-56-0 73-56- 7-0 76- 4-57'0 Log. Sines. 9'742J233 9-9954044 9-8720964 9-6989554 9-9826643 9-9870696 Log Distances. 5-1327901 5-3859712 5-2626632 5-1327901 5-4164990 5-4208943 Distances. feet 135765-7 243204-3 1 83089-4 135765-7 2609150 263568-9 La CaUle'a Distances. feet 135810-3 243283-6 183148-8 135810-3 261000-4 263654-8 La Caille in Excess. + 44-6 + + ■+ + + 79-3 59-4 44-6 85-4 85-9 CALCULATION OP THE MODERN TELLNGTJLATION OF THE ASSUMED STATIONS. 611 Calculation of the Meridional Distance between La Caille's Observatory in Cape Town and the Signal Fire at Klip Fontein, making use of his Angles and the lengths of the sides as derived from the Modern Base. According to La Caille, the Azimuth of his Station at Kapoo Berg, as observed at hia o / » Observatory and measured from the North towards the West, is 2-26-24 The Spherical Angle between Kapoc Berg and Eiebeek's Kasteel is 33-31-46'9 .-. The Azimuth of Eiebeek's Kasteel— reckoning from North towards the East is ... 31- 5-22-9 STATION AND NODE. •xs OQ 0) • 1^,^ 3 M-h"^ o Log. Sines. Log. Distances. Distances in feet. No. 1.— La Caille's Observatory to Eiebeek's Kasteel = 243204-3 Feet. Log. 5-3859712. n La Caille's Observatory... Eiebeek's Kasteel 180+£. 24-40-48-8 31- 5-22-9 124-13-62-6 180- 0-14-3 ff # 4-8 44-0 4-8 18-1 4-7 57-9 9-6206901 9-7129521 9-9173790 5-4782332 5-6826601 300769-1 481570-8 No. 2.— Klip Fontein Signal Fire to Node, (300769-1 - 260915-0) = 39854-1 Feet. Log. 4-6004730. P n Klip Fontein Signal Fire.. 180+e. 90- 0- 24-40-48-8 65-19-11-3 180- 0- 0-1 0-0 0-8 0-0 48-8 0-1 11-2 0-0000000 9-6207121 9-9583978 4-2211851 4-5588708 16641-2 36213-5 Hence the Meridional Distance of La Caille's Observatory to Node „ „ „ Node to Perpendicular (p) Meridional distance ; La Caille's Observatory to Perpendicular from Signal Fire Eeduction to parallel Meridional Distance, La Caille's Observatory to parallel of Signal Fire „ „ According to La Caille Excess of La Caille's Measurement „ feet 481570-8 - 36213-5 445357-3 + 4-2 445361-5 445505-5 144-0 Calculation of the Reduction to parallel at Klip Fontein. r , tan. lat. ••• — • 2 Normal (ar. co.) Eeduction = 4-24 feet Logs. 8-44237 9-80750 2-37791 0-62778 § 11. Calculation of the Meri- dional length of La Caille's Arc in terms of the Modern Base, em- ploying his Triangles. Meridional length of La Caille's Arc in terms of his own Base is longer by 144 feet than in terms of the Modem Base. 618 VERIFICATION AND EXTENSION OF LA CAILLE'S ARC OF THE MERIDIAN. §11. Calculation of the Meridi- onal distance between the supposed ter- mini o£ La Caille's Arc. Calculation of the Meridional Distance between the supposed Positions of La Caille's Observatory and his Signal Fire at Klip Fontein, The Azimuth of Eiebeek's Kaeteel at Rogge Bay, reckoned from the North towards „ , , the East, is (p. 578 No 36) 31-4- 4-62 Reduction, Eogge Bay to La Caille's Obseryatory (p. 612) + 59-90 „ Biebeek's Kasteel Angle Point to La Caille's File (p. 452) ... -j- 14-23 Hence, Azimuth of La Caille's File, Riebeek's Easteel, on the horizon of La Caille's Observatory ... = 31-5-18-7S STATIONS AND NODE. ANGLES. M O ^ c^ bo CJ (0 -