CORNELL UNIVERSITY LIBRARY arY295 ^°'"^' University Library S?i&i?i»l?,S"®''^' "'''"y tables- olln.anx 3 1924 032 194 239 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/cu31924032194239 LECKY'S GENERAL UTILITY TABLES; FOR THE QUICK SOLUTION OF MANY EVERYDAY PROBLEMS IN NAVIGATION; MORE ESPECIALLY TIME-AZIMUTHS AND ALT-AZIMUTHS OF SUN, MOON, PLANETS, AND STARS; GREAT CIRCLE AND COMPOSITE SAILING. THE TABLES WILL ALSO BE FOUND VERY CONVENIENT AS AUXILIARIES IN CONNECTION WITH DOUBLE AND SIMULTANEOUS ALTITUDES BY A. C. JOHNSON'S FAMOUS METHOD. BY S. T. S. LECKY, Master Mariner, Author of "' Wtinkles' in Practical Navigation," " The Danger Angle and Off-Shoie Distance Tables," &'c. GEORGE PHILIP & SON, Ltd., LONDON: THE LONDON GEOGRAPHICAL INSTITUTE, 32 FLEET STREET, E.G. LIVERPOOL: PHILIP, SON & NEPHEW, Ltd., 45 to 51 SOUTH CASTLE STREET. [All Rights Jieservea.] 191 1 . THESE PAGES ARE INSCRIBED WITH SINCERE GOOD WISHES TO Captain H. S. BLACKBURNE, (Late of the P. & O. Co.'s Service) TO WHOM THE AUTHOR WAS ORIGINALLY INDEBTED FOR THE NUCLEUS OF TABLES A AND B AND TO WHOM THE PROFESSION AT LARGE IS INDEBTED FOR HIS EFFORTS TO SECURE FOR TABLES OF THIS CHARACTER THE PROMINENCE WHICH THEY UNDOUBTEDLY DESERVE. PREFACE. But little is required by way of Introduction, for the latter-day history of the A B C and D Tables is already chronicled in the 9th and succeeding editions of " Wrinldes" ; also some few of the uses to which they may conveniently be applied. The present Tables, though precisely on the same lines, are a very considerable expansion of those in " Wrinkles," and are published independently at the suggestion of professional friends, who urged — not without reason — that they would be infinitely more get-at-able if freed from, the encumbrance of a bulky volume; which volume, by the way, was apt to suffer unduly from over- much thumbing if happily the Tables should be resorted to as frequently as they ought to be : indeed the increased length and breadth of page left no alternative. Once committed to separate publication, the way was paved for other improvements ; thus the spacing of the type is more open and agreeable to the eye, precepts have been repeated on each page, and the headings amplified. Altogether it may fairly be claimed that the present issue is a marked advance on its predecessor. Nor is there need to particularise the amount of expansion, since any one possessing a copy of the ubiquitous " Wrinkles " can readily see and appreciate the difference : suflBce it to say that interpolation, usually so provoking, is now in the principal problems well nigh dispensed with, and in the remainder is comparatively trifling : thus time is saved, temper preserved, and accur.aey ensured. Not the least of the advantages accruing from the expansion of the Tables is their vastly increased suitability for the speedy determination of Great Circle Courses and Distances, and the various items pertaining to this and Composite Sailing. These Sailings are a feature in the new curriculum of the Board of Trade which comes into force at the commencement of 1898. It will be demonstrated further on that the ABC and D Tables are capable of solving many problems which daily occur in modern chart-room practice ; but putting that fact on one side for the moment, and regarding them solely as Azimuth Tables, it can honestly be said that they constitute by far the most complete and comprehensive of any as yet submitted to the sea- faring community. Both Latitude and Declination have a wide range, namely, from 65° N. to 65" S. Unlike other Tables, the Azimuth of Sun, Moon, or Planet is obtainable for any Declination, Altitude, or Hour-angle* A special Table (B*) affords similar facilities in the case of some 54 selected Stars ; this, with an auxiliary list comprising nearly as many more {to be used with Table B), places all the best Navigational Stars at the service of the Mariner. He has therefore plenty to pick and choose from at all seasons and in all frequented Latitudes. * To observe Azimuths with an altitude exceeding 55° or 60° is not commendable ; but a knowledge of the Azimuth at higher altitudes is not infrequently required for purposes other than Compass Deviation. ii ^ ^ PREFACR Table B* is computed for the epoch A.v, 1900, but owing to the extreme slowness of change in stellar declination, it will hold good for another half century or more, when the science of Navigation will probably have entered upon a phase undreamt of by this out-of-date generation, and entirely novel methods will have been devised to suit the altered conditions of ocean transit. ^ , From the foregoing brief description it will be seen that in the matter of Latitude the scope of the Tables is all that can be desired for vessels navigating anywhere on the Equatorial side of the Arctic and Antarctic Circles; and that in the matter of Declination they embrace everything in the Heavens of practical value. They therefore stand unrivalled as Azimuth Tables. It is not generally known by seafarers, and hence attention is drawn to the fact, that the adaptability of the A B C and D Tables to the various problems in Nautical Astronomy is almost unlimited; but to work out some of them— brief though the operation may be— entails such a turning topsy-turvy of the Tables, and such a shuffling of the Arguments, with the pro- bability of a misdeal at the finish, that it was felt to be more prudent to restrict their use to the problems to which they appeared to be best suited, leaving the others to be dealt with by the processes hitherto in vogue. \ It will be noticed further on that in solving the various examples of the round dozen or so of problems there dealt with, the ABC and D Tables do not require outside assistance from any other source whatsoever. They are entirely self-contained, and capable of doing their appointed work. This is obviously a feature of great value, even fr^ an economical point of view. It has been suggested that an Appendix, showing the mathematical relation of the Tables to the work they are capable of accomplishing, would prove interesting to certain of the Brotherhood, and such an Appendix was accordingly prepared; but for reasons with which the reader need not be troubled it was ultimately decided to keep it in abeyance ; the MS., however, will be preserved, and it will depend in a great measure upon the reception accorded to this booklet whether the Appendix is destined eventually to emerge from its retirement or to remain so much waste paper ; meanwhile the practical application of the Tables to their various uses will be dealt with in the Text immediately following this Preface. It only remains to state that in the matter of computation I am once more largely indebted to my old friend and co-worker, Captain Alfred Frv, of Liverpool, without whose unwearying assistance I am sorely afraid the present venture might not have seen the light of day for some years to come— if at all. It gives me much pleasure to make this acknowledgment of Captain Fry's services. S. T. S. L. Neylakd, Pembrokeshire. 1st January, 1S9/. Note .-—It iBiU be found conventem to keep this book in the Chart-drawer. PREFACE TO ENLARGED EDITION. Thoughtful navigators will realise that a valuable and welcome addition to the " General Utilitj' Tables " has been madi by the insertion of a new and entirely original series, to be distinguished henceforth as the ^E F G Alt- Azimuth Tables." More especially is this true as regards azimuths of the Moon, ^^lanets, and Stars, which. are now rendered quite as simple and equally as short as those of the Sun. The present high and ever increasing speed of ocean sls^eamers no longer permits of putting off till to-morrow what can — and ou£ht to — be done to-day ; or of complacently waiting, with lives and property at stake, till the *Rme-honoured Sun shall graciously see fit to smile upon the expectant (but oft disappointed) mariner. That day is past : Sun-navigation must now be supplemented by Ste'llar-navigation ; and, of the two, the latter is far and away the better, for reasons well known to students of "Wrinkles." Nor will it be long before Courts of Enquiry, in stranding cases, take to looking closely into the question of whether the hapless navigator had diligently availed himself of the inany and varied means at disposal to check his compass courses when making land or coasting along it. Signs are not wanting either that the modern, up-to-date. Nautical Assessor will look upon the use of the antiquated " Deviation-Card " as direct evidence of careless or unskilled navigation, unless it can bo shown that observations of the heavenly bodies (not merely those of the Sun) were altogether impossible previous to the casualty. Of course no one now-a-days would dream of consulting a Deviation-Card after opportunities had been afforded of starting the indispensable " Compass- Record." (F/de page 629 of "Wrinkles." It is only too obvious that if, from constitutional apathy, happy-go-lucky ignorance, or over-confidence, a man wilfully neglects to make intelligent use of his resources, he must expect to be held culpable in the likely event of his ship coming to grief. So, Gave canem. Hitherto, the disinclination on the part of some " Nautical Astronomers " to invoke the aid of the Moon, Planets, and Stars to detect compass vagaries, has been chiefly due to the somewhat longer process involved in arriving at the Hour-Angle, which is one of the three factors in the ordinary Azimuth Tables ; but the E F G Tables, wherein Altitude is substituted for Hour-Angle, effectually dispose of the Sidereal Bogie, and smooth the way to the popularity of observations of this class. Where frequent observations are a necessity — as in the case of compasses — reliable " short-cuts " constitute a positive blessing. It stands to reason that the easier a thing is made, the less likelihood of its being shirked. Anyone familiar with the exceptionally trying conditions of life on board ship — more especially on bad weather routes — will readily understand why officers, as a body, evince a distaste for long calculations ; hence the very natural and proper demand for trust- worthy Tables to abbreviate them. Moreover, the longer the calculation the greater the chance of its containing a mistake of some sort. This important fact is too often lost sight of by irresponsible shore critics with a consuming craze for conundrums, controversy, and — notoriety. Of course the Sun will never entirely be deserted — even by the most ardent of Stellar devotees ; it is therefore no harm to point out that the E F G Tables can be utilised for the Azimuth as soon as iv PREFACE TO ENLARGED. EDITION. the customary morning and afternoon sights have been taken, without waiting to work out the " Apparent Time at Ship." To some people this will be an attraction no doubt. On the other hand the method has its drawbacks ; for example, when " swinging ship " in a land-locked harbour the Alt-Azimuth is quite " out of it " — one can't have everything — but in such a case the A B C portion of the never-failing G. U. Tables promptly comes to the rescue, and is right under one's hand to fall back upon. Letters from quarter-deck friends prove that some prefer the Time method, and some the Altitude method of dealing with Azimuths — evidently great minds don't always think alike— just as some say " Scotch " and others " Irish " when invited to splice the main brace. However, users of the G. U. Tables can now take their choice (of methods) and be happy. Again, there are a few who are disappointed because the Tables do not give the Azimuth by inspection absolutely at sight — admittedly an advantage, other things being equal. But the advantage is far more than balanced by their superior scope in Latitude, Declination, Hour-Angle, and Altitude : in fact there are no other Azimuth Tables — or combination of Azimuth Tables — which can compete with them in this respect : one book — not half a dozen by various authors — suffices to meet all the cases likely to occur in practical navigation within the ordinary limits of sea-borne commerce, say between 65° N. and 65° S. But putting all this on one side for the moment, the mere addition or subtraction of 6, or at most, 8 figures to get the desired result cannot be seriously regarded hy any one as a stumbling block, much less by a full-blown Navigator with a certificate of competency. To attach the least weight to so paltry an operation would indeed be making a mountain out of a mole-hill, and unworthy of the profession. In Tables C and Q the Azimuth does not exceed 90°, so there ia never any occasion to subtract from 180° and reverse the name as in other Tables. This in itself is a saving of figures. The shape also of the Tables has occasionally been criticized as rendering them unfit for the cabin bookshelf; quite true, but officers may be reminded that where the chart-drawer is not available (as it always should be) such a flat book can easily be stowed under their own sofa-cushion, where it is not liable to be " spilt " by the motion of the ship : there is good in everything, if one. can only see it. The existing size permits of nice, readable type, with clear spacing, so that mistakes consequent upon taking out numbers from a jumbled-up page, when perhaps the light is not of the best and the ship herself in a lively humour, are rendered next to impossible. The Author is convinced that — given a fair trial — the G. U. Tables, as now reinforced, cannot fail to commend themselves to the prudent navigator desirous of being ready to profit by whatever the gods may send him. The Azimuth — whether by Time or by Altitude — is only one of many useful problems the G. U. Tables undertake to solve: they are in fact "A host in themselves," and conveniently contained within one cover. What more, in reason, could anyone desire ? Once again — and for the last time — I have to express my cordial acknowledgtaents to Captain Alfred Fry for most valuable aid in the arduous task of computing the new E F G Tables. May they prove as popular as I anticipate. . „ S. T. S. L. Mentok, AipebMakitimeb, France, Jaimary 1st, 1900. TABLE OF CONTENTS. INTRODUCTORY PROBLEM I. — Error in the Longitude due to an error of 1' in the Latitude PROBLEM II. — Error in the Longitude due to an error of 1' in the Altitude PROBLEM III.— To find True Azimuth of Sun, Moon, Planet or Star TANGENT OR GREAT CIRCLE SAILING. -Principal Features . PROBLEM IV.— To find Initial and Final Courses .... PROBLEM v.— To find the True or Great Circle Distance PROBLEM VI.— To find the Meridian of Vertex ..... PROBLEM VIT. — To find the Latitude of Vertex ..... PROBLEM VIII.— To lay down a Great Circle Track on the Chart COMPOSITE SAILING PROBLEM IX. — To find the Longitude of the Point of Tanoency WINDWARD GREAT CIRCLE SAILING PROBLEM X.— To identify an unknown Star .... PROBLEM XL— To ascertain Altitude for a predetermined Time at Ship TABLES A AND B TABLES A AND B* TABLE TABLE D LIST OF SELECTED STARS, in order of Right Ascension LIST OF SELECTED STARS, in order of Declination, as in Table B* AUXILIARY LIST OF STARS, for use with Table B EXAMPLES in use op Auxiliary Stars ...... ADDENDUM • . ALTITUDE-AZIMUTH RULES AND EXAMPLES ALTITUDE- AZIMUTH TABLES E and F . ALTITUDE-AZIMUTH TABLE G PiOB 111 XVI xviii xix xxiii XXV xxvi xxvii xxxi 1—24 . 25-48 49-60 . 61- 66 67 68 69 70 71 72 73—112 115—126 EXPLANATORY. Except perhaps to " Old Boys " of the Blue-coat School or similar institutions, not forgetting the Conway and Worcester, the innocent little word " Spherics " has quite an alarming sound to the average merchant-service oiEcer. It is, however, merely a dread of the unknown which is common to us all in greater or lesser degree. When morning dawns the midnight ghost of the grave-yard generally turns out to be nothing more gruesome than a weather-bleached tombstone, or the Parson's venerable donkey grown grey in the service. So it is with Spherical Trigonometry. It may have a forbidding aspect during the dark hours of ignorance, but when enlightenment comes it proves to be a most enticing study. In fact it is impossible for the Navigator to understand " Spherics " and not like it. In view of the excellent graphic and Kinder-garten methods now adopted by the best teachers, it may be said to be comparatively easy of attainment. The word " easy " must not be taken to intimate that trouble is not required — far from it. There is no royal road to learning. " Knowledge is power," and power is essentially the reward of the diligent. The disciples of the " Take it easy " school must not growl when they find themselves left behind in the race. They cannot have everything. To the Quarter-deck officer. Spherical Trigonometry ought to be of special interest, seeing that it is the foundation upon which rests the whole science of Navigation, and that without a fair knowledge of it he is blindly working in the dark, and liable at any moment to be tripped up by quite a legion of lurking ghosts. It would almost look as if this were the prelude to a treatise on " Spherics," but such is far from the intention. Although the Tables which follow are based upon " Spherics," and upon nothing else, their use does not involve any mathematical Icnowledge whatever, nor will anything be found within these pages which cannot be understood by the least mathematically inclined of sailors. Allusion to other methods of solving the various problems herein given will be strictly avoided, as the object is to shew that the " General Utility Tables " are a host in themselves, and can accomplish all they profess without going beyond their own covers. We will now lead up to the practical part by a few words explanatory of the formation of the Tables. Those who wish to do so may skip the next half-dozen paragraphs and be none the worse. Know, then, that the solution of most of the Problems in Nautical Astronomy depends upon a consideration of the Triangle of Position. This is the name given to the spherical triangle formed on the celestial sphere by the Zenith of the observer, the Elevated Pole, and the observed object The three Angles of this triangle are — 1. The Azimuth. 2. The Polar Angle. 3. The Angle of Position. The three Sides of this triangle are — 1. The Co-latitude of the observer. 2. The Polar Distance of the observed object. 3. The Zenith Distance of the observed object. GENERAL UTILITY TABLES. Great Circle Sailing. Each one of these three sides forms the arc of a Great Circle, having for its centre the centre of the Earth. A simple transformation of the formulae of the Triangle of Position leads to the construction of the A, B, C and D Tables, wherein the natural numbers depend upon the values assigned to the Arguments used in the " Head-line " and " Margin " of each Table respectively. In Table A the Arguments are Hour-Angle and Latitude. „ B and B* the Arguments are Hour-Angle and Declination. C and D ,, „ . Azimuth and Latitude. The formulae for finding the Tabular Numbers are given on pages 427 and 545 of 9th Edition of " Wrinkles." Bearing in mind the above, it does not require special mathematical knowledge to see that by a simple process of substitution, or in other words, by manipulating the Tables in accordance with certain brief rules to follow, an easy solution may be obtained of a large number of Navigational Problems, among which may be included : — 1. The error in the Longitude (or Hour- Angle) due to an error of 1' in the Latitude worked with. 2. The error in the Longitude (or Hour- Angle) due to an error of 1' in the Altitude worked with. 3. The True Azimuth for any Hour-Angle, Altitude, or Declination of Sun, Moon, Planet, or listed Star. 4. Initial and Final Courses. 5. The True Distance. 6. and 7. Position of Vertex. 8. Intermediate points for Chart Track. 9. Composite Sailing. 10. Identification of an unknown star. IL Altitude of a celestial body at any given time. 12. Equation of Equal Altitudes, 13. Time of rising or setting of a celestial object. 14. Latitude by Ex-meridian Altitude. And many other spherical problems. Looking at the foregoing list (which might be enlarged), is it any wonder that they are described as "General Utility Tables"? But that is not all, for the student of "Wrinkles" knows what an important part the Tables take in Double and Simultaneous Altitudes and the ready projection of Sumner Lines. The present booklet will therefore not deal with these last- mentioned problems; nor with Nos. 12, 13, and 14 for the following reasons: — No. 12 is a thing of the past, and no longer pertains to Practical Navigation. No. 13 is more interesting than useful. No. 14, good Ex-meridian Tables abound. To use the "General Utility Tables" a knowledge of Algebraic Addition is absolutely essential ; but this need not be a stumbling block in the path of the least educated, since it can be thoroughly mastered in less than ten minutes, and once understood it is hardly possible to forget it. It is just as well to say at the outset that the Tables will not give correct — ^nor anything like correct — results unless the two signs plus and minus are properly applied in each instance, so every care must be taken in dealing with them. Keep the signs right, obey the rules, and there will be neither error nor ambiguity in the result. A glance at the next page shews that there are but three cases to consider, and each one is the quintessence of simplicity [PROBLEM I.} GENERAL UTILITY TABLES. iii ALGEBRAIC ADDITION. 1. Positive quantities added together give a ^positive result Example. + 2 Added to + 4 Equal + 6 2. Negative quantities added together give a negative result. Example. 2 Added to - 4 Equal - 6 3. To add together unlike quantities, take their difference, and prefix the sign of the greater. Example. - 2 Added to + 4 Equal + 2 PROBLEM I. To FIND THE Error in the Longitude (or Hour-Angle) due to an Error OF 1' IN THE Latitude worked with. This can be effected by the combined use of A and B, or A and B* ; or by Table Q alone, according to the available arguments. Let us first use Tables A and B, or A and B*- They require the Hour-Angle, Latitude, and Declination, or name of star to be known : then — Enter A Under the Hour- Angle in " Head-line," and abreast the Latitude in " Margin," take out the corresponding "Number." Always prefix the -|- sign, except when the Hour- Angle exceeds 6 hours. Enter B o^ B*- Under the Hour- Angle in "Head-line," and abreast the Declination or Star in "Margin," take out the corresponding "Number." When Latitude and Declination are of contrary names, prefix the plus sign ; but when of same name, prefix the minus sign. The Algebraic sum of the two " Numbers " will be the error in the Longitude expressed in arc. To get the error in the Hour-Angle, multiply by 4 for seconds of time. IV GENERAL UTILITY TABLES. [problems Example 1. What is the error produced in the Longitude for each 1' of error in the Latitude worked with when the Hour-Angle of the observed body is 1 hr. 58m. p.m., its Declination 29° N., and the Latitude of the observer is 24° S. ? (Page 11) + -787 A ( „ 12) + 1126 B Sum + 1''913 = Error in the Longitude. X 4 + 7°-652 = Error in the Hour-Angle. Example 2. Use same data as before, but in this case let the Latitude be North. -I- -787 A - 1-126 B Sum - 0'"339 = Error in the Longitude. X 4 - 1"356 = Error in the Hour- Angle. Example 3. Hour-Angle 6 h. 20m. p.m., Declination 27° N., Latitude 20° N. (Page 23) - -032 A ( „ 24) - -511 B Sum - 0''543 = Error in the Longitude. X 4 - 2' 172 = Error in the Hour- Angle. Example 4. Hour- Angle of the planet Venus = 2hrs.'16m. East of the meridian. Declination 12° N., Latitude of observer 18° N. (Page 13) + -482 A („ 14) - 380 B Sum + 0'-102 = Error in the Lon^tude. X 4 + 0*408 = Error in the Hour- Angle. Example 5. ^ Hour-Angle of the Moon = 8hrs. 12m. West of the meridian, Declination 28° N., Latitude of the observer 60' N. (Page 19) - i'-i25 A ( » 20) - -634 B Sum - l'-759 = Error in the Longitude. X 4 - 7°036 = Error in the Hour-Angle. [PROBLEMS I. II. & III.] GENERAL UTILITY TABLES. v Sxample 6. Hour- Angle of * a Crucis 7 hrs. 28m. East of the meridian, and Latitude of the observer 50° S. (Page 45) - -481 A ( „ 46) - 2076 B* Sum - 2''557 = Error in the Longitude. V 4 -10=-228 = Error in the Hour- Angle. When the Latitude and Azimuth are known, the Error can be taken out at sight from Table Q. Example 7. Let the True Azimuth of planet Venus be S. 84J° E., and Latitude of observer 18° N. Required the error in the Longitude produced by an error of 1' in the Latitude. Enter Table C (page 60). Under 84 J° in " Head-line/' and abreast 18° in the " Margin," will be found the " Number " '-101. It is to be marked + in obedience to precept at foot of page, = + 0''101. Multiply by 4 for seconds of time. PROBLEM II. To FIND THE Error in the Longitude (or Hour-Angle) due to an error OF 1' IN the Altitude worked with. When the Latitude and Azimuth are known, the error can he taken out at sight from Table D- Example 8. Let the True Azimuth of ® be S. 23° E., and the Latitude of the observer 56° N. Required the error in the Longitude produced by an error of 1 ' in the Altitude. Enter Table D (page 62). Under 23° in the " Head-line," and abreast 66'' in the " Margin," will be found the " Number " 4'-577. Multiply by 4 for seconds of time. Note. — ^Under certain conditions of wind, weather, and sea — not to speak of sextant error — it would be very easy to have an error of 4' in the Altitude, in which case the error in the Longitude would be 4'-577 x 4 = 19' 18". (/See page 470 of " Wrinkles.") PROBLEM III. To FIND THE Azimuth. These Tables are of special value in this connection, since they are applicable to Sun, Moon, and Planets, as well as to 54 selected Stars. Practically speaking there is no restriction as to HovA--Angle, Altitude, or Declination; they are therefore the finest Azimuth Tables extant. In the case of Sun, Moon, or Planet, find the " Error " by Tables A and B ; but in the case of a listed Star, by A and B* Should the star not be in the list, its declination must not exceed 65°. Then enter C ^'^^ Latitude in the " Margin," and " Error " in the body of the Table. In the " Head-line " over the latter will be found the True Azimuth. By interpolation at sight it can be taken out to a quarter of a degree, or less. GENERAL UTILITY TABLES [problem hi.] RULE FOR NAMING THE AZIMUTH. In North Latitude put N for a - " Error " ; and S f or a + " Error." In South Latitude put S for a - " Error " ; and N for a + " Error." (This Rule is Treated at foot of each page of Table Q.) Take the previous examples by way of illustration. Example 1. Entering C (page 52), with Latitude 24° S., and "Error" + l'-913, at a glance we find the Azimuth to be 29f°. Being South Latitude and a + "Error," we name the Azimuth Noiik ; the Hour- Angle being p.m., the object is West of the meridian. Therefore the complete answer is N. 29i° W. Example 2. Entering Q (page 58), with Latitude 24° N., and " Error " — -339, we find the Azimuth to be 72f °. Being North Latitude and a - " Error," we name the Azimuth North ; the Hour- Angle being Post-meridian, the object is to the westward. Therefore the complete answer is N lif W. Example 3. Entering C (page 57), with Latitude 20" N., and " Error " — -543, we find the Azimuth to be 63°. Being North Latitude and a - " Error," we name the Azimuth North ; the Hour- Angle being P.M., the object is West of the meridian. Therefore the complete answer is N. 63° W. Example 4. Entering Q (page 60), with Latitude 18° N., and " Error" + -102, we find the Azimuth to be 84J°. Being North Latitude and a + " Error," we name the Azimuth South ; the Hour- Angle being A.M., the planet is East of the meridian. Therefore the complete answer is S. 84|° E. Example 5. Entering Q (page 65), with Latitude 60° N., and " Error " - 1"759, we find the Azimuth to be about 48f°. Being North Latitude and a - "Error," we name the Azimuth North; the Hour- Angle being P.M., the moon is West of the meridian. Therefore the complete answer is N. 48f W. Example 6. Entering Q (page 53), with Latitude 50° S., and " Error " - 2'*557, we find the Azimuth of « a Crucis to be about 31^°. Being South Latitude and a - " Error," we name the Azimuth South ; the Hour- Angle being Ante-meridian, the star is to the Eastward. Therefore the complete answer is S. 31i° E. Should the Azimuth be required to greater precision, proceed as follows : — To the log. of the " Error " add the Cosine of the Latitude. Their sum will be the cotangent of the Azimuth. Example 4, "Error" + -102 Log. 9-0086 Latitude 18° N Cos. 9-9182 Azimuth S. 84° 27' 30" E Cot. 8-9868 [PROBLEM III.] GENERAL UTILITY TABLES. vii Of course it is useless to work so closely as this unless you are certain of the absolute correctness of the data employed. {See page 318 of " Wrinkles ")• Lest there should be any misapprehension about the terms A.M. and p.m., it must not be forgotten that they apply solely to the Hour-Angle of the body observed. Should this be the Sun, AM. will of course refer to the forenoon, and p.m. to the afternoon. But in the case of Moon, Planet, or Star, their Hour-Angle may be P.M. in the morning, and A.M. in the evening of our solar day. Bear this in mind, or you may get "mixed" when naming the bearing E. or W. TANGENT OR GREAT CIRCLE SAILING. A popular explanation will be found in "Wrinkles" (Chapters II. and XVII, of Part II.), so beyond lightly touching upon the more notable features which the aspirant to quarter-deck honours will require to have off pit-pat after the expiry of the present year, but little will be said in these pages. In what follows it is assumed that the Earth is a true sphere — as round as a billiard ball. The shortest possible distance between any two places on the Earth's surface is traversed by following that portion of a Great Circle which joins them. Consequently, it is only when a ship steers along the connecting arc here mentioned that she sails directly towards her port. The number of Great Circles that may be drawn on the Earth's surface is infinite. A Great Circle is the largest circle which can possibly be drawn on the surface of the globe ; hence its name. Every Great Circle divides the Earth into two equal portions : to do this truly, its plane must pass through the dead-centre of the Earth. All Meridians are Great Circles ; so are the Equator and the Ecliptic ; but parallels of Latitude are Small Circles, because they do not equally divide the globe, and consequently their planes cannot pass through its centre. The Vertex is the point of highest Latitude touched by a Great Circle, not being the Equator; and there are of necessity two such vertices diametrically opposite each other in Latitude and Longitude, — one in the Northern, and the other in the Southern, hemisphere; but it is not usual or necessary to refer to more than one of them, this one being the Vertex nearest to the place of highest Latitude. The vertices are each 90° distant from the points where the Great Circle to which they belong intersects the Equator. Therefore if you know these points, you also know the Longitude of Vertex, and vice versd. It will be found that the angle of intersection is equal to the Latitude of Vertex. On a chart the position of Vertex is seen with half an eye, since the meridian passing throuo-h it (known as the Meridian of Vertex) is the only one which cuts the Great Circle at riffht angles. From this it follows that the course along a Great Circle at its Vertex is either due East or due West, Further, if the course has Northing in it as Vertex is approached, it will have Southing in it after the Vertex is passed, and viae versd. This again proves that the course at Vertex must — as just stated — be either East or West, since at that precise point the ship for a short period of time is making neither Northing nor Southing. The Vertex does not necessarily lie between the place of departure and the place of destination, but may fall outside the connecting arc. This is easily determined without consulting the chart, for a little reflection will shew that when the Initial Course (or first course at starting) from each place is less than 90° (reckoning both courses from the nearest pole), the viii GENERAL UTILITY TABLES. [problem hi.] Vertex must fall between them : but when one or other of the courses exceeds 90°, the Vertex lies outside the arc joining the two places, and beyond that one at which the angle is greater than 90'. The Meridian of Vertex in combination with the Equator divides a Great Circle into quadrants, in each of which the elements are identical : therefore if the Latitudes, Courses, and Distances corresponding to each degree of Longitude from Vertex be known for one quadrant, they are known for the remainder in the same Great Circle. It is important to know the position of Vertex, since — apart from other reasons to be presently given — it shews at once whether the Great Circle will lead into icy regions, where Navigation would be both retarded and risky. The Initial Course (known mathematically as the Angle of Position) is the angle at the starting point included between the plane of the Great Circle and the plane of the meridian: hence it is — as its name indicates — the first of the many courses to be steered ; since, except when sailing North or South on a meridian, or East or West on the Equator, the angle at which a Great Circle cuts successive meridians is ever altering, though the direction of the ship's head with respect to her destination never alters. The Angle of Position at the place of destination is termed the Final Course. To determine these two courses we have three things given ; — the Co-latitude of each place and the included Polar Angle, the latter being equal to the difference of Longitude. The Distance is represented by the arc of the Great Circle connecting the two places, and forms the third side of the spherical triangle referred to in the preceding paragraph. Like the other two sides, the Distance is always expressed in degrees, minutes, and seconds of arc. To reduce to geographical miles (which may also be taken as nautical miles), multiply the degrees by 60 and add the odd minutes and parts of a minute. Thus let the Distance be 40° 20' 30" in arc. X 60 Distance 2420J- in nautical miles. Unfortunately for the navigator, it happens that where Great Circle sailing would most benefit by lessening his Distance— namely, in high Latitudes— it is least available, "owing to the forbidding character of the regions to be traversed. Nevertheless, it is useful even then as shewing the true track between the place of departure and of destination. It sometimes happens, also, that land intervenes in the case of the Mercatorial track, and does not do so on the Great Circle track, in which event, even if the Great Circle cannot be followed strictly, it shews at all events on which side the obstruction should be passed to save distance; for it must be remembered that a course taken anywhere between the Great Circle course and the Mercatorial course will effect a saving of distance. Further, if the Great Circle track cannot be followed in its entirety, it may at all events be approximated by what is termed "Composite Bailing": this will be explained further on. But where a knowledge of the true (Great Circle) course is likely to be of special advantage is in •' Wivdwwrd Great Circle Bailing." This also will be dealt with by and bye. Before proceeding with the solution by the A, B, C Tables of other problems, it will be necessary to decide upon the names to be given to the conjuring levers of the mathematical machinery, by the manipulation of which we are to get our results. "Head-line" is the horizontal row at top of page. It contains angular measures in arc, and their equivalents in time. "Foot-line" is obviously the counter- part of "Head-line." [PROBLEMS III. & >v.] GENERAL UTILITY TABLES. ix " Margin."— la. Tables A and this is the vertical left-hand column marked Latitude ; and in Table B it is the vertical left-hand column marked Declination. The " Margin " of Table B * contains the names of 54 selected stars ; these take the place of their corresponding Declinations, as per list on pages 67 and 68, " Numbers."— The quantities in the body of each of the Tables will be so styled. It will save confusion to adhere to these terms throughout what follows. PROBLEM IV. To FIND THE Initial Course. Note. — The " Margin " of A is to be taken as representing the Latitude of the ship, or of the place of Departure. The " Margin " of B is to be taken as representing the Latitude of Destination, or place bound to. The " Head-line " and its counter-part, both in A and B, are to be taken as representing the Difierence of Longitude between the place of departure and the place of destination. Example 1. Find the Initial Course between Bergen (Norway) and a selected point near Belle Isle (Labrador). Bergen Lat. 60° N Long. 5° E. ) ^.„ .^ BeUe Isle Lat. 52^= N Long. 55° W. I ^'^- "^^""S" = ^"^ • Table A Lat. 60° in "Margin," and Difif. of Long. 60° in Head-line + roOO A Table B Lat. 52J° in " Margin," and „ „ „ „ - 1-505 B Sum - 0-505 O Using the Rule on page iii, but slightly altering the wording, . the plus sign has been prefixed to the first " Number " because the Diff. of Long, does not exceed 90°. In accordance with next Rule on same page, the minus sign has been prefixed to the secon South Cape 22° N 121° E.' f ■'^^^- °^ ^™S- = 129°. Lat. 23° N. and 129° - -344 f^ Lat. 22° N. and 129° - -520 B - -864 O Lat. 23° and - -864 give Initial Course, N. 51° 31' W. Lat. 22° N. and 129° - -327 A Lat. 23° N. and 129° - -546 B - -873 O Lat. 22° and - 873 give Final Course, S. 51° (T W. Lat. 22° K and 51° (suppl. of 129°) - -873 Lat. 22° N. and Course S. 51° W + -327 A {Please note the sign and remember the rule), - '546 O Complement of Course (39°) and - -546 give 67° 180 113° X 60 Trae Distance 6780 miles. The Mercatorial Course and Distance is S. 89° 31' W. 7113 miles. A difference in favour of G.C. sailing of 333 miles. (Note : — In above example no interpolation whatever is required), A study of the preceding and following examples will shew that the saving in Distance may vary very considerably. Notwithstanding that C. San Lucas and the island of Formosa are both within the Tropics, the gain is worth trying for : this is partly owing to the big distance, and partly to the places lying nearly on the same parallel of Latitude. Where the places of Departure and of Destination are on opposite sides of the Equator, or where the Course approaches the N. or S. points, the gain is next to nothing. This is well shewn in the next Example, though the G.C. Distance is even a bigger stretch than between C. San Lucas and Formosa. Example 7. Required the Initial and Final Gowrses from Hobart to Vancouver ; also the True Distance. Hobart 43° S 148° E. -j . x.n^ «■*= Vancouver 51° N 129° W.j ^'^- °f ^''"S- = ^^ • Lat. 43° S. and 83° + -114 A Lat. 51° N. and 83° + 1-244 B + 1-358 O Lat. 43° and + 1-358 give Initial Course, N. 45° 11' E *vi GENERAL UTILITY TABLES. [problems v. & vi.j Lat. 51° N. and 83° + -152 A Lat. 43° S. and 83° + '940 B + TODS O Lat. 51° and + 1092 give Final Course, N. 55° 31' E. Lat. 43° S. and 83° + -168 O Lat. 43° S. and N. 45° 11' E.... - -927 A {Please note the - sign) - "759 O Complement of Course (44° 49') and - '769 give 61° 42^', of which the Supplement is the True Distance. 180° 61° 42^' 118° 17^' X 60 True Distance 109^ miles,— a long run. The Mercatorial Course and Distance is N. 37i° E. 7133 miles. A difference of only 35 miles. Note.— Excepting in the case of Brest and Baltimore, the " possibilities " of the other G.O. tracks have not been taken into account. All sorts of obstructions may, or may not, intervene between the selected points. Nor is it in any degree claimed that these selected points are the best. It has only been a theoretical question of finding the Distance and the G.C. Courses at the start and at the finish between two given points. These particular tracks are not put forward as the correct ones. The writer has not gone into that question : it is one for a Sailing Directory, and involves many other things beyond the mere consideration of distance. This is mentioned to prevent misapprehension. PROBLEM VI. To FIND THE Meridian of Vertex. Example 1. For this purpose let us begin with the G.C. track between Bergen and Belle Isle given on page ix. By the Tables this is one of the most easily solved of all the problems. Enter " Margin " of Table A with the Latitude (60° N.) of place of Departure, and run the eye along the line abreast till we find the "Number" —'505 which gave the Initial Course from Bergen. Over this in the "Head-line" will be found 73° 45', which is the complement of the Diif. of Long. (16° 15') between Vertex and the Eastern starting point. Starting Point 5° 0' E. Diff. ofLong. 16° 15'W. Meridian of Vertex 11° 15' W. By way of proof, try it from the other end of the track. Example 2. Enter "Margin" of Table A with the Latitude (521° N.) of place of Departure, and run the eye along the line abreast till we find the "Number" — 1'248 which gave the Initial Course from Belle Isle. Over this in the "Head-line" will be found 46° 15', which is the complement of the Diff. of Long. (43' 45') between Vertex and the Western starting point. [PROBLEM VI.] GENERAL UTILITY TABLES. XVJl Starting point 55° 0' W. (Belle Isle). Diff. of Long 43° 45' E. Meridian of Vertex 11° 15' W. As each of the Initial Courses in this Example (reckoned from the same Pole) are less than 90^ the Vertex falls between the places of departure and destination. Example 3. Find the Meridian of Vertex of the Great Circle joining 0. Horn and C. Agulhas. (See page xii). Enter "Margin" of Table A with the Latitude (56° S.) of place of Departure, and run the eye along the line abreast till we discover the " Number " — -623 which gave the Initial Course from 0. Horn. Over this in the "Head-line" will be found 67° 12', which is the comflement of the Diff. of Long. (22° 48') between Vertex and the Western starting point. Starting point 67° 0' W. (0. Horn). Diff. of Long. 22° 48' E. Meridian of Vertex 44° 12' W. Each of the Initial Courses in this Example (reckoned from the same Pole) being less than 90°, the Vertex falls between the Horn and Agulhas. Example 4. Enter " Margin " of Table A with Latitude (35° S.) of place of Departure, and run the eye along the line abreast till we discover the " Number " — 1 '448 which gave the Initial Course from Agulhas. Over this in the " Head-line " will be found 25° 48', which is the complement of the Diff! of Long. (64° 12') between Vertex and Agulhas. Starting point 20° 0' E. (0. Agulhas). Diff. of Long 64° 12' W. Meridian, of Vertex 44° 12' W. So you see it- does not matter which end you start from to find the Longitude of Vertex. The next Example gives a case where the terminal points of the arc lie in opposite Latitudes, and the Vertex does not fall between, but outside them. Example 5. Find the Meridian of Vertex of the Great Circle passing through Hobart and Vancouver. {See page xv). The Vertex in this case is the one in the Northern Hemisphere, because Vancouver has a higher Latitude than Hobart Enter "Margin" of Table A with the Latitude (61° N.) of Vancouver, and run the eye alonof the line abreast till we discover the " Number " + 1'092 which gave the Initial Course from Vancouver. Over this in the " Head- line " will be found 48° 32', which is the complement of the Diff". of Long. (41° 28') between Vertex and Vancouver. Starting point 129° 0' W. (Vancouver). Diff. of Long 41° 28' E. Meridian of Northern Vertex... 87° 32' W. This being a specially instructive Example, we will proceed to find the Meridian (or Longitude) of the Southern Vertex. Enter "Margin" of Table A with the Latitude (43° S.) of Hobart, and run the eye along the line abreast till we discover the " Number " +1-358 which gave the Initial Course (N. 45° 11' E.) D xviii GENERAL UTILITY TABLES. [problems vi. & vii.] from Hobart. Over this in the " Head-line " will be found 34° 28', which is the complement of the Diff. of Long. (55° 32') between Vertex and Hobart. Starting point 148° 0' E. (Hobart). Difif. of Long. 55° 32' W. Meridian of the Southern Vertex ... 92° 28' E. Add together the Longitudes of the two vertices and you will find the sum equal to 180°, shewing at all events that the vertices are diametrically opposite as regards Longitude. Problem VIL will shew in its turn that the vertices are diametrically opposite as regards Latitude also. Harking back for a moment to the Hobart — Vancouver Example, it will be seen that, reckoning the Initial Courses from the same Pole, one of them exceeds 90°, consequently Vertex lies outside the arc of the G.O. joining Hobart and Vancouver, and a knowledge of its whereabouts is of no particular importance. PROBLEM VII. To FIND THE Latitude of Vertex. Example 1. Let us revert once more to the Bergen — Belle Isle track. Enter « Head-line " of Table Q with the Latitude (60° N.) of the place of Departure- say Bergen,— and take out the first " Number " underneath : this is -577. Next, enter "Margin" with the Diff". of Long. (16° 15') between Vertex and Bergen, and run the eye across the page till this same " Number " is again found : over it in the " Head-line " will be the Latitude of Vertex = 61° 0' N. Example 2. Find the Latitude of Vertex of the Great Circle joining 0. Horn and 0. Agulhas. Enter "Head-line" of Table Q with the Latitude (56° S.) of the place of Departure- say 0. Horn,— and take out the first "Number" underneath: this is -675. Next, enter "Margin" with the Diffi of Long. (22° 48') between Vertex and the Horn, and run the eye across the page till this same " Number " is again found : over it in the " Head-line " will be the Latitude of Vertex = 58° 8' S. Example 3. Find the Latitude of Vertex of the Great Circle connecting Hobart and Vancouver I. Enter "Head-line" of Table Q with the Latitude (51° N.) of the place of ■ Departure- say Vancouver,— and take out the first " Number " underneath : this is -810. Next, enter "Margin " with the Diff. of Long. (41° 28') between Vertex and Vancouver and run the eye across the page till this same "Number" is again found: over it in the "Head-line" will be the Latitude of Vertex = 58° 45' N. Example 4. Repeat previous Example, but this time find the Latitude of the Southern Vertex. fi , J^^^T "Head-line" of Table Q with the Latitude (43° S.) of Hobart. and take out the first "Number" underneath: this is 1-072. [PROBLEMS VII. & viii.i GENERAL UTILITY TABLES. xix Next, enter "Margin" with the Diff. of Long. (55° 32') between Vertex and Hobart, and run the eye across the page till this same " Number " is again found : above it in the " Head-line " will be the Latitude of Vertex = 58° 45' S. Now in Problem VI. it was shewn that the vertices were 180° apart in Longitude, dnd we must shew here that they are also the same distance apart in Latitude. From 58° 45' N. along the meridian of 87° 32' "W. to the North Pole is 31° 15' From the N. Pole along the opposite meridian of 92° 28' E. to the Equator is ... 90° 00' From the Equator, continuing on the same meridian, to 58° 45' S. is 58° 45' 180° 00' Or we may elect to measure round the globe in the other direction. From 58° 45' S. along the meridian of 92° 28' E. to the South Pole is 31* 15' From the S. I'ole along the opposite meridian of 87° 32' W. to the Equator is ... 90° 00' From the Equator, continuing on the same meridian, to 58° 45' N. is 58° 45' 180° 00' It is clear, therefore, that the vertices of a Great Circle are 180° apart both in Latitude and Longitude, and lie at opposite extremes of the same diameter : each one is the antipodes of the other. A previous statement will be remembered to the effect that every Great Circle intersects tlie Equator at two points, each of which is 90° from Vertex: from this it follows that, like tlie vertices, these two crossing points must also be 180° apart. Now if the Longitude of Vertex be known, it of necessity follows that the Longitude o£ each of the Equatorial crossing points is known, since they and the vertices are always 90° apart. Taking the Hobart — Vancouver Great Circle, the crossing point between these two places must be in 177° 32' W. On the other side of the globe it is in 2° 28' E. The careful reader will also remember that the angle of intersection of a Great Circle with the Equator is equal to the Latitude of Vertex. This amounts to saying that the Course at the Equator is equal to the Go-latitude of Vertex. Therefore, on the passage from Hobart to Vancouver, the Course when crossing the Equator in Long. 177° 32' W. would be N. 31° 15' E. These items in Great Circle Sailing had better be well understood before going up to be examined. Find the correct answer to the next example by way of practice. Final Example. Required the Initial and Final Courses between a place in Lat. 52° 14J' N., Long. 18° 44' W., and another place in Lat. 66° 12' N., Long. 161° 16' E. ; also the True Distance from place to place, and the position of Vertex. It is further required to know the Longitude of each of the places where the Great Circle will intersect the Equator, and the angle of intersection. PROBLEM VIM. To DETERMINE A SUCCESSION OF Poi.VTS ON THE GrEAT CiRCLE, SAY AT 5° OF LONGITUDE APART, WHEREBY TO LAT DOWN THE TbACK ON A MeRCATOR's ChART. RULE. Enter " Margin " of Table A '"'^^^ Latitude of place of Departure, and under the " Dijff. of Long." in the " Head-line " take out the corresponding " Number." Prefix the sign + or — according to whether the " Diff. of Long." is greater or less than 90°. Add together algebraically this " Number " and the one which previously served to find the Initial Couese at that end. XX GENERAL UTILHY TABLES. [problem vih.] Finally, enter g and under the " Biff, of Long." in " Head-line " look for the sum, of the Numbers '' just mentioned : in the " Margin " abreast will be found the Latitude of the required point. By " Diff. of Long." Is meant the difference between the Long, of the starting point and the Long, of each one of the meridians in succession for which the Latitude is required. Example 1. Bergen to Belle Isle. Let it be required to trace the arc of the Great Circle at each 5th degree of Longitude, starting from Bergen. This gives us eleven points to determine. Against each we will mark the Latitude in advance, and then proceed to shew how this Latitude is found. o o / Longitude Latitude 60 31| N. 5 W. „ 60 5l| N. „ 10 W , 61 00 N. 15 W „ 60 57 N. „ 20 W „ 60 43 N. 25 W „ 60 Hi N. 30 W , 59 39^ K 35 W „ 58 48 N. 40 W „ 57 42 N. 45 W „ 56 18^ N. 50 W „ 54 36 N. Enter "Margin" of A with Lat. of Bergen (60° N.), and under the " Ditf. of Long." (5°) in "Head-line" take out the corresponding "Number" ( — 19-80). Prefix the — sign because the " Diff. of Long." is less than 90°. Add this " Number " to the one ( — -505), which previously served to find the Initial Course (N. 75° 50' W.). - 19-800 A - 0-505 O Sum - 20-305 B Enter B, and under the "Diff. of Long." (5') in "Head-line" look for the "Number" — 20-305: in the "Margin" abreast will be found 60° 31|', the Latitude in which the G.C. track will cross the meridian of 0°. We next have to find the Latitude in which the track will cross the meridian of 5° W. Enter " Margin " of A with Lat. of Bergen (60° N.), and under the " Diff. of Lon<^." (now 10°) in "Head-line" take out the corresponding "Number" ( — 9-823). Prefix the — sign because the " Diff. of Long." still remains less than 90°. Add this "Number" to the one (--505), which previously served to find the hiitial Course (N. 75° 50' W.), - 9-823 A - -505 O Sum - 10-328 B Enter B, and under the "Diff. of Long." (10°) look for above "Number": in the "iMargin" abreast will be found 60° 51 1', the Latitude in which the G.C. track will cross the meridian of 5° W Do not mix up the " DilT. of Long." with the actual Longitude from Greenwich,— a mistake very easily made if you are not quite coiicentrated oii what you are doing. The student's attention is drawn to the fact that the "Number" --505 is a constant all through the operation, and that in practice the whole thing is very much shortened by arrangino' [PROBLEM VIII.] GENERAL UTILITY TABLES. xxi the work so as to take out all the "Numbers" from Table A at the same time, make all the additions at the same time, and subsequently take out the Latitudes from B at the same opening. The only trouble is the interpolation, and, unfortunately, there are no means of getting over it. This is the -way to arrange the work, but of course the navigator in actual practice would omit the embellishments : — "Diff. ofLong." 15° "Diff. of Long.- 20° "Difif. of Long." 25° "Diff. of Long." 30° "Diff. of Long." 35° "Diff. of Long. 40° A -6-464 - -505 -4-759 - -505 -3-714 - -505 -3-000 - -505 - 2-474 - -505 - 2-064 - -505 B -6-969 -5-264 - 4-219 -3-505 Lat. 60° 174' N. -2-979 - 2-569 Lat. 61° N. Lat. 60° 57' N. Lat. 60° 43' N. Lat. 59° 39r N. Lat. 58° 48' N. Long. 10° W. Long. 15° W. Long. 20° W. Long. 25° W. Long. 30° W. Long. 35° W. It is said to be a poor Rule that won't work both ways, so we will just commence at the Belle-Isle end of the track and determine a succession of points from West towards East. In this case the Constant will be -1-248, being the "Number" used to find the Initial Course, N. 52° 46' E. " Diff. of Long." 5° " Diff. of Long." 10° " Diff. of Long." 15° "Diff. of Long." 20 A -14-900 C - 1-248 -7-391 -1-248 -4-864 -1-248 -3-581 - 1-248 B -16-148 -8-639 -6112 -4-829 Lat. 54° 36' N. 56° I8i' N. 57° 42' N. 68° 48' N. Long. 50° W. 45° W. 40° W. 35° W. Example 2. Cape Horn to Cape Agulhas. In this case we will trace the passage of the Great Circle through every 10th meridian, and, as before, will first write down the various Latitudes, and then shew how they are obtained. 0. Horn Lat. 56° S Long. 67° W. 0. Agulhas Lat. 35° S Long.,20° E. Longitude 60°W Latitude 57° 8 S. 50 W „ 58 S. 40 W » 58 4 S. 30 W „ 57 20 S. 20 W „ 55 43i S. 10 W , 53 4 S. W „ 49 4 S. 10 E „ 43 15i S. Then write down in proper form as before, and use the Constant —-623, which previously served to find the Initial Course, S. 70° 47' E. , " Diff. of Long." "Diff. of Long." " Diff. of Long." " Diff. of Long." " Diff. of Long." 7° 17° 27° 37° 47° A -12-070 - "623 B -12 693 Long. 60° W. -4-849 - -623 -5-472 58° 0' S. 50° W. -2-910 - -623 -3-533 58° 4; S. 40° W. ■1-967 -1-383 ■ -6^3 - -623 -2-590 -2-006 Lat. 57° 8' S. 58° 0' S. 58° < S. 57° 20' S. 55° 43^ S. 30° "W. 20° W. xxii GENERAL UTILITY TABLES. [problem vim.] We will now test the Rule by working the remaining points from 0. Agulhas. The Constant will be -1-448, which served to find the Initial Course S. 40° 8' W. towards the Horn. "Diff. of Long." 10° "Diff of Long." 20° "Difif. of Long." 30° "Diff. of Long." 40° A -3-971 -1-448 -1-924 -1-448 -1-213 - 1-448 - -834 -1-448 B -6-419 -3-372 -2-661 - 2-282 Lat. 43° 15.i' S. 49° 4' S. 53° 4' S. 55° 43i' S. Long. 10° E. 0° 10° W. 20° W. Example 3. Cape San Lucas to Formosa 1. C. San Lucas Lat. 23° N Long. 110° W. Formosa Lat. 22° N Long. 121° E. The meridians will be taken at 10° apart, and the Constant corresponding to the Initial Course (N. 51° 31' W.) is --864. Data for Track. o o y Longitude 120 W Latitude 29 36 N. „ 130 W „ 34 46i N. „ 140 W. „ 38 38i N. 150 W „ 41 2lJ N. 160 W „ 43 3i K „ 170 W „ 43 50 K 180 , „ 43 44 N". „ 170 E „ 42 44i N. „ 160 E „ 40 49 N. 150 E , 37 54 N. 140 E „ 33 4] N, 130 E „ 28 11 N. " Diff. of Long." " Diff of Long." " Diff of Long." " Diff. of Long." " Diff. of Long." 70° 80° 90° 100° 110° A -'154 --075 -000 +-075 +'154 O --864 --864 -864 --864 -"864 B - 1-018 --939 --864 --789 --vio Lat. 43° 44' N. 42° 44^' N. 40° 49' N. 37°'54'N. 33° 41' N. Long. 180 ° 170° E . 160° E . 150° E. 140° E. Only a few of the points of this track have been worked out, as it is no use repeating the same thing over and over again. The above working introduces the case where the " Diff. of Lono-." exceeds 90°, and consequently the sign of the "Number" in A changes from minus to plus; otherwise there is no difference. Before finishing with Great Circle Sailing there are one or two items well worth attention. If the student will plot on a Mercator's chart (10 minutes' work) the G. 0. track given in the last example, he cannot fail to be struck with the interesting fact, that though 0. San Lucas and South Oape,_ Formosa I, both lie actually within the Tropics, the Great Circle nevertheless takes the ship into the comparatively high latitude of nearly 44° N., or just about double that of South Cape. [PROBLEM viii.l GENERAL UTILITY TABLES. xxiii By connecting the two places by a straight line, representing the Mercatorial Cowrse, it will be seen that there is a point of Tnaximum separation between the two tracks, and that at this point they lie apart some 1,200 and odd miles. This would mean very different conditions of wind and weather, and possibly of currents also. A sailing vessel would more especially consider this matter, and the selection of the Great Circle or Mercatorial track would depend upon whether she was bound East or West : it would be a question of which was the best Meteorological route. If bound from Formosa to California, the Great Circle track would coincide with the Meteorological route, and would therefore be preferable, not only on account of the saving of 333 miles, but more particularly on account of the favouring winds as compared with the Mercatorial track, which lies in the heart of the opposing N.E. trades. On the other hand, a full-powered passenger-carrying steamer might find it more politic to select the longer route, on account of the very much pleasanter weather ; or might compromise matters, and still keep in fine weather, by adopting an intermediate course ; and this brings us to COMPOSITE SAILING. It has already been stated in these pages that the G. 0. track is not always desirable, owing to its taking the navigator unpleasantly close to the Pole. In such cases a more or less satisfactory compromise is usually arrived at after the fashion about to be described. By this method the navigator has to face his responsibilities, weigh the pros and cons, and finally make up his mind as to what is the highest safe parallel of Latitude under the known or probable conditions which he can conscientiously venture to. This is styled the Maximum Latitude, or — better still — the Limiting Parallel. The ship then is steered on such a Great Circle as will pass through the starting point, and be a tangent to the Limiting Parallel. Having reached the tangential point, she steers due East or West (as the case may be) along the Limitvng Parallel till she meets another Great Circle touching the same Parallel, and passing through the place of destination. She then leaves the Limiting Parallel, and follows the second Great Circle. The above reads very nicely, no doubt, but to the novice it will be " Double Dutch," and he wiU hardly be able to translate it without a little verbal explanation, backed up by suitable pictorial assistance, and this latter is accordingly given in the shape of a Gnomonic Chartlet, which is so constructed that all straight lines thereon are arcs of Great Circles. By referring to the Chartlet it will be found to be quite unlike a Mercator's Chart. The meridians, instead of being parallel, radiate from the Pole, and, being straight lines, are arcs of Great Circles. The parallels of Latitude, instead of being straight lines, are smnll circles ; they are therefore not Great Circles. A Great Circle passing through any two places will be accurately shewn by a straight line drawn from one to the other, whereas on a Mercator's chart a Great Circle (except in the case of a meridian or the Equator) is depicted by a curved line of various decrees of curvature, according to circumstances. These things are repeated here by way of refreshing the memory, just as once a week we used to have "Kepetition" at school. Any reasonably neat-handed man may — with scarcely any trouble — make a chart similar to the one shewn further on, wherein the Tangent-Plane or centre of projection touches the South Pole. No calculation whatever is required, and no knowledge of any of the " ologies." Simply open a Table of Natural Co-tangents (to be found at end of " Lecky's Danger- Angle Tables") and take out the numbers, say, for every 5th parallel from 75° S. to 40° S. These are tabulated xxiv GENERAL UTILITY TABLES. [problem vim. for radius 1 at Latitude 45° ; but such a scale would be too small for practical purposes, so multiply the numbers by whatever you consider suitable, say by 10, which avoids " figuring," as you have merely to shift the decimal point one place to the right-hand. For example, the Natural Co-tangent of 40° is 1"-192 : when multiplied by 10 it becomes ll"-92 = the radius in inches with which you would describe the circle representing the parallel of 40° S. In like manner the radius of 43° would be 10"-72. At 45' S. it would of course be exactly 10"; and at 75° S. it would be 2''-68. To make a chart on this fairly large scale, your paper would need to be . about 28" square, so half a sheet of " Antiquarian " would do nicely. Drawing compasses (with lengthening bars) and a 12" diagonal scale (boxwood — cheap) would complete the outfit. To prevent the Ohartlet here given being too large for the page, the radius used was 3". It does not shew the land, so is merely a chart in blank for illustration purposes. It is just as well to say here that a chart on the Gnomonic projection, where the Pole is taken as the " Principal Point," cannot be drawn satisfactorily for a lower Latitude than 30° : the distortion of the land is too great. Further, as the Equator is approached, the circles of Latitude rapidly get more and more apart, and at the Equator itself their diameter becomes infinite ; so that such a chart within the Tropics is of no service whatever ; just in the same way that you cannot construct a Mercator's chart of the Polar regions : after 70° it gets badly distorted, and after 80° it begins to extend into space. Gnomonic charts can, however, be satisfactorily constructed for any portion of the globe, even for , the Tropics, and to embrace conveniently, say, 70° or thereabouts of Longitude. In this last case the Tangent Plane would touch the Equator. But to construct a Gnomonic chart in which the "Principal Point" does not touch the Pole is something not to be lightly undertaken, and is therefore 7iot recommended to the ordinary navigator. For example, by taking any other point on the Earth's surface than the Pole for the "Principal Point," the parallels of Latitude become oblique to the plane of projection, and will then be represented by Ellipses, Parabolas, and Hyperbolas — a variety of beautiful but bewildering curves with which the amateur chart-maker had better not meddle, lest the result be a muddle. (See Ohartlet). The tracks here delineated are purely mythical: as a matter of fact they put the ship (/S) in the wilds of Patagonia, but for the purpose in view she is just as well there as in her proper element. As before remarked, no account is taken in these illustrations of islands, rocks shoals, or other obstructions to Navigation : this booklet is not intended to be a Sailing Directory' and must not be taken as advocating any particular route or track. EXAMPLE IN COMPOSITE SAILING. The ship is supposed to be at 8, in Lat. 45° S. and Long. 70° W., and she wishes to reach P, in Lat. 50° S. and Long. 65° E., by the shortest route that is free from ice. The straight line connecting S with P is the arc of a Great Circle, of which the vertex V is in Lat. 70° 46' S. and Long. 0° 25' W. The Initial Course from 8 is S. 27° 46' E and the FiTbal Course at P is N. 30° 50' E. "' But to attempt to navigate in so high a Latitude as 70° 46' S. (unless the object were Antarctic exploration or a whaling expedition) would be most injudicious, so the careful commander selects the parallel of 55° S. as the one beyond which his ship must not go. Now, whereabouts shall the ship strike it and leave it, so as not to unduly increase the distance between 8 and P ? GNOMONIC CHART FOR GREAT CIRCLE or COMPOSITE SAILING. W. PV S = ARC OF GREAT CIRCLE PtTS == COMPOSITE ROUTE [PROBLEMS VIII. & IX.] GENERAL UTILITY TABLES. xxv Here Composite Sailing comes to the rescue. Accordingly, a straight line (arc of a G. 0.) is drawn from 8 to the point T, where it is a tangent to the parallel of 55° S. It then becomes visible that T is in Long. 24" 27' W. A similar line is drawn from P to the point t, where it becomes a tangent to the parallel of 55° S. The point t is seen to be in Long. 31° 34' E. This matter being arranged, the ship commences her voyage, and, for a distance of 1819 miles steers on a portion of a Great Circle from 8 to T ; thence due East for 1928 miles along the parallel of 55° S. till she reaches t, and lastly along a portion of another Great Circle from t to P for 1244 miles. The Composite route from 8 to P, vid T and t, is longer than the Great Circle track, but it is the next best thing to it under the restricting conditions. Mile.s. Distance S to P (Great Circle) 4636\ ^ | (Composite)..; 499l/\ ^^^- [845. (Mercator) 5481 '} Now, notwithstanding the simplicity of a Gnomonic Polar Chart, it is not every one who is provided with the means to construct it, so when a case occurs for Composite Sailing, and the means are not forthcoming, the Navigator can just fall back on the " General Utility Tables," of which there are of course several copies on board. O is the only one required for our present purpose, and the thing is done in a jifFy. PROBLEM IX. To FIND THE Longitude of the Point of Tangency of the Arc of a. Great Circle with THE "Limiting Parallel." (a.) Enter "Head-line" of Q with Latitude of Departure (45° S.), and take out the first "Number" below it (1-000). Next, look in the " Head-line " for the Limiting Parallel (55° S.), and run down the column till you find the same "Number" (1-000) as before. In the "Margin" abreast will be found the "Difi: in Long." between the place of Departure and the point of tangency. In this case the Diff. of Long, is 45° 33', therefore Starting point (S) 70° 0' W. "Diff. of Long." 45° 33' Eastward. Point of tangency (T) 24° 27' W. (b.) Enter "Head-line" with Latitude of Destination (50° S.) and take out the first "Number" below it (-839). Next look in the "Head-line" for the Limiting Parallel (55° S.), and run down the column till you find the same "Number" (-839) as before. In the "Margin" abreast will be found the "Diff. of Long." between the place of Destination and the point of tangency on that side. In this case it is 33° 26', therefore Place of Destination (F) 65° 0' E. "Diff. of Long." .JI3^ 26^ Westward. Point of tangency (t) 31° 34' E. Nothing can be quicker or easier. e xxvi GENERAL UTILITY TABLES. [problem ix.] By way of exercise, work out the subjoined questions by the ABC Tables. Avoid looking at the answers here given till you have obtained your own results. Verify them one by one, and act "on the square" with yourself. (a) Lat. and Long, of Vertex of G. C. joining the points 8 P. (b) Initial Course at S. (c) Final Course at P. (d) Distance between S and P. (e) A succession of points at 10° apart, whereby to lay down on a Mercator's Chart the arc SP. (/) Lat. and Long, of Vertex of the G. C. joining the points S T, (g) Initial Course at 8. (h) Final Course at T. (i) Distance 8 to T. (j) Distance by Parallel Sailing T to t. (k) Lat. and Long, of Vertex of the G. C. joining the points t P. (I) Initial Course at t. (m) Final Course at P. (n) Distance t to P. ANSWERS. (a) Lat. 70° 46' S., Long. 0° 25' W. (6) S. 27° 46' E. (c) N. 30° 50' E. (d) 4636 miles. (e) (60° W.— 55° 26' S.) (50° W.- 61° 43' S.) (40° W.— 65° 39' S.) (.30° W.— 68° 8' S.) (20° W.— 69° 41' S.) (10° W.— 70° 31' S.) (10° E— 70° 28' S.) (20° E.— 69° 35' S.) (30° K— 67° 58' S.) (40° E,— 65° 23 S.) (50° E.— 61° 18' S.) (60° E.-54° 45' S.) (/) Lat. 55° S. Long. 24° 27' W. ig) S. 54° 12' E. (A) East. (i) 1819 miles. (/) 1928 miles. (A) Lat. 55° S. Long. 31° 34' E. (O East. (m) N. 63° 10' E, (n) 1244 miles. WINDWARD GREAT CIRCLE SAILING. A just appreciation of the value of this sailing is of the utmost importance to "Wind- jammers," of which — ^notwithstanding the incursions of " Steam "—there are a good many still left. The Rule is simple enough. With a foul wind and sufficient sea-room, ascertain the " Initial Course " by the " General Utility Tables," and put your ship on the tack which lies nearest to it. Remember always that the TiiuE Course is the Great Circle Course, and not the Merca- torial Course. When the ship is being steered on the G. C. Course her bowsprit-end is all the time pointing right straight at the port or place bound to. Whereas, when steering the Mercatorial Course the ship's head is never pointing for her destination till it heaves in sight. But when we come to the case of a ship with a foul wind, things may be ever ao much worse. [PROBLEMS IX. & X.] GENERAL UTILITY TABLES. xxvii Suppose, for example, the wind is East, and the Mercatorial Course is also East ; or in other words — if we believe Mr. Mercator — the wind is right dead on end, and there is no question of a long leg and a short one — nothing but a pure thrash to windward. Under these circurastances it would, to the unsophisticated, seem immaterial which tack the ship was put on, and therefore we will imagine the yards to be sharp up against the "Scotchmen" on the starboard backstays. (N.B. — Scotchmen can stand many a hard rub and be none the worse.) But the wide-awake skipper jumps down and finds the Initial Course (a matter of 3 minutes). It turns out to be N.E. by E. Therefore the ship is heading exactly 9 points from her port, and is actually sailing away from it to the extent of 2 miles in every 10. This won't do, so " round she comes," and heads up N.N.E., or only 3 points from the true direction of her port, and every 10 miles she goes through the water will be a gain of 8^. Quite a different pair of shoes ! ! Don't you think so too ? This is all that need be said about Windward Great Circle Sailing. A blind man could see it. PROBLEM X. •To Identify an Unknown Star. It often happens on a clear but cloudy night, after days of overcast weather, that a star of the 1st or 2nd mag. is seen for a few minutes in a break, and in a favourable position for the determination of Position. At the moment, you may not be able to give it a name owing to its surroundings being invisible, nevertheless, if you stand in need of such an observation, snap it at once with sextant and chronometer, and at same time let some one else take the bearing by Standard Compass. The means at your command for identification purposes are then — (1) The Greenwich Mean Time. (2) The Observed Altitude. (3) The Observed Azimuth. (4) Ship's Position by Account. KULE. Correct the observed Altitude as usual. Correct the Compass bearing for Variation and Deviation. (With the present accurate appliances the True bearing thus obtained will be near enough for the present purpose.) Work out Sidereal Time at Ship in the usual way, and then you are ready to bring the never-failing Tables into action. Enter " Margin " of B witli the True Alt,, and under the True Azimuth in " Head-line " take out the corresponding "Number," and always mark it +. Enter "Margin" of A with the Latitude, and under the True Azimuth in "Head-line" take out the corresponding "Number." Prefix the - or + sign, according to whether the Azimuth is reckoned from the elevated or depressed Pole. Enter Q with the algebraic sum of these "Numbers" abreast of the Latitude in the "Marein" and the Hours and Minutes in the "Head-line" will represent the star's Hour-angle if the sum 'of the "Numbers" has the + sign, or its supplement if the - sign. In the latter case (with minus sign) subtract from 12 hrs. Then if the star is Eaat of the meridian, add its Hour-angle to the Sidereal Time at xxviii GENERAL UTILITY TABLES. [problem x.] ship ; but if West, subtract it. The result is the approximate Right Ascension of the unknown star. Duly armed with this you can refer to the star-list on page 67, and the star will be identified without diiBculty, for it will be observed that where the Right Ascensions are nearly the same the corresponding Declinations are widely apart ; and in most cases the bearing and altitude will easily settle the question as to which of two stars has the more northerly or southerly Declination. Remember, however, that there is always a possibility of a supposed >Sto?' being really a Planet, in which case you must turn to the Naut. Almanac and make your calculated Right Ascension match either with Jupiter, Venus, Saturn, or Mars. You will then no doubt be able to saddle the right horse. Having succeeded in locating your celestial friend, you can set about utilising him as may be convenient. Once you get the " hang " of the above, it becomes quite easy. The Sidereal Time at Ship or Right Ascension of the Meridian should be at the finger-ends of every Navigator. In " Wrinkles " considerable prominence is given to it, vide pages 129, 385, 402, &c. The Sidereal Time at Ship is also required in finding the Latitude by Pole *, vide page 635 of Faut. Almanac for 1899, and page 386 of "Wrinkles." Example 1 . September 1st, 1899, about 8h. 10m. in First watch A.T.S., Position by account being Lat. 52° N. and Long. 15° W., the observed alt. of an unknown star was 8° 21' at 9h, 10m. 5s. G.M.T. by Ohronom.5 the bearing by Standard Compass Was also observed and proved to be N. 85f° E., Deviation 1J° Ely., Variation 24|° Wly., Eye 22 feet. Therefore we have True Alt. of * 8° 10' True Azim. „ N. e2f° E. To FiNB Sidereal Time at Ship, OR Right Ascension of the Meridian. H. M, S. Greenwich Mean Time 9 10 5 Longitude in Time 1 COW. Mean Time at Ship 8 10 5 Sid. Time at Greenw. mean noon 10 41 44 (N. Al. page 147) Accelleration for G.M.T + 1 30 Sidereal Time at Ship -. 18 53 19 Enter B with *'s Alt. 8° 10' in "Margin" and Azimuth N. 62f E. in "Head-line." The resulting " Number " is -f- -161. Enter A with Lat. 52° in "Margin" and Azimuth N. 62f° E. in "Head-line." The corresponding " Number " is - '659. It is marked - because the True Azimuth is reckoned from the elevated Pole. + 161 B - -659 A Sum --498 Enter Q with the sum - '498 abreast Lat. 52' in the "Margin," and the hours and minutes (4hr. 52m.) in the "Head-line" will represent the supplement of the Hour-angle because of the minus sign. The Hour-angle is therefore equal to 12hrs. less 4hrs. 52m., = 7hrs. 8m. East. [PROBLEM X.] GENERAL UTILITY TABLES. xxlx Then we have H. M. S. Sidereal Time at Ship 18 53 19 *'s Hour-angle (East) 7 7 8 26 24 1 19 2 1 19 Approximate Eight Ascension of ».. Comparison with the Right Ascension of the stars on page 67 proves the * to be Hamel (a Arietis), and , the bearing shews it to be fairly well situated for the determination of Longitude. Table C gives the error in the Longitude as 0'-837 for each 1' of error in the Latitude worked with, and Table D gives the error in the Longitude as l'-827 for each 1' of error in the Altitude- worked with. The next Example deals with the same * West of the meridian. Example 2. November 12th, 1899, about 4 bells in the morning watch. Appar. Time at Ship. Position by Dead Reckoning being Lat. 52° N., Long. 15° W. The observed Alt. of an unknown star was 8° 21' at 18h. 44m. 45s. G.M.T. by chronometer. The Compass bearing by Standard was at same time observed to be N. 391° W., Deviation If Ely., Variation 24^ Wly., Eye 22 feet. Therefore we have „ „„ ,„, True Alt. of * 8° 10 True Azim. of * N. 62f W. To FIND Sidereal Time at Ship, OB Right Ascension of the Meridian. H, M. S. Greenwich Mean Time by chron. (Novr. 11th) 18 44 45 Longitude in Time ^ ° ^ ^• Mean Time at Ship 17 44 45 Sidereal Time at Greenwich Mean Noon 15 21 39 Naut. Aim. page 183. Accelleration for 18h. 45m +_ ^ f " " " ^^^• Sidereal Time at Ship ■ 9 9 ^9 Enter B with Alt. 8° 10' in "Margin," and Azimuth N. 62f° W. in "Head-line." The resulting "Number" is + -161. Always ^J^w. Enter A with Lat. 52rin "Margin," and Azimuth N. 62r W. in "Head-line," the corres- ponding " Number " is - '659. It is marked minus because the True Azimuth is reckoned from the elevated Pole. ^ ,^g^ - -659 A Sum, - -498 Enter O with the sum - -498 abreast Lat. 52° in the " Margin," and because of the minus si^n the Hours and Minutes (4h. 52m.) in the " Head-line " will represent the supplement of the Hour-angle. It is therefore equal to 12h. less 4h. 52m. = 7hrs. 8m. West. Then we have H. M S. Sidereal Time at Ship 9 9 29 *'s Hour- Angle (West) 7 8 (subtract because West). »'s Apiwoximate Eight Ascension... 2 1 29 agreeing with * Hamel. It must not be expected that ia practice the Right Ascension will come out so closely as it does in these examples. It largely depends upon the direction of the bearing, the accuracy XXX GENERAL UTILIl Y TABLES. [problem x.] ^. with which it is observed, and its subsequent reduction to True bearing. Under favourable circumstances the error in the R.A. should not exceed a couple or three minutes. For identification of a Navigational star that is quite good enough. Example 3. January 2nd, 1899, about 3h. 33m. in the middle watch, A.T.S. Position by D.R. being Lat. 10° N., and Long. 30' W, The Alt. of an unknown * was observed to be 8° 38' 43" at G.M.T. by chronometer I7h. 37m. 26s. of preceding day. At same time the compass bearing by Standard was recorded as S. 6° E. Variation 15^° W., assumed Deviation 2J° W. Eye 22 feet. Therefore we have True Altitude of * 8° 28' True Azim. „ S. 24° E. To FIND Sidereal Time at Ship. H. M. S. Greenwich Mean Time by chronometer (Jan. 1st) ... 17 37 26 Longitude in Time 2 W. Mean Time at Sliip 15 37 26 Sidereal Time at Greeuw, Blein Noon 18 43 41 (N. A. page 3). Acceleration for 17h. 37m. 26s + 2 54 ( „ „ 586). 34 24 1 24 Sidereal Time at Ship 10 24 1 Enter B with *'s Alt. 8° 28' in "Margin," and Azimuth S. 24° E. in "Head-line"; the resulting "Number" is + •366. Enter A with Lat. 10° N. in "Margin," and Azimuth S. 24° E. in "Head-line"; the resulting " Number " is + "396. It is marked + because the True Azimuth is reckoned from the depressed Eole. + -366 B + -396 A Sum + 762 C Enter O with the sum + '762 abreast Lat. 10° N. in the " Margin," and in the " Head-line " will be found the *'s actual Hour-angle (3h. 32in. 27s.), because the sign of the sum of the " Numbers "is + . Then we have H. M. S. Sidereal Time at Ship 10 24 1 Hour-angle of * (East) 3 32 27 Approx. Right Ascension of *... 13 56 28 Reference to page 67 shews at once that the observed * must be ^ Gentauri. Taken by itself it is not in a good position either for Latitude or Longitude, but would serve to check the Deviation of the compas.s. If coupled with simultaneous alt. of Benetnasch (i; Ursai Majoris) then bearing N. 36° E. (true), they would serve admirably to give both Lat. and Lonrr. Still better if the coupling were with Arcturus bearing N. 73° E. (true).* In Navigation there are all sorts of possibilities if only looked for intelligently. Example 4. December 1st, 1899, about 6h. 52m. in last dog-watch. Position by D.R. beincr Lat. 52° N. and Long. 15° W., the observed Alt. of an unknown « was 21° 1' 15" at G.M.T. 7h. 41m. 12s The compass bearing at same time was ascertained to be S. 66J° E. Variation 24i° W and Deviation 1° E. Eye 22 feet. ' A. C. Johnson's method. {Vide " Wrinkles," page 5tS), [PROBLEMS X. & XI.] GENERAL UTILITY TABLES. xxxi Therefore we have True Alt. of * 20° 54' True Azim. „ East. To FIND Sidereal Time at Ship. H. M. S. G.M.T. by chronometer 7 41 12 Longitude in Time 1 W. Mean Time at Ship 6 41 12 Sidereal Time at G.M. Noon 16 40 30 Acceleration for Vh. 41m. 12s + 1 16 Sidereal Time at Ship... 23 22 58 Enter B with Alt. of * 20° 54' in "Margin," and Azimuth 90° in "Head-line"; the corresponding " Number " is + •382. Enter A with Lat. 52° in "Margin," and 90° in "Head-line"; the resulting "Number" is -000. T -382 B •000 A Sum + •382 Enter O with + -382 abreast of Lat. 52° in "Margin," and in the "Head-line" will be found 5h. 7m. Owing to the sign being + this is the *'s actual Hour-angle. Then we have H. M. S. Sidereal Time at Ship 23 22 58 Hour-angle of * (East) 5 7 28 29 58 24 Approx. E.A. of * 4 29 58 It must therefore be Aldebaran (a Tauri), and as it was on the Prime Vertical when observed, the sight is a first-class one for Longitude determination. PROBLEM XI. Given the Latitude and Longitude by D.R. (or otherwise), to ascertaix the APPKOXIMATE Alt. OF A * FOR A PrE-DETERMINED TiME AT ShIP. Now this Problem is just the reverse of the last one, so by way of examples we will start with those in Problem X., and for easy reference will number them the same. Example 1. (page xxviii). September Isfc, 1899, about 8h. 10m. in First watch, in Lat. 52° N. and Long. 15° W, G,M.T. 9h. 10m. 5s. Required the Ti'ue Alt. of * Hamel. xxxii GENERAL UTILITY TABLES. [problem xi. To FIND Sidereal Time at Ship. H. M. S. G.M.T. by chronom 9 10 5 Long, in time 1 W. Mean Time at Ship 8 10 5 Sid. Time at G.M. Noon 10 41 44 (page 147 of N.A.) Accel, for G.M.T + 1 30 (page 586 of N.A. Sidereal Time at Ship ... 18 53 19 R.A, of * Hamel 2 1 31 Hour-angle of * Hamel... 16 51 48 W. 24 Hour-angle of * Hamel... 7 8 12 E. With foregoing data (Lat., Hour-angle, and Declin.) the ABO Tables give the True Azimuth of » Hamel as N. 62f° E. Then- Enter O with Lat. 52° in " Margin," and the sup-plement (4h. 51m. 48s.) of the Hour-angle in the " Head-line " ; the corresponding " Number " is — "498. It is marked minus because the Hour-angle exceeds 6 hrs. Enter A with Lat. 52° in " Margin," and Azimuth 62f ° in " Head-line " ; the corresponding " Number " is -|- '659. It is marked -f- because the Azimuth is reckoned from the elevated Pole. - -498 O + -659 A Sum + -161 B Enter B with -f- -161 under Azim. N. 62f° E. in " Head-line," and abreast it in the "Margin" will be found 8° 10', the required approximate Alt. Example 2. (page xxix). November 12th, 1899, about four bells ii the morning watch, in Lat. 52° N. and Long. 15° W. G.M.T. by chron. 18h. 44m. 45s. (Nov. 11th). Eequired the True Alt. of * Hamel. To FIND THE SiDEEEAL TiME AT ShIP. H. M. S. G.M.T. by chronom 18 44 45 Longitude in time 10 West. Mean Time at Ship 17 44 45 Sidereal Time at G. Mean Noon 15 21 39 Acceleration for G.M.T + 35 Sidereal Time at Ship 33 9 29 24 Sidereal Time at Ship 9 9 29 E.A. of * Hamel 2 1 31 Hour-angle 7 7 58 West. With data now available, the A B C Tables give the True Azimuth of * Hamel as N. 62f ° W. Then- Enter O with Lat. 52° N. in " Margin," and the supplement (4h. 52m.) of the Hour-angle in the "Head-line"; the corresponding "Number" is --498. It is marked minus because the Hour-angle exceeds 6 hrs. [PROBLEM XI.] GEKURAL UTILITY TABLES. xxxiii Enter A with Lat. 52° in "Margin," and Azimuth 63f° in "Head-line"; the corresponding " Number " is + "6 59. It is marked + because the Azim. is reckoned from the elevated Pole. -•498 O + ■659 A Sum +-161 B Enter B with + -161 under Azim. N. 62i° "W. in " Head-line," and abreast it in the " Margin" will be found 8° 10', the required Alt. Example 3, (page xxx). January 2nd, 1899, about 3h. 33m. in the middle watch, in Lat. 10° N. and Long. 30° W. G.M.T. I7h. 37m. 26s. (January 1st). Required the True Altitude of * /3 Gentauri. To FIND Sidereal Time at Ship. H. M. S. G.M T. by chronometer 17 37 26 Longitude in time 2 Mean Time at Ship 15 37 20 Sid Time at Greenwich Mean Noon 18 43 41 Acceleration for G.M.T + 2 54 Sidereal Time at Ship 34 24 1 K. A. of * /3 Centauri 13 56 41 Hour-angle 20 27 20 West 24 Hour-angle 3 32 40 East. The data now available give the True. Azimuth of * ^ Centauri as S. 24° E. Then — Enter O with Lat. 10° N. in "Margin," and Hour-angle 3h. 32m. 40s. in "Head-line"; the corresponding " Number " is + '762. It is marked -i- because the Hour-angle is less than 6 hrs. Enter A with Lat. 10° in " Margin " and Azimuth 24° in " Head-line" ; the corresponding " Number " is - '396. It is marked minus because the Azim. is reckoned from the depressed Pole. + ■762 O -■396 A + ■366 B Enter B with + -566 under Azim. S. 24° E. in "Head-line," and abreast it in "Margin" will be found 8° 28', the required Alt. Example 4. (page xxx). December 1st, 1899, about 6h. 52m. in the second dog watch, in Lat. 52° N. and Long. 15° W G.M.T. 7h. 41m. 12s. Required the True Altitude of » Aldebaran (a Tauri). xxxiv GENERAL UTILITY TABLES. Iproblem xi.] To FIND Sidereal Time at Ship. H. M. S. G.M.T. by Chronometer 7 41 12 Longitude in Time (West) 10 Mean Time at Ship 6 41 12 Sid. Time at Greenw. Mean Noon 16 40 30 Acceleration for G.M.T + 1 16 Sidereal Time at Ship 23 22 58 R. A. of * Aldebaran 4 30 10 Hour-angle 18 52 48 West. 24 Hour-angle 5 7 12 East. With the available data the True Azimuth is East. Then — Enter O with Lat. 52° N. in "Margin," and Hour-angle 5h. 7m. 12s. in "Head-line"; the corresponding "Number" is + -382. It is marked + because the Hour-angle is less than 6 hrs. Enter A with Lat. 52° in " Margin," and Azimuth 90° in " Head-line" ; the corresponding "Number" is -000. + -382 O ■000 A Sum + -382 B Enter B with + '382 under Azimuth 90° in "Head-line," and abreast it in "Margin" will be found 20° 54', the required Altitude. The next Example is to shew that when the sum of the " Numbers " has the minua sign, the object is helow the horizon. Example 5. Septr. 1st, 1899, about 6h. 22m. in second dog watch, in Lat. 52* N. and Long. 15" W. G.M.T. by Chron. 7h. 22m. 5s. Required the True Alt. of * Hamel. To FIND SiDEKEAL TiME AT ShIP. H. M. B. G.M.T. by Chronometer 7 22 5 Longitude in Time (West) 10 Mean Time at Ship 6 22 5 Sid. Time at Greenw. Mean Kaon 10 41 44 Acceleration for G.M.T + 1 13 Sidereal Time at Ship 17 5 2 R.A. of* Hamel 2 1 31 Hour-angle 15 3 31 West. 24 Hour-angle 8 56 29 East. The available data give True Azim. of # Hamel = N. 41J° E. Then- Enter O with Lat. 52° in " Margin," and 3h. 3m. 31s. (supplement of Hour-angle) in " Head- line"; the corresponding "Number" is - 1-576. It is marked minus because the Hour-angle exceeds 6 hrs. [PROBLEM XI] GENERAL UTILITY TABLES. xxxv Enter A with Lat. 52" in "Margin," and Azim. 41 J° in "Head-line"; the corresponding " Number " is + 1 4)47. It is marked + because the Azimuth is reckoned from the elevated Pole. - 1-676 O + 1-447 A Sum - 0129 B (Note the minus sign.) Enter B with - -129 under Azimuth 41 J', and abreast it in "Margin" will be found 4° 52', -which represents the amount that Hamel is helow the Eastern Horizon. It will rise with an Hour-angle of 8h. 11m. 33s., at which time its True Altitude will be 0° 0' 0". Don't forget the effect of refraction in making the * appear to rise earlier than it ought to do. The Apparent Alt. and the True Alt. are two different things. It follows from this example that should the sum of the " Numbers " have a minus prefix when you are certain the object is above the horizon, it is equally certain you have made a mistake somewhere in the working. Example 6. At 7h. 47m. 27s., G.M.T., April 2nd, 1899, required the True Altitude of + Spica (a Virginis). Latitude 33° S. and Long. 0^ The App. Time at ship being "about 7h. 45m. p.m. To FIND Sidereal Time at Ship. H. M. S. G.M.T. by chronometer 7 47 27 Longitude 0° " ^ Mean Time at Ship 7 47 27 Sid. Time at Greenw. Mean Noon 42 27 Acceleration for G.M.T + 1 17 Sidereal Time at Ship 31 11 On page 129 of "Wrinkles" we get the Rule for finding the Hour-angle, and we had better stick to it. It runs thus — From the Sidereal Time at Ship (increased if necessary by 24 hours) subtract the R. A. of the star: the remainder will be the Hour-angle West of the meridian. Should the remainder be greater than 12 hours, take it from 24 hours, and the result will be the Hour-angle East of the meridian. Should the remainder exceed 24 hours, reject 24 hours, and the result will be the Hour-angle West of the meridian.-* To avoid confusion of systems we will therefore carry on the process in " Wrinkles " fashion. H. M. 8. Sidereal Time at Ship 8 31 U Add 24 Sidereal Time at Ship + 24 hrs. 32 31 11 Right Ascension of * Spica 13 19 53 Hour-angle J 19 11 18 West. 24 Hour-angle 4 48 42 East. • To understand this, independent of any Printed Rule, refer to diagram and text on page 380 of " Wrinkles." xxxvi GENERAL UTILITY TABLES. [problem xi.] With the foregoing data, the A B C Tables give the True Azimuth of Spica as N. 89J° E. Then- Enter C with Lat. 33° in " Margin," and the Hour-angle 4h, 48ni. 42s. in " Head-line" ; the corresponding "Number'' is + "384. It is marked + because the Hour-angle is less than 6 hrs. Enter A with Lat. 33° in " Margin," and Azimuth 89|° in " Head-line" ; the corresponding " Number " is — 006. It is marked — because the Azimuth is reckoned from the depressed Pole. + -384 O - -006 A Sum + -378 B Enter B with + '378 under the Azimuth (89J°) in "Head-line," and abreast it in "Margin" M'ill be found 20° 41', which is the required Alt. of * Spica at 7h. 47m. 27s. M.T.S. Note.— With regard to the identification of a star : it would be interesting practice on a fine clear evening to observe the Alt. and Azimuth of a known star, and see if the method described in Problem X. comes out right. This would give confidence when really required. The same suggestion applies to Problem XI. Observe the Alt. and note time by Chronometer. Then calculate the Alt. by Problem XI., and see if it agrees fairly with the observed Alt., when the latter has been corrected for Index Error, Dip, and Eefraction. As before stated, you must not expect absolute agreement ; such a thing could only happen when the data employed were themselves absolutely correct, which is hardly likely on board ship, so do not blame the Tables. They are all right. Eemember that when the celestial object is on or near the Prime "Vertical its altitude is changing very rapidly, and its azimuth very slowly ; therefore at such times the Altitude is a specially good factor in determining the True Azimuth, but the Azimuth is not nearly so effective for determining the Altitude. The reverse of this is the case when the object is near the meridian. Its motion in altitude is then very slow, consequently the Altitude cannot be relied upon to give anything like a correct Azimuth ; but per contra, the Azimuth— which is then altering very rapidly— is useful in determining the Altitude. By simUar reasoning it will be seen that by employing Time at Ship as an argument, the Altitude can be calculated with more accuracy the nearer the object is to the meridian ; and that the Azimuth will be more correct the nearer the object is to the Prime Vertical. An error in the time will be of less consequence in both these cases. When boiled down, it comes to this, that the quicker movement should be used to determine the slower, irrespective of position. Tables a AND B The Head-line has various significations according to the Problem in use. In Problem IV. It represents Diff. of Long. In Problem V. the Initial Course. In Problem VI. the Complement of the Diff. Of Long. In Problem VIIL the Difi". of Long. In Problems X. and XL the True Azim. Lat. HOURS • m m m m m m m m m m m m m m m 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 (or) (oD (or) (1°) dr) (>i°) (in (2°) (2r) (2*°) (2r) (3°) (3r) (3i°) (3r) 0° •000 •000 -000 ■000 -000 -000 -000 •000 -000 •000 -000 -000 ■000 •000 •000 I 4'ooo 2-000 1-333 I -000 ■800 -667 ■571 -500 •444 -400 -363 -333 -307 •28s -266 2 8-003 4-002 2-668 2-001 1-600 1-334 I -143 i-ooo -889 -800 ■727 -666 -615 •571 -533 3 I2'0I 6-005 4-003 3-002 2-402 2-001 1-715 1-501 1-334 1-20O I -091 1-000 -923 •857 -800 4 16-03 8-013 5-342 4-006 3-205 2-670 2-289 2-002 1-780 1-602 1-456 1-334 1-231 1-143 I 067 5 20-05 10-03 6-683 5-012 4-010 3-341 2-864 2-505 2-227 2-004 I -821 1-669 1-541 1-430 1-335 !>< 6° 24-09 12-04 8-029 6 02 1 4-817 4-014 3-440 3-010 2-675 2-407 2-188 2-005 I -851 1718 1-604 7 28-14 14-07 9380 7-034 5-627 4-689 4-019 3-5'6 3-125 2-812 2-556 2-343 2-162 2-008 1-873 . E 8 32-21 i6-io 10-74 8-052 6-441 5-367 4-600 4-025 3-577 3-219 2-926 2-682 2-475 2-298 2-144 9 . 36 '30 18-15 12-10 9-074 7-259 6048 5-184 4-536 4-031 3-628 3-297 3-022 2-789 ^'Si° 2-417 S| 10 40-41 20 2 1 13-47 10-10 8081 6-734 5-771 5049 4-488 4-039 3-671 3-364 3-105 2-883 2-690 .s£ 11° 4455 22-27 14-85 11-14 8-908 7-423 6-362 5-566 4-947 4-452 4-047 3-709 3-423 3-178 2-966 12 48-71 24-36 16-24 I2-l8 9-741 8-117 6-957 6-087 5-410 4-868 4-425 4-056 3-743 3-475 3-243 13 52-91 26-45 17-64 13-23 10-58 8-817 7-556 6-61 1 5-876 5-288 4-806 4-405 4-066 3-775 3-522 3 14 57-14 28-57 1905 14-28 11-43 9-521 8-i6i 7-140 6-346 57" 5-191 4-757 4-391 4-076 ^'^0% °t IS 61-41 30-70 20-47 15-35 12-28 10-23 8-770 7-673 6-820 6137 5-578 5-113 4-719 4-381 4-088 Oh g 16° 65-72 32-86 21-90 J6-43 13-14 10-95 9-385 8-211 7-298 6-568 5-970 5-472 5-050 4-688 4-375 'Z 70-07 35-03 23-35 17-52 14-01 11-68 10-01 8-755 7-781 7-002 6-365 5-834 5-384 4-999 4-665 -^ a i8 74-47 37-23 -24-82 i8-6i 14-89 12-41 10-63 9-304 8-270 7-442 6-764 6-200 5722 5-312 4-957 19 7891 39-46 26-30 1973 15-78 13-15 11-27 9-860 8-764 7-886 7-J68 6-570 6-064 5630 5-253 20 83-42 41-71 27-80 20-85 16-68 13-90 11-91 10 42 9-264 8-336 7-577 6-945 6-410 5-951 5-553 21° 87-97 43 99 29-32 21-99 17-59 14-66 12-56 1099 9-770 8-792 7-992 7-325 6-760 6-276 S-857 22 92-60 46-30 30-86 23-'5 18-52 '5-43 13-22 I '-57 10-28 9-254 8-411 7-709 7-115 6-606 6-164 o ^ £ 23 97-28 4864 32-43 24-32 19-45 l6-2l 13-89 12-16 10-80 9-722 8-837 8-099 7-475 6-940 6-476 24 102-0 51-02 34-01 25-51 20-40 17-00 14-57 12-75 11-33 10-20 9-269 8-495 7-841 7-279 6-793 25 106-9 53-43 35-62 26-71 21-37 17-81 15-26 '3-35 11-87 10-68 9-708 8-897 8'2I2 7-624 7-115 CO ■♦J O O ^ © 26° III-8 55-89 37-26 27-94 22-35 18-63 15-96 13-97 12-41 11-17 10-15 9-307 8-589 7-974 7-441 :§ -« 27 1 16 -8 58-39 38-92 29-19 23-35 19-46 16-68 14-59 12-97 11-67 10-61 9-722 8-973 8-331 7774 03 Oh^ 28 121 -9 60-93 40-62 30-46 24-37 20-31 17-40 '5-23 13-53 12-18 11-07 10-15 9-364 8693 8112 29 1270 63-52 42-34 31-76 25-40 21-17 1814 15-87 1411 12-70 11-54 10-58 9-762 9-063 8-457 signi "Ship Lat. 30 1323 ■66-i6 44-10 33-08 26-46 22-05 18-90 16-53 14-69 13-22 12-02 11-02 1017 9-440 8-809 31° •377 68-85 45-90 34-42 27-54 22-95 19-67 17-21 15-29 13-76 12-51 11-47 10-58 9-824 9-167 3 og 32 i43'z 71-60 47 73 35-80 28-64 23-86 20-45 17-90 15-90 14-31 13-01 11-92 11-00 10-22 9-534 33 148-8 74-41 49-61 37-21 29-76 24-80 21-26 1 8 -60 16-53 14-87 13-52 12-39 11-44 10-62 9908 ■§5*^ 34 154-6 77-29 5 '-53 38-64 30-91 25-76 22-08 19-32 17-17 15-45 14-04 12-87 11-88 11-03 10-29 35 160-5 80-24 53-49 40-11 32-09 26-74 22-92 20-05 17-82 16-04 14-58 13-36 1233 11-45 10-68 g*2 36' 166-5 83-25 55-50 41-62 33-30 27-75 23-78 20-80 18-49 16-64 15-13 13-86 12-79 11-88 u-08 1 «§• 1727 86-35 57-56 43-'7 34-53 28-78 24-66 21-58 19-18 17-26 15-69 14-38 13-27 12-32 11-50 * §2 38 1791 89-53 59-68 44-76 35-81 29-84 25-57 22-37 19-89 17-89 16-27 14-91 1376 12-77 11-92 •S «>. 39 1856 92-79 61-86 46-39 3r'i 30-92 26-50 23-19 20-61 18-55 16-86 15-45 14-26 13-24 12-35 ^Il 40 192-3 96-15 64-10 4807 38-46 32-04 27-46 24-03 21-36 19-22 "7-47 1601 14-78 13-72 12-80 a J 41° 199-2 99-61 66-40 49-81 39-84 33-20 28-45 24-89 22-12 19-91 1810 16-59 15-31 14-21 13-26 5? 42 206-4 103-2 68-78 51-58 41-26 34-39 29-47 25-78 22 92 20-62 18-75 17-18 15-86 14-72 13-74 Is 43 2137 106-9 71-23 53-42 42-74 35 ti 30-52 26-70 23-73 21-36 19-41 17-79 16-42 15-25 14-23 +J -*J 44 221-3 110-7 73-77 55-32 44-26 36-88 31-61 27-66 24-58 22-12 20-10 18-43 17-01 15-79 14-73 45 229-2 114-6 76-39 57-29 45-83 38-19 32-73 28-64 25-45 22-90 20-82 19-08 17-61 16-35 15-26 S^ 46° 237-3 118-7 79-10 59-33 47-46 39-55 3389 29-66 26-36 23-72 21-56 19-76 18-24 16-93 15-80 9 "d 47 245-8 122-9 81-92 61-44 49-15 40-95 35-10 30-71 27-29 24-56 22-33 20-46 18-89 17-53 16-36 If § 48 254 -s 127-3 84-84 63-63 50-90 42-41 36-35 31-80 28-27 25-44 23-12 21-19 19-56 18-16 16-94 •a - 49 2636 131-8 87-88 65-91 52-72 43-93 37-65 32-94 29-28 26-35 23-95 21-95 20-26 i8-8i 17-55 s> SO 273-1 136-6 91-04 68-28 54-62 45-51 39-01 34-13 30-33 27-30 24-81 22-74 20-99 19-49 18-I8 Si° 283-0 141-S 94-33 70-75 56-59 47-16 40-42 35-36 3 1-43 28-28 2571 23-56 21-75 20-19 18-84 > 52 293-3 146-7 97-77 73-33 58-66 48-88 41-89 36-66 32-58 29-32 26-65 24-42 22-54 23-93 I9'53 £: S3 304-1 IS2-« 101-4 76-02 6082 50-68 43-43 38-or 33-78 30-39 27-63 25-32 23-37 21-70 20 25 M 315-4 1577 105-1 78-85 63-08 52-56 45-05 39-42 35-03 31-52 28-65 26-26 24-24 22-50 21-00 1 55 327-3 163-6 109 -I 81-81 65-45 54-54 4674 40-89 36-35 32-71 2973 27-25 25-15 23-35 21-79 S6° 339-8 1699 113-3 ff93 67-94 s^l^ 48-52 42-45 37-73 33-96 30-87 28-29 26-11 24-24 22-62 352-9 176-5 117-6 88-22 70-57 5881 50-40 44-10 39-'9 35-27 3206 29-38 27-12 25-18 23-49 t 58 366-8 183-4 122-2 91-69 73-34 61-11 52-38 45-83 40-73 36-65 33-32 30-54 28-18 26-17 24-42 b 59 381-4 I go -7 I27-I 95 '35 76-27 63-56 54-47 47-66 42-36 38-12 34-65 31-76 29-31 27-21 25-39 60 397-0 198-5 132-3 99-23 79-38 66-14 56-69 49-60 44-08 39-67 36-06 33-05 30-50 28-32 26-43 6i° 413-5 206-7 137-8 103-4 82-68 68-89 59-05 51-66 45-92 41-32 37-56 34-42 31-77 29-50 27-52 62 4310 2.55 I43'7 107-7 86-19 71-82 61-56 53-86 47-87 43-08 39-15 35-89 33-12 30-75 28-69 63 449-8 224-9 149-9 112-4 89-95 74-95 64-24 56-20 49-95 44-95 40-86 37-45 34-56 32-09 29-94 64 469-9 234-9 156-6 ■17-5 9396 78-30 67-11 58-71 52-18 46-96 42-68 39 12 36-11 33-52 3128 65 491-5 2457 163-8 122-9 98-28 81-90 70-19 61-41 54-58 49-12 44-65 40-92 37-77 35-06 32-72 m m m m m m m m m m m m m m m 59 58 57 56 55 54 53 52 51 50 49 46 47 46 45 (1791°) (i79i°) (i79r) (179°) (i78r) («78r) (i78r) (178°) (•77r) (1774°) (i77r) (177°) (i76r) (I76i°) (i76r) II HOURS. for the Azimuth;— The Sign Is always -I-, except when the Hour-Angle exceeds 6 hours. B In Problems IV. The Head-line has various signifleations, according to the Problem in use. and VIII. it represents the Diff. of Long. In Problems X. and XI. it represents the True Azimuth. Decl. HOURS. 1 (or) m 2 (oi°) m 3 (of) m 4 (1°) m 5 (iF) m 6 (ii°) (If) ni 8 (2°) m 9 (21°) in 10 (21°) m 11 (22°) m 12 (3°) m 13 (3i°) m 14 (3i°) m 15 (31°) a> •a 09 [0 m o u « IIS all a a" O "-"a, ^ B > s-i O.Q Cmt-i " O CJ p. V -s> a 4) a o 9 10 11° 12 13 14 IS 16° 19 20 21° 22 23 24 25 26° 27 28 29 30 31° 32 33 34 35 36° 38 39 40 41° 42 43 44 45 46' 47 48 49 50 51° 52 53 54 55 56° & 61° 62 P 65 •000 4"ooo 8-003 I2'OI 16-03 20 "05 24-09 28-14 32-21 36-30 40-41 44-SS 48-71 52-91 57-14 61-41 65-72 7007 74-46 78-91 83-42 87-98 92-60 97-28 102-0 106-9 111-8 116-8 121 -9 127-0 132-3 137-7 143-2 148-8 154-6 160-5 166-S 172-7 179-1 185-6 192-3 199-2 206-4 213-7 221-3 229-2 237-3 245-8 254-5 263-6 273-1 283-0 293-3 304-1 315-4 327-3 339-8 352-9 366-8 381-4 397-0 413-5 431-0 449-8 469-9 491-5 lU 59 (1791") •000 2-000 4-002 6 -006 8-013 10-03 12-04 14-07 16-10 18-15 20-21 22-27 24-36 26-46 28-57 30-71 32-86 35-03 37-23 39-46 41-71 43-99 46-30 48-64 51-02 53-44 55-89 58-39 60-93 63-52 66-16 68-85 71-61 74-42 77-29 80-24 83-26 86-35 89-53 92 '80 96-iS 99-61 103-2 106-9 110-7 114-6 118-7 122-9 127-3 131-8 136-6 141-5 146-7 152-1 157-7 163-7 169-9 176-5 183-4 190-7 198-S 206-7 215-5 224-9 235-0 245-7 m 58 (i79n 1-334 2-668 4-004 S-342 6-684 8-030 9-380 10-74 12-10 13-47 14-85 16-24 17-64 19-05 20-47 21-91 23-36 24-82 26-31 27-81 29-33 30-87 32-43 34-01 35-62 37-26 38-93 40-62 42-35 44-11 45-90 47-74 49-61 SI -53 53-49 55-51 57-57 59-69 61-86 64-10 66-41 68-79 71-24 73-78 76-40 79-11 Si -93 84-85 87-88 91-05 94-34 97-78 101-4 105-2 109-1 113-3 117-6 122-3 127-1 132-3 137-8 143-7 149-9 156-6 163-8 -000 rooo 2-001 3-003 4-007 5-013 6-022 7-035 8-053 9-075 11-14 12-l8 13-23 14-29 15-35 16-43 17-52 18-62 19-73 20-86 21-99 23-15 24-32 25-51 26-72 27-95 29-20 30-47 31-76 33-08 34-43 35-80 37-21 38-65 40-12 41-63 43-18 44-77 46-40 48-08 49-81 51-59 53-43 55-33 57-30 59-33 61-45 63-64 65-91 68-29 70-76 73-34 76-04 78-86 81-83 84-95 88-23 91-70 95-36 99-24 103-4 107-8 112-5 117-5 122-9 -000 -800 1-601 2-402 3-205 4-011 4-818 5-628 6-442 7-260 8-083 8-910 9-744 10-58 11-43 12-28 13-14 14-01 14-89 15-78 16-68 17-60 18-52 19-46 20-41 21-38 22-36 23-36 24-37 25-41 26-47 27-54 28-64 29-77 30-92 32-10 33-30 34-54 35-81 37-12 38-46 39-85 41-27 42-75 44-27 45-84 47-47 49-16 50-91 52-73 54-63 56-61 58-67 60-83 63-09 65-47 67-96 70-59 73-36 76-29 79-40 82-70 86-21 89-97 93-99 98-30 in 55 (1781°) -000 -667 1-334 2-002 2-671 3-342 4-015 4-691 5-369 6-051 6-736 7-426 8-120 8-820 9-525 10-24 10-95 11-68 12-41 13-15 13-90 14-66 15-43 16-22 17-01 17-81 18-63 19-46 20-31 21-18 22-06 22-95 23-87 24-81 25-77 26-75 27-76 28-79 29-85 30-94 32-05 33-21 34-40 35-62 36-89 38-20 39-56 40-97 42-43 43-95 45-53 47-17 48-90 50-70 52-58 54-56 56-64 58-83 61-14 63-58 66-17 68-92 71-85 74-97 78-32 81-92 -000 -572 I-I43 I -716 2-290 2-865 3-442 4-021 4-602 5-186 5-774 6-365 6-960 7-560 8-164 8-774 9-390 lo-oi 10-64 II -28 11-92 12-57 13-23 13-90 14-58 15-27 15-97 16-68 17-41 18-15 18-91 19-68 20-46 21-27 22-09 22-93 23-79 24-68 25-58 26-52 27-48 28-47 29-48 30-54 31-62 32-75 33-91 35-12 36-37 37-67 39-02 40-44 41-91 43-45 45-07 46-77 48-55 50-42 52-40 54-50 56-72 59-07 61-59 64-27 67-14 70-22 -000 -500 I -001 1-502 2-004 2-507 3-012 3-518 4-027 4-538 5-052 5-570 6-091 6-615 7-144 7-678 8-216 8-760 9-310 9-866 10-43 11-00 11-58 12-16 12-76 13-36 13-98 14-60 15-24 15-88 16-54 17-22 17-90 18-61 19-33 20 -06 20-82 21-59 22-39 23-20 24-04 24-91 25-80 26-72 27-67 28-65 29-67 30-73 31-82 32-96 34-15 35-38 36-68 38-02 39-44 40-92 42-48 44-12 45-86 47-69 49-63 51-69 53-89 56-24 58-75 61-45 in 54 (i78i°) m 53 (i78i°) m 52 (178°) •000 -44s -889 1-335 I -781 2-228 2-677 3-127 3-580 4-034 4-491 4-951 5-414 5-881 6-351 6-825 7-304 7-787 8-276 8-770 9-271 9-778 10-29 10 -8 1 11-34 11-88 12-42 12-98 13-54 14-12 14-71 15-30 15-92 16-54 17-18 17-84 18-51 19-19 19-90 20-63 21-37 22-14 22-93 23-75 24-60 25-47 26-38 27-31 28-29 29-30 30-36 31-45 32-60 33-80 35-06 36-38 37-76 39-22 40-76 42-39 44-12 45-95 47-90 49-99 52-22 54-62 -000 -400 -801 1-201 1-603 2-006 2-410 2-815 3-222 3631 4-042 4-456 4-873 5-293 5-716 6-143 6-574 7-009 7-449 7-894 8-344 8-800 9-263 9-731 10-21 10-69 11-18 11-68 12-19 12-71 13-24 13-78 14-33 14-89 15-46 16-05 16-66 17-28 17-91 18-56 19-24 19-93 20-64 21-38 22-14 22-93 23-74 24-58 25-46 26-37 27-32 28-31 29-34 30-42 31-55 32-74 33-99 35-30 36-69 38-15 39-71 41-36 43-12 44-99 47-00 49-16 -000 -364 -728 1-092 1-457 1-824 2-I9I 2-559 2-929 3-301 3-675 4-051 4-430 4-812 5-197 5-585 5-977 6-372 6-772 7-177 7-586 8-001 8-421 8-847 9-280 9-719 10-17 10-62 11-08 11-55 12-03 12-52 13-02 13-54 14-06 14-59 15-14 15-71 16-28 16-88 17-49 18-12 18-77 19-44 20-13 20-84 21-58 22-35 23-15 23-98 24-84 25-74 26-68 27-66 28-69 29-77 30-90 32-10 33-36 34-69 36-10 37-60 39-20 40-91 42-73 44-70 m 51 (1771°) m 50 (i77i°) m 49 (i77n -000 -334 -667 i-ooi 1-336 1-672 2-008 2-346 2-685 3-026 3-369 3-714 4-061 4-411 4-764 5-120 5 -479 5-842 6-208 6-579 6-954 7-335 7-720 8-110 8-507 8-910 9-319 9-736 10-16 10-59 11-03 11-48 11-94 12-41 12-89 13-38 13-88 14-40 14-93 15-47 16-03 16-61 17-20 17-82 18-45 19-11 19-79 20-49 21-22 21-98 22-77 23-60 24-46 25-36 26-30 27-29 28-33 29-42 30-58 31-80 33-09 34-47 35-94 37-50 39-18 40-98 m 48 (177°) -000 -308 -616 -924 1-233 1-543 1-854 2-i66 2-479 2-794 3-110 3-429 3-749 4-072 4-398 4-726 5-058 5-393 5-731 6-074 6-420 6-771 7-127 7-487 7-853 8-225 8-603 8-987 9-379 9-777 10-18 10-60 11-02 11-45 11-90 12-35 12-82 13-29 13-78 14-28 14-80 15-33 15-88 16-45 17-03 17-64 18-27 18-92 19-59 20-29 21-02 21-78 22-58 23-41 24-28 25-19 26-15 27-16 28-23 29-36 30-55 31-82 33-17 34-62 36-17 37-83 -000 ■286 -572 -858 1-145 1-433 1-722 2-01 1 2-302 2-594 2-888 3-184 3-482 3-782 4-084 4-389 4-697 5-008 5-322 5-640 5-962 6-288 6 -6 18 6-953 7-293 7-638 7-989 8-346 8-710 9-080 9-457 9-842 10-24 10-64 11-05 11-47 11-90 12-34 12-80 13-26 13-74 14-24 14-75 15-27 15-82 16-38 16-96 17-57 18-19 18-84 19-52 20-23 20-97 21-74 22-55 23-39 24-28 25-22 26-21 27-26 28-37 29-55 30-81 32-15 33-58 35-13 m 47 (i76r) -000 -267 -534 -801 1-069 1-338 1-607 1-877 2-149 2-422 2-696 2-972 3-250 3-530 3-812 4-097 4-384 4-675 4-968 5-265 5-565 5-869 6-177 6-490 6-807 7-130 7-457 7-791 8-130 8-475 8-828 9-187 9-554 9-929 10-31 10-71 ii'ii 11-52 11-95 12-38 12-83 13-29 13-77 14-26 14-77 15-29 15-83 16-40 16-98 17-59 18-22 18-88 19-57 20-29 21-04 21-84 22-67 23-54 24-47 25-45 26-48 27-58 28-76 30.01 31-35 32-79 lU 46 (I76J°) in 45 (i76i°) II HOURS. f When Latitude and Declination are of contrary names, the Sign is +. For the Azimuth: | ^^^^ Latitude and Deeliniation are of same name, the Sign is -. A The Head-line has vaFious significations, according' to the Problem in use. In Problem IV. it represents Diff. of Long. In Problem V. the Initial Course. In Problem VI. the Complement of the Diff. of Long. In Problem VIII. the Diff. of Long. In Problems X. and XI. the True Azim. Lat HOURS. m m m m m m m m m m m m m m m 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 (4°) UV) (44°) (41°) (5°) (SD (5i°) (51°) (6°) (6i°) (6i°) .(61°) (7°) (7J°) (74°) 0° ■000 -000 -000 -000 - -000 -000 -000 -000 -000 -000 •000 -000 •000 •000 •000 I •250 -23s -222 -210 -200 -190 -181 -173 ■166 -159 -153 -148 •142 •137 ■133 2 •499 •470 ■444 -420 -399 -380 -363 •347 -332 -319 •307 •295 -284 -275 •265 . 3 749 -705 •666 •631 -599 ■570 •544 -521 -499 -479 -460 •443 •427 -412 ■398 X 4 i-ooo -941 -889 -842 ■799 -761 -726 •694 -665 -639 ■614 •591 -570 •550 ■531 "2 5 I "251 I-I77 1-112 1-053 I -000 -952 -909 -869 -832 •799 •768 ■739 •713 -688 •665 § 6° I'soa 1-414 1-335 1-265 1-201 1-144 1-092 1-044 1-000 -960 •923 •888 -856 •826 •798 x" ? 1756 1-652 '■s^? 1-478 1-403 1-336 1-275 1-219 1-168 1-121 1-078 1-037 I^OOO •965 ■933 2"OIO I -891 1-786 1-691 1-606 1-530 1-460 1 -396 1-337 1-283 1-234 I -187 1-145 1-105 1-068 CO S 9 2-265 2-131 2-012 1-906 I -810 1-724 1-645 I -573 1-507 1-446 1-390 1-338 1-290 1-345 1-203 10 2-522 2-373 2-240 2-122 2-0x5 1-919 1-831 1-751 1-678 1-610 1-548 1-490 1-436 1-386 1-339 §2 li" 2-780 2-616 2-470 2-339 2-222 2-115 2-019 1-930 1-849 1-775 1-706 1-642 1-583 1-528 1-476 »£ 12 3-040 2-860 2-701 2-558 2-430 2-313 2-207 2-III 2-022 1-941 1-866 1-796 1-731 1-671 1-615 5 » 13 3-302 3-107 2-933 2-778 2-639 2-513 2-398 2-293 2-197 2-108 2-026 1-951 1-880 1-815 1-754 ■" (5 14 3-566 3-355 3-168 3-001 2-850 2-713 2-589 2-476 2-372 2-277 2-188 2-107 2-031 1-960 1-894 i IS 3-832 3-606 3-405 3-225 3-063 2-916 2-783 2-661 2-549 2-447 2-352 2-264 2-182 2-106 2-035 Is 16° 4-IOI 3-859 ^tt^ 3-451 3-278 3-121 2-978 2-848 2-728 2-6i8 2-517 2-423 2-335 2-254 2-178 ^1 '^ 4-372 4-114 3-8S5 3-679 3-495 3-327 3-175 3-036 2-909 2-792 2-683 2-583 2-490 2-403 2-322 18 4-647 4-372 4-128 3-910 3-714 3-536 3-374 3-227 3-091 2-967 2-852 2-745 2-646 2-554 2-468 19 4-924 ^l^l 4-375 4-144 3-936 3-747 3-576 3-420 3-276 3-144 3-022 2-909 2-804 2-707 2-615 20 5-205 4-898 4-625 4-380 4-160 3-961 3-780 3-615 3-463 3-323 3-195 3-075 2-964 2-861 2-765 o 21° 5-490 5-166 4-877 4-620 4-388 4-178 3-987 3-812 3-652 3-505 3-369 3-243 3-126 3-017 2-916 &»« 22 5-778 5-437 5-134 4-862 4-618 4-397 4-196 4-012 3-844 3-689 3-546 3-414 3-291 3-176 3-069 •9 i^ 23 6-070 5-712 5-393 5-108 4-852 4-620 4-408 4-215 4-039 3-876 3-726 3-586 3-457 3-337 3-224 ■2-1? 24 6-367 5-991 5-657 5-358 5-089 4-845 4-624 4-422 4-236 4-065 3-908 3-762 3-626 3-500 3-382 i«s 25 6-669 6-275 5 -925 5-612 5-330 5-075 4-843 4-631 4-437 4-258 4-093 3-940 3-798 3-666 3-542 §|| 26° 6-97S 6-563 6-197 5-870 5-575 5 -308 5-065 4-844 4-640 4-453 4-281 4-121 3-972 3-834 3-705 3-870 n^S ^ 7-287 7-604 6-856 f'^^t 6-132 5-824 5-545 5-292 5-060 4-848 4-652 4-472 4-305 4-150 4-005 fl ^.S 7-1SS 6-756 ^A^ 6-077 5-787 5-522 5-280 5-059 4-855 4-667 4-492 4-330 4-180 4 -010 .9 5s*' fli .0 29 30 7-927 8-256 7-459 7-769 7-043 7-336 6-671 6-948 6-336 6-599 6-033 6-283 5-757 5-996 5-505 5-734 5-274 5-493 5-061 5-272 4-865 5-067 4-683 4-878 4-514 4-702 4-357 4-538 4-210 4-385 31° 8-593 8-936 9-287 9-646 10-01 8-086 7-635 7-231 6-868 6-539 6-240 5-967 5-717 5-486 S-274 5-077 4-894 4-723 4-564 s *^ 32 8-409 7-940 7-520 7-142 6-Soo 6-490 6-206 5-945 5-706 5-484 5-279 5-089 4-912 4-746 "05 33 8-739 8-252 7-815 7-423 7-067 6-744 6-449 6-179 5-930 5-700 5-487 5-289 5-105 4-933 1^1 34 35 9-077 9-422 8-570 8-897 8-117 8-427 7-710 8-003 7-341 7-620 7-005 7-272 6-699 6-954 6-418 6-662 6-159 6-394 5-920 6-146 5-699 5-916 5-493 5-703 5-302 5-504 5-123 5-319 ^5| 36° 10-39 10-78 9-777 10-14 9-232 9-575 8-744 9-069 8-304 8-613 7-907 8-201 7-826 7-215 7-484 6-913 7-170 6-634 6-881 6-377 6-614 6-139 6-367 5-917 6-137 5-711 5-923 5-519 5-724 5-934 6-151 g tig 11-17 11-58 10-51 9-927 9-402 8-930 !'l°3 8-114 7-759 7-433 7-134 6-857 6-601 6-363 6-141 5 s ** 39 10-90 10-29 9-745 9-256 8-813 8-410 8-042 7-705 7-394 7-107 6-842 6*595 6-365 r 1- 40 12*00 11-29 10-66 10-10 9-591 9-132 8-714 8-333 7-984 7-662 7-365 7-096 6-834 6-596 6-374 41° 42 43 44 45 12-43 12-88 13-34 13-81 14-30 11-70 12-12 12-55 12-99 13-46 11-05 11-44 11-85 12-27 12-71 10-46 10-84 11-22 11-62 1203 9-936 10-29 10-66 11-04 11-43 9-460 9-799 10-15 10-51 10-88 9-028 9-351 9-685 10-03 10-39 8-633 8-942 9-261 9-590 9-931 8-271 8-567 8-872 9-188 9-514 7-937 8-222 8-515 8-818 9-131 7-630 8-185 8-476 8-777 7-345 7-607 7-879 8-159 S-449 7-080 7-333 7-865 8-144 6-833 7-078 7-330 7-591 7-861 6-603 6-839 7-083 7-335 7-596 I!3 46° % 49 SO 14-81 15-34 15-88 16-45 17-04 13-93 14-43 14-95 15-48 16-04 13-16 13-63 14-U 14-62 15-14 12-46 12-91 13-37 13-84 14-34 11-84 12-26 12-69 13-15 13-62 11-27 11-67 12-09 12-52 12-97 10-75 11-14 "•53 11-95 12-38 10-28 10-65 11-03 11-42 11-84 9-852 10-20 10-57 10-95 11-34 9-455 9-792 10-14 10-50 10-88 9-089 9-412 9-748 10-10 10-46 8-749 9-060 9-384 9-719 10-07 8-434 8-734 9-045 9-369 9-706 8-140 8-430 8-730 9-043 9-368 7-866 8-145 8-436 8-738 9-052 51° S2 53 54 55 17-66 18-30 18-98 19-68 20-42 16-62 17-22 17-86 18-52 19-22 16-26 16-86 17-49 18-15 14-86 15-40 16-56 17-19 14-11 14-63 15-17 15-73 16-32 13-44 13-93 14-44 14-98 15-54 12-82 13-29 13-78 14-29 14-83 12-26 12-71 13-18 13-67 14-18 11-75 12-l8 12-63 13-10 13-59 11-28 11 -69 12-12 12-57 13-04 10-84 11-23 11-65 12-08 12-53 10-43 10-81 11-21 11-63 12-07 10-06 10-42 10-81 11-21 11-63 9-707 io-o6 10-43 10-82 11-23 9-380 9-722 10-08 10-45 10-85 1 d 56° 1 21-20 22-02 22-89 23-80 24-77 19-95 20-72 2J-S4 22-40 23-31 18-84 19-57 20-33 21-15 22-01 17-84 18-53 19-26 20-03 20-84 16-95 17-60 18-29 19-02 19-80 16-13 16-76 17-42 i8-n 18-85 15-40 16-62 17-28 17-99 14-72 15-29 15-89 16-53 17-20 14-11 14-65 15-23 15-83 16-48 13-54 14-06 14-61 15-20 15-82 13-01 13-52 14-05 14-61 15-20 12-53 13-01 13-52 14-06 14-63 12-07 12-54 13-03 13-55 14-11 1 1-65 I2-IO 12-58 13-08 13-62 1 1 '26 II -70 I2'l6 12-64 13-16 -1 61° 62 64 65 25-80 26-90 28-07 29-32 30-67 * 24-28 25-31 26-41 27-59 28-86, 22-92 23-90 24-94 26-05 27-25 21-71 22-63 23-62 24-67 25-81 20-62 21-50 22-43 23-44 24-51 19-63 20-47 21-36 22-31 23-34 18-74 19-53 20-38 21-29 22-27 17-92 18-68 19-49 20-36 21-30 17-16 17-89 18-67 19-51 20-40 16-47 17-17 17-92 18-72 19-58 15-83 16-51 17-23 i8-oo 18-82 15-24 17-32 l8'12 14-69 15-32 15-98 16-70 17-47 14-18 14-78 15-43 I6-I2 16-86 13-70 14-29 14-91 15-57 16*29 A 44 m 43 m 42 m 41 m 40 m 39 m 38 ra 37 m 36 ' m 35 m 34 m 33 m 32 m 31 m 30 _ («76°; ('7sr) (1754°) (1751°) (175°) (1741°) (i74i°) (i74i°) (i74°):j (■731°) (■734°) (i73n («73°) (i7an (1724°) II HOURS. ' For the Azimuth .-—The Sign Is always +, except when the Hour- Angle exceeds 6 hours. B The Head-line has various significations, aeeordinpr to the Problem in use. In Problems IV. and VIII. it represents the Diff. of Long. In Problems X. and XI. it represents the True Azimuth. Decl. ' HOURS. in m m m m m m ra m m m m m m m 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 (4°) (4r) (4i°) (41°) (5°) (54°) (5i°) (51°) (6°) (64°) (6n (61°) (7°) (74°) (7n 0° •000 -000 •000 -000 -000 -000 -000 -000 -000 -000 -000 -000 ■000 -000 -000 5 I ■250 -236 -222 -211 -200 -191 •182 -174 -167 -160 •154 -149 •143 -138 -134 fe" 2 •SOI •471 •445 -422 -401 •382 -364 •349 ■334 -321 -308 -297 -287 -277 -268 .0 3 751 •707 -668 •633 -601 •573 -547 •501 -481 -463 •446 -430 -415 ■402 "S 4 I -003 •944 -891 -844 -80a •764 ■730 -698 -669 -642 -618 -595 -574 -554 -536 % S I '254 l-i8i 1-115 1-057 1-004 •956 ■913 •873 -837 -804 -773 ■744 -718 -693 -670 1 6° 1-50; 1-418 1-340. 1-269 l-206 1-149 1-097 1-049 i-oo6 -965 -928 •894 •862 -833 ■805 ^ I 1760 1-657 1-565 r483 1-409 1-342 1-281 1-226 1-I7S 1-128 1-085 1-045 i-oo8 -973 ■941 t 2-015 1-896 1-791 1-697 1-613 i^536 1-466 1-403 1-345 1-291 I -241 I -196 I-IS3 1-114 1-077 .1 9 2-271 2-137 2-019 1-913 .1-817 1-731 1-652 1-581 1-515 1-455 1-399 1-348 1-300 1-255 1-213 10 2-528 2-379 2-247 2-129 2-023 1-927 1-840 1-760 1-687 1-620 1-558 1-500 1-447 1-397 I -351 11° 2-787 2-623 2-477 2-347 2-230 2-124 2-028 1-940 1-860 1-785 1-717 1-654 1-595 1-540 I -489 " Sa 12 3-047 2-868 2-709 2-567 2-439 2-323 2-218 2-122 2-033 1-952 1-878 1-808 1-744 1-684 1-628 Hi 13 3-310 3-115 2-943 2-788 2-649 2-523 2-409 2-304 2-209 2-121 2-039 1-964 1-894 1-829 1-769 ^4 3-574 3-364 3-178 3 -01 1 2-861 2-725 2-601 2-489 2-385 2-290 2 -202 2-121 2-046 1-976 1-910 tm IS 3-841 3-616 3-415 3 •236 3-074 2-796 2-674 2-563 2-461 2-367 2-280 2-199 2-123 2-053 the Pi 3 meri True 16° 4-111 3-869 3-655 3^463 3-290 3'i34 2-992 2-862 2-743 2-634 2-533 2-440 2-353 2-272 2-197 17 4-383 4-125 3-897 3-692 3-508 3-341 3-190 3-052 2-925 2-808 a -701 2-601 2-509 2-423 2-342 18 4-658 4-384 4-141 3-924 3^728 3-551 3-390 3-243 3-108 2-985 2-870 2-764 2-666 2-575 2-489 sal 19 4-936 4-646 4-389 4-158 3-951 3*763 3-593 3-437 3-294 3-163 3-042 2-930 2-825 2-728 2-638 20 5-218 4-911 4-639 4-395 4-176 3-978 3-797 3-633 3-482 3-343 3-215 3-097 2-987 2-884 2-788 .S °1a 1 tag 21° 5-503 5-180 4-893 4-636 4-404 4-195 4-005 3-831 3-672 3-526 3-391 3-266 3-150 3-042 2-941 22 5-792 5-452 5-150 4-879 4-636 4-416 4-21S 4-033 3-865 3-711 3-569 3-437 3-315 3-202 3-095 §^l 23 6-085 5728 5-410 5-126 4-870 4^639 4-429 4-237 4-061 3-899 3-750 3"^" 3-483 3-364 3-252 Ha 24 6-383 6-008 5-675 5-377 5-108 4-866 4-645 4-444 4-259 4-090 3-933 3-788 3-653 3-528 3-411 25 6-685 6-292 5 '943 5-631 5-350 5-096 4-865 4-654 4-461 4-283 4-119 3-967 3-826 3-695 3-573 26° 6-992 6-581 6-216 5-890 5-596 5-330 5-089 4-868 4-666 4-480 4-308 4-150 4-002 3-865 3-737 S>*" 7-304 6-875 6-494 6-153 5-846 5-568 5-316 5-086 4-875 4-680 4-501 4-335 4-181 4-037 3-904 las 28 7-622 7-175 6-777 6-421 6-101 5-811 5-548 5 -307 5 -087 4-884 4-697 4-524 4-363 4-213 4-074 29 7-946 7-480 7-065 6-694 6-360 6-058 5783 5-533 5-303 5-092 4-897 4-716 4-548 4-392 4-247 all 30 8-277 7-791 7-359 6-972 6-624 6-310 6-024 5763 5-523 5-303 5-100 4-912 4737 4-575 4-423 ■a sjcs 31° 32 33 34 35 8-614 8-I08 7-658 7-256 6-894 6-567 6-269 5-997 5-748 5-519 5-308 5-112 4-930 4-761 4-603 S c>4 8-958 8-432 7-964 7-546 7-170 6-829 6-520 6-237 5-978 5-740 5 -520 5-316 5-127 4-951 4-787 0«M 9-310 8-763 8-277 7-842 7-451 7-097 6-776 6-482 6-213 5-965 5-737 5-525 5 -329 5-146 4-975 'Z s 9-669 9-102 8-597 8-145 7-739 7-372 7-037 6-732 6-453 6-196 5-958 5-739 5-535 5-345 5-168 >g3 10-04 9-448 8-924 8-456 8-034 7-652 7-306 6-989 6-699 6-432 6-185 5-957 5-746 5-548 5-364 i^l 36° 39 40 10-42 9-804 9-260 8-774 8-336 7-940 7-580 7-252 6-951 6-674 6-418 6-181 5-962 5-757 5-566 ^^: 10-80 10-17 9-604 9-100 8-646 8-235 7-862 7-521 7-209 6-922 6-657 6-41 1 6-183 5-971 5-773 11-20 10-54 9-958 9-435 8-964 8-538 8-151 7-798 7-474 7-177 6-902 6-647 6-411 6-191 5-986 •^'^"^ 1 1 -61 10-93 10-32 9-779 9-291 8-850 8-449 8-083 7-747 7-438 7-153 6-890 6-645 6-417 6-204 ss^ 12-03 11-32 10-69 10-13 9-628 9-170 8-755 8-375 8-027 7-708 7-412 7-139 6-885 6-649 6-429 41° 42 43 44 45 12*46 11-73 11-08 10-50 9^974 9-500 9-070 8-677 8-316 7-985 7-679 7-396 ^''U 6-888 6-660 gii^ 12-91 12-15 11-48 10-87 io^33 9-840 9-394 8-987 8-614 8-271 7*954 7-661 7-388 7-135 6-898 5-1 a, 13-37 12-58 11-89 11-26 10-70 10-19 9-729 9-308 8-921 8-566 8-238 7-934 7-652 7-389 7-144 5 in the Cirel n-84 13-03 13-49 12-31 11-66 11-08 10-55 10-08 9-639 9-239 8-870 8-531 8-216 7-924 7-652 7-398 14-34 12-75 12-08 11-47 10-93 10-43 9-981 9-567 9-186 8-834 8-508 8-206 7-924 7-661 -^ 46° 49 SO 14-84 13-97 13-20 12-51 11-88 11-32 10-80 10-34 9-907 9-512 9-148 8-810 8-497 8-206 7-934 15-37 15-92 16-49 14-47 14-99 15-52 13-67 14-16 1 4: -66 12-95 13-41 13-89 12-30 12-74 13-20 11-72 12-14 12-57 11-19 11-59 12-00 10-70 11-09 11-48 10-26 10-62 1 1 -01 9-850 10-20 10-57 9-473 9-811 10-16 9-124 9-449 9-787 8-799 g-113 9-439 8-497 8-800 9-116 8-2i6 8-509 8-813 ID 17-08 16-08 15-19 14-39 13-67 13-02 12-43 11-90 11-40 10-95 10-53 10-14 9779 9-443 9-130 51° 52 S3 54 55 17-70 18-35 16-66 17-27 15-74 16-31 14-91 15-46 14-17 14-69 13-50 13-99 12-88 13-35 12-33 12-78 11-81 12-24 11-34 11-76 10-91 11-31 10-51 10-89 10-13 10-50 10-89 9-785 10-14 9-461 9-806 £: 1 9 '02 17-91 16-91 16-03 15-23 14-50 13-85 13-25 12-70 12-19 11-72 11-29 10-52 10-17 1973 18-57 17-54 16-62 15-79 15-04 14-36 13-74 13-17 12-64 12-16 11-71 11-29 10-91 10-54 § 20-47 19-27 18 -20 17-25 16-39 15-61 14-90 14-25 13-66 13-12 12-62 12-15 11-72 11-32 10-94 f 56° 1 21-25 22-07 20-01 20-78 18-90 19-63 17-90 18-60 17-01 17-67 1 6 -20 16-83 15-47 16-07 14-80 15-37 14-18 14-73 13-62 14-14 13-10 13-60 12-61 13-10 12-17 12-64 "75 12-20 12-68 13-19 11-36 11-80 12-26 12-75 22-94 23-86 24-83 21-59 22-46 23-37 20-40 21-21 19-33 20-10 18-36 19-10 17-49 18-19 16-70 17-36 15-97 16-61 15-31 15-92 14-70 15-29 14-14 14-70 13-62 14-16 13-13 13-66 M 22-08 20-92 19-87 18-93 18-07 17-29 16-57 15-91 15-30 14-74 14-21 13-72 13-27 61° 62 65 25-86 26-96 28-14 29-39 3074 24;34 26-48 27-67 28-94 22-99 23^97 25-01 26-13 27 ^33 21-79 22-71 23-70 24-76 25-90 20-70 21-58 22-52 23-52 24-61 19-72 20-55 21-45 22-41 23-44 18-82 19-62 20-48 21-39 22-37 18-01 18-77 19-5? 20-46 21-40 17-26 17-99 18-78 19-61 20-52 16-57 17-28 18-03 18-83 19-70 15-94 16-61 17-34 i8-ii 18-94 15-35 16 -00 16-70 17-44 18-25 14-80 15-43 i6-io 16-82 17-60 14-30 14-90 15-55 16-25 16-99 13-82 14-41 15-04 15-71 16-43 m 44 m 43 m 42 m 41 m 40 m 39 m 38 m 37 m 36 m 35 m 34 m 33 m 32 m 31 m 30 (176°) (175*°) (i75i°) (1754°) (175°) (1741°) (1744°) (I74i°) (174°) (1731°) (1734°) (1734°) (173°) (1721°) (I72i°) 1 II HOURS. f When Latitude and Declination are of contrary names, the Sign is +. For the Azimuth: | ^^^^ Latitude and Declination are of same name, the Sign is -. The Head-line has various significations according to the Problem in use. In Problem IV. it represents Diff. of Long. In Problem V. the Initial Course. In Problem VI. the Cemjilement of the Diff. of Long, in Problem VIIL the Diff. of Long. In Problems X. and XI. the True Azim. Lat. HOURS. m 31 m 32 m 33 m 34 m 35 m 36 m 37 m 38 m 39 m 40 m 41 lU 42 m 43 m 44 m 45 1 (71°) (8°) (8i°) (84°) (81°) (9°) (9r) (9i°) (91') (10°) (ioi°) (lor) (101°) (11°) (iii°) 0° I 2 3 4 5 •000 •128 •514 ■643 •000 -124 •248 •373 •498 -623 -000 •120 ■241 •^82 •603 -000 -117 -234 •351 -468 •585 -000 ■113 -227 -340 -454 ■568 -000 ■no •220 -331 •442 -552 -000 -107 -214 •322 •429 •537 -000 •104 -209 ■313 -418 -523 -000 •102 ■203 •305 •407 -509 •000 -099 •198 •297 -397 -496 -000 •097 ;i93 -484 -000 ■188 •283 •377 -472 ■000 •276 •368 •461 -000 •090 •180 •270 •360 •450 •000 ■088 ■17$ •263 •352 •440 3 So 6° I 9 10 772 •902 1-033 I -164 1-296 •748 ■874 1-000 1-127 1-255 S5 -969 1-092 1-216 ■703 •822 -940 1-060 i-i8o •683 -798 ■913 1-029 1-146 ■664 -887 1-000 1-113 •645 •863 -973 1-083 -628 •734 •840 -946 1-054 -612 -715 -818 -922 1-026 •797 •898 1-000 ■S8i -679 VI -876 -975 •567 •662 •758 •855 •951 -647 -740 -834 -929 -632 ■723 -815 ■907 -528 -617 707 12 13 14 IS 1-428 1-562 1-696 1-832 1-969 1-383 1-512 1-643 1-774 1-907 I -341 1-466 1-592 1-720 1-848 1-301 1-422 I -545 1-668 1-793 1-263 1-381 1-500 1-620 1-741 1-227 1-342 1-458 1-574 1-692 1-194 1-305 1-418 1-531 1-645 1-162 1-270 1-380 1-490 i-6oi 1-131 1-237 1-344 1-451 1-559 1-102 1-205 1-309 1-414 1-520 1-075 1-175 1-277 1-379 1-482 1-049 1-147 1-246 1-345 1-446 1-024 1-120 I -216 1-313 1-411 i-ooo 1-094 1-188 1-283 1-378 •977 1-069 1-161 1-253 1-347 s, according to the the place of Departu observer. i6° 19 20 2-107 2-246 2-387 2-530 2-674 2-040 2-175 2-312 2-450 2-590 1-978 2-109 2-241 2-375 2-510 1-919 2-046 2-174 2-304 2-435 1-863 1-986 2-111 2-237 2-365 1-810 1-930 2-051 2-174 2-298 1-761 1-877 1-995 2-114 2-235 1-714 1-827 1-942 2-058 2-175 1-669 1-779 1-891 2-004 2-ii8 1-626 1-734 1-843 1-953 2-064 1-586 I -691 1-797 1-904 2-013 1-547 1-650 ^Vl 1-858 1-964 1-510 1-610 1-711 1-814 1-917 1-475 1-573 1-672 1-771 1-872 1-442 1-537 1-633 1-731 1-830 21° 22 23 24 25 2-821 2-969 3-119 3-271 3-426 2-731 2-875 3-020 3-168 3-318 2-647 2-787 2-928 3-071 3-216 2-568 2-703 2-840 2-979 3-120 2-494 2-625 2-758 2-893 3-030 2-424 2-551 2-680 2-8ii 2-944 2-357 2-481 2-606 2-734 2-863 2-294 2-414 2-537 2-661 2-787 2-234 2-351 2-470 2-591 2-714 2-177 2-291 2-407 2-525 2-645 2-123 2-234 2-347 2-462 2-579 2-071 2-i8o 2-290 2-402 2-516 2-022 2-128 2-236 2-345 2-456 1-975 2-079 2-184 2-291 2-399 1-930 2-031 2-134 2-238 2-344 ignifleatioD Ship, or of iat. of the 26° 29 30 3-584 3-744 3-907 4-073 4-242 3-470 3-625 3-783 3-944 4-108 3-364 3-514 3-667 3-823 3-982 3-263 3-409 3-558 3-169 3-310 3-455 3-601 3-751 3-079 3-217 3-357 3-500 3-645 2-995 3-129 3-265 3-404 3-545 2-915 3-045 3-177 3-312 3-450 2-838 2-965 3-094 3-226 3-360 2-766 2-890 3-015 3-144 3-274 2-818 2-940 3-065 3-193 2-632 2-749 2-869 2-991 3-II5 2S 2-801 2-920 3-041 2-509 2-621 2-735 2-852 2-970 2-452 2-562 2-673 2-787 2-903 various s he Lat. of 8 sent the I 31° 32 33 35 4-415 4-591 4-772 4-956 5'i4S 4-275 4-446 4-621 4-144 4-310 4-479 4-652 4-829 4-020 4-181 4-345 3-904 4-060 4-219 4-382 4-549 3-794 3-945 4-100 4-259 4-421 3-689 3-837 3-988 4-142 4-299 3-591 3-734 3-881 4-031 4-184 3-497 3-637 3-779 3-925 4-075 3-408 3-544 3-683 3-825 3-971 3-323 3-456 3-591 3-730 3-872 3-242 3-371 3-504 3-639 3-778 3-165 3-291 3-421 3-091 3-215 3-341 3-470 3-602 3-021 3'i4i 3-265 3-391 3-520 he degrees in the margin have VL, and VIIL they represent t they repre 36° 39 40 5-339 5-537 5-741 5-950 6-166 S-170 S-362 5-559 5-762 5-971 5-011 ^311 5-585 5-787 4-861 5-042 5-228 5-4IS 5-615 4-720 4-896 5-076 5-261 5-452 4-587 4-758 4-933 5-113 5-298 4-461 4-627 4-797 4-972 5-152 4-342 4-503 4-669 4-839 5-014 4-228 4-385 4-547 4-713 4-883 4-120 4-274 4-431 4-593 4-759 4-018 4-167 4-321 4-478 4-640 3-920 4-066 4-215 4-369 4-527 3-827 3-969 4-IIS 4-265 4-420 3-738 3-877 4-019 4-166 4-317 3-788 3-928 4-071 4-218 41° 42 43 44 45 6-387 6-616 6-852 7-096 7-348 6-185 6-407 6-635 6-871 7-115 5*995 6-210 6-660 6-897 S-8I7 6-025 6-240 6-462 6-691 5-648 5-850 6-059 6-274 6-497 5-488 5-685 5-888 6-097 6-314 5-338 S-529 5-726 5 -930 6-140 5-195 5-381 5-572 5-771 5 -976 5-059 5-240 5-427 5-620 5-820 4-930 5-106 5-289 S-477 5-671 4-807 4-979 5-157 5-340 5-530 4'^90 4-858 S-031 5-210 5-396 4-579 4-743 4-912 5-086 5-267 4-472 4-632 4-797 4-968 5-145 4-370 4-527 4-688 4-855 5-027 46° % 49 SO 7-880 8-i6i 8-453 8-757 7-368 7-630 7-902 8-185 8-480 7-142 7-396 7-660 7-934 8-219 6-929 7-175 7-697 7-974 6-728 6-967 7-216 7-474 7-743 6-538 6-771 7-012 7-263 7-524 6-358 6-585 6-819 7-064 7-318 6-188 6-408 6-637 6-874 7-122 6-026 6-241 6-463 6-695 6-936 5-873 6-082 6-299 6-524 6-759 5-727 5-930 6-142 6-362 6-590 5-786 5 -992 6-207 6-430 5"iS4 5-648 S-850 6-059 6-277 5-327 5-517 5-714 5-918 6-131 5-206 5-391 5-583 5-783 5-991 Si° 52 S3 54 55 9-074 9-405 9-751 lO-II 10-49 8-787 9-107 9-442 9-793 io-i6 8-517 8-828 9-152 9-493 9-850 8-263 8-564 8-879 9-210 9-556 8-023 8-316 8-622 8-942 9-279 7-797 8-081 8-379 8-690 9-017 7-583 7-859 8-148 8-451 8-769 7-379 7-649 7-930 8-225 8-534 7-187 7-449 7-723 8-010 8-311 7-003 7-259 7-526 7-806 8-099 6-829 7-078 7-339 7-611 7-898 6-663 6-906 7-160 7-426 7-706 6-504 6-742 6-990 7-250 7-522 6-353 6-585 6-827 7-081 7-347 6'2o8 6-672 6-920 7'i8o 3 1 a 56° 10-89 1 1 -3 1 11-76 12-23 12-73 10-55 10-96 11-39 11-84 12-32 10-22 10-62 11-04 11-48 "-95 9-920 10-30 10-71 11-14 11-59 9-632 10 -oo 10-40 10-81 11-25 9-361 9-722 10-10 10-51 10-94 9-103 9-455 9-826 10-22 10-64 8-859 9-202 9-563 9-945 10-35 8-628 8-961 9-313 9-686 io-o8 8-408 8-733 9-076 9-439 9-823 8-199 8-516 8-850 9-204 9-578 7-999 8-308 8-980 9-345 7-809 8-111 8-429 8-766 9-123 7-627 7-922 8-233 8-562 8-911 7-453 7-741 8-045 IS 6i° 62 65 13-26 13-82 14-42 15-07 15-76 12-84 13-38 13-96 14-59 15-26 12-44 12-97 13-54 14-14 14-79 12-07 12-58 13-13 13-72 14-35 11-72 12-22 12-75 13-32 13-93 11-39 11-87 12-39 12-95 13-54 11-08 11-55 12-05 12-59 13-17 10-78 11-24 11-73 12-25 12-82 10-50 10-95 11-42 11-93 12-48 10-23 10-67 11-13 11-63 12-l6 9-977 10-40 10-85 \7^ 9-734 10-15 10-59 11-06 11-57 9-502 9-906 10-34 10-80 11-30 9-281 9-675 10-10 10-55 11-03 9-070 9;455 10-31 10-78 m 29 (I72i°) *28 (172°) 27 (1711°) m 26 (1714°) m 25 (i7ii°) m 24 (171°) m 23 (1701°) m 22 (i7oi°) m 21 (1701°) m 20 (170°) m 19 (1691°) m 18 (■69i°) m 17 (i69i°) m 16 (169°) m (1681°), II HOURS. For the Azimuth .-The Sign is always +, except when the Hour-Angle exceeds 6 hours. B The Head-line has various significations, aeeording to the Problem in use. In Problems IV. and VIII. it represents the Diff. of Long. In Problems X. and XI. it represents the True Azimuth. Decl. HOURS. m m m m m m m m m m m m m m in 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 (0 5 (71°) (8°) (8r) (84°) (81°) (9°) (9i°) (9i°) (91°) (10°) (ioJ)° (104°) (lof) (11°) (iii°) 0° •000 -000 -000 ■000 •000 -000 ■000 -000 •000 -000 •000 -000 -000 -000 -000 I ■129 •125 -122 •118 -IIS •112 -109 ■106 -103 -101 -098 -096 -094 -091 -089 » >» 2 •259 -251 -243 -236 -230 •223 -217 -212 -206 -201 -196 -192 -187 -183 -179 * 43 3 •389 -377 •36s -355 ■345 •335 -326 -318 -309 -302 -295 -288 -281 -275 •269 % 4 •519 -502 -487 -473 -460 ■447 ■435 -424 •413 -403 -393 -384 ■375 -366 -358 0/ i 5 •649 -629 -610 •592 -575 -559 -544 •530 -517 ■504 -492 -480 •469 -459 -448 ° 6° 779 -755 -732 •711 -691 •672 ■654 -637 •621 -605 -591 -577 •563 -551 •539 .1 7 •911 -856 -831 •807 •785 -764 -744 -725 -707 -690 -674 -658 -643 •629 § I -042 i-oio -979 ■951 -924 •898 -874 •852 -830 -809 ■790 -771 -753 •737 •720 9 I-I7S 1-138 1-104 1-072 1-041 1-012 •985 •960 ■935 -912 -890 -869 -849 -830 -812 oi m 10 1-308 1-267 1-229 1-193 1-159 1-127 1-097 i-o68 1-041 1-015 -991 -968 ■945 •924 -904 3 g 11° I -441 1-397 1-355 1-315 1-278 1-243 1-209 1-178 1-148 1-119 1-092 1-067 1-042 1-019 -996 " Ss 12 1-576 1-527 1-481 1-438 1-397 1-359 1-322 1-288 1-255 1-224 1-195 1-166 1-140 1-114 1-090 II 13 1712 1-659 1-609 1-562 1-518 1-476 1-436 1-399 1-363 1-330 1-297 1-267 1-238 1-210 I -183 14 1-849 1-791 1-738 1-687 1-639 1-594 1-551 1-511 1-472 1-436 1-401 1-368 1-337 1-307 1-278 ll^ IS 1-987 1-925 1-867 1-813 1-761 1-713 1-667 1-623 1-582 1-543 1-506 1-470 1-437 1-404 1-373 -^Is 16° 2-126 2-060 1-998 1-940 1-885 1-833 1-784 1-737 1-693 1-651 1-61 1 'VI 1-537 1-503 1-470 2 |S 17 2-267 2-197 2-131 2-068 2-010 1-954 1-902 1-852 1-805 1-761 1-718 1-678 1-639 l-602 'IP 5 ^^ 18 2-409 2-335 2-264 2-198 2-136 2-077 2-021 1-969 I -919 1-871 1-826 'If 3 1-742 1-703 1-665 O .£3S 19 2-553 2-474 2-400 2-330 2-263 2-201 2-142 2-086 2-033 1-983 1-935 1-889 1-846 I -80s 1-765 20 2-699 2-615 2-537 2-462 2-393 2-327 2-264 2-205 2-149 2-096 2-045 1-997 1-951 1-908 1-866 21° 2-847 2-758 2-675 2-597 2-523 2-454 2-388 2-326 2-267 2-21 1 2-157 2-106 2-058 2-012 1-968 22 2-996 2-903 2-816 2-733 2-656 2-583 2-513 2-448 2-386 2-327 2-271 2-217 2-166 2-117 2-071 2-176 2-282 §-'2 23 3-148 3-050 2-958 2-872 2-790 2-713 2-641 2-572 2-507 2-444 2-385 2-329 2-276 2-225 1 sS" 24 3-302 3-199 3-103 3-012 2-927 2-846 2-770 2-598 2-629 2-564 2-502 2-443 2-387 2-333 «5S o Sa 25 3-458 3-351 3-250 3-155 3-065 2-981 2-901 2-825 2-754 2-685 2-621 2-559 2-500 2-444 2-390 26° 3-617 3-505 3-399 3-300 3-206 3-118 3-034 2-955 2-880 2-809 2-741 2-676 2-615 2-556 2-670 2-500 2-612 ^>^ 3-778 3-661 3-551 3-447 3-349 3-257 3-170 3-087 3-009 2-934 2-863 2-796 2-732 28 '3-943 3-820 3-705 3-597 3-495 3-399 3-308 3-222 3-140 3-062 2-988 2-918 2-851 2-787 2-725 2-841 29 4-111 3-983 3-863 3-750 3-644 3-543 3-448 3-358 3-273 3-192 3-115 3-042 2-972 Z^°l ai^ 30 4-281 4-148 4-024 3-906 3-795 3-691 3-592 3-498 3-409 3-325 3-245 3-168 3-095 3-026 2-959 •a sjcs 31° 4-456 4-317 4-187 4-065 3-950 3-841 3-738 3-641 3-548 3-460 3-377 3-297 3-221 3-149 3-080 / S B>< 32 4-634 4-490 4-355 4-228 4-108 3-994 3-887 3-786 3-690 3-598 3-512 3-429 3-350 3-275 3-203 O "-"m 33 34 35 4-816 4-666 4-526 4-394 4-269 4-151 4-040 3-935 3-835 3 '74° 3-650 3-564 ^'fl 3-403 3-329 ■§ s 5-002 4-847 4-701 4-563 4-434 4-312 4-196 4-087 3-983 3-884 3-791 3-701 3-616 3-535 3-670 3-457 3-589 ^§3 5-192 5-031 4-880 4-737 4-603 4-476 4-356 4-242 4-135 4-032 3-935 3-842 3-754 iil 36° 5-388 5-220 5-063 4-915 4-776 4-644 4-520 4-402 4-290 4-184 4-083 3-987 3-895 3-808 3-724 3-863 c4 Sfti »4 MM 5-588 5-415 5-252 5-098 4-954 4-817 4-688 4-566 4-450 4-340 4-235 4-135 4-040 4-189 3-949 39 40 5-794 5-614 5-445 5-286 5-136 4-994 4-860 4-734 4-613 4-499 4-391 4-287 4-095 4-005 •?! 6-005 5-819 5-643 5-479 5-323 S-I77 5-038 4-906 4-782 4-663 4-551 4-444 4-341 4-244 4-151 boQ 6-222 6-029 5-848 5-677 5-516 5-364 5-220 5-084 4-955 4-832 4-716 4-604 4-499 4-398 4-301 41° 42 43 44 45 6*446 6-246 6-058 5-881 5-714 5-557 5-408 5-267 5-133 5-006 4-885 4-770 4-660 4-556 4-456 4-615 4-780 erver. 21° 22 23 24 25 1-887 1-986 2-086 2-188 2-292 1-845 1-942 2-041 2-141 2-242 I -806 I -901 1-997 2-095 2-194 1-768 1-861 1-955 2-051 2-148 1-731 1-822 I -915 2-008 2-103 1-696 1-786 1-876 1-968 2 -06 1 1-663 1-750 1-839 1-928 2-020 1-630 1-716 1-803 1-891 1-980 1-599 1-683 1-768 1-855 1-942 1-569 1-651 1-735 1-819 1-906 1-540 1-620 1-702 1-786 1-870 1-511 1-591 1-671 1-753 1-836 1-484 1-562 1-641 1-722 1-803 1-458 1-535 1-612 1-691 1-771 1-433 1-508 1-740 cations, ac p, or of th of the obs 26° 29 30 2-397 2-504 2-613 2-725 2-838 2-345 2-450 2-556 2-665 2-776 2-295 2-397 2-501 2-608 2-716 2-246 2-347 2-449 2-SS3 2-659 2-200 2-298 2-398 2-500 z-604 2-155 2-252 2-350 2-450 2-552 2-113 2-207 2-303 2-401 2-501 2-071 2-i6< 2-258 2-354 2-452 2-032 2-122 2-215 2-309 2-405 1-993 2-082 2-173 2-265 2-359 1-956 2-044 2-133 2-223 2-316 1-920 2-006 2-094 2-183 2-273 1-886 1-970 2-056 2-143 2-232 1-853 1-935 2-020 2-105 2-193 1-820 1-902 1-984 2-069 2-155 ious signifl Lat. of Shi nt the Lat. 31° 32 33 34 35 2-953 3-071 3-192 3-315 "3-442 2-889 3-004 3-122 3-243 3-366 2-827 2-940 3-055 3-173 3-294 2-767 2-878 2-991 3-107 3-225 2-710 8^8i9 2^929 3-043 3-158 2-655 2-762 2-870 2-981 3^094 2-603 2-707 2-813 2-922 3-033 2-552 2-654 - 2-758 2-865 2-974 2-503 2-603 2-705 2-810 2-917 2-456 2-554 2-654 2-756 2-862 2-410 2-506 2-605 2-705 2-808 2-366 2-460 2-557 2-656 2-757 2-323 2-416 2-511 2-608 2-708 2-282 2-373 2-467 2-562 2-660 2-242 2-332 2-424 2-517 2-613 he margin have var L they represent the they repress 36° 39 40 3-571 3-704 3-840 3-980 4-124 3-493 3-623 3-756 3-893 4-034 3-418 3-545 3-676 3-810 3-948 3-346 3^471 3-598 3-730 3-865 3^277 3^399 3-524 3-653 3-785 3-211 3^330 3-453 3-579 3-708 3-147 3-264 3-384 3-508 3-635 3-086 3-200 3-318 3-439 3-564 3-026 3-139 3-254 3-373 3-495 2-969 3-080 3-193 3-309 3-429 2-914 3-022 3-134 3-248 3-365 2-86i 2-967 3-076 3-189 3^304 2-809 2-914 3-021 3-131 3-245 2-760 2-862 . 2-968 3-076 3-187 2'71I 2-812 2-916 3-022 3-132 41" 42 43 44 45 4-273 4-426 4-583 4-747 4-915 4-179 4-329 4-483 4-643 4-808 4-090 4-236 4^387 4-543 4-705 4-004 4-147 4-295 4-448 4-606 3-921 4-061 4-206 4-356 4-511 3-842 3-979 4-121 4-268 4-419 3-765 3-900 4-039 4-183 4-331 3-692 3-824 3-960 4-101 4-247 3-621 3-750 3-884 4-022 4-165 3-680 3-811 3-946 4-087 3-487 3-611 3-740 3-873 4-011 3^423 3-545 3-672 3-802 3-938 3-361 3-482 3-606 3-734 3^867 3-302 3-420 3-668 3-798 3-244 3-360 3-480 3-604 3-732 OJ oj © ►-5 46" % 49 SO 5-090 5-271 5 "459 5-654 5-858 4-979 5-156 5 -339 5-531 5-730 4-872 5-045 5-225 5-412 5-607 4-769 4-939 5-115 5-298 5-489 4-671 4-837 5-010 S-189 5-376 4-576 4-739 4-908 S-084 5-267 4-485 4-645 4-811 4-983 5-162 4-398 4-554 4-717 4-885 5-061 4-313 4-467 4-626 : 4^792 4-964 4-232 4-382 4-539 4-701 4-870 4-153 4-301 4-454 4-614 4-780 4-077 4-222 4-373 4-530 4-693 4-004 ■ 4^147 4-294 4-448 4-608 3-933 4-073 4-218 4-369 4-527 3-86S 4-002 4-145 4-293 4-448 > 51" 52 53 54 55 6-070 6-291 6-765 7-020 . 5-937 6-IS4 6-380 6-617 6-866 5-810 6-022 6-243 6-475 6-719 5-688 5-895 6-112 6-339 6-578 5 -570 S;773 5 -208 6-442 S-457 5^657 5-865 6-083 6-312 5-349 5-544 5-748 5-962 6-186 5-244 5-636 5-845 6-065 5-144 5 -33 1 5-528 s-733 S-949 S-047 5-231 5-423 5-625 S-836 4-953 5-134 5-322 5^520 5^728 4-862 5-040 5-225 5-420 5 -623 4-775 4-949 5-131 5 -322 5-522 4-690 4-862 5 -040 5-228 5-424 4-609 4-777 4-953 5 -137 5-330 s (D 1 a 56" 59 60 7-287 7-866 8-180 8-513 7-128 7-403 7-694 8-001 8-327 6-975 7-244 7-529 7-830 8-149 6-828 7-092 7-371 7-665 7-977 6-687 6-946 7-219 7-507 7-813 7-072 ' 7-355 7-655 6-422 6-670 6-932 7-209 7-502 6-296 6-540 6-796 7-068 7-356 6-175 6-414 6-666 6-932 7-2:5 6-059 6-293 7-078 5^946 6-176 6-419 6-675 6-947 S-838 6-063 6-301 6^553 6-820 5733 6-43S 6-697 5-631 5 -849 6-078 6-321 6-579 S-533 5-747 5 -973 6-21 1 6-464 61° 62 65 8-867 9-244 9-647 10-08 10-54 8-673 9-042 9-436 9-857 10-31 8-487 8-848 9-233 9-646 10-09 8-309 8-662 9-039 9-443 9-877 8-138 8-483 8-853 9-248 9-673 7-973 , 8-312 8-673 9-061 9-477 7-814 8-146 8-501 8-881 9-289 7-662 7-987 8-335 8-707 9-107 7-S14 ' 7-834 ' 8-175 ' 8-540 8-933 8-021 8-379 8-764 7-236 7-543 7-872 8-223 8-601 7-103 7-405 7-728 8-073 8-444 6-976 7-272 7-589 7-928 8-292 6-852 7-143 7^455 7-788 8-I4S 6-733 7-019 7^32S 7-652 8-003 m 14 ♦ I" 13 m 12 m 11 m 10 m 9 m 8 m 7 m 6 m 5 m 4 m 3 (i6sr) m 2 (i6sn m 1 (i6Si°) m (165°) (i68n (■68i°) (168°) (1671°) (1674°) (i67r) (167°) (1661°) (leei") ' (1661°) (I66-) For the Azimuth ;■ II HOURS. -The Sign is always +, except when the Hour-Angle exceeds 6 hours. B The Head-line has various slgnifleations, according to the Problem in use. In Problems IV. and VIII. it represents the Diff. of Long. In Problems X. and XI. it represents the True Azimuth. Decl. ' HOURS. m m m m m m m ra m m m m m ra m 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 (iii°) (I If) (12°) (12^) (124°) (12!°) (13°) (i3i°) (i3i°) (138°) (14°) (141°) (144°) (141°) (15°) > 7 •616 •603 -591 -579 •567 -556 -546 -536 -526 -517 -508 •4'99 -490 -482 -474 § 8 ■70s •690 -676 -662 -649 -637 -625 -613 -602 -591 -581 -571 -561 •552 -543 ..1 9 ■794 •778 -762 -746 -732 -718 •704 -691 -678 -666 -655 -643 ■633 -622 -612 10 ■884 •866 -848 -831 -815 -799 -784 -769 •755 -742 •729 -716 -704 -693 -681 11° •97S -955 •935 -916 -898 -881 •864 -848 -833 -818 -803 -790 -776 -763 •751 .a s♦' 27 2-556 2-502 2-451 2-401 2-354 2-309 2-265 2-223 2-183 2-144 2-106 2-070 2-035 2-001 1-969 SS>3 28 2-667 2-6ii 2-557 2-506 2-457 2-409 2-364 2-320 2-278 2-237 2-198 2-160 2-124 2-088 2-054 29 2-780 2-722 2-666 2-612 2-561 2-512 2-464 2-418 2-374 2-332 2-291 2-252 2-214 2-177 2-142 all 30 2-896 2-835 2-777 2-721 2-667 2-616 2-567 2-519 2-473 2-429 2-387 2-345 2-306 2-268 2-231 "£* 31° 3-014 2-951 2-890 2-832 2-776 2-723 2-671 2-622 2-574 2-528 2-484 2-441 2-400 2-360 2-322 § c>< -• 3 3-134 3-06S 3-005 2-945 2-S87 2-831 2-778 2-726 2-677 2-629 2-583 2-539 2-496 2-454 2-414 O'-'b, 33 3-257 3-189 3-123 3-061 3-000 2-943 2-887 2-833 2-782 2-732 2-684 2-638 2-594 2-551 ^J°t s* a 34 3-383 3-312 3-244 3-179 3-116 3-056 2-998 2-943 2-889 2-838 2-788 2-740 2-694 2-649 2-606 > S3 35 3-512 3-438 ■ 3-368 3-300 3-235 3-173 3-"3 3-055 2-999 2-946 2-894 2-845 2-797 2-750 270s have inati I Pro 36° 3-644 3-568 3-494 3-424 3-357 3-292 3-230 3-170 3-112 3-057 3-003 2-952 2-902 2-854 2-807 3-780 3-700 3-624 3-552 3-482 3-414 3-350 3-288 3-228 3-170 3-115 3-061 3-010 2-960 2-912 c "« 28 3-919 3-837 3-758 3-6S2 3-610 3-540 3-473 3-409 3-347 3-287 3-229 3-174 3-120 3-069 3-019 .5 o 39 4-062 3-977 3-895 3-817 3-741 3-669 3-600 3-533 3-469 3-407 3-347 3-290 3-234 3-181. 3-129 40 4-209 4-120 4-036 3-955 3-877 3-802 3-730 3-661 3-594 3-530 3-468 3-409 3-351 3-296 3-242 S°l 41° 4-360 4-269 4-181 4-097 4-016 3-939 3-864 3-793 3-724 3-657 3-593 3 -531 3-472 3-414 3-359 gta^ 42 4-516 4-422 4-331 4-244 4-160 4-080 4-003 3-928 3-857 3-788 3-722 3'^lc 3-596 3"IF 3-479 a ►Jo 43 4-677 4-579 4-485 4-395 4-308 4-225 4-145 4-069 3-995 3-923 3-855 3-788 3-724 3-663 3-603 s in ; the Cirel 44 4-844 4-742 4-645 4-551 4-462 4-376 4-293 4-213 4-137 4-063 3-992 3-923 3-857 3-793 3-731 45 5-016 4-911 4-810 4-713 4-620 4-531 4-445 4-363 4-284 4-207 4-134 4-063 3-994 3-928 3-864 <0 -Ejj 46° 5-194 5 "085 4-981 4-880 4-784 4-692 4-603 4-518 4-436 4-357 4-280 4-207 4-136 4-067 4-001 f?i£ 47 5 379 5-266 5-158 5 -054 4-955 4859 4-767 4-679 4-594 4-512 4-433 4-357 4-283 4-212 4-143 ^ £S 48 5-571 5-454 5-342 5-234 5-131 5-032 4-937 4-846 4-757 4-673 4-591 4-512 4-436 4-362 4-291 The ( hey rei 49 5-770 5-649 5-533 5-422 5-315 5-212 5-114 5-019 4-928 4-840 4-755 4-673 4-594 4-518 4-445 50 5-978 5-852 S-732 5-617 5-506 5-400 5-298 5-200 5-105 5-014 4-926 4842 4760 4-681 4-605 51° 6194 6-064 5-940 5-820 5 -706 5-595 5-490 5-388 5-290 5-196 5-105 5-017 4-932 4-850 4-771 +j 52 6-420 6-285 6-156 6-032 5-914 5-800 5-690 5-584 5-483 5-385 5291 5-200 5-112 5-027 4-945 > S3 6-656 6-517 6-383 6-254 6-131 6-013 5-899 5*790 5-685 5-583 5;485 5-391 5 -300 5-212 S-127 1— * 54 6-904 6-759 6-620 6-487 6-359 6-237 6-119 6-005 5-896 5-791 S-592 5-497 5-406 5-318 a 55 7-163 7-013 6-869 6-731 6-598 6-471 6-349 6-231 6-118 6-009 5-903 5-802 5-704 5-609 5-S18 s 56° 7-436 7-280 7'i3i 6-987 6-850 6-718 6-591 6-468 6-351 6-237 6-128 6-023 5-921 5-823 5-728 g 7-724 7-562 7-406 7-257 7-115 6-977 6-845 6-718 6-596 6-479 6-365 6-256 6-150 6-048 5-950 PL, 58 8-027 7-859 7-697 7-542 7-394 7-251 7-114 6-982 6-855 6-733 6-615 6-501 r'F! 6-286 6183 S9 8-348 8-173 8-005 7-844 7-689 7-541 7-398 7-261 7-129 7-002 6-879 6-761 6-647 6-537 ^^'^° HH §6 8-688 8-505 8-331 8-163 8-002 7-848 7-700 7-557 7-420 7-287 7-160 7-036 6-918 6-803 6-692 61° 9-049 8-859 8-677 8-503 8-335 8-174 8-020 7-871 7-728 7-590 7-457 7-329 7 -205 7-086 6-970 62 9-433 9-235 9-046 8-864 8-689 8-522 8-361 8-206 8-056 7-913 7-774 7-640 7-511 7-387 7-267 65 9-844 .-0 9-638 9-440 9-250 9-068 8893 8-725 8-563 8-407 8-257 8-113 7-973 7-839 7709 7-583 10-28 10-07 9-861 9-663 9-473 9-290 9-114 8-945 8-783 8626 ffj 8-329 8-189 8-053 r^i? 10-76 10-53 10-31 10-11 9-908 9-717 9 "533 9-356 9-186 9-022 8-864 8-712 8-565 8-423 8-286 ni m m m m m m m m m m m m m m 14 13 12 11 10 9 8 7 6 5 4 3 2 1 (i68i°) (i68i°) (168°) (1671°) (i67i°) (i67i°) {167°) (1661°) (1664°) (i66r) (166°) (1651°) (1654°) (i6sr) (i6s°) II HOURS. For the Azimuth ■■{ When Latitude- and Declination are of contrary names, the Sign is -f. When Latitude and Declination are of same name, the Sign is — . The Head-line has various significations according to the Problem in use. In Problem IV. it represents Diff. of Long. In Problem V. the Initial Course. In Problem VI. the Complement of the Diff. Of Long. In Problem VIII. the Diff. of Long. In Problems X. and XL the True Azim. Lat. 1 HOUR m m m m m m m m m m in m ni m m 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 (154°) (16°) (i6r) (17°) (i7i°) (18°) (184°) (19°) (194°) (20°) (2on (21°) (214°) (22°) (220 0° ■OCX) •000 -000 •000 -000 ■000 -000 -000 •000 •000 -000 -000 -000 -000 -000 I •063 •061 -059 -057 •OSS -054 •052 •051 -049 -048 -047 -046 -044 •043 -042 _; 2 ■126 -122 •118 •114 -III -108 -104 -101 •099 -096 -093 •091 -089 •086 -084 X 3 •189 -183 •177 -171 -166 -161 -157 -152 -148 -144 -140 -137 -133 -130 •127 ■a 4 •252 ■244 -236 •229 -222 -215 -209 •203 -198 -192 -187 -182 -178 -173 -169 § 5 •3IS •305 -295 •286 •277 -269 -262 •254 -247 -240 -234 -228 •222 •217 -211 X 6° •379 -367 -355. -344 •333 •323 -314 -305 -297 -289 •281 -274 -267 -260 -254 IB I ■443 -428 -415 -402 •389 -378 -367 -357 -347 -337 -328 ■320 -312 •304 -296 • g •507 -490 -474 -460 •446 •433 •420 -408 -397 -386 •376 -366 -357 -348 -339 a £ 9 •571 -552 -535 -518 -502 -487 -473 -460 -447 •435 -424 -413 -402 •392 -382 10 ■636 -615 -595 -577 •559 -S43 -527 -512 -498 -484 -472 -459 •448 -436 -426 11° 701 ■678 -656 -636 -616 ■598 -S8i -565 -549 -534 •520 -506 -493 ■481 -469 as 12 766 ■741 718 -69s -674 -654 -635 •617 •600 -584 -569 -554 •540 -526 -513 ^ 13 •832 -80s -779 -755 -732 711 -690 -670 -652 -634 -618 -601 -586 •571 "557 1 14 •899 -870 •842 -816 -791 •767 -745 -724 -704 -685 -667 ■650 -633 -617 -602 II IS ■966 -934 •905 -876 ■850 •825 -801 -778 -757 •736 -717 -698 -680 -663 -647 i6» I -034 I -000 •968 •938 •909 -883 -857 •833 •810 -788 •767 -747 -728 -710 •692 17 I'I02 1-066 1-032 i-ooo -970 -941 -914 -888 -863 -840 -818 -796 -776 •757 •738 o s 34 2-432 2-352 2-277 2 -206 2-139 2-076 2-016 1-959 1-905 1-853 1-804 1-757 I -712 1-669 1-628 > * 1 SI' 52 S3 54 55 4-453 4-615 4-785 4-963 5-150 4-307 4-464 4-628 4-800 4-981 4-169 4-321 4-480 4-647 4-821 4-039 4-187 4-341 4-502 4-671 3-917 4-059 4-209 4-365 4-530 3-801 3-939 4-084 4-236 4-395 3-691 3-825 3-966 4-114 4-268 3-586 3-717 3-854 3-997 4-148 3-487 3-614 3-747 3-887 4-033 3-393 3-517 3-646 3-782 3-924 3-303 3-423 l^ 3-820 3-217 3-334 3-586 3-720 3-135 3-249 3-369 3-494 3-626 3-056 3-168 3-285 3-407 3-535 2-981 3-090 3-204 3-323 3-448 5 56° i 5 -346 5-553 5-771 6-0OI 6-246 S-170 5-370 5-581 5-804 6-040 5-005 5-198 5-403 5-619 5-847 4-849 5-037 5-234 5-444 S-665 4-702 4-884 5-076 5-278 S-493 4-563 4-739 4-925 5-122 5-331 4-431 4-602 4-783 4-974 S-177 4-306 4-472 4-648 4^833 5-030 4-187 4-348 4-519 4-700 4-891 4-073 4-231 4-397 4-573 4-759 3-965 4-119 4-280 4-451 4-633 3-862 4-011 4-169 4-336 4-512 3-764 3-909 4-063 4-225 4-397 3-669 3 -81 1 3-961 4-119 4-287 3-579 3-864 4-018 4-182 . 61° 62 6-505 6-782 Torn 7-393 7-733 6-291 6-559 6*844 7-150 7-479 6-090 6-349 6-626 6-922 7-240 5-901 6-150 6-419 6-706 7-014 5-722 5-965 6-225 6-503 6-040 6-310 6-600 5-392 5-621 5-866 6-128 6-409 5-239 5-462 5-700 5-955 6-228 5-094 5-311 5-542 5-790 6-056 4-957 5-167 5 -392 5-633 5 -892 4-825 5-030 5-249 5 -484 S-736 4-700 4-899 S-113 S-34I S-587. 4-580 4-775 4-982 5-205 5-444 4-465 4-858 5-075 5-308 4-355 4^540 4^738 4-950 5-177 m 58 fee m 54 m 52 m 50 m 48 m 46 m 44 m 42 m 40 m 38 m 36 m 34 m 32 m 30 1 (i64i°) (164°) (■63i°) (163°) (I62j°) (162°) (i6ij°) (161°) (i6or) (i6o°) (iS9i°) (159°) (>s8n (158°) (iS7i°) 10 HOURS. •=<•' the Azimuth :-The Sign is always +. except when the Hour-Angle exceeds 6 hours. B 10 The Head-line has various signifleations, according to the Problem in use. In Problems IV. and VIII. it represents the Diff. of Long. In Problems X. and XI. it represents the True Azimuth. 1 HOUR. Decl. m m ni m m m m m m m m m m m ni 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 (iSi°) (16°) (i6n (17°) (i7i°) (18'-) m°) (19°) (194°) (20°) (2or) (21°) (2ri°) (22'") (22n C •000 -000 -000 •000 •000 -000 -000 -000 -000 -000 -000 •000 -000 -000 -000 I •06s •063 •061 -060 -058 -057 •055 -054 •052 -051 -050 -049 -048 •047 •046 2 •131 •127 ■123 ■119 -116 -113 -110 -107 -105 -102 -100 -097 •095 -093 -091 1 3 •196 -190 -185 •179 •174 •170 -165 •161 -157 -153 -150 -146 -'43 -140 ■137 ■*J 4 •262 •2S4 -246 -239 -233 •226 •220 -215 -209 -204 •200 -195 -191 -187 •183 ^ 5 •327 •317 -308 -299 -291 -283 -276 •269 -262 •256 •250 •244 -239 -234 •229 -a 01 6° ■393 •381 •370 •359 •350 •340 -331 -323 -31S -307 •300 -293 -287 -281 -275 m 7 •459 •44s •432 -420 -408 •397 ■387 -377 -368 -359 •351 •343 •335 ■328 •321 o p. 8 ■526 ■510 •495 •481 -467 -455 -443 -432 -421 •411 -401 -392 •383 -375 .367 3 9 •393 •S7S •558 -542 -527 •513 -499 -486 -474 •463 •452 -442 -432 -423 •414 10 ■640 •621 •603 -586 •571 -556 •542 ■528 -5i6 -504 -492 -481 -471 •461 i% 11° 727 705 -684 -665 -646 •629 -613 -597 -582 -568 •555 -542 -530 -519 •508 3 M 12 79S ■771 748 •727 •707 -688 -670 ■653 •637 -621 -607 ;593 •fo -567 •555 n S 13 •864 •838 -813 -790 -768 -747 -728 •709 •692 -675 -659 -616 •603 14 •933 -905 -878 -853 ■829 -807 -786 -766 -747 -729 -712 ■696 -680 -666 •652 IS 1-003 -972 -943 -916 ■891 ■867 -844 -823 -803 •783 765 •748 731 715 -700 III 16° 1-073 1-040 i-oio -981 -954 -928 -904 -881 -859 •838 -819 -800 -782 •765 •749 17 I-I44 I -109 1-076 1-046 1-017 -989 •964 ■939 ■916 -894 •873 -853 -834 -816 •799 *^ "S* 18 I -216 I-I79 1-144 i-iii 1081 1051 1-024 -998 -973 -950 -928 •907 -887 -867 •849 > 27 I -907 1-849 I '794 1-743 1-694 1-649 I 606 1-565 1-526 1-490 1-455 1-422 1-390 1-360 I -331 flag 28 1-990 1-929 1-872 1-819 1-768 1-721 1-676 1-633 1-593 1-555 I -518 1-484 1-451 1-419 1-389 •^c^ 29 2-074 2-01 1 1-952 1-896 1-843 1794 1-747 1-703 1-661 1-621 1-583 1-547 1-512 1-480 1-448 30 2-i6o 2-095 2-033 1-975 1-920 1-868 1-820 1-773 1-730 1-688 1-649 I -61 1 1-575 1-541 1-509 31° 2-248 2-180 2-116 2-055 1-998 1-944 1-894 1-846 i-8oo 1757 1-716 1-677 1-639 '1?t 1-570 32 2-338 2-267 2-200 2-137 2-078 2-022 1-969 1-919 1-872 1-827 1-784 1-744 1-705 1-668 1^633 a Sos 33 2-430 2-356 2-287 2-221 2-i6o 2-102 2-047 1-995 1-945 1-899 1-854 1-812 1-772 1734 1-697 34 2-524 2-447 2-375 2-307 2-243 2-183 2-126 2-072 2-021 1-972 1-926 1-882 1-840 I -801 1-763 35 2-620 2-540 2-465 2-395 2-329 2-266 2-207 2-151 2-098 2-047 1-999 1-954 1-9H 1-869 1-830 i i 36° 2-719 2-636 2-558 2-485 2-416 2-351 2-290 2-232 2-177 2-124 2-075 2-027 1-982 1-939 1-899 > as 2-820 2-734 2-653 2-577 2-506 2-439 2-375 2-315 2257 2-203 2-152 2-103 2-056 2-012 1-969 ive atic Pro 39 2-924 3-030 2-834 2-938 2-751 2-851 2-672 2-770 2-598 2-693 2-528 2-621 2-462 2-552 2-400 2-487 2-341 2-426 2-284 2-368 2-231 2-312 2-180 2-260 2-132 2-209 2-086 2-162 2-042 2-116 i-5fl 40 3-140 3-044 2-954 2-870 2-790 2715 2-644 2-577 2-514 2-453 2-396 2-341 2-289 2-240 2-193 Is- +3 »< 41* 3'2S3 3-154 3-061 2-973 2-891 2-813 2-740 2-670 2-604 2-542 2-482 2-426 2-372 2-321 2-272 42 3 '369 3-267 3-170 3-080 2-994 2-914 2-838 2-766 2-697 2-633 ^■|?' 2-513 2-457 2-404 2-353 43 3 '489 3-383 3-283 3-189 3-IOI 3-018 2-939 2-864 2-794 2-726 2-663 2-602 2-544 2-489 2-437 44 3"6i4 3-50; 3-400 3-303 3-211 3-125 3-043 2-966 2-893 2-823 2-757 2-695 2-635 2-578 ^Tl 2^ d iJ 0) 45 3742 3-628 3-521 3-420 3-326 3-236 3-152 3-072 2-996 2-924 2-855 2-790 2-729 2-669 2-613 in t the Cirel 46° 3 '875 3-757 3-646 3-542 3-444 3-351 3-264 3-181 3-102 3 028 2-957 2-890 2-825 ''Ifit 2-706 47 4-013 3-891 3776 3-668 3-566 3-470 3-380 3-294 3-213 3-135 3-062 2-992 2-926 2-863 2-802 M -e+j 48 4-156 4-029 3-910 3-799 3-693 3 '594 3-500 3 -41 1 3-327 3-247 3-171 3-099 3-030 2-965 2-902 49 4 '305 4-173 4-050 3-935 3-826 3723 3-625 3-533 3-446 3-363 3-285 3-21C 3-139 3-071 3-006 III 50 4460 4-324 4-196 4-076 3-963 3-857 3-756 3-661 3-570 3-484 3-403 3-326 3-252 3-181 3-114 ^1 51° 4-621 4-480 4-348 4-224 4-107 3-996 3892 3-793 3-699 3-611 3526 3-446 3-369 3-297 3-227 a, 1^ 52 4-790 4-644 4-507 4-378 4-256 4-142 4-034 3-931 3-834 ^'li^ 3-655 3-572 3-492 3-417 ^'^il S3 4-966 4-814 4-672 4-539 4-413 4-294 4-182 4076 3-975 3-880 3-789 3-703 3-621 3-543 3-468 54 5-150 4-993 4-846 4-708 4-577 4-454 4-338 4-228 4-123 4-024 3-930 3-841 3755 3-674 3-597 55 5*344 5-181 S-028 4-885 4-749 4622 4-501 4-387 4-278 4176 4078 3-985 3-897 3-812 3732 fc 56° 5 '548 5-379 5-220 5-071 4-930 4-798 4-672 4-554 4-441 4-335 4-233 4-137 4-045 3-958 3-874 a 5-762 5-587 5-422 5-267 5-121 4-983 4-853 4-730 4-613 4-502 4-397 '^■''I^ 4-202 4'iii 4024 l—t eg 5-988 5635 5^474 5-322 S-179 5-044 4-916 4-794 4-679 4-570 4-466 4-367 4-272 4-182 ■g 59 6-228 6-038 5-860 5-692 5-535 5-386 5-245 S-112 4-986 4-866 4-752 4-644 4-541 4-443 4-349 £ 60 6-481 6-284 6-098 5-924 5-760 5-605 5-459 5 -320 S-189 5-064 4-946 4-833 4-726 4-624 4-526 ^ 61° 6-751 6-545 6-352 6-170 5-999 5-838 5-686 5-541 5-404 5-275 S-151 5 -034 4-922 4-816 4714 62 7-038 7-'?44 6-823 6-622 6-433 6-254 6086 5 -927 5-777 5-634 5^499 5-370 5-248 5-132 5-021 4-91S 63 W w — J 7*120 6 9 10 6-713 6-527 6-351 6185 6-028 5-879 5738 5-604 5-477 5-355 5-239 5-129 64 7-672 / _ 7-438 7'2i9 7-013 6818 6-635 6-462 6-298 6-142 5-995 5-855 5-721 5-594 5-473 5-358 65 8-025 7-780 7-551 7-335 7-132 6-940 6-759 6-587 6-424 6-270 6124 5 -984 5-851 5 -725 5-604 ni m m m m m m m m m m ra in m m 58 56 54 52 50 48 46 44 42 40 38 36 34 32 30 (i64i°) (164°) (1631°) (163°) (1624°) (162°) d6ir) (161°) (1604°) (160°) (I59i°) (159°) (i58i°) (158°; (iS7i°) For the Azimuth: 10 HOURS. When Latitude and Declination are of contrary names, the Sign is +. When Latitude and Declination are of same name, the Sign is — . 11 The Head-line has various significations, aeeordinir to the Problem In use. In Problem IV. it represents Diff. of Long. In Problem V. the Initial Course. In Problem VI. Complement of the Diflf. of Long. In Problem VIII. the Diff. of Long. In Problems X. and XI. the True Azim. the Lat. 1 HOUR. m m m m m m m ra m m m m m m m 32 34 36 38 40 42 44 46 48 50 52 54 56 58 60 (23°) (23i°) (24°) (24i°) (25°) (25i°) (26°) (26i°) (27°) (27i°) (28°) (284°) (29°) (294°) (30°) 0° •000 -000 -000 ■000 -000 -000 -000 -000 -000 -000 -000 -000 •000 -000 -000 I ■041 -040 -039 •038 -037 -037 -036 -03s -034 -034 -033 -032 •031 •031 -030 2 •082 -080 -078 •077 •075 •073 -072 -070 -068 -067 -066 -064 ■063 -062 -060 , 3 ■123 -121 •118 •IIS -112 -110 -107 •105 -103 -101 -099 -097 -095 -093 -091 >^ 4 •16s -161 •157 -153 ■150 •147 -143 -140 -137 -134 -132 -129 -126 •124 •121 ■2 5 •206 -201 -197 -192 -188 •183 -179 -17s -172 -168 -16s -161 -158 ■15s -152 § 6° •248 -242 •236 -231 •225 -220 -215 -211 -206 -202 -198 •194 -190 -1S6 -182 X- 7 ■289 -282 •276 •269 -263 •257 •252 -246 -241 •236 -231 -226 -222 -217 •213 8 •331 -323 -3r6 -308 •301 •295 -288 -282 •276 -270 -264 -259 -254 -248 -243 CO J 9 •373 •364 -356 -348 -340 •332 -32s •318 •311 -304 -298 -292 -286 -280 -274 10 •41S •406 -396 •387 -378 •370 •362 •354 •346 -339 -332 -325 ■318 •312 -305 is 11° •458 -447 •437 -427 •417 -408 -399 •390 •38! -373 •366 •358 -351 -344 -337 s« 12 •SOI -489 -477 -466 -456 -446 •436 -426 -417 -408 -400 •391 -376 -368 .a fl 13 ■544 -531 -519 •507 •495 •484 -473 •463 -453 ■443 •434 -42s -416 -408 •400 " i-( 14 •S87 •573 -560 ■547 -535 •523 •511 •500 -489 -479 -469 -459 -450 -441 -432 § IS •631 -616 -602 -588 •575 ■562 •549 -537 -526 -515 -504 -494 -483 -474 -464 11 16° •676 -659 -644 •629 •615 •601 •588 -S7S -563 -551 -539 •528 ;si7 -507 ■497 % 720 -703 -687 -671 -656 -641 -627 -613 •600 -S87 -575 -563 ■540 -530 18 76s -747 -730 -713 -697 •681 -666 -652 •638 -624 -611 -598 ■586 -574 '•563 19 •811 -792 -773 •756 •738 -722 ■706 •691 -676 -661 -648 -634 •621 -609 '-596 20 •858 -837 -817 -799 -781 •763 -746 ■730 ■714 -699 -685 -670 -657 -643 •630 -^ 21° •904 -883 •862 -842 •823 •80s •787 -770 •753 •737 -722 -707 -693 •678 -66s §■» . 22 ■952 -929 •907 -887 -866 -847 •828 -810 •793 -776 -760 -744 •729 -714 -700 .3 o»; 23 I'OOO -976 •953 -931 -910 -890 •870 -851 •833 -815 -798 -782 •766 -750 -73s 24 I •049 1-024 I -000 •977 •9SS •933 •913 -893 -874 •855 ■837 -820 -803 -787 771 25 1-099 1-072 1-047 1-023 I -000 ■978 -956 -935 -915 -896 -877 •859 -841 -824 •808 «5| 26° I -149 1-122 1-09S 1-070 1-046 1-023 l^OOO -978 -957 •937 •917 -898 -880 -862 -84s 2 o2 27 I -200 I -172 1-144 1-118 1-093 1-068 1-045 1-022 I -000 -979 -958 -938 -919 -901 ■883 9 *^ 28 I -253 1-223 I -194 1-167 I -140 1-115 1-ogo 1-066 1-044 1-021 1-000 -979 ■959 ■940 -921 25 W ^^ 29 1-306 1-275 1-245 1-216 1-189 1-162 1-137 I-I12 1-088 1-065 1-043 1-021 I -000 -980 -960 30 1-360 1-328 1-297 1-267 1-238 1-210 1-184 1-158 1-133 I -109 1-086 1-063 1-042 1-020 1-000 31° I -416 1-382 1-350 1-318 1-289 1-260 1-232 1-205 I -179 I -154 1-130 1-107 1-084 1-062 1-041 32 1-472 1-437 1-403 1-371 1-340 1-310 1-281 1-253 1-226 1-200 1-175 1-151 1-127 1-104 1-082 «'g» 33 I-S30 1-494 1-459 1-425 1-393 1-362 1-331 1-303 1^275 1-248 1-221 1-196 1-172 1-148 1-125 a+i*" 34 1-589 1-551 1-515 1-480 1-446 1-414 1-383 1-353 1-324 1-396 1-269 1-242 1-217 1-192 ri68 3 o8« 35 1-650 1-610 1-573 1-536 1-502 1-468 1-436 1-404 1^374 1-345 1-317 1-290 1-263 1-238 1-213 ISs 36° 1-712 1-671 1632 1-693 1-594 1-558 1-523 1-490 1-457 1-426 1-396 1-366 1-338 1-311 1-284 1-258 !^^a 37 1 775 1-733 1-654 i-6i6 1-580 1-545 1-511 1-479 1-448 1-417 1-388 1-359 1-332 1-305 i|2 38 I -841 1-797 1-755 1-819 1-885 1-714 1-675 'I38 1-602 1-S67 1-533 1-501 1-469 1-439 1-409 1-381 1-353 39 1-908 1-862 1-777 1-737 1-698 1-660 1-624 1-589 1-556 1-523 1-491 1-461 i"43i 1-403 40 1-977 1-930 1-841 1-799 1-759 1-720 1-683 1-647 I -612 1-578 1-545 1-514 1-483 1-453 41° 2-048 1-999 1-952 1-907 1-864 1-822 1-782 1-744 1-706 1-670 1-635 1-601 1-568 1-536 1-506 %< fH 42 2-121 2-071 2-022 1-976 1-931 1-888 1-846 1-806 1-767 1-730 1-693 1-658 1-624 1-591 1-560 lo 43 2-197 2-145 2-094 2-169 2-246 2-046 2-000 1-955 1-912 1-870 1-830 1-791 1-754 1717 1-682 1-648 1-615 ^5 44 2-275 2-221 2-H9 2-071 2-025 1-980 1-937 1-895 1-855 I -816 1-779 1-742 1-707 1-673 5 a 45 2-356 2-300 2-194 2-145 2-097 2-050 2 -006 1-963 1-921 I -881 1-842 1-804 1-767 1-732 .S^ 46° 2-440 2-382 2-326 2-272 2-221 2-171 2-123 2-077 2-032 1-989 1-948 1-907 1-868 1-830 1-794 sl ""l ^■f^ 2-466 2-409 2-353 2-300 2-248 2-199 2-151 2-105 2-060 2-017 1-975 1-935 2-004 1-895 1-963 1-857 48 2-616 fl5^ 2-494 2-584 2-677 2-437 2-382 2-328 2-277 2-228 2-180 2-133 2-089 2-045 1-924 49 2-710 2 646 2-524 2-467 2-412 2-359 2-307 2-258 2-210 a-164 2-iig 2-075 2-033 1-992 50 2-808 2-741 2-615 2-556 2-499 2-443 2-390 2-339 2-289 2-241 2-195 2-150 2-io5 2-064 'a> SI- 2-909 2-840 2-774 2-875 2-981 3-091 3-208 2-710 2-648 2-589 2-532 2-477 2-424 2-372 2-323 2-274 2-228 2-18^ 2-139 52 i:?'l 2-944 2-809 2-745 2-683 2-624 2-567 2-512 2-459 2-407 2-357 2-309 2-262 2-217 2 S3 54 SS 3-126 3-243 3-36S 3-052 3-165 3-285 2-912 3-020 3-134 2-846 2-952 3-063 2782 2-886 2-994 2-721 2-822 2-928 2-662 2761 2-864 2-604 2-701 2-803 2-549 2-644 2-743 2-496 2-589 2-686 2-444 2-535 2-630 2-394 2-483 2-576 2-346 2-433 2-524 2-299 2-384 2-474 § 56- 3*493 3-410 3-330 3-253 3-179 3-108 3-040 2-974 2-910 2-848 2-788 2-731 2^675 2-887 3-002 3-125 2-620 2-568 2-667 2-772 2-S33 3-000 1 5 1 3-628 3-770 3-921 4-080 3-541 3-681 3-828 3-983 3-459 3-594 3-738 3-890 3-379 3-512 3-652 3-801 3-302 3-432 3-569 3714 3-228 3-355 3-489 3-631 3-157 3-281 3-412 3-551 3-088 3-210 3-338 3-474 3-022 3-141 3-266 3-399 2-958 3-074 3-197 3-327 2-896 3-010 3-130 3-258 2-836 2-947 3-065 3-190 2-722 2-829 2-942 3-061 6i' 62 65 4-250 4-431 4-624 4-830 5-052 4-149 4-325 4-514 4-71S 4-932 4-052 4-224 4-408 4-605 4^817 3-959 4-127 4-307 4-499 4-706 3-869 4-033 4-209 4-397 4-599 3-782 3-943 4-115 4-299 4-496 3-69? 3-856 4-024 4-204 4-397 3-6i8 3-772 3-936 4-112 4-301 3-541 3-691 3-852 4-024 4-209 3-466 3-613 3-770 3-939 4-120 3-393 3-537 3-691 3-856 4-033 3-323 3-464 3-615 3-776 3-950 3-255 3-393 3-541 3-699 3-869 3-189 3-324 3-469 3-624 3-790 3-125 3-258 3-399 3-551 3-714 m* 28 .26 m 24 m 22 m 20 m 18 m 16 m 14 m 12 m 10 m 8 m 6 m 4 m 2 m . (157°) (•56r) .{156°; (155*°) (155°) (1544°) (154°) ('S3i°) («53°) (1524°) (152°) (iSii°) (151°) (1504°) (150°) 10 HOURS. For the Azimuth. --The Sign is always +, except when the Hour-Angle exceeds 6 hours. B 12 The Head-line has various significations, according to the Problem in use. In Problems IV. and VIII. it represents the Difl". of Long. In Problems X. and XI. it represents the True Azimuth. 1 HOUR. Decl. m in m in m m m m m m m m m m m 32 34 36 38 40 42 44 46 48 50 52 54 56 58 ,60 . (23°) (234°) (24°) (244°) (25°) (2Si°) (26°) (264°) (27°) (274°) (28°) (284°) (29°) (294°) (30°) 0° •CXX) -000 •000 -000 •000 -000 •000 •000 •000 -000 •000 ■000 -000 •000 ■000 +3 I •04s '°^ -043 •042 •041 -041 •040 -039 -038 •038 •037 -037 -036 -035 -035 ^ 2 •089 -088 •086 •084 •083 -081 -080 •078 -077 •076 •074 •073 ■072 •071 -070 iQ 3 ■134 -131 -129 •126 •124 -122 -120 -117 -115 -113 -112 -110 -108 -106 -105 ffl 4 •179 -175 -172 -169 -165 -162 -160 -157 ■•154 -151 •149 -147 -144 -142 •140 n 5 •224 •219 •215 •211 •207 -203 -200 -196 -193 •189 -186 -1S3 -180 -178 •175 o 6° •269 •264 ■258 -253 -249 -244 -240 -236 •232 -228 •224 -220 -217 •213 .•210 >i i ■3i'l -308 ■302 •296 •291 -285 •280 -275 -270 -266 •262 -257 -253 -249 •246 "3 •360 -352 -346 -339 -333 -326 •321 -315 -310 -304 -299 -295 •290 •285 •281 > 9 ■405 •397 -389 -382 -375 -368 -361 -355 •349 -343 -337 -332 -327 -322 -317 it 10 •451 •442 •434 -425 -417 -410 •402 -395 •388 •382 -376 -370 -364 -358 -353 11° •497 -487 •478 •469 •460 -452 -443 -436 •428 •421 •414 -407 •401 -395 -389 i!l 12 ■544 -533 •523 -513 •503 -494 •485 -476 •468 ■460 -453 -445 -438 -432 -425 13 •591 -579 •568 -557 -546 -536 -527 •517 •509 -500 -492 -484 -476 -469 •462 ■2 is 14 •638 -62s •613 •601 -590 •579 •569 -559 -549 -540 -531 •523 -514 -506 -499 IS •686 ■672 •659 •646 -634 -622 -611 •601 -590 -580 -571 -S62 -553 -544 -536 |a| 16° 734 •719 •70s -691 -678 -666 -654 -643 -632 -621 •611 -601 -591 •582 -573 17 782 •767 •752 -737 -723 •710 -697 -685 -673 -662 -651 IS" .631- •621 •611 18 •832 -815 -799 •784 -769 -755 -741 •728 •716 -704 -692 -681 -670 -660 -650 2 5| SB'S II 19 •881 -864 •847 •830 •81S -Soo -78s -772 -758 -746 -733 -722 -710 -699 ■689 20 ■932 -913 -89s •878 -861 ■84s •830 -816 •802 -788 •775 •763 •751 -739 -728 fe tag 21° ■982 -963 -944 -926 -908 •892 -876 -860 -846 ■831 -818 •804 -792 •780 •768 22 i'034 1-013 -993 -974 •956 -938 -922 -905 -890 -875 -86 1 -847 -833 •820 -808 8^1 23 I -086 1-065 1-044 1-024 1-004 -986 -968 -951 -935 •919 -904 -890 •876 -862 -849 o CD Sr en ^ 24 I -139 1-117 1-095 1-074 1-054 1-034 1-016 -99S •981 -964 -948 -933 -918 -904 -890 25 I -193 1-169 I -146 1-124 1-103 1-083 1-064 1-045 1-027 i-oio -993 -977 -962 -947 -933 26° 1-248 1-223 1-199 1-176 1-154 1-133 1-113 1-093 1-074 1-056 1-039 1-022 1-006 -990 -975 ^>*' 27 1-304 1-278 1-253 1-229 l-206 1-184 I -162 1-142 1-122 I -103 1-085 1-068 1-051 1-035 1-019 28 1-361 1-333 1-307 1-282 1-258 1-235 1-213 1-192 1-171 1-152 1-133 1-114 1-097 1-080 1-063 29 I -419 1-390 1-363 1-337 I-3I2 1-288 1-264 1-242 I -221 1-200 1-181 1-162 1-143 1-126 1-109 a|-§ 30 1-478 1-448 1-419 1-392 1-366 1-341 1-317 1-294 1-272 1-250 1-230 1-210 I -191 1-172 1-155 l^"- 31° 1-538 1-507 1-477 1-449 1-422 1-396 1-371 1-347 1-324 1-301 1-280 1-259 1-239 1-220 1-202 -3 cX 32 1-599 1-567 1-536 1-507 1-479 1-451 1-425 1-400 1-376 1-353 I -331 1-310 1-289 1-269 1-250 S"2 33 1-662 1-629 1-597 1-566 1-537 1-508 I -481 1-455 1-430 1-406 1-383 1-361 1-340 1-319 1-299 1 J 34 1-726 1-692 1-658 1-627 1-596 1-567 1-539 1-512 1-486 1-461 1-437 1-414 1-391 1-370 1-349 35 1-792 1-756 1-722 1-688 1-657 1-626 1-597 1-569 1-542 1-516 1-491 1-467 1-444 1-422 1-400 p£ 36° 1-859 1-822 1-786 1-752 I -719 1-688 1-657 1-628 1-600 1-573 1-548 1-523 1-499 1-475 1-453 AS'i 1-929 1-890 1-853 1-817 1-783 1-750 1-719 1-689 1-660 1-632 1-605 1-579 1-554 1-530 1-507 «s- 38 2-000 1-959 1-921 1-884 1-849 1-815 1-782 1-751 1-721 1-692 1-664 1-637 1-612 1-587 1-563 39 2-072 2-031 1-991 1-953 1-916 1-881 1-847 1-815 1-784 1-754 1725 1-697 1-670 1-644 1-620 40 2-148 2-104 2-063 2-023 1-985 1-949 1-914 1-881 1-848 I -817 1-787 1-759 1-731 1-704 1-678 a'S 41° 2-225 2-180 2-137 2-096 2-057 2-019 1-983 1-948 1-915 1-883 1-852 1-822 1-793 1-765 1-739 »taS 43 43 2-304 2-258 2-214 2-171 2-131 2-091 2-054 2 -018 1-983 1-950 1-918 1-887 1857 1-829 1-801 5^.2 2-387 2-339 2-293 2-249 2-207 2-166 2-127 2-090 2-054 2-020 1-986 1-954 1-923 1-894 1-865 o S g 44 45 2-471 2-422 2-374 2-329 2-285 2-243 2-203 2-164 2-127 2-091 2-057 2-024 1-992 1-961 1-931 :!§ 2-559 2-508 2-459 2 -41 1 2-366 2-323 2-281 2-241 2-203 2-166 2-130 2-096 2-063 2-031 2-000 gi^ 46° tl 49 SO 2-650 2-597 2-546 2-497 2-450 2-405 2-362 2-321 2-281 2-243 2-206 2-170 2-136 2-103 2-071 60 gg 2-745 2-689 2-637 2-586 2-537 2-491 2-446 2-403 2-362 2-322 2-284 2-247 2-212 2-178 2-145 2-842 2-785 2-731 2-678 2-628 2-580 2-533 2-489 2-446 2-405 2-366 2-328 2-291 2-255 2-221 2-944 2885 2-828 2-774 2-722 2-672 2-624 2-578 2-534 2-491 2-450 2-411 2-373 2-336 2-301 3-050 2-989 2-930 2-874 2-820 2-768 2-719 2-671 2-625 2-581 2-538 2498 2-458 2^420 2-384 Si° 52 53 54 55 3-160 ■2-276 3-097 3-036 2-978 2-922 2-868 2-817 2-768 2-720 2-674 2-630 2-588 2-547 2^508 2-470 S 3-210 3-147 3-086 3-029 2-973 2-920 2-869 2-819 2-772 2-726 2682 2-640 2-599 2*560 2-654 ^ 3-396 3-328 3-263 3-200 3-140 3-082 3-027 2-974 2-923 2-874 2-827 2-781 2-737 2-839 2-946 2-695 s 3-523 3-452 3-384 3-319 3-257 3-197 3-140 3-085 3-032 2-9S1 2-932 ■ 2-885 2-795 2-753 2-856 s 3-655 3-582 3-511 3-444 3-379 3-317 3-258 3-201 3-146 3-093 3-042 2-993 2-900 1 56° i 3*794 3-718 3-645 3-575 3-508 3-444 3-382 3-323 3-266 3-211 3-158 3-107 3-058 3-176 3-011 2-965 3^080 o 3-941 4-096 4-259 4-433 3-862 3-786 3-713 3-644 3-577 3-513 3-451 3-392 3 '311 3-280 3-227 3-127 04 4-013 3-935 3-859 3-787 3-717 3-651 3-587 3-525 3-466 3-409 3"3S4 3-301 3-250 3-201 a 4-174 4-344 4-092 4-258 4-013 4-177 3-938 4-098 3-866 4-023 3-797 3-951 3-730 3-882 3-666 3-815 3-604 3-751 3-545 3-689 3-488 3-630 3-433 3-573 3-517 3-329 3-464 61° 4-617 4-524 4-435 4-350 4-269 4-190 4-115 4-043 3-974 3-907 3-843 3-781 3-721 3-879 4-048 3-664 3-819 3-986 3-608 3-761 62 4-813 5-023 5-247 5-488 4-717 4-624 4-535 4-450 4-369 4-290 4-215 4-143 4-073 4-006 3-942 64 65 4-922 4-825 4-733 4-644 4-559 4-477 4;399 4-323 4-250 4-180 4-113 3-925 5-142 5-378 5-041 5-272 4-944 5-171 4-851 5 -074 4-762 4-981 4-677 4-892 4-806 4-516 4-724 4-440 4-644 4-367 4-568 4-297 4-494 4-229 4-423 4-164 4-355 4-101 4-289 m 28 m 26 m 24 m 22 m 20 m 18 m 16 m 14 m 12 m 10 m 8 m 6 m 4 m 2 m (157°) (i56i°) (156°) (=554°) (155°) (1544°) (154°) (1534°) (153°) (1524°) (152°) (1514°) (151°) (1504°) (150°) 10 HOURS. f When Latitude and Declination are of contrary names, the Sign is +. For the Azimuth: | ^^^^^ Latitude and Declination are of same name, the Sign is — . 18 The Head-line has various significations aeeording to the Problem in use. In Problem IV. it represents Difif. of Long. In Problem V. the Initial Course. Complement of the Diff. Of Long. In Problem VIIL the Diff. of Long. In Problem VL the in Problems X. and XI. the True Azim. Lat. 2 HOURS. m m m m m m m m m m m m m ra m 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 (3oi°) (31°) (3ii°) (32°) (324°) (33°) (334°) (34°) (344°) (35°) (354°) (36°) (364°) (3^) (374°) 0° •000 ■000 ■000 -000 •000 •000 •000 •000 -000 -000 -000 •000 •000- -000 -000 I •030 ■029 -028 ■028 ■027 •027 •026 •026 •025 -025 •024 •02i. ■024 -023 -023 . 2 •059 -058 -057 •056 •OSS •054 ■053 •052 •051 -050 -049 •04! -047 -046 -046 X 3 ■089 -087 -086 •084 -082 •081 •079 •078 •076 •075 -073 •072 -071 -070 -068 •d 4 ■119 -116 -114 ■112 -no •108 •106 •104 •102 -100 •098 •096 -09s -093 -091 § 5 •149 -146 -143 -140 •137 ■13s •132 •130 •127 -125 -123 •120 -118 •116 •114 >< 6° ■178 -I7S •172 ■168 -165 •162 •159 •156 -153 ■150 -147 •145 -142 •139 -137 09 I ■208 -204 •200 •196 -193 •189 •186 •182 •179 -175 •172 •169 -166 •163 -160 a •239 -234 -229 •225 -221 •216 •212 •208 •204 •201 -197 -193 -190 -187 -183 aj a> 9 •269 -264 -258 -253 -249 ■244 -239 •235 •230 •226 •222 •218 -214 •210 -206 ^1 10 •299 -294 -288 •282 -277 •272 •266 •261 -257 •252 ■247 -243 -238 -234 -230 5£ 11° •330 •324 -317 -311 -30s ■299 -294 •288 •283 •278 -273 •268 •263 •258 •253 03 12 ■361 ■354 -347 -340 ■334 -327 •321 -315 ■309 -304 •298 ■293 -287 •282 •277 13 •392 •384 ■377 . -369 -362 -356 ■349 -342 -336 •330 -324 ■318 -312 ■306 -301 3 14 •423 ■415 -407 •399 -391 -384 -377 -370 ■363 -356 -350 •343 •337 -331 -325 Sg ^ 3 e tJ IS ■4SS -446 -437 -429 -421 •413 ■405 -397 -390 -383 -376 -369 -362 -356 -349 i6° •487 -477 -468 -459 -450 •442 •433 •425 •417 •410 •402 -395 -388 -381 -374 5| % •519 -509 -499 -489 -480 •471 •462 ■453 -445 -437 -429 •421 -413 -406 ■398 A (D i8 ■552 -541 ■530 ■520 •510 •500 ■491 •482 ■473 -464 -456 ■447 -439 -431 •423 So 19 ■585 -573 -562 -551 -540 •530 •520 •510 -501 •492 -483 -474 -465 -457 -449 . »o 20 •618 -606 -594 •582 •571 •S60 -550 -540 •530 •520 •510 -501 -492 -483 -474 21° •652 •639 -626 ■614 ■603 -591 •580 -569 -559 -548 -538 -528 -519 -509 -500 S|g 22 •686 -672 •659 •647 -634 •622 •610 -599 -S88 -577 -566 -556 ■546 -536 -527 « ab 23 ■721 •706 -693 -679 •666 •654 •641 •629 -618 •606 -595 -584 -574 -563 ■553 § «r® 24 756 -741 •727 713 •699 •686 •673 •660 •648 -636 •624 -613 -602 -591 -580 ca M o 25 •792 776 -761 •746 -732 •718 -705 •691 -678 •666 -654 -642 -630 -619 •608 l-ss 26° •828 -812 -796 -781 •766 751 ■737 723 -710 •697 •684 -671 -659 -647 •636 is.=s X •86s 'If '^^}o -815 •800 •770 -741 •728 714 -701 -689 -676 •664 o o^ 28- •903 -885 •868 1^' •835 •819 •803 •788 -774 -759 -745 •732 719 -706 -693 29 ■941 ■922 •905 -887 •870 -854 ■837 •822 -807 -792 777 -763 -749 -736 •722 30 •980 -961 ■942 -924 -906 •889 •872 •856 -840 -825 •809 -795 -780 -766 •752 31° I "020 rooo -981 -962 •943 -925 •908 •891 ■874 -858 •842 -827 -812 •797 783 s°-S 32 i^o6i 1-040 1-020 I -000 -981 ■962 •944 •926 -909 -892 •876 -860 -844 -829 •814 5^*" 33 fI02 I -081 1-060 1-039 1-019 I^OOO •981 -963 -945 -927 •910 -894 -878 -862 •846 vai lie Li sent 34 ri4S I -123 I-IOI 1-079 1-059 1-039 roig I^OOO -981 -963 •946 •928 -912 -895 -879 35 1-189 I -165 1-143 I -121 1-099 ro78 1-058 1-038 1-019 I -000 •982 -964 •946 •929 -913 36° 1-233 1-209 I -186 I -163 I -140 1^119 ro98 1-077 1-057 1-038 1^019 I -000 -982 -964 -947 37 1-279 1-254 1-230 1-206 1-183 i^i6o ri38 rii7 1-096 1-076 1-056 1-037 i-oi8 I -000 •982 o3 s€ 3° 1-326 1-300 1-275 1-250 1-226 1^203 I -180 riS8 1-137 1-116 1-095 1-075 1-056 1-037 roi8 39 I -375 1-348 I -321 1-296 1-271 1-247 1^223 I^20I I -178 1-156 1-135 i-iiS 1-094 1-075 1-055 40 I "425 1-396 1-369 1-343 I -317 1-292 1^268 1-244 I -221 1-198 1-176 1-155 1-134 1-114 1-094 41° 1-476 1-447 1-419 1-391 1-365 1-339 I -313 r289 1-265 I -241 1-219 1-196 1-175 1-154 1-133 II 42 1-529 1-499 1-469 1-441 1-413 1-387 1-360 1-335 1-310 1-286 1-262 1-239 1-217 1-195 1-173 43 ^'Pr. 1-552 1-522 1-492 1-464 1-436 1-409 1-383 1-357 1-332 1-307 1-283 1-260 1-237 1-215 a>-< 44 ;-§i 1-607 1-576 1-545 1-516 1-487 1-459 1-432 1-405 1-379 1-354 1-329 1-305 1-282 1-259 45 1-664 1-632 1-600 1-570 1-540 rsii 1-483 1-455 1-428 1-402 1-376 1-351 1-327 1-303 4fi° 1758 1723 1-690 1-657 1-625 1-595 1-565 1-535 1-507 1-479 1-452 1-425 1-399 1-374 1-350 •a . % I -82 1 1-885 1-848 1-750 I -812 I -716 1-777 1-683 1-743 1-651 r7io I^620 r678 1-590 1-647 1-560 1-616 1-586 1-503 1-557 1-476 1-529 1-449 1-501 1-423 1-474 1-398 1-447 49 I '953 I -915 1-877 i^84i 1-806 1-771 1-738 1-705 1-674 1-643 1-613 1-583 1-555 1-527 1-499 1^ SO 2-023 1-983 1-945 1-907 1-871 1-835 r8oi 1-767 1-734 1-702 I -67 1 1-640 i^6ii 1-582 I -553 > 51° 2-096 2-055 2-015 1-976 1-938 1^902 r866 1-831 1-797 1-764 1-731 1-700 r669 1-639 1^609 M 52 2'i73 2-130 2-089 2-048 2-009 1-971 1-934 r898 1-862 1-828 1-794 1-762 1-730 1-793 r86o 1-930 1-699 I -761 1-668 Si S3 2-253 2-209 2-166 2-124 2-083 2^043 2-005 1-967 1-931 1-895 1-860 1-827 1^729 ►H 54 55 2'337 2-425 2-291 2-377 2-246 2-331 2-203 2-286 2^i6o 2^242 2^II9 2^199 2-079 2-158 2^041 2^1I7 2^003 2^078 f966 2^040 1-930 2-002 1-894 1-966 1-827 1-895 1-794 r86i i S6° i 2-S17 2-614 2-717 2-825 2-940 2-467 2-563 2-663 2-770 2-883 2-419 2-513 2-6l2 2-716 2-826 2-373 2-464 2-561 2-663 2-772 2^327 2-417 2-512 2-612 2-719 2-283 2-371 2-464 2-S63 2-667 2-240 2-326 2-418 2-514 2-617 2^198 2^283 2-373 2-467 2-568 2-157 2*241 2*329 2^422 2^520 2-117 2-199 2-286 2-377 2-474 2-078 2-159 2-244 2-333 2-428 2-041 2-119 2-203 2-291 2-004 2-081 2-163 2-249 2-341 1-967 2-043 2-124 2-209 2-299 1-932 2-007 2-086 2-169 2-257 61° 62 3-063 3-193 3-332 3-481 3-641 3-002 3-130 3-266 3-412 3-569 2-944 3-069 3-203 3-346 3-500 2-887 3-010 3-142 3-281 3-432 2-832 2-952 3-081 3-218 3-366 2-778 2-896 3-022 3-157 3-302 2-726 2-841 2-965 3-098 3-240 2-675 2-788 2-910 3-040 3-179 2^625 2-736 2-856 2-983 3-120 2-576 2-686 2-803 2-928 3-063 2-529 2-637 .2-751 2-874 3-006 2-483 2-589 2-701 2-822 2-952 2-438 2-542 2-652 2-898 2-394 2-496 2-604 2-721 2-846 2-351 2-451 2-558 2-672 2-795 m 58 m 56 m 54 m 52 in 50 m 48 m 46 m 44 m 42 m 40 m 38 m 36 m 34 m 32 m 30 ('49i°) (149°) (i48i°) (148°) (1474°) (■47°) (1464°) (146°) (>4S4°) (145°) (■444°) (■44°) (■434°) (143°) (1424°) 9 HOURS. For the. Azimuth. --The. Sign. is always +, except when the Hour-Angle exceeds 6 hours. B 14 The Head-Jine has various signifleations, according' to the Problem in use. In Problems IV. and VIII. it represents the Diff. of Long. In Problems X. and XI. it represents the True Azimuth. Decl. 2 HOURS ■ m m m m m m m m m m m m m m ra 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 Ooi") (31°) (3ii°) (32°) (324°) (33°) 33i°) (34°) (344°) (35°) (354°) (36°) (364°) (37°) (374°) 0° •000 •000 -000 •000 •000 •000 •000 •000 •000 -000 •000 •000 -000 •000 -000 I ■034 -034 -033 -033 -032 •032 •032 -031 -031 •030 •030 •030 ■029 •029 -029 m 2 •069 -068 •067 ■066 •06s -064 •063 -062 -062 -061 -060 -059 -059 ■058 •057 ^ 3 ■103 -102 •100 -099 -098 •096 -095 -094 -093 -091 -090 •089 -088 •087 •086 *> 4 •138 •136 -134 -132 -130 •128 •127 -125 . -123 -122 •120 -119 •118 •116 •IIS ^ S •172 •170 -167 •165 -163 •161 -159 •157 •154 -153 -151 •149 •147 •I4S •144 6° •207 -204 -201 -198 -196 -193 -190 -188 •186 -183 -181 •179 ■177 •175 -173 « 7 •242 •238 -235 -232 •229 -225 -222 -220 •217 -214 -211 -209 -206 •204 -202 g 8 •277 -273 •269 •26S •262 -258 -25s -251 -248 -245 -242 ■239 •236 •234 •231 o 9 •312 •308 •303 -299 •29s -291 -287 -283 •280 •276 -273 -269 •266 ■263 •260 >f 10 •347 •342 -337 -333 •328 -324 -319 -31s •311 ■307 -304 •300 '296 •293 •290 2 'S H" •383 •377 -372 •367 •362 -357 •352 -348 -343 -339 -335 -331 •327 •323 -319 ^ ^ 12 ■419 •413 -407 •401 ■396 -390 -385 -380 -375 -371 -366 •362 -357 ;3S3 •349 s « 13 •4SS •448 ■442 -436 -430 ■424 -418 •413 -408 -403 -398 -393 -388 -379 0> M E3 14 •491 •484 •477 ■fi -464 -458 -452 •446 -440 -435 •429 -424 -419 -414 •410 IS •S28 -520 •513 -499 -492 •48s -479 •473 -467 •461 -456 -450 -445 -440 ■a 2t3 i6° •S6S •557 •549 -541 -534 -527 •520 -513 -506 ■500 -494 •488 -482 -476 •471 *< iS < 17 ■602 •594 -585 -577 -569 •561 -554 -547 •540 -533 •526 -520 -514 ■508 -502 '£ a> 18 •640 •631 -622 -613 -605 -597 -589 -581 -574 -566 -560 -553 -546 -540 -534 o Sd 5a^ 19 ■678 ■669 -659 -650 ■641 -632 -624 -616 •608 -600 -593 •586 -579 -572 -566 20 •717 •707 -697 •687 -677 -668 •659 •651 •643 -635 •627 •619 -612 -60s •598 s|| 21° •756 •745 -735 -724 -714 •705 •695 •686 •678 -669 ■661 -653 •645 -638 •631 60 4-.^ 22 •796 -784 -773 -762 -752 -742 -732 -723 -713 •704 -696 -687 -679 •671 -664 a o^ 23 •836 •824 •812 •801 -790 •779 -769 -759 -749 -740 •731 -722 -714 -70s -697 ?^S 24 •877 •864 -852 -840 -829 -817 •807 -796 •786 -776 ■767 -757 -749 •740 -731 1^1 25 ■919 •905 •892 , -880 •868 -856 •845 -834 -823 -813 •803 -793 -784 •775 •766 26° •961 -947 -933 •920 •908 ■896 -884 -872 -861 •850 -840 -830 -820 -810 •801 »-*^^ 27 1-004 -989 •975 •962 -948 •936 -923 -911 -900 •888 -877 -867 •857 -847 •837 liflcationi lem VIII. i XI. the; 28 1-048 I 032 I 018 1-003 -990 -976 •963 •951 -939 •927 -916 •905 -894 -884 •873 29 1-092 1-076 I -06 1 1-046 1-032 I -018 1-004 -991 -979 -966 -955 -943 -932 •921 -911 30 I -138 I-I2I I -105 I 090 1-075 I 060 1046 1-032 I -019 1-007 -994 -982 -971 -959 •948 31° 1-184 1-167 1-150 I -134 1-118 1-103 1-089 1-075 I -061 1-048 1-035 1-022 I -010 •998 •987 SoS 32 1-231 I -213 I -196 I -179 I -163 I -147 I -132 1-117 1-103 1-089 1-076 1-063 1-051 1-038 1-026 ■S g«s 33 1-280 1-261 1-243 1-225 1-209 1-192 1-177 1-161 1-147 1-132 1-118 1-105 1-092 I -079 1-067 O >-i m 34 1-329 I -310 1-291 1-273 I -255 1-238 1-222 1-206 1-191 1-176 1-162 I -148 1-134 I -121 I -108 35 1-380 1-360 1-340 1-321 1-303 1-286 1-269 1-252 1-236 I -221 1-206 1-191 1-177 1-163 1-150 1 .§ 36° 1-432 I -41 1 I -391 I -371 1-352 1-334 1-316 1-299 1-283 1-267 1-251 1-236 I -221 1-207 1-193 ■*§« 1-485 1-463 1-442 1-422 1-402 1-384 I -36s 1-348 1-330 1-314 1^298 1-282 1-267 1-252 1-238 g-|g 38 I '539 I "517 1-495 1-474 1-454- 1-435 I -416 1-397 1-379 1-362 1-345 1-329 1-313 1-298 1-283 fe|a: 39 1-596 1-572 1-550 1-528 1-507 1-487 1-467 1-448 1-430 I^4I2 1-394 1-378 1-361 1-346 1-330 *|5 40 1-653 1-629 1-606 1-583 1-562 1-541 1-520 1-501 1-481 1-463 1-445 1-428 1-411 1-394 1-378 a 3 'SnO 41° I -713 1-688 1-664 1-640 I -618 1-596 1-575 1-555 1-535 I -516 1-497 1-479 I -461 1-444 1-428 «7 " 42 1-774 1-748 1-723 1-699 1-676 1-653 1-631 1-610 1-590 1-570 1-551 1-532 ''s;4 1-496 1-479 *3fe 43 1-837 I -81 1 1-785 1-760 1-736 1-712 1-690 1-668 1-646 1-626 1-606 1-586 1-568 I -550 1-532 44 1-903 1-875 1-848 1-822 1-797 1-773 1-750 ^"^11 I -70s 1-684 1-663 1-643 1-623 1-605 1-586 45 1-970 1-942 I -914 1-887 I -861 1-836 I -812 1-788 1-766 1-743 1-722 1-701 1-681 1-662 1-643 in t the Cirel 46° 2-040 2-01 1 1-982 1-954 1-927 I -901 1-876 1-852 1-828 1-805 1-783 1-762 1-741 1-721 I -701 47 2-113 2-082 2*052 2-024 1-996 1-969 1-943 '■^i! 1-893 1-870 1-847 '1?'^ 1-803 1-782 1-762 S|s 48 2-188 2-156 2-126 2-096 2-067 2-039 2 -012 1-986 I -961 1-936 1-913 1-889 1-867 1-845 1-824 49 2-267 2234 2-202 2-171 2-141 2-112 2-084 2-057 2-031 2006 I -981 1-957 1-934 I -911 1-890 S* 2« 50 2348 2-314 2-281 2249 2-218 2-188 2-159 2-131 2-104 2-078 2-052 2-028 2-004 1-980 1-958 ■§§• Sx° 2-433 2-398 2-363 2*330 2-298 2-267 2-237 2 208 2-180 2^153 2-127 2-101 2-076 2-052 2-029 o 1^ 52 2-522 2-485 2-450 2-415 2-382 2-350 2-319 2-289 2-260 2-232 2-204 2-178 2-152 2-127 2-103 H ^ 53 2-615 2-577 2-540 2-504 2-470 2-437 2-404 2-373 2-343 2314 2-285 2-258 2-231 2-205 2^180 1 54 2-712 2-672 2634 2-597 2-562 2-527 ^■4§1 2-461 2-430 2-400 2-370 2-342 2-314 2-287 2-261 55 2-814 2-773 2-733 2-695 2-658 2-622 2-588 2-554 2-521 2-490 2-459 2-430 2-401 2-373 2-346 56° 2 '92 1 2-879 2837 2798 2 '759 2-722 2-686 2-651 2-617 ^■|!5 2-553 2-522 2-492 2-463 2-435 g 3-034 2-990 2-947 2-906 2-866 2-827 2-790 ""'PJ^ 2-719 2-685 2-652 2-620 2-589 2-559 2-530 •s 58 3-153 3-107 3-063 3-020 2-978 2-938 2-899 2-862 2-825 2-790 ""'It 2-723 2-690 2-659 2-629 •g 59 3-279 3-231 3-185 3-141 3-097 3-056 3-015 2976 2-938 2-902 2-866 2-831 2-798 2-765 2-734 »4 60 3-413 3-363 3-315 3-269 3-224 3-180 3-138 3-097 3-058 3-020 2-983 2-947 2-912 2-878 2845 5 61° 3-555 3-503 3-453 3-404 3-358 3-312 3-269 3-226 3-185 3-145 3-107 3-069 3-033 2-998 2-963 62 3706 3-652 3-599 3-549 3-500 3 453 3-408 3-363 3-320 3-279 3-239 3-200 3-162 3^125 3-089 63 3-867 3-811 3-756 3-704 3-653 3-604 3-556 3-510 3-465 3-422 3-380 3-339 3-299 3-261 3-224 64 4-040 3-981 3-924 3-869 3-816 3765 Hl^ 3667 3-620 3-575 3-531 3-488 3-447 3-407 3-368 65 4-225 4-164 4-104 4-047 3-991 3-937 3-885 3-835 3-786 3-739 3-693 3-648 3-605 3-563 3-523 rn m m m m m m m m m m in m m m 58 56 54 52 50 48 46 44 42 40 38 36 34 32 30 (i49r) 049°) (i48i°) (148°) {i47i°) (147°) (1464°) (146°) (1454°) (145°) (1444°) (144°) (1434°) (i43°J (1424°) 9 HOURS. c When Latitude and Declination are of contrary names, the Sign is +. For the Azimuth : | y^^^^ Latitude and Declination are of same name, the Sign is — . Missing Page Missing Page 17 The Head-line has various signifleatioris accoFding to the Problem in use. In Problem IV. it represents Diff. of Long. In Problem V. the Initial Course. In Problem VI. the Complement of the Diff. Of Long. In Problem VIII. the Diff. of Long. In Problems X. and XL the True Azim. ■a CO . a 2S ^ o as » o u &0 Cm O f. o cdfl o *^\^ a l» 03 > b "^ !-< o OJ w 33i°) 8 (47°) •000 -016 -033 -049 -065 -082 -114 -131 -148 -164 -181 -198 -215 -233 -250 -267 -285 -303 -321 -339 -358 -377 -396 ■415 -435 -455 -475 -496 -517 -538 -560 -583 -606 ■629 -653 -678 -703 •729 -755 -782 •811 -840 ■870 -901 •933 -966 i-ooo 1-036 1-073 X-III 1-152 I -194 1-237 1-283 1-332 1-383 1-436 1-492 1-552 I -615 1-682 1-754 1-830 1-912 2-000 m 52 ('33°) m 10 (474°) m 12 (48°) -000 -016 •032 -048 ■064 -080 -096 -113 •129 -145 ■162 ■178 -195 -212 •228 -246 -263 -280 -298 -316 •334 ■352 -370 -389 -408 -427 -447 -467 •487 -508 -529 -551 -573 -595 •618 -642 -666 -691 -716 •742 •769 -797 -825 •854 -885 -916 ■949 -983 I -018 1-054 1-092 1-132 I -173 I -216 I -261 1-309 1-359 I •411 1-466 1-525 1-587 1-653 1-723 1-798 1-879 1-965 m 50 (i32i°) ■000 -016 -031 -047 -063 ■079 •095 -III -127 -143 -159 -175 -191 -208 -224 -241 -258 ■275 ■293 •310 •328 -346 -364 -382 •401 -420 -439 -459 -479 -499 -520 -541 -563 -585 -607 •630 -654 -679 -703 -729 -756 -783 •811 -840 -870 -900 -932 ■966 I^OOO 1-036 1-073 I-II2 1-152 I -195 1-239 1-286 1-335 1-387 I -441 1-499 1-560 i^624 1-693 1-767 1^846 1-931 m 48 ('32°) m 14 (484°) -000 •015 -031 -046 ■062 -077 -093 -109 -124 -140 -156 -172 •188 -204 -221 -237 ■254 -270 -287 -305 •322 -340 -357 -376 •394 -413 •432 -451 -470 -490 •511 -532 •553 -575 -597 -619 -643 -667 ■691 -716 -742 ■769 -797 -825 -854 -88s •916 ■949 -983 1-018 1-054 1-093 1-132 1-174 1-218 1-264 1-312 I 362 I -416 1-472 1-532 1-596 1-664 1-736 1-814 1-897 m 46 (1314°) m 16 (49°) -000 ■015 •030 -046 -061 -076 -091 -107 -122 -138 -153 -169 -18s •201 -217 -233 -249 -266 -282 ■299 -316 -334 -351 -369 -387 -405 -424 •443 -462 -482 -502 •522 -543 -56s ■586 -609 •632 •655 -679 -704 -729 -756 •783 ■811 •839 •869 -900 -932 -965 1-000 1-036 1-073 I -113 1-154 1-196 I -241 1-289 1-339 1-391 1^447 1-506 1-568 1*635 1-706 1-782 1-864 m 44 (131°) m 18 (494°) -000 •015 ■030 ■045 -060 -075 -090 -105 -120 -135 -151 •166 -182 -197 -213 -229 -245 •261 -278 -294 -311 -328 -345 -363 -380 -398 •417 -435 -454 -473 -493 -513 •534 -555 •576 -598 ■621 -644 -667 -692 -717 -742 -769 -796 -825 •854 -916 -949 •983 1-018 1-055 1-093 1-133 1-176 1"220 1^266 1315 1-367 I -421 1-479 1-541 1-606 1-676 1-751 1-832 m 20 (50°) -000 ■015 ■029 -044 -059 -073 -088 ■103 -118 -133 -148 •163 -178 -194 ■209 -225 -241 -257 •273 -289 •305 •322 -339 -356 -374 -391 -409 -428 -446 -465 -484 -504 -524 -545 -566 •588 -610 -632 -656 -679 -704 ■729 -756 •782 -810 -839 -869 ■900 -932 •965 1^000 1-036 1-074 I-II4 1-155 1-198 1-244 1-292 1-343 1-396 I -453 1-514 1-578 1-647 1-720 1-799 m 22 (504°) -000 -0T4 '029 -043 -058 -072 -087 ■101 -116 •131 -145 -160 -175 -190 •206 -221 -236 -252 -268 -284 -300 -316 -333 -350 -367 -384 -402 •420 -438 -457 ■476 -495 •515 -535 -556 -577 -599 -621 -644 •668 -692 -717 -742 -769 -796 -824 -854 -884 -916 -948 -982 i-oi8 1-055 1-094 I -135 1-177 1-222 I 269 1-319 1-372 1-428 1-487 1^550 1-618 1-690 1-768 42 40 ('304°) (130°) m 38 (■294°) m 24 (51°) -000 -014 -028 ■042 -057 -071 -085 ■099 •114 -128 -143 -157 -172 -187 -202 -217 -232 ■248 ■263 -279 •295 -311 -327 -344 -361 -378 -395 -413 -431 -449 -468 •487 ■506 -526 •546 •567 -588 -610 -633 -656 -679 •704 -729 •755 -782 -810 -839 -868 -899 -932 ■965 1-000 1-036 1-075 1-115 1-156 1-201 1-247 1-296 1-348 1-403 1-461 1^523 1-589 1-660 1-737 m 36 ('29°) m 26 (514°) -000 •014 -028 -042 •056 ■070 •084 ■098 -112 -126 -140 -155 -169 -184 -198 •213 ■228 •243 -258 -274 -290 -305 •321 -338 -354 -371 -388 ■405 •423 -441 -459 ■478 -497 •517 ■537 -557 ■578 -599 -621 -644 -667 -691 -716 -742 •768 -795 -824 -853 -883 -915 -948 •982 1-018 1-056 1-095 1-136 1179 1-225 1-273 1-324 1-378 1-435 1-496 1-561 1-631 1-706 m 34 ('284°) m 28 (52°) -000 -014 -027 -041 •055 -068 -082 -096 -1 10 -124 •138 -152 •166 -180 •195 -209 ■224 -239 -254 •269 ■284 •300 -316 -332 -348 -364 -381 ■398 -415 -433 -451 -469 -488 -507 -527 -547 •568 •589 -610 •633 -656 •679 -703 -729 -754 ■781 •809 •838 ■868 ■899 -931 -965 1-000 1-037 1-075 1-1 16 1-158 1-203 1-250 1-300 1-353 1-409 1-469 i^533 l-602 1-675 m 32 (128°) ni 30 (524°) ■000 ■013 •026 ■040 •054 -067 -081 •094 ■108 •122 -135 ■149 -163 ■177 •191 •206 -235 -249 -264 -■279 -295 -310 -326 -342 -358 •374 -391 -408 -425 •443 -461 •479 •498 -518 -537 -557 -578 -600 -621 -644 -667 •691 ■716 -741 ■767 -795 -823 -852 -883 -914 -948 -982 1-018 1-056 1-096 1-138 1-182 1-228 1-277 1-329 1-384 1-443 1-506 1-573 1-646 m 30 (1274°) 8 HOURS. For the Azimuth :-The Sign is always +, except when the Hour-Angle exceeds 6 hours. B 18 The Head-line has various signifleations, according to the Problem in use. In Problems IV. and VIII. it represents the Diff. of Long. In Problems X. and XL it represents the True Azimuth. Decl. 3 HOURS . m m m m m m m m m m m m m m m 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 (4Si°) (46°) {46n (47°) (47i°) (48°) (48i°) (49°) (49i°) (50°) (5oi°) (51°) (51 n (52°) (52^ 0° •000 •000 -000 -000 •000 ■000 -000 •000 000 -000 -000 •000 -000 -000 -000 I •024 ■024 -024 -024 -024 ■023 -023 -023 -023 ■023 -023 •023 -022 •022 •022 2 •049 ■049 -048 -048 •047 -047 -047 -046 -046 ■046 -045 •045 -045 •044 -044 3 •073 ■073 -072 •072 -071 -071 -070 -069 -069 •068 -068 -067 -067 -067 -066 S 4 •098 -097 •096 •096 ■095 -094 -093 -093 -092 ■091 -091 -090 -089 -089 -088 ^ S •123 -122 -121 -120 -119 -118 -117 -116 -115 -114 •113 -113 -112 •111 -no "2 6° •147 •146 -145 -144 -143 -141 -140 -139 -138 •137 •136 ■135 -134 -133 •132 m 03 7 •172 -171 -169 -168 -167 •165 -164 -163 -161 •160 •159 ■158 •157 •156 •15s o 8 •197 -I9S -194 -192 -191 -189 •188 •186 -185 -183 -182 -181 •180 -178 ■177 o 9 •222 •220 •218 -217 -215 •213 -211 -210 -208 -207 •205 ■204 -202 -201 -200 ^ 10 •247 •245 -243 -241 •239 -237 -235 •234 ■232 -230 -229 -227 -225 -224 -222 s.g 11° •273 -270 -268 -266 -264 -262 -260 ■258 -256 -254 -252 •250 -248 •247 ■''11 3 s 12 •298 -295 -293 -291 -288 -286 •284 -282 -280 -277 -275 •274 -272 -270 -268 a S 13 •324 ■321 -318 -316 -313 -311 •308 •306 -304 -301 -299 -297 -295 -293 -291 ■" i« 14 •350 •347 -341 -338 -336 -333 -330 -328 -325 ■323 -321 -319 •316 ■314 aS| IS •376 -372 -369 -366 -363 •361 -358 •355 -352 ■350 •347 -345 -342 ■340 -338 e Probl( eridians ue Altiti i6° ■402 •399 •395 -392 •389 -386 •383 -380 •377 ■374 -372 -369 •366 •364 -361 17 •429 -425 -421 -418 •415 -411 -408 -405 ■402 -399 -396 -393 •391 •388 •385 i8 •456 -452 -448 -444 -441 -437 -434 •431 -427 ■424 -421 •418 -415 •412 -410 19 •483 •479 -475 ■471 -467 -463 -460 -456 -453 -449 -446 ■'•41 •440 •437 -434 ■u "H 20 •Sio -506 -502 -498 -494 •490 -486 -482 -479 -475 -472 •468 -465 -462 -459 2|| 21° •538 -534 -529 -525 -521 •517 -513 -509 •50s -501 •497 -494 -490 •487 •484 22 •566 -562 -557 -552 -548 -544 -539 •535 •531 ■527 •524 -520 -516 ■513 -509 B °a 23 ■S9S -590 -585 -580 -576 -571 -567 •562 ■s|? -554 -550 -546 -542 '^E •535 "g *^S 24 •624 -619 -614 ■609 -604 -599 -594 ■|92 -586 •581 -577 -573 -56? •565 -561 1.32 2S •6S4 -648 •643 -638 -632 -627 -623 -618 •613 ■609 -604 -600 -596 •592 -588 S|2 26° •684 -678 -672 -667 -662 -656 -651 -646 -641 -637 -632 -628 -623 •619 1'S •714 -708 -702 -697 -691 -686 -680 •675 -670 -665 -660 1§^ •651 -647 •642 a -5 2 28 745 -739 -733 -727 -721 -715 -710 -705 -699 -694 •689 -684 t^i -675 -670 .sag 29 •777 -771 -764 -758 -752 -746 -740 •734 -729 -724 -718 •713 •708 -703 t^i t^'*^ 30 ■809 -803 -796 -789 -783 ■777 •771 ■765 -759 -754 •748 •743 •738 •733 -728 si^ 31° 32 33 34 •842 -835 -869 -828 -822 ■815 -809 -802 •796 -790 -784 -779 •773 •768 -763 -757 as-g •876 -861 -854 -848 -841 -834 -828 -822 -816 -810 -804 •798 -793 -788 •a g§ •910 •946 •903 ■895 -888 -881 -874 -867 -860 -854 ■848 -842 •836 ■f^° "H -819 OUS ! In Pi sX. -938 ^7 J -930 -922 •915 -908 -9CI -894 -887 -881 -874 -868 ■862 it 113 35 •982 -973 •965 -957 ■950 •942 •935 -928 -921 -914 •907 -901 •895 •889 36° i"oio I -010 1-002 ■993 •985 -978 •970 -963 -955 -948 -942 •935 -928 -922 -916 >s3 * ^7 1-057 1-048 1-039 1-030 1-022 1-014 I -006 ■998 -991 -984 -977 •970 •963 -998 •956 -950 -985 (132°) (131*°) (131°) (i3oi°) (130°) (I29i°) (129°) (i28n (128°; (I27i°) 8 HOURS. For the Azimuth { When Latitude and Declination are of contrary names, the Sign is +. When Latitude and Declination are of same name, the Sign is — . 19 The Head-line has various significations, aeeording to the Problem in use. In Problem IV. it represents Dilf. of Long. In Problem V. the Initial Course- In Problem VI. the Complement of the Diff. of Long. In Problem VIII. the Diif. of Long. In Problems X. and XI. the True Azim. Lat. 3 HOURS. m m m m m in m m m m m m m m m 32 34 36 38 40 42 44 46 48 50 52 54 56 58 60 (53°) (534°) (54°) (544°) (55°) (554°) (56°) (564°) (57°) (574°) (58°) (584°) (59°) (594°) (60°) 0° •000 •000 -000 -000 -000 -000 -000 -000 •000 -000 -000 -000 -000 -000 -000 I •013 -013 •013 -012 -012 -012 -012 -012 •on -on -on -on -010 -010 • -010 2 ■026 -026 -025 -025 -025 -024 -024 -023 -023 -022 -022 -021 -021 -021 -020 , 3 •039 •039 -038 -037 •037 -036 -035 •035- -034 -033 -033 -032 -031 -031 -030 >^ 4 •053 •052 -051 •050 -049 -048 -047 ■046 •045 -045 -044 -043 -042 -041 -040 ■a 5 •066 -065 -064 -062 -061 -060 -059 ■058 •057 -056 -055 -054 •053 •052 -051 § 6° •079 •078 •076 -075 -074 ■072 -071 •070 -068 -067 -066 -064 -063 -062 -061 X 7 •093 ■091 ■089 -088 -086 -084 •083 •081 -080 -078 •077 -075 -074 -072 -071 8 •106 •104 -102 -100 -098 -097 -095 •093 -091 -090 -088 -q86 -084 •083 •081 9 •119 ■117 •115 -113 -III -109 -107 •105 ■103 -101 -099 •097 -095 -093 •091 ID •133 ■130 -128 -126 •123 ■121 •119 •117 •115 -112 -no -108 -106 •104 •102 il H° •146 •144 -141 •139 -136 •134 •131 •129 •126 -124 -121 -119 -117 •114 •112 ="£ 12 ■160 •157 ■'S4 -152 -149 -146 •143 •141 •138 -135 •133 •130 -128 •125 •123 .S s 13 •174 •171 -168 •165 -162 •159 •156 •153 -ISO ■147 •144 •141 •139 •136 •133 1-^ 14 ■188 -184 -181 -178 •175 -171 •168 ■165 162 -159 •156 -153 •ISO •147 •144 % 15 •202 -198 •195 -191 -188 ■184 •181 •177 •174 -171 -167 •164 •161 •158 •15s |g i6° •2l6 -212 -208 -205 -201 •197 •193 -190 -186 -183 •179 •176 •172 -169 •166 £| '2 ■230 -226 •222 -218 -214 •2IO -206 -202 -199 ■195 •191 •187 •184 -180 •177 i8 •245 ■240 ■236 -232 -228 -223 -219 •215 -211 -207 •203 •199 •195 •191 •188 ' A » 19 •259 •255 -250 -246 •241 •237 •232 -228 -224 -219 •215 •211 •207 •203 •199 t3 (D 20 ■274 -269 -264 -260 -255 ■250 ■246 -241 •236 -232 •227 ■223 •219 -214 •210 -^ 21° •289 -284 •279 •274 -269 -264 -259 -254 •249 -245 •240 •235 •231 -226 -222 bBg, 22 •304 •299 -294 •288 -283 -278 -273 -267 -262 •257 •252 •243 •238 ■233 gp.1; 23 •320 •314 -308 •303 •297 -292 -286 -281 -276 -270 •265 •260 -255 -250 •245 24 •336 •329 •323 -318 •312 •306 -300 -29s -289 -284 •278 •273 -268 -262 •257 25 •351 •345 ■339 •333 ■327 •320 •315 -309 •303 -297 •291 •286 -280 •275 •269 «5| 26° •368 ■361 •354 •348 •342 •335 -329 •323 -317 •311 •305 -299 -293 •287 •282 2 o2 ^ •384 •377 '%l -363 ■357 •350 •344 •337 -331 •325 •318 -312 -306 •300 •294 O P4-M •401 •393 -386 -379 •372 •365 •359 •352 -345 •339 •332 •326 •319 •313 ■307 53 o rC d' 36° •547 •538 •528 -S18 •509 •499 -490 •481 •472 •463 ■454 •445 ■437 •428 •419 o a % •568 -558 •547 •538 •528 -518 -508 •499 •489 •480 •471 •462 •453 ■4'14 •435 >fig •589 •578 •568 ■"? •547 •537 -527 •517 -507 •498 •479 •469 •460 •451 39 40 •610 •632 •599 -621 •588 -6io •578 -599 •567 •588 •557 •577 •546 •566 •536 ■555 •526 -545 •S16 •535 •So6 •524 •496 •514 •487 ■504 •477 •494 •468 •484 Is? 41° 42 43 1" ■679 •643 •666 -690 •632 •654 •678 •620 -642 -665 •609 •630 •653 •597 -619 -641 •586 -607 -629 -617 •554 •574 •594 •543 •563 •583 •533 •552 •571 •522 •560 •S12 •530 •WO ■502 •520 •538 •558 o5 44 •728 •715 ■702 -689 -676 '^J^ •651 •639 •627 •6is •603 •592 •580 J7" •569 -B 45 ■754 -740 -727 •713 -700 -687 •675 -662 -649 •637 -62? ■6?3 -6oi J_7 •589 ■577 s ^ 46° % 49 50 ■780 •808 ■898 •766 •752 •739 ■72s •712 -698 -685 •672 •660 -647 •63s •622 •610 •598 11 a, i-i > 3 •794 -822 11^ •779 -807 -836 -866 -765 ■792 •821 •850 -751 •778 •805 •834 •737 -763 •791 -819 •723 •749 •776 -804 -710 •735 -761 -789 •696 •721 ■747 •774 -683 ■708 •733 •759 -670 -694 •719 •74S ■70s •730 •644 -667 -691 •716 •632 §^ •702 •619 •641 •664 •688 51° 52 S3 54 55 •931 •965 I'OOO I -037 1-076 -914 •947 ■982 i-oi8 I -057 •897 -930 -964 I -000 1-038 -881 •913 •947 -982 I 019 -86s -896 -929 -964 I -000 •849 -880 -912 -946 -982 -928 •963 -817 -847 -878 -911 -945 •802 •862 •894 •927 •910 -772 -800 -829 -860 •892 •875 •742 ■769 •797 •827 •858 •727 •811 •841 713 i 1 1 56° i I-II7 I "160 I -206 1-254 1-305 1-097 I -139 I -184 1-232 1-282 1-077 I-H9 1-163 1-209 1-258 1-058 1-098 I -142 I -187 1-038 1-078 1-121 I -165 I -019 1-058 i-ioo I -144 I -000 1-039 1-079 I -123 ■981 1-019 I -059 I -102 -963 I -000 1-039 1-081 -944 •981 1-020 1-060 -926 -962 1-000 1-040 •909 It. 1-020 •891 •92s •962 i-ooo •873 •907 •943 •980 •924 •961 5 '•235 1-213 I -190 I -168 1-146 1-125 1-103 1-082 i-o6i I -041 1^020 1-000 61° 62 '•359 I -417 1-479 I "545 I '616 '•335 1-311 1-366 1-426 1-490 1-558 1-287 1-263 1-240 I -217 1-194 1-172 1-149 1-127 I -106 1-084 1-063 1-042 65 1-392 1-452 1-517 1-587 '•342 1-400 1-462 I -317 1-374 1-436 1-293 1-349 1-409 1-269 1-324 1-383 1-245 1-299 I -357 I "221 1-275 1-331 1-198 1-250 1-306 1-226 1-281 '•I53 1-203 1-256 1-130 1-179 1-232 1-108 1-156 1-208 1-086 I "133 1-184 ^ I •530 1-502 1-474 1-446 1-419 1-393 I •366 1-340 1^3 14 1-289 1-263 1-238 111 28 • m 26 m 24 m 22 m 20 m 18 m 16 m 14 m 12 m 10 m 8 ni 6 m 4 m 2 m (127°) (>26J°) (I26°J (l2Si°) (125°) (I24i°j (124°) (1234°) (123°) (1224°) (122°) (1214°) (121°) (1204°; (120°) 8 HOURS. For the Azimuth :— The Sign is always +, except when the Hour- Angle exceeds 6 hours. B 20 The Head-line has vaFious slgnifleations, according to the Problem in use. In Problems IV. and VIII. it represents the Diff. of Long. In Problems X. and XI. it represents the True Azimuth. Decl. 3 HOURS. ra m m ra m in m ni m m m m m m m 32 34 36 38 40 42 44 46 48 50 52 54 56 58 60 o J3 (53°) (534°) (54°) (544°) (55°) (554°) (56°) (564°) (57°) (574°) (58°) (584°) (59°) (594°) (60°) 0° ■000 •000 -000 •000 ■000 ■000 -000 -000 -000 ■000 -000 -000 -000 -coo -000 ♦3 I ■022 •022 022 -021 -021 -021 -021 -021 -021 -021 -021 -020 -020 -020 -020 ^ 2 ■044 •043 •043 •043 ■043 -042 -042 -042 -042 -041 -041 -041 -041 -041 -040 ,0 3 •066 •065 -065 -064 -064 •064 -063 •063 •062 -062 -062 -061 -061 -061 -061 ■d 4 •088 •087 -086 -086 -085 •085 -084 -084 •083 ■083 -083 -082 •0S2 -081 -081 1 5 •no -109 •108 ■107 ■107 •106 -106 -105 -104 ■104 •103 -103 -102 -102 -lOI 6° •132 •131 •130 -129 -128 -128 •127 •126 ■125 -125 -124 -123 -123 -122 -121 >a I •154 •153 -152 •151 -150 -149 -148 -147 -146 -146 •145 -144 -143 •143 -142 > 23 ■532 -528 •525 -521 -518 •515 -512 •509 -506 ■503 -501 •498 ■495 •493 -490 24 •557 •554 •550 •547 -544 -540 ■537 -534 •531 -528 ■52s -522 -519 -517 ■ft 25 •584 -580 •576 •573 •569 •566 •562 •569 •556 ■553 •550 •547 -544 •541 -538 Sa 26° ■611 -607 -603 •599 •595 -592 •588 •585 -582 -578 •575 -572 -569 ■see ■563 ■■B'**" •638 •634 -630 •626 -622 -618 •615 -611 -608 -604 •601 -598 -594 •591 -588 28 •666 -661 •657 •653 •649 -645 -641 •638 •634 -630 -627 •624 ■620 -617 •614 29 ■694 -690 -685 -681 •677 •673 -669 -665 -661 -657 -654 •650 -647 ■643 -640 al^ 30 •723 ■718 •714 -709 -705 •701 -696 -692 -688 ■685 -681 -677 ■674 •670 -667 ■K^eS 31° •752 •747 •743 •738 -734 •729 •725 -721 ■716 -712 •709 •705 -701 ■697 -694 S c>< 32 ■782 •777 •772 -768 ■763 -758 •754 •749 ■745 •741 •737 •733 -729 •72s -722 «M 33 •813 •808 ■803 -798 •793 •788 •783 -779 •774 -770 -766 -762 -758 'W^ •750 ^§1 34 •84s •839 •834 -829 •823 -818 -814 -809 -804 -800 •795 -791 -787 •783 -779 -809 35 •877 -871 -866 -860 -855 -850 -845 -840 -835 -830 -826 -821 -817 •813 36° •910 •904 -898 -892 -887 -882 -876 -871 -866 -861 IF -852 -848 -843 -839 •870 •944 •937 ■931 •926 -920 -914 -909 •904 -899 -893 -889 •884 ■879 -87s 38 ■978 •972 -966 -960 ■954 -948 -942 -937 -932 -926 -921 •916 ■911 -907 -902 39 I 014 1-007 I -001 •995 -989 -983 •977 -971 -966 -960 •955 -950 -945 ■940 -935 -969 40 ro5i 1-044 1-037 1-031 1-024 1-018 1-012 1-006 1-001 -995 -989 -984 -979 -974 a*§ 41° 42 43 1-088 I -081 1-074 1-068 i-o6i 1-055 1-049 1-042 1-037 1-031 1-025 1-020 1-014 1-009 1-004 2^^ 1-127 I -120 1-113 1-106 1-099 1-093 1-086 1-080 1-074 1-068 1-062 1-056 '■°§2 1-045 1-040 *j_2 I -168 I -160 i"iS3 I'I45 1-138 1-132 1-125 1-118 1-112 I -106 1-100 1-094 1-088 1-082 1-077 c S £ 44 45 1-209 I -201 1-194 1-186 1-179 1-172 I -165 1-158 1-151 '■'55 1-139 1-133 '''11 1-121 1-115 •f5 ■S-tl 1-252 1-244 1-236 1-228 1-221 1-213 1-206 I -199 1-192 1-186 1-179 1-173 1-167 i-i6i 1-155 46° 47 1-297 1-288 1-280 1-272 1-264 1-257 1-249 1-242 1-235 1-228 1-221 1-214 1-208 1-202 1-196 1-238 1-282 1-328 1-376 So s£ i'343 I '334 1-326 I -317 1-309 1-301 1-294 1-286 1-279 1-271 1-265 1-258 1-251 1-296 1-342 1-390 1 '245 1-289 1-383 J3 49 SO 1-391 1-440 1-492 1-382 1^43 1 1-483 f373 1-422 1-473 1-364 I -413 1-464 1-356 1-404 1-455 1-348 1-396 1-446 1-340 1-388 1^438 1-332 1-380 1-429 1-324 1-372 I -42 1 1-317 1-364 I -413 1-310 1-356 1^405 1-303 1-349 1-398 51° 52 S3 54 55 1-546 1-536 1-526 1-517 1-508 1-498 1-490 1-481 1-472 1-464 1-456 1-448 1-441 1-433 1-485 1-540 1-597 1-657 1-426 1-478 1-532 1-589 1-649 53 1-603 1662 '■^^^ 1-788 1-592 I -65 1 1-712 1-777 1-582 1-640 1-701 1-765 1-572 1-630 1-691 1-754 1-563 1-620 1-680 1-743 I -553 i-6io 1-670 1-733 1^544 I -601 1-660 1-723 I -535 1-591 I -65-1 1-713 1-526 1-582 I -641 1-703 1-518 I -573 1-632 1-693 1-509 1-565 1-623 1-684 1-501 1-556 1-614 I -67s 1-493 1-548 I -606 1-666 2 56° 1-856 1-928 2-004 2-084 2-169 1-844 1-916 1-991 2 070 2-iSS 1833 1-903 1-978 2-057 2141 1-821 I -891 1-966 2-044 2128 1-810 I -880 1-954 2-032 2-114 1-799 1-868 1-942 2-019 2-102 1-788 1-857 1930 2 007 2-089 1-778 1-847 1-919 1-996 2-077 1-768 1-836 1-908 1-984 2-065 1-758 ■1-826 1-897 1-973 2-054 1-748 I -816 1-887 1-962 2-042 1-739 I -806 1-877 1-952 2-031 1-730 1-796 1-867 1-942 2 021 1-721 1-787 1-857 1-932 2-010 1-712 1-778 1-848 1-922 2-000 61° 62 65 2-259 2-355 2-457 2 567 2685 2-244 2-340 2-441 2-551 2668 2-230 2-325 2-534 2 651 2-216 2 310 2-411 2-518 2634 2 -202 2-296 2-396 2-503 2618 2-189 2-282 2-381 2-488 2 602 2176 2-269 2-367 2-473 2-587 2-163 2-255 2-354 2-459 2-572 2-151 2-243 2-340 2-445 2-557 2-139 2230 2-327 2431 2-543 2-127 2 218 2-314 2-418 2529 2-116 2-206 2-302 2405 2-515 2-105 2-194 2-290 2-392 2 502 2-094 2-183 2-278 2-380 2-489 2083 2-172 2-266 2367 2-476 m 28 m 26 m 24 m 22 m 20 m 18 m 16 m 14 m 12 m 10 m 8 m 6 m 4 m 2 m (127°) (i26r) (126°) (1254°) (125°) (1244°) (124°) (1234°) (123°) (1224°) (122°) (1214°) (121°) (I20i°) (120°) 8 HOURS. f -When Latitude and Declination are of contrary names, the Sign is +. For the Azimuth : | ^-^^^ Latitude and Declination are of same name, the Sign is — . 21 ?^ Jr'fLonr ^*''"" '*'"'"''°" TnTSlm v'JhrTnS LS In Problem IV. it represents Dlff. of Long ^n nuuio. _ _ __, ^, Complemmt of the Diff. Of Long. '" 'in Problem VIIL the Diff. of Long. In Problem VI. the in ProbremsT/aiid *XI. the True Azim. Lat. 4 HOURS. ■a . S 2S != O •l-l *^ S5 .o o - u s> "^ 3 *" P. sS ■a " .• b °> ^ OS a)M m -M O fl &_, _ O o «> <« .o M Offl > •a - 33 •142 -152 •163 ■173 •183 -194 •204 •21s •226 •237 •248 •259 •271 •283 ■295 •307 '3«9 •332 •345 ■359 •372 •386 •401 ■415 •431 •446 •462 •479 •496 •513 •532 •551 •570 •591 •6i2 ■634 •657 •681 •706 •732 •759 •788 ■819 •851 •885 •921 •959 i-ooo 1-044 1-090 1-140 ra 12 (63°) m ► 52 (118°) •000 -009 •018 -027 •036 .045 •054 •063 •072 ■081 •090 -099 •108 •118 •127 •137 •146 •156 -166 •175 •185 -196 •206 •216 ■227 •238 ■249 •260 -271 •282 •294 •306 •318 ■331 ■344 •357 •370 •384 ■398 ■413 •428 •443 ■459 •475 -492 • -510 •528 •546 -566 •586 -607 •629 •652 -676 •701 -728 •755 •78s ■815 ■848 •8S3 •919 •958 I'OOO I -045 1-093 m 16 (64°) m 48 ("7°) •000 -009 •017 ■026 •034 •043 -OS I ■060 -069 •077 ■086 -09S -104 ■113 -122 ■131 •140 -149 -168 •178 •187 •197 •207 •217 •227 •238 -249 •259 -270 -282 ■293 ■305 •317 •329 •342 •354 •368 •381 ■395 ■409 -424 •439 •455 -471 •488 •505 •523 ■542 -561 -S8i -602 -624 •647 -671 •697 •723 ■751 ■781 -812 •845 -880 -917 •957 I -000 1-046 m 20 (6S°) m 44 (116°) -000 ■008 •016 -024 •033 -041 ■049 •057 -066 -074 -082 •091 -099 •108 •116 -I2S •«34 •143 •IS2 -161 ■170 •179 -188 -198 •208 -217 •227 •238 -248 -2S8 -269 •280 ■291 ■303 ■315 •327 •339 •351 •364 •378 •39" •405 •420 •435 •450 -466 •483 •500 ■518 ■536 •556 •576 •597 •619 -642 •666 -691 -718 ■746 -776 •io8 -841 •877 •915 •956 m 24 (66°) m 40 (115°) -000 •008 ■016 ■023 ■031 ■039 -047 ■055 •063 •071 ■079 •087 ■09s •103 ■III •119 -128 -136 •I4S •153 •162 •171 •180 •189 -198 •208 -217 •227 ■237 -247 •257 •258 •278 -289 ■300 •312 •323 •336 •348 •361 •374 •387 •401 •415 •430 •445 •461 •477 ■494 •512 •53' •550 •570 -591 ■613 •636 -660 -686 •713 •741 •771 •803 •837 •874 •9'3 •955 m 28 (67°) m 36 (114°) -coo -007 •ois -022 -030 •037 -04s -052 •060 ■067 •075 ■083 -090 •098 -106 •114 •122 •130 •138 -146 ■'54 ■163 ■171 -180 -189 -198 ■207 •216 •226 •235 ■245 ■255 -26 s -276 ■286 -297 ■308 -320 •332 •344 •356 •369 •382 •396 •410 •424 •440 •455 •471 •488 •506 •524 •543 ■563 •584 -606 •629 •654 •679 •706 •735 •766 -798 •833 •870 ■910 m 32 (68°) -000 -007 -014 •021 -028 ■035 •043 -cso •057 •064 •071 ■079 ■086 -093 -lot •108 ■116 •124 -131 •139 ■147 •'55 •163 ■171 •180 ■188 •197 •206 ■21s •224 •233 ■243 •252 ■262 •273 ■283 ■294 •304 ■316 -327 ■339' •351 •364 •377 -390 •404 •418 •433 •449 •465 •499 •517 •536 ■556 •577 •599 ■622 •647 ■672 ■700 •729 •760 •793 •828 •866 ni 36 (69°) m 32 (113°) -000 -007 ■013 ■020 •027 •034 •040 •047 ■054 •061 •068 ■075 ■082 ■089 ■096 -103 •no -117 ■125 •132 ■140 -147 ■'55 ■163 ■171 ■'79 •187 -196 -204 ■213 •222 •231 -240 ■249 •259 •269 •279 •289 •300 •3" •322 •334 •346 •358 ■371 ■384 •398 •412 ■426 •442 ■457 •474 •491 •509 •528 ■548 •569 •591 •614 •639 •665 •693 ■722 •753 •787 823 m 40 (70°) •000 ■006 •013 019 •026 •032 ■038 •045 •051 •058 •064 •071 -077 -084 -091 -098 •104 -III •118 •125 -132 -140 -147 •154 -162 -170 ■178 -185 -194 -202 •210 ■219 •227 -236 -246 ■255 •264 ■274 •284 ■295 ■305 ■316 -328 '339 •351 •364 •377 •390 •404 ■419 •434 •449 •466 •483 •501 •520 •540 •560 •582 •606 •630 •657 •68s •714 •746 •781 m 28 (112°) m 24 (111°) m 44 (71°) ■000 ■006 -012 •018 -024 •030 -036 -042 •048 ■05s -061 •067 ■073 ■079 -086 •092 -099 •105 -112 •-119 ■125 -132 •'39 •146 ■153 •161 -168 ■175 ■183 -191 •199 •207 •215 -224 ■232 •241 •250 •259 ■269 ■279 •289 •299 ■310 ■321 •333 •344 •357 •369 •382 •396 •410 •425 •441 •457 ■474 •492 •510 •530 •551 •573 •596 •62 T •648 ■676 -706 •738 m 48 (72°) m 20 (110°) m 16 (.09°) •000 •006 •oil •017 ■023 •028 ■034 -040 -046 -051 ■057 -063 •069 ■075 -081 -0S7 ■093 -099 ■106 •112 -118 -125 •131 -138 ■145 •152 •158 -166 •173 -i8o -188 •'95 •203 •211 -219 -228 •236 •24s •254 •263 •273 -282 •293 •303 •314 •325 •336 •348 •361 •374 ■387 ■401 '416 •43' •447 ■464 -482 -500 •520 •541 •563 •586 ■611 ■638 ■666 ■697 m 52 (73°) m 56 (74°) m 12 (108°) -000 •00s ■on ■016 •021 •027 •032 •038 ■043 •048 ■054 ■059 ■065 -071 •076 •082 -088 •093 ■099 -los -III -117 •124 •130 •136 •143 •149 •156 ■163 -169 •177 ■184 •191 •199 •206 ■214 •222 ■230 •239 -248 -257 •266 •27s -285 •295 •306 ■3'7 •328 •340 •352 •364 •378 ■391 ■406 •421 •437 •453 -471 ■489 •509 ■530 •552 •575 -600 -627 •656 8 (.07°) •000 ■005 -010 •015 -020 -02s •030 •035 •040 ■045 •051 •056 ■061 -066 •071 •077 -082 •088 ■093 •099 •104 -no -116 -122 •128 ■134 •140 -146 -152 ■159 -166 -172 ■'79 -186 ■193 •201 •208 •216 •224 ■232 •241 •249 •258 •267 •277 •287 -297 •307 ■318 •330 •342 •354 •367 •381 •395 •410 •425 •442 ■459 ■477 ■497 ■517 •539 •563 ■588 ■615 m 60 (75°) 4 (106°) •000 ■005 ■009 •014 •019 -023 -028 •033 •038 -042 ■047 ■052 ■057 ■062 ■067 072 •077 ■082 ■0S7 -092 •098 -103 •108 -114 -n9 -125 -131 ■137 -142 •149 ■'55 •161 •167 •174 -181 •188 •'95 •202 •209 •217 -225 ■233 •241 •250 -259 •268 •277 •287 ■298 •308 •3'9 •331 •343 •356 •369 •383 •397 •413 ■429 •446 -464 •483 ■504 ■326 •549 ■575 (105°) 7 HOURS. For the Azimuth :— The Sign is always +, except when the Hour- Angle exceeds 6 hours. B 22 The Head-line has various significations, according to the Problem in use. In Problems IV. and VIII. it represents the Diff. of Long. In Problems X. and XI. it represents the True Azimuth. Decl. 4 HOURS . m m m m m m m m m m m m m m III 4 8 12 16 20 24 28 32 36 40 44 48 52 56 60 (6i°) (62°) {63°) (64°) (65°) (66°) (67°) (68°) (69°) (70°) (71°) (72°) (73°) (74°) (75°) 0° •000 -000 -000 -000 -000 -000 -000 •000 •000 -000 •000 -000 •000 •000 -000 I •020 •020 -020 •019 -019 -019 •019 •019 •019 -019 •018 -018 •018 •018 -018 (D 2 •040 -040 •039 -039 •039 ■038 -038 ■038 ■037 -037 ■037 -037 -037 •036 -036 A 3 ■060 -059 -059 -058 •058 -057 •057 ■057 ■056 ■056 •055 •055 -055 ■055 -054 +J 4 ■080 -079 -078 -078 -077 •077 •076 ■07s ■075 ■074 •074 ■074 -073 ■073 -072 ^ S •100 -099 •098 •097 -097 -096 -095 ■094 •094 •093 ■093 -092 -091 ■091 •091 "g 6° •120 -119 •118 •117 ■116 •115 •114 •113 -113 -112 •III •III -110 •109 •109 Eg I •140 ■139 -138 -137 •135 •134 •133 •132 •132 -131 •130 '129 •128 ■128 -127 g ■161 -159 ■158 •156 ■155 -154 -153 -152 •151 •150 -149 '148 -147 •146 ■145 o 9 ■181 ■179 •178 •176 -175 -173 •172 •171 -170 -169 •168 •167 •166 ■'f5 -164 ^ 10 •202 -200 -198 -196 -19s •193 -192 •190 -189 -188 •186 •18S -184 •183 •183 .S.fc 11° •222 -220 •218 •216 •214 ■213 -211 •210 •208 •207 -206 •?.ni\ •203 -202 •201 3 m 12 •243 -241 •239 -236 -235 -233 •231 -229 •228 -226 -225 •223 -222 -221 •220 13 •264 -261 ■259 -257 -255 •253 ■251 -249 -247 •246 •244 -243 •241 •240 ■239 14 ■28s -282 •280 -277 -275 •273 -271 -269 -267 -265 •264 -262 -261 -259 -258 IS •306 -303 •301 -298 -296 •293 -291 -289 •287 -285 •283 -282 -280 -279 -277 lis 16° •328 -325 •322 -319 -316 •314 -312 •309 -307 -30s -303 •302 •300 •298 •297 Is^ I? •350 -346 -343 ■340 -337 -335 ■332 -330 •327 -325 -323 •321 -320 •318 -317 S 03 i8 •371 •368 -365 -362 ■359 ■356 -353 -350 •348 -346 ■344 ■342 •340 •338 -336 (D (D 9 19 •394 -390 -386 -383 •380 ■377 -374 -371 -369 •366 •364 •362 -360 •358 -356 5 BS 20 •416 -412 -408 •405 -402 ■398 -395 •393 •390 -387 •385 -383 -381 •379 •377 o 2 a> 21° •439 ■43s -431 -427 -424 -420 •417 •414 ■411 •408 -406 •404 -401 •399 •397 &BVc^ 22 •462 •458 -453 •450 -446 ■442 -439 -436 •433 •430 -427 -42s -422 •420 •418 B "a 23 •48s -481 -476 -472 -468 •465 •461 -458 •455 -452 -449 •446 -444 •442 -439 accord he Lat. represe 24 •509 •504 •500 -495 -491 -487 •484 •480 -477 -474 .471 •468 -466 -463 •461 25 •S33 -528 -523 ■519 -515 •510 ■507 -503 -499 •496 -493 -490 •488 -48S -483 26° •558 •552 •547 ■543 -538 ■534 -530 •526 •522 •519 -516 -513 •510 ■507 •50s «-*">, 27 •583 ■577 -572 -567 -562 -558 ■S54 -550 -546 •542 -539 -536 •533 •530 •527 d HH « 28 ■608 -602 -597 -592 ■587 -582 ■578 •573 ■570 ■566 •562 ;559 ■556 -553 -550 atio VII [. th 29 •634 -628 -622 -617 -612 -607 -602 •598 ■594 -590 ■586 -580 -577 -574 30 ■660 •654 -648 -642 -637 ■632 •627 ■623 -618 -614 •6n -607 -604 •601 -598 31° •687 -681 -674 ■669 -663 -658 -653 -648 ■644 ■639 •635 •632 •628 -625 -622 32 •714 •708 •701 -695 -689 -684 -679 ■674 -669 •665 •661 1^7 -653 •650 -647 •a g<« 33 743 •735 -729 •723 -717 -711 -705 -700 -696 •691 •687 •683 -679 •676 -672 34 •771 -764 -757 -750 -744 -738 -733 727 -722 ■718 713 -709 -705 •702 •698 35 ■801 •793 •786 779 773 •766 -761 ■755 ■750 -745 •741 -736 -732 •728 -725 36° ■831 •823 -815 -808 -802 -795 •789 •784 ■778 773 •768 -764 -760 •756 •752 ^ S2 •862 ■853 -846 -838 -831 •825 -819 •813 -807 -802 -797 •792 -788 •784 ■780 £-|g 38 •893 •885. ■877 -869 -862 -855 -849 ■843 ■837 ■831 -826 -821 •817 •813 'l°i S|fi 39 •926 •917 •909 ■901 ■893 •886 -880 ■873 -867 •862 ■856 -851 -847 -842 -838 *|5 40 •959 -950 -942 -934 -926 •919 -912 •905 -899 -893 -887 •882 -877 -873 -869 p. 41° ■994 -985 •976 •967 -959 -952 ■944 -938 -931 ■92s -919 -914 -909 •904 •900 42 I -029 1-020 I -01 1 I -002 ■993 -986 ■978 -971 -964 ■958 •952 -947 -942 -937 •932 S^l 43 I -066 1-056 1-047 1-038 1-029 I -021 1-013 I -006 -999 •992 -986 -981 -975 -970 •96s 44 I '104 I -094 1-084 1-074 1-066 1-057 1-049 1-042 1-034 1-028 1-021 1-015 1-010 1-005 i-ooo .s:^: 45 I '143 1-133 I -122 1-113 1-103 1-095 I -086 1-079 1-071 1-064 1-058 1-051 1-046 1-040 1^035 46° 1-184 1173 1-162 1-152 I -143 I -134 I '125 i-ir; I -109 I -102 1-095 1-089 1-083 1-077 1-072 ^Sq 47 I "226 I -215 1-204 I -193 1-183 1-174 1-165 I-I57 I -149 I-I4I I -134 I -128 1-121 1-116 I -no 48 I 270 1-258 1-246 1-236 1-225 I -216 1-207 I -198 I -190 I -182 i^i75 I-J68 i-l6i I-I55 1-150 49 '•31s 1-303 I -291 1-280 1-269 1-259 1-250 1-241 1-232 1-224 I -217 I -210 1-203 1-197 1-191 lgl SO 1-363 1-350 1-338 1-326 1-315 1-305 1-295 1-285 1-277 1-268 1-260 1^253 1-246 1-240 1^234 « p. 51° 1-412 I '399 1-386 1-374 1-363 1-352 1-342 1-332 1-323 '■314 1-306 1-298 1-291 1-285 1-278 CO ■319 •331 •343 •356 ;29s •318 •330 •272 •282 •293 •304 •249 •278 •226 ■234 ■243 •252 ■203 •210 •218 •226 •180 •187 •193 •201 •157 •163 •169 •17s •135 ■139 ■145 •150 ■112 •116 •120 •I2S •090 •093 •096 •100 •022 •023 •024 •025 •000 •000 •000 •000 3 g a 56° i ■370 •384 •399 •41 s •432 ■342 •3S6 ■369 •384 •400 ■315 •327 •340 •368 •288 •299 •3" •324 •337 •261 •272 •282 •293 •305 •235 •244 •264 •274 •208 •216 •225 ■234 •243 •182 •189 •196 •204 •213 •iS6 •162 •168 •182 •130 •135 •140 •146 •152 •104 •108 •112 ■116 •121 •078 •081 •084 •087 •091 •052 •054 •056 •058 •060 •026 •027 •028 •029 •030 •000 •000 •000 •000 •000 61° 62 6s ■450 •469 •489 •511 ■53S •416 •434 •4S3 •473 ■495 •383 •400 •417 •436 •456 •351 •366 •381 •399 •417 ■318 •332 •346 ■362 •378 •286 •298 •3" •325 •340 •254 •264 •276 •288 •301 •222 •231 •241 •252 •263 •190 •198 •206 •21 s •22s •158 •16S •172 •179 ■188 •126 •132 ■157 ■'45 •150 ■095 •099 •103 •107 •I 12 •063 •066 •069 •072 •07s •031 •033 •034 ■036 •037 •000 •000 •000 •000 •oou m 56 ' 52 m 48 m 44 m 40 in 36 m 32 m 28 m 24 m 20 m 16 111 12 m 8 m 4 ni (104°) ('03°) (102°) (101°) (100°) (99°J (98°) (97°) (96°J (95°) (94°) (93') (92°) (91°) (90°) 6 HOURS. For the Azimuth :-ThB Sign is always +, except when the Hour- Angle exceeds 6 hours. B 24 The Head-line has various significations, aeeording' to the Problem in use. In Problems IV. and VIII. it represents the Diff. of Long. In Problems X. and XL it represents the True Azimuth. Decl. 5 HOURS ■ m m m m m m 111 m m m m m m m m 4 8 12 16 20 24 28 32 36 40 44 48 52 56 60 (76°) (77°) (78°) (79°) (80°) (81°) (82°) (83°) (84°) (85°) (86°) (87°) (88°) (89°) (90°) 0° •000 -000 ■000 -000 -000 -000 -000 -000 •000 •000 -000 -000 -000 •000 -000 I ■018 •018 •018 -oiS -018 •018 -018 -018 •018 -018 -017 -017 -017 -017 -017 o 2 •036 -036 •036 ■036 •035 ■035 ■035 •035 -035 ■035 -035 •035 -035 -035 •035 5 3 ■OS4 •054 •054 •053 •053 ■053 •053 •053 -053 •053 -053 -052 -052 -052 -052 -♦J 4 •072 -072 •071 •071 •071 -071 •071 -071 -070 -070 -070 -070 •070 -070 -070 ^ 5 ■090 ■090 •089 •089 •089 -089 -088 -088 -088 •088 •088 -088 -088 •088 •087 03 6° •108 •108 •107 •107 •107 •106 -106 ■106 -106 ■106 -105 -105 -105 •105 -105 S 7 •127 -126 •126 ■125 •125 ■124 -124 •124 ■123 -123 -123 -123 ■123 -123 -123 g 8 •14s -144 •144 ■143 ■143 -142 ■142 -142 -141 -141 -141 -141 -141 •141 -141 o 9 •163 •163 -162 -161 •161 -160 -160 •160 ■159 •159 •159 ■159 •158 •158 -158 ^ 10 •182 -181 •180 •180 •179 -179 -178 ■178 •177 -177 •177 -177 -176 -176 -176 6 ^ 11° ■200 .199 •199 •198 •197 •197 •196 ■196 •195 •195 •195 •195 ■194 •194 -194 3 CO ^ ca 12 •219 -218 -217 •217 -216 -215 -215 ■214 -214 ■213 •213 -213 -213 •213 -213 .s § 13 •238 •237 •236 •235 •234 ■234 •233 •233 ■232 ■232 -231 -231 -231 •231 -231 14 •257 •256 -255 •254 ■253 •252 -252 •251 -251 -250 -250 -250 ■249 -249 -249 15 •276 ■275 •274 •273 •272 •271 •271 -270 -269 •269 •269 -268 -268 ■268 -268 16° •296 •294 •293 •292 •291 •290 -290 -289 -288 ■288 •287 -287 -287 -287 ■287 •So H •3"S •314 •313 ■311 •310 •310 -309 •308 ■307 ■3Q7 •306 -306 •306 -306 -306 i8 •33S ■333 ■332 •331 ■330 -329 -328 -327 •327 ■326 •326 •325 ■325 -325 -325 ID <]> S 19 •35s •353 •352 •351 ■350 ■349 •348 -347 •346 ■346 •345 •345 ■345 ■344 -344 -B S,?i 20 •375 •374 ■372 •371 ■370 ■369 ■368 ■367 •366 -365 •365 ■364 ■364 -364 •364 5|| 21° •396 •394 •392 ■391 -390 ■389 ■388 •387 ■386 •38s •385 -384 ■384 ■384 •384 bfiCM^ 22 •416 •415 •413 •412 -410 ■409 -408 -407 •406 -406 •405 -405 •404 •404 •404 .5 ° a 23 •437 •436 •434 ■432 ■431 ■430 -429 -428 -427 -426 -426 •425 ■425 -425 -424 aeeord he Lat. represe 24 •459 •457 •455 ■454 •452 •451 -450 •449 -448 -447 -446 ■446 -446 -445 ■445 25 •481 •479 •477 ■475 ■474 -472 -471 •470 -469 -468 -467 -467 -467 -466 -466 26° •503 •SOI •499 ■497 •495 ■494 ■493 -491 -490 •490 •489 •488 -488 •488 •488 »*">» 27 •52s •523 •521 -519 •517 -516 ■515 •513 -512 •511 -511 •510 ■510 -510 -510 Sd2 28 •548 •546 •544 ■542 ■540 ■538 ■537 ■536 ■535 -534 ■533 •532 ■532 •532 -532 29 ■571 •569 ■567 •565 ■563 -561 •560 ■558 -557 ■556 ■556 -555 •555 •554 -554 TO • 30 •595 •593 •590 •588 •586 ■585 ■583 ■582 •581 -580 ■579 •578 •578 -577 -577 31° •619 •617 •614 •612 -610 ■608 •607 •605 -604 ■603 -602 -602 -601 •601 -601 32 •644 •641 •639 •637 •635 •633 -631 -630 -628 -627 -626 -626 ■625 -625 -625 M Sh ^ 33 •669 -666 •664 -662 -659 •658 -656 •654 -653 •652 -651 -650 -650 •650 -649 Oi . 34 ■695 •692 •690 •687 ■685 •683 -681 •680 •678 •677 •676 -675 -675 •675 -675 35 •722 •719 •716 •713 •711 •709 •707 ■705 •704 -703 -702 -701 -701 -700 -700 C« . 03 36° •749 -746 ■743 •740 ■738 -736 •734 •732 ■731 •729 •728 -728 •727 •727 -727 > gs •777 •773 •770 -768 ■76s ■763 -761 •759 •758 •756 ■755 •75s •754 "^^f" •754 «, 3 1 2*0 1 6-005 4003 3-002 2-402 2-001 1-715 1-501 1-334 1-200 1-091 i-ooo •923 -857 -800 ■rt 4 16-03 8-013 5-342 4-006 3-205 2-670 2-289 2-002 1-780 1-602 1-456 1-334 1-231 I -143 1 067 ^3 S 20-05 10-03 6-683 5-012 4-010 3-341 2-864 2-505 2-227 2-004 I -821 1-669 1-541 1-430 1-335 « 6° 24-09 12-04 8-029 6-021 4-817 4-014 3-440 3-o[o 2-675 2-407 2-188 2-005 1-851 1718 1-604 1 28-14 14-07 9-380 7-034 5-627 4-689 4-019 3-5"6 3-'25 2-812 2-556 2-343 2-162 2-008 1-873 CO 0) (D 8 32-21 16-10 10-74 8-052 6-441 5-367 4-600 4-025 3-577 3-219 2-926 2-682 2-475 2-298 2-144 9 36-30 18-15 12-10 9-074 7-259 6048 5-184 4-536 4-031 3-628 3-297 3-022 2-789 2-590 2-417 31 10 40-41 20 2 1 13-47 10-10 808 1 6-734 5-771 5049 4-488 4-039 3-671 3-364 3-105 2-883 2-690 .a£ 11° 4455 22-27 14-85 u-14 8-908 7423 6-362 5-566 4947 4-452 4-047 3-709 3-423 3-178 2-966 as 12 48-71 24-36 16-24 12-18 9-741 8-117 6-957 6-0S7 5-410 4-868 4-425 4-056 3-743 3-475 3-243 13 52-91 26-45 17-64 13-23 10-58 8-817 7-556 6-611 5-876 5-288 4-806 4-405 4-066 3-775 3-522 3 14 57-14 28-57 19-05 14-28 "-43 9-521 8-161 7-140 6-346 5-711 5-191 4-757 4-391 4-076 3-804 , 2 £ IS 61-41 30-70 20-47 15-35 12-28 10-23 8-770 7-673 6-820 6137 5-578 5-113 4719 4-381 4-088 ^ g i6° 65-72 32-86 21-90 16-43 13-14 10-95 9-385 8-211 7-298 6-568 5 -970 5-472 5-050 4-688 4-375 ^S % 70-07 35-03 23-35 17-52 14-C1 ri-68 lOOI 8-755 7-781 7-002 6-365 5-834 5-384 4-999 4-665 1 i8 74*47 37-23 24-82 18-61 14-89 12-41 10-63 9-304 8-270 7-442 6-764 6-200 5722 5-312 4-957 2p 19 7891 39-46 26-^0 19-73 '51! 13-15 11-27 9-860 8-764 7-886 7-168 6-570 6-064 5630 5-253 60 "g 2a 8342 41-71 27-80 20-85 16-68 13-90 11-91 10-42 9-264 8-336 7-577 6-945 6-410 5-951 5-553 3 o • 21° 87-97 4399 29-32 21-99 17-59 14-66 12-56 10-99 9-770 8-792 7-992 7-325 6-760 6-276 5-857 2 S lu 22 92-60 46-30 30-86 23-15 18-52 15-43 13-22 I '-57 10-28 9-254 8-411 7-709 7-115 6-606 6-164 23 97-28 4864 32-43 24-32 19-45 16-21 13-89 12-16 10-80 9-722 8-837 8-099 7-475 6-940 6-476 24 102-0 51-02 34-01 25-51 20-40 17-00 14-57 12-75 11-33 10-20 9-269 8-495 7-841 7-279 6-793 •^ (D en 03 "^ O 25 106-9 53-43 35-62 26-71 21-37 17-81 15-26 13-35 11-87 10-68 9708 8-897 8-212 7-624 7-115 g-S" 26° 111-8 55-89 37-26 27-94 22-35 18-63 15-96 13-97 12-41 11-17 10-15 9-307 8-589 7-974 7*441 s^5 27 n6-8 58-39 38-92 29-19 23-35 19-46 16-68 14-59 12-97 11-67 10-61 9-722 8-973 8-331 7774 g&^ 28 121-9 60-93 40-62 30-46 2437 20-31 17-40 1523 13-53 1218 11-07 10-15 9-364 8-693 8-112 a -^ 29 127-0 63-52 42-34 31-76 25-40 21-17 18-14 15-87 1411 12-70 ii-54 10-58 9-762 9-063 8-457 asti 30 J 32 3 66-16 44-10 33-08 26-46 22-05 18-90 '6-53 14-69 13-22 12-02 11-02 10-17 9-440 8-809 Ci-i 31° '37-7 68-85 45-90 34-42 27-54 22-95 19-67 17-21 15-29 13-76 12-51 11-47 10-58 9-824 9-167 [ous Lt. o: the 32 143-2 71-60 47-73 35-80 28-64 23-86 20-45 17-90 15-90 14-31 13-01 11-92 11-00 10-22 9-534 33 148-8 7441 49-61 37-21 29-76 24-80 21-26 18-60 16-53 14-87 13-52 12-39 11-44 10-62 9-908 34 154-6 77-29 51-53 38-64 30-91 25-76 22-08 19-32 17-17 15-45 14-04 12-87 11-88 11-03 10-29 33 160-5 80-24 53-49 40-11 32-09 26-74 22-92 20-05 17-82 16-04 14-58 13-36 1233 11-45 10-68 «S| 36° 166-S 83-25 55-50 41-62 33-30 27-75 23-78 20-80 18-49 16-64 15-13 13-86 12-79 11-88 11-08 bj -H Pi 37 172-7 86-35 "■s^ 43-17 34-53 28-78 24-66 21-58 19-18 17-26 '569 14-38 13-27 12-32 11-50 38 179-r 89-53 59-68 44-76 35-81 29-84 25-57 22-37 19-89 17-89 1627 14-91 1376 12-77 11-92 •S £>. 39 185-6 92-79 6 1-86 46-39 3r'3 30-92 26-50 23-19 20- 6 1 18-55 16-86 15-45 14-26 13-24 12-35 12-80 40 192-3 96-15 64-10 4807 38-46 32-04 27-46 24-03 21-36 19-22 '7-47 16-01 14-78 1372 41° 199 -a 99-61 66-40 49-81 39-84 33-20 28-45 24-89 22-12 19-91 18-10 16-59 15-31 14-21 13-26 0) 07 42 2o6'4 103-2 68-78 51-58 41-26 34-39 29-47 25-78 22 92 20-62 18-75 17-18 15-86 14-72 55 43 213-7 106-9 71-23 53*42 42-74 35-61 30-52 26-70 23-73 21-36 19-41 17-79 16-42 15-25 14-23 44 221 '3 iij-7 73-77 55-32 44-26 36-88 31-61 27-66 24-58 22-12 20-10 18-43 17-01 i';-7o 1473 15-26 ■"5 45 229-2 1146 76-39 57-29 45-83 38-19 32-73 28-64 25-45 22-90 20-82 19-08 1761 16-35 46° 237-3 118-7 79-10 59-33 47-46 39-55 3389 29-66 26-36 23-72 21-56 19-76 18-24 16-93 15-80 4Z 245-8 122-9 81-92 61-44 49-15 40-95 35-10 30-71 27-29 24-56 22-33 20-46 18-89 17-53 18-16 16-36 16-94 18-18 g''»3 48 ^l'*'! 127-3 84-84 63-63 50-90 42-41 36-35 31-80 28-27 25-44 23-12 21-19 1956 -a . 49 2636 131-8 87-88 65-91 52-72 43-93 37-65 32-94 29-28 26-35 23-95 21-95 20-26 18-81 5^' SO 273-1 136-6 91-04 68-28 54-62 45-51 39-01 34-13 30-33 27-30 24-81 22-74 20-99 19-49 Si° 283-0 141-5 94-33 70-75 ^ol? 47-16 40-42 35-36 31-43 28-28 25-71 23-56 21-71; 20-19 20-93 21-70 22-50 23-35 18-84 19-53 2025 21-00 52 293-3 146-7 97-77 73'33 58-66 4888 41-89 36-66 32-58 29-32 26-65 24-42 22-54 p: S3 54 304-1 315-4 152-1 157-7 101-4 105-1 76-02 78-85 60-82 63-08 50-68 52-56 43-43 45-05 38-01 39-42 33-78 35-03 30-39 31-52 27-63 28-65 25-32 26-26 23-37 24-24 25-15 09 55 327-3 163-6 109-1 81-81 65*45 54-54 4674 40-89 36-35 32-71 29-73 27-25 21-79 1 56° 339-8 169-9 113-3 84-93 67-94 56-62 48-52 42-45 37-73 33-96 30-87 28-29 26-11 24-24 25-18 26-17 27-21 28-32 22-62 % 352-9 366-8 176-5 183-4 117-6 122-2 88-22 91-69 70-57 73-34 5881 6i-ii 50-40 52-38 44-10 45-83 39-19 40-73 35-27 36-65 3206 33-32 29-38 30-54 27-12 28-18 23-49 24-42 25-39 26-43 12 381-4 igo-7 127-1 95 '35 76-27 63-56 54-47 47-66 42-36 38-12 34-65 7 ^1-76 29-31 30-50 5 60 397-0 198-5 132-3 99-23 79-38 66-14 56-69 49-60 44-08 39-67 36-06 0* /** 33-05 61° 62 64 65 413-5 4310 449-8 469-9 491-5 206-7 2'5S 224-9 234-9 245-7 137-8 i43'7 149-9 156-6 1638 103-4 107-7 112-4 .17-5 122-9 82-68 86-19 89-95 9396 98-28 68-89 71-82 74-95 78-30 81-90 59-05 61-56 64-24 67-11 70-19 51-66 53-86 56-20 5871 61-41 45-92 47-87 49-95 52-18 54-58 41-32 43-08 46 96 49-12 37-56 39-15 40-86 42-68 44-65 34-42 35-89 37-45 39 12 40-92 3177 33-12 34-56 36-11 37-77 29-50 30-75 32-09 33-52 35-06 27-52 28-69 29-94 3128 3272 m 59 m ' 58 m 57 m 56 m 55 m 54 m 53 m 52 ni 51 m 50 m 49 m 48 m 47 m 46 m 45 (1791°) (i79n (i79i°) (179°) (1781°) (■78^) (178*°) (178°) (■771°) (1774°) (i77i°) ("77°) (■761°) (i76i°) (i76r) for the Azimuth ; II HOURS. -The Sign is always -(-, except when the Hour-Angle exceeds 6 hours. B 26 USEFUL NAVIGATIONAL STARS IN ORDER OF DECLINATION. 4 3 Names of Stars. HOURS. m 1 m 2 m 3 m 4 m 5 m 6 m 7 m 8 m 9 m 10 m 11 m 12 m 13 m 14 m 15 (oi°) (04°) (of) (1°) dn (iF) (If") (2°) {21°) (24°) (2i1 (3°) (3*°) (34°) (31°) 2-7 1-9 Var. 0-3 Menkar . . . Procyon . . . Bellatrix . . Bbtblgubse . . RlGEL .' . . . 14-81 2 '99 25-14 2972 33-50 7-405 n-oo 12-57 14-86 16-75 4937 7-33' 8-379 9907 II-I7 3-703 5-499 6-284 7-430 8-376 2-962 4-399 5-028 5-944 6-701 2-469 3-666 4-190 4954 5-585 2-116 3-142 3-591 4-246 4-787 1-852 2-750 3-143 3716 4-189 1-646 2-444 2-794 3-303 3724 1-482 2-200 2-514 2-973 3-351 1-347 2-000 2-286 2-703 3-047 1-235 1-834 2-096 2-478 2-793 1-140 1-693 1-935 2-287 2-579 1-059 1-572 1-797 2-124 2-395 •988 1-467 1-677 1983 2-235 I'O 27 2-4 1-2 Altair. . . . k[ffa borealis Enif . . . . Spica . . . 34-68 36-36 38-01 43-05 17-34 i8-i8 19-00 21-53 11-56 12-12 .2-67 14-35 8-670 9-090 9-503 10-76 6-936 7-272 7-602 bol 1 5-780 6 -060 6-335 7-176 4-955 5-195 5-431 6-151 4-335 4-546 4-752 5-383 3 854 4-041 4-224 4-785 3-469 3-637 3-802 4-307 3-154 3-306 3'457 3-915 2-891 3-031 3-169 3-589 2-669 2-798 2-925 3-314 2-478 2-599 2717 3-077 2-313 2.-426 2'S36 2-872 1-4 2-2 2-6 2-2 Regulus . . . Kas Alhague . Markab . . . Denebola . . 50-62 51-37 59-99 61-97 25-31 25-68 29-99 30-99 16-88 17-12 20-00 20-66 12-66 12-84 15-00 15-49 10-13 10-27 12-00 12-40 8-438 8-562 9-999 10-33 7-233 7-339 8-571 8-855 6-329 6-422 7-500 7-748 5-626 5-709 6-667 6-888 5064 5-138 6-000 6-199 4-604 4-671 5 "155 5 -636 4-221 4-282 5-001 5-167 3-896 3-953 4-617 4-770 3-618 3-671 4-287 4429 3-377 3-427 4-002 4-134 i-o 2-0 -1-4 2-1 Aldebaran . . Alhena . . . SlRIUS .... Deneb-Kaitos . 67-05 67-82 68-23 76-84 33'53 33-91 34-12 38-42 22-35 22-6l 22-74 25-61 16-76 16-96 17-06 19-21 13-41 13-57 1365 15-37 iri8 11-30 "•37 12-81 9581 9-690 9-749 10 98 8-383 8-479 8-531 9-607 7-452 7-538 7-583 8-540 6708 6-784 6-825 7-687 6-098 6-168 6-205 6-988 5 -590 5-654 5-689 6-406 5-161 5-220 5-252 5-914 4-793 4-847 4-877 5-492 4'473 4-525 4-552 5-126 o-o 2-S 2-0 Arcturus . . Algeiba . . . Hamel. . . . Antarbs . . . 82-07 84-99 97-23 112-8 41-04 42-50 4862 56-41 27-36 28-33 32-41 37-61 20-52 21-25 24-31 28-21 16-42 17-00 19-45 22-57 13-68 14-17 16-21 18-81 11-73 12-14 13-89 l6-12 10-26 10-63 12-16 14-11 9-122 9-446 10-81 12-54 8-2IO 8-502 9726 11-29 7-464 7-730 8-843 10-26 6-843 7 -086 8-107 9-406 6-317 6-541 7-484 8683 5-866 6-075 5-475 5-670 6-487 7-527 2-3 2-4 I'l 1-9 a Sap'tlarii . . Alphacca . . Pollux . . . Nath . . . . "3-9 117-0 123-2 124-6 5694 61-62 62-28 37-96 39-01 41-08 41-52 2847 29-26 3081 31-14 22-78 23-41 24-65 24-91 18 -98 19-51 20-54 20-76 16-27 16-72 17-61 17-80 14-24 14-63 15-41 15-57 12-66 13-01 13-70 13-84 11-39 1 1 71 12-33 12-46 10-36 10-64 11-21 11-33 9-494 9-757 10-27 10-38 8-764 9-007 9-485 9-586 8-139 8-365 8808 8-902 7-597 8-222 8-310 I -5 I -3 2-0 27 Adara .... Fomalhaut . . Castor. ... Phact 126-2 1 33-' 143-8 155-3 63-09 66-57 71-91 77-66 42-06 44-38 47-94 51-78 31-55 3328 3595 38-83 25-24 26-63 28-76 31-07 21-03 22-19 23-97 25-89 18-03 19-02 20-55 22-19 15-78 16-64 17-98 1942 14-02 14-80 15-98 17-26 12-62 13-32 14-39 15-54 U-48 1211 13-08 1413 10-52 11-10 11-99 12-95 9711 10-25 11 07 11 95 9-019 ?o^-2i ii-io 8'4i8 8-882 9-594 10-36 2'I 2-2 17 0-2 Kaus Australis Mirach Mizar . e Centauri . . Vega . . . . '57-1 i6i"o 165-8 •83-5 78-56 80-51 82-88 91-78 52-37 53-67 55-26 61-18 39-28 40-26 41-44 45-89 31-43 32-21 33-16 36-71 26-19 26-84 2763 30-59 22-45 23-01 23-68 26-23 19-64 20-13 20-72 22-95 17-46 17-90 18-42 20-40 15-72 16-11 16-58 18-36 14-29 14-64 15-08 16-69 13-10 13-42 13-82 15-30 12-09 12-39 12-76 14-13 11-23 11-51 11-85 13-12 10-48 10-74 11-06 12-25 2-2 2-4 2-1 I -5 Almach . . . a Pkeenicis . . e Scarpa . . . Arided. . . . 205-3 2I2'6 213-2 2286 102-6 106-3 1066 II4-3 68-43 7087 71-08 76-19 51-32 53-15 53-31 57-14 41 06 42-52 42-65 45-72 34-22 35-44 35-54 3810 29-33 30-37 30-47 32-66 25-66 26-58 2666 28-58 22-81 23-63 23-70 25-40 20-53 21-27 21-33 22-86 1867 19-33 19-39 20-79 17-11 17-72 17-78 19-06 15-80 16-36 16-41 17-59 14-67 15-19 1524 16-34 13-69 14-18 14-23 15-25 0-2 1-9 1-9 2-0 Capella . . . o Grm's . . . MiRFACK . . . Benetnasch. . 2365 249-6 268-4 -71-3 llS-2 124-8 134-2 1357 78-83 83-21 89-47 90-44 59-12 62-41 67-10 67-83 47-30 49-93 53 -6^ 54-27 39-42 41-61 44-74 45-22 33-79 35-67 38-35 38-77 29-56 31-21 33-56 33-92 26-28 27-74 29-83 30-15 2365 24-97 26-85 27-14 21-51 22-70 24-41 24-67 1971 20-81 22-38 22-62 18-20 19-21 20-66 20-88 16-90 17-84 19-18 19-39 15-78 16-65 17-91 i8-io 2-4 0-4 Var. 2'I Etanin . . . Canopds . . . Schedar . . . o ravonis . . . 288-1 300-2 3.59-6 3537 144 -I I50-I 169-8 176-8 96-05 lOO-I 1 13-2 117-9 72-04 75-06 84-91 88-42 57-63 60 05 67-93 7074 48-03 50-04 56-61 58-95 41-17 42-89 48-53 50-53 36-02 37-53 42-46 44-22 32-02 33-36 37-75 39-31 28-82 3003 33-97 35-38 26-20 27-30 30-89 32-16 24-02 25-03 28-32 29-49 22-18 23-11 26-14 27-22 20-59 21-46 24-27 25-28 19"22 20-03 22-66 23-59 I'O 17 I "2 Achernar . . Tureis .... /3 Cyucis . . . j8 Centauri . . 363-2 379-3 3836 395-2 181 -6 189-6 191 -8 197-6 121 -I 126-4 127-9 I3I7 90-79 94-82 72-64 75-86 7672 79-05 60-53 63-22 63-94 65-88 51-89 54-19 54-80 56-47 45-40 47-42 47-96 49-41 40-36 42-15 42-63 43-92 36-33 37-94 38-37 39-53 33-03 34-49 34-88 35-94 30-28 3162 31-98 32-95 27-95 29-19 29-52 30-42 25-96 27-11 27-42 28-25 24-23 25-30 25-59 26-37 2-0 i4 2-2 2-0 2-1 DUBHE .... ai Cruets . . . a Tri. Austral. . /3 ArgHs . . . Kochab . . . 436-4 441 -I 592-2 606-7 830-0 218-2 220-6 296-1 303*3 415-0 145-5 147-0 197-4 202-2 2767 109-1 110-3 148-1 1517 207-5 87-28 88-23 118 5 121-3 1660 72-73 73-52 98-72 lOl-l 138-4 62-35 63-02 84-62 86-68 118-6 54-56 SS-15 74-04 75-85 103-8 48-50 49-02 65-82 67-43 92-25 43-65 44-12 59-24 60-69 8303 39-68 40-12 53-86 55-17 75-48 36-38 3677 49-37 50-58 69-20 33-58 33-95 46-69 63-88 31-19 31-53 42-33 43-36 59-32 29-11 29-43 3951 40-47 55-37 m 59 m 58 m 57 m 56 m 55 m 54 m 53 m 52 m 51 m 50 m 49 m 48 m 47 m 46 m 45 (1791*) {I79i°) (i79r) (179°) (1781°) (1784°) {'7H°) (178°) (1771°) (1774') (1771°) (177°) (i76r) (1764°) (i76i°) For the Azimuth -{ M HOURS. When Latitude and Declination are of contrary names, the Sign is +. When Latitude and Declination are of same name, the Sign is — . 27 The Head-line has vaFious significations, according to the FFoblem in use. In Problem IV. it reppesents Diff. of Long. In Problem V. the Initial Course. Complement of the Diff. of Long. In Problem VIIL the Diff. of Long. In Problems X. and XI. In Problem VI. the True Azim. the Lat. HOURS. m 16 (4') m 17 (4i°) m 18 (4*°) m 19 (41°) m 20 (5°) 21 (Si") m 22 (SF) m 23 (51°) m 24 (6°) m 25 (6J°) m 26 (6i°) m 27 (61°) m 28 (7°) m 29 m 30 (7i°) g u a s| .So S3 ^ o « o , Sag; (d .o ft . P KJiJ 01 .*" ^|S a g -u a> * a O £ 5 o' I 2 3 4 5 6' 7 8 9 10 12 13 14 IS 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- 42 48 49 SO 51° 52 S3 54 55 S6° 57 58 61° 62 64 65 •000 •250 •499 •749 i"ooo I "251 I "503 1756 2"OIO 2*265 2 '522 2780 3-040 3-302 3-S66 3-832 4'ioi 4"372 4-647 4-924 5-205 5-490 5-778 6-070 6-367 6-669 6-975 7-287 7-604 7-927 8-256 8-593 8-936 9-287 9-646 lO'OI 10-39 10-78 11-17 11-58 12-00 12-43 12-88 13-34 13-81 14-30 14-81 15-34 15-88 16-45 17-04 17-66 18-30 18-98 19-68 20-42 21-20 22 -02 22-89 23-80 24-77 25-80 26-90 28-07 29-32 30-67 44* (176") -000 ■235 •470 -70s •941 1-177 I -414 1-652 I -891 2-131 2-373 2-616 2-86o 3-107 3-355 3-606 3-859 4-114 4-372 4-633 4-898 5-166 S-437 5712 5-991 6-275 6-563 6-856 7-I5S 7-459 7-769 8-086 8-409 8739 9-077 9-422 9-777 10-14 10-51 10-90 11-29 11-70 12-12 12-55 12-99 13-46 13-93 14-43 14-95 15-48 16-04 16-62 17-22 17-86 18-52 19-22 19-95 20-72 21-54 22-40 23-31 24-28 25-31 26-41 27-59 28-86 m 43 (■751°) •000 -222 •444 -666 •889 1-112 1-33S 1-560 1-786 2-012 2-240 2-470 2-701 2-933 3-168 3-405 3-643 3-885 4*128 4-375 4-625 4*877 5 -134 5-393 5-657 5-925 6-197 6*474 6756 7-043 7-336 7-635 7-940 8-252 8-570 8-897 9-232 9-575 9-927 10-29 10-66 11-05 11-44 11-85 12-27 12-71 13-16 13-63 14-11 14-62 15-14 15-69 16-26 16-86 17-49 18-15 18-S4 19-57 20-33 21-15 22-01 22-92 23-90 24-94 26-05 27-25 ' m 42 (i7sn •000 ■210 -420 -631 -842 1-053 1-265 1-478 1-691 1-906 2-339 2-558 2778 3-001 3-225 3-451 3-679 3-910 4-144 4-380 4-620 4-862 5-108 5-358 5-612 5-870 6-132 6-399 6-671 6-948 7-231 7-520 7-815 8-117 8-427 8*744 9-069 9-402 9-745 10-10 10-46 10-84 11-22 11-62 12-03 12-46 12-91 13-37 13-84 14-34 14-86 15-40 15-97 16-56 17-19 17-84 18-53 19-26 20-03 20-84 21-71 22*63 23*62 24*67 25-81 41 ('75i°) -000 -200 •399 -599 •799 l-QOO 1 -201 ' 1-403 i-6o6 1-810 2-015 2-222 2-430 2-639 2-850 3-063 3-278 3-495 3-714 3-936 4-160 4-388 4-618 4-852 5-089 5-330 5-575 5-824 6-077 6-336 6-599 6-868 7-142 7-423 7-710 8-003 8-304 8-613 8-930 9*256 9-591 9-936 10*29 10-66 11-04 11-43 11-84 12-26 12-69 13-15 13-62 14-11 14-63 15-17 15-73 16-32 16-95 17-60 18-29 19-02 19-80 20-62 21-50 22-43 23-44 24-51 ra 40 (>75°) •000 -190 -380 -570 -761 -952 1-144 1-336 1-530 1-724 1-919 2-115 2-313 2-513 2713 2-916 3-121 3-327 3-536 3-747 3-961 4-178 4-397 4-620 4-845 5-075 5-308 5-545 5-787 6-033 6-283 6-539 6-800 7-067 7-341 7-620 7-907 8-20I 8-503 8-8x3 9-132 9-460 9-799 10-15 10-51 10-88 11-27 11-67 12-09 12-52 12-97 13-44 13-93 14-44 14-98 15-54 16-13 16-76 17-42 18-11 18-85 19-63 20-47 21-36 22-31 23-34 m 39 (1741°) -000 -181 -363 -544 -726 -909 1-092 1-275 1-460 1-645 1-831 2-019 2-207 2-398 2-589 2-783 2-978 3-175 3-374 3-576 3-780 3-987 4-196 4-408 4-624 4-843 S-065 5-292 5-522 5-757 5-996 6-240 6-490 6-744 7-005 7-272 7-545 7-826 8-114 8-410 8714 9-028 9-351 9-685 10-03 10-39 10-75 11*14 11-53 11-95 12-38 12-82 13-29 13-78 14-29 14-83 15-40 15-99 16-62 17-28 17-99 18-74 19-53 20-38 21-29 22-27 m 38 (1744°) -173 -347 -521 -694 -869 1-044 1-219 1-396 I -573 1-751 1-930 2-111 2-293 2-476 2-661 2-848 3-036 3-227 3-420 3-615 3-812 4-012 4-215 4-422 4-631 4-844 5-060 5-280 5-505 5-734 5-967 6-206 6-449 6-699 6-954 7-215 7-484 7-759 8-042 8-333 8-633 8-942 9-261 9-590 9-931 10-28 10-65 11*03 11-42 11-84 12-26 12-71 13-18 13-67 14-18 14-72 15-29 15-89 16-53 17-20 17-92 18-68 19-49 20-36 21-30 111 37 (1741°) ■000 *i66 •332 •499 -665 -832 1-000 I -168 1-337 1-507 1-678 1-849 2-022 2-197 2-372 2-549 2-728 2-909 3-091 3-276 3-463 3-652 3-844 4-039 4-236 4-437 4-640 4-848 5-059 5-274 5 -493 5-717 5-945 6-179 6'4i8 6-662 6-913 7-170 7-433 7-705 7-984 8-271 8-567 8-872 9-188 9-514 9-852 10-20 10-57 10-95 11-34 11-75 12-18 12-63 13-10 13-59 14-11 14-65 15-23 15-83 16-48 17-16 17-89 18-67 19-51 20-40 m 36 (174°) -000 •159 -319 •479 -639 -799 -960 1-121 1-283 1-446 1-610 1-775 1-941 2-108 2-277 2-447 2-618 2-792 2-967 3-144 3-323 3-505 3-689 3-876 4-065 4-258 4-453 4-652 4-855 5-061 5-272 5-486 5-706 5-930 6-159 6-394 6*634 6*881 7-134 7-394 7-662 7-937 8-222 8-515 8-818 9-131 9-455 9-792 10-14 10-50 10-88 11-28 11-69 12-12 12-57 13-04 13-54 14-06 14-61 15-20 15-82 16-47 17-17 17-92 18-72 19-58 m 35 (173?°) -000 -153 -307 -460 -614 -768 -923 1-078 1-234 1-390 i-54« 1*706 1*866 2-026 2-i88 2-352 2-517 2-683 2-852 3-022 3-195 3-369 3-546 3-726 3-908 4-093 4-281 4-472 4-667 4-865 5-067 5-274 5-484 5-700 5-920 6*146 6-377 6-614 6-857 7-107 7-365 7-630 7-903 8-185 8-476 8777 9-089 9-412 9-748 10-10 10-46 10-84 11-23 11-65 12-08 12-53 13-01 13-52 14-05 14-61 15-20 15-83 16-51 17-23 18-00 18-82 m 34 (i73i°) -000 -148 -295 -443 -591 -739 •888 1-037 1-187 1-338 1-490 1-642 1-796 1-951 2-107 2-264 2-423 2-583 2-745 2-909 3-075 3-243 3-414 3-586 3-762 3-940 4-121 4-305 4-492 4-683 4-878 5-077 5 -279 5-487 5-699 S-916 6-139 6-367 6-601 6-842 7-090 7-345 7-607 7-879 8-159 8-449 8-749 9-060 9-384 9-719 10*07 10*43 io-8i 11-21 11-63 12-07 12-53 13-01 13-52 14-06 14-63 15-24 lS-89 16*58 17-32 18*12 m 33 (1734°) *142 *284 -427 *570 -713 -856 1*000 1-145 1*290 1-436 1-583 1-731 i*88o 2*031 2*182 2-335 2*490 2*646 2-804 2*964 3*126 3*291 3-457 3-626 3-798 3-972 4-150 4-330 4-514 4-702 4-894 5-089 5-289 5-493 5-703 5-917 6-137 6-363 6-595 6-834 7-080 7-333 7-595 7-865 8-144 8-434 8-734 9-045 9-369 9-706 10-06 10-42 10-81 11-21 11-63 12-07 12-54 13-03 13-55 14-11 14-69 15-32 15-98 16*70 17-47 m 32 (173°) -000 -137 -275 -412 -550 -688 -826 -96s 1*105 I -245 1-386 1-528 1-671 1-815 1-960 2-106 2-254 2-403 2-554 2-707 2-861 3-017 3-176 3-337 3-500 3-666 3-834 4-005 4-180 4-357 4-538 6-833 7*078 7-330 7-591 7-861 8-140 8-430 8*730 9-043 9*368 9-707 10-06 10-43 10-82 11-23 11*65 12*10 12*58 13-08 13-62 14-18 14-78 15-43 l6-I2 16-85 31 (1721°) 4-723 4-564 4-912 4-746 5-105 4-933 5-302 5-123 5 -504 5-319 5-711 5-519 5-923 5-724 6-141 5-934 6-36^ 6-151 6-596 6-374 •133 ■265 •398 -531 -665 798 -933 1-068 1*203 1-339 1*476 1-615 1-754 1-894 2-035 2*178 2*322 2*468 2*615 2-765 2-916 3-069 3-224 3-382 3-542 3-705 3-870 4-039 4-210 4-385 6-603 6-839 7-083 7-335 7-596 7*866 8-145 8-436 8-738 9-052 9-380 9-722 10-08 10-45 10-85 11*26 11*70 12*16 12-64 13-16 13-70 14-29 14-91 15-57 16-29 m 30 (I72i°) For the Azimuth :—' II HOURS. The Sign is always +, except when the Hour-Angle exceeds 6 hours. B 28 USEFUL NAVIGATIONAL STARS IN ORDER OF DECLINATION. 1 1 Names of Stars. HOURS. m 16 m 17 m 18 m 19 m 20 m 21 m 22 m 23 m 24 m 25 m 26 m 27 m 28 m 29 m 30 (4°) (4r) (4r) (41°) (5°) (5i°) (5i°) (51°) (6°) (6i°) (64°) (61°) (7°) (7i°) (7i°) 27 1-9 Var. 0-3 Menkar . . . Procyon . . . Bellatrix . . Betelguese . , RlGEL .... •926 1-376 1-572 I -859 2-096 -872 I -29s 1-480 1-750 1-973 •824 1-223 1-398 1-653 1-863 -780 I -159 1-324 1-566 1-765 -741 I-IOI 1-258 1-677 -706 1-049 I -199 1-417 1-598 -674 I -001 1-144 1-353 1-525 -645 -958 1-095 1-294 1-459 -618 -918 1-049 I -241 1-399 -594 -881 1-007 1-191 1-343 •lis -969 1-146 I -291 ■^59 •816 •933 1-103 1-244 -530 ■787 -900 1-064 I -200 -512 -760 -869 1-028 1-158 ■495 •735 •840 -993 1-120 i*o 27 2-4 1*2 Altair. . . . KlFFA BOREALIS Enif . . . . Spica .... 2-169 2-274 2-377 2-693 2-042 2-141 2-238 2-535 1-928 2-022 2-II4 2-394 1-827 1-916 2-003 2-269 1-736 1-820 1-903 2-155 1-654 J -734 l-8l2 2-053 1-579 1-655 1-730 1-960 1-510 1-583 1-655 1-875 1-448 1-518 1-587 1-797 1-390 1-457 1523 1-726 1-337 1-401 1-465 1-659 1-287 1-350 1-411 1-598 1-242 1-302 1-361 1-541 1-199 1-257 I -314 1-489 1-159 1-215 1-271 1-439 1 "4 2-2 2-6 2 "2 Regulus . . . RasAlhague . Markab . . . Denebola . . 3-167 3-213 3-7S2 3-876 2-981 3-024 3-532 2-815 2-857 3-336 3-446 2-668 2-707 3-161 3-265 2-534 2-572 3-003 3-103 2-414 2-449 2-860 2-955 2-305 2-338 2-731 2-821 2-205 2-237 2-6l2 2-699 2-113 2-144 2-504 2-587 2-029 2-059 2-404 2-484 1-951 1-980 2-312 2-389 1-879 1-907 2-227 2-301 1-813 1-839 2-148 2-219 1750 1-776 2-074 2-143 1-692 1717 2-005 2-072 i-o 2-0 -1-4 2-1 Aldebaran . . Alhena . . . SiRIUS .... Dkneb-Kaitos . 4-194 4-242 4-268 4-807 3-948 3-993 4-017 4-524 3-729 3-772 3-795 4-273 3-533 3-574 3-595 4-049 3-357 3-395 3-416 3-847 3-198 3-234 3-053 3-087 3-106 3-498 2-920 2-954 2-972 3-347 2-799 2-831 2-848 3-208 2-687 2718 2-735 3-080 2-585 2-614 2-630 2-962 2-489 2-518 2-533 2-853 2-401 2-428 2-443 2-751 2-318 2-345 2-359 2-657 2-242 2-267 2-281 2-569 o-o 2-0 I'l Arcturus . . Algeiba . . . Hamel. . . . Antares , . . S-134 S-316 6-082 7-057 4-832 5 -004 6-643 4-564 4727 5-407 6-274 4-325 4-478 5-123 5-945 4-109 4-255 4-868 5-648 3-914 4-053 4-637 5-380 3-736 3-869 4-427 5-136 3-574 3-702 4-235 4-914 3-426 3-548 4-059 4710 3-289 3-406 3-897 4-522 3-163 3-276 3-748 4-349 3-047 3-155 3-610 4-188 2-938 3-043 ■ 3-481 4-039 2-838 2-939 3-362 3-901 2-744 2-841 3-250 3-771 2-3 2-4 I'l 1-9 a Sagitlarii . . Alfhacca . . Pollux . . . Nath .... 7-123 7-320 7-709 7-791 6-704 6-891 7-256 7-334 6-333 6-508 6-853 6-927 6-000 6-167 6-494 6-563 5-701 5-859 6-170 6-236 5-430 5-581 5-877 5-940 5-184 5-328 5-610 5-670 4-959 5-097 S-367 5-425 5-144 5-199 4-564- 4-691 4-939 4-992 4-389 4-511 4750 4-801 4-227 4-345 4-575 4-624 4-077 4-190 4-412 4-460 ' 3-937 4-046 4-261 4-307 3-807 3-912 4-120 4-164 1-3 2-0 27 Adara .... Fomalhaut . . Castor. . . . Phact .... 7-893 8-328 8-996 9716 7 '429 7-838 8-467 9-145 7-017 7-404 7-998 8-638 6-649 7-015 7-578 8-185 6-317 6-665 7-200 7-776 6-017 6-349 6-858 7-407 5-744 6-061 6-547 7-071 5-495 5-798 6-263 6-765 5-267 5-557 6-003 6-484 5-057 5 -336 5-764 6-225 4-864 5-131 5-543 5-987 4-684 4-942 5-33? 5-766 4-518 4-767 5-149 5-561 4-363 4-603 4-972 5-370 4-218 4-450 4-807 5-192 2'I 2-2 17 0"2 Kaus Australis MiRACH MiZAR . Centaori . . Vega .... 9-828 10-07 Jo-37 11-48 9-250 9-480 9-760 10-81 8737 8-955 9-219 10-21 f'^79 8-484 8735 9-672 7-866 8-061 8-299 .9-189 7-492 7-678 7-905 8-753 7-152 7-330 7-546 8-356 6-842 7-012 7-219 7-994 6-558 6-721 6-920 7-662 6-297 6-644 7-357 6-056 6-206 6-389 7-075 5-832 5-977 6-154 6-814 5-625 5-765 5-935 6-572 5-432 5-567 5-731 6-346 5-252 5 -383 6-136 2 "2 2-4 2"I Almach . . . a Phanicis . . e Scorpii . . . Abided. . . . 12-84 13-30 13-34 14-30 12-09 12-52 13-46 11-42 11-82 11-86 1271 10-82 11-20 11-24 12-04 10-28 10-64 10-67 11-44 9-789 10-14 10-17 10-90 9-345 9-678 9-707 10-41 8-940 9-259 9-286 9-954 8-569 8-874 8-901 9-541 8-227 8-521 8-546 9-161 7-912 8-194 8-219 8-810 7-620 7-892 7-916 8-485 7-349 7-611 7-634 8-183 7-097 7-350 7-372 7-903 6-862 7-107 7-128 7-641 0-2 1-9 1-9 2"0 Capella . . . a Gruis , . . MjRFACK . . . Benbtnasch . . 14-79 15-61 16-79 16-97 13-92 14-70 15-80 15-97 14-93 15-09 12-46 13-15 14-14 14-30 11-84 12-50 13-44 13-58 11-28 11-90 12-80 12-94 1077 11-36 12-22 12-35 10-30 10-87 11-69 11-82 9-871 10-42 11-20 11-33 9-478 10-01 10-76 10-87 9-114 9-622 10-34 10-46 8778 9-267 9-963 10-07 8-466 8-938 9-609 9-714 8-176 8-631 9-280 9-381 7-905 8-345 8-972 9-070 2-4 0-4 Var. 2'I Etanin . . . Canopus . . . SCHEDAR . . . a Pavonis. . . 1 8 -02 18-78 21-24 22-ia 16-96 17-68 20-00 20-82 16-02 16-70 18-89 19-67 15-18 15-82 17-90 18-64 14-42 15-03 17-00 17-71 13-74 14-32 16-20 16-86 13-12 13-67 15-46 16-10 12-55 13-07 14-79 15-40 12-03 12-53 14-18 14-76 11-55 12-03 13-61 14-17 ii-ii 11-57 13-09 13-63 10-70 11-14 12-61 13-13 10-32 1075 12-16 12-66 9-962 10-38 11-74 12-23 9-632 10-04 11-35 11-82 I-O 2-S 17 1*2 ACHBRNAR . . TUREIS .... /3 Crucis . . . p Centauri , . 22-72 23-72 23-99 24-72 21-38 22-33 22-58 23*27 20-20 21-09 21-33 21-98 19-14 19-98 20-21 20-82 18-18 18-99 19-20 19-79 17-32 18-08 18-29 18-85 16-53 17-27 17-46 17-99 15-82 16-52 16-71 17-21 15-16 15-83 i6-oi 16-50 14-56 15-20 15-37 15-84 14-00 14-62 14-78 15-23 13-48 14-08 14-24 14-67 13-00 13-58 13-73 14-15 12-56 13-11 13-26 13-66 12-14 12-68 12-82 13-21 2-0 2-2 2-0 2-1 Dubhe .... a' Crucis . , . a Tri. Austral. . /3 Argils . . . KOCHAB . . . 27-29 27-59 37-04 37-9S 51-92 25-69 25-97 34-87 35-72 48-87 24-27 24-53 32-94 33-74 46-16 22-99 23-24 31-21 31-97 43-74 21-85 22-08 29-65 30-37 41-55 20-81 21-03 28-24 28-93 39-58 19-87 20-08 26-96 27-62 37-79 19-00 19-21 25-79 26-42 36-15 I8-2I 18-41 2472 25-32 34-65 17-49 17-68 23-74 24-32 33-27 16-82 17-00 22-83 23-38 3 1 "99 16-20 16-37 21-98 22-52 30-81 15-62 15-79 21-20 21-72 29-72 15-09 15-25 20-48 20-98 28-70 14-59 14-75 19-80 20-28 27-75 m 44 m 43 m 42 m 41 m 40 m 39 m 38 m 37 m 36 m 35 m 34 m 33 m 32 m 31 m 30 (176°) (1751°) (•7Si°) {.mil (■75°) 0748°) ('74i°) (i74i°) (174!) (■731°) (i73i°) (I73i°) ('73°) (■721°) ("72i°) For the Azimuth : il HOURS. When Latitude and Declination are of contrary names, the Sign is +. When Latitude and Declination are of same name, the Sign is — . 29 The Head-line has various significations according to the Problem in use. In Problem IV. it represents Diflf. of Long. In Problem V. the Initial Course. In Problem VI. the Complement of the Diff. of Long. In Problem VIIL the Diff. of Long. In Problems X. and XI. the True Azim. X •n % 01 . S ^1 I- ^^ .Q g a> *^ a 2S ^o 3 a> .. Sub 3 c8£ S Pi|!4 •« oS CO -u O fi -° a a • r* "-< *j ■SPS«s Moo O 4.|S "2 eS > (U 01 •d - a o Lat. 0' I 2 3 4 S 6° 7 8 9 11° 12 13 14 IS i6° 17 i8 19 20 21° 22 23 24 2S 26° 27 28 29 30 31° 32 33 34 35 36° H 38 39 40 41° 42 43 44 45 46° 42 48 49 SO Si° 52 53 54 SS S6° 57 S8 60 61° 62 ^4 65 HOURS. 31 (71°) •128 •257 •38s •514 •643 772 •902 1-033 I •164 I "296 I '428 1-562 1-696 1-832 2-107 2*246 2-387 2-530 2-674 2-821 2-969 3-119 3-271 3-426 3-584 3-744 3-907 4-073 4-242 4-41S 4-591 4-772 4-956 S-I4S 5-339 5-537 5-741 S-950 6-166 6-387 6-616 6-852 7-096 7-348 7-609 7-880 8-161 8-453 8-757 9-074 9-405 9-751 lo-ii 10-49 10-89 11-31 11-76 12-23 12-73 13-26 13-82 14-42 15-07 15-76 m 29 (I72i°) m 32 (8°) -124 -248 -373 -498 -623 •748 ■874 I -000 1-127 I -255 1-383 1-512 1-643 1-774 1-907 2-040 2-175 2-312 2-450 2-590 2-731 2-875 3-020 3-168 3-318 3-470 3-625 3-783 3-944 4-108 4-275 4-446 4-621 4-799 4-982 5-170 5-362 5-559 5-762 5-971 6-185 6-407 6-635 6-871 7-115 7-368 7-630 7-902 8-185 8-480 8-787 9-107 9-442 9-793 10-16 10-55 1 0-96 11-39 11-84 12-32 12-84 13-38 13-96 14-59 15-26 in 33 m 28 (172°) ■000 •120 '241 •361 •482 •603 ■725 •847 •969 1-092 I -216 I -341 1-466 1-592 1-720 1-848 1-978 2-109 2*241 2-375 2-510 2-647 2-787 2-928 3-071 3-216 3-364 3-514 3-667 3-823 3-982 4-144 4-310 4-479 4-652 4-829 5*011 5-197 5-388 5-585 5-787 5*995 6*210 6-431 6*660 6-897 7-142 7-396 7*660 7 "934 8-219 8-517 8*828 9*152 9-493 9*850 10*22 10*62 11*04 11*48 11-95 12*44 12*97 13-54 14*14 14*79 m 27 (1711°) m 34 (8i°) *00O ■117 -234 •351 •468 •58s •703 -822 -940 I -060 1*180 1*301 1*422 1-545 1*668 1-793 1*919 2*046 2*174 2*304 2-435 2*568 2*703 2*840 2*979 3*120 3-263 3-409 3-558 3-709 3-863 4*020 4*181 4-345 4513 4*685 4*861 5*042 5*228 5-418 5-615 5-817 6*025 6*240 6*462 6*691 6*929 7-175 7-431 7-697 7-974 8-263 8-564 8*879 9*210 9-556 9-920 10-30 10*71 11*14 "■59 12*07 12*58 13-13 13*72 14-35 m 26 (i7ii°) m 35 (81°) *ii3 •227 ■340 •454 •568 •683 •798 -913 1*029 I -146 1-263 I -381 1*500 1*620 1*741 1-863 1*986 2-II1 2-237 2-365 2-494 2*625 2*758 2*893 3-030 3*169 3-310 3-455 3-601 3-751 3-904 4 '060 4-219 4-382 4-549 4*720 4*896 5076 5*261 5-452 5*648 5-850 6*059 6*274 6*497 6*728 6*967 7*216 7-474 7-743 8-023 8-316 8-622 8*942 9*279 9-632 10*00 10*40 10*81 11*25 11*72 12*22 12-75 13-32 13-93 m 25 m 36 (9°) *ooo *iio *220 -331 -442 ■552 *664 ■775 •887 1-000 1*113 1*227 1-342 1-458 1-574 1*692 1*810 1*930 2*051 2*174 2*298 2*424 2-551 2-68o 2*811 2*944 3-079 3*217 3-357 3-500 3-645 3-794 3-945 4*100 4*259 4-421 4-587 4-758 4-933 5-113 5-298 5*488 5-685 5*888 6*097 6-314 6-538 6*771 7*012 7-263 7-524 7-797 8*081 8-379 8*690 9*017 9*361 9*722 10*10 10*51 10*94 11*39 11*87 12*39 12*95 13-54 m 37 (9i°) m 24 (i7ii°) I (171°) -000 -107 -214 *322 ■429 •537 -645 ■754 -863 •973 1*083 1*194 1-305 1-418 1-531 1-645 1*761 1*877 1-995 2*114 2*235 2-357 2*481 2-606 2-734 2-863 2-995 3-129 3-265 3-404 3-545 3-689 3-837 3-988 4-142 4-299 4-461 4*627 4-797 4-972 5-152 5-338 5-529 5*726 5-930 6-140 6-358 6*585 6*819 7*064 7*318 7-583 7-859 8-148 8-451 8*769 9*103 9-455 9*826 10*22 10*64 11*08 11-55 12*05 12-59 I3-I7 m 23 (1701°) m 38 (9n *ooo *104 *209 -313 -418 -523 -628 -734 •840 -946 1-054 1*162 1*270 1*380 1*490 i*6oi 1-714 1*827 1*942 2*058 2*175 2-294 2-414 2-537 2-661 2-787 2-915 3-045 3-177 3-312 3-450 3-591 ' 3-734 3-881 4-031 4-184 4-342 4-503 4-669 4-839 5-014 5-195 5-381 5-572 5-771 5-976 6-188 6-408 6-637 6*874 7*122 7-379 7*649 7-930 8-225 8-534 8-859 9-202 9-563 9-945 10-35 10-78 11-24 11-73 12-25 12-82 m 22 (i7oi°) m 39 (91°) ■000 •102 •203 ■305 -407 -509 *6l2 -715 *8i8 •922 1*026 1*131 1-237 1-344 1-451 1-559 1*669 1*779 1*891 2*004 2*118 2*234 2-351 2*470 2*591 2*714 2*838 2*965 3-094 3*226 3-360 3-497 3-637 3-779 3-925 4-075 4*228 4-385 4-547 4-713 4-883 5-059 5*240 5-427 5*620 5*820 6*026 6*241 6*463 6-695 6*936 7-187 7-449 7-723 8*oio 8*311 8*628 8*961 9-313 9-686 io*o8 10-50 10-95 11-42 11-93 12-48 ni 21 ('7oi°) m 40 (10°) *00O •099 *198 •297 •397 •496 ■596 •696 ■797 •898 1*000 1*102 1*205 1*309 1*414 1*520 1*626 1-734 1-843 1-953 2*064 2-177 2*291 2*407 2-525 2*645 2*766 2-890 3-015 3-144 3-274 3-408 3-544 3-683 3-825 3-971 4-120 4-274 4-431 4-593 4-759 4-930 5-106 5*289 5-477 5-671 5-873 6-082 6*299 6-524 6-759 7-003 7-259 7-526 7-806 8-099 8-408 8-733 9*076 9-439 9-823 10-23 10-67 11*13 11*63 12*16 41 (ioi°) m 42 (io§°) m 20 (170°) •000 -097 •193 -290 -387 •484 •581 •679 -777 ■876 •975 I -07s I-I75 1-277 1-379 1*482 1*586 1*691 1*797 1*904 2*013 2*123 2-234 2-347 2*462 2-579 2-697 2*8i8 2*940 3*065 3-193 3-323 3-456 3-591 3-730 3*872 4*018 4-167 4-321 4-478 4-640 4-807 4-979 5-157 5-340 5-530 5-727 5-930 6-142 6-362 6-590 6-829 7-078 7-339 7-611 7-898 8*199 8-516 8-850 9*204 9-578 9-977 10*40 10-85 11-34 11*86 m 43 (lof) -094 •188 -283 -377 -472 -567 •662 ■758 •855 •951 1-049 1*147 1-246 1-345 1-446 1-547 1-650 1-753 1-858 1*964 2*071 2*180 2*290 2*402 2-516 2*632 2*749 2*869 2*991 3-115 3-242 3-371 3-504 3-639 3-778 3*920 4*066 4-215 4-369 4-527 4*690 4-858 5-031 5*210 5-396 5-587 5-786 5-992 6*207 6-430 6-663 6-906 7*160 7*426 7*706 7-999 8-308 8-635 8-980 9-345 9-734 10-15 10-59 11*06 11*57 m 19 ("691°) m 13 (i69i°) *000 *092 ■184 •276 -368 -461 •554 •647 -740 •834 •929 1*024 1*120 1*216 1-313 1*411 1-510 1-610 1-711 1-814 1-917 2*022 2*128 2*236 2-345 2-456 2-569 2-684 2 'So I 2*920 3-041 3-165 3-291 3-421 3-553 3-688 3-827 3-969 4-115 4-265 4-420 4-579 4-743 4-912 5-086 5-267 5-454 5-648 5-850 6-059 6-277 6*504 6-742 6*990 7*250 7-522 7-S09 8-111 8-429 8*766 9-123 9*502 9*906 10*34 10*80 11-30 m 17 ('69i°) II HOURS. Fot the Azimuth. --The Sign is always +. except when the Hour-Angle exceeds 6 hours. m 44 (11°) •000 •090 •180 •270 •360 •450 ■541 -632 •723 -815 •907 1*000 1*094 i*i88 1-283 1-378 1-475 1-573 1*672 1-771 1*872 1-975 2*079 2*184 2*291 2-399 2*509 2*621 2-735 2-852 2*970 3-091 3-215 3-341 3-470 3-602 3-738 3-877 4-019 4*166 4-317 4-472 4-632 4-797 4-968 5-145 5-327 5-517 5-714 5-918 6*131 6-353 6-585 6*827 7*081 7-347 7*627 7*922 8-233 8*562 8*911 9*281 9-675 IO*10 10-55 11-03 m 16 (169°) m 45 (I If) •000 *o88 *176 -263 •352 •440 ■528 •617 •707 •796 •886 •977 1*069 i-i6i 1-253 i'347 1*442 1-537 1-633 I -731 1-830 1*930 2*031 2*134 2*238 2-344 2-452 2*562 2*673 2*787 2*903 3-021 3-141 3-265 3-391 3*520 3-653 3*788 3*928 4*071 4*218 4-370 4-527 4*688 4-855 5-027 5-206 5-391 5-583 5-783 S'99i 6 -208 6-435 6-672 6-920 7-180 7-453 7-741 8-045 8-367 8*708 9*070 9-455 9-867 10*31 10*78 m 15 (1681°) B 30 USEFUL NAVIGATIONAL STARS IN ORDER OF DECLINATION. 1 Nambs of HOURS. Stars. m 31 m 32 m 33 m 34 m 35 m 36 m 37 ra 38 m 39 m 40 m 41 m 42 m 43 m 44 m 45 (71°) (8°) m°) (8i°) (81°) (9°) (91°) (94°) (91°) (10°) (loD (ioi°) (ion (11°) (iii°) 27 0-5 1-9 Var. 0-3 Menkar . . . Procyon . . . Bellatrix . . Betelgubse . . RlGEL .... •479 712 •813 ■962 1-084 ■464 -690 •788 •932 1-050 •450 •669 •764 •904 1-019 •437 •649 -742 -877 -989 •425 -631 -721 -852 -961 •413 -613 -701 •829 -934 -402 -807 -909 -392 ;58i •786 ■886 -382 •567 -648 -766 -863 •372 •553 •632 •842 •363 •539 -616 •729 •822 ;33S -602 712 -802 ■346 -514 •588 -695 •784 -339 -503 -Ml •766 -331 -492 -562 •665 -749 I"0 27 2-4 1-2 Altair. . . . KlFFA BOREALIS Enif .... Spica .... I-I22 I-I76 1-230 1-393 1-087 1-140 1-192 1-350 1-054 1-106 1-156 1-309 1-024 I -073 I -122 1-271 -995 1-043 I -090 1-235 -967 I -014 1-060 1-201 -941 •987 1-032 1-169 •917 •961 1-005 1-138 -893 -937 -979 1-109 •871 -914 -955 1-082 -850 •892 •932 1-056 -830 -871 -910 1-031 -811 •850 -889 1-007 |93 -869 -985 -776 -813 -850 -963 1 "4 2 "2 2-6 2*2 Regulus . . . Ras Alhague . Markab . . . Denebola . . 1-638 1-941 2 -00s 1-587 1-610 1-881 1-943 1-539 1-562 1-824 1-884 1-494 1-516 1-771 1-829 1-452 1-473 1-721 1-778 I -412 1-433 1-673 1-729 1-374 1-394 1-628 1-682 1-338 1-358 1-586 1-638 1-304 1-323 1-546 1-597 1-272 1-291 1-507 1-557 1-241 1-260 I -47 1 1-520 1-212 1-230 1-436 1-484 1-184 1-202 1-403 1-450 1-158 1-175 1-372 1-417 1-132 I -149 1-342 1-386 I"0 2-0 -1-4 2-1 Aldebaran . . Alhena . . . SiRIUS .... Deneb-Kaitos . 2-170 2-194 2-208 2-486 2-102 2-126 2-139 2-409 2-039 2-062 2-075 2-337 1-979 2-002 2-014 2-268 1-923 1-945 1-957 2-204 1-870 1-892 1-903 2-143 1-820 1-841 1-852 2-086 1-773 1-793 1-804 2-031 1-728 1-747 1-758 1-980 1-685 1-704 1715 1-931 1-644 1-663 1-884 1-605 1-624 1-634 1-840 1-569 1-587 1-596 1-798 i;S33 1-560 1-757 1-500 1-517 1-526 1 719 O'O 2-S 2-0 I'l Arcturus . . Algeiba . . . Hambl. . . . Antares . , . 2-656 2750 3'i46 3-651 2-573 2-665 3-048 3-537 2-496 2-584 2-957 3-431 2-423 2-509 2-870 3-330 2-354 2-438 2-789 3-236 2-289 2-371 2-712 3-147 2-228 2-307 2-639 3-063 2-170 2-247 2-S7I 2-983 2-115 2-190 2-505 2-907 2-062 2-136 2-443 2-835 2-013 2-084 2-384 2766 1-965 2-035 2-328 2-701 1-920 1-988 2-275 2-639 1-877 1-944 2-223 2-580 1-836 I -901 2-175 2-523 2-3 2-4 I'l 1-9 a Sagitiarii . . Alphacca . . Pollux . . . Nath .... 3-684 IS 4-030 3-669 3-864 3-905 3-463 3-559 3-747 3-787 3-361 3-455 3-638 3-677 3-266 3-357 3-535 3-573 3-176 3-264 3-437 3-474 3-091 3-177 3-345 3-381 3-010 3-094 3-258 3-293 2-934 3-015 3-175 3-209 2861 2-941 3-097 3-130 2-792 2-870 3-022 3-054 2-726 2-802 2-951 2-982 2-664 2-738 2-883 2-914 2-604 2-676 2-818 2-848 2-547 2-618 2756 2-786 1-3 2"0 27 Adara .... fomalhaut . . Castor. . . . Phact .... 4-083 4-308 4-653 5-026 3-956 4-174 4-509 4-870 3-837 4-048 4-373 4-723 3-725 3-930 4-245 4-585 3-619 3-819 4-125 4-455 3-519 3713 4-011 4-332 3-425 3-614 3-904 4-216 3-336 3-520 3-802 4-106 3-251 3-430 3-705 4-002 3-171 3-345 3-614 3-903 3-094 3-265 3-526 3-809 3-021 3-188 3-443 3-719 2-952 3-114 3-364 3 '634 2-885 3-044 3-289 3-552 2-822 2-978 3-216 3-474 2-1 2-2 17 0"2 Kaus Australis MiRACH MIZAR . e Centauri . . Vega .... 5-084 5-210 S-364 S-939 4-926 5-048 5-197 5-755 4777 5-041 5-581 4-638 4-753 4-893 5-418 4-506 4-618 4-755 5-26S 4-382 4-491 4-624 5-120 4-265 4-371 4-500 4-982 4-154 4-257 4-382 4-852 4-048 4-149 4-271 4729 3-948 4-046 4-165 4-612 3-853 3-948 4-065 4-501 3-762 3-855 3-969 4-395 3-675 3-767 3-878 4-294 3-593 3-682 3-791 4-197 3-514 3-601 3-707 4-105 2-2 2-4 2-1 Almach . . . a Phanicis . . 9 Scarpa . . . Arided. . . 6-642 6-879 6-899 7-396 6-436 6-665 6-685 7-166 6-242 6-464 6-484 6-950 6-060 6-276 6-294 6-747 5-888 6-098 6-116 6-556 5-726 5-930 5-947 6-375 5-572 5-788 6-204 5-427 5-620 5-637 6-043 5-289 5-477 5-494 5-889 5-158 5-342 S-358 5-743 5-033 5-213 5-228 5 -60s 4-915 5-090 5-105 5-473 4-802 4-973 4-988 5-347 4-694 4-861 4-876 5-227 4-591 4755 4-769 5-112 0'2 1-9 1-9 2'0 Capella . . . a Gtuts . . . MiRFACK . . . Benetnasch. . 7-651 8077 8684 8-779 7826 8-414 8-506 7-191 7-591 8-i6r 8250 6-981 7-369 7-923 8-009 6783 7-160 7-698 7782 6-596 6963 7-486 7-568 6-419 6776 7285 7-365 6-251 6599 7095 7-173 6-093 6432 6915 6-991 5-942 6-273 6-744 6-818 5-798 6-121 6-581 6-653 5-662 5 977 6-426 6-496 ^;§32 6-278 6-347 5-407 5-708 6-137 6-204 5-289 5-583 6003 6-068 2-4 0-4 Var. 2'I Etanin . . . Canopus . . . SCHEDAR . . . o Pavonis. . . 9323 9714 10-99 11-44 9-033 9412 1065 11-09 8-761 9-129 10-33 10-75 8-506 8-862 1003 10-44 8-264 8 611 9742 10-14 8037 8-373 9 473 9864 7-821 8-149 9-219 9-600 7617 7-936 8-979 9350 7-424 7735 8751 9112 7-240 7-543 8-534 8-887 7-065 7-361 8-328 8-672 8132 8-468 6-740 7-023 7-945 8-273 111 7-767 8-087 6-444 6714 7-596 7910 i-o 2-S 17 1-2 ACHERNAR . . TUREIS. . . . /S Crucis . . . /S Centauri . . 11-75 12-27 12 41 12-79 11-39 11-89 12-03 12-39 11-04 11-53 II 66 12-02 10 72 11-20 11-32 11-67 10-42 1088 11-00 11-34 10-13 10-58 10-70 11 02 9-858 10-29 10-41 10-73 9-601 10-03 10-14 1045 9-357 9771 9883 1018 9-125 9530 9-638 9-931 8-905 9-300 9-406 9-691 8-695 9-081 9-184 9463 8872 8-973 9-245 8-305 8673 8771 9037 8-122 8-482 8-579 8-839 2-0 li 2*2 2-0 2-1 DUBHE. . . . a} Crueis . . . a Tri. Austral. . ;8 ArgAs . . . KOCHAB . . . 14-12 14-27 19-16 13-68 13-83 18-57 1902 26*02 13-27 13-41 18 01 18-45 25-24 12-88 13-02 ,17-48 17-91 24-50 12-52 1265 1699 17-40 23-81 1217 12-30 16-52 16-92 23 -IS 1 1 84 11-97 1608 1647 22-53 11-54 1 1 66 15-66 16-04 21-94 11-24 11-36 15-26 15-63 21-39 10-96 11-08 14-88 15-24 20-86 10-70 10-82 14-52 14-88 2035 10-45 10-56 14-18 14-53 19-87 10-21 10-32 13-85 14-19 1942 9-978 1009 13-54 1387 18-98 9-759 9865 13-25 13-57 18-56 m 29 m 28 m 27 m 26 m 25 m 24 m 23 m 22 m 21 m 20 m 19 m 18 m 17 m 16 m 15 (1724°) (172°) (■711°) (i7ii°) ('7ii°) (171°) (i70f) (1704°) (i7oi°) (170°) (1691°) (1694°) (■69i°) (169°) (■681°) For the Azimuth -{ II HOURS. When Latitude and Declination are of contrary names, the Sign is When Latitude and Declination are of same name, the Sign is — . 31 The Headline has yarlous signifleations, aeeoFdin? to the Problem in use. In Problem IV. it repFesents Diff. of Long. In Problem V. the Initial Course. In Problem VI. the Compitment of the Diff. of Long. In Problem VIII. the Diff. of Long. In Problems X. and XI. the True Azim, Lat. HOURS. m m m m m m m m m m m m m m ni 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 (I in (iir) (12°) (i2i°) (124°) (121°) (13°) (13*°) (i3n (131°) (14°) (I4i°) (I4i°) (141°) (15°) 0° ■000 -000 -000 -000 •000 -000 -000 -000 -000 -000 -000 -000 -000 •000 -000 I •086 •084 -082 -080 -079 -077 -076 -074 -073 -071 -070 -069 -067 -066 -065 2 •172 •168 •164 -161 -158 -154 -151 -148 •145 ■143 -140 •138 -135 -133 •130 , 3 •258 -252 •247 •241 •236 -232 ■227 •223 -218 •214 -210 -206 ■203 •199 •196 4 •344 -336 •329 •322 -315 -309 •303 -297 -291 •286 -280 -275 ■270 -266 -261 'd S •430 -421 -412 -403 •395 -387 •379 -372 •364 •358 -351 •344 ■338 ■332 •327 § 6° •S17 •505 -494 -484 -474 -464 -455 -446 -438 •430 -422 -414 •406 ■399 -392 X' 7 ■604 ■590 -578 ■566 -554 •543 •532 -521 -511 -502 •492 -483 -475 •466 -458 8 •691 •676 -661 •647 -634 -621 •609 -597 •585 -574 -564 -553 -543 -534 ■525 CO a 03 9 •778 •761 -745 .729 -714 -700 ■686 -673 •660 -647 -63s -624 -612 -602 •591 10 •867 ■848 •830 •812 -795 •779 -764 -749 -734 •721 -707 -694 -682 -670 -658 it 11° •95s •935 -914 •895 •877 -859 -842 •826 •810 •794 •780 •765 ;7S2 ■738 -725 3^ 12 I -045 I -022 I -000 .979 -959 -939 -921 -903 •885 -869 •853 -837 -807 -793 a n 13 I-I3S I -1 10 1-086 1-063 1-041 1-020 1-000 •980 -962 -943 -926 -909 -893 •877 -865 ■" M 14 1*225 I -199 I -173 I -148 1-125 1-102 i-o8o 1-059 1-039 1-019 1-000 -982 •964 -947 -931 i IS 1-317 1-288 1-261 1-234 1-209 1-184 1-161 1-138 1-116 1-095 1-075 1-055 1-036 1-018 1-J300 ? £ i6° 1-409 1-379 1-349 1-321 1-293 1-267 1-242 1-218 1-194 1-172 1-150 1-129 1-109 1-089 1-070 '1 Q *2 1-503 1-470 1-438 1-408 1-379 1-351 1-324 1-298 1-273 1-249 1-226 1-204 1-182 i-i6i 1-141 i8 I-S97 1-562 1-529 1-496 1-466 1-436 1-407 1-380 1-353 1-328 1-303 1-279 1-256 1-234 1-213 19 i"692 1-655 1-620 '■5^^ 1-553 1-522 1-491 1-462 1-434 1-407 1-381 1-356 I -331 1-308 1-285 20 1789 1-750 1-712 1-676 1-642 1-609 1-577 1-546 1-516 1-487 1-460 1-433 1-407 1-382 1-358 o 21° 1-887 1-845 i-8o6 1-768 1-731 1-696 1-663 1-630 1-599 1-569 1-540 1-511 1-484 1-458 1-433 t»»« 22 1-986 1-942 1-901 1-861 1-822 1-786 1-750 1-716 1-683 1-651 1-620 1-591 1-562 1-535 1-508 •S 2»H- 23 2 -086 2-041 1-997 I -955 1-915 1-876 1-839 1-803 1-768 1-735 1-702 1-671 1-641 1-612 1-584 t^> 24 2-i88 2-141 2-095 2-051 2 -008 1-968 1-928 1-891 1-855 1-819 1-786 1-753 1-722 1-691 1-662 25 2-292 2-242 2-194 2-148 2-103 2-061 2 '020 1-980 1-942 1-906 1-870 1-836- 1-803 1-771 1-740 26° 2-397 2-345 2-295 2-246 2 -200 2-155 2-113 2-071 2-032 1-993 1-956 1-920 1-886 1-853 1-820 r^ T3 (D 27 2-504 2-450 2-397 2-347 2-298 2-252 2-207 2-164 2-122 2-082 2-044 2-006 1-970 1-935 1-902 g °^ 28 2-613 2-556 2-501 2-449 2-398 2-350 2-303 2-258 2-215 2-173 2-133 2-094 2-056 2-020 1-984 ■SoZ 29 *P5 2-665 2-608 2-553 2-500 2-450 2-401 2-354 2-309 2-265 2-223 2-183 2-143 2-105 2-069 30 2-838 2-776 2-716 2-659 2-604 2-552 2-501 2-452 2-405 2-359 2-316 2-273 2-232 2-193 2-155 31° 2 -953 2-889 2-827 2-767 2-710 2-655 2-603 2-552 2-503 2-456 2-410 2-366 2-323 2-282 2-242 32 3-071 3-004 2-940 2-878 2-819 2-762 2-707 2-654 2-603 2-554 2-506 2-460 2-416 2-373 2-332 "«5 33 3-192 3-122 3-055 2-991 2-929 2-870 2-813 2-758 2-705 2-654 2-605 2-557 2-511 2-467 2-424 CO {« 34 3-315 3-243 3-173 3-107 3-043 2-981 2-922 2-865 2-810 2-756 2-705 2-656 2-608 2-562 2-517 .2 J fl 35 3-442 3-366 3-294 3-225 3-158 3-094 3-033 2-974 2-917 2-862 2-8o8 2-757 2-708 2-660 2-613 E <» i 2S 36° 3-571 3-493 3-418 3-346 3-277 3-211 3-147 3-086 3-026 2-969 2-914 2-861 2-809 2-760 2-711 37 3-704 3-623 3-545 3-471 3-399 3-330 3-264 3-200 3-139 3-080 3-022 2-967 2-914 2-862 2-812 £ S® 38 3-840 3-756 3-676 3-598 3-524 3-453 3-384 3-318 3-254 3-193 3-134 3-076 3-021 2-968 2-916 GO 65-) II HOURS. / When Latitude and Declination are of contrary names, the Sign is -h. For the Azimuth: ^y ^jj^^ Latitude and Declination are of same name, the Sign is — . 33 The Head-line has various significations according to the Problem in use. In Problem IV. it represents Diflf. of Long. In Problem V. the Initial Course. In Problem VI. the Complement of the Dlff. Of Long. In Problem VIII. the DifF. of Long. In Problems X. and XI. the True Azim. Lat. 1 HOUR. m 2 m 4 in 6 m 8 m 10 m 12 m 14 ra 16 m 18 m 20 m 22 m 24 m 26 m 28 m 30 (154°) (>6°) (i6r) (17°) (174°) (18°) (i8n (19°) (194°) (20°) (204°) (21°) (214°) (22°) (224°) 0° •000 -000 -000 -000 -000 -000 -000 -000 -000 -000 -000 -000 -000 •000 -000 >< I 2 3 4 S •063 •126 •189 ■252 •31S -061 -122 ■183 -244 •305 -059 -118 -177 -236 -295 -057 -114 -171 -229 -286. -055 -III ■166 -222 -277 -054 -loS -161 -215 -269 -052 -104 -157 -209 -262 -051 -lOI -152 -203 -254 •049 -099 -148 -198 -247 -048 -096 •144 -192 -240 -047 -093 -140 -187 -234 -046 -091 -137 -228 -044 -089 -133 -178 -222 -043 -086 ■130 -173 •217 -042 -084 -127 -169 •211 >< ^1 6° I 9 ID ■379 •443 •507 •571 ■636 •367 -428 •490 -552 -615 -355 -415 •474 -535 •595 -344 -402 -460 -518 -577 •333 •389 -446 -502 -559 •323 ;378 -487 -543 -314 ■367 -420 -473 -527 •305 -357 -408 -460 •512 -297 -347 -397 -447 -498 -289 -1 -484 -281 -328 -376 -424 -472 •274 -320 -366 •413 •459 -267 •312 -357 •402 -448 -260 -304 -348 -392 -436 -254 -296 •339 -382 -426 h 11° 12 13 14 IS 701 766 ■832 •899 ■966 ■678 -870 -934 •656 718 ■779 -842 -905 -636 •695 -876 ■616 -674 -732 -791 •850 -598 •654 711 -767 -825 -581 -635 -690 -565 -617 -670 -724 -778 -652 -704 •757 •634 -685 -736 -520 -569 -618 -667 717 -506 -554 -601 -650 -698 -493 -481 ;S26 -617 •663 -469 -513 -602 -647 16° % 19 20 1-034 l'I02 I '172 I "242 1-312 i-ooo 1-066 I -133 I -201 1-269 •968 1-032 1-097 I -162 1-229 -938 I -000 1-063 I -126 I -190 -909 -970 1-031 1-092 I -154 •883 •941 I -000 I -060 I -120 -857 ■914 -971 1-029 1-088 -833 -888 -944 I -000 1-057 -810 -863 -918 -972 1-028 -788 -840 -893 -946 I-ooo •767 -818 -869 ■921 -973 -747 -796 -846 •897 -948 -728 -776 -825 -874 -924 ■710 -757 -804 •852 -901 -692 ? -879 is, aceordii the place observer. 21° 22 23 24 25 1-384 I -457 I -60s I -681 ■ 1-339 1-409 1-480 1-296 1-364 1-433 1-503 1-574 1-256 7-322 1-388 1-456 1-525 1-217 I -281 1-346 I -412 1-479 1-181 1-243 1-306 1-370 1-435 1-147 1-208 1-269 1-331 1-394 1-115 1-173 1-233 1-293 1-354 1-084 I -141 I -199 1-257 I -317 1-055 I'lIO I -166 1-223 I -281 1-027 i-oSi 1-135 1-191 1-247 I-ooo 1-053 I -106 I -160 1-215 -974 1-026 1-078 1-130 I -184 -950 I-ooo I -051 1-102 I -154 -927 -975 1-025 1-075 1-126 ignifleatior Ship, or of .at. of the 26° 29 30 1-759 1-837 I -917 1-999 2-082 I -701 1-777 1-854 1-933 2-013 1-647 1-720 1-795 1-871 1-949 1-888 1-686 1-758 1-831 1-501 1-568 1-636 1-706 1-777 1-458 1-523 1-589 1-657 1-726 I -416 1-480 1-544 I -610 1-677 1-377 1-439 1-502 1-565 1-630 1-340 1-400 1-461 1-305 1-363 1-422 1-483 1-544 I -27 1 1-327 1-385 1-444 1-504 1-238 1-294 1-350 !:t6l 1-207 1-261 1-316 1-372 1-429 1-177 1-230 1-284 1-338 1-394 i various s he Lat. of i isent the I 31° 32 33 34 35 2-167 2-2S3- 2-342 2-432 2-525 2-095 2-179 2-265 2-352 2-442 2-028 2-II0 2-192 2-277 2-364 1-965 2-044 2-124 2-206 2-290 1-906 1-982 2 -060 2-139 2-221 1-849 1-923 1-999 2-076 2-155 1-796 1-868 1-941 2-oi6 2-093 1-745 1-815 1-886 1-959 2-034 1-697 1-765 1-834 1-905 1-977 1-651 1 717 1-784 1-853 1-924 1-607 I -671 1-737 1-804 1-873 1-565 1-628 1-692 1-757 1-824 1-649 I -712 1-778 1-487 1-547 1-607 1-669 1-733 I -451 1-509 1-568 1-628 1-690 III 36° 39 40 2-620 2717 2-817 2-920 3-026 2725 2-824 2-926 2-453 2-544 2-638 2734 2-833 2-376 2-465 2-555 2-649 2-745 2-304 2-390 2-478 2-568 2-661 2-236 2-319 2-405 2-492 2-582 2-I7I 2-252 2-335 2-420 2-508 2-110 2-188 2-269 2-352 2-437 2-052 2-128 2-206 2-287 2-370 1-996 2-070 2-147 2-225 2-305 1-943 2-015 2-090 2-166 2-244 1-893 1-963 2-036 2-HO 2-186 1-844 I -913 1-984 2-056 2-130 1-798 1-865 1-934 2-004 2-077 1-754 I -819 1-887 I -955 2-026 II 41° 42 43 44 45 3-135 3-247 3-363 3-482 3-606 3-032 3-140 3-487 2-935 3-040 3-148 3-260 3-376 2-843 2-945 3-050 3-159 3-271 2-757 2-856 2-958 3-063 3-172 2-675 2-771 2-870 2-972 3-078 2-598 2-691 2-787 2-886 2-989 2-525 2-615 2-708 2-805 2-904 2-455 2-543 2-633 2-727 2-824 2-388 2-474 2-562 2-653 2-747 2-325 2-408 2-494 2-583 2-675 2-265 2-346 2-429 2-516 2-605 2-207 2-286 2-367 2-452 2-539 2-152 2-229 2-308 2-390 2-475 2-099 2-174 2-251 2-331 2-414 03 ^ IS 46° % 49 SO 3-734 .3-867 4-005 4-148 4-297 3-611 3-740 3-873 4-012 4-156 3-496 3-620 3-749 3-884 4-023 3-387 3-508 3-633 3-284 3-401 3-522 3-649 3-780 3-187 3-300 3-418 3-540 3-668 3-095 3-205 3-319 3-438 3-562 3-007 3-114 3-225 3-341 3-461 2-924 3-028 3-136 3-249 3-365 2-845 2-946 3-051 3-161 3-274 2-770 2-868 2-970 3-077 3-187 2-698 2-794 2-893 2-997 3-105 2-629 2-722 2-819 2-920 3-025 2-563 2-654 2-749 2-847 2-950 2-500 2-777 2-877 >* SI" 52 S3 St 55 4-453 4-61S 4-785 4-963 5-150 4-307 4-464 4-628 4-800 4-981 4-169 4-321 4-480 4-647 4-821 4-039 4-187 4-341 4-502 4-671 3-917 4-059 4-209 4-365 4-530 3-801 3-939 4-084 4-236 4-395 3-691 3-966 4-114 4-268 3-586 3-717 3-854 3-997 4-148 3-487 3-614 3-747 3-887 4-033 3-393 3-517 3-646 3-782 3-924 3-303 3-423 3-549 3-681 3-820 3-217 3-334 3-457 3-586 3-720 3-135 3-249 3-369 3-494 3-626 3-285 .3-407 3-535 2-981 3-090 3-204 3-323 3-448 1 a 56" 1 5-346 5-553 5-771 6-001 6-246 5-170 5-370 5-581 5-804 6-040 5-005 5-198 5-403 5-619 5-847 4-849 5-037 5-234 5-444 5-665 4-702 4-884 5-076 5-278 5-493 4-563 4739 4-925 3-122 5-331 4-431 4-602 4-783 4-974 S-177 4-306 4-472 4-648 , 4-833 5-030 4-187 4-348 4-519 4-700 4-891 4-073 4-231 4-397 4-573 4-759 3-965 4-119 4-280 4-451 4-633 3-862 4-OII 4-169 4-336 4-512 3-764 3-909 4-063 4-225 4-397 3-669 3 -81 1 3-961 4-119 4-287 3-579 4-018 4-182 61" 62 6-505 6-782 7-077 7-393 7-733 6-291 6-844 7-150 7-479 6-090 6-349 6-626 6-922 7-240 5-901 6-150 6-4:9 6-706 7-014 5-722 5-965 6-225 6-503 ^7^18 6-040 6-310 6-600 5-392 5-621 5-866 6-128 6-409 5-239 5-462 5-700 5-955 6-228 S-094 5-311 5-542 S-790 6-056 4-957 S-167 5-392 5-633 5 -892 4-825 5 -030 5-249 5-484 5-736 4-700 4-899 5-113 5-341 5-587 4-580 4-775 4-982 5-205 5-444 4-465 4-655 4-858 5-075 5-308 4-355 4-540 4-738 4-950 S-177 ( in 58' i64i°J m 58 {164°) m 54 i63r) m 52 (163°) m 50 162^) m 48 (162°) m 46 (i6ir) m 44 (161°) 111 42 (i6oi°) ra 40 (160°) m 38 (■594°) m 36 059°) m 34 ('S«4°) m 32 (158°) m 30 (iS7i°) - 10 HOURS. For the Azimuth :~The Sign is always +. except when the Hour-Angle exceeds 6 hours. B 34 USEFUL NAVIGATIONAL STARS IN ORDER OF DECLINATION. t Names of Stars. 1 HOUR. ni 2 m 4 m 6 ra 8 in 10 m 12 m 14 m 16 m 18 m 20 ra 22 m 24 m 26 ra 28 m 30 dsn (16°) (i6n (17°) (i7i°) (i8°) (i8n (19°) (194°) (20°) (204°) (21°) (214°) (22°) (224°) 27 1-9 Var. 0-3 Menkar , . , Procyom . . . Bellatrix . . Betelguese . . RlGEL .... •242 •359 •410 •48s •547 •234 •348 •398 -470 •530 -228 -457 •515 -221 ■328 •375 -444 •500 -215 -319 ;365 -486 •209 ■311 •355 •420 •473 -204 -302 •346 •409 •461 •198 -295 -337 •398 -449 -194 -287 •438 -189 -281 -321 •379 -427 -185 •274 •313 •370 -417 -180 -268 -306 •362 •408 -.76 -262 •299 •354 -399 •173 •256 •293 ■390 -169 -251 -287 -339 ■382 I'O 2-7 2-4 I "2 Altair. . . . KlFFA BOREAI.IS Enif .... Spica .... •566 •594 •621 •703 ;549 -602 ■682 •533 -559 •Si8 -643 1? •490 •513 •477 •500 •523 -592 -465 -487 -509 -577 •453 •475 •497 •563 -442 -464 -485 •549 •432 -453 -474 -536 -422 -443 -463 •524 •413 •433 •453 •513 •404 •423 -443 -501 -395 -415 -433 -491 I '4 2-2 2-6 2 "2 Rkgulus . . . Ras Alhague . Markab . . . Denebola . . •827 •839 •979 I "012 -801 •813 •778 •789 -922 -952 •756 -767 -895 -925 •735 •745 •870 •899 715 •725 -847 •875 -696 -706 -82s •852 -678 -688 •804 -831 -662 -671 •784 -810 -646 -65s •765 -791 -631 -640 •747 772 -616 -625 -730 755 -603 -612 714 -738 •590 -598 •699 -722 •577 •586 -684 -707 I'O 2-0 -1-4 2-1 Aldebaran . . Alhena . . . SiRIUS .... Deneb-Kaitos . I -095 i"io7 fii4 1^255 I -061 1-074 1-080 1-216 1-030 1-042 1-048 1-181 i-ooi 1-012 1-018 1-147 •973 •984 •990 1-115 •947 •958 1-085 -922 •933 -938 1-057 -899 •909 -914 1-030 -876 -887 -892 1-004 •870 -980 •83s •845 -850 -957 -816 •826 -831 •936 -798 -807 -812 ■91S -781 -790 •795 •895 -765 -773 778 -876 0"0 2-S 2-0 Arctorhs . . Algbiba . . . Hambl. . . . Antares . . . 1-340 1-388 I 588 1-842 1-299 1-345 1-261 1-306 1-494 1-733 1-225 1-268 1-451 1-684 1-191 1^233 1-411 1-637 1-159 1-200 1-373 I -593 1-129 1-169 1-337 1-551 1-100 1-139 1-303 1-512 1-073 i-iii 1-271 1-475 1-047 1-084 1-240 1^439 1-023 1-059 1-21 1 1-406 •999 1-035 1-184 1-374 •977 1-012 I -158 I '343 -956 -990 I -133 I -314 •936 -969 1-109 1-286 2-3 2-4 I"I 1-9 a Sagittarii . . Alphacca . . Pollux . . . Nath .... 1-859 i-gii 2-OI2 2-034 1-803 1-853 1-951 1-972 1-749 1-798 1-893 1-914 1-699 1-747 1-839 1-859 1-652 1-698 1-788 1-807 1-608 1-652 1-740 1-759 1-566 1-609 1-695 1 713 1-526 1-568 1-652 1-669 1-488 1-530 1-611 1-628 '•453 I "493 1-572 I -589 1-419 1^458 1-535 '•552 1-386 1-425 1-500 1-517 '•356 1^393 1-467 1-483 1-326 1-363 1-435 i^45i 1-298 1-334 1-405 1-420 1-3 2"0 27 Adara .... fomalhaut . . Castor. . . . Phact .... 2-060 2-174 2-348 2^S36 1-997 2-107 2-277 2-459 1-939 2-045 2-209 2-386 r883 1-987 2-146 2-318 1-831 1-932 2-087 2-254 1-782 1-880 2-031 2-193 1-735 1-831 1-978 2-136 I -691 1-784 1-927 2-082 1-649 1-740 1-880 2-030 1-610 1-698 1-835 1-982 f572 1-659 1-792 1-935 1-536 1-621 I -751 1-891 1-502 1-585 1-712 1-849 1-470 1-551 1-675 1-809 1^439 1-518 1-640 1-771 2-1 2-2 17 0'2 Kaus Australis MiRACH MiZAR . e Centauri . . Vega .... 2-565 2-629 2-707 2-997 2-487 2-549 2-624 2-906 2-414 2-474 2-547 2-820 2-345 2-403 2-474 2-739 2-280 2-336 2-405 2-663 2-218 2-274 2-341 2-592 2-160 2-214 2-279 2-524 2-106 2-158 2-222 2-460 2-054 2-105 2-167 2-399 2-004 2-054 2-115 2-342 1-958 2-006 2-065 2-287 1-913 1-960 2-018 2-235 1-870 1-917 1-973 2-185 1-830 1-875 1-931 2-138 I -791 1-836 1-890 2-093 2-2 2-4 2'I Almach . . . a Phcenicis . . 9 Scorfii . . . Arided. . . . 3^352 3-471 3-481 3732 3-249 3-365 3'37S 3-618 3-266 3-276 3-5" 3-063 3-173 3-182 3-41 1 2-979 3-085 3-094 3-317 2-898 3-002 3-011 3-227 2-823 2-923 2-932 3-143 2751 2-849 2-858 3-063 2-683 2779 2-787 2-988 2-619 2-712 2-720 2-916 2-558 2-649 2-657 2-848 2*499 2-588 2-596 2-783 2-444 2-531 2-539 2-721 2-391 2-476 2-484 2-662 2-341 2-424 2-431 2-606 0'2 1-9 1-9 2-0 Capblla . . . o G> Ill's . . . MiRFACK . . . Benetnasch. . 3-861 4-076 4-382 4^430 3-743 3-952 4-249 4-295 3-633 3-835 4-123 4-168 3-529 3-725 4-005 4-049 3-43' 3-622 3-894 3-937 3-339 3-525 3-790 3-831 3-252 3-433 3-691 3731 3-169 3-346 3-597 3-636 3-091 3-263 3-508 3-547 3-017 3-185 3-424 3-461 2-946 3-110 3-344 3-380 2-879 3-303 2-815 2-972 3-195 3-230 2754 2-908 3-126 3-160 2-696 2-846 3-060 3-094 2-4 0-4 Var. 2'I Etanin . . . Canopus . . . Schedar . . . a Pavonis. . . 4-704 4-902 5-545 5774 4-561 4752 5-376 S-5>8 4-427 4-612 5-218 5^433 4-300 4-480 5069 5-278 4-181 4-356 4-928 5-132 4-068 4-239 4-796 4-994 3-962 4-128 4-670 4-863 3-862 4-023 4-552 4-740 3-766 3-924 4-439 4-623 3-676 3-830 4-333 4-512 3-590 3-740 4-232 4-406 3-508 3-655 4;i35 3-430 3-574 4-043 4-210 3-356 3-497 3-956 4-119 3-285 3^423 3-872 4-032 I"0 2-S 17 I "2 ACHBRNAR . . TURBIS .... P Ct^cis . . . P Centauri . . 5-929 6-192 6-263 6-453 5-749 6-004 6-072 6-256 5-826 5^893 6-072 5-420 5-660 5 -724 5 -898 5-270 5-503 5-566 5-735 5-128 S-3SS S-416 S-580 4-994 5"2iS 5 '275 5^435 4-867 5-083 S-141 5-297 4-747 4-957 5-014 5-166 4-633 4-838 4-893 5-042 4-525 4725 4779 4-924 4-422 4-618 4-670 4-812 4-324 4-515 4-567 4-705 4-230 4-468 4-603 4-141 4-324 4-373 4-506 2-0 li 2 "2 2-0 2*I DuBKE .... ai Crucis . . . a Tri. Austral. . p ArgAs . . . KOCHAB . . . 7^125 7-202 9-669 9-906 13^55 6-908 6-983 9-375 9-604 13-14 6-704 6777 9-098 9-320 1275 6-512 6-583 8-838 9-054 12-39 6-332 6-400 8-593 8-803 12-04 6-161 . 6-228 8-362 8-566 11-72 6-000 6-066 8-144 8^343 IX -41 5-848 5-912 7^937 8-131 11-12 5 -704 5-766 7-741 7-930 10-85 S-567 5-627 7-555 7-740 10-59 5-437 5 -496 7-379 7-559 10-34 5-313 5-371 7-211 7-387 lo-ii S-I9S 5^251 7-051 ''123 9-882 5-083 5-138 6-898 7-067 9-668 4-975 5-029 6752 6-917 9-464 m 58 (164^) m 56 (164°) m 54 ('634°) m 52 '(163°) m 50 (.62^) m 48 (162°) m 46 (■614°) m 44 (161°) m 42 (i6o4°) m 40 (160°) m 38 (1594°) m 36 (159°) m 34 {■584°) m 32 (158°) m 30 ('57i°) > 10 HOURS. / When Latitude and Declination are of contrary names, the Sign is -^. Far the Azimuth: | ^^^^ Latitude and Declination are of same name, the Sign is -. 35 In The Head-line has various signifleations. according' to the Problem in use. Problem IV. it represents Diff. of Long. ^ In Problem V the Initial Course. ^ I" ^pue Azta Commmeni of the Diff. of Lonff. In Problem VIII. the Diif. of Long. In Problems X. and XI. the True Azim. ^••-"•'•'" "i f VAAU M^X IK» \l^ t-V "&. -1 ** " Lat. 1 HOUR. m 32 . m 34 m 36 m 38 m 40 m 42 m 44 m 46 m 48 m 50 m 52 m 54 m 56 m 58 m 60 (23°) (23i°) (24°) (241°) (25°) (254°) (26°) (264°) (27°) (274°) (28°) (284°) (29°) (294°) (30°). 0° •000 -000 •000 -000 -000 -000 -000 -000 -000 -000 -000 -000 -000 -000 •000 I 2 •041 •082 -040 -080 •039 •078 -038 ■077 -037 -075 ■037 •073 -036 -072 -035 •070 -034 •068 ■°d^ :°M -032 •064 -031 •063 -031 -062 •030 -060 3 ■123 -121 •118 •IIS •112 -no -107 -105 •103 •101 -099 -097 •158 •093 -091 *- 4 •16s -161 •157 -153 -150 -147 -143 -140 ■137 -134 -132 -129 ■124 '121 X 5 •206 •201 •197 -192 •188 •183 -179 •175 •172 -168 ■16s •161 -155 •152 6° •248 -242 •236 -231 -225 -220 -215 -211 •206 -202 -198 -194 •190 •186 •182 • 7 •289 -282 •276 -269 -263 •257 -252 -246 •241 •236 •231 -226 •222 •217 •213 X 8 •331 -323 -316 -308 -301 •295 -288 -282 •276 •270 -264 -259 -286 -318 •248 ■280 •243 0) 9 ■373 -364 -3S6 •348 -340 -332 -325 •318 •311 •304 -298 ■292 •274 10 •41S -406 -396 -387 -378 -370 -362 •354 -346 -339 -332 -325 •312 -305 11° •458 -447 -437 -427 •417 -408 •399 •390 -381 -373 •366 -358 •351 •344 •337 S CM 12 •501 ■489 -477 -466 •456 -446 -436 -426 -417 •408 -400 -391 •383 •376 -408 -368 .S a (—1 13 ■544 -531 -519 -507 -495 -484 -473 -463 -453 •443 -434 ■425 ■416 -400 14 ■587 -560 ■547 -535 -523 -5" -500 •489 ■479 -469 -459 '.H°. •441 -432 g IS •631 -616 -602 -588 ■575 •562 -549 -537 -526 -515 -504 -494 -483 -474 -464 Is 16° •676 -659 -644 •629 -615 -601 -588 -575 •563 -551 -539 •528 -517 -507 -497 1 a I? •720 -703 -687 -671 -656 •641 -627 -613 -600 •587 -575 •563 ■^11 -540 '53° "^S I8 765 -747 •730 -713 -697 -681 -666 -652 -638 •624 -611 -598 -586 -574 -563 5| 19 •811 •792 -773 -756 •738 -722 •706 -691 -676 •661 -648 ■634 -621 ■609 -596 20 •858 -837 -817 •799 -781 -763 -746 -730 -714 •699 -685 -670 -657 ■643 •630 -? 21° •904 •883 -862 -842 -823 -805 -787 -770 -753 -737 -722 •707 -693 -678 -665 !«« 22 ■952 •929 -907 -887 •866 -847 •828 -810 -793 •776 -760 ■744 -729 •714 -700 a Si^ 2^ I'OOO ■976 -953 -931 -910 ■890 -870 -851 -833 -815 -798 -782 -766 •750 -735 accord] the pla abserve: 24 f049 1-024 I -000 -977 -955 -933 -913 ■893 -874 -855 -837 •820 •803 ■787 -771 25 1-099 1-072 1-047 1-023 I -000 -978 -956 -935 -915 •896 -877 •859 -841 •824 -868 26° I "149 I -122 1-095 1-070 1-046 1-023 I -000 -978 -957 •937 -917 -898 -880 •862 -845 -IM I -200 I "172 1-144 I-II8 1-093 I -068 I -045 1-022 1-000 -979 -958 ■938 -919 -901 -883 n o^ 28 I '253 1-223 I -194 I -167 I -140 i-iiS 1-090 1-066 1-044 1-021 I -000 -979 -959 -940 -921 .2 ^*' 29 I -306 I -27s 1-245 I-2I6 1-189 I -162 I -137 I-II2 1-088 1-065 1-043 1-021 1-000 •980 -960 ■♦J o^ CO rT 30 1-360 1-297 1-267 1-238 I -210 1-184 I -158 1-133 I -109 I -086 1-063 1-042 1-020 I -000 gnifl Shi] Lat. 31° 1-416 1-382 1-350 I -318 1-289 1-260 1-232 1-205 I -179 I -154 1-130 1-107 1-084 1-062 1-041 32 1-472 1-437 1-403 I -371 1-340 1-310 I -281 1-253 1-226 1-200 . I -175 1-151 1-127 1-104 1-082 "^® 33 '■530 1-494 1-459 1-425 1-393 1-362 1-331 1-303 1-275 1-248 1-221 1-196 1-172 1-148 I -125 m .{*" 34 1-589 I -551 I -515 1-480 1-446 1-414 1-383 1-353 1-324 1-296 1-269 1-242 I -217 I -192 1-168 .2 ija 35 1-650 I -610 1-573 1-536 1-502 1-468 1-436 1-404 1-374 1-345 1-317 1-290 1-263 1-238 1-213 1 So 36° I -712 1-671 1-632 1-594 1-558 1-523 • 1-490 I -457 1-426 1-396 1-366 1-338 1-311 1-284 1-258 ■^^l 177s 1-733 1-693 1-654 I -616 1-580 1-545 i-Sii 1-479 1-448 1-417 1-388 I -359 1-332 1-305 » «aj 38 1-841 1-797 I -755 1-714 1-675 1-638 1-602 1-567 1-533 I -501 1-469 1-439 1-409 I -381 1-353 C9 a> 39 1-908 1-862 I -819 1-777 1-737 1-698 1-660 1-624 1-589 1-556 1-523 1-491 1-461 I -431 1-403 43 %>> £2 40 1-977 1-930 1-885 1-841 1-799 1-759 1-720 1-683 1-647 I -612 1-578 1-545 1-514 1-483 1-453 41° 2-048 1-999 1-952 1-907 1-864 1-822 1-782 1-744 1-706 1-670 1-635 I -601 1-568 1-536 1-506 42 2-I2I 2-071 2-022 1-976 I -931 1-888 1-846 1-806 1-767 1-730 1-693 1-658 1-624 1-591 1-560 i| 43 2-197 2-145 2-094 2-046 2-000 1-955 I -912 1-870 1-830 1-791 1-754 1-717 1-682 1-648 1-615 44 2:275 2-221 2-169 2-II9 2-071 2-025 1-980 1-937 1-895 1-855 I -816 1-779 1-742 1-707. 1-673 45 ,2-356 2-300 2-346 2-194 2-145 2-097 2-050 2 -006 1-963 1-921 I -881 1-842 1-804 1-767 1-732 s > 46° 2-440 2-382 2-326 2-272 2-221 2-171 2-123 2-077 2-032 1-989 1-948 1-907 1-868 1-830 1-794 47 2-526 2-466 2-409 2-353 2-300 2-248 2-199 2-151 2-105 2-060 2-017 1-975 1-935 1-895 1-857 S'S 48 2-616 2-554 2-494 2-437 2-382 2-328 2-277 2-228 2-180 2-133 2-089 2-045 2-004 1-963 1-924 £ ^ 49 2-710 2-646 2-584 2-524 2-467 2-412 2-359 2-307 2-258 2 -2 10 2-164 2-119 2-075 2-033 1-992 o >-? 50 2-808 2-741 2-677 2-615 2-556 2-499 2-443 2-390 2-339 2-289 2-241 2-195 2-150 2-106 2-064 .§> 51° 2-909 2-840 2-774 2-710 2-648 2-589 2-532 2-477 2-424 2-372 2-323 2-274 2-228 2-183 2-139 52 3-015 2-944 2-875 2-981 2-809 2-745 2-683 2-624 2-567 2-512 2-459 2-407 2-357 2-309 2-262 2-217 53 3-126 3-052 2-912 2-846 2-782 2-721 2-662 2-604 2-549 2-496 2-444 2-394 2-346 2-299 ii 54 3 "243 3-165 3-091 3-208 3-020 2-952 2-886 2-822 2-761 2 "70 1 2-644 2-589 2-535 2-483 2-433 2-384 s 55 3-365 3-285 3-134 3-063 2-994 2-928 2-864 2^803 2-743 2-686 2-630 2-576 2-524 2-474 1 56° IVi 3-410 3"54i 3-330 3-459 3-253 3-379 3-179 3-302 3-108 3-228 3-040 3-157 2-974 3-088 2-910 3-022 2-S48 2-958 2-788 2-896 2-731 2-836 2-675 2-778 2-620 2-722 2-568 2-667 58 3-770 3t^i 3-594 3-738 3-890 3-512 3-432 3-355 3-281 3-210 3-141 3-074 3-010 2-947 2-887 2-829 2-772 £ ^ 3-921 3-828 3-652 3-569 3-489 3-412 3-338 3^266 3-197 3-130 3-065 3-002 2-942 2-883 a 4-080 3-983 3-801 3-714 3-631 3-551 3-474 3-399 3-327 3-258 3-190 3-125 3-061 3-000 61° 4-250 4-149 4-052 3-959 3-869 3-782 3-699 3-618 3-541 3-466 3-393 3-323 3-255 3-189 3-125 62 4-431 4-325 4-224 4-408 4-605 4-817 4-127 4-033 3-943 3-856 3-772 3-691 3-613 3-537 3-464 3-393 3-324 3-258 ^3 4-624 4-514 4-307 4-209 4-115 4-024 3-936 3-852 3-770 3-691 3-615 3-541 3-469 3-399 ^4 4-830 4-715 4-499 4-397 4-299 4-204 4*112 4-024 3-939 3-856 3-776 3-699 3-624 3-551 65 5-052 4-932 4-706 4-599 4-496 4-397 4-301 4-209 4-120 4-033 3-950 3-869 3-790 3-714 m • m m m m m m m m m m ra m m m 28 26 24 22 20 18 16 14 12 10 8 6 4 2 (157°) (■564°) (156°) (i55i°) (155°) (1544°) (154°) (■534°) 053°) (i52n (152°) (i5in (151°) (1504°) (150°) 10 HOURS. For the Azimuth :— The Sign is always +, except when the Hour-Angle exceeds 6 hours. B S6 USEFUL NAVIGATIONAL STARS IN ORDER OF DECLINATION. 1 Names of Stars. 1 HOUR. HI 32 m 34 111 36 m 38 m 40 ra 42 m 44 m 46 m 48 ra 50 m 52 m 54 m 56 m 58 m 60 (23°) (23^) (24°) (24i°) (25°) (254°) (26°) (264°) (27°) (274°) (28°) (284'') (29°) (294°) (30°) 27 1-9 Var. 0-3 Menkar . . . Procyon . . , Bet.t.atrix . . Betelguese . , RlGEL .... •165 •246 •281 •332 ■374 ■162 •241 •27s •325 •367 •159 -236 ■270 •319 •359 •156 •231 -264 ■313 -353 •153 -227 -260 -307 -346 -150 -223 -255 -301 •340 -147 -219 -250 -296 -333 •145 -215 ■246 -291 •328 ■142 -211 -242 •286 -322 -140 -208 -238 •281 ■317 •138 •204 -234 •276 •311 •13s •201 -230 •272 •306 •133 -198 -226 -267 -302 •131 ■195 •223 •263 •297 •129 •192 ■219 -259 ■292 i"o 27 2-4 I -2 Altair. . . . KlFFA BOREAI.IS Enif .... Spica .... •387 •406 •424 ■481 •379 -398 •416 •471 •372 •390 •408 ■462 •365 •383 ■400 -453 -358 •375 •392 •445 •38s •436 -345 -362 -378 -429 •339 •356 -372 -421 •333 •349 •365 •414 -328 -344 -359 •407 •322 -338 -353 ■400 •317 -332 •348 ■394 •312 •327 -342 -387 •307 ■322 •337 ■381 •303 •317 •332 •376 I "4 2-2 2-6 2-2 Regulus . . . Ras Alhague . Markab . . . Denebola . . ■565 ■574 •670 •692 ;554 ■656 •678 •543 ■551 •643 •66s •533 -540 •631 •652 •523 -530 -619 -640 •513 •521 •628 -504 •511 -597 -617 •495 -502 -587 -606 •487 -494 -577 -596 •478 •485 •586 -471 -477 -558 ■576 •463 -470 -549 -567 •456 -462 •540 •558 •449 •455 •532 •549 •442 •448 •523 •541 I"0 2-0 -1-4 2"I Aldebaran . . Alhena . . . SiRIUS .... Deneb-Kaitos . •749 •757 762 •858 •734 •742 •747 •841 ■719 728 732 •824 ■706 714 718 •809 ■692 •700 •704 •793 -680 •687 •692 ■779 -667 •675 •679 -765 -656 -663 -667 -751 -644 -652 -656 -739 •634 •641 •623 •630 •634 714 ■613 •620 •624 703 -603 •610 •614 •692 •594 •601 •605 •681 •585 •592 •595 -671 O'O 2-0 I -I Arcturus . . Algeiba . . . Hamel. . . . Antares . . . •917 •949 1-086 1-260 -898 -930 1-064 1-235 -880 -912 1-043 1-210 •864 -894 1-023 I -187 •847 -878 1-004 1-165 ■985 i^i« -817 •846 -968 1-123 -803 -831 ■951 1-103 •789 -817 •935 1-084 776 -803 1-066 •763 •790 -904 1-049 751 -777 -889 1-032 -739 -765 -875 1-015 ■727 753 -862 i-ooo 716 •742 -849 ■985 2-3 2-4 I"I 1-9 a Sagtttarii . . Alphacca . . rOLLUX . . . Nath .... 1-272 1-307 1-376 1-391 1-246 1-281 1-349 1-363 1-222 1-255 1-322 1-336 1-198 1-231 1-297 I -31 1 1-176 1-208 1-272 1-286 1-154 1-186 1-249 1-262 1-133 i"i6s 1-227 1-240 1114 1-144 1-205 1-218 1-094 1-125 I -184 1-197 1-076 I -106 1-165 1-177 1-058 1-088 1-145 1-158 1-041 1-070 1-127 1139 1-025 1-053 I -109 1-121 1-009 1-037 1-092 1-104 -994 1-021 1-075 1-087 1-3 2'0 27 Adara .... fomalhaut . . Castor. . . . Phact .... 1-409 1-487 1-606 1 735 I -381 1-457 1-574 1-700 1-354 1 -428 1-543 1-666 1-328 1-401 1-513 1-634 1-303 1-375 1-485 1-604 1-279 1-349 1-458 1-574 1-256 1-325 1-431 1-546 1-234 1-302 1-406 1-519 1-213 1-280 1-382 1-493 1-192 1-258 1-359 1-468 I -173 1-237 1-337 1-444 I -154 1-217 1-315 1-420 1-136 1-198 1-294 1-398 I-1I8 1-180 1-274 1-376 l-IOI 1-162 1-255 1-355 2-1 2-2 17 0-2 Kaus Australis Mirach Mizar . e Centauri . . Vega .... 1754 1-798 1-851 2-050 1719 1-762 1-814 2-oo8 1-685 1-727 1-778 1-969 1-653 1-694 1-744 1-931 1-622 1-662 1-711 1-895 1-592 1-632 I -680 1-860 1^564 1-603 1-650 1-827 1-536 1-575 1-621 1-795 1-510 1-548 1-593- 1-764 1-485 1-522 1-566 1-734 1-460 1-497 1-541 1-706 1*437 1-472 1-516 1-678 1-414 1-449 1-492 1-652 1-392 1-427 1-469 1-626 1-371 I '405 1-447 I -602 2-2 2-4 2'I Almach . . . Phosnicis . . 9 Scarpa , . . Arided. . . . 2-292 2 '374 2-381 2-552 2-246 2-326 2333 2-501 2-202 2-281 2-287 2-452 2-160 2-237 2244 2-405 2119 2-195 2-201 2-360 2-oSo 2-I5S 2-l6l 2-317 2-043 2-116 2-122 2-275 2-007 2-079 2-085 2-235 1-973 2-043 2-049 2-197 1-940 2-009 2-015 2-i6o 1-908 1-976 1-982 2-124 1-877 1-944 1-950 2-090 1-847 1-913 1-919 2-057 1-819 1-884 1-889 2-025 1-791 1-995 0-2 1-9 1-9 2-0 Capella . . . a Gruis . . . Mirfack . . . Benetnasch . . 2-641 2788 2-997 3-030 2-588 2-732 2-937 2-969 2-537 2-678 2-879 2-911 2-488 2-627 2-824 2-855 2-441 2-577 2771 2 -801 2-397 2-530 2-720 2-750 2-354 2-485 2-671 2-701 2-312 2-441 2-625 2-653 2-273 2-399 2-579 2-608 2-235 2-359 2-536 2-564 2-198 2-320 2-494 2-522 2-162 2-283 2-454 2-481 2-128 2-247 2-416 2-442 2-095 2-212 2-378 2-404 2-064 2-178 2-342 2-368 2-4 0-4 Var. 2-1 Etanin . . . Canopus . . . Schedar . . . a Pavonis . . . 3-218 3-352 3-793 3-949 3-IS3 3-285 3-716 3870 3-091 3-220 3-643 3-794 3-032 3-159 3-574 3-721 2-975 3-099 3-507 3-651 2-920 3-043 3-442 3-584 2-868 2-988 3-381 3-520 2-818 2-936 3-321 3-458 2-885 3-264 3-399 2-723 2-837 3-209 3-342 2-678 2790 3-157 3-287 2-635 2745 3-106 3-234 2593 2-702 3-057 3183 2;S53 3-009 3-134 2-514 2 620 2-964 3-086 I'O 2-S 17 I -2 Achernar . . Tureis .... /3 Crucis . . . j8 Centauri . . 4-055 4-235 4-283 4-413 3 "974 4-150 4-197 4-325 3-896 4-068 4-115 4-240 3-821 3-990 4-036 4-158 3-749 3-916 3-960 4-080 3-681 3-844 3-888 4-006 3-615 3-775 3-818 3-934 3-551 3-709 3-751 3-865 3-490 3-645 3-687 3-798 3-432 3-584 3-625 3735 3-375 3-525 3-565 3-673 3-321 3-468 3' 508 _ 3-614 3-268 3-413 3-452 3-557 3-218 3-361 3-399 3-502 3-169 3^310 3-347 3-449 2-0 2 "2 2-0 2"I Dubhe .... ai Crucis . . . a Tri. Austral. , P Argas . . . Kochab . . . 4-873 4-926 6-613 6775 9-269 4-775 4-827 6-480 6-639 9-082 4-681 4-732 6-353 6-508 8-904 4-591 4-641 6-231 6-383 8-733 4-505 4-554 6-114 6-264 8-570 4-423 4^47 • 6-002 6-149 8-412 4-343 4-390 5-895 6-039 8-262 4-267 4-313 5-791 5 933 8-117 4-194 .4-239 5-692 5-831 7-977 4-123 4-168 5-596 5 -733 7-843 4-056 4-100 5-504 5-639 7714 3-990 4-034 5-416 5-548 7-590 3-927 3-970 5330 5-460 7-470 3;867 5 -376 7-355 3-808 3-849 5-168 5-294 7 -243 m 28 m 26 m 24 m 22 m 20 m 18 m 16 m 14 m 12 m 10 m 8 m 6 m 4 m 2 m (157°) (iS6i°) (156°) (iSSi°) «ss°) (1544°) (154°) (1534°) (153°) (1524°) (152°) (1514°) (151°) (1504°) {150°) 10 HOURS. / When Latitude and Declination are of contrary names, the Sign is +. For the Azimuth: | ^yhen Latitude and Declination are of same name, the Sign is — . 3? The Head-line has various significations according to the Problem in use. In Problem IV. it represents Diff. of Long. In Problem V. the Initial Course. In Problem VI. the tompiement of the Diff. of Long. In Problem VIII. the Diff. of Long. In Problems X. and XI. the True Azim. Lat. 2 HOURS. m m m m m m m m ni m m m m m m 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 (3oi°) (31°) (3-4°) (32°) (32i°) (33°) (334°) (34°) (34i°) (35°) (35r) (36°) (36i°) (37°) (37i°) 0° •000 ■000 •000 -000 -000 -000 -000 •000 -000 •000 -000 -000 •000 •000 -000 I •030 ■029 •028 •028 •027 -027 -026 -026 -025 •025 ■024 •024 •024 -023 •023 ^^ 2 •059 -058 -057 -056 -055 •054 -053 -052 -051 -050 •049 •048 -047 •046 -046 X 3 •089 •087 •086 •084 •082 •081 -079 •078 -076 ■07S •073 •072 •071 -070 •068 ii 4 •119 •116 -114 •112 •110 •108 •106 •104 -102 •100 •098 •096 •095 •093 •091 1 S •149 •146 -143 •140 -137 •135 •132 •130 -127 •125 •123 •120 -118 •116 •114 X 6° •178 •175 •172 •168 -165 •162 ■159 •156 -153 •150 ■147 •145 -142 -139 •137 7 •208 ■204 -200 •196 •193 •189 ■186 -182 -179 -175 -172 •169 -166 -,63 ■160 g 8 •239 ■229 -225 •221 •216 -212 -208 ■204 •201 •197 •193 •190 •187 ■183 a3 ® 9 •269 ■264 -258 -253 -249 -244 -239 •235 ■230 -226 •222 •218 ■21i. •210 •206 ^1 10 •299 •294 •288 •282 •277 •272 •266 -261 •257 -252 -247 •243 •238 -234 •230 .s£ n° •330 -324 -317 •311 -305 •299 •294 -288 -283 •278 •273 •268 •263 •258 -253 12 •361 -354 -347 -340 -334 -327 •321 •31s -309 •304 -298 ■293 •287 ■282 -277 13 ■392 •384 •377 -369 -362 -356 -349 •342 -336 -330 -324 •318 •312 •306 •301 3 14 ■423 ■415 •407 -399 •391 •384 -377 •370 -363 -356 -350 •343 -337 •331 •32s o . 11 IS ■4SS ■446 •437 -429 •421 •413 -405 •397 -390 -383 •376 •369 •362 •356 -349 i6° •487 •477 •468 -459 -450 •442 -433 -425 •417 •410 •402 •395 -388 •38. ■374 H •519 ■509 •499 -489 •480 -471 •462 ;453 -445 •437 •429 •421 -413 •406 •398 *^ p. i8 •552 •541 ■530 •520 •510 •500 -491 •473 -464 -456 •447 -439 •431 •423 £« 19 •58s •573 •562 '^V- -540 -530 •520 -510 •501 -492 -483 -474 •465 '""V •449 ^o 20 •618 •606 -594 -582 -571 •560 •550 -540 •530- •520 -510 -501 •492 -483 •474 ■3 ® .. 2X° 11? -639 •626 •614 ■603 •591 •580 -569 •559 •548 -538 -528 •519 -509 -500 22 •686 -672 -659 •647 -634 •622 •610 -599 •588 -577 •566 -556 •546 •536 -527 iftS 23 ■721 •706 -693 •679 ■666 •654 -641 -629 •618 •606 •595 -584 •574 -563 -553 tj ffl 24 756 •741 •727 713 -699 •686 -673 -660 -648 -636 •624 -613 -602 -591 -580 01 -w O 25 792 •776 •761 -746 •732 •718 ■705. •691 •678 •666 •654 •642 -630 •619 -608 .2^2 26° ■828 •812 -796 •781 •765 ■751 ■737 723 710 •697 •684 -671 -659 •647 ■636 ^s.^ 27 •865 -848 •831 -815 •800 •785 770 •741 •728 •714 •701 •689 •676 -664 S °<»-' 28 •903 -885 •868 11' -835 •819 -803 •788 •774 •759 •745 •732 719 •706 -693 29 •941 ■922 •905 •887 -870 •854 -837 -822 -807 ■792 777 763 -749 •736 •722 30 •980 -961 -942 -924 •906 ■889 •872 •856 -840 -82s •809 •795 •780 •766 •752 31° I -020 I -000 •981 -962 •943 •925 •908 •891 •874 •858 •842 -827 -812 •797 -783 32 I -061 1-040 1-020 1-000 •981 •962 -944 •926 •909 •892 -876 -860 •844 -829 •814 33 1-I02 I -081 i-o5o 1-039 1-019 1-000 ■981 •963 -945 •927 •910 -894 •878 •862 •846 S-^a 34 1-145 1-123 i-ioi 1-079 1-059 1-039 i-oig l^OOO •981 •963 •946 •928 •912 •895 •879 '^SS 35 1-189 1165 I -143 1-121 1-099 1-078 1-058 1-038 1-019 I -000 •982 •964 •946 •929 •913 have )nt ti •epre 36° 1-233 1-209 1-186 1-163 1-140 1-119 1-098 1-077 1^057 1-038 1-019 1-000 ■982 •964 -947 37 1-279 1-254 1-230 l-206 1-183 I -160 1-138 rii7 1-096 1-076 1-056 1^037 1-018 I -000 -982 .- s*- 38 1-326 1-300 1-275 1-250 1-226 1-203 ri8o 1-158 I -137 i-ii6 1-095 I '075 1^056 1-037 1-018 argil •epre they 39 1-375 1-348 1-321 1-296 1-271 1-247 1-223 1-201 1-178 1-156 1-135 rii5 1-094 I -07s 1-055 40 1-425 1-396 1-369 1-343 I -317 I "292 1-268 1-244 1-221 1-198 1-176 1-155 1-134 1-II4 ro94 s; 4t° 1-476 1-447 1-419 1-391 1-365 1-339 1^313 1-289 1-265 1-241 1-219 1-196 1-175 1-154 1-133 II 42 1-529 1-499 1-469 1-441 1-413 1-387 1-360 1-335 1-310 1-286 1-262 1*239 1-217 I^lQ? 1-173 43 1-583 1-552 1-522 1-492 1-464 1-436 1-409 1-383 1-357 1-332 1^307 1^283 1-260 *7j 1-237 1^215 e H-i 44 !§i 1-607 1-664 1-576 1-545 1-516 1-487 1-459 1-432 1-405 1-379 1-354 1-329 1-305 1-282 1-259 45 1-632 1-600 1-570 1-540 1-511 1-483 1-455 1-428 1*402 1-376 1-351 1-327 1-303 46° % 49 SO 1-758 1-821 1-885 1-953 2-023 1-723 1-785 1-848 I -915 1-983 1-690 1-750 1-812 1-877 1-945 1-657 1-716 1-777 1-841 1-907 1-625 1-683 1-743 1-871 1-595 1-651 1^710 1-771 1-835 1-620 1-678 1-738 1-801 1-535 1-590 1-647 1-705 1-767 1-507 1-560 ■1-616 1-674 1734 1-479 1-586 1-643 1-702 1-452 1-503 1-557 1-613 1-671 1-425 1-476 1-529 1-583 1-640 1-399 1-449 1-501 1-555 I -61 1 1^374 ■•423 1-474 1-527 1-582 1-350 1-398 1-447 1-499 I -553 51° S2 2-096 2-173 2-055 2-130 2-015 2-089 1-976 2-048 1-938 2-009 1-902 1-971 1-866 1-934 1-831 1-898 1-797 1-862 1-764 1-828 1^731 I '794 1-700 1-762 1-669 I '730 1-639 1-699 r^ i. S3 54 55 2-253 2-337 2-425 2-209 2-291 2-377 2-166 2-246 2-331 2-124 2-203 2-286 2-083 2-160 2-242 2-043 2-119 2-199 2-005 2-079 2-158 1-967 2-041 2"I17 I -931 2-003 2-078 2-040 1-860 1-930 2 '002 1-827 1-894 1-966 i^793 1-860 1-930 I -761 i^827 1-895 1-729 1-794 1-861 1 d 56° i 2-517 2-614 2-717 2-825 2-940 2-467 2-563 2-663 2-770 2-883 2-419 2-S13 2-6l2 2716 2-826 2-373 2-464 2-561 2-663 2-772 2-327 2-417 2-512 2-612 2-719 2-283 2-371 2-464 2-240 2-326 2-418 2-514 2-617 2-198 2-283 2-373 2-467 2-568 2-157 2-241 2-329 2-422 2^520 2-117 2-199 2-286 2-377 2-474 2-078 2-IS9 2-244 2-333 2-428 2-041 2-119 2-203 2-291 2-384 2-004 2-081 2-163 2-249 2^341 1-967 2-043 2-124 2-209 2-299 1-932 2-007 2 -086 2^169 2-257 61° 62 3-063 3-193 3-332 3-481 3-641 3 -502 3-130 3-266 3-412 3-569 i 2-944 3-069 3-203 3-346 3-500 2-887 3-010 3-142 3-281 3-432 2-832 2-952 3-081 3-218 3-366 2778 2-896 3-022 3-157 3-302 2-726 2-841 2-965 3-098 3-240 2-675 2-788 2-910 3-040 3-179 2^625 2-736 2-856 2-983 3-120 2-576 2-686 2-803 2-928 3-063 2-529 2-637 2-751 2-874 3-006 2-483 2-589 2-701 2-822 2-952 2-438 2-542 2-652 2^898 2-394 2-496 2-604 2-721 2-846 2^351 2-451 2^558 2-672 2-795 58* 56 m 54 m 52 m 50 m 48 m 46 m 44 m 42 in 40 m 38 m 36 m 34 m 32 m 30 . (i49r) (149°) (i48i°) ('48°) (i47i°) ('47°) (I46i°) (146°) ('4Si°) (145°) (•44i°) 044°) (■43i°) (143°) (I42i°) 9 HOURS. For the Azimuth .--The Sign is always +, except when the Hour- Angle exceeds 6 hours. B 38 USEFUL NAVIGATIONAL STARS . IN ORDER OF DECLINATION. 1 1 Names of Stars. 2 HOURS. m 2 m 4 m 6 m 8 m 10 Ill 12 m 14 m 16 m 18 m 20 m 22 111 24 m 26 m 28 m 30 (30^) (31°) (3ii°) (32°) (324°) (33°) (334°) i'34°) (34i°) (35°) (35i°) (36°) (36r) (37°) (374°) 2-7 0-s 1-9 Var. 0-3 Menkar . . . Procyon . . . Bellatrix . . Betelguesb . . RlGEL .... ■128 •189 •216 •213 ■252 •284 •124 •184 -210 •248 •280 -122 •181 •207 -245 •276 •120 -179 -204 •241 -272 -119 •176 •201 -117 •174 -199 -235 -265 -116 -172 -196 -232 -261 -114 -169 -194 •229 •258 -113 •167 -191 •226 •255 •111 •165 -189 -223 -252 -110 ■163 •187 •221 ■249 -109 -161 -184 -218 •246 •107 •159 •182 •215 ■243 •106 -15S -180 •213 -240 I"0 27 2-4 1-2 Altair. . . . KlFFA BOREAI.IS Enif . . . . Spica .... •298 ■313 ■327 •370 •294 •308 •322 •36s •290 •304 •317 •360 •286 •299 •313 •355 •282 •295 •309 •350 •278 •291 •305 ■345 -274 -287 -300 -340 •271 •284 •297 •336 •267 -280 -293 •332 -264 •277 •328 -261 •273 -286 •324 ■257 -270 •282 ■320 -254 -267 •279 •316 •251 •264 •276 •312 •249 -261 •272 •309 I "4 2-2 2-6 2-2 Regulus . . . Ras Alhague . Markab . . . Denebola . . •435 •442 •S16 •S33 •429 ■435 •508 •525 •423 ■429 ■501 •518 -417 -423 •494 ■510 •411 •417 •487 •503 •406 •412 •481 •496 •400 •406 ■ -474 •490 -395 •401 •468 -484 •390 -396 •462 -477 •385 -391 •456 •471 •380 -386 •451 •466 •376 ■381 •44s -460 -371 •377 •440 •455 •367 •372 •435 •449 •430 ■444 i-o 2'0 -1-4 2"I Aldebaran . . Aliiena . . . SiRlOS . . . . Dbnbb-Kaitos . ■57^ ■583 ■587 •661 •568 •575 •578 •651 •560 •566 •570 •642 ■552 ;5S8 -633 •545 ;s5i •624 •537 •543 -547 •616 •530 -536 •539 -607 -523 ■529 •600 •517 -522 •526 ■592 •510 •516 •519 •585 •504 •510 •513 •577 •498 •503 •507 -570 •492 •497 •501 •564 •486 •492 •495 •557 -481 -486 •489 •551 0"0 2-0 Arcturus . . Algbiba . . . Hamel. . . . Antares . . . 705 731 •836 •970 •695 •720 •824 •956 •685 710 •812 •942 •676 •700 •801 •929 -667 •690 •790 -916 •658 •681 •779 •904 -649 -672 •769 ■892 -640 -663 -759 •880 -632 ■655 749 •869 -624 -647 -740 -858 •617 •639 •731 •848 •609 •631 •722 •838 •602 •623 •828 •595 •616 •705 •818 •588 •609 •697 •809 2-3 2-4 I-I i-g (7 Sagittarii . . Alphacca . . Pollux . . . Nath . . . . ■979 I 006 I 059 1-071 •965 •991 I -044 1-055 •951 •977 1-029 1-040 -938 -964 1015 1-026 •925 •950 I -001 I -01 1 •912 -938 -987 •998 •900 -925 •974 •985 •889 •913 -962 -972 ■877 •902 •949 •960 •866 -890 -937 -948 •856 •879 •926 •936 ■845 •869 •915 •925 'in •858 •904 •914 •826 ■849 •893 •903 •S16 •839 •883 •893 I "3 2-0 27 Adara . . . . fomalhaut . . Castor. . . . Phact . . . . 1-085 I -145 1-236 I -335 1-128 I -218 1-316 1^054 I-II2 I -201 1-297 1-039 1-096 I -184 1-279 1-025 I -081 1-168 1-261 I'OU 1-067 1-152 1-244 •998 1-052 1-137 1-228 •985 1-039 1-122 1-212 •972 1-026 1-108 I -197 •960 1-013 1-094 1-182 •948 I^OOO 1-081 1-167 i-o68 I-IS3 •926 ■977 I'OSS 1-139 •91S •96s 1-043 1-126 •904 •954 I 03 1 I-1I3 2-1 2 -2 17 0-2 Kaus Australis MiRACH MiZAR . e Centauri . . Vbga . . . . 1-384 1-425 1-578 1-331 1-364 1-404 1-555 I -312 1-345 1^384 1^533 1-294 1-326 1^365 r5ii 1-276 1-308 1^346 1-491 1-259 1-290 1-328 1-470 1-242 1-273 1-310 1-451 1-226 1-256 1-293 1-432 I -210 1-240 1-277 1-414 1-195 1-225 1-261 1-396 I-18I I-2IO 1-246 I "379 1-166 1-195 1-231 1-363 1-153 i'i8i l-2l6 1-346 1-139 I '167 1-202 I •SSI I'I26 I "154 I "188 1-316 2 '2 2-4 2"I 1-5 Almach . . . o rhcenicis , . Scarpa . . . Arided. . . . 1-833 I -96s 1-739 I -801 1-806 1-936 1714 1-775 1-781 1-909 1-690 1750 1-756 1-882 1-667 1-726 1732 1-856 1-645 1-703 1-708 1-831 1-623 1-68 1 1-686 1-807 1-602 1-659 1-664 1-783 1-581 1-638 1-643 1-761 1-562 1-617 1-622 1-739 1-542 1-597 I -602 1717 I "524 1-578 1-583 1-697 1-506 1-559 1-564 1-677 1-488 I •541 1^546 1-657 I •471 1-524 1-528 1-638 0-2 1-9 1-9 2-0 Capella . . . a Gruis , . , MiRFACK . . . Benetnasch. . 2-033 2-146 2-307 2-333 2-003 2-115 2-274 2-299 1^975 2-085 2-241 2-266 1-947 2-055 2-210 2-234 1-920 2-027 . 2iSd 2-203 1-894 2-000 2-150 2-174 1-869 1-973 2-122 2-145 1-845 1-948 2-094 2-117 1-822 2:^6i 2-090 1-799 1-899 2-042 2-064 1-777 1-876 2-017 2-039 1-755 1-853 1-992 2-014 1-735 1-831 1-969 K990 1714 I -810 1-946 1-967 1-695 1-789 1-924 1^945 2-4 0-4 Var. 2'I Etanin . . . Canopos . . . SCHEDAR . . . a Pwvonis. . . 2-477 2-581 2-920 3-040 2-441 2-543 2-877 2-996 2-406 2-507 2-836 2^953 2-372 2-472 2-797 2-912 2-340 2-438 2-758 2-872 2-308 2-405 2-721 2-833 2-278 2-373 2-685 2-796 2-248 2-342 2-650 2-760 2-220 2-313 2-616 2724 2-192 2-284 2-584 2-690 2-165 2-256 2-552 2-657 2-139 2-229 2-521 2-625 2^114 2-202 2-491 2-594 2*089 2-177 2-462 2-564 2-065 2-152 2-434 2-535 fO 2-S 17 I "2 ACHBRNAR , . TURBIS .... j8 Crucis . . . P Centauri . . 3-122 3-260 3-298 3-398 3-077 . 3-213 3-250 3-348 3-033 3-167 3-203 3-300 2-990 3-123 3^158 3^254 2-949 3-080 3-I1S 3-209 2-909 3-038 3-073 3-166 2-871 2-998 3-032 3-124 2-834 2-959 2-993 3-084 2-798 2-922 2-955 3-045 2-763 2-885 2-918 3-006 2-729 2-850 2-882 2-970 2-696 2-815 2-847 2-934 2-664 2-782 2-814 2-899 2-633 2-750 2-781 2-865 2-603 2718 2-749 2-833 2-0 li 2-2 2-0 2-1 DUBHE .... oi Crucis . . . a Tri. Austral. . P ArgAs . . . KOCHAB , . . 3-751 3-792 5-091 5-216 7-136 3-697 3-737 5-017 5-140 7-032 3-644 3-684 4-946 5-066 6-931 3-593 3-632 4-876 4-995 6-834 3-544 3-582 4-809 4-927 6-740 3-496 3-534 4-745 4-860 6-650 3-450 3-487 4-682 4-796 6-562 3-405 3-442 4-621 4734 6-477 3-362 3-398 4-562 4-674 6-394 3-319 3-356 4-505 4-615 6-314 3-279 3-314 4-450 4-559 6-237 3-239 3-274 4-396 6-161 3-201 3-236 4-344 4-450 6-089 3-164 3-198 4-294 4-399 6-018 3-128 3-162 4-245 4-348 5-949 m 58 m 56 m 54 m 52 m 50 m 48 m 46 m 44 m 42 m 40 m 38 m 36 in 34 m 32 m 30 (H9n (149°) (Mi") (148°) (>47n 047°) (i46i°) (146°) (1454°) ("45°) (I44i°) (■44°) ('434°) (143°) (■424°) 9 HOURS. f When Latitude and Declination are of contrary names, the Sign is +. For the Azimuth : | ^^^^ Latitude and Declination are of same name, the Sign is — . 89 The Head lipe has various signifleations, according to the Problem in use. In Problem IV. it represents Diff. of Long. In Problem V, the Initial Course. In Problem VI. Complement oj the Diff. of Long. In Problem VIII. the Diff. of Long. In Problems X. and XL the True Azim. the Lat. 2 HOURS. m m 111 m ni in m m 111 111 ra 111 m m ni 32 34 36 38 40 42 44 46 48 50 52 54 56 58 60 (38°) (38J°) (39°) (39^) (40°) (4or) (41°) {414°) (42°) (42i°) (43°) {43i°) (44°) (444°) (45°) 0° •000 -000 •000 -000 -000 -000 ■000 -000 -000 -000 -000 •000 •000 •000 •000 I •022 -022 •022 -021 -021 ■020 -020 -020 -019 -019 -019 •018 •018 ■018 •017 2 •04s -044 -043 •042 -042 •041 -040 •039 •039 -038 •037 -037 -036 ■036 •03s , 3 •067 -066 -065 -064 -062 -o6i -060 -059 -058 -057 •056 ■055 -054 •053 •052 4 ■090 -088 •086 -085 •083 -082 -080 -079 -078 •076 •07s -074 -072 ■071 •070 "S 5 •112 -no •108 -106 •104 -102 -101 -099 •097 •09s •094 -092 -091 -089 ■087 § 6° •13s •132 -130 -128 -125 ■123 •121 •119 -117 •IIS ■113 •III •109 -107 ■105 X' 7 ■IS7 •154 -152 •149 -146 •144 -141 ■139 •136 -134 ■132 -129 •127 . •125 •123 8 •180 -177 -174 -170 -167 -165 •162 -159 -156 •153 •151 •148 •146 •143 •141 ■ 51° I -581 1-638 1-699 I -552 1-525 1-498 1-472 1-446 1-421 1-396 1-371 1^348 1^324 1-301 1-279 1-257 I '235 ,4 > S^ 1-609 1-581 1-553 1-525 1-499 1-472 1^447 1-422 1^397 1-373 1^349 1-325 1^302 1-280 H . S3 1-668 1-639 I -610 1-582 I -554 1-527 1-500 1-474 1-448 1-423 1-398 1-374 f3So 1-327 t 54 SS 1-762 1-828 1-730 1-795 1-700 1-764 1-670 1-732 1-640 1-702 1-612 1-672 1-583 1-643 1-556 1-614 I 529 1-586 1502 1^559 1-476 1-532 1-450 1-505 1-425 i"479 I •401 I '453 I •376 1-428 0) S6° 1-898 1-864 I -831 1-798 1-767 1-736 1-705 1-676 1-647 1-618 1-590 I -562 I -535 I -595 1-657 1-509 1-567 1-629 1-694 1-763 I ■483 1-540 i-6oo 1 58 1-971 2-048 1-936 2-012 1-902 1-976 1-868 1-941 1-835 1-907 1-803 1-874 1-771 1-841 1-741 1-710 1-777 1-680 1-746 1-651 1-716 1-623 1-686 ^ 2-130 2-217 2-092 2-177 2-055 2-139 2-019 2-I0I 1-983 2-064 1-949 2-028 I -915 1-992 I -881 1-958 1-848 1-924 i-8i6 1-890 1-785 I -857 1-754 1-825 1-723 1-794 1-664 1-732 61° 62 65 2-309 2-407 2-512 2-624 274s 2-268 2-364 2-467 2-578 2-696 2-228 2-323 2-424 ^■532 2-648 2-188 2-282 2-381 2-487 2-601 2-150 2-241 2-339 2-443 2-556 2-II2 2-202 2-298 2-401 2-511 2-075 2-164 2-258 2-359 2-467 2-039 2-126 2'2l8 2-317 2-424 2-004 2-089 2-180 2-277 2-382 1-969 2-052 2-142 2-238 2-340 1-935 2-017 2-105 2-199 2-300 I -901 1-982 2-068 2-161 2-260 1-868 1-948 2-032 2-123 2-221 1^836 1-914 2-086 2-182 r8o4 r88i 1-963 2-050 2-145 m • 28 m 26 m 24 m 22 m 20 m 18 m 16 m 14 m 12 m 10 m • 8 m 6 m 4 m 2 m (142°) {■4ii°) (141°; (I40i°) (140°) (139^ (139°) (i38n (138°) (i37i°) (137°) (i36i°) (136°) (i3S4°J (I3S°) 9 HOURS. For the Azimuth :— The Sign is always +, except when the Hour-Angle exceeds 6 hours. B 40 USEFUL NAVIGATIONAL STARS IN ORDER OF DECLINATION. 4 1 Names of Stars. 2 HOURS. m 32 m 34 m 36 ra 38 m 40 m 42 m 44 m 46 m 48 m 50 ra 52 m 54 m 56 m 58 m 60 (38°) (384°) (39°) (39i°) (40°) (4oi°) (41°) (414°) (42°) (42i°) (43°) (43lr°) (44°) (44r) (45°) 27 o-s 1-9 Var. 0-3 Menkar . . . Procyon . . . Bellatrix . . Betelguesb . . RlGEL .... •los •178 •211 ■237 -104 •176 •208 -23s -103 -152 •174 -206 -232 -102 •151 •172 -204 -230 -101 -149 -171 •202 -227 -100 -148 -169 -200 -225 -099 -146 -167 ■198 •223 -098 -145 -166 -196 '221 •097 •143 -164 -194 -218 -096 -142 -162 -192 -216 -095 -141 ■161 -190 ■214 -094 -139 ■159 -188 •212 -093 -138 -158 -187 -210 •092 •137 •156 -185 -209 -091 -136 -15s -183 -207 I"0 27 2-4 1*2 Altair. . . . Kiffa Borealis Enif .... Spica .... •246 •269 •30s ■243 •25s -266 •302 •240 ■252 -299 ■238 ■249 -261 •29s ■23s -247 -258 •292 -233 •244 -231 -242 -253 -285 -228 -239 -250 -284 -226 -237 •248 -281 -224 -235 -245 -278 -222 -233 -243 -275 -220 -230 -241 -273 -218 -228 •239 -270 -216 -226 -268 ■214 -224 1 "4 2-2 2-6 2 "2 Regulus . . . Ras Alhague . Markab . . . Denebola . . •359 ■364 ■425 ■439 -355 •360 •420 ■434 -351 -356 -416 ■430 •347 ■ ^352 -411 ■425 -344 -349 -407 -421 -340 -345 ■403 •416 ■337 -342 -399 -412 -333 ;338 -408 -330 -335 •391 -404 -327 -332 -387 -400 -324 -329 -3S4 -396 -321 -326 -380 -393 •318 -323 -377 -389 -315 -320 •312 ■317 -370 ■382 i-o 2-0 -1-4 2-1 Aldebaran . . Alhena . . . SiRIUS .... Deneb-ICaitos . ■47S •481 •484 •S4S •470 -475 -478 •539 -465 -470 -473 •533 -460 •465 -468 -527 •455 -460 -463 -522 ■451 -456 -458 -516 -446 •451 -454 -511 •442 -447 -449 -506 •437 -442 •445 •501 -438 -441 •496 -429 -434 -437 -492 -425 -430 -433 -487 -421 -426 •429 -483 -417 -422 -42s -478 •414 -418 -421 ■474 o-o 2-5 2-0 I 'I Arcturus . . Algeiba . . . Hamel. . . . Antares . . . •582 •602 •689 •800 :s7s -682 791 -569 -589 -674 -782 •563 •667 •774 •557 -766 -551 -571 -653 -758 ;546 -647 -750 -540 •560 -640 -743 •535 •554 •634 •736 -530 -729 -525 -544 -622 -722 -520 -539 -616 715 -516 -534 -611 •709 •5" -702 •506 -524 -600 -696 2-3 2-4 1-9 a Sagitiatii . . Alphacca . . Pollux . . . Nath .... •807 •829 ■873 •883 •798 -820 -864 -873 •790 -811 -854 -864 -781 ■803 •845 •854 773 •794 •837 -845 •765 -786 -828 -837 -757 -778 -820 -828 -750 -771 -812 -820 •743 •763 -804 ■812 -735 -756 -796 -804 -729 -749 -788 -797 -722 -742 -781 -790 715 -735 -774 •782 -709 -729 -767 -775 -703 -722 -760 •769 I -5 1-3 2-0 27 Adara . . Fomalhaut . . Castor. . . . Phact .... •894 •944 1-019 I-IOI -884 •933 1-008 1-089 -875 -923 -997 1-077 -866 •913 -987 1-066 •857 -904 -976 1-054 -848 -894 -966 1-044 -839 -885 •956 1-033 •831 -877 -947 1-023 -823 •868 -938 1-013 -815 -860 -929 1-003 ■807 •852 -920 ■994 -800 -844 •912 -985 -793 -836 •903 ■976 -786 -829 ■895 -967 •779 -822 -887 •958 2'I 2-2 17 0-2 KaUS AUSTRALIS MiRACH MiZAR . B Centauri . . Vega .... I-II3 I ■141 I -175 1-301 I-IOI I -129 I -162 1-287 1-089 1-116 I -149 1-273 1-078 I -105 1-137 1-259 1-067 1-093 1-125 1-246 1-056 1-082 1-114 1-233 I -045 I -07 1 1-102 1-221 I -03s 1-060 1-092 1-209 1-025 1-050 I -081 I -197 1-015 1-040 1-071 1-185 1-005 1-030 I -06 1 1-174 -996 1-021 1-051 1-163 -987 I -oil 1-041 1-153 -978 1-002 1-032 1-143 -969 -994 1-023 1-133 2*2 2-4 2-1 Almach . . . a Fhcenicis , . 9 Scarpa . . . Arided. . . I -455 1-507 i-Sii 1-620 I '439 1-490 1-495 I -602 1-423 1-474 1-478 1-585 1-408 1-458 1-463 1-568 1-393 1-443 1-447 1-552 1-379 1-428 1-433 1-536 1-365 1-414 1-418 1-520 1-352 1-400 1-404 1-505 1-339 1-386 1-390 1-490 1-326 1-373 1-377 1-476 1-313 1-360 1-364 1-462 1-301 1-348 1-352 1-449 1-289 1-335 1-339 1-436 1-278 1-323 1-327 1-423 1-267 1-312 1-316 1-410 0-2 1-9 I "9 2-0 Capella . . . a Gtuis . . . MlRFACK . . . Benetnasch . . 1-676 1-769 1-902 1-923 1-657 1750 I -881 i-go2 1-640 1 731 I -861 I -881 1-622 1-712 I -841 1-861 1-605 1-695 1-822 1-842 1-589 1-677 1-803 1-823 1-785 1-804 1-644 1-767 1-787 1-542 1-628 1-750 1-769 1-527 1-612 1-733 1-752 1-513 1-597 1-717 1-736 1-499 1-582 1-701 1-720 1-686 1-704 1-472 1^554 1-671 1-689 1-459 1-540 1-656 1-674 2-4 0-4 Var. 2*1 Etanin . . . Canopus . . . Sciiedar . . . a Pavonis, , . 2-042 2-128 2-407 2-506 2-020 2-104 2-381 2-479 1-998 2-081 2-355 2-452 1-976 2-059 2-330 2-426 1-956 2-038 2-305 2-401 1-936 2-017 2-282 2-376 1-916 1-997 2-259 2-352 1-897 1-977 2-236 2-329 1-879 1-958 2-215 2-306 1-861 1-939 2-194 2-284 1-843 1-921 2-173 2-263 1-826 1-903 2-153 2-242 1-810 1-886 2-133 2-221 1-794 1-869 2-114 2-202 1-778 1-852 2-096 2-182 I'O 2-S 17 1*2 Achernar . . Tureis .... j3 Cruets , . , j8 Centauri . , 2-574 2-688 2718 2-801 2-658 2-689 2-770 2-518 2-629 2-659 2-740 2-491 2 -602 2-631 2-711 2-465 2-574 2-604 2-683 2-440 2-548 2-577 2-655 2-415 2-522 2-551 2-628 2-391 2-497 2-526 2-602 2-368 2-473 2-501 2-577 2-345 2-449 2-477 2-552 2-323 2-426 2-454 2-529 2-302 2-404 2-431 2-505 2-281 2-382 2-409 2-482 2-261 2-361 2-388 2-460 2-241 2-340 2-367 2-439 2-0 2-2 2-0 2'I Dubhe. . . . ai Cruris , , , a Tri. Austral, . ;8 Arg^s , . , Kochab . . . 3 '093 3-126 4-197 4-300 5-883 3-059 3-092 4-151 4'SS2 5-818 3 "025 3-058 4-106 4-206 5-755 2^993 3-026 4-062 4-162 5-694 2-962 2-994 4 "020 4-I18 5-634 2-932 2-964 3-979 4-076 5-576 2-902 2-934 3-935 4 -035 5-520 2-873 2-905 3-900 5-466 2-845 2-876 3-862 3-956 S-412 2-818 2-849 3-825 3-918 5-361 2-792 2-822 3-789 3-881 5-310 2-766 2-796 3-754 3-846 5-261 2-741 2-771 3-720 3-811 S-214 2-716 2-746 3-687 3-777 5-167 2-693 2-722 3-654 3-744 5-122 m 28 m 26 m 24 m 22 m 20 m 18 m 16 m 14 m 12 m 10 m 8 m 6 m 4 m 2 m ;i (142°) (1414°) (Hi°) (140^) (140°) (i39n (139°) (i38n (138°) (■37^) (137°) (i36i°) (136°) (i3S4°) (•35°) 9 HOURS. / When Latitude and Declination are of contFary names, tlie Sign Is -f. tor the Azimuth: | y^^^^^ Latitude and Declination are of same name, tlie Sign is -. 41 The Head-line has various sierniflcations according to the Problem in use. In Problem IV. It represents Diff. of Long., In Problem V. the Initial Course. In Problem VI. the Complement of the Difif. of Long. In Problem VIIL the Diff. of Long. In Problems X. and XI. the True Azim. Lat. 3 HOURS. m m m m m m m m lU in in m m in ra 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 (4Si°) (46°) (464°) (47°) (474°) (48°) (48i°) (49°) (494°) (50°) (504°) (51°) (514°) (52°) (524°) 0° ■000 •000 -000 •000 -000 •000 -000 ■000 -000 -000 •000 -000 -000 -000 •000 I ■017 ■017 •017 •016 -016 •0x6 •015 -0x5 -0x5 •0x5 •014 -014 -014 ■014 -013 ,,j 2 •034 -034 •033 -033 -032 -031 -031 -030 •030 •029 -029 -028 -028 •027 -026 X 3 •DS2 -051 •050 •049 -048 •047 ■046 -046 -045 •044 *043 -042 -042 •041 •040 ■d 4 •069 ■068 -066 -065 -064 •063 •062 -06 X -060 -059 -058 -057 -056 •05s -054 § 5 •086 •084 -083 •082 -080 •079 -077 •076 -075 ■073 -072 •071 •070 ■068 *o67 >k 6° •103 ■lOI •100 ■098 -096 •095 ■093 -09 X -090 -088 -087 -085 •084 ■082 *o8i U3 7 •121 •119 •117 •114 -113 ■XIX •109 -X07 -105 -103 •lOX •099 •098 ■096 -094 S 8 •138 -136 ■133 -131 -X29 -127 -124 -122 -120 •118 -X16 -114 •112 *iio *io8 to -< 44 ■949 ■983 •933 •916 -901 -885 -870 1|4 •839 -825 -810 •796 •768 ■754 ■741 s 45 •966 ■949 -933 •9x6 •900 -885 -869 -854 •839 -824 -8io ■795 ■781 -767 46° I -018 I •coo •983 •966 ■949 •932 •916 -900 -884 •869 •854 •839 -824 -809 -79s % I "054 1-036 I -0x8 I -000 •983 •966 -949 -932 -916 -900 -884 -868 -853 -838 •823 I '091 1-073 1-054 1-036 1-0x8 l^OOO -983 -965 -949 -932 -916 -899 -883 • *868 -852 49 50 I •130 i-iii 1-092 1-073 1-054 1-036 i-oi8 x-ooo •983 ■965 •948 -932 ■915 ■899 -883 r. > 1*171 1-151 1*131 i-iii x-092 1-073 1-054 x-036 I -018 i-ooo -982 -965 -948 -931 -914 SI- 52 S3 St 55 I*2I4 r2s8 '■^^1 I -172 I -152 I -132 I-IX2 1-093 1-073 1-055 1-036 1*018 I^OOO -982 ■965 -948 r 1-236 1-215 I -194 I -173 1-152 1-132 1-113 1-093 1-074 1*055 1-036 1*0x8 I -000 •982 >^ I '304 1-282 1-259 1-237 x-2x6 I -195 1-174 I -154 i"i33 1-114 1*094 1-075 1*056 1-037 1-018 HH 1*353 1-329 1-306 1-283 X-26X 1-239 x-218 I -196 I -176 1*155 1*135 I-I15 1*095 1-075 1-056 CO a I '403 1-379 1-355 1-332 1-309 x-286 1-264 1-241 1-220 I -198 1*177 1*156 1*136 1*116 ro96 5 A S6° i I -457 1-432 1-407 1-383 f3S9 1-335 1-312 1-289 1-266 1-244 1*222 I -201 1*179 1*158 1-138 g 1-513 1487 I '461 1-436 1-4IX 1-387 1-362 i"339 1-315 1-292 1 269 1-247 1-225 1-203 1-182 £ I '573 1-635 1-702 I '545 1-607 1-673 1-519 1-492 1-466 1-441 1-416 1-391 1-367 1*343 1-319 1-296 1*273 1*250 1*228 s I '579 1-552 1-6x5 1-525 1-587 1-499 x-560 1-472 1-532 1^447 1-506 1-421 1-479 1*396 1-453 1-372 1*428 1*348 1*403 1*324 1*378 1*300 1*353 1*277 1*329 6i° 62 65 1773 1-848 r929 1-742 r8i6 I^7I2 1-785 r862 1-682 1-754 1-830 1-653 1-723 1-798 1-624 1*693 1*767 1-596 1-664 1-736 1-568 1-635 1-706 1-541 I -606 I •676 1*514 1*578 1*647 1-487 1-6x8 I •461 1*523 1*589 1*435 1*496 1*561 1-409 1-469 1-533 1-384 1*443 1-506 2 '01 5 1*946 1-9x2 r879 I •846 1-8x4 1-782 1-751 1^720 1*690 I •660 1*631 X*602 1-573 2-107 • 2-071 2-035 2-000 I -965 1-931 1-897 x-864 1-832 1*799 1*768 1-737 1*706 1-675 1-646 111 ' m m m m ai m m ni m m m m m m 58 56 54 52 50 48 46 44 42 40 38 36 34 32 30 (i34n {134°) (1334°) (■33°) («324°) (■32°) 11314°) (131°) 1 (•304°) (130°) 0294°) (129°) (1284°) (128°) (1274°) 8 H 1 U R S. For the A zimuth :- -The Si ?n is al nravs +. excent when tl [le Hour -Angle ( 3xeeeds 6 hours, B 42 USEFUL NAVIGATIONAL STARS IN ORDER OF DECLINATION • u ■a 3 Names of Stars. 3 HOURS. m m m m m m m m m m m m m m m tl 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 (4Si°) (46°) (46i°) (47°) (47i°) (48°) (484°) (49°) (49i°) (50°) (5oi°) (5«°) (514°) (52°) (52i°; 27 Menkar . . . Procyon . . . Bellatrix . . Betelgubsb . . RiGEL . . , . •091 -090 -089 -088 •088 -087 -086 •086 -085 -084 -084 •083 -083 -082 -081 o"5 •13s ■133 ■132 •131 ■130 -129 -128 -127 -126 -125 -124 -123 •123 •122 ■121 I '9 Var. •I 54 •182 :;i^ -151 -179 •150 -177 •149 -176 -148 •174 •146 -173 •145 -172 -144 -171 -143 -169 -142 -168 ■]i^ -140 -166 •139 -16s -138 •163 0-3 •20S -203 •202 •200 •198 •197 -195 -194 -192 -191 -189 -188 •187 -186 •184 I-O 27 Altjur. . . . Kiffa Borealis Enif , . . . Spica . . . . •212 "222 •210 -221 ■209 -219 ■207 •217 •205 •215 •204 -213 -202 ■212 -200 •210 -199 -209 -198 -207 -196 -206 -195 -204 •193 •203 -192 -201 -191 -200 2-4 1-2 •233 •253 -231 -261 -229 -259 •227 •257 -225 -255 •223 •253 •221 •251 -220 -249 -218 •247 ■216 -245 -215 -243 •213 -242 -212 -240 -210 -238 -209 -237 1-4 2 '2 2-6 Regulus . . . Ras Alhague . Markab . . , Denebola . . •310 •314 -307 •312 -305 -309 •302 •306 •300 -304 •297 •302 -295 -299 -293 -297 -290 -294 -288 •293 -286 ■290 -284 -288 •282 -286 •280 -284 .t ■367 -364 -361 -358 •355 •352 -349 •347 -344 •342 -339 ■337 •334 •332 "330 2*2 •379 •376 •373 -370 -367 •364 -361 •358 -356 •353 -350 •348 •346 •343 •341 1-0 Aldebaran . . Alhena . . . SiRIUS . . . . Deneb-Kaitos . •410 ■407 •403 -400 •397 •394 -391 -388 -385 -382 •379 -376 ■374 -371 •369 2'0 •4IS -411 ■408 -405 •401 •398 -395 •392 -389 -386 -384 -381 •378 -376 -373 -1-4 2"I •417 •470 •414 •466 •410 •462 -407 •458 -404 •455 -401 •451 -398 -448 -394 -444 -392 •441 -389 -438 -386 -435 •383 -431 -380 -428 -378 -425 -375 -423 o-o Arcturus . . Algeiba . . . Hamel. . . . Antares . . . •502 -498 -494 -490 •486 -482 -478 -475 -471 -467 -464 -461 •458 -454 -451 2-5 •520 -516 '^l' -507 •503 -499 -495 •491 -488 -484 -481 ■477 -474 •471 -467 2'0 '^ ■|i° •585 -580 ■575 -571 -566 -562 •558 -554 -550 -546 -542 -538 -535 I"I •690 -684 -679 -673 -668 -662 -657 -652 -647 -643 ■638 ■633 -629 -625 -621 2-3 a Sagittarii . . Alphacca . . Pollux . . . Nath .... '^l -691 -685 -679 -674 -669 -663 -658 -653 -649 -644 -639 -635 -631 -626 2 "4 716 710 -704 -698 -693 -687 -682 -677 ■672 -667 •662 -657 -652 -648 -644 I'l 'U'^ -748 •741 -735 -729 -724 718 -712 ■707 -702 •697 -692 -687 ■682 -678 I "9 762 -756 749 -743 737 -731 ■726 -720 715 •709 -704 -699 -694 ■690 ■685 1-3 Adara .... Fomalhaut . . Castor. . . . Phact .... 772 ■814 ■■1% -759 -801 -753 -794 -747 ■788, •782 -735 -776 -730 -770 •724 -764 719 758 714 -753 -708 ■747 -704 -742 -699 737 •694 732 2"0 •880 -872 •865 -858 •851 -844 -838 ■831 -825 ■819 -813 -807 -802 -796 -791 27 ■950 -942 -934 •927 ■919 -912 -905 -898 -891 -885 -878 -872 -866 -860 -854 2-1 Kaus Australis MiRACH MiZAR . 9 Centauri . . Vega .... •961 -953 -945 -937 -930 •922 -915 ■908 -902 -895 -888 ■882 -876 -870 -864 2-2 •98s -977 -969 -961 -953 ■945 ■938 -931 -924 -917 -911 -904 ■898 -892 -886 17 I -014 1-005 ■997 -989 ■981 -973 •966 -958 -951 -944 -937 ■931 -924 -918 -912 0"2 I -123 1-113 J -104 1-095 I -086 I -078 1-069 i-o6i 1-053 1-045 1-038 1-031 1-023 1-016 1-009 2-2 Almach . . . Phanicis . . 6 Scarpa . . . Arided. . . . 1-256 1-245 1-235 1-225 1-215 1-205 1-196 1-187 1-178 1-169 1-161 1-153 1-144 1-137 1-129 2-4 1-301 1-290 1-279 1-268 1-258 1-248 1239 1-229 1-220 1-211 1-202 1-194 1-185 I -177 1-169 2"I 1-304 1-293 1-283 1-272 1-262 1-252 1-242 1-233 1-224 1-215 1-206 1-197 1-189 1-181 1-173 I'S 1-398 1-386 I-37S 1-364 1-353 1-342 1-332 1-321 1-312 1-302 1-292 1-283 1-274 1-266 1-257 0*2 Capella . . . a Gruis . . . I '447 1-434 1-422 I -41 1 1-399 1-388 1-378 1-367 1-357 1-347 1-337 1-328 1-318 1-309 1-301 1-9 1-527 1-514 1-502 1-489 1-477 1-466 1-454 1-443 1-432 1-422 1-412 1-402 1-392 1-382 1-373 1-9 Mirfack . . . 1-642 1-628 I -614 i-6oi 1-588 1-576 1-564 1552 1-540 1-529 1-518 1-507 1-496 1-486 1-476 2"0 Benetnasch. . 1-660 1-646 1-632 1619 i-6o6 1-593 1-581 1-569 I -557 1-545 1-534 1-523 1-513 1-502 1-492 2-4 Etanin . . . 1763 1-748 1-733 1-719 1-705 1-692 1-679 1-666 1-653 I 641 1-629 1-618 1-606 I -595 1-585 0-4 Canopus . . . 1-837 I -821 I -806 I -791 1777 1-763 1749 1-736 1-723 1-710 1-698 1-686 1-674 1662 1-651 \'ar. Schedar . . . 2-078 2 -060 2-043 2-026 2-010 1-994 1-979 1-964 1-949 1-935 1-921 1-907 1-894 1-881 1-868 2-1 a Pavonis, . , 2-164 2-145 2-127 2-110 2-093 2-076 2-060 2-045 2-029 2-014 2-000 1-986 1-972 1-958 1-945 I"0 Achernar . . 2-222 2-203 2-185 2-167 2-149 2-132 2-116 2-100 2-084 2-069 2-054 2-039 2-025 2-011 1-997 2-5 TUREIS .... 2-320 2-300 2-281 2-263 2-244 2-227 2-209 2-193 2-176 2-160 2-145 2-129 2-114 2-100 2 -086 17 j8 Cfucis , . , 2-347 2-327 2-307 2-288 2-270 2-252 2-235 2-2l8 2-201 2-185 2-169 2-154 2-139 2-124 2-110 I '2 j3 Centauri . , 2-418 2-397 2-377 2-358 2-339 2-320 2-302 2-285 2-268 2-251 2-235 2-219 2-203 2-188 2-174 2-0 Dubhb. . , , 3-669 2-647 2-625 2-603 2-582 2-562 2-542 2-523 2-504 2-485 2-467 2-450 2-433 2-416 2-400 li a' Cruets , , , 2-698 2-676 2-653 2-632 2-6io 2-590 2-570 2-550 2-531 2-512 2-494 2-477 2-459 2-442 2-426 2-2 a Trt. Austral. . 3-623 3-592 3-562 3-533 3-505 3-477 3-450 3-424 3-398 3-373 3'349 3-325 3-302 3-279 3-257 2'0 8 Argus . . . 37" 3-680 3-649 3-620 3-590 3-562 3-534 3508 3-481 3-456 3-431 3-406 3-382 3-359 3-337 2'I KOCHAB . . . 5-078 5-035 4-993 4-952 4-912 4-873 4-836 4'799 4-763 4728 4-694 4-660 4-628 4-596 4-565 m m m m m m m m m ra m m m m m f 58 66 64 62 60 48 46 44 42 40 38 36 34 32 30 (I34i°) (134°) ('334°) (133°) (•32i°) (132°) (I3ii°) (131*) (i3oi°) (130°) (I29i°) (129°) (1284°) (128°) (1274°) For the Azimuth 8 HOURS. ( When Latitude and Declination are of contrary names, the Sign is +. \ When Latitude and Declination are of same name, the Sign is — . M 43 The Head-line has various signifleations, accordinir to the Problem in use. In Problem IV. it represents Diff. of Long.. In Problem V. the Initial Course- Complement of the Diff. of Long. In Problem VIIL the Diff. of Long. In Problems X. and XI. In Problem VI. the True Azlm. the Lat. 3 HOURS. ra 32 (53°) m 34 (S3i°) m 36 (S4°) m 38 (544°) m 40 (55°) m 42 (5Si°) m 44 (56°) m 46 (564°) m 48 (57°) m 50 (574°) m 52 (58°) m 54 (584°) m 56 (59°) m 58 (594°) m 60 (60°) X ■a a x' CO a o ^ tu S c S o ^ «2 ^«. 73 C^ 03 O ►*>< § »s .2 ^*^ S -° •S ■* S bo •-< .S J o S 03 Oi 03« •^ T3 fr( 2 "03 CS 03 s 2 03 -w .S> CO "S 03 S 03 d ■a >• 03 ^r S o 03 0° I 2 3 4 5 6° 7 8 9 xo 11° 12 13 14 IS 16° '2 18 19 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° 48 49 SO Si° 52 S3 54 55 56° 58 60 61° 62 ^3 65 ■000 •013 •026 •039 •053 •066 •079 •093 •106 ■119 •133 •146 •160 •174 •216 •230 •245 ■259 •274 •289 •304 ■320 •336 •351 ■368 ■384 •401 •418 ■435 ■453 •471 •489 ■508 ■528 •547 •568 •589 •610 •632 •655 •679 ■703 ■728 754 •780 •808 ■837 •867 •898 •931 ■965 I'OOO 1-037 I '076 i'ii7 I "160 1'206 I -254 1-305 I '359 1-417 i'479 I '545 i-6i6 m 28 (127°) •013 -026 •039 •052 -065 •078 -091 -104 -117 •130 ■144 •157 -171 -184 -198 -212 -226 •240 ■255 -269 -284 •299 •314 •329 •345 •361 •377 •393 -410 •427 •445 •462 •481 •499 •518 •538 •558 •578 •599 •621 •643 -666 -690 •715 -740 -766 •794 -822 -851 •882 -914 ■947 •982 I -018 1-057 1-097 i'i39 1-184 1-232 1-282 '•335 1-392 i'452 f5i7 1-587 m 26 (I26i') •013 •025 -038 •051 -064 -076 •089 •102 •IIS -128 •141 •154 •168 -181 •195 -208 •222 •236 -250 -264 •279 •294 •308 •323 •339 ■354 •370 •386 •403 •419 •437 •454 •472 •490 •509 •528 •547 •568 •588 -610 ■632 -654 -678 -702 -727 ■752 •779 -807 •836 -866 •897 -930 •964 I -000 1-038 1-077 1-119 1-163 1-209 1-258 I -311 1-366 1-426 1-490 1-558 m 24 (126°) -012 -025 -037 -050 -062 -075 -088 •100 -113 •126 •139 -152 -165 -178 -191 -205 •218 ■232 -246 -260 -274 -288 -303 -318 •333 •348 -363 -379 -395 -412 -429 •446 •463 •481 •499 ■518 •538 •557 •578 •599 •620 •642 •665 -689 •713 -739 -765 •792 ■821 -850 •881 •913 •947 -982 1-019 1-058 1-098 I -142 1-187 r235 1-287 1^342 1^400 1-462 1-530 -000 -012 -025 -037 •049 ■061 -074 -086 -098 -III •123 •136 •149 -162 ■175 -188 -214 -228 -241 •255 •269 •283 -297 •312 -327 •342 •357 •373 •388 •404 •421 •438 •455 -472 ■490 ■509 -528 -547 -567 -588 •609 ■630 •653 ■676 -700 -725 •751 •778 -805 -834 -865 -896 •929 -964 1-000 1-038 1-078 1-121 1-165 1-213 1-263 1-317 1-374 1-436 1-502 m 22 (I25i°) m 20 (125°) -012 -024 -036 -048 -060 -072 ■084 -097 -109 •121 -134 -146 -159 -171 -184 -197 •210 -223 -237 •250 -264 -278 -292 -306 •320 •335 •350 •36s •381 •397 -413 -429 -446 -464 -481 -499 ■518 -537 •557 •577 •597 -619 -641 •664 -687 -712 •737 •763 -791 •819 ■849 -880 -912 -946 -982 1-019 1-058 1-100 ri44 1^190 1^240 1^293 1-349 1-409 1-474 m 18 (1244°) -000 -012 -024 ■035 ■047 -059 -071 •083 •095 •107 ■119 •131 •143 ■156 •168 •181 •193 -206 •219 -232 -246 -259 -273 -286 ■300 -315 -329 -344 -359 -374 •389 •405 •421 •438 •455 -472 -490 -508 -527 -546 •566 -586 -607 -629 -651 -675 -698 -723 -749 -776 -833 •863 •89s -928 -963 1-000 1-039 ro79 1-123 1-168 1-217 1-269 1^324 1-383 1-446 m 16 (124°) -000 -012 -023 -035 -046 ■058 -070 ■081 ■093 ■105 •117 •129 -141 ■153 •165 -177 -190 -202 •215 •228 •241 •254 -267 -281 •295 -309 -323 •337 -352 -367 -382 •398- •414 •430 •446 •463 ■481 •499 •517 •536 -555 -575 •596 •617 ■639 -662 ■685 •710 -735 ■761 -789 -817 •847 •878 •911 •945 •981 I -019 1-059 1-102 1-146 1-194 1-245 1-299 I -357 I -419 -000 -on -023 -034 •045 •057 •068 •080 •091 •103 •IJ5 •126 •138 -150 162 •174 -186 -199 -211 -224 -236 •249 -262 •276 -289 •303 •3J7 ■331 -345 -360 -375 •390 -406 •422 -438 -455 •472 -489 •507 -526 -545 ■565 •585 •606 •627 ■649 -672 •696 -721 -747 -774 -802 •831 -862 -894 -927 ■963 1-000 1-039 1-081 1-125 1-172 1-221 I -275 I -331 1-393 m 14 (1234°) m 12 (123°) •000 •on -022 •033 -045 •056 •067 •078 -090 -loi •112 •124 •135 -147 -159 •171 -183 -195 •207 -219 •232 ■245 -257 -270 •284 •297 •3" •325 •339 •353 •368 •383 •398 -414 •430 -446 •463 -480 •498 -516 -535 -554 •574 -594 -637 -660 •683 -708 -733 •759 -787 -845 -877 -910 -944 •981 1-020 I '060 1-103 ri49 1-198 1"2S0 1-306 f366 m 10 (1224°) -000 -on -022 •033 •044 •055 •066 •077 -088 -099 -no •121 -133 -144 -156 •167 -179 -191 -203 •215 •227 -240 •252 -265 -278 -291 •305 -318 -332 •346 •361 •375 •390 •406 -421 •438 •454 -471 •488 •506 •524 -543 -563 -583 603 •625 ■647 -670 -694 -719 -745 -772 •800 •829 -860 -892 -926 -962 1-000 I "040 I '082 1-127 I "175 1-226 1-281 1-340 ■000 ■on •021 •032 -043 •054 -064 •075 -086 -097 •108 •119 •130 •141 ■153 •164 •176 •187 -199 -211 -223 •235 •248 •260 •273 -286 -299 •312 •326 -340 -354 •368 •383 •398 ■413 ■429 •445 •462 •479 •496 -514 -533 -552 ■571 •592 -613 -63s -657 -681 -705 ■730 •757 -784 -813 -843 -875 -909 -944 -981 1-020 1-061 i-io6 1-153 1-203 1-256 1-314 8 (122°) 6 (121 n •000 ■010 •021 -031 -042 -053 '063 -074 •084 •095 ■106 •117 ■128 •139 •ISO -161 -172 -184 -195 -207 -219 •231 -243 -255 -268 -280 -293 -306 •319 •333 -347 -361 -375 -390 -405 -421 -437 -453 -469 -487 •504 -522 -541 -560 -580 -601 •622 -644 -667 -691 -716 •742 -769 •797 -827 -858 -891 -925 •962 I -000 1-041 1-084 1-130 1-179 1-232 1-289 4 (131*) -000 -010 -021 ■031 -041 -052 -062 •072 •083 •093 •104 -114 -125 •136 •147 •158 -169 -180 •191 •203 -214 -226 •238 -250 -262 -275 •287 •300 -313 -327 •340 •3S4 •368 •383 •397 -412 •428 •444 ■460 -477 ■494 ■512 -530 -549 -569 -589 •610 -632 -654 -678 -702 -727 -754 •782 -811 •841 •873 •907 ■943 -980 1-063 I -108 1-156 I '208 1-263 2 (I20i°; ■000 -oro •020 -030 -040 -051 •061 -071 -081 •091 -102 -112 -123 -133 -144 -155 -166 -177 -188 •199 -210 -222 -233 -245 •257 -269 -282 -294 •307 -320 -333 •347 -361 -375 •389 -404 •419 -435 •451 -468 -484 •502 -520 •538 -558 •577 •598 -619 •641 ■664 -688 •713 -739 -766 -795 -825 -856 -889 -924 •961 I -000 1-042 1-086 I-I33 I -184 1-238 (120°) 8 HOURS. For the Azimuth .--The Sign is always +, except when the Hour-Angle exceeds 6 hours. B 44 USEFUL NAVIGATIONAL STARS IN ORDER OF DECLINATION. For the Azimuth: B HOURS. When Latitude and Declination are of contrary names, the Sign is +, When Latitude and Declination are of same name, the Sign is — . ■a 3 ■& Names of Stars. 3 HOURS. m in in m m m m m IB m m m ni m m S 32 34 36 38 40 42 44 46 48 50 52 54 56 58 60 (53°) (534°) (54°) (544°) (55°) (55i°) (56°) (56i°) (57°) (57i°) (58°) (58i°) (59°) (S9i°) (60°) 27 1-9 Var. Menkar . . . ppAfvnw •081 -080 -080 -079 -079 ■078 -078 •077 -077 •077 •076 -076 •075 -075 •07s A X\V/^XUlN ■ ■ ■ Bellatrix . . Betelguese . . Rigel . . , . 'I20 ■137 •162 •119 •136 -161 •119 •136 •160 -118 -135 •159 -117 -134 -158 ■116 -133 -157 -116 •132 •156 -115 -132 -156 -114 •131 -155 •114 -130 •154 -113 -129 -153 -113 -129 -152 -112 -128 -151 -III -127 -150 -HI -127 -150 0-3 •183 •182 •181 -180 •178 •177 •176 -175 -174 -173 -172 -171 -171 -170 •169 l-o 27 Altair. . . . KlFFA Borealis Enif . . . . Spica . , . . •189 •199 -188 •197 •187 •196 -186 -195 •18s -194 •184 -192 •183 •191 -181 -190 -180 -189 -179 -188 -178 -187 -177 -186 •177 -18s -176 -184 •175 •183 2-4 •208 ■206 •205 ■204 -202 -201 ■200 -199 -198 -197 -196 -195 •193 -192 -191 I '2 ■23s •234 •232 ■231 -229 -228 -227 •225 -224 ■223 •222 •220 -219 -218 -217 1-4 2-2 2-6 Regulhs . . . Ras Alhague . Markab . . . Denebola . . •277 •281 •328 -275 •279 •326 -273 -277 -324 -271 •275 •321 -270 -274 •320 •268 •272 •318 -266 •270 •316 -26s •269 •314 -263 -267 •312 -262 -266 •310 -260 -264 -309 -259 •263 •307 •258 -261 -305 -260 -304 •255 •259 •302 2*2 •339 •336 •334 -332 -330 •328 ■326 •324 •322 •321 ■319 -317 -315 -314 •312 i-o Aldebaran . . Alhena . . . SiRIUS . . . . Deneb-Kaitos . •366 -364 •362 -359 •357 -355 •353 •351 •349 •347 •345 -343 -341 •340 •338 2*0 ■371 •368 •366 -363 •361 -359 -357 •355 -353 •351 ■349 -347 -345 •343 ■342 -1-4 2-1 ■373 •420 -370 -417 •368 -414 •366 •412 •363 -409 •361 •407 -359 -404 -357 -402 -355 •400 ii -351 •395 -349 -393 -347 -391 •346 •389 1^^ 0"0 Arcturus . . Algeiba . . . Hamel. . . . Antares . , . ■448 •445 -443 •440 •437 •435 -432 ■429 -427 •425 •422 -420 -418 ■416 •414 2-5 •464 -461 -458 •456 -453 •450 -447 •445 •442 ■440 -437 -435 -433 •430 -428 2'0 •531 -528 -524 •521 ■518 -515 •512 •509 •506 •503 -500 -498 -495 •492 •490 I*I •616 -612 •608. -60s -601 -597 -594 -590 -587 -S84 -S80 •577 -574 •571 •568 2-3 a Sagittarii . . Alphacca . . Pollux , . . Nath .... ■622 -618 -614 -610 -607 ■603 -599 •596 -592 -589 -586 •583 -580 "577 •574 2-4 ■639 -635 •631 -627 •623 -620 -616 -612 •609 •60? •602 •599 -596 -593 •590 .I"I 'iP ■669 •66s -660 •656 -652 -649 -645 -641 ■638 -634 •631 •627 -624 -621 I "9 •681 ■676 -672 ■668 •663 -659 -656 -652 -648 •644 -641 -637 -634 •631 -628 i-s Adara .... Fomalhaut . . Castor. . . . •689 -685 -681 •676 -672 -668 -664 -660 •656 •653 -649 •646 -642 -639 •636 I "3 .727 ■723 718 714 •709 -70s •701 -697 -693 •689 •685 •681 -678 -674 •671 2-0 786 •781 776 771 •766 •761 757 752 ■748 •744 -740 -736 •732 •728 •725 27 Phact .... ■849 •843 •838 •832 -827 -822 -818 -813 •808 •804 -799 -795 •791 •787 •783 2*1 Kaus Australis •858 -853 •847 -842 -837 •832 -827 -822 -817 •813 -808 •804 -800 796 •792 2 "2 MiRACH MiZAR . •880 -874 •868 -863 -858 ■852 -847 -843 -838 •833 •828 -824 -820 -815 •811 17 e Centauri . . Vega .... •906 •900 •894 -888 ■883 -878 -872 •867 -862 •858 -853 -848 -844 •839 -835 0-2 1-003 -996 •990 -984 -978 •972 -966 •960 -955 -950 -944 •939 -934 •929 ■925 2*2 Almach . . . I -122 I-XI4 I -107 I -100 1-093 1-087 1-080 1-074 1-068 1-062 1-056 1-050 1-045 1-040 1-034 2-4 a Phcenicis . . 9 Scarpa , . . 1x61 I -154 I -147 ri39 1-132 1-126 1-119 1-112 1-106 I -100 1-094 ro88 1-082 1-077 1-071 2"I 1-165 1-157 1-150 I -143 1-136 1-129 1-122 I-I16 I -109 I -103 1-097 I -09 1 1-085 1-080 1-074 I-S Arided. . . . 1-249 I -241 1-233 1-225 1-217 I -210 1-203 1-196 1-189 I -182 1-176 1-170 1-163 1-157 1-152 0"2 Capella . . . 1-292 1-284 1-275 1-267 1-260 1-252 1-245 1-237 1-230 1-223 1-217 I -210 1-204 1-197 1-191 1-9 Gruts . . . 1-364 I -355 1-346 1-338 r33o 1-322 1-314 r3o6 1-299 1-291 1-284 1-277 1-271 1-264 1-258 1-9 Mirfack . . . 1-466 1-457 1-448 1-438 1-430 I -421 1-413 1-404 1-396 1-389 1-381 1-373 1-366 1-359 1-352 2'0 Benetnasch . . 1-482 1-473 1-463 1-454 1-445 1^436 1-428 1-420 1-412 1-404 1-396 1-388 1-381 1-374 1-367 2-4 Etanin . , . I -574 1-564 I -554 1-544 1-535 1-525 1-516 1-508 1-499 1-491 1-482 1-474 1-467 1-459 1-452 04 Canopus . . . 1-640 1-630 1-619 1-609 1-599 1-589 1-580 1-571 1-562 1-553 1-545 i^536 1-528 1-520 1-513 Var. Schedar . , . 1-856 1-844 1-832 1-820 1-798 1-788 1-777 1-767 1-757 1-747 1^738 1-729 1-720 1711 2"I a Pavonis , . , 1-932 1-920 1-907 1-895 1-884 1-872 1-861 i^85i 1-840 1-830 T-820 1-810 t-800 1-791 1-782 1-0 Achernar . . 1-984 I -971 1-959 1-946 1-934 1-923 1-91 1 1-900 1-889 1-879 1-869 1-858 1-849 1-839 1-830 2-S TUREIS .... 2-072 2-059 2-045 2-033 2-020 2-008 1-996 1-984 i;973 1-962 1-951 1-941 I -931 1-921 1-91 1 17 /S Crucis . . . 2-096 2-082 2-069 2-056 2-043 2-031 2 019 2-007 1-984 1-974 1-963 1-953 1-942 1-933 1-2 p Centauri . . 2-159 2-145 2-132 2-118 2-105 2-092 2-080 2-068 2-056 2-045 2-033 2-022 2-012 2-001 I -991 2'0 Dubhe. , , . 2-384 2-369 2-353 2-339 2-324 2-310 2-297 2-283 2-270 2-258 2-245 2-233 2'22I 2 "2 10 2-199 14 ai Crucis . . . 2-410 2*394 2 '379 2-364 2-350 2^335 2-322 2-308 2-295 2-282 2-270 2-257 2-245 2-234 2-222 2 "2 Tri. Austral. . 3-236 3-215 3-194 3-174 3-155 3-136 3-117 3-099 3-081 3-064 3047 3^031 3'°'S 2-999 2-984 2-0 3 Argils . , . 3315 3-293 3-272 3-252 3-232 3-212 3-193 3-174 3-156 3-139 3-121 3-105 3-088 3-072 3-057 2-1 ECochab . . . 4535 4-505 4-477 4-449 4-421 4-395 4-368 4^343 4-318 4-294 4-271 4-248 4-225 4-203 4-182 m m m m m m m m m m m m m m m 28 26 24 22 20 18 16 14 12 10 8 6, 4 2 (127°) (i26n (126°) (l2Si°) (125°) (I24i°) (124°) (i23n (123°) (I22i°) (122°) (I2li°) (■21°) (i2on (120°) 45 The Head-line has various signifleations according: to the Problem in use. In Problem IV. it represents DHT. of Long. In Problem V. the Initial Course. In Problem VI. the Complemint of the Diff. Of Long. In Problem VIII. the Diif. of Long. In Problems X. and XI. the True Azim. Lat. 4 HOURS. 4 (61°) 8 (62°) m 12 (63°) m 16 (64°) m 20 (65°) m 24 (66°) m 28 (67°) m 32 (68°) m 36 (69°) m 40 (70°) m 44 (71°) m 48 (72°) m 52 (73°) ra 56 (74°) ra 60 (75°) . s S3 is ^ « . o oSP C3 ';S ^ S SISh to -M O S ft . 050 *3 « S -o S Sf • to ■»►-? «^„ 2 +3+3 p- a) a> ^ )3 ID Cm ~H ® t>» 0) m o" I 2 3 4 5 6° 7 8 9 10 11° 12 13 14 IS 16° 17 18 19 20 21° 22 23 24 25 26° 28 29 30 31° 32 33 34 35 36° 37 38 39 40 41° 42 43 44 45 46° 47 48 49 50 51° 52 53 54 55 56° 58 60 61° 62 65 •000 •010 •019 •029 •039 ■048 •058 •068 ■078 •088 •098 •108 ■118 •128 •138 •149 •159 •169 ■180 ■191 •202 >213 •224 •235 •247 •258 •270 •282 ■295 •307 •320 •333 '346 ■360 ■374 •388 •403 •418 •433 •449 ■46s •482 ■499 •517 •535 •554 •574 •594 •6i5 •638 •661 •68s ■709 •736 •763 •792 ■822 •854 ■8S7 •923 •960 1*000 '•043 1-088 riSg ■000 •009 •019 •028 •037 •047 •056 •065 •075 •0S4 ■094 •103 •113 •123 •'33 •142 •152 •163 •173 •183 •194 ■204 •21 s •226 •237 •248 •259 •271 •283 •29s •307 '319 •332 ■345 •359 ■372 •386 •401 •415 •431 ■446 •462 •479 •496 •513 •532 ■55' •570 •591 •612 I •634 •657 ■681 •706 ■732 •759 •819 •851 •S85 ■921 •959 I^OOO 1-044 1-090 i'i40 ■000 -009 •018 •027 •036 •04s •054 •063 •072 ■081 •090 •099 •108 •118 ■127 •137 •146 •156 •166 ■175 ••85 •196 •206 •216 •227 •238 •249 •260 -271 •282 •294 •306 •318 •331 •344 •357 •370 •384 •398 •413 •428 •443 •459 •475 •492 •510 •528 •546 •566 •586 i •607 •629 •652 •676 •701 •728 •755 •785 •81S •848 •883 •919 •958 I^OOO I -04s 1-093 m 56* m 52 ra 48 ■000 •009 ■017 -026 •034 •043 •051 •060 •069 •077 •086 •095 •104 -113 •122 ■131 -187 •197 ■207 ■217 ■227 •238 •249 •259 •270 •282 ■293 •305 •317 •329 ■342 •354 •368 •381 •395 •409 -424 •439 •455 •471 •488 •505 •523 •542 •561 -581 -602 •624 •647 ■671 -697 •723 •751 •781 -812 ■84s •880 •917 •957 1-000 1-046 -000 •008 •016 -024 •033 •041 •049 •057 ■066 •074 ■082 •091 ■099 •108 •116 •125 140 •134 149 •143 '58 '152 168 •161 178 •170 m 44 •179 -188 •198 ■208 •217 •227 •238 •248 •258 •269 -280 -291 •303 •315 •327 •339 •35' •364 •378 •391 •405 •420 •435 •450 •466 •483 -500 •518 •536 •556 •576 •597 •619 •642 •666 -691 •718 •746 •776 •S08 •841 •877 •915 •956 m 40 •000 •008 •016 •023 •031 ■039 •047 •055 -063 -071 -079 •087 ■095 •103 •III •119 •128 •136 •145 •153 '162 •171 ■180 -189 -198 -208 -217 •227 •237 ■247 ■257 •268 •278 •289 •300 •312 •323 •336 •348 •361 •374 •387 •401 ■415 •430 "445 •461 ■477 •494 •5'2 •531 •550 •570 •59' •613 ■660 •686 •713 •741 •77' •803 ■837 •874 •9'3 •955 m 36 ("9°) I (118°) I (1,7°) j (n6°) (1,5°) (,140, -000 •007 •ois -022 -030 •037 •045 •052 •060 •067 •075 -083 -090 •098 •106 •"4 -130 •'38 •146 •154 •163 -171 -180 -189 -198 •207 ■216 •226 •235 •245 •255 •265 -276 •286 •297 •308 •320 •332 •344 •356 •369 •382 •396 •410 -424 •440 •455 •471 •488 •506 •524 •543 •563 •584 •606 •629 •654 -679 •706 ■735 •766 798 •833 •870 •910 ra 32 •000 •007 •014 •021 •028 •035 •043 •C50 •057 •064 -071 ■079 -086 -093 -loi •108 •116 ■124 -131 -139 •147 •'55 •'63 •171 -180 -188 •197 •206 •21s •224 •233 •243 •252 ■262 •273 •283 •294 •304 •3'6 •327 •339 •35' •364 •377 •390 •404 •418 •433 •449 •465 •481 •499 •517 •536 •556 •577 •599 •622 •647 •672 •700 •729 ■760 •793 -828 •866 m 28 ('13°) (112°) •007 •013 •020 -027 •034 •040 •047 ■054 •o5i •068 •075 ■082 •089 •096 •103 -no •117 •125 •132 •140 •'47 •155 •163 •171 •179 •187 •196 •204 •213 •222 •231 •240 •249 •259 •269 •279 •289 •300 •3" •322 •334 •346 •358 •371 •384 •398 •412 •426 •442 •457 •474 •491 •509 •528 •548 •569 •591 -614 •639 •66s •693 ■722 ■753 •787 823 ni 24 (in°) -000 •006 •013 019 ■026 -032 •038 •045 -OS' -058 •064 •071 •077 •084 •091 •098 -104 •III •118 •I2S •'32 •140 -147 •'54 •162 •170 •178 ■18S •194 •202 -210 •219 •227 ■236 •246 •255 •264 •274 •284 •295 •305 •316 •328 •339 •351 ■364 •377 •390 •404 •419 •434 •449 •466 •483 •501 •520 •540 •560 •582 •606 •630 •657 •68s •714 •746 781 lU 20 (110°) •000 •006 •012 -oi8 •024 •030 -036 •042 •048 •055 •061 ■067 •073 •079 •086 •092 •099 •IDS •112 •119 •125 •132 ■'39 •146 •153 •161 •168 •175 -183 •191 •199 -207 •2'5 •224 •232 •241 ■250 •259 •269 •279 •289 •299 •310 •321 •333 ■344 •357 •369 •382 ■396 '410 •425 •441 ■457 •474 •492 •S'o •530 ■55' •573 ■596 •621 •648 •676 •706 ■738 m 16 (109°) •000 ■006 •on •017 •023 •028 •034 •040 •046 •051 •057 •063 •069 •075 •081 •087 •093 •099 •106 •112 •118 •125 •131 •138 •145 •152 -158 •166 ■173 •180 •188 •'95 •203 -211 •219 •228 •236 •24s ■254 •263 •273 •282 •293 ■303 ■314 •325 ■336 ■348 ■361 ■374 •387 •401 •416 ■43' •447 •464 •482 •500 •520 ■541 •563 •586 ■611 ■63S •666 •697 in 12 ('08°) •000 ■005 •on •016 •021 •027 ■032 -038 ■043 •048 •054 ■059 •065 •071 •076 •082 -088 •093 •099 •105 •III •117 -124 •130 •136 •'43 •149 •'56 •163 •169 •177 ■184 •191 •199 •206 •214 •222 •230 •239 •248 •257 •266 •27s •28s •295 •306 •317 •328 •340 •352 ■364 ■378 •39' •406 '421 •437 •453 •471 •489 •509 ■530 ■552 "III •600 •627 •656 m 8 (107°) •000 -COj •010 •015 •020 •02s ■030 •035 ■040 •04s •05' •140 •146 •152 •159 •166 •172 •'79 -186 ■'93 •201 •208 •216 •224 •232 •241 •249 •258 •267 •277 •287 ■297 ■307 •318 ■330 •342 •354 •367 •381 •395 •410 •42s •442 ■459 ■477 •497 •517 •539 •563 ■588 •61S 4 (io6*) 7 HOURS. For the Azimuth :-Th9 Sign is always +, except when the Hour-Angle exceeds 6 hours. •000 •005 •009 •014 •019 •023 ■028 •033 ■038 ■042 •047 •056 -052 •o5i ■057 ■066 •062 •071 •067 •077 •072 -082 •077 -088 •082 ■093 •087 •099 •092 •104 ■098 •no •103 •116 ■108 ■122 •114 •128 •119 •'34 •125 •131 •'37 •142 •149 ■155 •i6i •167 •'74 •181 •188 ■'95 •202 •209 •217 •225 •233 •241 ■250 ■259 •268 •277 ■2S7 •298 •308 •3 '9 •331 •343 ■356 •369 ■383 •397 •4'3 ■429 •446 •464 ■483 •504 •526 ■549 •575 (105°) B USEFUL NAVIGATIONAL STARS IN ORDER OF DECLINATION. 46 4 1 Names of Stars. 4 HOURS. m 4 m 8 m 12 m 16 ra 20 m 24 m 28 m 32 in 36 m 40 m 44 m 48 ni 52 111 56 m 60 (61°) (62°) (63°) (64°) (65°) (66°) (67°) (68°) (69°) (70°) (71°) (72°) (73°) (74°) (75°) 27 Menkar . . . Procvon . . . •074 "IIO -073 -109 :?^i -072 -071 •106 ■071 -070 -070 ■069 -069 •068 •o6g •068 -067 -067 I'O Bellatrix . . •148 ■167 -107 •105 -104 -104 -103 -102 -101 -lOI ■100 ■100 -099 vJ. Betelguesk . . -124 •147 -166 •123 •146 -164 -122 -121 ■120 ■119 •118 •117 ■"Z -116 ■115 •115 -114 -114 0-3 RlGEL . . . , -144 -163 •143 -161 •142 ■160 -141 •159 -140 •158 -139 -157 -.38 •156 •137 -155 •136 •154 ■136 -153 •135 •152 ■134 -151 i-o 27 Alt AIR. . . . KlFFA BOREAI.IS •173 •181 •171 •180 •188 •213 •170 •178 •186 -211 •168 -167 -166 -164 •163 -162 -161 -160 •159 -158 •157 -157 2-4 1'2 Enif . . . . Spica . . . . •190 ■2IS ■209 -17s -183 -207 •174 -182 -206 •172 -180 -204 •171 •179 •203 -170 -178 •201 ■169 -176 -200 -168 •175 •199 •167 -174 -198 •166 •165 -173 -195 -164 -172 -194 1-4 2 '2 Regulus . . . Ras Alhague . ■253 •256 •299 •309 -250 •248 •246 •244 -242 -240 •238 •237 -23s -234 •232 •231 •230 •229 2-6 2 "2 Markab . . . Dbnebola . . •254 -296 •306 ■252 -294 •303 -249 -291 -301 •247 -245 -2S7 -296 •243 -284 •294 -242 ■282 -292 •240 •280 •290 ■239 ■III •237 -277 •286 -236 •284 -234 -274 -283 -233 -272 -281 -232 -271 -280 1-0 2*0 Aluebaran . . Alhena . , . •335 •338 •331 •328 •326 •323 -320 •318 •316 •313 -311 •309 ■308 •306 •304 -303 -'■4 2*1 SiRIUS . . , . ■335 ■332 •329 -327 -324 •321 -319 -317 ■315 •313 •311 -309 •308 -306 Deneb-Kaitos . "340 •383 ■337 ■380 -334 •376 •331 •373 •329 •370 -326 -367 -323 •364 -321 ■362 -319 ■359 -317 -357 -315 •355 -313 •353 •311 -351 -310 ■349 -308 -347 o-o 2-0 1 *1 Arcthrus . . Algeiba . . . •409 •406 -402 -398 -395 •392 -389 -386 -384 •381 •379 •377 ■374 •373 -371 Hamel. . . . Antakes . . •424 •48S •563 -420 •481 •SS8 -416 -476 -413 -472 ■409 -468 -406 -464 -403 -461 ■400 •458 •397 -454 -395 -451 •392 -449 -390 •446 ■388 -444 -386 •441 -384 -439 •552 -548 •543 -539 -535 •531 •527 •524 ■521 ■518 •515 -512 ■510 2-3 2-4 I 'I ir Sagittarii . . Alphacca , . •S68 •584 61S •621 ■563 •558 :!ii -548 -544 -540 ■536 -532 •529 •525 •522 ■520 •517 •514 POLT IIX ■573 •568 •563 ■559 ■5|s ■5|' -547 -543 -540 -537 •534 •531 -529 1-9 Nath -609 -603 •598 -593 -589 -584 ■5f° •576 •572 -569 -565 •562 ■559 -557 •616 •610 •60s -600 •595 -590 •586 -582 -578 •575 -571 •568 •56s -563 1-3 Adara .... fomalhaut . . Castor. . . . Phact .... •629 •664 •624 -658 •618 -652 {4 -607 -641 •603 -636 -598 -631 •594 -627 •590 -622 ■586 •6i8 •614 -579 -611 -^ •573 •604 •570 •601 2'0 27 717 711 -704 -698 -692 -687 -682 -677 -672 -668 -664 ■660 -656 -653 -650 775 -768 -761 -754 -748 •742 -736 -731 •726 -721 •717 •713 •709 •70s •702 2"I 2 2 17 Kaus Australis Mirach Mizar . Centauri . . Vega .... 784 •803 •827 •776 -796 -819 -769 •789 •812 •763 -782 -805 •756 -750 •769 792 -739 -758 ■780 •734 753 775 •730 •748 770 •725 721 •739 •761 717 -735 •756 •713 -731 -752 710 727 -749 0'2 •916 •907 -899 •891 •8S4 •877 -870 -864 -858 -852 •847 •842 •837 -833 •829 2*2 Almach , . . a Phanicis . . 9 Scarpa , . . Arided. . . . 1-024 I -014 1-005 -997 -988 -980 -973 •966 ■959 -953 •947 -942 •937 -932 ■927 .2'4 I '061 1-051 1-041 1-032 1-023 1-015 i-oo8 i-ooo -994 •987 -981 •975 •970 '965 -960 2*1 1-064 I -054 1-044 1-035 1-027 i-oi8 I -oil 1-003 •997 •990 •984 •978 •973 ■968 -963 ''5 I -140 I 130 1-119 I -1 10 i-ioo 1-092 1-083 1-076 1-068 I -061 i-oSS 1-049 1-043 1-037 1-032 0*2 Capella . . . Gruis . . . MiRFACK . . . Benetnasch. . i-i8o I -169 1-158 I -148 I -138 1-129 1-121 1-113 1-105 1-098 1-091 1-085 1-079 I -073 1-068 1-9 1-9 2*0 1-245 1-339 I -354 i"234 1-326 1-341 1-222 1-314 1-329 I -212 1-303 I -317 I -202 1-292 1-306 I -192 1-282 1-296 I -183 1-272 1-286 I -175 1-263 1-277 I -167 1-254 1-268 1-159 1-246 1-260 I -152 1-239 1^252 1-145 1-231 1-245 1-139 1-225 1-238 1-133 l-2l8 1-232 1-128 1-212 1-226 2-4 Etanin . . . Canopus . . . sciiedar . . . a Pavonis. , . 1-437 1-424 I -411 1-399 1-387 1-376 1-366 1-356 1-347 1-338 1-330 1-322 I -315 1-308 1-302 0*4 Var. 1-498 1-484 1-470 I -457 1-445 1-434 1 423 1-413 1-403 1-394 1^385 1-377 1-370 1-363 1-356 1-694 1-678 1-663 1-649 1-635 1-622 I -610 1-598 1-587 1-577 1-567 1-558 1-550 1-542 1-534 2'I 1-764 1-748 1-732 1-717 1-703 1-689 1-676 I -664 1-653 1-642 1-632 1-623 1-6x4 1-605 1-598 10 ACHERNAR . . TUREIS. . . . I -812 1-795 1-778 1-763 1-748 1-735 I -721 1-709 1-697 1-686 1-676 1-666 1-657 1-648 1*640 2-5 1-892 1-874 1-857 1-841 1-826 I -81 1 1-798 1-785 f773 1-761 1-750 1-740 1-730 1-721 1-713 17 j8 Cruets . . . P Centauri , . 1-914 1-896 1-878 1-862 1-847 1-832 i-8i8 1-805 1^793 1-781 1-770 1-760 1-750 1-741 i'733 1-2 1-972 I -953 1-935 I -919 1-903 1-888 1-873 1-860 1-847 1-835 1-824 1-813 1-803 1-794 1-785 2"0 Odbhb. . . . 2-177 2156 2-137 2-118 2-IOI 2-084 2-068 2-054 2-039 2-026 2-014 2-002 1-991 1-981 1-971 li a' Crucis . . . 2-201 2 -180 2-160 2-141 2-124 2-107 2-091 2-076 2-062 2-048 2 036 2 024 2-013 2-002 1-993 2 "2 s Tri. Austral. . 2-954 2-927 2-900 2-875 2-851 2-829 2-807 2787 2768 2750 2733 2717 2-702 2-688 2-675 2-0 9 Argils . . . 3-027 2-998 2-971 2-945 2-921 2-898 2-876 2-855 2-835 2-817 2-800 2783 2-768 2-754 2-741 2'I ^OCHAB . . . 4-141 4-102 4-065 4-029 3-996 3-964 3-934 3-906 3-879 3854 3-830 3-808 3-787 3-768 3-749 m m m m m m m m m m m m m m m 56 52 48 44 40 36 32 28 24 20 16 12 8 4 - (119°) (118°) (117°) (116°) (■15°) (114°) (113°) (112°) (111°) {■10°) (109°) (io8") (107°) (106°) ('05°) 7 HOURS. f When Latitude and Declination are of contrary names, the Sign is +. or e zimu . | ^jjgjj Latitude and Declination are of same name, the Sign is — . 47 The Head-line has vapious signifleations, according to the Problem in use. In Problem IV. it represents Diff. of Long. In Problem V. the Initial Course. In Problem VI. Complement of the Diff. of Long. In Problem VIII. the Diff. of Long. In Problems X. and XI. the True Azim. the Lat. 5 HOURS. m m m m m m m ra m 111 m m m 111 in 4 8 12 16 20 24 28 32 36 40 44 48 52 56 60 (76°) (77°) (78°) (79°) (80°) (81°) (82°) (83°) (84°) (85°) (86°) (87°) (88°) (89°) (90°) 0° •000 •000 •OCX) •000 •000 •000 •000 •000 •000 •000 •000 •000 •000 •000 •000 I •004 •(X)4 •004 •003 ■003 •003 •003 •002 •002 •002 •001 •001 •001 ■000 •000 2 ■CXD9 •008 ■007 •007 •006 •006 •005 •004 ■004 ■003 •002 •002 •001 •001 •000 3 •013 •012 •oil •010 •009 •008 •007 •006 •006 •005 •004 ■003 •002 •001 •000 y 4 •017 •016 •ois •014 •012 •on •010 •009 •007 •006 •005 •004 •002 •001 •000 •a 5 '022 ■020 •019 •017 •015 •014 ■012 •on •009 ■008 •006 ■005 •003 •002 •000 § 6° •026 •024 •022 •020 •019 •017 ■015 •013 •on •009 •007 •006 •004 •002 •000 X' 7 •031 •028 ■026 •024 •022 •019 •017 •015 •013 ■on •009 •006 ■004 •002 •000 8 •03s •032 ■030 •027 •02s •022 •020 •017 •015 •012 •010 •007 ■005 •003 •000 03 9 •039 •037 •034 •031 •028 •025 ■022 •019 •017 •014 •on •008 ■006 ■003 •000 10 ■044 •041 •037 ■034 ■031 •028 •025 •022 •019 •OIS •012 ■009 •006 •003 •000 11° •048 •04s •041 ■038 ■034 •031 •027 •024 •020 •017 •014 •010 ■007 •003 •000 '^ cu 12 •OS3 ■049 ■04s •041 •037 •034 •030 •026 •022 •019 •015 •on ■007 •004 •000 .a c 13 •058 •053 •049 •045 •041 ■037 •032 ■028 •024 •020 ■016 •012 ■008 •004 •000 l-H 14 •062 ■058 •053 •048 •044 •039 •035 •031 ■026 •022 •017 •013 ■009 •004 •000 a IS •067 •062 •057 •052 •047 •042 •038 •033 •028 •023 •019 •014 •009 ■005 •000 Is i6° •071 ■066 ■061 •056 ■051 ■045 •040 ■035 •030 •035 ■020 •015 •010 ■005 •ooo * 5 .a ft '2 •076 •071 ■06s •059 •054 •048 •043 ■038 •032 •027 •021 •016 •on •005 ■000 i8 ■081 •075 •069 •063 •057 •051 •046 •040 •034 •028 •023 •017 •on ■006 •000 19 •086 •079 ■073 •067 •061 ■05s •048 •042 •036 •030 •024 •018 •012 ■006 •000 w o „ O 20 ■091 •084 •077 •071 •064 •058 •051 •045 •038 •032 •025 •019 •013 ■006 •000 -% 21° •096 •089 •082 ■075 •068 •061 •054 •047 •040 •034 •027 ■020 •013 ■007 •000 ^ . 22 •lOI •093 •086 ■079 •071 •064 •057 •050 •042 ■03s •028 ■021 •014 ■007 •000 Ill 23 •106 •098 •090 •083 •075 •067 •060 •052 •045 •037 ■030 •022 •015 •007 •000 24 •III •103 •095 •087 •079 •071 •063 •055 •047 •039 ■031 •023 •016 •008 •000 25 ■116 •108 •099 •091 •082 •074 •066 ■057 •049 •041 •033 •024 •016 •008 •000 26° •122 •113 •104 •095 •086 •077 •069 •060 •051 •043 •034 •026 ■017 •009 •000 a o2 27 •127 ■118 •108 •099 •090 •081 •072 ■063 •054 •045 •036 •027 •018 ■009 •000 § ^5 28 •133 •123 •113 •103 •094 •084 •075 •065 •056 •047 •037 •028 •019 •009 •000 •Bst: 29 •138 •128 •118 •108 •098 •088 •078 •068 •058 •049 •039 •029 •019 •010 •000 Oft° 30 •144 •133 •123 •H2 •102 •091 •081 •071 •061 •051 •040 •030 •020 •010 •000 31° ■'^2 •139 •128 ■117 •106 •095 •084 •074 •063 •053 •042 •031 •021 •010 •000 32 '1^ •144 •133 •121 •110 ■099 •088 •077 •066 ■055 •044 ■033 ■022 •on ■000 •a'S» 33 •162 •168 :'5a •138 •126 •115 •103 •091 •080 •068 •057 •04S •034 ■023 •on •000 34 '1^ •143 •131 •119 •107 ■09s ■083 •071 •059 •047 •035 •024 •012 •000 35 ■I7S •162 •149 ■136 •123 •III •098 •086 •074 •061 •049 •037 ■024 •012 •000 36° •181 •188 •168 '^l^ ■"^1 •128 •"5 •102 •089 •076 •064 •051 •038 •025 ■013 •000 38 •174 •160 •146 •133 •119 •106 •093 •079 •066 •053 •039 ■026 ■013 ■000 » *3 S* 2 Sh^ •195 •180 •166 •152 •138 •124 •no •096 •082 •068 •055 •041 •027 •014 •000 39 •202 •187 •172 •IS7 ■143 •128 ■"1 •099 •085 •071 •057 •042 •028 ■014 •CIS •000 40 •209 •194 •178 ■163 •148 •133 •118 ■103 •088 ■073 •059 •044 •029 ■000 41- •217 ■201 •185 •169 •153 •138 •122 •107 •091 •076 •061 •046 •030 ■015 ■016 •000 42 ■224 •208 •191 •I7S •159 •143 •127 •in •095 •079 •063 •047 •031 ■033 •000 1^ 43 •233 •215 •198 •181 •164 ■148 •131 •114 •098 •082 •06s ■049 •oi6 •000 fl 44 •241 ■223 •205 •188 •170 •153 •136 •119 •lOI •085 •068 •051 •034 ■017 •000 s 5-5 45 •249 •231 •213 •194 •176 •158 •141 •123 •105 •088 •070 •052 •03s •017 ■000 46° % 49 •267 •277 ■287 ■248 ■266 •220 •228 •236 •245 •201 •208 •216 •224 •183 •189 •196 •203 •164 •170 •176 •182 •146 •162 •127 •132 •136 •141 •109 •113 •117 •121 •091 ■094 •097 •lOI •072 ■07s •078 •080 •054 •056 ■058 •060 •036 ■037 •039 •040 •042 ■018 •019 •019 •020 •000 •000 •000 •000 m i-T SO •297 •27s ■253 •232 •210 •189 •167 •146 •125 •104 ■083 •062 •021 •000 SI- 52 S3 54 SS •308 •28s •262 •240 •218 •196 ■'24 •152 •130 •108 ■086 •065 ;043 •046 •048 •050 •022 •000 > CO ■319 •331 •343 •3S6 •318 •330 •272 •282 ■293 •304 •249 •268 •278 •226 •234 •243 •252 •203 •210 •218 •226 •180 •187 •193 •201 •157 :;§ •'75 •135 •139 •145 •150 112 •116 •120 •125 •090 •093 •096 •100 ■067 •070 •072 •07s •022 •023 ■024 •025 •000 •000 •ooo ■000 1 56° i •370 •384 •399 •41S •432 •342 •356 ■369 •384 •400 •31S •327 ;340 •288 •299 •311 •324 •337 •261 •272 282 ■293 •30s •235 ■244 •264 •274 •208 •216 •225 •234 ■243 •182 •189 •196 •204 •213 •162 •168 ■'Zs •182 •130 ■135 •140 •146 ■152 •104 •108 •112 •116 •121 •078 •081 •084 •087 •091 •052 •054 ■056 ■058 ■060 •026 •027 •028 •029 •030 ■000 ■000 ■000 ■000 ■000 6i° 62 65 •450 •469 •489 •S" ■S3S ■416 •434 •4S3 •473 •49s •383 •400 •417 ■436 •456 f •381 •399 •417 •318 ■332 •346 ■362 •378 •286 •298 •311 ■325 ■340 ■254 ■264 •276 •288 ■301 •222 •231 •241 •252 •263 •190 •198 •206 •215 •225 •158 •165 •172 •126 •132 •137 •143 •ISO •095 ■099 ■103 •107 •112 •063 •066 •069 •072 •07s •031 •033 ■034 •036 ■037 •000 •000 •000 •000 •000 56 m . 52 m 48 m 44 m 40 m 36 m 32 m 28 m 24 m 20 m 16 ra 12 m 8 m 4 m ■ (104°) («03°) (102°) (101°) (100°) (99°) (98°) (97°) (96°; (95°) (94°) (93°) (92°) (91°; (90°) 6 HOURS. For the Azimuth:— The Sign is always +, except when the Hour-Angle exceeds 6 hours. B* USEFUL NAVIGATIONAL STARS IN ORDER OF DECLINATION. 48 1 'S Names of Stars. 5 HOURS. m m ra m m m m m m m ra m m m m 4 8 12 16 20 24 28 32 36 40 44 48 52 56 60 (76°) (77°) (78°) (79°) (80°) (81°) (82°) (83°) (84°) (85°) (86°) (87°) (88°) (89°) {90°) 27 Menkar . . . •067 -066 •066 •066 -066 •065 •065 -065 •065 •065 •065 •06s •065 -065 -065 o'S Procyon . . . •099 ■098 •098 -098 •097 •097 -097 -097 ■096 *096 -096 •096 •096 -096 ■096 1-9 Bellatrix . . •113 -113 •112 •112 •III -III •III •110 •no -no -no •no •no -no •no Var. Betelguese . . •134 •133 •133 •132 •132 •131 •131 •131 •130 •130 -130 •130 •130 •130 •130 0-3 RlGEL .... •151 -ISO ■149 •149 *I48 ■148 •148 -147 •147 -147 •147 •146 -146 •146 -146 I'O Altair. . . . •156 •^ss •iii •IS4 ■IS4 •153 •153 -152 •152 •152 -152 *IS2 •151 •151 •151 27 KlFFA BOREALIS •163 ■163 •162 •162 •161 -161 •160 ■160 *i6o -159 •IS9 •159 •159 *1S9 •«59 2-4 Enif .... •171 •170 •170 •169 •168 -168 *i67 •167 •167 -166 -166 •166- -166 ■166 •166 1-2 Spica .... •194 •193 •192 •191 •191 -190 -190 •189 *i89 -189 -188 *i88 *i88 *i88 *i88 I "4 Regulus . . . •228 ■227 •226 -225 •224 -224 -223 -223 •222 -222 -221 *221 *221 *221 •221 2-2 Ras Alhague . •231 •230 •229 ■228 •228 •227 -226 -226 -225 -225 ■225 •224 -224 •224 ■224 2-6 Markab . . . •270 •269 •268 ■267 -266 -265 -264 -264 -263 ■263 -262 •262 •262 -262 -262 2 '2 Denbbola . . •279 •278 ■276 ■27s ■275 -274 •273 -272 -272 -271 -271 ■271 -271 -270 •270 i-o Aldebaran . . •302 •300 ■299 -298 •297 -296 -295 -295 •294 -294 -293 •293 •293 •293 •293 2-0 Alhena . . . •30s •304 •303 -301 -300 •300 •299 ■298 -298 -297 -297 •296 -296 -296 -296 -1-4 SiRIUS .... •307 -306 •304 ■303 •302 -301 -301 •300 •299 ■299 -298 -298 -298 •298 •298 2-1 Deneb-Kaitos . •346 •344 •343 •342 •340 •339 •339 -338 •337 ■337 •336 •336 •335 •335 •335 o-o Arctorus . . •369 •368 •366 •36s ■364 •363 •362 •361 •360 •359 •359 •359 •358 •358 •358 2-5 Algeiba . . . •382 •381 •379 •378 •377 ■375 •374 -374 •373 ■372 •372 •371 •371 •371 •371 2'0 Hamel. . . . •437 •43S •434 ■432 ■431 •430 -428 -427 •427 •426 •425 •425 •425 -424 -424 J"l Antares . . . ■507 •505 •503 -501 *5oo •498 •497 •496 ■495 •494 •493 ■493 •493 •492 •492 2-3 a Sitgitiarii . . •512 •510 •508 -506 •505 •503 -502 *Soi •500 •499 •498 -498 •497 •497 •497 2-4 Alphacca . . •526 •524 •522 •520 ■519 -517 •516 ■514 •513 •5'3 •512 ■5'J ■5'J ■5'J ■5'c !•! Pollux . . . •SS4 •SS2 •550 •548 ■546 •544 ■543 -542 •541 -540 •539 •538 •538 •538 •538 1-9 Nath .... •S6o •SS8 •ss^ •SS4 •552 •SSO •549 ■548 •546 •546 •545 -544 •544 •544 •543 i-S Adara .... •567 ■565 •563 -561 •559 •557 •556 ■555 •554 •553 •552 ■551 •551 •551 •551 1-3 Fomalhaut . . •599 •596 "594 •592 •59° •588 •587 ■585 •584 •583 -582 -582 ■^^i ■|^J •581 2-0 Castor. . . . •647 ■644 -642 •639 •637 •635 •634 ■632 -631 •630 -629 -628 -628 -628 -627 27 Phact .... •698 -696 •693 •690 -688 •686 -684 ■683 -681 -680 •679 -679 -678 -678 -678 2-1 Kaus Australis 707 ■704 701 -698 -696 •694 •692 *69i -689 -688 -687 -686 •686 -686 -686 2-2 MiRACH MiZAR . 724 •721 •718 716 713 711 -709 -708 -706 -70s -704 -704 •703 -703 •703 17 e Centauri . . 74S -742 739 737 •734 •732 •730 •729 727 ■726 ■725 -724 •724 -723 •723 0*2 Vega . . . . •82s -822 •819 -816 •813 -811 -809 -807 •805 -804 -803 •802 -801 -801 *8oi 2*2 Almach . . . ■923 •919 ■916 •912 -909 •907 -904 -902 -901 •899 -898 •897 -896 •896 •896 2-4 a Phanicis . . •956 -952 •948 ■94s •942 •939 •937 •935 -933 -931 •930 -929 -928 *928 *928 2'I 6 Scarpa . . . ■959 ■9SS •951 -948 •945 •942 -940 ■937 -935 -934 -933 •932 -931 -931 -930 I '5 Arided. . . . 1-028 1-024 1-020 i-oi6 1-013 I -010 1-007 1-005 1-003 i-ooi i-ooo ■999 •998 ■997 •997 0"2 Capella . . . I 063 1-059 1-055 1-051 1-048 1-045 1-042 1-040 1-037 ro36 1-034 1-033 1*032 1-032 1-032 1-9 Gtuis . . . 1-123 i-ii8 1-114 I-IIO 1-106 1-103 i-ioo 1-097 1-095 1-093 1^092 1-091 1*090 1*089 1-089 i"9 MiRFACK . . . 1-207 1-202 1-197 I -193 1-189 t-i86 1-183 i-i8o 1-178 1-176 1-174 1-173 1*172 1*171 1-171 2-0 Benetnasch. . 1-220 1-215 I -210 1-206 1"202 1-199 1-195 1-193 1-190 1-188 1-187 1-185 1-185 1*184 1-184 2 "4 Etanin . . . 1-296 1-290 1-285 I -281 1-277 1^273 1-270 1-267 1*264 1-262 1-260 1-259 1-258 1*257 1-257 o'4 Canopus . . . 1-350 I '344 I "339 I "334 1-330 1-326 1-323 1-320 1-317 ''^\i 1-313 1-312 1-311 I -310 1-310 Var. SCHEDAR . . . 1-527 1-521 ^'S^i 1-510 1-505 1-500 1-496 I '493 1-490 1-488 1-486 1-484 1-483 1-482 1-482 2'I a Pavonis. . . 1-590 1-584 1-578 1-572 I-567 1-562 1-558 1^555 1-552 1-549 1-547 1-545 I -544 1-543 1-543 I'O ACHERNAR . . I'dw 1-626 1*620 1*614 1-609 1*604 1*600 1-596 i;S93 i-59« 1*588 1-587 1-586 1-585 1-585 2-S 17 TUREIS. . . . 1 70s 1-725 1-698 1718 1-6Q2 1-686 1-680 I '675 1*671 1-667 1-661 ■1S9 '157 1656 1-655 I •ess /S Crucis , . . 1-711 1-705 1-699 1*695 1*690 1-686 1-683 1-680 1*678 1-676 1-675 1-674 1-674 1-2 P Centauri , . 1777 1770 1-763 I -757 1-751 1*746 1*741 1^737 I '734 I -731 1*729 1-727 1725 1-725 1724 2-0 DUBHB .... 1-962 I '954 I 947 1*940 i^933 1-928 1-923 I -918 ^1-914 I -91 1 1*909 1*907 1*905 1-904 1-904 li o» Crucis . . . 1-984 I "975 1-968 1-961 1^954 1*949 1-944 1-939 I '935 I '932 1929 1*927 1-926 1-925 1*925 *3 2 '2 a Tri. Austra'. . 2-663 2-728 3733 2-652 2717 2-642 2-632 2-624 2-616 2-609 2-603 2-598 2-594 2*590 2*588 2-586 2-584 2-584 2'0 /3 ArgAs . . . 2-706 2-697 2-688 2-680 2673 2^667 2-662 2-657 2^654 2-651 2-649 2-64!: 2-647 2-I KOCHAB . . . 3717 3703 3-689 3-678 3-667 3-657 3-649 3-642 3-635 3-630 3-627 3-624 3-622 3-622 m in in m m m m m m m m m m m m 56 52 48 44 40 36 32 28 24 20 16 12 8 4 (104°) (103°) (102°) (101°) Coo") (99°) (98°) (97°) (96°) (95°) (94°) (93°) (92°) (91°) (90°) 1 6 HOUF ?s. f Wl tien Lat itude a nd Declination are of contFa py nam es, the Sign is +, For the ' Azimut ft- ,„ UaM T At 14-11/Ia o nA Tian inafinn 9pn nf QnniA r nmn. t' [10 $;iErn is — . Table c. 49 The Head-line has various signiflcations, accordins: to the Problem in use. In Problem III. it represents the True Azimuth. In Problem IV. the Initial Course. In Problem V. the Diff. of Long., also the True Distance. In Problem VII. the Lat. of Departure, also Lat. of Vertex. In Problem IX. the Lat. of Departure or of Destination, also Limiting Parallel. In Problems X. and XL the Hour-Angle or its supplement. H K o 'Sfi 1^ Lat. OF Obsek VER. TRUE AZIMUTH. or h (O 2) h m (o 4) h m (o 6) h m (o 8) 2^ h m (o 10) h m (o 12) h m (o 14) b m (o i6) 4r h m (o i8) h m (O 20) 5r h m (O 22) 6° h m (o 24) h m (o 26) T h m (o 28) 7r h m (o 30) >< §« • o . S M -go .S Stj « _ .F^ O J3 B -3 bo X o Go ^ ffic _ OM B <» /IN So Eh t3 o S'aJ £2 a*^ ■a* £» 0° I 2 3 4 5 6° 7 8 9 ID H° 12 13 14 IS 16° '2 18 19 20 21° 22 23 24 2S 26° 28 29 30 31° 32 33 34 35 36° H 38 39 40 41° 42 43 44 45 46" 47 48 49 50 51° 52 53 54 55 56° 58 60 61° 62 65 114-6 II4"6 "47 1 147 114-9 115-0 115-2 iiS'4 "57 1 16-0 ii6'4 116-7 117-1 117-6 ii8-i 1 18-6 1 19-2 119-8 120-5 121 -2 121-9 122-7 123-6 124-5 125-4 126-4 127-5 128-6 129-8 131-0 i32"3 1337 i3S"i 136-6 138-2 139-9 141-6 143 'S 145 '4 147 -4 149-6 151-8 154-2 1567 iS9'3 162-1 165-0 168-0 171-3 1747 178-3 182-1 186-1 190-4 194-9 199-8 204-9 210-4 216-2 222-5 229-2 236-4 244-1 252-4 261-4 271-1 S7"29 S7'30 57-32 57-37 57-43 57-51 57-61 57-72 57-85 58-00 58-17 58-36 58-57 58-80 59-04 59-31 59-60 59-91 60-24 60-59 60-97 61-37 61-79 62-24 62-71 63-21 63-74 64-30 64-88 65-50 66-15 66-84 67-56 68-31 69-10 69-94 70-81 71-73 72-70 7372 74-79 75-91 77-09 78-33 79-64 81-02 82-47 84-00 85-62 87-32 89-13 91-03 93-05 95-20 97-47 99-88 102 5 105-2 108-1 III -2 ii4'6 118-2 122-0 126-2 130-7 135-6 38-19 38-19 38-21 38-24 38-28 38-33 38-40 38-48 38-56 38-66 38-78 38-90 39-04 39-19 39-36 39-54 39-73 39-93 40-15 40-39 40-64 40-91 41-19 41-49 41-80 42-14 42-49 42-86 43-25 43-66 44-10 44-55 45-03 45-53 46-06 46-62 47-20 47-82 48-46 49-14 49-85 50-60 5' -39 52-22 53-09 54-01 54-97 55-99 57-07 58-21 59-41 60-68 62-03 63-46 64-97 6658 68-29 70-12 72-06 74-15 76-38 78-77 81-34 84-12 87-11 90-36 28-64 28-64 28-65 28-68 2871 28-75 28-79 28-85 28-92 28-99 29-08 29-17 29-28 29-39 29-51 29-65 29-79 29-94 30-11 30-29 30-47 30-67 30-89 31-11 31-35 31-60 31-86 32-14 32-43 32-74 33-07 33-41 33-77 34-14 34-54 34-96 35-40 35-86 36-34 36-85 37-38 37-94 38-53 39-16 39-81 40-50 41-22 41-99 42-80 43-65 44-55 45-50 46-51 47-58 48-72 49-93 51'21 52-58 5404 55-60 5727 5907 6i-oo 63-08 65-32 67-76 22-90 22-91 22-92 22-94 22-96 22-99 23-03 23-08 23-13 23-19 23-26 23-33 23-42 23-51 23-60 23-71 23-83 23-95 24-08 24-22 24-37 24-53 24-70 24-8S 25-07 25-27 25-48 2571 25-94 26-19 26-45 26-72 27-01 27-31 27-63 27-96 28-31 28-68 29-07 29-47 29-90 30-35 30-82 31-32 31-84 32-39 32-97 33-58 34-23 34-91 35-63 36-39 37-20 38-06 38-97 39 93 40-96 42-05 43-22 44-47 45-81 47-24 48-79 50-45 52-25 54-19 19-08 19-08 19-09 19-11 19-13 19-15 19-19 19-22 19-27 19-32 19-38 19-44 19-51 19-58 19-67 19-75 19-85 19-95 20-06 20-18 20-31 20-44 20-58 20-73 20-89 21-05 21-23 21-42 21-61 21-82 22-03 22-26 22-50 22-75 23-02 23-29 23-59 23-89 24-21 24-SS 24-91 25-28 25-68 26-09 26-53 26-98 27-47 27-98 28-52 29-08 29-68 30-32 30-99 3171 32-46 33-27 34-12 35-03 36-01 37-05 38-16 39-36 40-64 42-03 43-53 45-15 16-35 16-35 16-36 16-37 16-39 16-41 16-44 16-47 16-51 16-55 i6-6o 1666 16-72 16-78 16-85 16-93 17-01 17-10 17-19 17-29 17-40 17-51 17-63 17-76 17-90 18-04 18-19 18-35 18-52 18-69 18-88 19-07 19-28 19-49 19-72 19-96 20-21 20-47 20-75 21-04 21-34 21-66 22-00 22-36 22-73 23-12 23-54 23-97 24-43 24-92 25-44 25-98 26-56 27-17 27-82 28-51 2924 30-02 30-85 31-74 32-70 33-72 34-83 36-01 37-30 38-69 14-30 14-30 14-31 14-32 14-34 14-36 14-38 14-41 14-44 14-48 14-52 14-57 14-62 14-68 14-74 14-81 14-88 14-95 15-04 15-12 15-22 15-32 15-42 15-54 «5-65 15-78 15-91 16-05 16-20 16-35 16-51 16-68 16-86 17-05 17-25 17-46 17-68 17-91 18-15 18-40 18-67 18-95 19-24 19-55 19-88 20-22 20-59 20-97 21-37 21-80 2225 22-72 23-23 23-76 24-33 24-93 25-57 26-26 26-99 27-77 28-60 29-50 30-46 31-50 32-62 33-84 12-71 12-71 12-71 12-72 12-74 12-75 12-78 12-80 12-83 12-86 12-90 12-94 12-99 13-04 13-10 13-15 13-22 13-29 13-36 13-44 13-52 13-61 13-70 13-80 13-91 14-02 14-14 14-26 14-39 14-53 14-67 14-82 14-98 15-15 15-33 15-51 1571 15-91 16-12 16-35 16-59 16-84 17-10 17-37 17-66 17-97 18-29 18-63 18-99 19-37 19-77 20-19 20-64 21-11 21-62 22-15 22-72 23-33 23-98 24-67 25-41 26-21 27*06 27-99 28-99 30-07 11-43 11-43 11-44 11-45 11-46 11-47 11-49 11-52 11-54 11-57 11-61 11-64 11-69 11-73 11-78 11-83 11-89 11-95 12-02 12-09 12-16 12-24 12-33 12-42 12-51 12-61 12-72 12-83 12-95 13-07 13-20 13-33 13-48 13-63 13-79 13-95 '4-13 '4-31 14-50 14-71 14-92 15-14 15-38 15-63 15-89 16-16 16-45 16-76 17-08 17-42 17-78 i8-i6 18-57 18-99 19-45 19-93 20-44 20-99 2157 22-19 22-86 23-58 24-35 25-18 26-07 27-05 10-39 10-39 10-39 10-40 10-41 10-43 10-44 10-46 10-49 10-51 10-55 10-58 10-62 10-66 10-70 1075 10-80 10-86 10-92 10-98 11-05 11-12 11-20 11-28 11-37 11-46 11-55 11-66 11-76 11-87 n-99 12-12 12-25 12-38 12-53 12-68 12-84 13-00 13-18 13-36 13-56 13-76 13-97 14-20 14-44 14-69 1495 15-23 15-52 15-83 16 16 16-50 16-87 17-26 17-67 18-11 18-57 19-07 19-60 20-16 20-77 21-42 22-12 22-88 23-69 24-57 9-514 9-516 9-520 9-527 9538 9-551 9-567 9-586 9-608 9-633 9-661 9-692 9-727 9765 9806 9-850 9-898 9-949 10-00 10-06 10-12 10-19 10-26 10-34 10-41 10-50 10-59 10-68 10-78 10-88 10-99 11-10 11-22 11-34 11-48 11 -61 11-76 11-91 12-07 12-24 12-42 12-61 12-80 13-01 13-23 13-46 13-70 13-95 14-22 14-50 14-80 15-12 15-45 15-81 16-19 1659 17-01 17-47 17-95 18-47 19-03 19-62 20-27 20-96 21-70 22-51 To name Azimuth j J" ^°^*^ latitude put N f or a - ' Error,' and S for a + • ( In South latitude put S for a - ' Error,' and N for a + • 8-777 8-778 8-782 8-789 8-798 8-810 8-825 8-843 8-863 8-886 8-912 8-941 8-973 9-008 9-046 9-087 9-131 9-178 9-229 9-283 9-340 9-401 9-466 9-535 9-607 9-684 9-765 9-851 9-940 0-04 0-13 0-24 0-3S 0-47 0-59 0-71 0-85 0-99 1-14 1-29 1-46 1-63 1-81 2-00 2-20 2-41 2-63 2-87 3-12 3-38 3-65 3-95 4-26 4-58 4-93 5-30 5-70 6-12 6-56 7-04 7-55 8-10 8-70 9-33 20-02 20-77 8-144 8-146 8-149 8-156 8-164 8-175 S-189 8-206 8-224 8-246 8-270 8-297 8-326 8-359 8-394 8-432 8-473 8-516 8-563 8-614 8-667 8-724 8-784 8-848 8-915 8-986 9-061 9-141 9-224 9-312 9-404 9-501 9-604 9-711 9-824 9-942 10-07 10-20 10-34' 10-48 10-63 10-79 10-96 11-14 11-32 11-52 11-72 11-94 12-17 12-41 12-67 12-94 13-23 13-53 13-86 14-20 14-56 14-95 15-37 15-81 16-29 16-80 17-35 17-94 18-58 19-27 7-596 7-597 7-600 7-606 7-614 7-625 7-638 7-653 7-670 7-690 7713 7-738 7-765 7-796 7-828 7-864 7-902 7-943 7-987 8-033 8-083 8-136 8-192 8-252 8-315 8-381 8-451 8-603 8-685 8-771 8-861 8-957 9-057 9-162 9-273 9-389 9-511 9-639 9-774 9-916 10-06 10-22 10-39 10-56 10-74 10-93 ll'i4 11-35 11-58 11-82 12-07 12-34 12-62 12-92 13-24 13-58 13-95 14-33 14-75 15-19 15-67 16-18 1673 17-33 17-97 Error.' Error.' ^'""^^ZZZ!^ "^f'fl "^ "^ '^''''"' ""^ '^ ^^^"'"'^ "-^ '*« o^J'"' «'»*«-'"«^. t^ '*«'^»«-' «« *h<' iodv of thu Table shew the error in th* Longitude produced h, an error of 1' in the Latitude worked with. They rJpreeent the sum or difference of the A and bZZT 50 Tn Pi.nwa irr .* ^^^ Head-line has various signineations, according to thb Problem in use. the Tp^a ni«f=rr„®i'''®/'®"n^ l^° '^'^^?, Azimuth. In Problem IV. the Initial Course. In Problem V. the Diff. of Long., also ine irue Distance. In Problem VII. the Lat. of Departure, also Lat. of Vertex. In Problem IX. the Lat. of Departure or or Destination, also Limiting Parallel. In Problems X. and XI. the Hour-Angle or its suppument. II Lat. OF Obser- TRUE AZIMUTH. 8° sr 9° 9r 10° lor 11° iir 12° 12^ 13° isr 14° 14i° 15° ver. h m h m . h m h m h m h in h m h ni h m h HI h m h tn h m h in li ni (0 32) (0 34) (036) (0 38) (0 40) (0 42) (0 44) (046) (0 48) (0 50) (0 52) (0 54) (0 56) (0 58) (r 0) 0° 7-iiS 6-691 6-314 5 -976 5-671 5-396 S'I45 4-915 4-705 4-511 4-331 4-165 4-01 1 3-S67 3-732 %% I 7'ii6 6-692 ^■3'§ 5 -977 5 -672 S-396 S-145 4-916 4-705 4-5II 4-332 4-166 4-011 3-S67 3-733 ■s** 2 7 "120 6-695 6-318 5 -979 5-675 5-399 S-148 4-918 4-707 4-513 4-334 4-168 4-013 3-869 3'734 3 7-125 6-700 6-322 5-984 ^'%^ 5-403 5-152 4-922 4-711 4-517 4-337 4-171 4-016 3-872 3-737 »o 4 7'i33 6-707 6-329 5-990 5-685 5-409 5-157 4-927 4-716 4-522 4-342 4-175 4 02 1 3-876 3-741 5 7-143 6-717 6-338 5 -999 S-693 S-416 5-164 4-934 4-723 4-528 4-348 4-181 4-026 3-881 3-746 6° 7-iSS 6-728 6-349 6-009 5-703 5-425 5-173 4-942 4-731 4-536 4'3SS 4-188 4-033 3-888 3-753 so*' 7 7-169 6-741 6-361 6-021 5-714 5-436 5-183 4-952 4-740 4-545 4-364 4-197 4-041 3-896 3-760 8 7-18S 6-757 6-376 6-034 5-727 5-449 5-195 4-963 4-751 4-555 4-374 4-206 4-050 3-905 3-769 s%>< 9 7-204 6-775 6-392 ^■°^o 5-742 5-463 5-209 4-976 4-763 4-567 4-385 4-217 4-061 3-915 3 779 10 7-225 6-794 6-411 6-068 5-759 5 -479 5-224 4-991 4-777 4-580 4-398 4-230 4-073 3-926 3-790 11° 7-249 6-816 6-432 6-088 5 -777 5-497 5-241 5-007 4-793 4-595 4-413 4-243 4-086 3-939 3-802 ll><" 12 7-274 6-841 6-455 6-109 5 -798 5-516 5-259 5-025 4-810 4-61 1 4-428 4-258 4-100 3-953 3-815 13 7-303 6-867 6-480 6-133 5-820 5-537 5-280 5-044 4-828 4-629 4-445 4-275 4-1 16^^ 3-968 3-830 he P 1 V. 1 lems 14 7-333 6-896 6-507 6-159 5-845 5-561 5 -302 5-066 4-849 4-649 4-464 4-293 4-134 3-985 3-846 IS 7-366 6-927 6.-536 6-187 5-871 5-586 5-326 5-089 4-871 4-670 4-484 4-312 4-152 4-003 3-864 to t blem Prob 16° 7-402 6-961 6-568 6-217 5-900 5-613 5-352 5-113 4-894 4-692 4-506 4-333 4-172 4-023 3-882 17 7-440- 6-997 6 -602 6-249 5-930 5-642 5-380 5-140 4920 4-717 4-529 4-356 4-194 4-043 3-903 M) °d 18 7-482 7-035 6-639 6283 5-963 5-673 5409 5-168 4-947 4-743 4-554 4-380 4-217 4-066 3-924 _g BL|>-I 19 7-525 7-077 6678 6-320 5-998 5-706 5-441 5-.98 4976 4-771 4-581 4-405 4-242 4-090 3-947 20 7-572 7-I2I 6-719 6-359 6-035 5-742 5-475 5-231 5-007 4-800 4-609 4-433 4-268 4-115 3-972 § « « ID O 21° 7-622 7-167 6763 6-401 6-075 5-779 5-511 5-265 5-039 4-832 4-640 4-462 4-296 4-142 3998 ^ £>J 22 7-674 7-217 6-810 6-445 6-117 5819 5-549 5-301 5-074 4-865 4-672 4-492 4-326 4-170 4-025 si° 23 7-730 7-269 6-859 6-492 6-161 5-861 5-589 5-340 5-ni 4-900 4-706 4-525 4-357 4-201 4-054 24 7-789 7-324 6-911 6-541 6-208 5-906 5-631 5-380 5 150 4-938 4-741 4-559 4-390 4-333 4-0S5 5 ftfc 25 7-851 7-383 6-966 6-594 6-258 5-953 5-676 5-423 5-19' 4-977 4-779 4-596 4-425 4-266 4-118 go« 26' 7-917 7-445 7-025 6-649 6-310 6-003 5-724 5-469 5-234 5-019 4-819 4-634 4-462 4-302 4-152 2 ©.a 27 7-986 7-510 7-086 6-707 6-365 6-056 5-774 5-516 5-280 5-062 4-861 4-675 4-501 4-340 4-189 a .-M hflM 28 8-059 7-578 7-151 6-768 6-423 6-111 5-827 5 -567 5328 5-109 4-906 4-717 4-542 4-379 4-227 ious sij the La lem IX. 29 8-135 7-650 7-219 6-832 6-484 6-169 5-882 5-620 5-379 5-157 4-952 4-762 4-586 4-421 4-267 30 8-216 7-726 7-290 6-900 6-549 6-230 5-940 5-676 5-432 5-209 5-002 4-810 4-631 4-465 4-309 31° 8-301 7-806 7-366 6-972 6-616 6-295 6-002 5 -734 5 -489 5-262 5-053 4-859 4-679 4-5" 4-354 «>■§ 32 8-390 7-890 7-445 7-046 6-6S7 6-362 6-066 S-796 5-548 5-319 5-108 4-912 4-729 4-560 4-401 > >-'S 33 8-484 7-978 7-528 7-125 6-762 6-433 6-134 5-861 5-610 5 -378 5165 4-967 4-782 4-611 4-450 o S"^ 34 8-583 8-071 7-616 7-208 6-841 6-508 6-205 5-929 5-675 5-441 5-225 5-024 4-838 4-664 4-502 1 gfl 35 8-686 8-168 7-708 7-295 6-923 6-587 6-280 6-000 5 -743 5-507 5-288 5-085 4-896 4-720 4-556 36° 8 -795 8-271 7-804 7-386 7-010 6-669 6-359 6-075 5 -81 5 5-576 5-354 5-149 4-958 4-780 4-613 8-909 8-378 7-906 7-482 7-101 6-756 6-442 6-154 5-891 5-648 5-424 5-216 5-022 4-842 4-673 38 9030 8-491 8-012 7-583 7-197 6-847 6-529 6-237 5-970 5 -724 5-497 5-286 5-090 4-907 4-736 39 9-156 8-610 8124 7-689 7-298 6-943 6-620 6-325 6-054 5-804 5-574 5-360 5-161 4-976 4-802 40 9-288 8-735 8-242 7-801 7-403 7-043 6-716 6-416 6-141 5-888 5-654 5-437 5 -236 5 -048 4-872 sl| 41° 9-428 8-866 8-366 7-918 7-515 7-149 6-817 6-513 6-234 5 -977 5-739 5-519 5-314 5-123 4-945 — 43* 42 9 575 9-004 8-496 8-041 7-631 7-260 6-923 6-614 6-331 6-070 5-829 5-605 5-397 5-203 5-022 43 9-729 9-149 8-633 8-171 7-754 7-377 7-034 6-721 6-433 6-168 5-923 5-695 5-484 5-287 S-103 44 9-892 9-302 8-777 8-307 7-884 7-501 7-152 6-833 6-540 6-271 6-021 5-790 5-576 5-375 5-188 i^s 45 10 -06 9-463 8-929 8-451 8 -020 7-630 7-275 6-951 6-653 ■6-379 6-126 5-891 5 -672 5-468 5-278 »ti^ 46° ■ 10-24 9-632 9-089 8-602 8-164 7-767 7-406 7-076 6773 6-493 6-235 5 -996 5-774 5-566 5-372 •^^s 47 10-43 9-811 9-258 8-762 8-316 7-911 7-543 7-207 6-898 6-614 6-351 6-107 5-881 5-670 5-472 » I 3-6o6 3-488 3-376 3-271 3-172 3-078 2-989 2-905 2-824 2-748 2-675 2-605 2-539 2-475 2-415 |5 2 3-608 3-490 3-378 3-273 3-174 3-080 2-991 2-go6 2-826 2-749 2-676 2-607 2-540 2-477 2-416 4-< 3 3-611 3-492 3-381 3-275 3-176 3-082 2-993 2-908 2-828 2751 2-678 2-609 2-542 2-478 2-418 0,-0 4 3'6iS 3-496 3-384 3-279 3-179 3-085 2-996 2-91 1 2-831 2-754 2-681 2-61 1 2-545 2-481 2-420 M 5 3-620 3-501 3-389 3-283 3-184 3-089 3-000 2-915 2-835 2758 2-685 2-615 2-548 2-485 2-423 n (D 6° 3626 3-507 3-395 3-289 3-189 3-095 3-005 2-920 2-839 2-763 2-689 2-619 2-553 2489 2-428 S « S 3633 3-514 3-401 3-295 3-195 3-101 3 -01 1 2-926 2-845 2-768 2695 2-625 2-558 2-494 2-432 go*' 3 '64 1 3-522 3-409 3-303 3-203 3-108 3-018 2-933 2-852 2-774 2-701 2-631 2-564 2-499 2-43S -; c ox 9 3-651 3-531 3-418 3-312 3-211 3-116 3-026 2-940 2-859 2-782 2-708 2-638 2570 2-506 2-444 10 3662 3-541 3-428 3-321 3-221 3-125 3-035 2-949 2-867 2-790 2-716 2-645 2-578 2-513 2-451 11° 3-673 3-553 3-439 3-332 3-231 3-135 3-045 2-959 2877 2-799 2-725 ^ll'^ 2-586 2-521 2-459 12 3-686 3-565 3-45> 3-344 3-242 3-146 3-055 2-969 2-887 2-809 2734 2-663 2-595 2-530 2-468 gl^^ 13 3-701 3-579 3-465 3 357 3-255 3-159 3-067 2-981 2-898 2-820 2-745 2-674 2-605 2-540 2-478 On "» j2 m 14 3-716 3-594 3-479 3-371 3-269 3-172 3-080 2-993 2-910 2-832 2-757 2-685 2-616 2-551 2-488 15 3-733 3-610 3-495 3-386 3-283 3-186 3-094 3007 2-924 2-844 2-769 2-697 2-628 2-562 2-499 5 s3 16° 3-751 3-628 3-512 3-403 3-299 3-202 3-109 3-021 2-938 2-858 2-782 2-719 2-641 ''■5?l 2-512 17 3-771 3-647 3-530 3-420 3-317 3-218 3-125 3-037 2-953 2-873 2-797 2-724 2-655 2-588 2-525 ^la 18 3-791 3-667 3-550 3-439 3-335 3-236 3-142 3-054 2-969 2-889 2-812 2-739 2-669 2-&02 2-538 19 3-814 3-688 3570 3-459 3-354 3-255 3- 161 3-072 2-987 2-906 2-829 2-755 2-685 2-618 2-553 20 3-837 3-7U 3-593 3-481 3-375 3-275 3-180 3-091 3-005 2924 2-846 2-772 2-702 2-634 2-569 21° 3-862 3-736 3-6i6 3-504 3397 3-297 3-201 3-111 3-025 2-943 2-865 2-790 2-719 2-651 2-586 S £3 22 3-889 3-761 3-641 3-528 3-421 3-319 3-223 3-132 3046 2963 2-885 2-810 2-738 2-669 2-604 «s^ 23 3-917 3-789 3-667 3-553 3-445 3-343 3-247 3-155 3-068 2-985 2-906 2-830 2-758 2-689 2623 e rt° 24 3-947 3-817 3-695 3-580 3-472 3-369 3-272 3-179 3-091 3-007 2 928 2-852 2-779 2709 2-643 5 &SH 25 3-979 3-848 3725 3-609 3-499 3-396 3-298 3-204 3-116 3-032 2-951 2-874 2-801 2-731 2-664 liflca of D he D 26° 4-012 3-880 3756 3-639 3529 3-424 3-325 3-231 3-142 3-057 2-976 2-898 2-825 2-754 2-686 27 4-047 3-914 3789 3-671 3-560 3-454 3-354 3-259 3-169 3-084 3-002 2-924 2-849 2-778 2710 1 sm-M . 28 4-084 3-950 3-823 3-704 3-592 3-486 3-385 3-289 3-198 3-112 3-029 2-950 2-875 2-803 2734 'ious sii the La lem IX. 29 4-123 3-987 31^2 3-740 3-626 3-519 3-417 3-321 3-229 3-141 3-058 2-979 2-903 ^1-52 2-760 30 4-164 4-027 3-898 3-777 3-662 3-554 3-451 3-353 3-261 3-173 3-088 3-008 2-931 2-858 2-788 31° 4-207 4-069 3-938 3-8i6 3-700 3-591 3-487 3-388 3-294 3-205 3-120 3-039 2-962 2-888 2-817 S>'g 32 4-252 4*112 3-981 3-857 3-740 3-629 3-524 3-425 3-330 3-240 3-154 3-072 2-994 2-919 2-847 >^° 33 4-300 4-158 4-025 3-900 3-782 3-670 3-564 3-463 3-367 3276 3-189 3-106 3-027 2-951 2-879 ? s*^ 34 4-349 4207 4-072 3-945 3-826 3-712 3-605 3-503 3-406 3-314 3226 3-142 3-062 2-985 2 912 ^3- 35 4-402 4-257 4-121 3-993 3-872 3757 3-649 3-545 3-447 3-354 3-265 3-180 3-099 3022 2-947 ^ o 36° 4-457 4-311 4-173 4-043 3-920 3-804 3-694 3-590 3-491 3-396 3-306 3-220 3-138 3-059 2-984 .a Oc a 4-51S 4-367 4-227 4-096 3-971 3-854 3-742 3-636 3-536 3-440 3 "349 3-262 3-179 3-099 3023 38 4-576 4-426 4-284 4 151 4-025 3-906 3-793 3-685 3-584 3-487 3-394 3-306 3-222 3-141 3-064 39 4-640 4-487 4-344 4-209 4081 3-960 3-846 3737 3-634 3-535 3-442 3-352 3-267 3-185 3-107 40 4-707 4-552 4-407 4-270 4-140 4-018 3-901 3-791 3-686 3-587 3491 3-401 3-314 3-231 3-152 5ll _ so 41° 4-778 4-621 4'473 4-334 4-202 4-078 3-960 3-848 3-742 3-640 3-544 3-452 3-364 3-280 3-199 42 4-852 4-693 4-543 4-401 4-268 4-141 4-022 3-908 3-800 3-697 3-599 3-505 3-416 3-331 3-249 43 4-930 H^l 4-616 4-472 4-337 4-208 4-087 3-971 3-861 3757 3-657 3-562 3-471 3-384 3-301 44 5-013 4-848 4-693 4-547 4-409 4-278 4-155 4-037 3-926 3-819 3718 3-622 3-529 3-441 3-356 £ 03 45 S-099 4-932 4774 4-626 4-485 4-353 4-227 4-107 3-994 3-886 3-782 3-684 3-590 3-500 3-414 46° S-191 5-020 4-860 4-709 4-566 4-431 4-302 4-181 4-065 3-955 3-850 3750 3-655 3-563 3-475 42 5-287 5-114 4950 4-796 4-650 4-513 4-382 4-258 4-141 4-029 3-922 3-820 3-722 3-629 3-540 The the 'obl( 48 5-389 5-212 5-045 4-888 4-740 4-600 4-467 4-340 4-220 4-106 3-997 3-893 3-794 3-699 3-608 49 5-496 S-316 5-146 4-986 4-834 4'^9i 4-556 4-427 4-304 4-188 4-077 3-971 3-870 3-773 3-680 ^ ^"^ SO 5-610 S-425 5-252 5-089 4-934 4-788 4-650 4-518 4 '393 4-274 4-161 4-053 3 949 3-851 3756 51° 5-730 fif 5-364 5-197 5-040 4-890 4-749 4-615 4-487 4-366 4250 4-140 4034 3-933 3-836 SLc 52 5-857 5-665 5-483 5-313 5-152 4-999 4-854 4717 4:587 4-463 4-344 4-231 4-123 4-020 3-921 0) n S3 5 -992 5795 5-610 5 -435 5-270 5-114 4-966 4-826 4-692 4-565 4-444 4-329 4-218 4-113 4-012 u^ 54 ^:'i^ Pl^ 5-743 S-565 5-396 5-236 5-085 4-941 4-804 4-674 4-550 4432 4-319 4-211 4-107 ^0 ®C3 55 6-287 6-080 5-886 5 -703 5-530 5-366 5-2II 5-063 4-923 4-790 4-663 4-542 4-426 4-315 4-209 ^1 S6° 6-448 6-237 6-037 S-849 5-672 5 504 5-345 5-194 5-050 4-913 4-783 4-659 4-540 4-426 4-317 a*3 57 6-621 6-403 6-198 6-006 5-823 5151 5-487 5-332 5-185 5-045 4-911 4-783 4-661 4-544 4-433 S-3 58 6-805 6-581 6-371 6-172 5-985 5 -808 5640 S-480 5-329 5-185 5-047 4-916 4-791 4-671 Ilem ;he I: 12 7-001 6-771 6-SSS 6-351 6-158 5-976 5 -803 5-639 5-483 5*335 5-193 5-058 4-929 4-806 4-687 7-212 6-975 6-752 6-542 6-343 6-155 5-977 5-808 5-648 5-495 5-349 5-210 5-077 4-950 4-828 2^ 61° 62 6S 7-438 7-193 6-963 f'f 6-542 6-348 6-16S 5-990 5-825 5-667 5-517 5 -373 5-236 S-ioS 4-980 £0 7-681 7-428 7-191 6-967 ^■^^f 6-556 6-366 6-186 6 -015 5-852 5-697 5-549 5-407 5-272 5-142 a 7-943 7-682 7-436 7-205 6986 6-779 6-583 6-397 6 -220 6-052 5-891 5738 5-592 5-452 5-318 Hi 8-226 7-955 7-701 7-461 7-235 7-021 6-818 6-625 6-442 6-267 6-I0I 5-943 5-791 5-646 5-507 8-532 8-252 7-988 7-739 7-505 7-282 7-072 6-872 6-682 6-501 6-329 6-164 6-007 5-857 5713- To name Azimuth I ^° North latitude put N for a - • Error,' and S for a + ' Error.' I In South latitude put S for a - 'Error,' and N for a + 'Error.' Depending vpon the Latitude of the observer and the Azimuth of the object observed, the numbers m the borly qf this Table shew the error in the Longitude produced by an error of 1' in the Latitude worked with. 2 hey represent the sum or difference of the A and B valuee. 52 The Head-line has various slgnifleations, aeeording to the Problem in use. In Problem III. it represents the True Azimuth. In Problem IV. the Initial Course. In Problem V. the Diff. of Long., also the True Distance. In Problem VII. the Lat. of Departure, also Lat. of Vertex. In Problem IX. the Lat. of Departure or of Destination, also Limiting Parallel. In Problems X. and XI. the Hour-Angle or its suppiemen;. \ I Si o£ ay's ^ > 2 0*" O I.J Cj Ok ■" O .S "^"^ "3 a . u . S 2 JS O t3 o o , «4 a_] a .-s iaO+3 A A^ H *3p -•-'Ou g" £S &§ go ^^ a'^ Lat. OF Obser- ver. TRUE AZIMUTH. 23° h m (I 32) 23r h m (I 34) 24° h m (I 36) 24|° h m (I 38) 25° h m (I 40) 25r h m (I 42) 26° h m (I 44) 23r h m (I 46) 27° h m (I 48) 27r h m (I so) 28° h m (I 52) 28r h m (I 54) 29° h m (1 56) <2Q\' h m (I 58) 30° h m (2 O) a 0° I 2 I 9 ID 11° 12 13 14 !S 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 51° 52 53 54 55 56° 57 58 60 61° 62 6s 2-356 2-356 2-357 2-359 2-362 2-365 2-369 2-374 2-379 2-385 2-392 2-400 2-408 2-418 2-428 2-439 2-451 2-463 2-477 2-492 2-507 2-523 2-541 2-559 2-579 2-599 2-621 2-6<14. 2668 2694 2-720 2-748 2-778 2 809 2 842 2-876 2-912 2950 2-990 3031 3-075 3-122 3-170 3-221 3-275 3-332 3 '391 3-454 3-521 3-591 3-665 3-743 3-827 3-915 4-008 4-107 4-213 4-326 4-446 4-574 4-712 4-859 5-018 5-189 S-374 5-574 2-300 2-300 2-301 2-303 2-305 2-309 2-313 2-317 2-322 2-329 2-335 2-343 2-351 2-360 2-370 2-381 2-393 2-405 2-418 2-432 2-447 2-463 2-480 2-498 2-517 2-538 2-559 2-581 2-605 2-630 2-656 2-683 2-712 2-742 2-774 2 -808 2-843 2 -880 2-919 2-959 3-002 3-047 3-095 3-145 3-197 3-252 3-3" 3-372 3-437 3-506 3-578 3-654 3-736 3-822 3-913 4-010 4-113 4-223 4-340 4*465 4-600 4-744 4-899 5-066 5-246 5-442 2-246 2-246 2-247 2-249 2-252 2-255 2-258 2-263 2-268 2-274 2-281 2-288 2-296 2-305 2-315 2-325 2-337 2-349 2-362 2-375 2-390 2-406 2-422 2-44T 2-459 2-478 2-499 2-521 2-544 2-568 2594 2-620 2-648 2-678 2-709 2-742 2-776 2-812 2-850 2-890 2932 2-976 3-022 3-071 3-122 3-176 3-233 3-293 3-357 3-424 3-494 3-569 3-648 3-732 3-821 3-916 4-017 4-124 4-238 4-361 4-492 4-633 4-784 4-947 5 -'24 5-3IS 2-194 2-195 2-196 2-197 2-200 2-203 2-206 2-2II 2216 2-222 2-228 2-235 2-243 2-252 2-261 2-272 2-283 2-295 2-307 2-321 2-335 2-350 2-367 2-384 2-402 2-421 2-441 2-463 2-485 2-509 2-534 2-560 2-587 2-6i6 2-647 2-679 2-712 2-748 2-785 2-S24 2-864 2-907 2-953 3-000 3-050 3-103 3-159 3-217 3-279 3-345 3-414 3-487 3-564 3-646 3-733 3-826 3-924 4-029 4-141 4-260 4-389 4-526 4-674 4-833 5-006 5-192 2-I4S 2-145 2-146 2-147 2-150 2-153 2-156 2-161 2-166 2-171 2-178 2-185 2-192 2 -201 2-210 2 -220 2-231 2-242 2-255 2-268 2 282 2-297 2-313 2-330 2-347 2-366 2-386 2-407 2-429 2-452 2-476 2-502 2-529 2-557 2-587 2-618 2-651 2-685 2-721 2-759 2-799 2-841 2-886 2-932 2-981 3-033 3-087 3-144 3-205 3-269 3-336 3-408 3-483 3-563 3-648 3-739 3-835 3-937 4-047 4-164 4-289 4-423 4-568 4724 4-892 5-074 2-097 2-097 2-098 2-099 2 102 2-105 2-108 2-112 2-I17 2-123 2-129 2-136 2-143 2 152 2-161 2-171 2-181 2-192 2-204 2-217 2-231 2-246 2-261 2-278 2-295 2-313 2-333 2-353 2-374 2-397 2-421 2-446 2-472 2-500 2-529 2-559 2-591 2-625 2 661 2-698 2-737 2-778 2-821 2-867 2-915 2-965 3-018 3-074 3-133 3-196 3-262 3-331 3-405 3-484 3-567 3-655 3-749 3-849 3-956 4-071 4-193 4-324 4-466 4-618 4-783 4-961 2-050 2-051 2-052 2-053 2-055 2-058 2-062 2-066 2-070 2-076 2-082 2-089 2-096 2-104 2-113 2-123 2-133 2-144 2-156 2168 2-182 2-196 2-211 2-227 2-244 2-262 2-281 2-301 2-322 2-344 2-367 2-392 2-418 2-445 2-473 2-503 2-534 2-567 2-602 2-638 2-676 2-717 2-759 2-803 2-850 2-900 2-952 3-006 3-064 3-125 3-190 3-258 3-330 3-407 3-488 3-575 3-667 3-765 3-869 3-981 4-101 4-229 4-367 4-516 4-677 4-851 2-006 2-006 2-007 2-008 2-011 2-013 2-017 2-021 2-025 2-031 2-037 2-043 2-050 2-058 2-067 2-076 2-087 2-097 2-109 2-121 2-134 2-148 2-163 2-179 2-196 2-213 2-232 2-251 2-272 2-293 2-316 2-340 2-365 2-392 2-419 2-448 2-479 2-511 2-545 2-581 2-618 2-658 2-699 2-742 2-788 2-836 2-887 2-941 2-997 3-057 3-120 3-187 3-258 3-333 3-412 3-497 3-587 3-683 3-78S 3-894 4-011 4-137 4-272 4-418 4-575 4-746 1-963 1-963 1-964 1-965 1-967 1-970 1-973 1-977 1-982 1-987 1-993 1-999 2-006 2-014 2-023 2-032 2-042 2-052 2-064 2-076 2-089 2-102 2-117 2-132 2-148 2-166 2-184 2-203 2-223 2-244 2-266 2-290 2-314 2-340 2-367 2-396 2-426 2-457 2-491 2-525 2-562 2 -600 2-641 2-684 2-728 2-776 2-825 2-878 2-933 2-992 3-053 3-119 3-188 3-261 3-339 3-422 3-510 3-604 3-704 3-811 3-925 4-048 4-180 4-323 4-477 4-644 I -921 1-921 1-922 1-924 1-926 1-928 1-932 I -93s 1-940 1-945 I -95 1 1-957 1-964 1-972 1-980 1-989 1-998 2-009 2-020 2-032 2-044 2-058 2-072 2-087 2-103 2-120 2-137 2-156 2-176 2-196 2-218 2-241 2-265 2-291 2-317 2-345 2-374 2-405 2-438 2-472 2-508 2-545 2-585 2-627 2-670 2-717 2-765 2-817 2-871 2-928 2-989 3-052 3-120 3-192 3-268 3-349 3-435 3-527 3-625 3-730 3-842 3-962 4-092 4-231 4-382 4-545 1-881 1-881 1-882 1-883 1-885 1-888 1-891 1-895 1-899 1-904 1-910 1-916 I 923 1-930 1-938 1-947 1-957 1-967 1-978 1-989 2-001 2-015 2-02S 2-043 2-059 2-075 2-092 2-UI 2-130 2-150 2-172 2-194 2-218 2-243 2-269 2-296 2-325 2-355 2-387 2-420 2-455 2-492 2-531 2-572 2-615 2-660 2-707 2-758 2-811 2-867 2-926 2-989 3-055 3-125 3-200 3-279 3-363 3-453 3-549 3-652 3-761 3-879 4-006 4'i43 4-290 4-450 1-842 1-842 1-843 1-844 1-846 1-849 1-852 1-856 i-86o 1-865 1-870 1-876 1-883 1-890 I 898 1-907 1-916 1-926 1-937 1 -948 1-960 1-973 1-986 2-001 2-016 2-032 2-049 2-067 2-086 2-106 2-127 2-149 2-172 2-196 2-222 2-248 2-277 2-306 2-337 2-370 2-404 2-440 2-478 2-518 2-560 2-605 2-651 2-701 2-752 2-807 2-865 2-927 2-992 3 '060 3-133 3-211 3 "294 3-382 3-476 3-576 3-684 3-799 3-923 4-057 4-201 4-358 1-804 1-804 1-805 1-807 1-808 1-811 I -814 1-818 1-822 1-827 1832 1-838 1-844 1-852 1-859 1-868 1-877 1-886 1-897 1-908 1-920 1-932 1-946 1-960 1-975 1-991 2-007 2-025 2-043 2-063 2-083 2-105 2-127 2-151 2-176 2-202 2-230 2-259 2-289 2-321 2-355 2-390 2-428 2467 2-508 2-551 2-597 2-645 2-696 2-750 2-807 2-867 2-930 2-998 3-069 3-145 3-226 3-312 3-404 3-503 3608 3-721 3-843 3-974 4-115 4-269 1-767 1-768 1-769 1-770 1-772 1-774 1-777 1-781 I -78s 1-790 1-795 1-801 1-807 1-814 1-822 1-830 1-839 1-848 1-858 1-869 1-881 1-893 1-906 1-920 1-935 1-950 1-967 1-984 2-002 2-021 2-041 2-062 2-084 2-107 2-132 2-158 2-185 2-213 2-243 2-274 2-307 2-342 2-378 2-417 2-457 2-500 2-544 2-592 2-641 2-694 2-750 2-809 2-871 2-937 3-007 3-082 3-161 3-245 3-335 3-432 3-535 3-646 3-765 3-893 4-032 4-182 ■732 -732 -733 -734 -736 ■739 ■742 -745 -749 -754 -759 -764 -771 -778 -785 -793 -802 -811 -821 -832 •843 -855 -868 -882 -896 -911 -927 -944 -962 -980 2-000 2-021 2-042 2-065 2-089 2-114 2-141 2-169 2-198 2-229 2-261 2-295 2-331 2-368 2-408 2-449 2-493 2-540 2-589 2-640 2-695 2-752 2-813 2-878 2-947 3-020 3-097 3-180 3-269 3-363 3-464 3-573 3689 3-815 3-951 4 098 I In North latitude put N for a - 'Error,' and S for a + 'Error.' To name Azimuth j j^ g^^^j^ latitude put S for a - 'Error,' and N f or a + 'Error. 53 The Head-line has various significations, aeeording to the Problem In use. In Problem III, it represents the True Azimuth. In Problem IV. the Initial Course. In Problem V. the Diff. of Long., also the True Distance. In Problem VII. the Lat. of Departure, also Lat. of Vertex. In Problem IX. the Lat. of Departure or of Destination, also Limiting Parallel. In Problems X. and XI. the Hour-Angle or its supplement. 5 u Lat. OF Obser- TRUE AZIMUTH. 30J- 31° 2,\\ 32° 32r 33° 33i° 34° 341° 35° 35^ 33° 36r 37° 37r So ver. h m h m h m h m h m h m h m h in h m b m h m h m h m h m h m (2 2) (24) (2 6) (28) (2 10) (2 12) (2 14) (2 16) (2 18) (2 20) (2 22) (2 24) (2 26) (2 28) (2 30) 0° 1-698 1-664 1-632 1-600 1-570 1-540 1-511 1-483 1-455 i'-428 1-402 1-376 1-351 1-327 1-303 I 1-698 1-665 1-632 1-601 1-570 1-540 1-511 1-483 1-455 1-428 1-402 1-377 1-352 1-327 1-303 2 1-699 1-665 1-633 1-601 I -57 1 I -541 1-512 1-483 1-456 1-429 1-403 1-377 1-352 1-328 1-304 .■tt 3 1-7CX3 1-667 1-634 1-603 1-572 1-542 1-513 1-485 1-457 1-430 1-404 1-378 1-353 1-329 1-305 a) o 4 1-702 1-668 1-636 1-604 1-574 1-544 1-515 1-486 1-459 1-432 1-405 1-380 1-355 1-330 1*306 V *? 5 1-704 1-671 1-638 1-606 1-576 1-546 I -517 1-488 1-461 1-434 1-407 1-382 1-357 1-332 1*308 . p,a> 6° 1-707 1-673 1-641 1-609 1-578 1-548 I"SI9 1-491 1-463 1-436 1-410 1-384 1-359 1-334 1*310 £ SS 7 I -710 1-677 1-644 I 612 1-581 1-551 1-522 1-494 1-466 1-439 1-412 1-387 1-362 1-337 1*313 So*t 8 1-714 I -681 1-648 1-616 1-585 I -555 1-526 1-497 1-469 1-442 1-416 1-390 "■'^M 1-340 1-316 I in t. of d XI 9 1-719 1-685 1-652 1620 1589 1-559 1-530 1-501 1-473 1-446 1-419 1-394 1-368 1-344 1-319 10 1-724 1-690 1-657 1-625 I -594 1-564 1-534 1-505 1-477 1-450 1-424 1-398 1-372 1-348 1*323 11° 1-729 1-695 1-662 1-630 1-599 1-569 1-539 1-510 1-482 1-455 1-428 1-402 1-377 1-352 1*328 12 1736 1-701 1-668 1-636 1-605 1-574 1-545 1-516 1-488 1-460 1-433 1-407 1-382 1-357 1-332 13 1-742 1-708 1-675 1-642 1-611 1-5S0 1-551 1-522 I -493 1-466 1-439 1-413 1-387 1-362 1*338 lie P V. 1 lems 14 1-750 1715 1-682 1-649 i-6i8 1-587 1-557 1-528 1-500 1-472 1-445 1-419 1-393 1-368 1*343 15 1758 1-723 1-689 1-657 1-625 I -594 1-564 1-535 1-506 1-479 I -451 1-425 1-399 1-374 1-349 *3 B-g 16° 1-766 1-731 1-698 1-665 1-633 1 -602 1-572 1-542 1-514 1-486 1-458 1-432 1-406 1-381 1-356 Ss£ 17 1775 1-740 1-706 1-673 1-641 I -610 1-580 1-550 1-521 1-493 1-466 1-439 I -413 1-388 1*363 bn S a 18 1785 1-750 1-716 1-683 1-650 1-619 1-589 1-559 ,1-530 1-502 1-474 1-447 1-421 1-395 1-370 C Oc"-! 19 1795 1-760 1-726 1-693 1-660 1-629 1-598 1-568 1-539 1-510 1-483 1-456 1-429 1-404 1-378 |5ii 20 1-807 1-771 1-737 1-703 1-670 I 639 1-608 1578 1-548 1-520 1-492 1-465 1438 1-412 1-387 g s 21° I -818 1-783 1-748 1-714 r68i 1-649 I -618 1-588 1-559 1-530 1-502 1-474 1-448 1-421 1*396 A £-< 22 I -83 1 I -79s 1-760 1-726 1-693 1-661 1-629 1-599 1-569 1-540 1-512 1-484 1-458 1-431 1-406 »-2^ 23 1-844 i-8o8 1-773 1-739 1-705 1 -673 1-641 1 61 1 1-581 1-551 1-523 1-495 1-468 1-442 1-416 CO (L, o 24 1-858 1-822 1-786 1-752 1-718 1-686 1-654 1-623 1-593 1-563 1-535 1-507 1-479 1-453- 1-427 5 a.*a 25 1-873 1-836 1-801 1-766 1-732 1-699 1-667 1-636 1-605 1-576 I -547 1-519 1-491 1-464 1-438 liflca of D ;he £ 26° i-88g 1-852 1-816 I 781 1-746 1-713 1-681 1-650 1-619 1-589 1-560 1-531 1-504 1-476 1-450 27 1-905 1-868 1-831 1-796 1-762 1-728 1-696 1-664 1-633 1-603 1-573 1-545 1-517 1-489 1-463 28 1-923 1885 1-848 1-812 1778 1-744 1-711 1-679 1-648 1-617 1-588 1-559 1-531 J -503 1-476 •a.lx 29 1-941 1-903 1-866 1-830 1-795 1-761 '■727 1695 1-664 1-633 1603 1-574 1-545 1-517 1-490 ■ious the 1 tlem 1 30 1960 1-922 1-884 1-848 1-813 1-778 1-745 1-712 1-680 1-649 1-619 1-589 1-560 1-532 1-505 31° 1-981 1-942 I 904 T-867 1-831 1-796 1-763 1-730 1-697 1-666 r-636 1-606 1-577 1-548 1-520 S>o 32 2-002 1-962 1-924 1-887 1-851 1-816 1782 1-748 1-716 1-684 1-653 1-623 1-594 1-565 1-537 > ►- IL, £6 = 33 2-024 1-984 1-946 1-908 1-872 1-836 1-801 1-768 1-735 1-703 1-672 1-641 1-611 1-582 1-554 34 2-048 2-007 1-968 1-930 1-893 1-857 1822 1-788 1755 I 723 I -69 1 1-660 1-630 1-601 1-572 Is- 35 2-072 2-032 1-992 1-954 1-916 1-880 1-844 I -810 1-776 '743 1-711 1680 1-650 1-620 I -591 A^ 36° 2-098 2-057 2-017 1-978 1940 1-903 '-867 1-833 1-798 1-765 I 733 1 701 1-670 1-640 1-611 OD O 37 2-126 2 084 2-043 2-004 1-965 1-928 1-892 1-856 1-822 1-788 1755 1-723 1-692 1-662 1-632 l^cj 3" 2-154 2-112 2-071 2-031 1-992 1-954 1-917 I -881 1-846 1-812 1-779 ■747 1715 1-684 1-654 39 2-184 2-142 2-100 2-059 2 -020 1-981 1-944 1-908 1-872 1-838 1-804 1-771 1-739 1-708 1-677 40 2-216 2-173 2-130 2-089 2-049 2-010 1-972 I -93s 1-899 1-864 1-830 1-797 1-764 1-732 1-701 41° 2-249 2-205 2-162 2-120 2 -080 2-040 2-002 1-964 1-928 1-892 1-858 1-824 1-791 1-758 1*727 03'-' 42 2-284 2-240 2-196 ^■'^§ 2-112 2-072 2-033 1-995 1-958 1-922 1-887 1-852 1-819 1-786 1754 43 2321 2-276 2-231 2-i88 2-146 2-105 2-066 2-027 1-989 1-953 1-917 1882 1-848 1-815 1*782 44 2-360 2-314 2-269 2-225 2-182 2-141 2-I0O 2 06 1 2-023 1985 1-949 1-913 1-879 1-845 1-812 &,*s 45 2-401 2-354 2-308 2-263 2-220 2-178 2-137 2-097 2-058 2-020 1-983 1-946 I -91 1 1-877 1-843 _ as 46° 2-444 2-396 2-349 2-304 2-260 2-217 2-175 2-134 2-095 2-056 2-018 1-981 I -945 1-910 1*876 % 2-489 2-440 2-393 2-347 2-302 2-258 2-215 2-174 2-133 2-094 2-056 2-018 1-982 1-946 I -91 1 The the >obli 48 ^'■ss^ 2-487 2-439 2-392 2-346 2-301 2-258 2-216 2-174 2-134 2-095 2-057 .2-020 1-983 1-948 49 2-588 2-537 2-487 2-439 2-393 2-347 2-303 2-260 2-2l8 2-177 2-137 2-098 2-060 2-023 1-986 S« SO 2-641 2-589 2-539 2-490 2-442 2-396 2-350 2-306 2-264 2-222 2-181 2-141 2-102 2-065 2-027 §5 Si° 2-698 2-645 2-593 2-543 2-494 2-447 2-401 2-356 2-312 2-269 2-228 2-187 2-147 2-109 2-071 ^ 52 2-757' 2-703 2651 2-599 2-550 2-501 2-454 2-408 2-363 2-320 2-277 2-236 2-195 2-155 2-117 &S 53 2-821 2-765 2-712 2-659 2-608 2-559 2-510 2-463 2-418 2-373 2-330 2-287 2-246 2-205 2-165 "1 54 2-888 2-831 2-776 2-723 2-671 2-620 2-570 2-522 2-475 2-430 2-385 2-342 2-299 2-258 2-217 ^1 55 2-960 2-902 2-845 2-790 2-737 2-685 2-634 2-585 z-537 2-490 2-444 2-400 2-356 2-314 2-272 5^ 56° 3-036 2-976 2-918 2-862 2-807 2-754 2-702 2-651 2-602 2-554 2-507 2-461 2-417 2-373 2-331 hhS % 3-117 3-056 2-996 2-938 2-882 2-827 2-774 2-722 2-672 2-622 2-574 2-527 2-481 2-437 2-393 3-204 3'i4i 3-079 3-020 2-962 2-906 2-851 2-798 2-746 2-695 2-646 2-597 2-550 2-504 2-459 s"^ ^ 3-296 3-231 3-168 3-107 3-048 2-990 2-933 2-879 2-825 2-773 2-722 2-672 2-624 "2-577 2-530 1^ 3-395 3-329 3-264 3-201 3-139 3-080 3-022 2-965 2-910 2-856 2-804 2753 2-703 2-654 2-606 2fe 61° 62 f.|?l 3-433 3-366 3-301 3-238 3-176 3-116 3-058 3-001 2-946 2-892 2-839 2-788 2737 2-688 B,® 3-616 3-545 3-476 3-409 3-344 3-280 3-218 3-158 3-099 3-042 2-986 2-932 2*879 2-827 2776 C 3-739 3-666 3-594 3-525 3-458 3-392 3-328 3-266 3-205 3-146 3-088 3-032 2-977 2-923 2-871 HH 3-873 3-797 3-723 3-651 3-581 3-513 3-446 3-382 3-319 3-258 3-198 3-140 3-083 3-027 2-973 4-017 3-938 ^ 3-861 3-787 3714 3-644 3-575 3-508 3-443 3-379 3-317 3-257 3-198 3-140 3-084 To name Azimuth In North latitude put N for a - 'Error,' and S f or a -<- 'Error.' In South latitude put S for a - 'Error,' and N for a + 'Error.' Depending upon the Latitude of the observer and the Azimuth of the object observed, the numbers in the body of this Table shew the error im, the Longitude produced by an error of 1' iai the Latitude worked ivith. They represent the sum or difference of the A (tnd B values. 54 The Head-line has various slgrnlfleatlons, aeeopdlng to the Problem In use. " *u ^®'" y?- ** represents the True Azimuth. In Problem IV. the Initial Course. In Problem V. the Diff. of Long., also the True Distance. In Problem VIL the Lat. of Departure, also Lat. of Vertex. In Problem IX. the Lat. of Departure or of Destination, also Limiting Parallel In Problems X. and XI. the Hour-Angle or its supplement. \ Lat. OF Obser- TRUE AZIMUTH 38° 38^ 39° 39r 40° 40|° 41° 41 -r 42° 42i° 43- 431° 44° 441° 45° tfc ver. h m h in h m h m h m h m h m h m h m h ra h m h m h m h in h m 21 1: (2 32) (234) (236) (238) (2 40) (2 42) (2 44) (2 46) (248) (2 50) (2 52) (254) (2 56) (258) (3 0) 0° 1-280 1-257 1-235 I -213 1-192 1-171 1-150 1-130 1-111 1-091 1072 1-054 1-036 1-018 1-000 ss I 1-280 1-257 1-235 I -213 1-192 1-171 1-151 1-130 l-lll 1-091 1-073 1-054 1-036 1-018 i-ooo ■s-g 2 I -281 1-258 1-236 1-214 I -192 1-172 1-151 1-131 l-iii 1-092 1-073 1-054 1-036 1-018 1-001 .o 3 1-282 1-259 1-237 1-215 1-193 1-172 1-152 1-132 1-112 1-093 1-074 1-055 1-037 I -019 1-001 §^ 4 1-283 1-260 1-238 I-2l6 I -195 1-174 1-153 I -133 1-113 1-094 1-075 1-056 1-038 1-020 1-002 n S 1-285 1-262 1-240 I -218 1-196 1-175 1-155 I -13s 1-115 1-095 1-076 1-058 1-039 1-021 1-004 cSffi 6° 1-287 I -7,64 1-242 I -220 I -198 1-177 1-157 1-137 1-117 1-097 1-078 1-060 1-041 1-023 1-006 s2a 7 1-290 1-267 1-244 1-222 I -201 1-180 1-159 1-139 1-119 1-100 1-080 1-062 1-043 1-025 1-008 8 1-293 1-270 1-247 I 225 1-203 1-182 1-162 1-141 1-122 1-102 1-083 1-064 1-046 1-028 1-010 g^i^ 9 1-296 1-273 1-250 1-228 1-207 1-185 1-165 1-144 1-124 1-105 I -086 1-067 1-048 1-030 1-012 •stil 10 1-300 1-277 1-254 1-232 I -210 1-189 1-168 1-148 1-128 1-108 1-089 1-070 1-052 I '033 1-015 « j5« 11° 1-304 1-281 1-258 1-236 1-214 1-193 1-172 1-151 1-131 I-II2 1-092 1-074 1-055 1-037 1-019 12 1-309 1-285 1-262 1-240 I -218 1-197 1-176 1-156 I -135 1-116 1-096 1-077 1-059 1-040 1-022 3«« 13 I -314 1-290 1-267 1-245 1-223 1-202 i-i8i I -160 1-140 1-120 l-ioi 1-081 1-063 1-044 1-026 2>a M I -319 1-296 1-273 1-250 1-228 1-207 1-186 1-I6S I -145 1-125 1-105 1-086 1-067 1-049 1-031 ^al IS 1-325 1-302 1-278 1-256 1-234 1-212 1-191 1-170 1-150 1-130 l-IIO 1-091 1-072 1-054 1-035 lis i6° 1-332 1-308 1-285 1-262 1-240 1-218 1-197 1-176 1-155 I -135 1-116 1-096 1-077 1-059 1-040 ♦"o-^ ^l 1-338 I -315 1-291 1-269 1-246 1-224 1-203 I -182 1-161 1-141 1-121 1-102 1-083 1-064 1-046 2a:£ i8 1-346 1-322 1-298 1-276 1-253 1-231 1-210 I -188 1-168 1-147 1-128 1-108 1-089 1-070 1-051 6eS . 19 I -354 1-330 1-306 1-283 1-260 1-238 1-217 I -195 I -175 1-154 I -134 1-114 1-095 1-076 1-058 20 1-362 1-338 1-314 I -29 1 1-268 1-246 1-224 1-203 1-182 1-161 1-141 1-I2I 1-102 1-083 1-064 %t% 21° I -37 1 1-347 1-323 1-299 1-277 1-254 1-232 1-2II 1-190 1-169 1-149 I -129 1-109 1-090 1-071 Ib^ 22 1-380 1-356 1-332 1-308 1-285 1-263 1-241 I -219 1-198 1-177 I-I57 I -137 1-117 1-098 1-079 vi £jo 23 1-390 1-366 1-342 1-318 1-295 1-272 1-250 1-228 1-207 1-186 I -165 I -145 1-125 1-105 1-086 els 24 I -401 1-376 1-352 1-328 i-3°S 1-282 1-259 1-237 l-2l6 1-195 1-174 1-154 I -134 1-114 1-095 25 1-412 1-387 1-363 1-339 1-315 1-292 1-269 1-247 1-225 1-204 1-183 1-163 I -143 1-123 1-103 eatic . of the ] 26° 1-424 1-399 1-374 1-350 1-326 1-303 1-280 1-258 1-236 1-214 1-193 1-172 1-152 1-132 1-113 27 1-437 1-411 1-386 I -361 1-338 1-314 1-291 1-269 1-246 1-225 1-204 1-183 1-162 1-142 1-122 Sts,j 28 1-450 1-424 1-399 1-374 1-350 1-326 1-303 1-280 1-258 1-236 1-215 1-193 1-173 1-153 I-I33 29 1-463 1-437 I -412 1-387 1-363 1*339 i;3is 1-292 1-270 1-248 1-226 1-205 1-184 1-163 I -143 30 1-478 1-452 1-426 I -401 1-376 1-352 1-305 1-282 1-260 1-238 1-217 1-196 I-17S I 155 3x° 1-493 1-467 1-441 I -415 1-390 1-366 1-342 1-319 1-296 1-273 1-251 1-229 1-208 1-187 1-167 S^P 32 1-509 1-482 1-456 1-430 1-405 1-381 1-356 1-333 1-310 1-287 1-265 1-243 1-221 1-200 1-179 have var Problem Ig. In Pr 33 1-526 1-499 1-472 1-446 1-421 1-396 1-372 1-348 1-324 1-301 1-279 1-256 1-235 1-213 1-192 34 1-544 1-516 1-490 1-463 1-438 1412 1-388 1-363 1-340 1-316 1-294 I -271 1-249 1-227 1-206 3S 1-563 1-53S 1-508 I -481 1-455 1-429 1-404 1-380 1-356 1-332 1-309 1-286 1-264 1-242 1-221 36° 1-582 I -554 1-526 1-499 1-473 1-447 1-422 1-397 1-373 1-34? 1-326 1-303 1-280 1-258 1-236 b" ."ft 37 1-603 1-574 1-546 1-519 1-492 1-466 1-440 I -41 5 1-391 1-366 1-343 1-319 1-297 1-274 1-252 38 1-624 I -595 1-567 1-539 1-512 1-486 1-460 1-434 1-409 1-385 1-361 1-337 I -314 1-291 1-269 39 1-647 1-618 1-589 1-561 1-534 1-507 1-480 1-454 1429 1-404 1-380 1-356 1-333 1-309 1287 * si® 2 go Coo 40 1-671 I -64 1 l-6l2 1-584 1-556 1-528 1-502 1-475 1-450 1-425 1-400 1-376 1-352 1-328 1-305 4i* 1-696 1-666 1-636 1-607 1-579 1-551 1-524 1-498 1-472 1-446 1-421 1-396 1-372 1-348 1-325 42 1-722 1-692 1-662 1-632 1-604 1-576 1-548 1-521 1-494 1-468 1-443 1-418 1-393 1-369 1-346 43 1-750 I -719 1-689 1-659 1-630 I 601 1-573 1-545 I-5I9 1-492 1-466 1-441 I -416 1-391 1-367 t3 > ^ 44 1-779 1-748 I -717 1-686 1-657 1-628 1-599 I -571 1-544 1-517 1-491 1-465 1-440 1-415 1-390 s°S 45 I -810 1-778 1-746 I -716 1-685 1-656 1-627 1-598 I -571 1-543 1-517 1-490 1-464 1-439 1-414 (]> M\ (D 4fi° 1-843 I -810 1-778 1-746 1-716 1-686 1-656 1-627 1-599 1-571 1-544 1-517 1-491 1-465 1-440 S 1-877 1-843 I -811 1-779 1-747 1-717 1-687 1-657 1-628 1-600 1-572 1-545 1-518 1-492 1-466 1-913 1-879 1-846 1-813 1-781 1-750 1-719 1-689 1-660 1-631 1-603 1-575 1-548 1-521 1-494 »*"£ 49 1-951 1-916 1-882 1-849 1-817 1-785 I -753 1-723 1-693 1-663 1-635 1-606 1-578 I -55 1 1-524 gs£ SO 1-991 1-956 1-921 1-887 1-854 1-822 1-790 1-758 1-728 1-698 1-668 1-639 i'6ii 1-583 1-556 we 51° 2-034 1-998 1-962 1-928 1-894 1-860 1-828 1-796 1-765 1-734 1-704 1-674 1-645 1-617 1-589 Oi . S2 2-079 2-042 2 -006 1-970 1-936 1-902 1-869 '■f36 1-804 1-773 1-742 1-712 1-682 1-653 1-624 £S S3 2-127 2-089 2-052 2-016 1-980 1-946 1-911 1-878 '1^5 1-813 1-782 1-751 1-721 1-691 1-662 !lS 54 2-178 2-139 2-101 2-064 2-028 1-992 1-957 1-923 1-889 1-857 1-824 1-793 1-762 1-731 I -701 55 2-232 2-192 2-153 2-115 2-078 2-041 2 -006 1-971 1-936 1-903 1-870 1-837 1-805 1-774 1-743 S6° 2-289 2-248 2-208 2-169 2-131 2-094 2-057 2-021 1-986 1-952 1-918 1-8R1 1-852 1-820 1-788 57 2-350 2-308 2-267 2-227 2-188 2-150 2-112 2-075 2-039 2-004 1-969 1-935 1-901 1-868 1-836 a-s 58 2-415 2-372 2-330 2-289 2-249 2-209 2-171 2-133 2-096 2-059 2-024 1-989 1-954 1-920 1-887 ^ 2-485 2-441 2-398 2-355 2-314 2-273 2-234 2-195 2-156 2-119 2-082 2-046 2-011 1-976 1-942 35 2-560 2-514 2-470 2-426 2-384 2-342 2-301 2-261 2-221 2-183 2-145 2-108 2-071 2-035 2-000 1:: 61° 2640 2-593 2-547 2-502 2-458 2-415 2-373 2-331 2-291 2-251 2-212 2-174 2-136 2-099 2-063 OiS 62 2-726 2-678 2-630 2-584 2-538 2-494 2-450 2-408 2-366 2-325 2-284 2-245 2-206 2-168 2-130 H ^3 2-819 2-769 2-720 2-672 2-625 2-579 2-534 2-490 2-446 2-404 2-362 2-321 2-281 2-241 2-203 hH 64 2-920 2-868 2-817 2-767 2-719 2*671 2-624 2-578 2-533 2-489 2-446 2-404 2-362 2-321 2-281 65 3-029 2-975 2-922 2-870 2-820 2-770 2-722 2-675 2-628 2-582 2-537 2-493 2-450 2-408 2-366 To Name Azimuth I In North latitude put N for a - ' Error,' and S for a + ' Error,' ' In South latitude put S for a - ' Error,' and N for a + * Error.' Dtpmding vpon the Latitvde of the observer and the Atimuth of the object observed, the numbers in tha body of this Table shew the error in the Longitude produced by an error of 1' v^ the Latitude worked with. They represent the sum or difference of the f^ and B valves. 55 The Head-line has various signifieationsAaeeording to the Problem in use. In Problem III. it represents the True Azimuth. In Problem IV. the Initial Course. In Problem V. the Diff. of Long., also the True Distance. In Problem VII. the Lat. of Departure, also Lat. of Vertex. In Problem IX, the Lat. of Departure or of Destination, also Limiting Parallel. In Problems X. and XI. the Hour-Angle or its suppiemtm. 1 Lat. OF Obser- TRUE AZIMUTH. 45r 46° 46} 47° 47r 48° 481° 49° 491° 50° 5or 51° 5ir 52° 52J° tl ver. h m h m h m h m h m h m h m h m h m h m h m h m b m h m h m II (32) (3 4) (36) (3 8) (3 10) (3 12) (3 14) (3 16) (3 18) (320) (3 22) (324) (3 26) (328) (330) 0° ■983 '•966 '■949 '-933 -916 '-900 '•885 '-869 '•854 '•839 '-824 '•810 '795 '-78I 767 9S I •983 •966 -949 -933 -916 -901 -885 -869 •854 -839 -824 •810 •796 •781 •767 41 2 •983 •966 •950 •933 -917 •goi •885 •870 •855 •840 -82s -810 •796 -782 •768 •\ •984 •967 -950 -934 -918 -902 -886 -870 •855 •840 •82s •811 •797 -782 768 £* 4 5 •985 ■968 ■951 -935 -919 ■903 -887 •871 -856 -841 -826 •812 -797 -783 -769 sti ■986 -969 -9S3 -936 •920 -904 -888 -873 •857 -842 •827 •813 798 •784 -770 l« 6° •988 •971 -9S4 •938 •921 -905 •890 -874 •859 -844 -829 •814 -800 -786 •772 I •990 -973 •956 •940 •923 •907 •891 •876 -860 -845 '831 -816 -801 -787 -773 gP*' •992 •97S •958 -942 -925 -909 -893 -878 -862 •847 •832 -818 -803 -789 775 9 •995 •978 -961 -944 -928 -912 •896 -880 -865 -850 -835 -820 1°l 791 777 ID •998 •981 •964 -947 ■930 •914 -898 -883 -867 -852 •837 -822 •808 -793 -779 Et«g 11° I -001 •984 -967 •950 -933 -917 •901 -886 •870 -855 •840 •825 -810 •796 782 p^ m. 3 12 I "005 •987 •970 -953 -937 -921 -904 -889 -873 -858 -843 •828 -813 •799 •784 g^>< 13 1-009 •991 -974 -957 •940 -924 -908 -892 -877 -861 -846 •831 -816 •802 -78S the P] em V. t 'Oblems 14 1-013 •99S -978 -961 -944 -928 -912 -896 -880 -865 -850 -835 -820 -805 -791 15 I -017 I -000 •982 -965 -949 -932 •916 -900 -884 -869 -853 -838 •823 -809 -794 16° 1-022 1-005 -9S7 -970 •953 -937 ■920 -904 -888 ■873 •858 •842 •827 -813 ■798 4j ;QPL| 17 1-028 i-oio •992 -975 -958 -942 -925 •909 -893 -877 -862 -847 13? -817 -802 18 1-033 1-015 -998 -981 •963 -947 -930 -914 -898 •882 •867 -851 -836 -821 -807 19 1-039 I -02 1 1-004 -986 -969 -952 -936 •919 •903 -887 -872 -S56 •841 -826 -812 ? a . 20 1-046 1-028 i-oio -992 -975 •958 -942 -925 -909 -893 -877 •862 -846 -831 •817 g « 21° I-0S3 1034 I -016 •999 -982 -964 -948 •931 -915 -899 -883 -867 -852 -837 -822 22 i-o6o 1-042 I 023 i-oo6 -988 •971 -954 ■938 •921 -905 ■889 -873 -858 -843 -828 ^4h 23 1-068 I -049 1-031 1-013 -995 -978 -961 -944 -928 -912 -896 -880 -864 -849 -834 24 1-076 1-057 1-039 I -021 1-003 -986 -968 -952 -935 •919 -902 -886 -871 -855 -840 1 »43 25 1-084 1-066 1-047 1-029 I -on •993 -976 -959 -942 -926 -910 -893- •878 •862 -847 26° 1093 1-074 1-056 1-038 1-020 1-002 •984 •967 •950 -934 -917 -901 -885 -869 -854 ^ °l 27 I "103 1-084 1-065 1-047 1-028 l-OII -993 -976 •959 -942 -925 •909 -893 -877 -861 a*i*! 28 I-II3 1-094 1-075 1-056 1-038 1-020 1-002 -985 •967 •950 -934 -917 •901 •885 -869 >ious sij the La ilem IX, 29 1-124 1-104 1-085 1-066 1-048 1-029 1-012 -994 ■977 -959 -943 -926 -909 -893 -877 30 I-I3S 1-115 1-096 1-077 1-058 1-040 1-022 1-004 •986 -969 -952 •935 •918 -902 -886 31° I -146 I -127 1-107 1-088 1-069 1-050 1-032 1-014 -996 -979 -962 -945 •928 •911 ■89s 3>^ 32 I -159 I -139 1-119 1-100 1-081 1-062 1-043 1-025 1-007 -989 -972 -938 ■921 -905 33 I -172 1-151 1-132 1-112 1-093 1-074 I -OSS 1-037 1-018 i-ooi -983 -966 -948 •932 -915 34 1-185 1-165 I-I4S 1-125 1-105 1-OS6 1-067 1-049 1-030 1-012 -994 -977 -959 -942 •926 5 3 35 I -200 1-179 1-158 1-138 1-119 1-099 1080 1-061 1-043 1-024 I -006 -989 •971 -954 -937 * P.- 36° I -215 1-194 '■'^1 '■'11 1-133 1-113 1-094 1-074 1-056 1-037 1-019 1-001 -983 -966 -948 .s P>4 a bo o i 1-230 1-209 I -188 1-168 I -147 1-127 i-ioS 1-088 1-069 I -05 1 1-032 1-014 -996 -978 •961 S £-> 1-247 1-225 1-204 1-183 1-163 I -143 1-123 1-103 1-084 1-065 1-046 1-028 1-009 -991 •974 39 1-264 1-243 I -221 1-200 1-179 1-159 1-138 1-119 1-099 1-080 1-061 1-042 1-024 1-005 ■987 40 1-283 I -26 1 1-239 1-217 1-196 I 175 1-155 I-I3S 1-115 1-095 1-076 1-057 1-038 I 020 1-002 ^Is 41° 1-302 1-280 1-257 1-236 1-214 I -193 I -172 I -152 1-132 1-112 1-092 1-073 1-054 1-035 1-017 S "> >n 42 1-322 1-299 1-277 1-255 1-233 1-212 1-191 I -170 1-149 1-129 1-109 1-090 1-070 1-051 1-033 :§l 43 '■^tt 1-320 1-298 1-275 1-253 1-231 1-210 1-189 1-168 1-147 1-127 I -107 1-088 1-068 1 049 44 1-366 '■^l? 1-319 1-296 1-274 1-252 1-230 1-208 1-187 1-166 I -146 I -126 i-io6 1-086 1-067 l"g' 45 1-390 1-366 1-342 1-319 1-296 1-273 1-251 1-229 1-208 I -187 1-166 I -145 I -125 I -105 1-085 46° 1-415 1-390 1-366 1-342 I -319 r-296 1-274 1-251 1-229 i-2o8 1-187 1-166 1-14S 1-125 1-105 '^l 1-441 1-416 1-391 1-367 1-344 1-320 1-297 1-275 1-252 1-230 1-209 I -187 1-166 1-146 1-125 2 ©-S h5| 48 1-469 1-498 1-443 I -418 1-394 1-369 1-346 1-322 1-299 1-276 1-254 1-232 I -210 I -189 I -168 1-147 . 49 1-472 1-446 1-421 1-397 1-372 1-349 1-325 1-302 1-279 1-256 1-234 1-212 1-191 1-170 s-s SO 1-529 1-502 1-476 1-451 1-426 1-401 1-376 1-352 1-329 1-305 1-282 . 1-260 1-237 I -215 1-194 §5 5«° I 562 1-596 1-633 1-672 'iff 1-508 1-482 1-456 1-431 1-406 1-381 1-357 1-333 1-310 1-287 1-264 I -241 1-219 52 1-569 I 541 1-515 1-488 1-462 1-437 1-412 1-387 1-363 '-339 1-315 1-292 1-269 1-246 S3 1-605 I -577 1-550 1-523 1-496 1-470 1-444 I -419 1-394 1-370 1-346 1-322 1-298 1-275 i 54 1-643 1-684 1-614 '■|^A 1-559 1-532 1-505 1-479 1-453 1-428 1-402 1-378 1-353 1-329 1-305 55 1713 1-654 1-626 1-598 1-570 1-542 1-516 1-489 I '463 1-437 1*412 1-387 1-362 1-338 aS 56' I -757 1-804 1854 1-908 1-965 1727 1-697 1-668 1-639 I -610 1-582 I '555 1^527 1-501 I '474 1*448 1-422 1-397 1-372 as P 1-773 1-822 1-742 1-712 1-682 1-653 1-624 1-596 1-S6S I -541 1-514 1-487 1-460 1-43S 1-409 s-3 1-791 1-760 1-729 1-699 1-670 1-640 l-6l2 1-583 1-556 1-528 1-501 1-474 1-448 B"^ io' I 875 1-843 I -Si I 1-779 1-748 1-718 1-688 1-658 1-629 i-6oi 1-572 1*544 1-517 1-490 1^ 1-931 1-898 1-865 1-833 i-8oi 1769 '•739 1-708 1-678 1-649 I '620 1-591 1-563 1-535 61° 62 P 2-027 1-992 I -957 1-923 1-890 1-857 1-825 1-793 1-762 1-731 1-700 1-670 I -641 I -6X2 1-583 2093 2-165 2-057 2-021 1986 1-952 1-918 1-885 1-852 1-819 1-787 1756 1-725 1694 1-664 1-634 £ 2-127 2-090 2-054 2-018 1-983 1-949 1-915 1881 1-848 1-816 1-784 1-752 1-721 1-690 »-^ ,2-242 2-203 2-165 2-127 2-090 2-054 2-018 1-983 1-948 1-914 1-880 1-847 1-815 1-782 1-750 2-325 « 2-285 2-245 2-207 2-168 2-131 2093 2-057 2-021 1-985 1-951 1-916 1-882 1-849 I -816 To name Azimuth | l"" North latitude put N for a - 'Error,; and S for a + • ( In South latitude put S for a - 'Error,' and N for a -h ' Error." Error.' Dqiending upon the Latitude of the observer and the Azimuth of the object observed, the numbers in the body of this Table shew the error in the Longitude produced by an error of 1' in the Latitude worked with. They represent the mm or difference of the A and B values. 56 - _ . , , The Head-line has various slgnlfleations, according to the Problem in use. fhi'^®'" W'}^ represents the True Azimuth. In Problem IV. the Initial Course. In Problem V. the DliT. of Long., also tne irue Distance. In Problem VII. the Lat. of Departure, also Lat. of Vertex. In Problem IX. the Lat. of Departure or of Destination, also Liniitlng Parallel. In Problems X. and XI. the Hour-Angle or its supplement. is Lat. OF Obser- TRUE AZIMUTH 53° 53r 54° 54^ 55° 55r 56° 56r 57° 57r 58- 58r 59° 59r °60 ft ver. h m h in h m h m h ra h m h m h m h m h m h m h m h m h m h m (3 32) (3 34) (3 36) (3 38) (3 40) (3 42) (3 44) (346) (3 48) (3 50) (3 52) (3 54) (356) (358) (4 0) 0° '754 '-740 '727 713 '■700 '-687 '•675 '•662 '-649 '■637 '•62s -613 ■601 '•589 '•577 I •754 ■740 727 713 •700 -687 •675 •662 ■650 •637 •62s •613 ■601 •589 •577 ■3«H 2 7S4 -740 727 714 ■701 -688 •675 •662 -650 •637 -625 -613 ■601 -589 •578 .0 3 75S •741 •728 714 -701 •688 ■675 ■663 -650 -638 -626 -614 -602 ■590 -578 §S 4 755 -742 ■728 715 •702 •689 -676 •664 •651 •639 -626 •614 •602 ■590 ;S79 n S 756 •743 -729 716 •703 -690 -677 •664 -652 •640 -627 •615 -603 -591 c3 0) 6° 758 •744 •731 717 -704 -691 -678 •666 -653 •641 -628 •616 •604 •592 •581 7 759 -746 •732 719 •705 -692 -680 -667 •654 •642 -630 617 -605 •593 •582 use. of 1 XI. 8 761 747 •734 -720 ■707 -694 ■681 •668 •656 •643 •631 •619 -607 •595 •583 9 763 •749 •736 -722 •709 •696 ■683 -670 -6s8 •645 -633 •620 -608 •596 ■585 s^l 10 765 751 •738 724 711 -698 -68s -672 •659 ■647 • -63s •622 -610 •598 •586 11° 76S •754 -740 727 713 . ^700 -687 -674 -662 -649 •637 •624 -612 •600 •588 12 770 S56 •743 •729 716 •703 •690 ■6>7 -664 -651 •639 •626 -614 •602 •590 1*^1 13 773 •759 -746 ■732 719 •705 ■692 •679 -666 •654 •641 •629 -617 -60s •593 14 777 •763 •749 735 722 -708 •69s ■682 •669 •657 •644 •632 -619 •607 •595 •^ S3 15 780 ■766 •752 738 725 712 -698 -68s ■672 -660 •647 •634 -622 •610 •598 03 •S3& 16° 784 ■770 756 •742 -728 715 ■702 -689 •676 •663 •650 •637 •625 ■613 -601 ?^(*^ 17 788 774 •760 •746 732 719 ■70s -692 •679 •666 •653 •641 -628 ■616 -604 2 £5 18 792 •778 -764 •750 •736 723 •709 •696 -683 •670 •657 -644 -632 •619 -607 t-^ 19 797 •783 -768 754 741 727 713 -700 -687 •674 •661 •648 •635 -623 -611 20 •802 ■787 773 759 •745 731 718 -704 -691 -678 ■66s -652 •639 -627 -614 |25 21° •807 •793 778 764 -750 •736 •722 -709 -696 -682 •669 ■656 -644 -631 -618 22 •813 •798 •784 •769 755 -741 •727 714 -700 -687 •674 •661 -648 ■635 •623 S "S 23 •819 -804 •789 775 -761 ■747 •733 719 -70s •692 ■679 •666 •653 -640 -627 Ltions, i }f Depa ,e Dlff. 24 •82s •810 •795 ■781 ■766 752 •738 •725 711 •697 -684 •671 -6s8 •645 •632 25 •831 ■816 •802 ■787 773 758 ■744 •730 717 •703 -689 •676 -663 -650 -637 26° ■838 -823 -808 •794 •779 •765 •750 •736 •723 •709 •695 •682 -669 •65s -642 S .5 27 •846 ■830 -815 -801 -786 -771 •757 •743 -729 715 •701 •688 •674 -66i -648 Sts^- 28 •853 ■838 -823 ■808 •793 778 -764 •750 •736 •722 -708 •694 -681 -667 •654 a J>< 29 ■862 -S46 -831 -816 •801 -786 -771 757 •743 •728 714 •701 -687 •673 •660 ■a 2fl. 30 870 •854 •839 -824 -809 794 •779 •764 •750 •736 -722 •708 •694 •680 •667 lous [V. I] oblei 31° •879 -863 -848 ■832 -817 -802 •787 772 •758 •743 •729 715 •701 -687 •674 32 •889 •873 •857 ■841 -826 •810 •795 •780 •766 751 •737 ■723 -709 •695 •681 gs- 33 •899 882 -866 •851 •835 -819 •804 •789 774 •760 •745 •731 716 -702 •688 34 ■909 •893 •876 -860 •845 -829 ■814 •798 •783 ■768 •754 -739 725 711 -696 35 •920 •903 •887 -871 •855 •839 ■823 •808 •793 778 •763 •748 -734 719 -70s Us 36° •931 ■915 •898 -882 •866 •850 •834 -818 -803 -787 •772 757 •743 •728 714 •944 •927 -910 ■893 •877 ■S6r •845 -829 ■813 vl •782 767 •752 738 -723 38 •956 •939 •922 •90s -889 •872 ■856 -840 -824 •808 793 -778 •763 •748 •733 39 •970 ■952 •935 -918 -901 -884 •868 -852 •836 •820 ■789 •773 ■758 •743 40 •984 •966 •948 •931 -914 -897 •881 •864 •848 ■832 •816 -800 -784 •769 •754 4X° •998 -980 •963 •945 -928 ■911 -894 •877 •860 -844 •828 •812 -796 -780 765 42 I -014 •996 •978 -960 ■942 ■925 •908 •891 1^5 •8S7 •841 •82s -809 •793 777 o5 43 1-030 I -012 •993 •975 •957 ■940 -922 •90s •888 •871 1|4 •838 •822 -80s •789 S°* 44 1-048 1-029 I'OIO -992 ■973 •955 •938 •920 •903 •886 •869 -852 -83s -819 •803 45 1-066 1-046 1-027 1-009 -990 -972 •954 •936 -918 •901 •884 •867 •850 •833 -817 B degree the Lat oblem V 46' 1-085 1-065 1-046 1-027 1-008 -989 -971 •953 •935 •917 •900 •882 l^s -848 -831 % 1-105 1-085 1-065 1-046 1-027 1-008 •989 •971 •952 •934 •916 •899 -881 -864 ■847 1-126 I -106 1-086 1-066 1-046 1027 i-ooS •989 •971 •952 •934 •916 -898 -880 •863 49 I -149 I -128 1-107 1-087 1-067 1-048 1-028 1-009 •990 •971 •952 •934 •916 -898 -880 gs£ SO 1-172 i-iSi I -130 I-IIO 1-089 1-069 1-049 1-030 l^OIO •991 •972 •953 •935 -916 •898 0) 03 51° I -197 1-176 I -154 I •133 1-II3 1-092 1-072 1-052 1-032 roi2 •993 •974 •955 •936 -917 52 1-224 1-202 I -180 I -159 i'i37 1-116 1-096 I -07s I -OSS 1-035 i^ois •995 -976 •957 -938 53 1-252 1-230 1-207 1-185 1-163 I -142 1-121 I -100 1-079 1-059 1-038 roi8 •998 •979 -959 **1 54 1-282 1-259 1-236 I -214 I -191 1-169 I -148 I -126 I -105 1^084 1-063 I •043 1-022 1-002 -982 55 i^3i4 I -290 1-267 1-244 I '221 I -198 1-176 i^i54 1-132 i-iii ro89 I •068 1-048 1-027 1-007 ^S s'S 32 •667 tl'* •640 ■627 -614 ■601 -588 -575 •562 •550 •537 ■525 ■513 •501 -488 ? a_ 33 67s ■661 -647 ■634 •621 ■608 •594 ■582 -569 •556 ■543 53' ■518 -506 •494 34 '682 •669 t|5 •641 •628 •61s •601 •588 -575 •562 •550 ■537 ■524 -512 •500 II- 3S •691 ■677 -663 •649 •635 •622 ■609 •595 ■582 ■569 ■556 •544 ■531 ■5.8 •S06 «|«i 36° •699 ■685 ■^2' \n •643 •630 -616 -603 •590 •576 •563 •550 ■537 •525 •512 •3.'^§ 37 •708 •694 •680 •666 •652 ■638 ■624 •611 ■597 ■584 •571 ■557 -544 ■532 ■519 |c3 3" '7'? 703 -689 '%^ •661 •647 •633 •619 •605 •592 •578 •565 ■552 ■539 -526 39 •728 ■713 •699 •684 •670 •656 642 ■628 -614 ■600 •586 ■573 ■546 ■533 40 ■739 •724 709 ■694 ■680 ■665 -651 -637 -623 •609 •595 •581 •568 ■554 ■541 ^is 41° If •734 719 •70s ■690 •675 •661 •646 -632 •618 ■604 •590 -576 •562 549 S (0 ni 42 •761 ■746 •731 715 -700 ■686 ■671 -656 •642 •627 -613 •599 •585 ■571 •557 43 ■774 •787 •800 •758 -742 727 -712 ■697 ■682 •667 -652 •638 ■623 •609 ■59s ■580 •566 44 ■771 '755 -739 ■724 •708 ■693 •678 -663 •648 •634 -619 •604 ■590 •576 I^S 45 •784 -768 -752 •736 ■721 -705 ■690 -675 •659 644 ■630 •615 •660 •586 ®t3 46° •814 •830 ■846 •862 •880 ■798 •782 -76s •749 ■733 718 -702 •687 •671 •656 ■641 ■626 ■611 •596 \ I'l •796 •780 •763 •747 •731 •715 •699 ■684 •668 -653 ■638 ■622 -607 The nt the Probli 48 49 50 •828 ■845 •862 •811 •828 •84s -795 •810 827 •778 •793 •810 •761 •777 •793 760 776 -729 -743 •759 -713 -727 -742 •697 711 •725 ■681 •695 ■709 •679 •693 •650 •663 •676 •634 -647 -660 •619 -631 ■644 51° 52 S3 54 55 ■899 •919 •940 ■986 •881 •900 ■921 ■943 •966 -863 •882 •902 •924 ■947 •84s ■864 •«8i •90s •927 •827 •846 •86s •886 •908 •810 •828 •888 -792 •810 •828 ■848 ■869 -775 •792 810 ■830 •850 -758 ■775 •793 •811 -832 -741 •757 ■775 ■793 ■813 •724 740 •757 •775 •795 •707 •723 •740 •757 •776 •691 •706 •723 •740 •758 -674 •689 •70s •722 •740 •658 •70s •722 51 56° roi2 1-039 1068 -991 r-oi8 I 046 •971 -997 . I -025 •9SI •976 roo3 •931 •956 •982 •911 •892 -915 •941 •872 •896 •920 •853 •876 •900 ll ■81S •837 •860 •796 -817 •840 •778 •798 •821 -759 •782 ■s5 1 1-099 I -132 I 076 I -109 1-054 1-086 1-032 1-063 I -on I '041 •989 roig ■968 •997 -947 -975 •926 •954 -905 -933 •885 •911 -8^4 •890 •844 •870 -824 •849 •804 ■828 In Prol of 1 61° 62 64 65 I -167 1-205 I '246 1*291 1-339 '-143 i-i8i 1-221 1-264 1-312 I '120 I -157 1-196 1-239 1-285 1-097 I -133 fi7i I "213 1-258 ro74 1-109 I 147 1-188 1-232 1-051 1-085 1-122 I -162 I -206 1-028 1062 1-098 I -137 I -180 1-006 1-039 I -074 I-II3 1^154 ■984 I -016 1-051 1-088 1-129 -962 ■993 1-027 1-064 1-103 •940 •971 1^004 I "040 1-078 •918 I -016 1-053 •897 •926 •958 •992 • •029 •876 •904 •968 1^004 -912 •945 •980 To name Azimuth In North latitude put N for a - • Error,' and S for a + • Error.' In South latitude put S for a - 'Error,' and N for a + 'Error.' Blending v/pon the Latitude of the observer and the Azimuth of the object observed, the numbers in the body of this Table shew the error in, the Longitude produced by an error of 1' in the Latitude worked with. They represent the sum or difference of the A and B values. 58 The Head-line has various significations, according to the Problem in use. ^"^"^m®™ y?- J* represents the True Azimuth. In Problem IV. the Initial Course. In Problem V. the Dlff. of Long., also the True Distance. In Problem VII. the Lat. of Departure, also Lat. of Vertex. In Problem IX. the Lat. of Departure or of Destination, also Limiting Parallel. In Problems X. and XI. the Hour-Angle or its supplement. •i ^ Lat. OF Obser- TRUE AZIMUTH 1. 68° 68^° 69° 69^ 70' 7or 71° 711° 72° 72r 73° 73r 74° 74r 75° \^ ver. h m h in h m h m h m h m h m h m h in h m h m h m h m h m h m as So (432) (4 34) (436) (4 38) (4 40) (4 42) (4 44) (4 46) (4 48) (4 50) (4 52) (4 54) (456) (458) (5 0) 0° '•404 '•394 '•384 '•374 '•364 •354 '•344 '•33s '•325 '•315 '•306 '•296 '•287 •277 '•268 gs I ■404 •394 •384 ■374 •364 •354 •344 •335 •325 •315 •306 •296 •287 •277 •268 "3 "a 2 ■404 •394 •384 •374 •364 •354 •345 •335 •325 •315 •306 •296 •287 ■277 •268 s 14 ■416 •406 •396 •385 ■375 •365 •35s ■345 •335 ■325 ■315 ■305 •?96 •286 •276 ^as IS •418 •408 •397 •387 •377 •367 •356 ■346 •336 •326 •317 •307 ■297 •287 ■277 lis 16° •420 •410 •399 ■389 •379 •368 •358 •348 •338 •328 •318 •308 •298 •289 •279 ■^ 0*" 17 •422 ■412 •401 •391 •381 •370 •360 •350 ■340 •330 ■320 •310 •300 •290 •280 3 £,5 18 •42s •414 ■404 ■393 •383 •372 •362 •352 ■342 •332 •321 •311 ■302 •292 •282 ■.. a 19 •427 •417 ■406 ■395 ■385 •375 •364 •354 •344 •333 •323 •3«3 ■303 •293 •283 s^ 20 •430 ■419 •408 •398 •387 •377 •366 •356 •346 •336 ■325 •315 ■30s •295 •285 |g| 21° •433 •422 ■411 •400 •390 •379 •369 •358 •348 •338 •327 •317 •307 •297 •287 22 •436 ■425 •414 •403 ■393 •382 •371 •361 •350 •340 •330 •319 •309 •299 ■289 * ^° 23 •439 ■428 •417 ■406 •395 •385 •374 ■3^1 ■353 •343 •332 •322 •312 •301 ■291 2 ® is" 24 •442 •431 •420 •409 ■398 •388 •377 •366 •356 •345 ■335 •324 •3 "4 •304 •293 25 •446 •435 •424 •413 •402 •391 •380 •369 •359 •348 ■337 •327 •316 •306 •296 ^ o2 26° •45° •438 •427 ■416 •405 •394 •383 •372 •362 •351 •340 •330 •319 •309 ■298 § °5 27 •453 •442 •431 ■420 •408 •397 •386 •376 ■3^1 •354 •343 •332 •322 •311 •302 Sts^- 28 •458 •446 •43s •423 •412 •401 •390 •379 •368 •357' •346 •335 •325 •314 •303 &^>< 29 •462 •450 •439 ■427 •416 •405 •394 ■3?3 •371 ■360 •350 •339 , •328 ■317 •306 lous sig [V, the oblem 1 30 ■467 •455 •443 •432 •420 •409 •398 •386 ■375 ■364 •353 •342 •331 ■320 •309 31° ■471 •460 ■448 ■436 ■425 ■413 •402 •390 •379 •368 •357 •346 •335 •324 •313 32 •476 •464 •453 •441 •429 •418 •406 ■395 •383 ■372 •361 •349 •338 •327 •316 ga- 33 ■482 •470 ■458 •446 •434 •422 •411 •399 •387 •376 ■365 •353 •342 •331 •319 34 •487 ■475 ■463 •451 •439 •427 •415 •404 •392 •380 •369 •357 •346 •335 •323 %%^ 35 ■493 •481 •469 •456 ■444 •432 •420 •408 •397 •385 •373 •362 •350 •339 •327 £S3 36° •499 ■487 •474 •462 •450 •438 •426 •414 •402 •390 ■378 •366 •354 •343 •331 •S06 ■493 •481 •468 •456 •443 •431 •419 •407 •395 ■3!l •371 ■359 •347 •336 38 •513 ■500 •487 •474 ■462 •449 •437 •425 •412 •4CX) ■388 •376 ■364 ■352 •340 gf «M 39 •520 •507 ■494 •481 •468 •456 •443 •431 •418 •406 •393 •381 •369 ■357 ■345 ci ® • ^|0 40 •527 •514 ■501 •488 •475 ■462 •449 •437 •424 •412 •399 •387 •374 •362 •350 41° •S3S •522 •509 •495 ■482 •469 •456 •443 ■431 ■418 •405 •392 •380 •367 •355 42 •S44 ■53° •517 ■503 •490 •477 •463 •450 ■437 •424 •411 ■399 ■386 •373 3^i "'OA 43 •552 ■539 •52s •511 •498 •484 •471 •458 ■444 •431 •418 •405 ■392 •379 •366 BZ^ 44 •S62 •548 ■534 •520 •506 •492 •479 •46s ■452 •438 •425 •412 •399 •386 •372 S*e 45 571 ■557 •543 •529 ■515 •501 •487 •473 •460 ■446 •432 ■419 •406 ■392 •379 46° •582 •567 •553 •538 •524 •510 •496 ■482 •468 •454 •440 •426 •413 ■399 •386 47 592 •578 •563 •548 •534 •519 •505 •491 •476 •462 •448 •434 •420 •407 ■393 •§*s 48 •589 •574 •559 •545 ■529 •515 ■500 •486 •471 '^^1 •443 •429 •414 ■400 H Oft- 49 •616 •600 •585 •570 •555 ■540 •525 •510 •495 •481 •466 •452 •437 •423 •408 SO •629 •613 •597 •582 •566 •551 •536 ■521 •505 491 •476 •461 •446 •431 •417 S5 51° ■642 ■626 •610 •594 •578 ■563 •547 ■532 •516 •501 •486 •471 '^t •441 •426 »4 52 •656 •640 •623 •607 •591 ■575 •559 ■543 •528 ■512 •497 •481 •466 •450 •435 Pf • S3 ■671 •655 •638 ■621 •60s ■588 •572 ■556 ■540 ■524 •508 •492 •476 •461 •445 **£ 54 •687 •670 ■653 •636 619 •602 •586 •569 •553 •536 •520 •504 •488 ■472 •456 &o SS •704 •687 ■669 •652 ■635 •617 •600 •583 •566 •550 •533 •516 •500 •484 •467 5^ S6° ■723 704 •686 •669 •651 •633 •616 •598 ■S81 •564 •547 ■530 •513 •496 •479 s-JS ■742 •723 •705 •686 •668 •650 •632 •614 •597 •579 •561 •544 •526 •509 ■492 5^ •762 •743 •724 •706 •687 •668 •650 •631 •613 •595 •577 •559 •541 ■523 •506 0) 0) 04 O 59 ■784 •765 •745 •726 •707 •688 •669 ■650 •631 •612 ■594 •575 •557 •538 •S20 6a •808 •788 •768 •748 •728 •708 •689 •669 ■650 •631 •6u •592 •573 •555 •536 61° •833 •813 ■792 •771 ■751 •730 •710 •690 •670 •650 •631 •611 ■591 •572 ■553 62 •86i •839 ■868 •818 •796 •775 •754 ■733 •713 •692 •672 •651 •631 •611 ■591 •571 a 63 •890 ■922 •956 •846 •824 •802 •780 •758 •737 •716 ■695 ■673 •652 ■632 ■611 •590 M 64 •899 •932 •876 •853 •830 •808 •78s •763 •741 ■719 •697 •676 ■^54 •633 •611 65 •908 •885 ■861 •838 •815 •792 •769 ■746 •723 •701 •678 •656 ■634 In North latitude put N for a . . *!. Un Nortft latiiuae put « lor To name Azimuth j j^ ^^^^^ latitude put S for ' Error,' and S for a -h ' Error.' • Error,' and N f or a -f ' Error.' Depending vmm the Latitude of the observer and the Azimuth of the object observed, the numbers in the body of this Table shew, the error in the produced by an error of 1' in the Latitude worked vnth. They represent the sum or difference of the ^ and S values. 59 The Head-line has various significations, accordingr to the Problem in use. In Problem III. It represents the True Azimuth. In Problem IV. the Initial Course. In Problem V. the Diff. of LongM also the True Distance. In Problem VII. the Lat. of Departure, also Lat. of Vertex. In Problem IX. the Lat. of Departure or of Destination, also Limiting Parallel. In Problems X. and XI, the Hour-Angle or its supplement. 5 i* Lat. OF Obser TRUE AZIMUTH. 75r 76° 76r 77° 77r 78° 78|° 79° 791° 80° 80i' 81° 8U° 82° 82i° SI VER. h m b m h m h m h m h m h m h m b m b m h in li m b m b m h m (S«) (5 4) (56) (58) (5 10) (5 12) (5 14) (5 16) (5 18) (5 20) (522) (524) (526) (528) (530) 0° '•2S9 '•249 1 ■240 '•231 •222 '•213 '■203 '•194 '•X8S '•176 '•167 '■158 '•149 '•141 '•132 S.S I •2S9 •249 •240 •231 •222 •213 •203 •194 •18S •176 •167 •158 •149 •141 •132 ^* 2 •2S9 •249 •240 ■231 •222 •213 •204 •194 •185 '176 •167 •158 •150 •141 •'32 .*-" 3 •259 •250 •240 •231 •222 ■213 '204 •195 •186 ■177 •168 •159 •150 •141 •'32 (0 o 4 •259 ■250 •241 •231 •222 •213 •204 •195 •186 •177 •168 •159 •150 •141 •'32 5 •260 ■250 •241 •232 •223 •213 •204 •195 •186 •177 •168 ■159 •150 •141 •'32 6° ■260 •251 •241 ■232 ■223 •214 •20s •195 •186 •177 '168 •159 •150 •141 •13a sss I •261 •251 •242 •233 •223 •214 •20s •196 •187 •178 '169 •160 •151 •142 •'33 20« •261 •252 '242 ■233 •224 •21S •20s •196 •187 '178 '169 •160 •151 •142 ■'33 1 in t. of dXL 9 •262 •252 •243 •234 •224 •215 •206 •197 •188 •179 •169 •160 •151 •142 •'33 ID •263 •253 •244 •234 •22s •216 •207 •197 •188 •179 •170 •161 •152 •143 •'34 03 fcaeS 11° ■263 •254 •245 •235 ■226 ■217 •207 •198 •189 •180 •170 •161 •152 •143 •'34 "S 0>kJ 12 •264 •25s •245 •236 •227 •217 •208 •199 •189 •180 •171 •162 •153 •'44 •'35 2-^^ 13 •26s •256 •246 •237 •228 ■218 •209 •199 •190 •181 •172 •163 •>53 •'44 •'35 he P 1 V. 1 lems 14 ■^^2 ■257 •247 •238 •228 •219 •210 •200 •191 •182 •172 •163 •»S4 •145 •136 IS ■268 ■258 •249 •239 •230 •220 •211 •201 •192 •183 •173 •164 •155 •»4S •136 to tl blem Prob 16" ■269 •259 •250 •240 •231 •221 ■212 •202 •"93 •183 •174 •16S •155 •146 •137 17 •270 •261 •251 •241 •232 •222 •213 •203 •194 •184 •175 •166 •156 •'47 •'38 bo »4 a i8 •272 •262 •252 •243 •233 ■223 •214 '204 •195 'i8s •.76 •167 •157 •148 •138 aac>-> 19 •274 •264 •254 '244 •234 •225 •21S •206 •196 ■186 •177 •168 •158 •149 ■'39 20 •275 •26s •255 •246 •236 •226 •217 •207 •197 '188 •178 •169 •159 •150 •140 g a o (d9 21° •277 •267 •257 •247 . ^237 •228 •218 •208 •199 '189 •179 •170 •160 •'5' •141 Cjgj 22 •279 ■269 •259 •249 •239 •229 •219 •210 •200 '190 •180 •171 •161 •152 •142 -S'fe 23 •281 •271 •261 •251 •241 •231 '221 •211 '20I '192 •182 •172 '162 ■'53 ■143 B C3... 24 •283 •273 •263 •253 •243 •233 •223 •213 •203 ■193 •183 •173 •164 •»54 ■144 33 fl}"^ 25 •28s •275 •26s •25s ■245 •235 •224 •214 '204 ■'95 •i8s •>7S •16s •155 •'45 26° ■288 •277 •267 •257 •247 •236 •226 •216 •206 •196 •186 •176 •166 •'S6 •146 % ■290 •293 •280 •282 •269 •272 •261 •249 •251 •239 •241 •228 •230 •218 •220 •208 •210 •198 '200 •188 •190 •178 •179 •168 •169 •158 •159 •148 ■'49- ■E3.3X 29 •296 ■^fl •274 •264 ■253 •243 •233 •222 •212 '202 •191 •181 •171 •161 ■'5' •ious the 1 )lem 1 30 •299 •288 '277 •267 •256 •245 •235 •224 •214 '204 •193 •183 •173 •162 •'52 31° •302 •291 •280 •269 •259 •248 •237 •227 •216 •7n6 •195 •18s •174 •164 ■'54 3i>-3 32 •30s •294 'il •272 •261 ■251 •240 •229 •219 •208 •197 •187 •176 •166 ■'55 33 •308 •297 •286 •275 •264 •253 •243 •232 '221 •210 •200 •189 •178 •168 •'57 34 ■312 •301 •290 •278 •267 •256 •245 •234 •224 •213 •202 •191 •180 •170 •159 t> 0} a 5 3"^ 35 •316 •304 •293 •282 •271 •259 •248 •237 •226 '2IS •204 •193 •182 •172 •161 36° •320 •308 •297 ■28s •274 •263 •251 •240 •229 '2l8 '207 •196 •185 ■174 •'63 •a § S7 •324 •312 •301 •289 •278 •266 •255 •243 •232 -221 '2IO •198 •187 •176 •'65 3" •328 •316 •305 •293 ■281 •270 •258 •247 •235 '224 •212 •201 •190 •178 •167 39 •333 •321 •309 •297 •28s •274 •262 •250 •238 '227 •215 •204 •192 •181 •169 40 ■338 •325 ■3«3 •301 •289 •277 •266 •254 •242 •230 '2l8 •207 •195 •183 •172 41° •343 •330 •318 •306 •294 ■282 •270 •258 •246 •234 '222 •210 •198 •186 •'74 42 ■348 •336 ■323 •311 •298 •286 •274 ■262 '249 •237 '225 •213 •201 •189 ■'77 03 b^ 43 •354 •341 •328 ■316 •303 •291 •278 ■266 •253 •241 •229 •217 •204 •192 •180 44 .1^ ■347 •334 •321 •308 •295 ■^'f^ •270 •258 •245 •233 •220 •208 •'95 •183 45 •306 •353 •340 •326 •314 •301 •288 •27s •262 •249 •237 •224 •211 •'99 •186 46° •372 ■3|? •346 •332 •3 '9 •306 •293 •280 267 •254 •241 •228 •21S •202 •190 HI •379 •366 •352 •339 •325 ■3:2 •298 •28s '272 •259 •245 ■232 •219 •206 •'93 2 ^-S ^-1 48 ■386 •373 •359 •345 •331 •318 •304 •290 '277 •264 •250 •237 •223 •210 •'97 49 •394 •380 •366 •352 •338 •324 •310 •296 •283 •269 •255 •241 •228 •214 •201 ^£ SO '402 •388 •373 •359 •345 •331 •317 ■302 •288 •274 •260 •246 •233 •219 •20s 03 a 51° •411 •396 ■381 •367 •352 •338 •323 •309 •295 •2R0 •266 •252 ■237 •223 •209 1 . 52 •420 •405 •390 •375 ■3^2 •345 •330 •316 •301 '286 •272 •257 •243 •228 •214 Am S3 •430 •414 •399 •384 •368 •353 •338 •323 •308 ■293 •278 '263 •248 •234 •Z19 54 •440 •424 ■408 •393 '^V. ■362 •346 •331 •315 •300 •285 •269 •254 •239 •224 55 ■451 •435 •419 •403 •387 •371 ■355 •339 •323 ■307 •292 •276 •261 •245 •230 ^S 56° •462 ■446 •458 •471 •484 •499 •429 ;4i3 •396 •380 •364 ■348 •331 •315 •299 •283 •267 •251 ■23s 58 ■til •441 •436 •407 •418 •390 •401 S •357 •367 •340 •350 •324 •333 •307 •316 •291 •299 •282 •242 •248 IS f2 •502 •517 •466 •480 •448 •462 •430 ■443 •413 •425 •395 •407 •377 •389 ■360 •371 •342 •353 •325 •335 •368 •317 •290 •299 •273 •281 % 6i» 62 65 •533 •514 •495 •476 •457 ■438 •420 •401 •382 •364 •345 ■327 ■308 •290 •272 Ph ° •551 •531 ■511 •492 •472 •453 •433 •414 •395 •376 •356 •337 •318 •299 •310 ■321 •333 •280 a •570 •590 •612 •549 •569 •590 •529 ■548 •568 •509 •527 ■546 •488 ■S06 •525 ■468 •485 •503 •448 •464 •481 •428 •443 •460 •408 •423 •439 ■388 '402 •417 •369 •382 •396 •349 •361 •375 •329 •341 •354 •290 •300 •312 To name Azimuth \ ^'^ ^°^'^ latitude put N for a - 'Error,' and S for a ■^ 'Error.* i In South latitude put S for a - 'Error,' and N for a + 'Error.' Depending upon tlui Latitude of the olierver and the Azimuth of the object observed, the numhen in the body of this Table shew the error tn Lo7igitude produced by an error of 1' in the Latitude worked with. They represent the sum~'or difference of the A and B values. the 60 _ _^ The Head-line has various signifleations, according to the Problem in use. ^^ T^„ n:„i* represents the True Azimuth. In Problem IV. the Initial Course. In Problem V. the DifT. of Long., also tne irue Distance. In Problem VIL the Lat. of Departure, also Lat. of Vertex. In Problem IX. the Lat. of Departure or of Destination, also Limiting Parallel. In Problems X. and XI. the Hour-Angle or its suppiemtnt. tfe Lat. OF Obser- TRUE AZIMUTH. 83° 83r 84° 84^ 85' 85r 86° 86J° 87° 87r 88° 88r 89' 89r 90° lg ver. - b m h in h m h m h m h m h m h m h m h m h m b m h m b m h m eg ■So (s 32) (5 34) (5 36) (538) (5 40) (542) (5 44) (5 46) (548) (550) (552) (5 54) (5 56) (SS8) (60) 0° '•123 '•114 '•los '•096 '•087 '•079 '•070 '•061 ■052 ' -044 '035 026 •017 '•009 •000 S.S I •123 •114 •los •096 •088 •079 •070 •061 ■052 •044 ■035 •026 •017 •009 •000 ■3^ 2 •123 •114 •los ■096 •088 •079 •070 •061 •052 ■044 •035 ■026 •017 •009 •000 o'S 3 •123 •114 •10s •096 •088 ■079 •070 ■061 •052 ■044 •035 •026 •017 •009 •000 4 •123 ■114 •los •097 •088 ■079 •070 •061 053 •044 ■03s •026 •017 •009 •000 p 5 •123 •114 •106 •097 •088 •079 ■070 •061 •053 •044 •035 •026 •018 •009 •000 • DiA 6" •123 •"5 •106 •097 •088 •079 •070 •062 ■053 •044 •035 ■026 •018 •009 •000 S.5?5 i •124 •IIS •106 •097 ■088 •079 •070 •062 •053 •044 •03s •026 •018 •009 •000 S«*t ■124 •IIS •106 •097 •088 •079 •071 •062 •053 •044 •035 •026 •018 •009 •000 lem in Lat. of and XI 9 ■124 •IIS •106 •097 •089 ■080 •071 ■062 ■OS3 •044 •035 •027 •018 •009 ■000 ID •I2S •116 •107 •C3g8 •089 •080 ■071 •062 •053 •044 •035 •027 •018 •009 •000 11" •I2S •116 •107 •098 •089 •080 •071 •062 •053 •044 •036 •027 •018 •009 •000 l|x- 12 •126 •116 •107 •098 •089 •080 ■071 •063 •054 •045 •036 •027 •018 •009 •000 13 •126 •117 •108 •099 •090 •081 •072 •063 •054 •045 •036 •027 •018 •009 •000 tie P 1 V. 1 lems 14 •127 •117 •108 ■099 •090 •081 •072 •063 •054 •045 •036 •027 •018 •009 ■000 IS •127 •118 •109 •100 •091 •081 •072 •063 •054 •045 •036 •027 ■018 •009 •000 to tl blera Prob i6° •128 •119 •109 •100 ■091 •082 •073 ■064 •055 •045 •036 •027 •018 •009 •000 17 ■128 •119 •no •lOI •091 •082 •073 •064 •05s •046 •037 •027 •018 •009 •000 ^£5 i8 •129 ■120 •III •lOI ■092 •083 •074 •064 •055 •046 •037 •028 •018 •009 •000 19 •130 •121 •III •102 •093 •083 •074 •06s •05s •046 •037 •028 •018 •009 •000 ^5^ 20 •131 •121 •112 •102 ■093 •084 •074 •06s •os6 •046 •037 •028 •019 •009 •000 Ijgl 21" •132 •122 •113 •103 •094 ■084 •075 •066 •os6 •047 ■037 •028 •019 •009 •000 22 ■132 •123 •113 ■104 •094 •08s •075 ■066 •OS7 •047 •038 •028 •019 •009 •000 23 •133 •124 •114 •los •095 •08s •076 •066 •057 •047 •038 •028 •019 •009 •000 24 •134 •I2S •IIS •los •096 •086 ■077 •067 •057 •048 ■038 •029 •019 •010 •000 •^ tr.'.'l 25 •13s •I2S •116 •106 •097 •087 •077 •067 •os8 •048 •039 •029 •019 •010 •000 26"' •137 •127 •117 •107 ■097 •088 ■078 •068 •os8 •049 •039 •029 ■019 •010 •000 ? °5 2y •138 •128 •118 •108 •098 •088 ■078 •069 •059 ■049 •039 ■029 •020 •010 •000 a*^*' 28 •139 •129 •119 •109 •099 •089 ■079 •069 •OS9 •049 •040 •030 •020 •010 •000 ious si| the La lem IX. 29 •140 ■130 •120 •no •100 •090 ■080 •070 •060 •oso •040 •030 ■020 •010 •000 30 •142 •132 •121 ■III •lOI •091 ■081 - ^07 1 •061 ■050 •040 •030 •020 •010 •000 31° ■143 •«33 •123 •112 •102 •092 •082 •071 •061 •OS I •041 ■031 •020 •010 •000 s>-s 32 •145 •134 •124 •114 •103 •093 •082 •072 ■062 •OS I •041 •031 •021 •010 •000 gsg 33 •146 •136 ■125 •us •104 •094 •083 •073 •062 •0S2 •042 •031 •021 •010 •000 57-33 57-38 57-44 57-52 28-65 2866 2867 2869 28-72 28-76 / 19-11 19-11 19-12 19- '3 19-15 1918 14-34 14-34 14-34 14-36 14-37 14-39 11-47 11-48 11-48 11-49 11-50 11-52 9567 9-568 9573 9-580 9-590 9603 8-206 8-207 8-211 8-2i7 ■ 8 226 8-237 7-185 7-186 7-190 7-195 7 '203 7-213 6-392 6-393 •6-396 6-401 6-408 6-417 5-759 5-760 5-762 5-767 5-773 5 -781 5-241 5 242 5-244 5 -248 5-254 5-261 4-810 4-810 4-813 '4-816 4:821 4-828 4'-445 4-446 4-448 4-452 4-456 4-462 4-134 4-134 4-136 4-139 4-144 4-149 3-864 3-864 3-866 3-869 3-873. 3-878 6° \ 9 10 5761 5773 57-86 5801 58-18 28-81 28-87 28-94 29 01 29-10 19-21 19-25 19-30 i9'35 19-40 14-41 14-44 14-48 14-51 14-56 11 '54 11-56 11-59 11-62 u-65 9-619 9-639 9-661 9-686 9714 8-251 8-267 8-286 8-308 8-332 7-225 7-23? 7-256 7-275 7-296 6-428 6-440 6-455 6-472 6-491 5-790 5-802 5-815 5-83' 5-848 5-270 5-280 5-292 5-306 5-322 4-836 4-846 4-857 4-870 4.-884 4-470 4-479 4-489 4-501 4-514 4-156 4-165 4-174 4-185 4-197 3-885 3-893 3-902 3-912 3-923 11° 12 13 14 IS 58-37 58-58 58-81 59-05 59-32 29-19 29-29 29-41 29-53 29-66 19-46 1953 19-61 19-69 19-78 14-60 14-66 1471 14-77 14-84 11 69 11-73 11-78 11-82 11 88 9-746 9-780 9-818 9-860 9-904 8-359 8-389- 8421 8-457 8-495 7-320 7-346 7-374 7 -405 7-439 6-512 6-535 6-561 6-588 6-618 5-867 5-887 5-910 5-935 5-962 5-339 5-358 5-379 5-401 5-426 4-900 4-917 4-936 4-957 4-979 4-529 4-545 4-562 4-582 4-602 4-211 4-226 4-242 4-260 4279 3-936 3950 3-965 3-952 4-000 i6° 59-61 29-81 19-88 14-91 11-94 9-952 8-536 7-475 6-650 5-991 5-452 5-004 4-625 4-300 4-019 % 59-92 29-96 19-98 14-99 12-00 10-00 8-5S0 7514 6-685 6-022 5-480 5-030 4-649 4-322 4-346 4-040 4*063 4-086 6D-25 30 13 20-09 15-07 12-06 10-06 8628 7-555 6-721 6-055 5-511 5-057 4-674 19 20 60 -60 30-30 20-21 15-16 12-13 10-12 8-678 7-599 6-761 6-091 5 -543 5-087 4-702, 4-372 6o'98 '30-49 20-33 15-26 12-21 10-18 8-732 7-646 6-803 6-128 5-577 5-118 4-731 4-399 4-112 21° 61-38 30-69 20-47 15-36 12-29 10-25 8-789 7-696 6-847 6-168 5614 S-IS2 4-762 4-428 4-458 4-139 4167 22 61-80 30-90 20-61 15-46 12-37 10-32 8-850 7-750 6-894 6-211 5-652 5-187 4-795 23 62-25 31-13 20-76 15-57 12-46 io'39 8-914 7'8=6 6 •945 6-256 5-693 S-225 4-829 4-491 4-197 24 62-72 31-37 20-92 15-69 12-56 10-47 8-982 7-865 6-997 6-304 5-737 5-265 4-866 4-525 4-561 4-229 4-263 25 63- 22 31-62 21-08 .5-82 12-66 10-56 9-054 7-928 7053 6-354 5-783 5-307 4-905 26° 63-75 31-88 21-26 15-95 12-77 10-64 9-129 7-994 7-112 6-407 5-831 5 -35 1 4-946 4-599 4-299 64-31 32-16 21-44 16-09 12-88 10-74 9-209 8-064 7-174 6-463 5-882 5-398 4-989 4-639 4-336 4-376 4-418 4-461 28 64-89 32-45 2 1 '64 16-24 12-99 10-84 9-293 8-138 7-240 6-S22 5-936 5-447 5-035 4-682 29 65-51 32-76 21-85 16-39 13-12 10-94 9-382 8-215 7-309 6-584 5-992 5-499 5-083 4-726 30 66-16 33-09 22 -06 16-55 13=25 11-05 9-475 8-297 7-381 6-650 6:052 5-554 5-133 4-773 31° 66-85 33-43 22-29 16-72 13-39 ii-i6 9-573 8-383 7-458 6-718 6-lM 5-611 5-186 4822 4-508 4-556 32 67-57 33-79 22-53 16-90 13-53 11-28 9-676 8-473 7-538 6-791 6-180 5-672 5-242 .4-874 33 68-32 34-17 22-78 17-09 1368 11-41 9-784 8-567 7-622 6-867 6-249 5-735 5-301 4-929 4-607 34 69-11 34-56 23-05 17-29 13-84 11-54 9-898 8-667 . 7-711 6-946 6-322 5-802 5-362 4-986 4-660 35 69-95 34-98 23-33 17-50 14-01 11-68 10-02 8-772 7-804 7-030 6-398 5-872 5-427 5-046 4-717 36° 70-83 35-42 23-62 17-72 14-18 11-83 10-14 8-882 7-902 7-118 6-478 5 -945 5-495 5-109 4-776 4-838 71-75 35-88 23-92 17-95 14-37 n-98 10-27 8-997 8-004 7-211 . 6-562 6-022 5-566 5-176 38 72-71 36-36 24-25 r8-i9 14-56 12-14 10-41 9-118 8-112 7-308 6-651 6-104 5-641 5-246 4-903 39 73-73 36-87 24-59 18-45 14-76 12-31 10-56 9-246 8-226 7-410 6-744 6-189 5-720 5-319 4-972 40 74-80 37-40 24-94 1871 14-98 12-49 10-71 9-380 8-345 7-518 6-841 6-279 5-803 5-396 5-044 41° 75-92 37-97 25-32 18-99 15-20 12-68 10-87 9-521 8-470 7-630 6-944 6-373 5-890 5 -477 5-119 42 77-10 38-56 25-71 19-29 15-44 12-87 11-04 9-669 8-602 7-749 7-052 6-472 S-982 5-562 5-199 43 78-35 39-18 26-13 19-60 15-69 13-08 11-22 9-825 8-741 7-874 7-166 6-576 6-078 5-652 5-283 44 79-65 39-83 26-56 19-93 15-95 13-30 11-41 9-989 8-887 8-C06 7-286 6-686 6-180 5-746 5-371^ 45 81-03 40-52 27-02 20-27 16-23 13-53 11-60 10-16 9-040 8-144 7-412 6-802 6-287 5-846 5-464 46° 82-48 41-25 27-51 20-64 16-52 13-77 11-81 10-34 9-202 8-290 7-544 6-924 6-399 r^i' ^'^^ 47 84-02 42-01 28-02 21-02 16-82 14-03 12-03 10-54 9-373 8-444 7-685 7-052 6-518 6-061 5-665 48 85-63 42-82 28-56 21-42 17-15 14-30 12-26 10-74 9-553 8-606 7-832 7-188 6-644 6-178 5774 49 87-34 43-68 29-12 21-85 17-49 14-58 ■12-51 10-95 9-744 8-778 7-988 7-331 6-776 6-301 5-889 SO 89-14 44-58 29-73 22-30 ■7-85 14-88 12-77 11-18 9-945 8-959 8-153 7-483 6-916 6-431 6-011 51° 91-05 45-53 30-36 22-78 18-23 15-20 13-04 11-42 10-16 9-151 8-328 7-643 7-064 6-568 !"'^^ 52 93-07 46-54 31-04 23-28 18-64 15-54 13-33 11-67 10-38 9-354 8-513 7-812 7-221 6-714 6-276 S3 95-21 47-61 31-75 23-82 19-07 15-90 13-63 11-94 10-62 9-569 8-708 7-992 7-387 6-868 6:420 54 97-48 48-75 32-51 24-39 19-52 16-28 13-96 ^ 12-22 10-88 9-797 8-916 8-i8j 7-563 7-032 6-573 55 99-90 49-96 33-31 24-99 20-00 16-68 l4-3« 12-53 11-14 10-04 9-137 8-386 7750 7-207 6-736 56° 102-5 51-24 34-17 25-64 20-52 17-11 14-67 12-85 11-43 10-30 9-372 8-601 7-950 7-392 6-909 % 105-2 52-61 35-08 26-32 21-07 17-57 15-07 13-19 11-74 10-57 9-623 8-831 8-162 7-590 7-094 58 108-1 54-07 36-06 27-05 21-65 18-05 15-48 13-56 12-06 10-87 9-890 9-076 8-389 7-800 7-291 |9 111-3 55-63 37-10 27-83 22-28 18-57 15-93 13-95 12-41 11-18 10-18 9-339 8-631 8-026 7-502 60 1 14-6 57-31 38-21 28-67 22-95 19-13 16-41 14-37 12-78 11-52 10-48 9-619 8-891 8-267 7-727 61° 1 18-2 59-10 39-41 29-57 23-67 19-73 16-93 14-82 13-19 u-88 10-81 9-921 9-169 8-526 7-970 62 122-0 61-03 40-70 30-54 24-44 20-38 17-48 15-31 13-62 12-27 11-16 10-24 9-469 8 -805 8-230 ^3 126-2 63-12 42-09 31-58 25-27 21-07 18-07 15-83 14-08 12-69 "•54 10-59 9-792 9-105 8-511 64 130-7 65-36 43-59 32-70 26-17 21-82 18-72 16-39 14-58 13-14 11-96 - 10-97 10-14 9429 8-814 65 135-6 67-80 45-21 33-92 27-15 22-64 19-42 17-00 "5-13 13-63 12-40 11-38 10-52 9-781 9-142 . m. s. To convert into Time, Multiply by 4. Thus 114-6 x 4 = 7 38-4. This applies also to the quantities in Table C. 62 Shewing the error produced iij the Longitude by an error of I' in the Altitude. Lat. TRUE AZIMUTH. 16° ir 18° 19° 20° - 21° 22° 23° 24° 25° 26° 27° 28° 29° 30° h m h m h m h m h m • h m h m h m h m h m h m h m h m h m h m (I 4) (I 8) (1 12) (1 >6) (1 20) (1 24) (1 28) (I 32) (1 36) (I 40) (I 44) (1 48) (1 52) (1 56) (2 0) 0° 3-628 3'-420 3-236 3-072 2-924 2-790 2-669 2-559 2-459 2-366 2'-28l 2-203 2-130 2'-o63 2-000 I 3-629 3-421 3-237 3072 2-924 2-791 2-670 2-560 2 -459 2-367 2-282 2-203 2-130 2-063 2-000 2 3-630 3422 3-238 3-073 2-926 2-792 2-671 2-561 2-460 2-368 2-283 2-204 2-131 2-064 2-obi 3 3-633 3-425 3-241 3-076 2-928 2-794 2-673 2-563 2-462 2-369 2-284 2-206 2-133 2-065 2-003 4 3-637 3-429 3-244 3-079 2-931 2-797 2-676 2-566 2-465 2-372 2-287 2 208 2-135 2-068 2-005 S 3-642 3-433 3-248 3-083 2-935 2-801 2-680 2-569 2-468 2-375 2-290 2-211 2-138 2-071 2-008 6° 3-648 3-439 3-254 3-088 2-940 2-806 2-684 2-573 2-472 2-379 2-294 2-215 2-142 2-074. 2011 7 3 -65s 3-446 3-260 3-095 2-946 2 -81 1 2-690 2-579 2-477 2-384 2-298 2-219 2-146 2-078 2-015 8 3664 3-454 3-268 3-102 2-953 2-818 2-696 2-584 2-483 2-389 2-304 2-224 2-151 2-083 2 -020 9 3-673 3-463 3-376 3-110 2-960 2-825 2-703 2-591 2-489 2-396 2-310 2230 2157 2-088 2-025 10 3684 3-473 3-286 3-119 2-969 2-833 2-711 2-599 2-497 2-403 2-^16 2-237 2-163 2-094 2-031 11° 3-696 3-484 3-297 3-129 2-979 2-843 2-719 2-607 2-505 2-410 2-324 2-244 2-170 2-101 2-037 12 3-709 3-497 3-308 3-140 2-989 2-853 2-729 2-6i6 2-514 2-419 2-332 2-252 2-178 2-109 2-045 13 3-723 3-510 3-321 3-152 3-001 2-864 2-740 2-627 2-523 2-428 2-341 2-261 2-186 2-117 2-053 14 3-739 3-525 3-335 3-166 .3-013 2 '876 2-751' 2-638 2-534 2-439 2-351 2-270 2 -195 2-126 2-061 »S 3-756 3-541 3-350 3-180 3-027 2-889 2-764 2-650 2-545 2-450 2-362 2-280 2-205 2-135 2-071 i6° 3-774 3-558 3-366 3-195 3-042 2-903 2-777 2-662 2-558 2-462 2-373 2-291 2 -2 16 2-146 2-081 I? 3-7.94 3-577 3-384 3-212 3-057 2-918 2-791 2-676 2-571 . 2-474 2-385 2-303 2-227 2-157 2-091 i8 3-8iS 3-596 3-403 3.230 3-074 2-934 2-807 2691 2-585 2-488 2-399 2-316 2-240 2-169 2-103 19 3-837 3-617 3-423 3-249 3-092 2-951 2-823 2-707 2-600 2-503 2-413 2-330 2-253 2-182 2-115 20 3-861 3-640 3-444 3-269 3-111 2-970 2-841 2-724 2-616 2-518 2-428 2-344 2-267 2-195 3-128 21° 3-886 3-664 3-466 3-290 3-132 2-989 2-859 2-741 2-634 2-535 2-443 2-359 2-282 2-209 2-142 22 3-913 3-689 3-490 3-313 3-153 3-010 2-879 2-760 2-652 2-552 2-460 2-376 2-297 2-225 2-157 23 3-941 3-716 3-516 3-337 3-176 3-031 2 900 2-780 2-671 2-571 2-478 2-393 2-314 2-241 2-173 24 3-971 3-744 3-542 3-362 3-201 3-055 2-922 2 -802 2-691 2-590 2-497 2-411 2-332 2-258 2-189 25 4-003 3-774 3-571 3-389 3-226 3-079 2-945 2-824 2-713 2-611 2-517 2-430 2-350 2-276 2-207 26° 4-036 3-805 3-600 3-417 3-253 3-105 2-970 2-847 2-735 2-633 2-538 2-451 2-370 2-295 2-225 27 4-072 3-839 3-632 3-447 3-281 3-132- 2-996 2-872 2-759 2-656 2-560 2-472 2-391 2-315 2-245 28 4-169 3-874 3665 3-479 3-311 3-160 3-023 2-899 2-785 2-680 2-584 2-495 2-412 2-336 2-265 29 4-148 3 -91 1 3-700 3-512 3-343 3-190 3-052 2-926 2-8ii 2-705. 2-608 2-518 2-435 , 2-358 2-287 30 4-189 3-949 3-737 3-547 3-376 3-222 3-082 2-955 2-839 .. 2-732 2-634 2-543 2-460 2-382 2-309 31° 4-232 3-990 3-775 3-583 3 -41 1 3-255 3-114 2-986 2-868 2-760 2-661 2-570 2-485 2-406 2-333 32 4-278 4-033 3-816 3-622 3-448 3-290 3-148 3018 2--899 2-790 2-690 2-597 2-512 2-432 2-358 33 4-326 4-078 3-859 3-662 3-486 J -327 3-183 3-052- 2-932 2-821 2-720 2-626 2-540 2-459 2-385 34 3-376 4-126 3-903 3-705 3-527 3-366 3-220 3-087 2-966 ^IS* 2-752 2-657 2-569 2-488 2-412 35 4-429 4-175 3-951 3-750 3-569 3-406 3-259 3-124 3-001 2-889 2-785 2^689 2-600 2-518 2-442 36° 4-484 4-228 4-000 3-797 3614 3-449 3-300 3-163 3-039 2-925 2-820 2-723 2-633 2-550 2-472 37 4-543 4-283 4-052 3846 3-661 3-494 3-343 3-205 3-078 2-963 2-856 2-758 2-667 ^IH 2-504 38 4-604 4-340 4-107 3-898 3-710 3-541 3-388 3-248 3-120 3-003 2-895 2795 2-703 2-6i8 2-538 39 4-668 4-401 4-164 3-952 3-762 3-591 3-435 3-293 3-164 3-045 2-935 2-834 2-741 2-654 2-574 40 4-736 4-465 4-224 4-010 3-817 3-643 3-485 3-341 3-209 3-089 2-978 2-875 2-781 2-693 2-611 41° 4-807 4-532 4-288 4070 3-874 3-697 3-537 3-391 3-258 3-135 3-023 2-919 2-822 2-733 2-650 42 4-882 4-602 4-355 4-133 3-934 3-755 3-592 3-444 3-308 3-184 3-070 2-964 2-866 2-776 2-691 43 4-961 4-677 4-425 4-200 3-998 3815 3-650 3-499 3-362 3-235 3-119- 3-012 2-912 2-820 2-735 44 5-043 4-755 4-499 4270 4-065 3-879 3-711 3-558 3-418 3-289 3-171 3-062 2-961 2-867 2-780 45 5-131 4-837 4-576 4-344 4-135 3-946 3-775 3-619 3-477 3-346 3-226 3-115 3-012 2-917 2-828 46° 5-223 4-924 4-659 4-422 4-209 4-017 3-843 3-684 3-539 3-406 3-284 3-171 3-066 2-969 2-879 47 5-320 5-015 4-745 4-504 4-287 4-092 3-914 •3-753 3-605 3-470 3-345 3-230 3-123 3-024 2-933 48 5-422 5-112 4-836 4-590 4-370 4-170 3-989 3-825 3-674 3-536 3-409 3-292 3-183 3-083 2-989 49 5-530 5-213 .4-933 4-682 4-457 4-253 4-069 3-901 3-74S 3-607 3-477 3-357 3-247 3-144 3-049 SO 5-644 5-321 5-034 4-778 4-549 4-341 4-153 3-982 3-825 3-681 3-549 3-427 3-314 3-209 3-111 SI* 5-765 5-435 5-142 4-881 4-646 4-434 4-242 4-067 3-907 3-760 3-625 3-506 3-385 3-278 3-178 52 5-893 5-555 5-256 4-989 4-749 4-532 4-336 4-157 3-993 3-843 3-705 3'|l^ 3-460 3-350 3-249 S3 6-028 S-683 5-377 5-104 4-858 4-637 4-436 4-253 4-085 3-932 3-790 3-660 3-539 3-427 3-323 54 6-172 5-819 5-506 5-226 4-974 4-747 4-542 4-354 4"'fl 4-026 3-881 3-Z47 3-840 3-624 3-509 3-403 55 6-325 5-963 5-642 5 -355 5-097 4-865 4-654 4-462 4-286 4-125 3-977 3-714 3-596 3-487 S6° 6-488 6-117 5-787 5-493 5-229 4-990 4-774 4-577 4-397 4-231 '^'°li 3-939 3-809 3-689 3-577 6-661 6-280 5-942 5-640 ■5-368 5-123 4-901 4-699 4-514 4-345 4-188 4-044- 3-911 3-787 3-672 58 6-846 6-454 6-107 5-796 S-517 5-266 5-037 4-830 4-640 4-465 4 -30s 4-157 4-020 3-892 3^74 3-883 59 7-044 6-641 6-283 5-964 5-677 5-418 ' 5-183 4-969 4-774 4-594 4-429 4-277 4-136 4-005 60 7-256 6-841 6-472 6-143 5-848 5-581 5-339 5-119 4-917 4-732 4-562 4-405 4-260 4-125 4-006 61° 7-483 7-055 6-675 6-336 6-031 5-756 5-506 5-279 5 -071 4-881 4-705 4-543 4-394 4-255 4-125 62 7-728 7-285 6-893 6-543 6-228 5-944 5-686 5-451 5-237 .5-040 4-859 4-692 4-537 4-394 4-260 63 7-991 7-534 7-128 6-766 6-440 6-146 5-880 5-637 5-416 5-212 5-025 4-852 4-692 4-543 4-405 64 8-276 7-802 ■7-382 7-007 6-670 6-365 6-090 5-838 st°f 5-398 5-204 5 -025 4-859 4-705 4-562 65 8-584 8-093 7-657 7-268 6-918 6-603 6-316 6-056 5-818 5-599 5 -398 5-212 5-040 4-881 4-732 To convert into Time, Multiply by 4. Thus 7*256 x 4 This applies also to the quantities in Table C. 29-024. 63 Shewing the error produced in the Longitude by an error of 1' In the Altitude. Lat. TRUE AZIMUTH. 31° 32° 33° 34° 35° 36° 37° 38' 39° •40° 41° 42° 43° 44° 45° h m h m h m h m . h m h m h m h m h m ' h m h m h m h m h m h m (2 4) (2 8) (2 12) (2 16) (2 20) (2 24) (2 28) (2 32) (2 36) (2 40) (2 44) (2 48) (2 52) (2 56) (3 0) 0° i'942 i'887 1-836 1788 1743 1701 1-662 I '-624 1-589 1-556 i'-524 i'-494 1-466 i'-440 1-414 I 1-942 1-887 1-836 1-789 1-744 1-702 1-662 1-625 1-589 1-556 1-524 1-495 1-467 1-440 1-414 2 I '943 1-888 1-837 1-789 1-745 1-702 1-663 't^k 1-590 I -557 1-525 1-495 1-467 1-440 1-415 3 1-944 1-890 1-839 1-791 1-746 I 704 1-664 1626 1-5^1 I -558 1-526 1-497 1-468 1-442 I -416 4 1-946 1-892 I -841 1-793 1-748 1-705 1-666 1-628 1-593 1-560 1-528 1-498 1-470 1-443 I -418 5 1-949 1-894 1,-843 1-795 1750 1-708 1-668 1-630 1-595 1-562 1-530 1-500 1-472 1-445 1-420 6° 1-952 1-897 1-846 1-798 1753 1711 1-671 1-633 1-598 1-564 1-533 1-503 1-474 1-447 1-422 7 1-956 1-901 1-850 1-802 1-757 1714 1-674 1-636 1-601 1-567 1-536 1-506 1-477 1-450 1-425 8 I -961 1-906 1-854 1-806 1-761 1 718 1-678 1-640 1-605 I -57 1 1-539 1-509 I -481 1-454 1-428 9 1-966 1-911 1-859 rSii 1-765 1-723 1-682 1-645 1-609 1-575 1-543 1-513 1-485 1-458 1-432 10 J -972 I -916 1-864 i-Sifl 1770 1-728 1-687 1-649 1-614 1-580 1-548 1-518 1-489 1-462 1-436 11° 1-978 1-922 1-870 1-822 1-776 1-733 1-693 '■^|s 1 -&I9 1-585 1-553 1-522 1-494 1-467 1--441 12 1-985 1-929 1-877 1-828 1-782 1-739 1-699 1-661 1-625 1-590 1-558 1-528 1-499 1-472 1-446 13 I '993 1-937 1-884 1-835 1-789 1-746 1-705 1-667 1-631 1-597 1-564 1-534 I -505 1-477 I -451 14 2-001 I '945 1-892 1-843 1-797 1753 1713 'tl^ 1-638 1-603 I -571 1-540 I -51 1 1-484 1-458 IS 2-010 I -954 1-901 1-851 1-805 1-761 1-720 1-682 1-645 l-6ii 1-578 I -547 1-518 1-490 1-464 16° 2-020 1-963 I -910 1-860 1-814 1770 1729 1-690 1-653 I -618 1-586 1-555 1-525 1-498 1-471 17 2-030 1-973 1-920 1-870 1-823 1-779 1-738 1-698 1-662 1-627 1-594 1-563 1-533 1-505 1-479 18 2-042 1-984 1-931 1-880 1-833 1-789 1-747 1-708 1-671 1-636 1-603 1-571 1-542 1-514 1-487 19 2-053 1-996 1-942 1-891 1-844 1-799 1757 1-718 1-681 1-645 1.-6 1 2 1-581 1-551 1-523 1-496 20 2-066 2-008 1-954 1-903 1-855 I -810 1-768 1 729 1-691 1-656 1-622 1-590 1-560 1-532 1-505 21° 2 -080 2-021 1-967 1-916 1-867 1-822 1-780 1-740 1-702- 1-666 1-633 i-6oi 1-571 1-542 1-515 22 2-094 2-035 1-980 1-929 I -880 1-835 1-792 1752 1714 1-678 1-644 1-612 1-581 1-S53. 1-525 23 2-109 2 050 1-995 1-943 1-894 1-848 1-805 1-765 1726 1-690 1-656 1-624 1-593 1-564 1-536 24 2-125 2 -066 2-OI0 1-958 1-908 1-862 1-819 1778 1-739 1-703 1-669 1-636 1-605 ''Ht 1-548 2S 2-142 2-082 2-026 1-973 1-924 1-877 1-833 1-792 1753 1717 1-682 1-649 1-618 1-588 1-560 26° 2-160 2-100 2-043 1-990 1-940 1-893 1-849 1-807 1-768 1-731 1-696 1-663 1-631 1-602 i'-573 27 2-179 2-ii8 2-o6i 2-007 1-957 1-909 1-865 1-823 1-783 1-746 1711 1-677 1-646 1-616 1-587 28 2-199 2-137 2-079 2-025 1-975 1-927 1-882 1-840 i-8oo 1-762 1726 1-693 1-661 1-630 1-602 29 2-220 2-158 2-099 2-04S 1-993 1-945 1-900 ■157 1-817 1-779 1-743 1-709 1-676 1-646 1-617 30 2-242 2-179 2-120 2-065 2013 1:964 I -919 1-876 1-835 1-796 1-760 1-726 1-693 1-662 1-633 31° 2-265 2-202 2-142 2-086 2-034 1-985 1-939 1-895 1-854 1-815 1-778 1-744 1 711 1-679 1-650 32 2-289 2-225 2-165 2-109 2-056 2 -006 1-959 I -915 1-874 1-834 1-797 1-762 1-729 1-697 1-668 33 2-315 2-250 2-189 2-132 2-079 2-029 1-981 1-937 1-895 1-855 1-817 1-782 1-748 1-716 1-686 34 2342 2-276 2-215 2-157 2-103 2-052 2-004 1-959 1-917 1-877 1-839 1-803 1769 1736 1-706 3S 2-370 2-304 2-241 2-183 2-128 2-077 2-028 1-983 1-940 1-899 1-861 1-824 1-790 1757 1726 36° 2-400 2-333 2-270 2-210 2-155 2-103 2-054 2-008 1-964 1-923 1-884 1-847 I -812 1-779 1-748 37 2-431 2363 2-299 2-239 • 2-183 2-130 2-081 2-034 1-990 1-948 1-909 I -871 1-836 1-803 1-771 38 2-464 2-395 2-330 2-269 2-212 2-159 2-109 2 -061 2-016 1-974 1-934 1-897 1-861 1-827 1-795 39 2-498 2-428 2363 2-301 2-243 2-189 2-138 2-090 2-045 2-002 1-961 1-923 1-887 1-852 1-820 40 •2-S3S 2-463 2-397 2-334 ' 2-276 2-221 2-169 2-120 2-074 2-031 1-990 1-951 1-914 1-879 1-846 41° 2-573 2-500 2-433 2-370 2-310 2-254 2-202 2-152 2-105 2-o6i 2-020 1-980 1-943 1-907 1-874 42 2-613 2-539 2-471 2-406 2-346 2-289 2-236 2-186 2-138 2-093 2-051 2-011 1-973 1-937 1-903 43 2-655 2-580 2-511 2-445 2384 2-326 2-272 2-221 2-173 2-127 2084 2-043 2-005 1-968 1-934 44 2-699 2-623 2-552 . 2-486 2-424 2-365 2-310 2258 2-209 2-163 2-119 2078 2-038 2-001 1-966 45 2-746 2-669 2-597 2-529 2-466 2-406 2-350 2-297 2-247 2-200 2156 2-114 2-074 2-036 2"000 4$° 2-795 2-717 2-643 2-574 2-510 2-449 2-392 2-338 2-287 2-240 2-194 2-151 2-111 2-072 2-036 '*^ 2-847 2-767 2-692 2-622 2-556 2-495 2-436 2-382 2330 2-281 2-235 2-191 2-150 2-111 2-074 48 2-902 2-820 2744 2-673 2606 2-543 2-483 2-427 2-375 2-325 2-278 2-233 2-191 2-151 2-II4 49 2-959 2-876 2-799 2-726 2657 2-593 2-533 2-476 2-422 2-371 2-323 2-278 2-235 2-194 2-156 30 3-021 2-936 2-856 2782 2712 2-647 2 -58s 2527 2-472 ,2-420 2-371 2-325 2-281 2-240 2-200 Si° 3-085 2-999 2-918 2-842 2770 2-703 2-640 2-581 2-525 2472 2-422 2-375 2-330 ~ 2-287 2-247 52 3-154 3-065 2-982 2-905 2-832 2-763 2-699 2-638 2-581 2527 2-476 2-427 2-382 2-338 2-297 S3 3-226 3-136 3-051 2-971 2897 2827 2-761 2-699 2-640 2-585 2-533 2-483 2-436 2-392 2-350 S4 3-303 3-210 3-124 3-042 2-966 2-894 2-827 2-763 2-703 2-647 2-593 2-543 2-495 2-449 2-406 S5 3-385 3-290 3-201 3-118 3-040 2-966 2897 2-832 2770 2-712 2-657 2-606 2-556 2-510 2-466 S6° 3-472 3-375 3-283 3-198 3-118 3-042 2-971 2-905 2-842 2-782 2-726 2-673 2-622 2-574 2-529 S7 3 -565 3-465 3,-371 3-283 3-201 3-124 3-051 2-982 2-918 2-856 , 2-799 2-744 2-692 2-643 2-597 58 3-664 3-561 3-465 3-375 3290 3-210 3-136 3-065 2-999 2-936 2-876 2-820 2-767 2717 2-669 ^ 3-770 3-664 3-565 3-472 3385 3-303 3-226 3-154 3-085 3-021 2-959 2-902 2-847 2-795 2-746 60 3-883 3-774 3-672 3-577 3-487 3-403 3-323 3-249 3-178 3-111 3-049 2-989 2-933 2-879 2-828 61° 62 64 6S 4-005 3-892 3787 3-689 3-596 3-509 3-427 3-350 3-278 3-209 3-144 3-083 3-024 2-969 2-917 4-136 4-020 3-911 3-809 3714 3-624 3-539 3-460 3-385 3-314 3-247 3-183 3-123 3-066 3-012 4-277 4-157 4-044 3-939 3-840 3747 3-660 3-578 3-500 3-427 3-357 3-292 3-230 3-171 3-iiS 4-429 4-305 4-r88 4-079 3-977 3-881 3-790 3-705 3-625 3-549 3 477 3-409 3-345 3284 3-226 4-594 4-465 4-345 4-231 4-125 4-026 3-932 3-843 3-760 3-681 3-607 3-536 3-470 3-406 3-346 To convert into Time, Multiply by 4. Thus 3-883 x 4 = 15-532. This applies also to the quantities in Table C. D 64 Shewing the erpoi? produced in the Longitude by an error of 1' in the Altitude. Lat, - TRUE AZIMUTH. 46° 47° 48° 49° 50° 51° 52° 53° 54° 55° 56° 57° 58° 59° 60° h m h m h m h m h m li m h m h m h m h m h m h m h m h m b m (3 4) (3 8) (3 -2) (3 "6) (3 20) (3 24) (3 28) ■ (3 32) (3 36) (3 40) 13 44) (3 48) (352) (356) (4 0) 0° 1-390 1-367 1-346 1-325 1-305 i'-287 1-269 , 1-252 1-236 1-221 1-206 1-192 1-179 i'i67 I-I55 I 1-390 1-368 1-346 1-325 1-306 1-287 1-269 1-252 1-236 1-221 1-206 1-193 1-179 1-167 I-15S 2 1-391 1-368 1-346 1-326 1-306 1-288 1-270 1-253 1-237 1-222 1-207 1-193 1-180 1 167 i-'5S 3 1-392 1-369 1-347 1-327 1-307 1-289 1-271 1-254 1-238 1-222 1-208 1-194 1-181 1-168 1-156 4 1-394 I -37 1 1-349 1-328 1-309 I 290 1-272 1-255 1-239 1-224 1-209 1-195 1-182 1-169 I -158 5 I '395 1-373 I -35 1 1-330 1-310 1-292 1-274 1-257 1-241 1-225 1-211 1-197 1-184 1-171 1-159 6° 1-398 1-375 1-353 1-332 1-313 1-294 I 276 1-259 1-243 1-227 1-213 1-199 1-186 I -173 i'i6i 7 I -401 1-378 1-356 1-335 1-315 1-296 1-279 1-262 1-245 1-230 1-215 1-201 1-188 1-175 1-163 8 1-404 1-381 1-359 1-338 1-318 1-299 1-281 1-264 1-248 1-233 1-218 1-204 1-191 1-178 1-166 9 1-407 1-384 1-362 1-342 1-322 1-303 V285 1-268 1-251 1-236 1-221 1-207 1-194 1-181 1-169 10 I -412 1-388 1-366 1-345 I -326 ' 1-307 1-289 1-271 1-255 . 1 -240 1-225 1-211 1-197 1-185 1-173 , 11° 1-416 1-393 1-371 1-350 1-330 1-311 1-293 1-276 1-259 1-244 1-229 1-215 1-201 1-188 1-176 12 I -42 1 1-398 1-376 1--3SS 1-335 1-316 1-297 1-280 1-264 1-248 1-233 1-219 I -206 I -193 i-i8o 13 1-427 1-403 1-381 1-360 1-340 1-321 1-302 1-285 1-269 1-253 1-238 1224 1-210 1-197 1-185. 14 1-433 1-409 1-387 1-366 1-345 1-326 1-308 1-290 1-274 1-258 1-243 1-229 1-215 1-202 I -190 IS 1-439 1-416 1-393 1-372 1-351 1-332 I -314 1-296 1 -280 1-264 1-249 1-234 I -22 1 1-208 1-195 i6° 1-446 1-422 1-400 1-378 1-358 1-339 1-320 1-303 1-286 1-270 1-255 1-240 1-227 1-214 I -201 17 i-4S4 1-430 1-407 1-386 1-365 1-346 1-327 1-309 1-293 1-277 1-261 1-247 1-233 1-220 1-207 18 1-462 1-438 1-415 1-393 1-373 1-353 1-334 1-317 1-300 1-284 1-268 1-254 1-240 1-227 1-214 19 1-470 1-446 1-423 1-401 1-381 1-361 1-342 1-324 1-307 1-291 1-276 1-261 1-247 - 1-234 I -221 20 1-479 I-4SS 1-432 I -410 1-389 1-369 1-350 1-332 1-315 1-299 1-284 1-269 1-255 1-242 1-229 21° 1489 1-465 1-441 1-419 1-398 1-378 1-359 1-341 1-324 1-308 1-292 1-277 1-263 1-250 1-237 22 1-499 1-475 1-451 1-429 1-408 1-388 1-369 1-350 1-333 1-317 1-301 1-286 1-272 ''■''1? 1-245 23 1-510 1-485 1-462 1-439 1-418 1-398 1-379 1-360 1-343 1-326 I -310 1-295 1-281 1-267 1-254 24 1-522 1-497 1-473 1-450 1-429 1-409 1-389 1-371 1-353 1-336 1-320 1-305 1-291 1-277 1-264 25 I-S34 1-509 1-485 1-462 1-440 1-420 1-400 1-382 1-364 1-347 1-331 1-316 1-301 1-287 . 1-274 26° I "547 1-521 1-497 1-474 1-452 1-432 1-412 1-393 1-375 1-358 1-342 1-327 - 1-312 1-298 1-285 27 1-560 I -535 1-510 1-487 1-465 1-444 1-424 1-405 1-387 1-370 1-354 1-338 1-323 1-309 1-296 28 1-574 1-549 1-524 1-501 1-478 1-4S7 1-437 I -418 1-400 1-383 1-366 1-350 1-336 1-321 1-308 29 1-589 1-563 1-539 1-515 1-493 1-471 1-451 1-432 1-413 1-396 1-379 1-363 1-348 1-334 1-320 30 1-605 1-579 1-554 1-530 1-507 1-486 1-465 1-446 1-427 1-410 1-393 1-377 1-362 1-347 1-333 31° 1-622 ■ 1-595 1-570. 1-546 1-523 1-501 1-480 1-461 1-442 1-424 1-407 1-391 1-376 1-361 1-347 32 1-639 1-612 1-587 1-562 1-539 1-517 1-496 1-476 1-458 1-440 1-422 1-406 1-390 1-376 1-362 33 1-658 1-630 1-604 1-580 1-557 1-534 1-513 1-493 1-474 1-456 1-438 1-422 1-406 1-391 1-377 34 1-677 1-649 1-623 1-598 i'57S 1-552 1-531 1-510 r-491 1-473 1-455 1-438 1-422 1-407 1-393 35 1697 1-669 1-643 1-618 1-594 1-571 1-549 1-529 i'509 1-490 1-473 1-456 1-440 1-424 1-410 36° 1-718 1-690 ' 1-663 1-638 i.-6i4 1-591 1-569 1-548 1-528 1-509 1-491 1-474 1-458. 1-442 1-427 1-741 I -712 1-685 1-659 1-635 1-611 1-589 1-568 1-548 1-529 1-510 1-493 1-476- 1-461 1-446 38 1-764 1-735 1-708 1-681 1-657 1-633 1-610 1-589 1-569 1-549 1-531 1-513 1-496 1-480 1-465 39 1-789 1-759 1-732 1-705 1680 1-656 1-633 1-611 1-591 1-571 1-552 1-534 1-517 1-501 1-486 40 1-815 1-785 1-757 1-730 1-704 i-68o 1-657 1-635 1-614 1-5941 1-575 1-557 1-539 1-523 1-507 41° 1-84Z 1-812 1-783 1-756 i-730 1-705 1-681 1-659 1-638 1-618 1-598 1-580 1-562 1-546 1-530 42 1-871 1-840 I -81 1 1-783 1-757 1-732 1-708 1-685 '•663 1-643 1-623 1-604 1-587 1-570 I -554 ■ 43 1-901 1-870 1840 l-8l2 1-785 1-759 1735 1-712 1-690 1-669 1-649 1-630 1-612 I -595 1-579 44 1-933 1-901 1-871 1-842 I -815 1-789 1-764 1-741' 1-718 1-697 1-677 1-658 1-639 1-622 1-605 45 1-966 1-934 1-903 1-874 1-846 1-820 1-795 1-771 1-748 1-726 1-706 1-686 1-668 1650 1-633 46° 2-001 1-968 1-937 1-907 1-879 1-852 1-827 1-803 1-779 1-757 1-736 1-716 1-697 1-679 1-662 % 2-038 2-005 1-973 1-943 1-914 1-887 1-861 1836 1-812 1-790 1-769 1-748 1-729 1-711 1-693 2-078 2-043 2-011 1-980 1-951 1-923 1-897 1-871 1-847 1-824 1-803 1782 1-762 1-744 1-726 49 2-119 2-084 2-051 2-020 1-990 1-961 1-934 1-909 1-884 1-861 1-839 1-817 1-797 1-778 1-760 50 2-163 2-127 2-093 2-061 2-031 2 002 1-974 1-948 1-923 1-899 1-877 1-855 1-834 1-815 1-796 51° 2-209 2-173 2-138 2-105 2-074 2-045 2-016 1-990 • 1-964 1-940 1-917 1-895 1-874 1-854 '1H 52 2-258 2-221 2-186 2*152 2-120 2-090 2-061 2-034 2-008 1983 1-959 1-937 1-915 1-895 1-876 53 2-310 2-272 2 236 2-202 2-169 2-138 z-109 2-081 2-054 2-028 2-004 1-981 1-959 J -939 1-919 54 2-365 2-326 2-289 2-254 2-221 2-189 2-159 2 -130 2-103 2-077 2 052 2-029 2 -006 1-985 1-964 55 2-424 2-384 2-346 2-310 2-276 2-243 2-212 2-183 2-IS5 2-128 2-103 2-079 2-056 2-034 2-013 56° 2-486 2-445 2-406 2-370 2-334 2-301 2-269 2-239 2-210 2-183 2157 2-132 2-109 2-086 , 2-065 2-552 2-511 2-471 2-433 2-397 2-363 2-330 2-299 2-270 2-241 2-215 2-189 2-165 2-142 2-120 58 2-621 2-580 2-539 2-500 2-463 2 -428 2-395 2-363 2-333 2-304 2-276 2-250 2-225 2-202 2-179 59 2-699 2-655 2-613 2-573 2-535 2-498 Z--464 2-431 2-400 2-370 2-342 2-315 2-289 2-265 2-242 gs 2-780 2 -735 2-691 2-650 2-611 2-574 2-538 2-504 2-472 2-442 2-412 2-385 2-358 2-333 2-309 6i° 2-867 2-961 3-062 3-171 3-289 2-820 2-776 2-733 2-693 2-654 2-618 2-583 2-550 2-518 2-488 - 2-459 2-432 2-406 2-382 62 2-912 3-012 3-119 3-235 2-866 2-822 2-781 2-741 2-703 2667 2633 2-600 2-569 'Tl 2-512 2-485 2-460 63 2-964 2-919 2-875 2-834 2-795 2-758 2-723 2-689 2657 2-626 2-597 ''Il°r IJi^, 65 3-070 3-184 3-023 3-135 2-978 3-089 2-935 3-045 2-895 3-003 2-856 2-963 2-820 2-925 2-785 2-889 2-752 2-854 2-720 2-821 •2-690 2-790 2 -66 1 2-760 2-634 2-732 To convert into Time, Multiply by 4. Thus 2-780 x 4 = 11-120. This applies also to the quantities in Table C. 65 D Shewing the error produced in the Longitude by an error of I' in the Altitude. Lat. TRUE AZIMUTH. 61° 62° 63° 64° 65° 66° 67° 68° 69° 70° 71° 72° 73° 74° 75° h m h in h in h m h m h m li m h m li m h m h m h m h m h m h in (44) (48) (4 12) (4 16) (420) (4 24) (4 28) (4 32) (4 36) (4 40) (4 44) (448) (4 52) (4 56) (5 0) 0° i'i43 1-133 1-122 I-II3 1-103 1-095 i'o86 1-079 1-071 1-064 i'o58 1-051 1-046 1 1-040 1-035 I I -144 1133 1-122 1113 1 104 1-095 1 -087 1-079 1-071 1-064 1-058 1-052 1-046 1-040 1-035 2 1-144 I-I33 1-123 1-113 I -104 I -095 1 087 1 079 1-072 1-065 1-058 1-052 1-046 I -041 1-036 3 I -145 I -134 1-124 I-I14 I -105 • 1-096 1-088 1-080 1-073 1-066 1-059 1-053 1-047 1-042 1-037 4 1-146 I -135 I-12S i-iiS rio6 1-097 1-089 1-081 1-074 1-067 1-060 1-054 1-048 1-043 1-038 5 I ■148 1-137 I 127 I-II7 I -108 1-099 1-091 1-083 1-075 1-068 1-062 1-05S 1-050 1-044 1-039 6° I '150 1-139 I-I29 1-119 1-J09 I-IOI 1-092 1-084 1-077 1-070 1-063 1-057 1-051 1-046 1-041 I 1-152 I -141 I-I3I 1-121 1-112 1-103 1-095 1-087 1-079 1-072 1-066 1-059 1-054 1-048 1-043 8 I -155 I -144 1-133 1-124 1-114 1-105 1-097 1-089 1-082 1-075 i-o68 1-062 1-056 1-051 1-045 9 1-158 1-147 I -136 1-126 1-117 1-108 l-IOO I -092, 1-084 1-077 1-071 1-065 1-059 1-053 1-048 10 1-161 1-150 I -140 1-130 I -120 1-112 1-103 I -095" 1-088 1-081 1-074 1-068 1-062 1-056 1-051 11° 1-165 1-154 I -143 1-133 I -124 i-iiS I -107 1-099 1-091 1-084 1-077 1-071 1-065 1-060 1-055 12 1-169 1-158 1-147 I -137 1-128 I-II9 l-Ill 1-103 1-095 I -088 i-o8i 1-075 1-069 1-064 1-058 ■ 13 I -173 I -162 1-152 1-142 1-132 1123 1-115 1-107 1-099 1-092 1-085 1-079 1-073 1-068 1-063 M I -178 1-167 1-157. 1-147 1-137 1-128 1-120 1-112 1-104 1-097 1-090 1-084 I -078 1-072 1-067 IS I -184 1-173 I -162 1-152 1-142 I-I33 ■ 1-125 1-117 1-109 1-102 1-095 1-089 1-083 1-077 1-072 i6- I -189 1-178 I -168 I-I57 1-148 1-139 1-130 1-122 1-114 1-107 I -100 1-094 1-088 1-082 1-077 11 1-196 1-184 1-174 I -163 1-154 1-145 I -136 1-128. 1-120 1-113 1-106 I -100 1-093 1-088 1-083 I -202 I -191 I -180 1-170 I -160 1-151 1-142 1-134 I -126 I -119 1-112 1-106 I -100 1-094 1-089 19 1-209 1-198 I -187 1-177 1-167 1-158 1-149 1-141 1-133 I-12S 1-119 1-112 1-106 I -100 1-095 20 I -217 1-205 1-194 I -184 1-174 1-165 1-156 I -148 1-140 1-132 1-125 1-119 1-113 1-107 1-102 21° I -225 1-213 1-202 1-192 1-182 1-173 1-164 I-IS5 1-147 1-140 1-133 I -126 1-120 1-114 1-109 22 1-233 1-222 I-2IO 1-200 I -190 . 1-181 1-172 1:163 i-iSS I -148 1-141 I -134 1-128 I -122 1-117 23 1-242 ' I -230 1-219 1-209 1-199 1-189 i-i8o 1-172 1-164 1-56 1-149 I -142 1-136 1-130 1-125 24 I -252 1-240 1-229 1-218 1-208 I -198 1-189 1-181 1-173 I-165 1-158 1-151 1-145 1-139 1-133 25 1-262 1-250 1-238 1-228 1-217 1-208 1-199 1-190 I -182 1-174 1-167 1-160 1-154 1-148 1-142 26° 1-272 1-260 1-249- 1-238 1-228 1-218 1-209 1-200 1-192 1-184 1-177 1-170 1-163 1-157 1-152 7s r-283 I -27 1 1-260 1-249, 1-238 1-229 1-219 1-210 1-202 1-194 1-187 1-180 1-174 I -168 I -162 1-295 1-283 I -271 1-260 1-250 i-240 1-230 1-222 1-213 1-205 1-198 1-191 1-184 1-178 1-173 29 1-307 1-295 1-283 1-272 1-262 1-252 1-242 1-233 1-225 1-217 1-209 1-202 1-196 1-189 I -184 30 1-320 1-308 1-296 1-285 1-274 1-264 1-254 1-245 1-237 1-229 I -221 1-214 1-207 1-201 1-195 31° 1-334 1-348 I 363 I -321 1-309 1-298 1-287 1-277 1-267 1 -258 1-250 1-242 1-234 I. -227 I -220 T-2I4 1-208 32 1-336 i-3?3 1-312 1-301 1-291 I -281 1-272 1-263 1-255 1-247 1-240 1-233 1-227 1-221 33 1-350 1-338 1327 1-316 1-305 1-295 1-286 1-277 1-269 1-261 1-254 1-247 1-240 1-234 34 1-379 1-366 1-354 1-342 I -331 1-320 1-310 1-301 1-292 1284 1-276 1-268 1-261 1-255 1-249 35 1-396 1-383 1-370 1-358 1-347 1336 ■ 1 326 1-317 1-308 1-299 1-291 i-?8,I 1-277 1-270 1 264 36° 39 40 1-413 1-400 1-387 1-375 1-364 1-353 1-343 1-333 1-324 1-315. 1-307 1-300 1-293 1-286 1-280 1-432 I -418 1-405 1-393 1-382 1-371 1-360 1-350 1-341 1 332 1-324 1-317 1-309 1-303 1-296 I "45 1 1-437 1-424 1-412 1-400 1-389 1-379 '■3^g 1-359 1-350 1-342 1-334 1-327- 1-320 1-314 1-471 1-457 1-444 1432 1-420 1-409 1-398 1-388 1-378 1-369 1-361 1-353 1-346 I -339 l-^^2 1-493 1-478 1-465 1-452 1-440 1-429 I -418 1-408 1-398 1-389 1-381 1-373 1-365 JJ7 1-358 1-351 41° , 43 43 44 45 1-515 1-539 1-563 1-589 I -617 1-501 1-524 1-549 1-S74 1-602 1-487 1-510 I -535 1-560 1-587 1-474 1-497 1-521 1-547 1-573 1-462 1-485 1-509 1-534 1-560 1-450 1-473 1-497 1 -522 1-548 1-439 1-462 1-485 I -510 1-536 1-429 1-451 1-475 1-499 1-525 1-419 1-441 1-465 1-489 1-515 1-410* 1-432 I -455 1-479 1-505 1-401 1-423 1-446 1-470 1-496 1-393 1-415 1-438 1-462 1-487 1-386 1-407 1-430 1-454 1-479 t-378 1-400 1-422 1-446 I -471 1-372 1-393 1-416 1-439 1-464 46° 49 50 1-646 1-676 1709 1743 1-779 1-630 I -661 1-693 1-726 1-762 1-616 1-646 1-677 I -71 1 1-746 1-602 1 631 1-663 1-696 1-731 1-588 1-618 1-649 1-682 1-717 1-576 1-605 1-636 1-669 1-703 1-564 1-593 1-624 1-656 1-690 1-553 1-581 I -612 1-644 1-678 1-542 1-571 1-601 1-633 1-666 1-532 1-560 1-590 1-622 1-656 1-523 1-551 1-581 1-612 1-645 1-514 1-542 1-636 1-505 1-533 1-563 1-594 1-627 1-498 1-525 1-555 1-586 i'6i8 1-490 1-518 1-547 1-578 I 611 51° 52 53 54 55 I -817 1-857 I '900 I '945 1-993 i-8oo 1-840 1-882 1-927 I "975 1-783 1-823 1-865 1-909 1-957 1-768 1-807 1-849 1-893 1-940 I-7S3 1-792 1-833 1-877 1-924 1-739 1-778 1-819 1862 1-908 1-726 1-765 i-'8o5 1-848 1-894 1-714 1-752 1-792 1-702 1-740 1-780 1-822 1-867 1 691 1-729 1768 I 810 I -855 1-681 I -718 1-757 1-799 1-844 1-671 1-708 1-747 1-789 1-833 1-662 1-698 1-738 1-779 1-823 1-653 1-690 1-729 1-770 I -814 1-645 1-682 1-720 I -761 1-805 56° i 2-045 2-099 2-158 2- 220 2287 2-025 2-079 2-137 2-199 2 '265 2*007 2-o6i 2-118 2-179 2-245 1-990 2-043 2-100 2 -160 2-225 1-973 2-026 2-082 2-142 2 '207 1-958 2-010 2-066 2-125 2-189 1-943 1-995 2-050 2-109 2-173 1-929 1-980 2-035 2-094 2-157 1-916 1-967 2-021 2-080 2-142 1903 1-954 2-008 2 -066 2-128 1-891 1-942 1-996 2053 2-115 1-880 I -931 1-984 2-042 2-103 1-870 1-920 1-973 2-030 2-091 1-860 I -910 1-963 2-020 2-081 1-851 1-901 1-954 2-010 2-071 61° 62 6s 2-358 2-435 2-518 2 -608 2-705 2-336 2-412 2-495 2-584 •2-680 .« 2-315 2-391 2-472 2-5|pO 2-656 2-295 2-370 2-451 2-538 2-633 2-276 2-350 2-430 2-517 2 -611 2-258 2-332 2 -41 1 2-497 2-590 2-241 2-314 2-393 2-478 2-571 2-225 2-297 2-376 2-460 2-552 , 2-209 2-282 2-359 2-443 2-535 2-195 2-267 2-344 2-428 2-518 2-182 2253 2330 2-413 2-503 2-169 2-240 2-316 2-399 2-488 2-157 2-227 2-303 2-385 2-474 2 146 2-216 2-291 2-373 2-462 2-13S 2-205 2-280 2-362 2 -450 To convert into Time, Multiply by 4. Thus 2-287 x 4 = 9'l48. This applies also to the quantities in Table C. 66 Shewing the eFPor produced in the Longitude by an error of 1' in the Altitude. TRUE AZIMUTH. • Lax. 76° 77° 78° 79° 80° 81° 82° 83° 84° 85° 86° 87° 88° 89° 90° b m h m h m h III h m h m h m h m h m h m h m h m h m h m h m (S4) (5 8) (5 12) (5 16) (5 20) (5 24) (5 28} (5 32) (5 36) (5 40) (5 44) (5 48) (5 52) (5 56) (60) 0° 1-031 1-026 1-022 1-019 1-015 1-012 i-oio i-008 1-006 1-004 1-002 i-ooi l-OOI 1-000 I -000 I 1-031 1-026 1-022 1-019 1-016 1-OJ3 i-oio 1-008 1-006 1-004 1-003 1-002 I-OOI 1-000 I -000 2 1-031 1-027 1-023 1-019 I -016 10! J I -010 1-008 1-006 1-004 1-003 1-002 l-OOI l-OOI i-ooi 3 1-032 1-028 1-024 1-020 1-017 -1-014 I -oil 1-009 1-007 1-005 1-004 1-003 1-002 1-002 1-001 4 5 1-033 1-029 1025 i-o?i 1-018 1-015 I -01 2 l-OIO 1-008 1-006 1-005 1-004 1003 1-003 1-002 I -03s 1-030 1-026 1-023 1-019 I -016 I'0I4 lOlI 1-009 I -008 1-006 1-005 1-004 1-004 1-004 6° 1-036 1-032 1-028 1-024 I -02 1 I -018 1-015 I 013 I -oil 1-009 i-oo8 1-007 I -006 1-006- i-oo6 I 1-038 1-034 1-030 1-026 1-023 I -020 I -017 1-015 I -013 roll 1010 I -009 I -008 I -008 1-008 1-041 1036 1-032 1029 1-025 1-022 1-020 1-017 1-015 I -014 I -012 ' l-OII l-OIO I-OIO 1-010 9 10 1-043 1-039 1-035 1-031 1-028 1-025 1-022 1-020 1-018 1016 1-015 I -014 1-013 1-013 I -012 1-047 1-042 1038 1034 1-031 1-028 1-025 1-023 I -021 1-019 I -018 I -017 1-016 I -016 I -015 11° 1-050 1-046 1-041 1-038 1-034 1-031 1-029 1-026 1-024 1-023 I -021 1-020 1-019 1-019 I -019 12 1-054 1-049 1-045 1-041 1-038 1-035 1-032 1-030 1-028 1-026 1-025 1-024 1-023 1-022 1-022 13 14 IS 1058 1-053 1-049 1 -046 ^ 1-042 1-039 1-036 1-034 1032 1-030 1-029 1-028 1-027 1-026 1-026 1-062 1-058 1-054 1-050 1-047 1-043 1-041 1-038 1-036 1-035 1-033 1-032 1-031 1-031 1-031 1-067 1-063 1-058 1-055 1-051 1-048 1-045 1-043 1-041 1-039 1-038 1-037 1-036 1-035 1035 i6° 1-072 1-068 1-064 1-060 1-056 I -053 1-051 1-048 1-046 1-044 1-043 1-042 1-041 1-040 1-040 11 1-078 1-073 1-069 1-065 1-062 1-059 1-056 1-054 I -051 1-050 1-048 1-047 1-046 . 1 -046 1-046 1-084 1-079 1-075 1-071 i-o68 1-065 1-062 1-059 1-057 1-055 1-054 1-053 1-052 1 -052 1-051 1-058 19 20 1-090 1 085 1-081 1-077 1-074 1-071 1-068 1-066 1-063 1-062 i'o6o I -059 I -058- 1-058 1-097 1-092 1-088 1-084 1-081 1-077 1-075 1-072 1-070 1-068 1-067 1-066 1-065 1-064 1-064 21° 1-104 1-099 1-095 1-091 1-088 1-084 1-082 1-079 1-077 1-075 1-074 1-073 1-072 I -07 1 I -07 1 22 I-1I2 I -107 1-103 1-099 1-095 1-092 1-089 1-087 1-084 1-083 1-081 1-080 1-079 1-079 I -087 1-079 1 -086 23 24 25 I -120 1-115 1-111 1-107 I 103 i-ioo 1-097 1-095 1-092 i-ogi 1-089 1-088 1-087 I-I28 1-123 1-119 1-115 1112 1108 1-105 1-103 l-IOI 1-099 1-097 1-096 1-095 1-095 1-095 I -137 1-132 1-128 1-124 1-120 1-117 1-114 1-112 I -109 I -108 1-106 * 1-105 1-104 1-104 1-103 26° 1-147 1-142 1-137 I -133 1-130 1-126 I -124 1-I2I 1-119 1-117 1-115 1-114 I-II3 1-II3 1-113 1-157 I 167 1-152 1-162 1-147 1-158 1-143 1-154 1-140 1-150 1-136 1-147 I-I33 I -144 I-I3I I-I4I 1-129 1-139 1-127 1-137 1-125 1-135 1-124 1-134 1-123 1-133 1-122 '■133 1 -122 1-133 29 30 1-178 1-173 1-185 1-169 1-165 1-161 1-158 1-155 1-152 1-150 I -148 1-146 1-145 I -144 1-144 i->43 1-190 1-180 1-176 1-173 I -169 1-166 1-163 I -161 1-159 1-158 1-156 1-155 ■•155 1-155 31° 32 33 - 34 35 1-202 1-215 1-229 1-243 1-258 1-197 I -210 1-193 1206 1-188 1-201 1-185 1-197 i-i8i 1-194 1-178 1-191 I-I75 1-188 I-I73 I-I86 1-171 1-184 1-169 I -182 1-168 1-181 1-167 1-180 V167 1-179 1-167 1-179 1-224 1-238 I -253 1-219 1-233 1-248 1-215 1-229 1-244 1-21 1 1-225 1-240 1-207 1-221 1-236 1-204 1-218 1-233 1-201 1-215 1-230 1-199 I -213 1-227 1-197 1-211 1-225 1-195 1-209 1-224 1-194 1-208 1-222 ,1-193 1-207 1-222 1-193 1-206 1-221 1-192 1-206 1 -221 36° 39 40 1-274 1-290 1-308 1-326 I -345 1-269 1-285 1-302 1-321 1-340 1-264 1-280 1-297 1-316 1-335 1-259 1-276 1-593 1-311 1330 1-255 1-271 1-289 1-307 1-326 1-251 1-268 1-285 1-303 1-322 1-248 1-264 1-281 1-299 1-318 1-245 1-262 1-279 1-296 1-31S 1-243 1-259 1-276 1-294 1-313 1-241 1-257- 1-274 1-292 1-310 1-239 1-255 1-272 1-290 1-309 1-238 1254 1-271 1-289 1-307 1-237 1-253 1-270 I 288 1-306 1-236 1-252 1-269 1-287 1-306 1-236 1-252 1-269 1-287 1-305 41° 42 43 44 45 1-366 1-387 1-409 1-433 1-458 1-360 1-381 1-403 1-427 1-451 1-355 1-376 1-398 1-421 1-446 1-350 1-371 1-393 I -416 1-441 1-388 1-412 1-436 1-342 1-362 1-384 1-407 1-432 _ 1-338 1-359 1-381 1-404 1-428 1-335 1-356 1-378 1-401 1-425 1-332 1-353 1-375 1-398 1-422 1-330 1-351 1-373 1-395 1-420 1-328 -1-349 1-371 1-394 I -418 1-327 1-347 1-369 1392 1-416 1-326 1-346 1-368 1-391 I -415 1-325 1-346 1-368 1-390 1-414 I -325 1-346 1-367 1-390 1-414 46° 49 50 1-484 1-511 1-540 I -571 1-603 1-477 1-505 1-534 1-564 1-597 1-472 1-499 1-528 1-558 1-590 1-467 1-494 1-522 '•553 1-585 1-462 1-489 1-518 1-548 1-580 i'-458 1-485 1-513 1-543 1-575 1-454 1-481 1-509 1-539 1-571 1450 1-477 1-506 1-536 1-567 1-447 1-474 1-503 1-533 1-564 1-445 1-472 1-500 1-530 1-562 1-443 1-470 1-498 1-528 1-560 1-442 1-468 1-497 1-526 1-558 1-440 1-467 1-495 1-525 1-557 1-440 1-467 1-495 1-524 1-556 1-440 1-466 1-494 1-524 1-556 51° 52 53 54 55 1-638 1-674 I -713 I-7S3 1-797 1-631 1-667 1-705 1-746 1-789 1-625 1-661 1-699 1-739 1-782 1-619 1-655 1-693 1-733 1-776 1-614 1-649 1-687 1-728 1-770 1-609 1-645 1-682 1-723 1-765 1-605 1-640 1-678 1-718 1-761 1-601 1-636 1-674 1-714 I -757 1-598 1-633 I -67 1 1-711 1-753 1-595 1-630 1-668 1-708 1-750 I -593 1-628 1-666 1-705 1-748 1-591 1-626 1-664 1-704 1-746 1-590 1625 1-663 1-702 I -745 1-589 1-625 1-662 1-702 1-744 1-589 1-624 1-662 1-701 1-743 56° 1-843 1-892 1-945 1-835 1-884 1-937 1-828 1-877 1-929 1-985 2-045 1-822 1-870 1-922 1-978 2-037 I -816 1864 1-916 1-972 2-031 I -811 1-859 1-911 1-966 2-025 i-8o6 1-854 1-906 1-961 1-802 1-850 1-901 1-956 1-798 1-846 1-897 1-952 1-795 1-843 1-894 1-949 1-793 1-841 1-892 1-946 1-791 1-839 1-890 1-944 1-789 1837 1-888 1-943 1-789 1-836 1-887 1-942 1-788 1-836 1-887 1-942 i 2-OOI 2'06l 1-993 2-053 2 "020 2 -01 5 2-011 2-008 2-005 2-003 2-001 2-000 2-000 ^ 2094 2-163 2-088 2-083 2-078 2-074 2-071 2-068 2-065 2-064 2-063 2-063 61° 2-126 2-117 2-109 2-IOI , 2-157 2-230 2-310 2-396 2-151 2-224 2-304 2-389 2-146' 2-219 2-298 2-142 •2-138 2-135 2-133 2-131 2-130 2-130 62 2-I9S 2-186 2-178 2-170 2-215 2-211 2-208 2 -206 2-204 2-203 2-203 63 2-270 2-261 2-252 2-244 2-237 2-316 2-403 2-294 2-290 2-287 2-284 2-283. 2-282 2-281 § 2-351 2-439 2-341 2-428 2-332 2-419 2-324 2-410 2-384 2-379 2-375 2-372 2-369 2-368 2-367 2-366 To convert into Time, Multiply by 4. Thus 2-061 x 4 This applies also to the quantities in Table c. 8-244. LIST OF 54 SELECTED STARS. (67) THE MEAN PLACES Mag. 2-4 Var. 2*1 2 "2 I"0 2-2 2'0 2-7 1-9 I'O 0-2 0-3 1-9 1-9 2 7 Var. 0-4 2*0 -1-4 i"S 2-0 o-s !•! 2-0 2-S '•4 2-S 2'0 2*2 i4 17 1 "2 2"0 I '2 17 O'O 2*1 2 7 2-4 I'l 2*2 2"I 2-2 2-4 2"I 0-2 2-3 I'O 2"I «-s 2-4 1-9 I '3 2-6 54 SELECTED NAVIGATIONAL STARS (In Order of Right Ascension) FOR JANUARY I^t A.D. 190O. Names of Stars. a Phcenicis SCHEDAR. a Cassiopeia Dbneb-Kaitos. /3 Ceti . Mirach MlZAR. /3 An.iromeda ACHERNAR. o Eridani . Almach. 7 ' Andromeda Hamel. u Arietis . MenkaR. a Ceti . MiRFACK. a Persei . Aldebaran. a Tauri . Capella. o Auriga RiGEL. /3 Orionis . Bellatrix. 7 Orionis Nath. jS Tauri . Phact. a Co'uviba . BetELGUESE. a Orionis Canopus. a ArgAs . Alhena. 7 Geminorum SlRlUS. o Canis Majoris Adara. f Canis Majoris Castor, o^ Geminorum , Procyon. u Canis Minoris Pollux. § Geminorum . ^ ArgAs TuREis. I Argus Rkgulus. a Leonis Algeiba. 7' Leonis DoBHE. o Ursa Majoris Denbbola. /3 Leonis , a ' Crucis /3 Crucis . Spica. a Virginis Bknetnasch. j) Ursa Majoris P Centauri . S Centauri Arcturus. a Bootis Kochab. (i Ursa Minoris KlFFA Boreams. /3 Libra . Ai.phacca. o Corona Antares. a Scorpii a Irianguii Australis e Scorpii Ras Alhague. a Ophituhi Etanin. 7 Draconis . Kaus Australis. e Sagittarii Vbga. a Lyra a Sagittarii Altair. a Aquila a. Pavonis Arided. o Cygni Enif. £ Pegasi .... a Gruis , Fomalhaut. a Piscis Australis Markab. u. Pegasi Right Ascension. H. O o o I I H. S. 21 20 34 50 38 34 4 8 33 59 1 57 45 2 I 32 2 S7 3 3 17 II 30 II 9 18 9 44 19 46 5 19 SS 5 36 2 5 49 45 621 44 6 3' Sfi 6 40 44 6 54 42 7 28 13 7 34 4 7 39 12 9126 9 14 25 10 3 3 10 14 28 10 57 34 11 43 58 12 21 2 12 41 52 13 19 55 13 43 36 13 56 46 14 o 48 14 II 6 14 SI o 15 II 37 15 30 27 16 23 16 16 38 4 17 30 8 17 30 17 17 54 17 18 17 32 18 33 33 18 49 4 «9 45 54 20 17 44 20 38 I 21 39 16 22 I 56 22 52 7 22 59 47 Annual Change. s. + 2-97 + 3-38 + 3-01 + 3-35 + 2-24 + 3-66 + 3-37 + 3-I3 + 4*26 + 3 '44 + 4"43 + 2-88 + 3 '22 + 379 + 2-i8 +3-25 + i"33 + 3*47 + 2-64 + 2-36 + 3-83 + 3'«4 + 3-68 + 0-67 + i'6o + 3-20 + 3"3i + 374 + 3-06 + 3-30 + t47 + 3-15 + 2-37 + 4-19 + 3-52 + 273 -0'22 + 3-22 + 2-54 +3-67 +6-31 +4-31 +278 + i"39 + 3-98 + 2-03 + 372 + 2-93 + 477 + 2-04 + 2-95 + 3-80 + 3 '32 + 2-98 Declination. 42 50 57 S. 55 59 19 N. 18 32 8 S. 35 S 26 N. 57 44 41 S. 41 51 o N. 22 59 23 N. 3 41 5' N- 49 30 19 N. 16 18 30 N. 45 S3 47 N. 8 19 I S. 6 IS 32 N. 28 34 7 52 31 23 N. 7 38 S. 23 19 N. 38 28 S. 16 29 S N. 16 34 46 S. 28 50 9 S. 32 6 29 N. S 28 54 N. 28 16 4 N. 69 18 19 S. 58 5" '9 S. 12 27 i22 N. 20 20 50 N. 62 17 27 N. 15 7 52 N. 62 32 41 S. 59 8 31 S. 10 38 22 S. 49 48 44 N. 59 53 26 S. 35 52 40 S- 19 42 II N. 74 33 SI N- 9 o 51 S. 27 3 4 N. 26 12 36 S. 68 50 39 S. 42 56 3 S. 12 37 58 N. 51 30 2 N. 34 25 55 S. 38 41 26 N. 26 25 15 S. 8 36 14 N. 57 3 20 S. 44 55 22 N. 9 24 59 N. 47 26 43 S. 30 9 8 S. 14 40 2 N. Annual Change. - 19 '54 + 1978 - i9"8o + i9"i9 - 18-32 + 17-41 + 17-16 + 14-29 + 13-04 7-47 3*97 4-37 3 49 3-30 2*07 0"92 1-90 2-82 475 473 7'6i - 9-03 - 8-46 + 14-85 + 14-98 - 17-48 -i8-io - 19-38 -20"I0 + 20 "02 + '975 + 18-86 - 18-05 + 17-55 + 17-83 - 1883 -14-74 + 13-46 - 12-27 + 8-24 + 7-10 + 2-60 - 2-81 - 0-53 - 1-39 + 3-22 - 4-21 + 9-33 - 1 1 -24 + 12-76 + 16-40 -17-30 - 19-02 + 19-33 Note. — In this Table + means Add, and - means Subtract. (68) THE MEAN PLACES OF 54 SELECTED NAVIGATIONAL STARS (In Order of Declination) FOR JANUARY ISt a.D. 19OO. Mag. Names op Stars. Declination. 27 o-s 1-9 Var. 0-3 I"0 27 2-4 1*2 1 "4 2*2 2-6 2-2 I'O 2-0 -1-4 2"I O'O 2-S 2'0 IT 2-3 2-4 I"l 1-9 •■5 ••3 2*0 27 2T 2'2 17 0"2 2 "2 2-4 2T 1-5 0-2 1-9 19 2*0 2-4 0-4 Var. 2*1 I'O 2-S 17 I "2 2-0 • •s 2-2 2'0 2T Menkar. a Ce/j Procyon. u, Crf«K Minoris . BelI-ATRIX. 7 Ononis . Betelguese. a Orionis RiGEL. j3 Orionis . Altair. a Aquila Kiffa Boreai.is. )3 Zjfovz Enif. e Pegasi Spica. a Virginis Regulus. a Leonis Ras Alhague. u. Ophitichi Markab. a Pegasi Denebola. ^ Leonis Aldebaran. a Tauri . Alhena. 7 Geminonim SIRIUS. a Ca«/.r Majoris Deneb-Kaitos. /S Ceti Arcturus. a Bootis Algeiba. 7' Leonis Hamel. u, Arietis Antares. i» Scarpa IT Sagittarii , Ai.PHACCA. a Corona Pollux, p Geminonim. Nath. /3 Tauri AnARA. f Ca«« Majoris roMAl.llAUT. o Piscis Australis Castor, a- Geminonim Pi I ACT. u Co'uvibie . Kaus Australis. e Sagittarii MiRACH Mizar. ^ Andromeda e Centauri , Vega, a /^>'?« Almach. 7 ' AndfomeJa , a Phoinicis — Scarpa Arided. o Cygni . Capella. o Auriga . a Gruis . MiRFACK. o Persei Benetnasch. jj Ursa Majoris Etanin. 7 Drcuon'S . Canopus. a Argds . SCHEDAR. o Cassiopeia o Pavonis Achernar. a Eridani . TUREIS. « Argus |3 Crtuis. j3 Centauri DUBHB. o Ursa Majoris a ' Cruets a Triangu'.i Australis ;3 ArgAs . Kochab. /S Ursa Minoris , 41 5' N. 28 54 N. IS 32 N. 23 19 N. 8 19 8 36 14 N. 9 o SI S. 9 24 S9 N. 10 38 22 S. 12 27 22 N. 12 37 s8 N. 14 40 2 N. 15 7 52 N. 16 18 30 N. 16 29 5 N. 16 34 46 S. 18 32 8 S. 19 42 II N. 20 20 so N. 22 59 23 N. 26 12 36 S. 26 25 IS s. 27 3 4 N. 28 16 4 N. 28 31 23 N. 28 so 9 S. 30 9 8 S. 32 6 29 N. 34 7 38 S. 34 2S S5 S. 35 S 26 N. 35 52 40 S. 38 41 26 N. 41 S' o N. 42 50 57 S. 42 S6 3 •'^• 44 55 22 N. 45 53 47 N. 47 26 43 -S. 49 30 19 N. 49 48 44 N. 51 30 2 N. 52 38 28 S, 55 59 '9 N. 57 3 20 S. 57 44 41 S. 58 SI 19 s. 59 8 31 S. 59 S3 26 S. 62 17 27 N. 62 32 41 S. 68 so 39 S. 69 18 19 S. 74 33 5« N. Annual Change. + 14-29 - 9 '03 + 3 '49 + 0-92 - 4'37 + 9 "33 + 13-46 + 16-40 + 18-86 -17-48 - 2-81 + 19-33 - 20-10 + 7-47 - 2-82 + 475 - 19-80 -18-83 -18-10 + 17-16 + 8-24 - 4-21 - 12-27 - 8-46 + 3 '30 -t- 473 - 19-02 - 7-61 - 2-07 - i'39 + 19-19 + 17-83 + 3'22 + 17-41 -1954 + 2 -60 + 12-76 + 3*97 - i7'30 + 13-04 - iS-os - o"53 + 1-90 + 1978 -n-24 -18-32 + 14-98 -H975 + «7-55 - 19-38 + 20-02 + 7-10 + 14-85 -14-74 Right AsCENStON: 2 57 3 7 34 4 s 19 46 5 49 45 5 9 44 19 45 54 15 " 37 21 39 16 13 "9 55 10 3 3 17 30 17 22 59 47 11 43 58 4 30 II 6 31 56 6 40 44 o 38 34 14 II 6 10 14 28 2 I 32 16 23 16 18 49 4 15 30 27 7 39 12 5 19 58 6 54 42 22 52 7 7 28 13 5 36 2 18 17 32 I 4 8 14 o 48 18 33 33 I 57 45 021 20 17 30 8 20 38 I 5 9 18 22 I 56 3 17 II 13 43 36 17 54 17 621 44 34 50 20 17 44 1 33 59 9 14 25 12 41 52 13 56 46 10 57 34 12 21 2 16 38 4 9126 14 51 o Annual Change. s. + 3-13 + 3-14 + 3-22 •<-3-25 + 2-S8 + 2-93 + 3-22 + 2-95 + 3-15 + 3-20 + 2-78 + 2-98 + 3-06 + 3-44 + 3-47 + 2-64 + 3-01 + 2-73 + 3-31 + 3-37 + 367 + 372 + 2-54 + 3-68 + 3-79 + 2-36 + 3-32 + 3-83 + 2-18 + 3-98 + 3-35 + 3-52 + 2-03 + 3-66 + 2-97 + 4-31 + 2-04 + 4-43 + 3;8o + 4-26 +2-37 + 1-39 + 1-33 +3-38 + 477 + 2-24 + i-6o + 3-47 + 4-19 + 374 + 3-30 + 6-31 + 0-67 -0-22 NcxTE.— In this Table + means Add, and - means Subtract. (69) AUXILIARY STAR LIST. MEAN PLACES OF 38 NAVIGATIONAL STARS OF MAGNITUDE NOT LESS THAN 28, AND OF DECLINATION NOT EXCEEDING 65° Though the special Table B* does not include these stars, they nevertheless come within the range of the ordinary Table B, as will be seen by the examples on opposite page. Where interpolation is necessary it can be done at sight. Thus nearly loo stars are at the disposal of the navigator. This is better than one Sun or one Moon. EPOCH 1900, Mag. 2-| 2-4 2-3 2-6 Var. 27 27 1-8 2-2 2'I 2-0 19 27 2-4 2-S 2'I 2 "2 2-S 2"0 2-6 2-6 2"0 2-8 2-4 1-8 2-6 2-S 2-6 27 2 5 2-2 2-6 17 2-6 2-3 2-6 2-8 2-2 Var. Names of Stars. a ANDROMBD..G [Alpheratz] P CASSIOPEIiG {Ca/i&) y CASSIOPEIiE . Eridani ;8 Persei (A/ffoi) 1 AURIGiG a Leporis (Artub) . e Orionis (Alnilam) K Orio.nis /3 AURlG/1! (Menkalinan) j8 Canis Major. (Mirzam i Canis Major. . n- Arg^s . ij Canis Majoris t ARGfis . f AKGi^s S ArgAs . X Argus a HYDRiE (A^pkard) /3 UaSiE Major. (Merak) 7 Urs.« Major. (Pkecda) y Crucis ;8 CORVI . 7 Centauri . e Urs^ Major. (Aiioth) t Centauri . ij Centauri « Lupi . a Serpentis {Unukalkai) S SCORPII e SCORPII . IJ Ophiuchi . x scorpii . k scorpii 7 Cygni . a Cbphei (Alderamiri^ a TOUCANI /3 Gruis. j3 Pegasi (Scheat) Right Ascension. s. «3 5° 40 28 3 I 39 4 50 29 5 28 19 S 31 8 5 43 I 5 52 12 6 18 18 7 4 19 7 «3 37 7 20 8 804 8 20 28 8 41 57 9 4 19 9 22 40 10 ss 48 11 48 34 12 25 37 12 29 8 12 36 o 12 49 38 '3 33 33 14 29 9 >4 35 «7 15 39 20 15 54 25 16 43 41 17 4 38 17 26 49 >7 35 34 20 18 38 21 16 12 22 II 39 22 36 42 22 58 55 Annual Change. + 3-09 + 3-18 + 3-59 + 2-27 + 3-89 + 3 "90 + 2-64 + 3-04 + 2-84 + 4-40 + 2-64 + 2-44 + 2-I2 + 2-37 + 2-II + 1-24 + 1-66 + 2 "20 + 2-95 +3-65 +3-17 + 3 '30 + 3'i4 + 3-29 + 2-65 + 378 + 379 + 3 "97 + 2-95 + 3VS4 + 3-88 + 3*44 + 4-07 + 4'iS + 2-15 + ••43 + 4-15 + 3-60 + 2-90 Declination. 28 32 58 35 60 10 40 42 40 34 33 o «7 53 I 15 9 42 44 56 >7 54 26 14 iZ N. 53 N. 30 N. 19 S. 14 N. 29 N. 38 S. 57 S. 19 S. 14 N. 36 55 4 S. 29 6 28 S. 39 43 «6 S. 59 II IS S. 54 20 32 S. 43 I 44 S. 8 13 30 S. 56 55 7 N. 54 '5 3 N. 56 33 12 S. 22 50 38 S. 48 24 38 S. 56 30 9 N. 52 57 28 S. 4« 43 6 S. 46 57 32 S. 6 44 24 N. 22 20 14 S, 34 6 42 S. IS 36 5 S. 37 I SI S, 38 58 42 S. 39 56 12 N. 62 9 42 N. 60 45 30 S. 47 24 28 S. 27 32 25 N. Annual Change. + 19'90 + 19-86 + 19-55 - 14'55 + 14-08 + 5-98 - 2-77 - 2-52 1-49 0-67 I -60 S-56 6-32 6-86 9 "99 + ii'5i + 13-12 + 14 "43 + 15-46 - 19-22 - 20-02 + 20-21 + 19-94 + 19-81 - 19 60 + 18-42 + 15-96 + 15-64 -11-49 + 10-47 + 6-82 + 4-70 + 2-94 + 2-|6 + 1 1 -42 + 15-17 -17-81 - 18-69 + 19-48 Note.— In this Table + means Add, and - means Subtract, When the star places are taken '^rom this Table anterior to 1900, the application of the signs must of course be reversed, GENERAL UTILITY TABLES. 70 Examples shewing how the Stars in the Auxiliahy List can be utilised for any desired purpose. Example 1. What is the error produced in the Longitude for each 1' of error in the Latitude worked with when the Hour-angle of # X Scorpii is 3h. 32m. p.m., the Latitude of the observer being 49° S., and the star's Declination 37'' S. ? A + 0'-867 (page 19). B - -944 (page 20). - 0''077 Error in the Longitude. X 4 0''308 Error in the Hour-angle. The error being so very small, shews that « X Scorpii must be near the Prime Vertical. Let us test this. Enter O with Latitude 49" in "Margin," and "Error" - O'-0'77 in body of the Table. The corresponding Azimuth is S. 87° W. Reference to Table D (p^ge 66) shews that for each 1' of error in the Altitude the error in the Longitude would be 1''526, and 6°104 in the Hour-angle. Example 2. What is the error produced in the Longitude for each 1' of error in the Latitude when the Hour-anofle of e Gentauri is 2h. 20m. A.M., the Latitude of the observer being 36° S., and the star's Declination 53° S. ? A + 1"038 (page 13). B - 2 -314 (page 14). - 1''276 Error in the Longitude. X 4 5''104 Error in the Hour-angle, To find the Azimuth. Enter C with Latitude 36° in " Margin," and " Error " - l'-276 in body of the Table. The corresponding Azimuth is S. 44° E. Table D (page 68) shews that for each 1' of error in the Altitude the error in the Longi- tude would be l'-779, and 7°116 in the Hour-angle. Example 3, What is the error produced in the Longitude for each 1' of error in the Latitude when the Hour-angle of Alphard (a Hydrce) is 2h. 56m. p.m., the Latitude of the observer being 10° N., and the star's Declination 8^° S. ? A + 0'-183 (page 15). B + 0-208 (page 16). + 0''391 Error in the Longitude. ^ 4 + l''564 Error in the Hour-angle. Enter O with Latitude 10° in " Margin," and " Error " -i- 0'-391 in body of the Table. The corresponding Azimuth is S. 69° W. Table D (page 65) shews that for each 1' of error in the Altitude the error in the Longitude would be l'-088, and 4°-352 in the Hour-angle. Note -No reference is made to the value of the Tables in connection with Johnson's "Double Chronometer" problem, nor to Sumner's method, because these subjects are fully dealt with in "Wrinkles." (71) ADDENDUM. NOTE ON GREAT CIRCLE SAILING. To further elucidate matters it may not come amiss to direct the student's attention to an interesting feature — omitted on page xv. — regarding the position of Vertex. It is this, that when the Latitude of the place of Departure is the same as the Latitude of Destination, things are much simplified. For example : — 1. The Meridian of Vertex is equal to the middle Longitude. 2. The distance of Vertex from either place is exactly the same. 3. The Initial and Final courses have the same angular value. Taking Example 6 on pages xiv. and xv., and assuming Formosa to be in 23° N., the same as 0. San Lucas, we quickly obtain the following results : — 1. Meridian of Vertex = 174° 30' W. 2. The True Distance between terminal points being 6,742 miles, Vertex would be 3,371 miles from both, or just half-way. 3. The Initial course at C. San Lucas would be N, 60° 41' W., and the Final course at Formosa would be S. 50° 41' W, The Latitude of Vertex would be 44° 35' N. Such a case is very unlikely to occur in sea practice, but all the same it helps the learner to master the Mysteries and pick up the Principles ; and this is what is wanted. FINIS. (72) E F G ALT-AZIMUTH TABLES. Whereas the A B C tables serve to determine the Azimuth by means of the How-Angle, the E F G tables effect the same purpose by substituting the Altitude. The two sets of Tables are so very much alike in principle that anyone familiar with the Time-Azimuth process will be quite at home when using the present Tables. The application of the sign for each Table is given at foot of every page, so that no effort of memory is needed. To ascertain the Azimuth by this method is exceedingly simple, and involves a knowledge of only three things, namely. Latitude of the observer, with Altitude and Declination of the body observed. No more than two openings of the Tables are required, so the method is also expeditious in a high degree. RULES. 1st opening. Table E. Under the Altitude and abreast the Latitude take out the corresponding number and prefix the sign according to instructions at foot of page. Same opening. Table F. Under the Altitude and abreast the Declination take out the corresponding number and prefix the sign according to instructions. Find the algebraic sum of these two numbers : — that is to say, if the numbers have different signs take their difference and prefix the sign of the greater ; but if the numbers have like signs add them together and prefix the common sign : call this the " Azimuth Number." 2nd opening. Table G. Abreast of Latitude in margin look for the "Azimuth number," and over it in the head- line will be found the Azimuth. Latitude 5° N. Altitude 2° E Declination 3° S, '] Example I. Alt. 2° and Lat. 5° + -0030E Alt. 2° and Declin. 3° + -0524F "Azimuth Number" + -0554 G In Table G, abreast Lat. 5°, and over -0554 is the Azm. S. 86J° E. Latitude 45° S. ' Altitude 22° W. Declination 65° S. Example II. Alt. 22° and Lat. 45° -'2857 E Alt. 22° and Declin. 65° + -9775 F 'Azimuth Number" -|-'6918 G In Table G, abreast Lat. 45°, and over -6918 is the Azm. S. 12° W. Example III. In Lat. 51° N. the Altitude of * Dubhe in the " Plough " was 25° W. of meridian. Declin. 62° N. + ■3624 E — •9742 F - -6118 G = Azm. N. 13j° W. Example IV. In Lat. 54° N. the Altitude of * Gapella was 16° E. of Meridian. Declin. 46° N. + •2320 E -•7483 F - ^5163 G = Azim. N. 28^° E. Example V. In Lat. 46° S. the Altitude of /S Gentawi was 20° W. of meridian. Declin. 60° S. - -2618 E + ■9216 F + •6598 G = Azim. S. ]8j° W. Example VI. Nearing the North Cape, Norway, Lat. 65° N. Alt. of Moon 6° W. of meridian. Declin. 28° N. + •0953 E — ^4721 F - ^3768 G = Azim. N. 27° W. To enable the foregoing examples to be verified by the -A B Time- Azimuth Tables, the Hour- Angles are subjoined. Ex. I., h^ 50" 54= Ex. II., 10" 11" 58« Ex. III., 10" 12"' 32» Ex. IV., 9" U" 26« Ex. V., 9" 35"' 57' Ex. VL, 9" 57"" 20' The first page of Table G is coloured red as a warning, since Alt- Azimuths mar the meridian cannot give good results owing to the motion in altitude at such times being usually very slow. Time- Azimuths are then preferable {see p. xxxvi.). jj 73 ALT-AZIMUTH TABLES. Under Altitude In head-line, and abreast of Latitude in marg-in, take out the tabular quantity and mark it + or according' as the Latitude is N. or S. TRUE ALTITUDE, Lat. 0" I 2 3 4 S 6° I 9 10 11° 12 ^? IS i6° 17 i8 19 20 21° 22 23 24 25 26° 28 29 30 31° 32 33 34 35 36° 32 38 39 40 41° 42 43 44 45 46° 42 48 49 SO 51° 52 53 54 55 56° 57 58 60 61° 62 65 0° 10 •0000 •0000 •CXXX) •0000 •0000 •0000 •0000 ■0000 •0000 •0000 •0000 •0000 •cooo •0000 ■cooo •0000 0000 •0000 •0000 •0000 •0000 •0000 •0000 ■0000 0000 0000 "OOOO •0000 ■0000 0000 0000 •0000 •0000 "OOOO •0000 •OOOO •OOOO •OOOO ■OOOO •OOOO •OOOO •OOOO •OOOO •OOOO •OOOO OOOO OOOO "OOOO •OOOO •OOOO •OOOO •OOOO •OOOO •OOOO •OOOO •OOOO OOOO •OOOO •OOOO OOOO •OOOO •OOOO •OOOO •OOOO •OOOO •OOOO •OOOO •OOOO •0001 ■0002 •0002 0003 •0003 ■0004 •0004 ■000s •0005 •0006 •ooo5 •0007 •0007 •0008 •0008 •0009 •0009 0009 •0010 0010 •001 1 •001 1 •0012 •0012 •0013 •0013 •0014 •0014 •0015 •ooij •0015 •0016 •0016 •0017 •0017 ■0018 •0018 ■0018 ■0019 ■0019 ■0019 ■0020 ■0020 ■0021 ■0021 0021 ■0022 ■0022 ■0022 •0023 •0023 ■0023 ■0024 '0024 •0024 'Q024 •0025 •0025 •002s ■0025 •0026 ■0026 ■0026 0026 10 20 •OOOO •0001 •0002 •0003 •0004 •0005 ■0006 •0007 •0008 •OC09 •0010 •001 1 •0012 •0013 .0014 •0015 •0016 •0017 •0018 ■0019 •0020 •0021 0022 •0023 •0024 •0025 0026 ■0026 •0027 •0028 •0029 •0030 •0031 •0032 ■0033 •0033 •0034 ■003s ■0036 •0037 ■0037 0038 ■0039 •0040 •C040 •0041 •0042 ■0043 ■0043 •0044 •0045 •004S ■0046 •0046 •0047 •0048 •0048 •0049 0049 ■0050 ■0050 0051 •0051 •005a •0052 •0053 30 20 •OOOO •0002 •0003 •0005 •0006 •0008 0009 ■001 1 ■0012 ■0014 •0015 •0017 ■0018 •0020 002 1 •0023 •0024 ■0026 ■0027 ■0028 •0030 •0031 •0033 •0034 ■003s •0037 ■0038 ■0040 ■0041 ■0042 •0044 •004s •0046 •0048 •0049 ■0050 •0051 ■OOS3 ■0054 •ooss •0056 •0057 ■0058 •0060 ■0061 •0062 •0063 •0064 •0065 ■ •0066 '0067 ■0068 •0069 •0070 ■0071 ■0071 •0072 •0073 •0074 •0075 ■0076 •0076 •0077 •0078 ■0078 ■0079 40 •OOOO ■0002 •C004 ■0006 ■0008 •0010 •0012 •0014 ■0016 •0018 ■0020 •0022 •0024 •0026 •0028 •0030 •0032 •0034 •0036 •0038 •0040 ■0042 0044 ■004s •0047 •0049 •0051 ■0053 •ooss •0056 •0058 •0060 ■0062 ■0063 •006s •0067 •0068 0070 ■0072 •0073 •007s •0076 •0078 •0079 •0081 •0082 •0084 0085 ■0086 •0088 •0089 •oogo •0092 ■0093 •0094 •009s •0096 ■0098 •0099 •0100 •oioi •0102 •0103 ■0104 'oios •oios 30 40 50 •OOOO •0003 •ooos •0008 •0010 •0013 •oois •0018 ■0025 •0028 •0030 •0033 •003s •0038 •0040 •0043 ■004S •0047 •0050 •0OS2 •00S4 •0057 ■OOS9 •0061 0064 •0066 •0068 •0071 •0073 •007s •0077 •0079 •008 1 ■0083 •008s •0088 ■0090 •0092 •0093 •009s •0097 •0099 ■OIOI •0103 •OIOS •oio5 •0108 •Olio •01 1 1 •01 13 ■01 IS ■01 16 •01x8 •01 19 •0I2I •0122 •0123 •01 2S •0126 •0127 •0128 ■0130 ■0I3I •0132 50 •OOOO •0003 ■0006 •0009 •0012 •OOIS •0018 •0021 •0024 •0027 0030 •0033 ■0036 •0039 •0042 ■004s •0048 •0051 •00S4 ■00S7 ■0060 •0063 •0065 •0068 •0071 •0074 •0077 0079 •0082 •0085 •0087 •0090 ■0092 •009s •0098 0100 ■0103 OIOS •0107 •QUO 0II2 ■01 IS •01 17 •01 19 •0I2I •0123 •0126 •0128 •0130 •0132 •0134 ■0136 •0138 •0139 •0I4I ■0143 •0145 •0146 •0148 •0150 •01 SI •0IS3 •0IS4 •0156 •0IS7 •01 s8 10 •OOOO •0004 •0007 •001 1 •0014 •0018 •0021 •0025 •0028 •0032 •003s •0039 •0042 •0046 •0049 •0053 •0056 ■0060 ■0063 •0066 •0070 ■0073 ■0076 •0080 ■0083 ■0086 •0089 •0092 •0096 •0099 ■0102 •OIOS •0108 •on I ■01 14 •01 17 •0120 0123 0125 •0128 •0I3I ■0134 •0136 •0139 •0I4I •0144 ■0146 •0149 •0151 •0154 ■0156 •0158 •0160 •0163 ■0165 •0167 ■0169 ■0I7I •0173 •0I7S •0176 •0178 •0180 ■0I8I •0183 ■0185 20 •OOOO ■0004 •0008 •0012 •0016 •0020 0024 •0028 ■0032 ■0036 •0040 •0044 •0048 ■0052 ■0056 •0060 •0064 •0068 •0072 •0076 •0080 ■0083 ■0087 ■0091 ■0095 •0098 ■0102 •0106 •0109 •0II3 •01 16 •0120 •0123 •0127 •0130 •0134 •0137 ■0140 ■0143 ■0146 •0150 •0153 ■0156 ■0159 ■0162 ■0165 ■0167 ■0170 ■0173 •0176 ■0178 •oi8i •0183 •0186 •0188 ■0I9I ■0193 •0195 •0197 •0200 •0202 •0204 •0206 ■0207 •0209 •021 1 30 10 20 •OOOO •0005 •0009 0014 •0018 ■0023 •0027 •C032 •0036 ■0041 •004s ■0050 •0054 ■OOS9 ■0063 ■0068 •0072 •0077 •0081 •0085 •0090 •0094 •0098 •01 02 •0107 01 II •0115 •011.9 •0123 •0127 •0I3I ■013s ■0139 •0143 •0146 •0150 ■0IS4 •0158 •0I6I •0165 •0168 •0172 •017s •0179 •0182 ■0185 •0188 •0192 •0195 •0198 ■0201 ■0204 •0206 •0209 •0212 •0215 •0217 •0220 •0222 •0224 •0227 •0229 •0231 ■0233 •0235 •0237 40 30 •OOOO ■0005 •0010 ■0015 0020 ■0025 ■0030 ■0035 •0040 •0046 •0051 •0056 •0060 0065 •0070 •0075 •0080 •0085 ■0090 •0095 •0100 •0104 •0169 •01 14 •0II8 •0123 0128 •0132 •0137 •0I4I ■0145 0150 ■0154 •0158 •0163 •0167 •0I7I •0175 ■0179 •0183 •0187 •0I9I •0195 •0198 ■0202 •0206 •0209 •0213 •0216 •0220 •0223 •0226 0229 •0232 •023s •0238 ■0241 •0244 •0247 •0249 •0252 ■0254 •0257 •0259 •0262 •0264 50 "OOOO •0006 •001 1 •0017 •0022 ■0028 •0033 •0039 •0045 •0050 •0056 ■0061 •0067 ■0072 •0077 •0083 •0088 •0094 •0099 •0104 ■0109 ■0115 ■0120 •0125 •0130 ■0135 •0140 ■014s ■0150 ■015s •0160 ■0165 ■0170 •0174 ■0179 •0184 •0188 ■0193 ■0197 ■0201 ■0206 •0210 ■0214 ■0218 ■0222 •0226 0230 ■0234 ■0238 0242 ■0245 ■0249 ■0252 ■0256 •0259 •0262 •0265 ■0268 ■0271 •0274 ■0277 •0280 •0283 •0285 •0288 •0290 40 50 •OOOO •0006 •0012 ■0018 •0024 •0030 •0037 ■0043 •0049 •OOSS •0061 •0067 •0073 •0079 •0084 0090 •0096 •0102 ■0108 •01 14 •01 19 ■0125 •0I3I •0136 ■0142 •0148 •0153 •0159 ■0164 ■0169 •OI7S •0180 ■0185 ■0190 ■019s •0200 •0205 •0210 •0215 •0220 •0224 0229 •0234 •0238 •0243 •0247 ■0251 •0255 ■0260 •0264 •0268 10 •0305 •0308 •03 1 1 •0314 ■0316 •OOOO •0007 •0013 •0020 •0026 •0033 •0040 •0046 •0053 ■0059 •0066 •0072 •0079 •0085 •0092 •0098 •0104 •01 1 1 •01 1 7 •0123 •0129 •0136 •0142 •0148 ■0154 ■0160 •0166 •0172 •0178 •0183 •0189 •0195 ■0200 •0206 •0212 •0217 •0222 •0228 •0233 •0238 •0243 •0248 •0253 •0258 •0263 ■0268 •0272 ■0277 •0281 •0286 •0290 0271 027s •0294 •0298 0279 0283 0286 •0302 ■0306 •0310 •0290 •0314 0293 0296 •0317 •0321 0299 0302 ■0324 •0328 •0331 •0334 ■0337 •0340 ■0343 20 10 •OOOO ■0007 •0014 •0021 •0028 •0036 •0043 •0050 •0057 •0064 •0071 •0078 •0085 •0092 •0099 •0105 •01 12 •01 19 ■0126 •0133 •0139 0146 ■0153 •0159 •0166 •0172 ■0179. •0185 •OI9I •0198 0204 •0210 •0216 ■0222 ■0228 •0234 •0240 •0245 ■0251 ■0256 ■0262 •0267 ■0273 •0278 •0283 •0288 •0293 •0298 •0303 ■0308 •0312 •0317 •0321 •0325 •0330 •0334 •0338 ■0342 •0346 •0349 ■03S3 •0356 •0360 •0363 ■0366 •0369 30 •OOOO •0008 •0015 •0023 •0030 •0038 •0046 ■0053 •0061 •0068 "0076 ■0083 ■0091 0098 ■oio6 ■01 13 •0120 •0128 •0135 •0142 ■0149 ■0156 ■0164 •01 7 1 •0178 •0185 •0191 •0198 •0205 •0212 •0218 •0225 •0231 •0238 ■0244 •0250 ■0257 ■0263 •0269 ■0275 •0281 ■0286 0292 ■0298 •0303 •0309 •0314 ■0319 •0324 ■0330 ■0334 ■0339 ■0344 •0349 ■03S3 •0358 •0362 •0366 •0370 ■0374 •0378 ■0382 •0386 •0389 •0392 •0396 20 30 When the Latitude is North the sign is + When the Latitude is South the sign is - ALT-AZIMUTH TABLES. 74 Under Altitude and abreast of Declination, take out the tabular quantity and mark it + or — , according as Declination is S. or N. Add Algebraically E and F. Dec- lina- tion. TRUE ALTITUDE, 0° I 2 3 4 5 6° 7 8 9 ID 11° 12 13 14 IS i6° 17 i8 19 20 21° 22 23 24 25 26° 28 29 30 31° 32 33 34 35 36° 37 38 39 40 41° 42 43 44 45 46° 47 48 49 50 51° 52 53 54 55 56° 57 58 60 61° 62 ^3 65 10 0000 •017s •0349 •0523 ■0698 •0872 •1045 •1219 •1392 •1564 •1736 •1908 •2079 ■2250 •2419 •2588 ■2756 •2924 •3090 ■3256 •3420 ■3584 •3746 ■3907 •4067 •4226 ■4384 •4540 •469s •4848 •5000 •5150 •5299 ■5446 ■SS92 •5736 •5878 •6018 •6157 •6293 ■6428 •6561 •6691 6820 •6947 •7071 ■7193 •7314 •7431 •7547 •7660 •7771 ■7880 7986 ■8090 •8192 ■8290 •8387 •8480 ■8572 •8660 ■8746 ■8829 •8910 •9063 20 30 0000 •0I7S •0349 •0523 •0698 •0872 •I04S •1219 •1392 •1564 ■1736 •1908 •2079 ■2250 •2419 ■2588 ■2756 •2924 •3090 •3256 ■3420 •3584 •3746 •3907 ■4067 •4226 ■4384 •4540 •469s •4848 •5000 •5150 •5299 •5446 •5592 ■5736 •S878 •6018 •6157 •6293 •6428 •6561 ■6691 •6820 ■6947 ■7071 •7193 •7314 •7431 •7S47 ■7660 •7771 ■7880 •7986 •8090 •8192 ■8290 •8387 •8481 •8572 •8660 •8746 ■8830 ■8910 ■9063 •0I7S •0349 •0523 ■0698 •0872 ■I04S •1219 •1392 •1564 ■1737 ■1908 ■2079 •2250 •2419 •2588 •2756 •2924 •3090 •3256 ■3420 •3584 •3746 •3907 ■4067 ■4226 ■4384 ■4540 •4695 •4848 ■5000 ■5150 ■5299 ■5446 •5592 •5736 •S878 •6018 ■6157 •6293 •6428 •6561 ■6691 •6820 ■6947 •7071 ■7194 ■7314 •7432 •7547 •7661 •7772 •7880 ■7986 •8090 ■8192 •8291 •8387 •8481 •8572 •8660 •8746 ■8830 ■8910 10 ■9063 40 50 ■0000 •017s ■0349 •0523 0698 ■0872 •1045 •1219 ■1392 •1564 •1737 •1908 •2079 ■2250 ■2419 ■2588 •2756 ■2924 •3090 •3256 •3420 •3584 •3746 ■3907 ■4068 •4226 •4384 •4540 • 469s 20 ■5000 •5151 •5299 •5447 •5592 •5736 •5878 •6018 ■6157 •6293 •6428 •6561 •6692 •6820 •6947 •7071 •7194 •7314 •7432 •7547 •7661 •7772 •7880 •7987 •8090 •8192 •8291 •8387 •8481 •8572 •8661 •8747 ■8830 •8910 •9063 •0000 •OI7S ■0349 •0523 •0698 •0872 •1045 •1219 •1392 •1564 •1737 •1908 •2079 •2250 •2419 2588 ■2757 •2924 ■3090 •3256 •3420 ■3584 •3746 •3908 •4068 •4226 ■4384 •4540 ■4695 30 •5000 •5151 ■5300 ■5447 •5592 •5736 •5878 •6019 ■6157 ■6294 •6428 •6561 •6692 •6820 •6947 •7072 •7194 ■7314 •7432 •7548 •7661 •7772 •7881 ■7987 •8091 •8192 •8291 •8387 •8481 ■8572 •8661 ■8747 •8830 •9064 10 ■0175 •0349 •0523 •0698 •0872 •1045 •1219 •1392 •156S •1737 •1908 •2079 •2250 •2419 •2588 •2757 •2924 •3090 •3256 •3421 •3584 •3746 •3908 •4068 •4227 •4384 •4540 •4695 •4849 •5001 •5151 •5300 •5447 ■5593 •5736 •5878 •6019 •6157 ■6294 ■6429 •6561 ■6692 •6821 •6947 •7072 •7194 ■7314 •7432 •7548 •7661 •7772 ■7881 •7987 •8091 •8192 •8291 40 0000 •0175 •0349 •0523 •0698 •0872 •1045 ■1219 •1392 ■1565 ■1737 •1908 •2079 •2250 •2420 ■2589 •2757 •2924 •3091 ■3256 •3421 •3584 ■3747 •3908 ■4068 •4227 •4384 •4541 ■469s •4849 •5001 •5151 ■5300 •5447 ■5593 •5737 ■5879 ■6019 •6158 ■6294 •6429 ■6562 •6692 •6821 •6948 •7072 •7194 •73 '5 •7433 ■7548 ■7662 ■7773 ■7881 ■7988 •8091 ■8193 •8292 •8573 •8661 •8747 •8830 ■89 1 1 8989 •9064 50 •8573 •8662 •8748 •8831 •89 II 20 30 •9064 ■0000 ■0175 ■0349 •0523 •0698 •0872 •1046 •1219 •1392 •1565 •1737 •1908 •2080 •2250 ■2420 •2589 •2757 •2924 •3091 ■3256 •3421 •3584 •3747 •3908 •4068 •4227 •4385 •4541 •4696 •4849 •5001 •5151 •5300 ■5448 •5593 •5737 •5879 •6019 •6158 •6295 •6429 •6562 •6693 •6821 ■6948 •7073 •719s ■731S ■7433 •7549 ■7662 •7773 ■7882 ■7988 •8092 •8193 •8292 •8573 ■8662 ■8748 •8831 •8912 •8990 •9065 40 50 •0000 ■0175 ■0349 •0524 •0698 0872 •1046 •1219 •1392 •1565 •1737 •1909 •2080 •2250 ■2420 •2589 •2757 •2925 •3091 •3257 •3421 •3585 •3747 •3908 •4068 •4227 •4385 •4541 •4696 •4849 •5001 •5152 •5301 •5448 ■5593 •5737 •5879 •6020 •6158 •6295 •6430 •6693 ■6822 •6948 •7073 ■7195 •7316 •7433 ■7549 •7663 •7774 •7882 •7989 •8092 •8194 •8293 10 •8483 •8574 •8663 •8749 ■8832 •8912 ■8990 ■9066 •QOOO •0175 •0349 ■0524 •0698 •0872 •1046 •I2I9 •1392 •1565 •1737 ■1909 ■2080 •2250 •2420 •2589 ■2757 •2925 ■3091 •3257 •3421 •3585 •3747 •3909 •4069 •4228 •4385 ■4541 •4696 •4850 ■5002 •5152 •5301 •5448 ■5S94 •5738 •5880 ■6020 ■6159 •6295 •6430 ■6563 •6694 •6822 ■6949 •7073 ■7196 ■7316 •7434 ■7550 ■7663 ■7774 •7883 •7989 •8093 ■8194 •8293 •8390 ■8483 •8575 •8663 •8749 •8833 •8913 •8991 •9066 20 0000 •0175 •0349 •0524 •0698 •0872 •1046 ■1219 •1392 •1565 •1737 •1909 •2080 ■2250 •2420 •2589 •2758 •2925 •3091 •3257 •3422 •3585 •3748 •3909 •4069 ■4228 •4386 •4542 •4697 •4850 •5002 ■5153 •5301 •5449 •5594 •5738 ■5880 •6021 ■6159 •6296 ■6431 •6563 •6694 •6823 ■6950 •7074 •7196 •7317 •7435 •7550 •7664 •7775 •7883 •7990 •8094 •8195 •8294 •8390 •8484 ■8575 •8664 •8750 ■8833 •8914 •8992 •9067 30 40 •0000 •0175 •0349 ■0524 •0698 •0872 •1046 •1219 •1392 •1565 •1737 •1909 •2080 •2251 •2420 •2590 •2758 •2925 •3092 •3257 •3422 •3586 •3748 •3909 •4069 •4228 ■4386 •4542 •4697 •4851 •5003 •5153 •5302 •5449 •5595 •5739 •5881 •6021 •6160 •6296 •6431 •6564 •6695 •6823 •6950 •7075 •7197 •7317 •7435 •7551 •7664 ■7775 •7884 •7990 •8094 •8196 •8295 ■8391 •8485 •8576 •8665 •8751 •8834 •8915 •9068 10 •0000 •0175 •0349 •0524 •0698 •0872 •1046 •1219 •1393 •1565 •1738 •1909 •2080 •2251 •2421 ■2590 •2758 •2925 •3092 •3258 •3422 •3586 •3748 •3910 ■4070 •4229 •4386 •4543 •4698 •4851 •5003 •5154 •5302 ■5450 •5595 •5739 •5881 •6022 ■6160 ■6297 •6432 •6565 •6695 •6824 •6951 •7075 •7198 •7318 •7436 •7552 •7665 •7776 •7885 •7991 •8095 •8197 •8295 •8392 •8486 •8577 •8666 50 20 •8752 •8835 ■8915 ■8993 9069 •0000 •0175 •0349 •0524 •0698 •0872 •1046 •1220 •1393 •1565 •1738 •1909 •2081 •2251 •2421 •2590 •2758 •2926 ■3092 •3258 ■3423 •3586 •3749 ■3910 •4070 •4229 •4387 •4543 •4698 •4852 •5004 •5154 •5303 •5450 •5596 •5740 •5882 •6022 ■6161 •6298 •6432 •6565 •6696 ■6825 •6952 •7076 •7199 •7319 ■7437 •7552 •7666 •7777 •7886 •7992 •8096 •8197 •8296 •8393 ■8487 •8578 •8666 •0000 •0175 •0349 •0524 •0698 •0872 ■1046 ■1220 •1393 •1566 •1738 •1910 •2081 •2251 •2421 •2590 •2759 •8752 •8836 ■8916 •8994 ■9070 •3093 •3258 •3423 •3587 •3749 •3911 •4071 •4230 •4387 •4544 •4699 ■4852 •5004 •5155 •5304 •5451 •5597 •5741 •5883 •6023 •6162 •6298 ■6433 ■6566 •6697 •6826 •6952 •7077 •7199 •7320 •7438 •7553 •7667 •7778 •7887 ■7993 •8097 •8198 •8297 •8394 30 •8579 •8667 •8753 •8837 •8917 •899s •9071 ■0000 •0175 •0349 •0524 •0698 •0872 •1046 •1220 •1393 •1566 ■1738 •1910 •2081 •2252 •2422 •2591 •2759 •2927 •3093 •3259 •3423 •3587 •3750 •39 1 1 •4071 •4230 •4388 ■4544 •4699 •4853 •5005 •5155 •5304 •5452 •5597 •5741 •5883 •6024 •6162 •6299 •6434 •6567 •6698 •6826 •6953 •7078 •7200 •7321 •7439 •7554 •7668 •7779 •7888 •7994 •8098 •8199 •8298 •8395 ■8489 •8580 •8669 ■8755 •8838 ■8919 •8997 •9072 10 20 30 ■When the Declination is North the sign is - • When the Declination is South the sign is + . ?? ALT-AZIMUTH TABLES. Under Altitude in head-line, and abreast of Latitude in margin, take out the tabular quantity and mark it + or according as the Latitude is N. or S. Lat. TRUE ALTITUDE. 2 30' 40' 50 3° 10' 20' 30 40' 80 4 10 20' 30 40 50' 5 0° •0000 •0000 ■0000 •0000 •0000 •0000 ■0000 •0000 •nnoo •0000 0000 ■0000 •0000 •0000 ■0000 ■0000 I •0008 ■0008 •0009 •0009 •ooio •OOIO •001 1 •001 1 ■0012 •0012 ■0013 •0013 •0014 •0014 ■0015 •0015 2 •0015 •0016 •0017 ■0018 •0019 •0020 •0021 ■0022 ■0023 ■0024 ■0025 ■0026 •0027 •0028 •0030 •0031 3 •0023 •0024 •0026 •0027 •0029 ■0030 •0032 ■0034 •0035 •0037 •0038 •0040 ■0041 •0043 •0044 ■0046 4 •0030 •0032 •003s •0037 •0039 •0041 •0043 •0045 •0047 •0049 ■0051 •0OS3 ■0055 ■0057 •0059 •0061 5 •0038 •0041 ■0043 •0046 •0048 •0051 •0053 •0056 ■0058 ■0061 •0063 ■0066 •0069 •0071 ■0074 ■0076 6° •0046 •0049 •0052 •ooSS •0058 ■0061 ■0064 •0067 •0070 •0073 •0076 •0079 •0082 ■0085 •0088 •0091 7 •0053 •0057 ■0060 ■0064 •0067 ■0071 •0075 •0078 •0082 •0085 •0089 •0092 •0096 ■0099 •0103 •0107 8 •0061 •006s •0069 ■0073 •0077 •0081 •0085 •0089 •0093 ■0097 •OIOI •0105 ■Olio ■0114 ■on 8 ■0122 9 •0068 •0073 •0077 •0082 •0087 •0091 •0096 •0100 •0105 •0109 ■01 14 ■01 19 •0123 ■0128 •0132 ■0137 10 •0076 •0081 •0086 ■0091 •0096 •OIOI •0106 •GUI •01 16 ■0121 ■0127 •0132 •0137 •0142 ■0147 •0152 11° •0083 •0089 ■0094 ■0100 •0106 •01 1 1 •01 17 •0122 •0128 •0133 ■0139 ■0145 •0150 •0156 •0161 ■0167 12 •0091 ■0097 •0103 ■0109 "oiiS •0I2I •0127 •0133 •0139 ■0145 ■0I5I •0158 ■0164 •0170 •0176 •0182 13 •0098 ■oios •GUI 0118 •0124 ■OI3I •01 38 •0144 ■0151 •0157 •0164 •0170 ■0177 •0184 •0190 •0197 14 ■0106 •01 13 •0120 •0127 •0134 ■OI4I •0148 •0155 •0162 ■0169 •0176 •0183 ■0190 ■0197 •0205 ■0212 IS •01 13 •OI2I ■0128 ■0136 •0143 •01 5 1 •0158 •0166 •0173 ■0181 ■0189 ■0196 •0204 •02 II •0219 ■0226 i6° ■0120 •0128 •0136 ■0144 •0152 ■0161 •0169 •0177 •0185 •0193 ■0201 ■0209 ■0217 •0225 •0233 ■0241 17 •0128 •0136 •014s •OIS3 •0162 ■0170 •0179 •0187 •0196 •0204 ■0213 ■0222 ■0230 •0239 •0247 •0256 i8 •0135 ■OI44 •0153 •0162 •0171 ■0180 •0189 ■0198 •0207 •0216 ■0225 ■0234 ■0243 •0252 •0261 •0270 19 •0142 •0152 •OI61 •01 7 1 ■oi8o ■0190 •0199 ■0209 ■0218 ■0228 ■0237 •0247 •0256 ■0266 •0275 •0285 20 ■0149 ■0159 •0169 ■0179 •0189 •0199 •0209 •0219 ■0229 •0239 •0249 •0259 •0269 ■0279 •0289 •0299 21° •0156 0167 •0177 •0188 •0198 •0209 ■0219 •0230 •0240 •0251 ■0261 •0272 ■0282 ■0293 •0303 •0313 22 ■0164 •0174 ■0185 •0196 •0207 ■0218 •0229 •0241 •0251 •0262 ■0273 ■0284 ■0295 ■0306 •0317 •0328 23 •01 7 1 0182 •0193 •0205 •0216 ■0228 •0239 ■0250 ■0262 ■0273 ■0285 ■0296 •0308 •0319 •0330 •0342 24 •0178 •0189 •0201 •0213 •0225 •0237 •0249 ■0261 •0273 •0284 ■0296 ■0308 ■0320 •0332 •0344 ■0356 25 ■0185 •0197 •0209 •0221 •0234 •0246 •0258 •0271 •0283 ■0296 •0308 ■0320 •0333 •0345 •0357 ■0370 26° •0191 ■0204 ■0217 •0230 •0243 •02SS •0268 •0281 •0294 •0307 ■0319 •0332 ■0345 •0358 •0371 ■0384 is ■0198 •02 1 1 •0225 •0238 •0251 •0264 0278 •0291 •0304 0317 •0331 •0344 •0357 •0371 ■0384 •0397 •0205 ■0219 •0232 ■0246 •0260 •0273 •0287 •0301 •0315 ■0328 •0342 •0356 •0369 ■0383 ■ ■0397 •041 1 29 •0212 ' ■0226 •0240 •02S4 •0268 •0282 •0297 •03 1 1 •0325 ■0339 •0353 ■0367 ■0382 ■0396 ■0410 •0424 30 •0218 ■0233 •0247 ■0262 •0277 •0291 •0306 •0320 •0335 •0350 •0364 ■0379 •0394 •0408 •0423 •0437 31° ■0225 •0^40 •02SS •0270 •028s ■0300 ■031S •0330 •034s •0360 •0375 •0390 •0405 ■0420 •0436 ■0451 32 ■0231 •0247 •0262 •0278 •0293 •0309 •0324 •0340 •03S5 •0371 ■0386 ■0402 ■0417 ■0433 •0448 ■0464 33 ■0238 •02S4 •0270 •0285 •0301 •0317 ■0333 •0349 •0365 •0381 •0397 •0413 •0429 •0445 ■0461 ■0476 34 ■0244 •026a . •0277 •0293 •0309 •0326 •0342 •0358 •0375 •0391 ■0407 •0424 ■0440 ■0456 •0473 ■0489 35 •0250 •0267 •0284 •0301 ■0317 •0334 •0351 •0368 •0384 •0401 ■0418 •043s •0451 ■0468 ■0485 •0502 36° •02S.7 •0274 •0291 ■0308 ■0325 •0342 ■0360 •0377 •0394 ■041 1 ■0428 •0445 •0463 •0480 ■0497 ■0514 % 0263 •0280 ■0298 •03 IS •0333 •0351 •0368 ■0386 •0403 •0421 ■0438 •0456 ■0474 •0491 ■0509 ■0527 ■0269 ■0287 •030s ■0323 •0341 •0359 •0377 ■0395 •0413 ■0431 ■0449 ■0467 •0485 ■0503 •0521 ■0539 39 •0275 •0293 0311 ■0330 •0348 •0367 •0385 •0403 ■0422 ■0440 •0458 •0477 ■0495 •0514 •0532 •0551 40 •0281 •0299 •0318 •0337 ■0356 •0374 •0393 •0412 •0431 ■0449 •0468 •0487 •0506 •0525 •0544 •0562 V-° ■0286 •0306 •0325 •0344 ■0363 •0382 •0401 •0420 •0440 ■0459 ■0478 •0497 ■0516 •0536 ■0555 ■0574 42 0292 •0298 •0312 •0331 •0351 •0370 ■0390 •0409 •0429 •0448 ■0468 •0487 ■0507 ■0527 •0546 ■0566 ■0585 43 •0318 •0338 ■03S7 ■0377 •0397 •0417 ■0437 •0457 •0477 ■0497 •0517 ■0537 •0557 •0577 •0597 44 •0303 0324 ■0344 ■0364 •0384 •040s •0425 ■044s •0465 0486 •0506 ■0526 •0547 ■0567 •0587 ■0608 45 •0309 •0329 •0350 •0371 •0391 •0412 ■0432 •0453 •0474 ■0494 •05IS ■0536 ■0557 •0577 •0598 •0619 46° •0314 •033s •0356 •0377 •0398 •0419 •0440 ■0461 •0482 ■0503 •0524 •0545 •0566 •0587 •0608 •0629 % •0319 •0341 ■0362 •0383 •0405 •0426 ■0447 •0469 ■0490 •051 1 ■0533 ■0554 •0576 •0597 •0618 ■0640 •0324 ■0346 ■0368 •0389 •04 n •0433 ■0455 •0476 •0498 ■0520 ■0541 ■0563 ■0585 •0607 ^628 •0650 ■0660 49 •0330 •0352 •0374 ■0396 •0418 •0440 •0462 •0484 •0506 ■0528 ■0550 ■0572 •0594 ■0616 •0638 SO ■0334 ■0357 •0379 ■0401 •0424 ■0446 •0469 ■0491 •0513 •0536 •0558 •0580 •0603 ■0625 •0648 •0670 51° •0339 ■0362 •0385 ■0407 •0430 •04S3 •047s •0498 •0521 ■0543 •0566 ■0589 ■0612 •0634 •0666 •0680 52 •0344 ■0367 •0390 •0413 •0436 •0459 ■0482 ■0505 •0528 •0551 •0574 ■0597 •0620 •0643 •0689 ■0699 53 ■0349 •0372 ■039s ■0419 •0442 ■046s •0488 •0512 ■0535 •0558 •0582 ■0605 ■0629 •0652 ■0675 54 •0358 •0377 •0382 '0400 •0424 ■0448 •0471 •0495 •0518 ■0542 •0566 ■0589 •0613 ■0637 ■0660 ■0684 ■0708 •0717 55 •040s •0429 •0453 •0477 •0501 •0525 ■0549 ■0573 •0597 . ■0621 ■0645 •0669 •0693 56° •0362 •03,66 •0386 •0410 ■0434 •04S9 '°'^l •0507 •0531 ■0555 ■0580 0604 •0628 •0652 •0677 •0701 ■0709 ■0717 ■0725 •0734 ■0742 1 0391 •04IS •0440 •0464 •0488 •0513 •0537 •0562 •0586 •06 1 1 •0636 •0660 ■0685 •0370 ■0395 •0420 ■0444 0469 •0494 •0519 •0543 ■0568 •0593 ■0618 •0643 •0667 ■0692 ■0374 ■0378 •0399 •0424 •0449 •0474 •0499 •0524 •0549 •0574 ■0599 ■0624 •0650 •0675 ■0700 •0725 ■0732 ■0750 •0758 ■0403 •0429 •04S4 •0479 ■0504 •0530 •0555 •0580 ■0606 •0631 •0656 •0682 •0707 61° 62 65 •0382 •0386 •0389 •0407 •0433 •0458 •0484 •0509 •0535 •0560 •0586 ■0612 •0637 •0663 •0688 ■0714 ■0740 •07*5 •0772 ■0780 ■0786 •0793 ■04 1 1 ■0437 0463 0488 ■0514 •0540 •0566 ■0592 •0617 ■0643 •0669 •0695 •0721 •0747 •041 5 •0441 •0467 •0493 ■0519 ■0545 •0571 •0597 •0623 ■0649 ■0675 ■0701 ■0727 / 1/ ■0753 •0392 ■0396 0419 ■044S •0471 •0497 •0523 •0550 •0576 •0602 ■0628 •0655 ■0681 •0707 •0734 ■0760 •0422 ■0449 •047s •0501 •0528 •0554 ■0581 •0607 •0634 •0660 •0687 •0713 •0740 •0766 2 30' 40' 50' 3' 10' 20' 30' 40' 50' 4 10 20' 30 40 50' 5 When the Latitude is North the sign is + When the Latitude is South the sign is - ALT-AZIMUTH TABLES. 76 Under Altitude and abreast of Declination, take out the tabular quantity and mark it + op — , according as Declination is S. or N. Add Algebraically E and F. Dec- . LINA- TION. TRUE ALTITUDE. 2 30 40 50' 3 10' 20' 30 40' 50' 4 10 20' 30 40 50' 5 0° ■0000 ■0000 •0000 •0000 ■0000 ■0000 •0000 •0000 •0000 •0000 •0000 •0000 ■0000 •0000 •0000 •0000 I 2 3 4 5 ■01 75 •0349 •0524 •0698 •0872 •0175 ■0349 •0524 •0698 0873 ■0175 •0349 •0524 •0698 ■0873 •0175 •0349 •0524 •0699 •0873 •0175 •0349 •0524 •0699 ■0873 •0175 •0350 •0524 •0699 •0873 •0175 •0350 •0524 •0699 ■0873 •0175 •0350 •0524 •0699 •0873 ■0175 •0350 •0525 •0699 •0874 •0175 ■0350 •0525 •0699 •0874 ■0175 •0350 •0525 ■0699 •0874 ■0175 •0350 •0525 •0700 •0874 •0175 •0350 ■0525 •0700 ■0874 •OI7S •0350 •0525 •0700 ■0874 •0175 •0350 •0525 •0700 •0875 •017s •0350 •0525 •0700 •0875 6° 7 ■1046 •1220 ■1046 •1220 ■1047 •1220 ■1047 ■1220 •1047 •1221 •1047 •I22I •1047 •1221 •1047 •I22I •1048 •1221 ■1048 •1222 •1048 ■1222 •1048 ■1222 ■1049 •1222 •1049 •1223 •1049 •1223 •1049 •1223 8 9 10 •1393 ■1566 ■1738 ■1738 •1393 •1566 •1739 ■1394 •1566 ■1739 •1394 ■1567 •1739 •1394 •1567 •1739 ■1394 ■1567 •1740 •1395 •1568 ■1740 •1395 ■1568 •1740 •1395 •1568 •1741 •1395 •1568 •1741 •1396 •1569 •I 741 •1396 ■1569 •1742 •1396 ■1570 •1742 •1397 •1570 •1743 •1397 •1570 •1743 11° 12 •1910 •2081 •1910 •2081 •1910 •2082 •1911 ■2082 •19.11 •2082 ' •I9II •2083 1912 •2083 •I912 ■2083 •1912 ■2084 •1913 •2084 •1913 •2085 •1914 •2085 •1914 •2086 ■•2^8^ •191S •2087 •1915 •2087 13 14 IS ■2252 •2422 ■2591 •2252 •2422 •2591 •2252 •2422 •2591 •2253 •2423 •2592 •2253 ■2423 2592 ■2253 ■2423 ■2593 •2254 •2424 •2593 •2254 •2424 •2593 •2255 •2425 •2594 ■2255 •2425 •2595 •2255 •2426 •2595 •2256 •2426 •2596 •2256 •2427 •2596 •2257 •2427 •2597 •2258 •242S •2597 ■2258 •2428 2598 i6° 19 20 •2759 •2927 •3093 •3259 •3423 •2759 •2927 ■3094 •3259 ■3424 •2760 •2927 ■3094 ■3260 ■3424 •2760 •2928 ■3094 •3260 •3425 •2761 •2928 •3095 •3261 ■3425 •2761 •2929 •309s •3261 •3426 •2762 •2929 •3096 •3262 •3427 ■2762 •2930 •3097 •3262 •3427 ■2763 •2930 •3097 ■3263 •3428 •2763 •2931 •3098 •3264 •3429 •2764 •2931 •3098 •3264 •3429 •2764 •2932 •3099 •3265 •3430 •2765 •2933 •3100 ■3266 •3431 •2766 ■2933 •3100 •3267 •3432 •2766 •2934 •3101 •3267 •3432 •2767 •2935 •3102 •3268 •3433 21° 22 23 24 25 ■3587 ■3750 ■391 1 ■4071 •4230 •3588 ■3750 •3912 •4072 •4231 •3588 •3751 ■3912 •4072 •4231 •3589 •3751 •3913 •4073 •4232 •3589 •3752 •3913 •4074 •4233 ■3590 •3752 •3914 •4074 •4233 •3590 ■3753 ■3915 •4075 •4234 •3591 •3754 •3915 •4076 •4235 •3592 •3754 •3916 •4076 ■4236 •3592 ■3755 ■3917 •4077 ■4237 •3593 •3756 •3918 •4078 •4237 •3594 •3757 •3919 •4079 •4238 •3595 •3758 •3919 •4080 •4239 •3596 •3759 ■3920 •4081 ■4240 ■3596 ■3759 •3921 •4082 •4241 •3597 ■3760 •3922 •4083 •4242 26° 29 30 •4388 ■4544 •4699 ■4853 •5005 •4388 •4545 •4700 ■4853 ■5005 •4389 •4545 •4700 •4854 •5006 •4390 •4546 •4701 •4855 •5007 •4390 •4547 •4702 ■4856 •5008 •4391 •4548 •4703 •4856 •5008 •4392 •4548 •4703 •4857 •5009 •4393 •4549 •4704 •4858 •5010 •4394 •4550 •4705 •4859 •501 1 ■4394 •4551 •4706 •4860 •5012 •4395 •4552 •4707 •4861 •5013 •4396 •4553 •4708 •4862 •5014 •4397 •4554 •4709 ■4863 •5015 •4398 •4555 •4710 •4864 •5017 ■4399 •4556 ■47 1 1 •4865 •5018 •4400 •4557 •4713 •4867 •5019 31° 32 33 34 35 •5155 •5304 •5452 ■5597 •5741 •5156 •5305 •5452 •5598 •5742 •5157 •5306 ■5453 •5599 •5743 ■5157 •5306 •5454 •5600 ■5744 •5158 •5307 • •5455 •5600 •5745 •5159 •5308 •5456 •5601 •5745 •5160 •5309 •5457 •5602 •5746 •5161 •5310 •5458 ■5603 •5748 •5162 •531 1 •5459 •5604 ■5749 •5163 •5312 •5460 •5606 •5750 ■5164 •5313 •5461 •5607 •5751 •5165 •5314 ■5462 •5608 •5752 •5166 •5316 •5463 •5609 •5754 •5168 •5317 •5465 •561 1 •5755 •5169 •53'8 •5466 •5612 •5756 •5170 •5319 •5467 •5613 •5758 36° 37 38 39 40 •5883 ■6024 •6162 •6299 •6434 •5884 •6025 ■6163 •6300 •6435 •5885 •6026 •6164 •6301 •6436 •5886 ■6026 ■6165 •6302 ■6437 •5887 •6027 ■6166 •6303 •6438 ■5888 •6028 •6167 •6304 •6439 •5889 •6029 •6168 •6305 •6440 ■5890 •6030 •6169 ■6306 ■6441 •5891 •6032 •6170 ■6307 •6442 •5892 ■6033- •6172 •6309 •6444 ■5893 •6034 ■6173 •6310 ■6445 •5895 •6035 •6174 •63 1 1 •6446 •5896 •6037 •6176 •6313 •6448 •5897 •6038 •6177 •6314 •6449 •5899 •6040 •6179 •6316 •6451 ■5900 •6041 ■6180 •6317 ■6452 41° 42 43 44 45 •6567 •6698 •6826 ■6953 •7078 •6568 •6699 •6827 •6954 •7079 •6569 •6699 •6828 •6955 •7080 •6570 •6700 ■6829 •6956 •7081 •6571 •6702 •6830 ■6957 •7082 ■6572 •6703 ■6832 ■6958 ■7083 ■6573 •6704 ■6833 •6960 •7084 •6574 •6705 ■6834 ■6961 •7086 •6575 •6706 •6835 •6962 •7087 •6577 •6708 •6837 •6964 ■7088 ■6578 ■6709 •6838 •6965 •7090 ■6579 ■6710 •6840 ■6967 •7091 ■6581 •6712 •6841 •6968 •7093 .6582 •6714 •6343 •6970 •7095 •6584 •6715 •6844 ■6971 •7096 •6586 ■6717 •6846" •6973 •7098 46° % 49 SO •7200 •7321 •7439 •7668 •7201 •7321 •7440 •7555 •7669 ■7202 •7322 •7441 •7556 •7670 •7203 ■7324 ■7442 •7557 •7671 •7204 ■7325 ■7443 ■7559 •7672 •7206 •7326 •7444 ■7560 •7673 ■7207 ■7327 ■7445 •7561 •7675 ■7208 ■7329 ■7447 •7563 •7676 •7210 •7330 ■7448 •7564 •7678 •721 1 •7331 •745° ■7566 •7679 •7212 •7333 •7451 •7567 •7681 •7214 •7335 •7453 •7569 •7682 ■7216 •7336 •7454 •7570 •7684 •7217 •7338 •7456 •7219 •7340 •7458 •7574 •7688 •7221 •7341 ■7460 •7576 ■7690 51° 52 S3 54 SS ■7779 •7888 •7994 •8098 •8199 •7780 •7889 •7995 •8099 ■8200 •7781 •7890 •7996 •8100 •8202 •7782 •7891 ■7997 •8101 •8203 ■7783 •7892 ■7999 •8103 •8204 •7785 •7893 •8000 •8104 •8205 •7786 ■7895 •8001 •810S •8207 •7787 ■7896 •8003 •8107 •8208 •7789 •7898 •8004 •8108 •8210 ■7790 ■7899 •8006 •Si 10 •8212 ■7792 •7901 •8008 •81 12 •8213 •7794 •7903 •8009 •8113 •8215 •7795 ■7904 •801 1 •811S •8217 •7797 •7906 •8013 •8117 •8219 •7799 •7908 •8015 •8n9 •8221 •7801 •7910 •8017 •8l2I •8223 56° •8298 •839s •8580 •8669 ■8299 •8396 •8490 •8581 •8670 •8301 ■8397 •8491 •8582 •8671 •8302 •8398 ■8492 •8583 •8672 •8303 •8400 •8493 •8585 •8673 •8304 •8401 •8495 ■8586 ■8675 •8306 •8402 •8496 •8588 •8676 •8307 •8404 •8498 •8589 •8678 •8309 ■8406 ■8499 •8591 •8680 •831 1 •8407 •8501 •8593 •8681 •8312 •8409 •8503 •8594 •8683 •8314 •8411 •8505 •8596 •8685 •8316 •8413 •8507 ■8598 ■8687 •8318 •8415 •8689 •8320 •8417 ■8511 •8602 ■8691 •8322 •8419 •8693 61° 62 65 ■8919 ■8997 •9072 •8756 •S839 •8920 •8998 •9073 ■8757 •8840 •8921 •8999 •9074 •8758 •8842 ■8922 •9000 ■9076 ■8760 •8843 •8924 •9002 •9077 •8761 •8844 ■8925 ■9003 •9078 ■8763 •8846 ■8927 •9005 •9080 •8764 ■8848 •8928 •9006 •9082 •8766 •8849 •8930 ■9008 •9083 •8768 •8851 •8932 •9010 •9085 •8769 •8853 •8934 •9012 •9087 •8771 •8855 •8936 •9014 •9089 •8773 •8857 •8938 •9016 •9091 ■8775 •8859 ■8940 •9018 •9093 •8777 ■8861 ■8942 •9020 •9095 ■8780 •8863 •8944 •9022 ■9098 2 30 40' 50 3 10' 20 30' 40' 50' c 4 10 20' 30 40 50 5 When the Declination is North the sign is - . When the Declination is South the sign is + . 77 ALT-AZIMUTH TABLES. Under Altitude in head-line, and abreast of Latitude in Margin, talte out the tabular quantity and mark it + or according as the Latitude is N. or S. Lat. TRUE ALTITUDE. 5° 10 20 30 40 50 6 10' 20 30 40' 50 7 10' 20 30' 0° •0000 •0000 •0000 •0000 •0000 ■0000 •0000 •0000 •0000 ■0000 •0000 •0000 ■0000 •0000 •0000 •0000 I ■0015 0016 •0016 •0017 •0017 ■0018 •0018 •0019 •0019 0020 •0021 •0021 •0021 ■0022 •0022 ■0023 2 •0031 •0032 ■0033 •0034 ■003s •0036 ■0037 •0038 ■0039 ■0040 •0041 •0042 ■0043 •0044 •0045 •0046 3 •0046 •0047 •0049 ■0050 ■0052 •0053 •0055 •0057 •0058 ■0060 ■0061 •0063 •0064 •0066 •0067 ■0069 4 .0061 •0063 •0065 •0067 •0069 •0071 ■0073 ■0075 •0077 •0079 0082 ■0084 •0086 •0088 •0090 •0092 5 •0076 •0079 •0081 •0084 ■0086 •0089 ■0092 •0094 •0097 •0099 ■0102 •0104 •0107 •Olio 0112 •01 1 5 6° •0091 ■0095 ■0098 •oioi •0104 •0107 •Olio •01 13 ■01 16 0119 •0122 •0125 ■0128 •01 3 1 ■0135 •0138 I •0107 •Olio •01 14 •01 17 ■0121 ■0125 ■0128 •0132 •0135 ■0139 •0142 •0146 ■0150 •0153 ■0157 •0160 •0122 ■0126 ■0130 •0134 •0138 ■0142 •0146 •0150 ■0154 ■0159 •0163 ■ "0167 ■01 7 1 ■0175 •0179 •0183 9 •0137 •0I4I ■0146 •0151 ■0155 •0160 0164 •0169 •0174 •0178 ■0183 •0187 •0192 •0197 •0201 •0206 10 ■0152 ■OIS7 ■0162 •0167 •0172 •0177 •0183 ■0188 •0193 •0198 •0203 ■0208 •0213 •0218 •0223 0229 11° •0167 ■0173 ■0178 •0184 •0189 ■0195 •0201 •0206 ■0212 •0217 ■0223 •0229 •0234 •0240 ■0246 ■0251 12 •0182 •0188. •0194 •0200 •02o5 0212 •0219 ■0225 •0231 •0237 •0243 •0249 ■0255 •0261 •0268 •0274 13 •0197 •0203 •0210 •0217 •6223 •0230 •0236 •0243 •0250 •0256 •0263 •0270 •0276 •0283 •0289 •0296 14 ■02 T 2 •0219 ■0226 •0233 ■0240 •0247 •0254 •0261 •0269 •0276 ■0283 •0290 •0297 •0304 ■03 1 1 ■0318 IS ■0226 •0234 •0242 •0249 •0257 •0264 ■0272 •0280 •0287 •0295 •0303 •0310 ■0318 •0325 ■0333 •0341 i6° •0241 •0249 •0257 •0265 ■0274 •0282 •0290 •0298 ■0306 •0314 •0322 •0330 ■0338 ■0347 ■0355 ■0363 ^l ■0256 •0264 •0273 •0282 •0290 ■0299 •0307 •0316 •0325 ■0333 ■0342 ■0350 ■0359 •0368 •0376 ■0385 l8 ■0270 •0279 ■0288 ■0298 •0307 ■0316 •0325 •0334 •0343 •0352 ■0361 •0370 •0379 ■0389 ■0398 •0407 19 ■0285 •0294 ■0304 •0313 •0323 •0333 •0342 •0352 ■0361 -0371 •0381 •0390 •0400 •0409 •0419 •0429 20 •0299 ■0309 •0319 •0329 •0339 •0349 •0359 •0370 0380 ■0390 •0400 ■0410 •0420 •0430 •0440 •0450 21° •0313 ■0324 0335 ■0345 ■0356 ■0366 •0377 •0387 •0398 •0408 •0419 •0429 •0440 ■0451 •0461 •0472 22 •0328 ■0339 ■0350 •0361 •0372 ■0383 ■0394 •0405 •0416 •0427 ■0438 ■0449 •0460 •0471 ■0482 ■0493 23 •0342 •03S3 ■036s •0376 •0388 •0399 •04 1 1 •0422 ■0434 ■0445 ■0457 •0468 ■0480 ■0491 ■0503 •0514 24 •0356 ■0368 •0380 ■0392 •0404 •0416 ■0427 •0439 •0451 ■0463 •0475 •0487 •0499 •05 1 1 •0523 •0535 2S •0370 •0382 •0395 ■0407 •0419 ■0432 ■0444 ■0457 •0469 ■0482 ■0494 •0506 •0519 •0531 ■0544 •0556 26° •0384 •0396 •0409 •0422 •0435 •0448 •0461 •0474 ■0487 •0499 ■0512 ■0525 •0538 •0551 •0564 •0577 27 •0397 •04 1 1 •0424 •0437 ■"'^l? •0464 •0477 •0491 •0504 ■0517 •0531 •0544 ■0557 •0571 •0584 •0598 28 ■041 1 •0424 •0438 •0452 •0466 •0480 •0493 •0507 •0521 ■0535 ■0549 •0563 •0576 •0590 •0604 •0618 29 •0424 ■0438 ■0453 ■0467 ■0481 •049s •0510 ■0524 ■0538 ■0552 ■0567 •0581 ■0595 •0610 ■0624 •0638 30 •0437 ■0452 ■0467 ■0481 •0496 •05 1 1 •0526 •0540 ■0555 ■0570 •0584 •0599 •0614 •0629 •0643 ■0658 31° IM\ •0466 •0481 ■0496 •0511 ■0526 •0541 0556 ■0572 ■0587 •0602 •0617 •0632 0648 ■0663 •0678 32 0464 •0479 •0495 ■0510 •0526 •0541 •0557 ■0573 ■0588 •0604 •0619 •0635 •0651 •0666 ■0682 •0698 33 •0476 •0492 •0508 •0524 •0540 •0556 ■0572 •0588 ■o6p4 ■0621 •0637 ■0653 •0669 •0685 •0701 •0717 34 •C489 •0506 '0522 ■0538 •OSSS •0571 •0588 ■0604 •0621 •0637 •0654 •0670 •0687 •0703 •0720 ■0736 35 •0502 •0519 •OS3S •0552 ■0569 •0586 •0603 ■0620 ■0637 ■0654 •0670 •0687 •0704 •0721 •0738 ■0755 36° ■0514 ■0531 •0549 ■0566 ■0583 ■0601 •0618 •0635 ■0652 •0670 •0687 •Q704 •0722 •0739 ■0756 •0774 38 •0527 ■OS44 •0562 •0579 ■0597 •0615 •0633 •0650 ■0668 •0686 ■0703 ■0721 ■0739 ■0757 ■0775 ■0792 •0539 •05S7 ■0575 ■0593 ■06 1 1 •0629 •0647 •0665 •0683 •0701 •0720 •0738 ■0756 ■0774 ■0792 •08 1 1 39 ■cSSi ■0569 •0587 ■0606 ■0624 •0643 •0661 •0680 •0698 ■0717 •0736 •0754 ■0773 •0791 •0810 ■0829 40 ■0562 ■0581 ■0600 •0619 •0638 •0657 •0676 •0695 •0713 ■0732 •0751 •0770 •0789 •0808 ■0827 ■0846 41° •OS74 ■0593 •0612 ■0632 •0651 •0670 •0690 •0709 ■0728 0747 ■0767 •0786 •0806 •0825 ■0844 •0864 42 ■0585 •0605 •0625 ■0644 ■0664 ■0684 •0703 ■0723 ■0743 ■0762 •0782 ■0802 ■0822 ■0841 •0861 •0881 43 •0597 •0608 •0619 ■0617 ■0637 ■°^F •0677 ■0697 ■0717 •0737 ■0757 ■0777 ■0797 •0817 •0837 ■0858 •0878 •0898 44 •0628 ■0648 ■0669 ■C689 •0710 ■0730 ■0751 ■0771 •0791 ■0812 •0832 ■0853 ■0873 •0894 •091S •0931 45 ■0639 •0660 •0681 ■0702 •0722 ■0743 •0764 ■0785 •0806 •0826 ■0847 •0868 ■0889 •0910 46° •0629 •0640 •0650 ■0660 ■0670 •0650 •0672 •0693 •0714 •0735 •0756 •0777 •0798 ■0820 ■0841 •0862 ■0883 •0904 •0926 ■0947 •0963 •0978 •0994 •1009 47 48 ■o65[ •0683 •0704 ■0726 ■0747 •0769 •0790 •0812 ■0833 ■0855 •0876 •0898 •0920 •0941 ■0672 ■0694 •0716 ■0737 •0759 ■0781 ■0803 •0825 •0847 •0869 •0891 •0912 ■0934 •0956 •0971 •0986 49 ■0682 •0705 •0727 •0749 •0771 •0793 •0815 ■0838 •0860 •0882 •0904 •0927 •0949 50 •0693 •0715 ■0738 •0760 ■0783 •0805 •0828 ■0850 •0873 •0895 •0918 •0941 •0963 51° •0680 ■0689 •0699 •0708 •0703 ■0725 •0748 0771 •0794 •0817 •0840 •0863 ■0885 ■0908 •0931 ■0954 •0077 •1000 •1023 •1037 •1051 ■1065 ■1078 52 S3 •0713 •0722 •0736 •0746, •0759 •0769 ■0782 ■0792 •0805 ■0816 ■0828 •0839 ■0851 •0863 ■0875 •0886 ■0898 ■0910 •0921 0933 •0944 ■0957 •0968 •0981 "7/ / •0991 •1004 •1014 •1028 54 •0732 •07SS •0779 •0803 •0827 •0850 •0874 •0898 •0922 0946 ■0969 •0993 •1017 •1041 ■1054 55 •0717 •0741 •0765 •0789 •0813 •0837 •0861 ■088s •0909 ■0933 ■0957 •0982 •1006 •1030 .56° •072s ■0734 •0742 ■0750 •0758 •0750 •0758 •0767 ■077S •0783 ■0774 •0783 •0792 •0800 •0808 •0798 •0808 •0817 •0825 •0834 ■0823 •0832 •0841 •0851 ■0859 •0847 •0857 •0866 •0876 •0885 •0871 •0881 ■0891 •0901 •0910 •0896 ■0906 •0916 ■0926 •0936 ■0920 •0931 ■0941 •0951 •0961 ■0945 •0956 •0966 •0977 •0987 •0969 ■0980 •0991 •1002 •1012 ■0993 •1005 •1016 ■1027 ■1038 •ioi8 •1030 •1041 •1052 •1063 •1042 ■1055 •io66 •1078 •1089 •1067 •1079 ■1091 •I 103 •HIS •1091 •I 104 •H16 •1128 •I 140 61° 62 64 65 •0765 •0772 •0780 •0791 •0798 •0816 •0824 •0842 •0850 •0868 ■0876 •0894 ■0902 ■0919 •0928 ■0945 •0954 •0971 •0980 ■0997 •1006 •1022 ■1032 •1048 •1058 •1074 •1084 •iioo •mo •I 126 •I 136 •I 147 ■1157 ■1166 •T jfiZ •0806 ■0832 ■0858 •0884 •0910 ■0936 •0963 •0989 ■1015 •1041 •1068 •1094 •1120 •II73 •I 183 •1193 ■0786 ■0813 •°f39 ■0865 •0892 •0918 ■0945 ■0971 •0998 •1024 •1051 ■1077 ■I 104 •I 130 ■0793 ■ogi9 •0S46 •0873 •0899 •0926 •0953 ■0979 ■1006 ■1033 •1059 •1086 ■1113 •1140 5° 10 20' 30 40 50 6° 10 20 30' 40 50 1 10' 20' 30' When the Latitude is North the sign is + When the Latitude is South the sign is ~ . ALT-AZIMUTH TABLES. 78 Under Altitude and abreast of Declination, take out the tabular quantity and mark it + or — , according as Declination is S. or N. Add Algebraically E and F. Dec- lina- tion. TRUE ALTITUDE. 0° I 2 3 4 5 6° 7 8 9 10 11° 12 13 14 IS i6° 17 i8 19 20 21° 22 23 24 25 26° 28 29 30 31° 32 33 34 35 36° 37 38 39 40 41° 42 43 44 45 46° 42 48 49 50 51° 52 53 54 55 56° 57 58 60 61° 62 ^3 65 •OCX)0 •017s •0350 •052s •0700 ■087s •1049 •1223 •1397 ■1570 •1743 •I9IS •2087 ■2258 •2428 ■2598 •2767 ■2935 •3102 •3268 ■3433 ■3597 •3760 •3922 ■4083 •4242 ■4400 •4557 •4713 •4867 ■5019 •5170 •5319 ■5467 •5613 •5758 •5900 •6041 •6180 •6317 •6452 •6586 •6717 •6846 ■6973 •7098 ■7221 •7341 •7460 •7576 ■7690 ■7801 •7910 ■8017 ■8121 •8223 •8322 •8419 •8S«3 •8604 •8693 •8780 •8863 ■8944 ■9022 •9098 10 20 •0000 •0175 •0350 •0525 ■07CX5 ■087s •1050 ■1224 •1397 •1571 •1744 •I9I6 •2088 •2259 •2429 •2599 ■2768 •2936 •3103 •3269 •3434 ■3598 •3761 •3923 •4084 ■4243 ■4402 •4558 ■4714 •4868 •5020 •5171 ■5321 •5469 •56IS ■5759 •5902 •6043 •6182 •6319 •6454 •6587 •6719 •6848 •6975 ■7100 ■7223 •7343 •7462 •7578 •7692 •7803 •7912 •8019 •8123 ■8225. •8324 •8421 •851S •8607 •8696 •8782 •8865 •8946 •9025 ■9100 30 ■coco •0175 •0351 •0526 ■0701 ■0875 ■1050 •1224 •1398 •1571 ■1744 •I9I6 •208S ■2259 •2430 •2599 •2768 •2936 •3104 •3270 ■343s ■3599 •3762 ■3924 ■4085 •4245 ■4403 •4560 •4715 ■4869 ■5022 •5173 ■5322 •5470 •5616 ■5761 •5903 ■6044 ■6183 •6321 •6456 ■6589 •6720 ■6850 •6977 ■7102 •7225 •7345 •7464 ■7580 •7694 ■7805 •7914 •8021 ■8125 •8227 ■8326 •8423 ■8517 •8609 •8698 •8784 •8868 ■8949 •9027 •9102 40 50 10 ■0000 •0175 •0351 •0526 ■0701 ■0876 ■1050 •1224 ■1398 ■1572 ■1745 •1917 •2089 •2260 •2430 •2600 •2769 •2937 •3104 •3271 ■3436 •3600 •3763 •3925 •4086 •4246 •4404 •4561 •4716 ■4871 •5023 •5174 ■5324 ■5472 •5618 ■5762 ■5905 ■6046 •6185 ■6322 •6458 ■6591 ■6722 •6852 •6979 •7104 •7227 •7347 •7466 ■7582 ■7696 ■7807 ■7917 ■8023 ■8128 •8229 ■8329 •8425 ■8520 •86 ri •8700 •8787 •8870 •8951 ■9030 •9105 20 •0175 •0351 •0526 •0701 •0876 •1050 •1225 ■1399 •1572 •1745 •1917 •2089 ■2261 •2431 •2601 •2770 •2938 •3105 ■3272 •3437 •3601 ■3764 •3926 •4087 •4247 ■4405 ■4562 •4718 •4872 ■5025 •5176 •5325 •5473 •5619 •5764 •5907 •6048 •6187 •6324 •6459 •6593 •6724 •6853 ■6981 •7106 •7229 •7349 •7468 •7584 •7698 ■7810 •7919 ■8026 ■8130 ■8232 ■8331 •8428 •8522 ■8614 •8703 6 30 ■8873 •8954 •9032 ■9108 ■0175 •0351 •0526 •0701 •0876 •1051 •1225 •1399 •1572 •1746 •1918 •2090 ■2261 •2432 •2602 •2771 •2939 •3106 •3273 •3438 •3602 •3766 •3928 40 •4248 •4407 •4564 ■4719 •4873 •5026 •5177 •5327 •5475 •5621 •5766 •5908 •6049 •6189 •6326 ■6461 •6595 •6726 ■6855 •6983 •7108 •7231 •7352 •7470 •7586 ■7700 •7812 ■7921 ■8028 ■8132 ■8234 •8334 •8430 •8525 ■8616 •8705 ■8792 ■8875 ■8956 ■9035 •91 10 10 20 •0175 ■0351 ■0526 ■0701 ■0876 ■1051 ■1225 •1399 •1573 ■1746 ■1919 ■2091 ■2262 •2433 ■2602 ■2772 ■2940 •3107 •3274 •3439 ■3603 •3767 ■3929 ■4090 ■4249 ■4408 •4565 •4721 •4875 •5028 •5179 ■5328 •5476 ■5623 ■5767 ■5910 ■6051 •6191 ■6328 ■6463 ■6597 ■6728 ■6858 ■6985 ■7 no ■7233 ■7354 •7472 •7589 ■7703 ■7814 •7924 •8030 •8135 •8237 •8336 •8433 ■8527 •8619 8708 ■8794 50 •8959 ■9037 ■9113 •0000 ■0176 ■0351 •0526 •0702 ■0877 ■1051 •1226 ■1400 ■1573 •1747 •1919 •2091 •2263 •2433 •2603 •2772 ■2941 •3108 ■3275 •3440 •3605 •3768 ■3930 •4091 ■4251 ■4409 •4566 ■4722 •4876 •5029 •5180 •5330 •5478 •5624 •5769 •5912 6053 ■6192 •6330 •6465 ■6599 •6730 ■6860 •6987 •7112 ■7235 •7356 •7475 • 7591 •7705 •7817 ■7926 •8033 •8137 ■8239 '8339 ■8436 •8530 ■8622 ■8711 •8797 ■8881 •8962 ■9040 ■9116 6 30 •0000 •0176 ■0351 •0527 ■0702 •0877 ■1052 ■1226 ■1400 ■1574 •1747 •1920 ■2092 ■2263 ■2434 ■2604 ■2773 ■2942 •3109 •3276 •3441 ■3606 •3769 ■3931 ■4092 ■4252 ■4411 ■4568 ■4724 •4878 •5031 •5182 •5332 •5480 •5626 •5771 •5914 ■6055 ■6194 •6332 •6467 ■6601 ■6732 ■6862 ■6989 •7 114 •7238 •7358 ■7477 •7593 •7707 •7819 •7928 •803s •8140 •8242 •8341 ■8438 ■8533 ■8624 •8713 ■8800 10 ■8965 ■9043 ■91 19 40 ■0000 ■0176 ■0351 ■0527 •0702 ■0S77 ■1052 ■1227 ■1401 •1574 ■1748 ■1920 ■2093 •2264 ■2435 ■2605 ■2774 •2943 ■3110 ■3277 ■3442 ■3607 ■3770 •3933 •4094 4254 ■4412 •4569 ■4725 ■4879 •5032 ■5184 •5333 ■5482 ■5628 ■5773 ■5916 •6057 ■6196 •6334 ■6469 ■6603 •6735 20 ■6992 ■7117 ■7240 •7361 ■7480 ■7596 •7710 •7822 •7931 •8038 •8143 •8245 ■8344 ■8441 •8535 ■8627 ■8716 •8803 ■9046 ■9122 50 •0000 •0176 •0351 •0527 ■0702 ■0877 ■1052 •1227 •1401 •1575 ■1748 ■1921 ■2093 ■2265 ■2436 ■2606 •2775 •2944 •31 II •3278 •3443 •3608 •3772 •3934 •409s •4255 •4414 ■4571 •4727 •4881 •5034 •5185 •5335 •5483 •5630 •5775 •5918 ■6059 ■6199 ■6336 ■6472 ■6605 ■6737 ■6866 •6994 •7119 ■7242 •7363 •7482 •7598 •7713 •7824 •7934 ■8041 •8145 •8247 •8347 •8444 ■8538 •8630 ■8719 ■8806 ■8971 •9049 •9125 30 •0000 •0176 •0351 ■0527 ■0703 ■0878 •1053 ■1227 •1402 •1576 •1749 •1922 •2094 ■2266 •2437 ■2607 ■2776 ■2945 ■3112 •3279 •3445 ■3609 •3773 •3935 •4096 •4256 •4415 •4572 •4728 •4883 ■5036 •5187 •5337 •5485 •5632 •5777 •5920 ■6o5i ■6201 •6338 ■6474 ■6608 •6739 ■6869 ■6996 ■7122 •7245 •7366 •7485 •7601 •7715 •7827 •7936 •8043 •8148 ■8250 •8350 •8447 ■8541 •8633 •8722 40 •8974 •9052 •9128 10 ■0000 ■0176 ■0352 ■0527 ■0703 ■0878 ■1053 •1228 •1402 •1576 •1750 ■1922 ■2095 ■2266 •2437 ■2608 2777 ■2946 •3113 ■3280 •3446 ■361 1 •3774 •3937 ■4098 •4258 •4417 •4574 •4730 ■488s •5038 ■5189 •5339 •5487 •5634 •5779 ■5922 •6063 ■6203 ■6340 ■6476 ■6610 ■6742 •6871 ■6999 •7124 •7247 •7368 ■7487 ■7604 •7718 ■7830 •7939 •8046 •8151 •8253 •8353 •8450 •8544 •8636 ■8725 ■0000 ■0176 ■0352 •0527 •0703 •0878 •1054 •1228 ■1403 ■1577 •1750 •1923 ■2095 •2267 •2438 •2609 ■2778 ■2947 •3" 5 ■3281 •3447 •3612 ■3776 ■3938 •4099 •4259 •4418 •4576 ■4732 •8977 •905s •9131 50 20 ■5039 •5191 •5341 •5489 •5636 •5781 ■5924 •6066 ■6205 •6343 •6478 •6612 •6744 ■6874 7001 ■7127 •7250 •7371 •7490 •76=7 •7721 ■7833 •7942 ■8049 •8154 •8256 ■8356 •8453 •8547 •8639 ■8728 •8815 •0000 •0176 ■0352 •0528 •0703 •0879 •1054 •1229 •1403 •1577 •1751 •1924 •2096 •2268 •2439 •2610 ■2779 •2948 •31 16 •3283 •3448 •3613 •3777 •3940 ■4101 •4261 •4420 •4577 •4733 ■8980 •9059 •9134 30 ■5041 •5193 ■5343 ■5491 •5638 •5783 •5926 •6068 •6207 •6345 ■6481 •6615 •6746 •6876 •7004 •7129 7253 •7374 •7493 •7609 •7724 ■7836 •7945 ■8052 •8157 •8259 •8359 •8456 ■8550 •8642 ■8732 •8818 •8902 10 •9062 •9138 •0000 •0176 •0352 •0528 •0704 ■0879 •1054 •1229 •1404 •1578 •1751 ■1925 •2097 ■2269 •2440 261 1 ■2780 •2949 ■3II7 •3284 ■3450 ■3615 ■3778 ■3941 •4102 •4263 •4422 ■4579 ■473s •4890 •5043 ■5195 ■5345 5493 •5640 ■5785 ■5929 ■6070 •6210 ■6348 •6483 ■6617 ■6749 ■6879 •7007 •7132 •7255 •7377 ■7496 ■7612 •7727 •7839 •7948 ■80SS •8160 ■8262 •8362 ■8459 ■8554 •8646 ■8735 •88221. •8906 •8987 ■9065 ■9141 20 30 When the Declination is North the sign is - • When the Declination is South the sign is + . 79 ALT-AZIMUTH TABLES. Under Altitude in head-line, and abreast of Latitude in margin, taise out the tabular quantity and mark It + or according as the Latitude is N. or S. Lat. TRUE ALTITUDE. 7 30' 40 50 8° 10 20' 30 40' 50 9 10 20 30 40 50' Id 0° ■0000 ■0000 •0000 •0000 ■0000 •0000 •0000 ■0000 ■0000 •0000 •0000 •0000 ■0000 ■0000 ■0000 •0000 I •0023 •0023 ■0024 •0025 ■0025 ■0026 •0026 0027 •0027 •0028 •0028 0029 •0029 •0030 ■0030 ■0031 2 •0046 ■0047 •0048 ■0049 •0050 •0051 ■0052 ■0053 •O0S4 •0055 ■0056 •0057 •0058 0059 ■0060 ■0062 3 ■0069 •0070 •0072 •0074 •0075 ■0077 •0078 •0080 ■0081 •0083 •0084 •0086 ■0088 0089 ■0091 ■0092 4 ■0092 •0094 0096 •0098 0100 ■0102 ■0104 ■0106 •0108 •Olio ■01 13 •01 15 •01 17 •01 19 ■0121 ■0123 5 •0115 •01 17 0120 •0122 •0125 •0128 •0130 •0133 •0135 •0138 0141 •0143 •0146 ■0148 •0151 ■0154 6° •0138 •0141 ■0144 ■0147 ■0150 •0153 •0156 ■0159 •0162 ■0166 •0168 •0172 ■0175 ■0178 •0181 ■0184 I 0160 •0164 •0168 •0171 •0I7S •0179 ■0182 ■01 85 •0189 ■0193 •0197 •0200 ■0204 •0208 •0211 ■0215 ■0183 •0187 ■0191 •0196 ■0200 •0204 ■0208 ■0212 ■0216 0220 •0225 ■0229 ■0233 0237 •0241 ■0245 9 ■0206 ■02 u ■0215 •0220 •0224 •0229 ■0234 •0238 ■0243 0248 •0252 ■0257 ■0261 •0266 •0271 ■0276 10 0229 ■0234 •0239 •0244 •0249 •0254 ■0260 •0265 •0270 ■0275 ■0280 ■0285 ■0291 ■0296 •0301 ■0306 11° ■0251 ■0257 •0263 ■0268 •027/ •0279 •0285 •0291 •0297 •0302 ■0308 •0314 ■0319 •0325 ■0331 ■0336 12 ■0274 •0280 •0286 •0292 •029! •0305 ■03 1 1 •0317 •0323 •0329 •0336 •0342 ■0348 ■0354 •0360 ■0367 13 ■0296 ■0303 ■0309 0316 •0323 •0330 •0336 ■0343 •0350 ■0356 •0363 •0370 ■0376 ■0383 •0390 ■0397 14 •0318 •0326 •0333 •0340 ■0347 •0354 •0362 •0369 ■0376 ■0383 ■0390 ■0398 •0405 0412 ■0419 •0427 IS •0341 •0348 •0356 ■0364 •0371 •0379 ■0387 ■0395 •0402 •0410 ■0418 •0425- ■0433 ■0441 ■0449 •0456 16° •0363 ■0371 ■0379 ■0387 •0396 •0404 •0412 ■0420 •0428 ■0437 ■0445 •0453 ■0461 •0470 •0478 ■0486 17 ■0385 ■0394 0402 0411 ■0420 •0428 •0437 ■0446 ■0454 •0463 ■0472 •0481 ■0489 ■0498 •0507 ■0516 18 ■0407 ■0416 •0425 •0434 ■0443 •04S3 ■0462 •0471 ■0480 •0489 ■0499 •0508 ■0517 •0526 ■0536 •0545 19 •0429 •0438 •0448 ■0458 ■0467 •0477 0487 •0496 ■0506 •0516 ■0525 ■0535 •0545 •0555 •0564 •0574 20 ■0450 ■0460 •0471 •0481 •0491 •0501 ■05 1 1 ■0521 •0532 •0542 ■0552 ■0562 •0572 •0583 ■0593 ■0603 21'" •0472 •0482 •0493 •0504 •0514 ■0525 •0536 •0546 •0557 ■0568 ■0578 ■0589 •0600 •0610 •0621 ■0632 22 ■0493 •0504 ■OS'S •0526 ■0538 ■0549 •0560 •0571 •0582 •0593 •0604 ■0616 •0627 •0638 •0649 •0661 23 •0514 •0526 •0538 ■0549 •0561 ■0572 ■0584 •0596 ■0607 0619 •0631 ■0642 ■0654 ■0666 •0677 •0689 24 ■OS3S •0548 ■0560 •0572 •0584 •0596 •0608 •0620 ■0632 •0644 •0656 •0668 •o68i ■0693 ■0705 ■0717 25 •0SS6 •0569 •0581 •0594 •0606 ■0619 •0632 •0644 •0657 •0669 •0682 •0695 ■0707 ■0720 •0733 ■0745 26° ■0577 •0590 •0603 ■0616 ■0629 •0642 ■0655 ■0668 •068 1 •0694 •0707 ■0720 •0734 ■0747 •0760 •0773 27 •0598 ■061 1 ■0625 •0638 ■0652 •0665 •0678 •0692 ■0706 •0719 •0733 ■0746 •0760 ■0773 •0787 •0801 28 ■0618 •0632 •0646 •0660 ■0674 •0688 ■0702 •0716 •0730 •0744 •0758 ■0772 •0786 ■0800 •0814 ■0828 29 •0638 ■o6S3 •0667 •068 1 ■0696 ■0710 •0725 •0739 ■0753 ■0768 •0782 ■0797 ■081 1 •0826 •0840 ■0855 30 •0658 ■0673 •o588 •0703 ■0718 •0732 ■0747 •0762 •0777 •0792 •0807 ■0822 •0837 ■0852 •0867 ■0882 31° ■0678 ■0693 •0709 ■0724 •0739 ■0754 •0770 ■0785 ■0800 •0816 •0831 •0846 ■0862 ■0877 •0893 ■0908 32 •0698 ■0713 ■0729 ■074s •0760 ■0776 ■0792 •0808 ■0824 •0839 ■0855 •0871 ■0887 ■0903 •0919 ■0934 33 ■0717 ■0733 ■0749 •0765 ■0782 ■0798 ■0814 •0830 •0846 ■0863 ■0879 ■0895 ■09 1 1 ■0928 •0944 •0960 34 ■0736 ■07S3 ■0769 •0786 ■0802 •0819 •0836 •0852 ■0869 •0886 •0902 ■0919 ■0936 •0952 •0969 •0986 35 ■07SS •0772 ■0789 •0806 •0823 •0840 •0857 •0874 •0891 •0908 •0926 •0943 ■0960 ■0977 •0994 •ion 36° •0774 ■0791 •0809 •0826 ■0844 •0861 •0878 ■0896 ■0913 •0931 •0948 •0966 ■0984 •lOOI •1019 •1036 ■0792 ■0810 •0828 •0846 ■0864 •0882 •0899 •0917 ■0935 ■0953 •0971 •0989 ■1007 •1025 •1043 •1061 ■oSii •0829 •0847 '°fo^ ■0884 •0902 ■0920 ■0938 •0957 ■0975 ■0993 •I0I2 ■1030 •I049 •1067 •1086 39 •0829 ■0847 ■0866 •0884 ■0903 •0922 •0941 •0959 •0978 ■0997 •1016 ■1034 ■1053 •1072 •1091 •IIIO 40 •0846 ■0865 •0884 •0903 ■0922 •0942 ■0961 ■0980 ■0999 ■1018 ■1037 •1056 ■1076 •1095 •1114 ■1133 41° •0864 •0883 •0903 •0922 •0941 •0961 •0980 •1000 •1020 ■1039 ■1059 •1078 ■1098 ■HI7 •1137 ■1157 42 ■0881 •0901 ■0921 •0940 ■0960 ■0980 •1000 •1020 •1040 ■1060 ■1080 •IIOO •1120 ■I 140 •I 160 •I 180 43 ■0898 ■0918 ■0938 •0958 •0979 •0999 •1019 ■1040 •1060 ■1080 •IIOI •1I2I ■I 141 ■I 162 •1182 •1203 44 •09 IS ■0935 ■0956 ■0976 •0997 •1018 ■1038 •IOS9 ■1080 ■iioo ■1121 •II42 ■I 162 •H83 •1204 •1225 45 •0931 ■0952 •0973 •0994 ■1015 ■1036 ■1057 •1078 •1099 ■I 120 ■1141 •1162 •1183 •1204 •1226 •1247 46° •0947 •0968 ■0990 ■lOII •1032 •1054 •107s •1096 •1118 ■1139 ■1161 •I182 •1204 •1225 •1247 •1268 42 ■0963 •0984 •ioo5 ■1028 •1050 •107 1 ■1093 ■HIS ■1137 ■1158 •I 180 1202 ■1224 •1246 •1268 •1290 48 ■0978 ■1000 •1022 •1044 ■1066 •1089 •nil ■"33 ■1155 •1177 •1199 •I22I ■1244 •1266 •1288 •1310 49 •0994 •1016 •1038 ■I06I •1083 •1105 ■1128 ■1150 •1173 ■1195 ■1218 •1240 ■1263 •1286 •1308 ■1331 SO ■1009 ■103 1 •I0S4 ■1077 ■1099 •1122 ■1145 ■1168 •I 190 ■1213 •1236 ■1259 ■1282 ■1305 ■1328 •1351 Si° •1023 •1046 •1069 ■1092 •HIS •I 138 ■rt6i ■1185 ■1208 ■1231 ■1254 •1277 ■1300 ■1324 •1347 ■1370 52 •1037 •1061 ■1084 •I 107 •1131 •"54 •1178 ■I20I •1225 ■1248 ■1272 •1295 ■1319 ■1342 •1366 •1389 53 ■1051 ■I07S •1099 •II22 •1146 •1170 •I 194 ■I217 •1241 ■1265 •1289 ■1313 ■1336 •1360 ■1384 •1408 54 •1065 •1089 •1113 •1137 •1161 •1185 •1209 ■1233 ■1257 ■1281 •1305 •1330 ■1354 •1378 ■1402 •1427 55 •1078 •I 103 •I 127 •II5I •1176 •1200 •1224 •1249 •1273 ■1297 •1322 ■1346 •1371 •I.39S ■1420 •1444 56° •1091 •1116 ■I 140 •I 165 •I 190 •1214 ■1239 •1264 •1288 •1313 •1338 ■1363 •1387 •1412 ■1437 •1462 57 •I 104 ■I 129 •"54 ■II79 •1204 •1228 ■1253 •1278 •1303 •1328 ■1353 ■1378 ■1403 •1429 ■1454 •1479 58 •1116 •I 142 •I 167 •II92 •1217 ■1242 ■1267 •1293 •1318 •1343 ■1368 ■1394 •1419 ■1445 •1470 •1495 1' •1128 •1154 •1179 ■1205 ■1230 •1256 •1281 •1307 •1332 •1358 •1383 •1409 ■1434 •1460 •i486 ■1511 60 ■I 140 ■1166 •1191 •I217 •1243 •1269 •1294 •1320 •134& ■1372 •1397 ■1423 ■1449 ■1475 •1501 •1527 61° •1151 •1177 ■1203 ■1229 •I2SS •1281 •1307 ■1333 •1359 •1385 •14H ■1437 •1464 •1490 •1516 ■1542 62 ■I 162 ■I 189 •121S •I24I ■1267 •1293 •1320 ■1346 •1372 ■1398 ■1425 •1451 ■1478 ■1504 ■1530 ■1557 *3 •1173 ■I 199 ■1226 ■1252 ■1279 •130S •1332 ■1358 •1385 ■1411 ■1438 •1464 •1491 •1518 ■1544 •1571 5'^ •I 183 •^210 ■1237 •1263 •1290 •1317 •1343 ■1370 •1397 •1424 •1450 •1477 ■1504 •1531 ■1558 ■1585 65 •I 193 ■1220 •1247 •1274 •I30I ■1328 ■I 354 •1381 •1408 ■1435 •1462 •1490 ■1517 ■1544 •1571 •1598 7 30' 40 50' 8 10' 20 30' 40' 50' 9 10' 20' 30' 40' 50' Id When the Latitude is North the sign is + . When the Latitude is South the sign is - . ALT-AZIMUTH TABLES. 80 Under Altitude and abreast of Declination, take out the tabular quantity and mark it + or — , according as Declination is S, or N. Add Algebraically E and F. Dec- lina- tion. TRUE ALTITUDE. 7 30 0° I 2 3 4 5 6° I 9 10 11° 12 13 14 IS i6° 17 i8 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° 42 48 49 50 51° 52 S3 S4 SS 56° H 58 60 61° 62 65 •0000 •0176 •0352 ■0528 •0704 •0879 •IOS4 •1229 •1404 •1578 ■1751 •1925 ■2097 •2269 •2440 •261 1 •2780 •2949 •3117 •3284 ■3450 •361 S •3778 •3941 •4102 ■4263 '4422 ■4S79 •4735 ■4890 ■5043 ■5195 •S34S 5493 •5640 •5785 5929 •6070 •6210 -6348 '6483 ■6617 ■6749 •6879 •7007 ■7132 72SS •7377 •7496 •7612 7727 7839 7948 •80SS •8160 '8262 '8362 •8459 '85S4 ■S646 ■873s ■8822 'Sgo6 '8987 •9065 '9141 40 50 ■0000 ■0176 ■0352 •0528 •0704 •0879 ■105s '1230 •1404 •1578 •1752 •1925 •2098 •2270 •2441 •2612 ■2781 •2950 •3118 •3285- •3451 •3616 . -3780 •3943 •4104 •4264 •4423 •4581 •4737 ■4892 •5045 ■5197 •5347 •5496 •5642 •5787 •5931 •6072 •6212 •6350 •6486 •6620 •6752 ■6881 •7009 7135 7258 •7380 •7498 7615 7730 7842 •7951 •8058 •8163 •826s ■836s ■8462 •8557 •8649 8738 ■882s ■8909 •8990 •9069 •9145 ■0000 •0176 ■0352 •0528 •0704 •0880 •loss •1230 •1405 •1579 •1753 '1 926 •2099 ■2271 •2442 •2613 ■2782 ■2951 •3119 ■3286 ■3452 ■3617 ■3781 •3944 •4106 •4266 •4425 ■4583 ■4739 •4894 •5047 •5199 •5349 •5498 •5645 •5790 •5933 ■6075 •6215 •6352 7 3d 40 •6622 •6754 •6884 •7012 7138 •7261 7382 7501 •7618 7733 •7845 7954 •8062 •8166 •8269 ■8368 •8466 8560 •8652 •8742 •8829 •8913 •8994 •9073 •9148 10 •0000 •0176 •0352 •0S29 •0704 ■0880 •ios6 •1231 •140S •1580 •1754 ■1927 •2100 •2272 •2443 •2614 •2783 •2952 •3121 ■3288 •3454 '3619 '3783 •3946 ■4107 •4268 •4427 •4585 •4741 •4896 •5049 ■5201 ■5351 •5500 ■5647 •5792 •5936 ■6077 ■6217 ■6355 •6491 •662s •6757 ■6887 •7015 •7141 7264 7385 ■7504 7621 ■7736 7848 7958 ■8065 •8170 •8272 •8372 •8469 •8564 •8656 •8745 •8832 •8916 ■9076 •9152 50 20 30 40 •0000 •0176 •0353 ■0529 ■0705 •0880 •1056 •I23I ■1406 •1580 ■1754 •1928 •2100 •2273 •2444 261S •2785 •2954 •3122 •3289 •3455 •3620 •3784 •3947 •4109 •4269 •4429 •4586 •4743 ■4898 ■5051 •5203 ■5353 •5502 •5649 •5795 •5938 ■6080 •6220 •6358 •6494 •6628 •6760 •6890 ■7018 7144 •7267 ■7388 7508 •7624 7739 7851 7961 •8068 ■8173 •8275 ■8375 •8473 •8567 •8659 •8749 •8836 ■8920 •9001 •9080 •9156 8 •0000 •0176 •0353 •0529 •0705 •0881 •1056 •1232 •1407 •1581 •1755 •1928 •2101 •2274 ■2445 •2616 •2786 •2955 ■3123 •3290 •3457 •3622 •3786 •3949 •41 1 1 •4271 •4430 •4588 •4745 •4900 ■5053 ■520S •5356 ■5505 •5652 ■5797 •5941 •6082 •6222 •6360 •6496 •6631 •6763 •6893 •7021 7147 •7270 7392 75" •7628 ■7742 ■7854 •7964 •8072 •8177 •8279 •8379 '8476 •8571 8663 •8753 •8840 •8924 •9005 •9084 •9160 10 •0000 •0176 •0353 ■0529 •0705 ■0881 ■1057 •1232 ■1407 •1582 •1756 •1929 ■2102 ■2274 ■2446 ■2617 •2787 •2956 •3124 •3292 •3458 ■3623 •3788 ■3951 •4113 •4273 ■4432 ■4590 •4747 ■4902 •5056 ■5208 •5358 •5507 ■5654 •5799 "5943 •608s •6225 ■6363 •6499 •6633 •6766 20 •7024 7150 •7273 7395 •7514 •7631 •7746 7858 •7968 •8075 •8180 •8282 •8382 •8480 ■8575 8667 ■8756 •8843 •9009 •9164 50 •0000 •0177 ■0353 •0529 •0706 •0882 •1057 ■1233 •1408 •1582 •1757 •1930 •2103 •2275 •2447 •2618 •2788 •2957 •3126 •3293 •3460 ■362s •3789 •3952 •4114 ■4275 •4434 •4592 •4749 •4904 ■5058 ■5210 •5360 •5509 •5657 •5802 •5946 •6088 •6228 •6366 ■6S02 •6636 •6769 •6899 •7027 7153 •7276 7398 7517 •7634 •7749 7861 •7971 •8079 •8184 •8286 •8386 •8484 •8578 ■8671 •8760 •8847 •8931 •9013 ■9092 •9168 30 ■0000 •0177 ■0353 •0530 •0706 •0882 •1058 •1233 •1408 •1583 •1757 •1931 •2104 •2277 •2448 •2619 •2789 •2959 ■3127 •3295 •3461 •3627 ■3791 •3954 •4116 •4277 •4436 •4594 •4751 •4906 •5060 •5212 •5363 •5512 •5659 •5805 ■5948 ■6090 ■6231 •6369 ■6505 •6639 ■6772 •6902 •7030 7156 •7280 •7401 7521 •7638 •7752 •786s 7975 •8082 •8187 •8290 •8390 ■8487 •8582 ■8675 •8764 •8851 •8935 ■9017 •9096 9172 40 10 ■0177 ■0353 •0530 ■0706 •0882 •1058 •1234 •1409 •1584 ■1758 •1932 •2105 ■2278 •2449 '2620 •2791 •2960 •3129 •3296 ■3463 •3628 •3793 ■3956 •4118 •4279 •4438 •4596 ■4753 ■4909 •5062 •5215 •536s •5514 •5662 •5807 ■5951 •6093 •6233 •6372 •6508 •6642 •6775 •6905 •7033 7159 ■7283 •7405 •7524 •7641 •7756 50 •7978 •8086 •8191 •8294 •8394 •8491 •8586 •8679 •8768 •8855 •8940 •9021 •9100 •9176 20 30 •0177 ■0354 •0530 •0707 •0883 •1059 ■1234 ■1410 •1585 •1759 ■1933 ■2106 ■2279 •2451 •2622 •2792 •2962 •3130 ■3298 •3464 •3630 •3795 •3958 •4120 •4281 •4440 •4599 ■4755 ■491 1 ■5065 ■5217 •5368 •5517 •5664 •5810 •5954 ■6096 •6236 •6375 •6511 •6645 •6778 •6908 •7036 7163 ■7286 7408 •7528 •7645 7760 •7872 •7982 •8090 •8195 •8297 8495 •8590 •8683 •8772 ■8944 •9025 •9104 •9180 9 •0000 •0177 ■0354 •0530 ■0707 ■0883 •1059 ■1235 •1410 •1585 •1760 ■1934 •2107 •2280 •2452 •2623 ■2793 •2963 ■3132 •3299 •3466 •3632 •3796 •3960 ■4122 •4283 •4443 •4601 •4758 •4913 ■5067 •5219 •5370 •5519 •5667 ■5813 •5957 •6099 •6239 •6378 ■6514 •6649 •6781 •6911 •7040 •7166 •7290 7412 7531 ■7648 ■7763 ■7876 •7986 •8094 •8199 •8301 •8402 •8499 •8594 •8687 •8776 •8864 10 •9030 •9109 •9185 40 50 •0177 ■0354 •0531 •0707 •0884 •ic6o ■1236 •1411 •1586 •1761 ■1935 •2108 •2281 •2453 •2624 •2795 ■2964 ■3133 •3301 •3468 •3634 ■3798 ■3962 •4124 •4285 •4445 •4603 •4760 •4916 ■5070 ■5222 ■5373 ■5522 •5670 •5816 ■5960 •6102 •6242 ■6381 •6517 •6652 •6784 ■6915 ■7043 7169 ■7293 ■7415 ■7535 7652 •7767 •7880 ■7990 •8097 •8203 ■8305 •8406 •8503 •8598 •8691 •8781 20 •8952 •9034 •9113 •9189 •0177 •0354 ■0531 •0708 •0884 •1060 •1236 •1412 •1587 •1761 •1936 •2109 •2282 •2454 •2625 ■2796 •2966 ■3135 ■3303 •3469 •3635 •3800 ■3964 ■4126 ■4287 •4447 •4605 ■4762 •4918 •5072 •5225 ■5376 •5525 •5672 •5818 •5963 •6 1 OS •6245 •6384 •6520 ■6655 •6788 •6918 7047 7173 •7297 •7419 7538 •7656 7771 •7883 •7994 •8101 •8207 •8310 ■8410 •8508 •8603 ■8695 •8785 •8872 •8957 •9038 •9117 •9194 30 •0000 •0177 ■0354 •0531 •0708 •0885 •1061 •1237 •1412 •1588 •1762 ■1937 •21 10 •2283 •2455 •2627 •2797 •2967 ■3136 ■3304 •3471 •3637 •3802 •3966 •4128 •4289 ■4449 •4608 ■4765 •4920 ■5075 •5227 •5378 ■5528 ■5675 ■5821 •5965 •6108 •6248 •6387 •6524 •6658 •6791 •6922 •7050 7177 7301 •7423 7542 •7660 ■7775 •7887 ■7998 ■8ibS •8211 ■8314 •8414 •8512 •8607 •8699 •8789 •8877 ■8961 •9043 •9122 •9198 40 10 •0000 •0177 ■0354 ■0531 •0708 •0885 •106 1 •1237 ■I4I3 •1588 •1763 •1938 •2III ■2284 •2457 •2628 •2799 •2969 •3138 •3306 •3473 •3639 •3804 •3968 •4130 •4291 •4451 •4610 •4767 •4923 •5077 •5230 ■5381 ■5530 ■5678 ■5824 •5969 •611 1 •6252 •6390 ■ •6527 ■6662 •6795 •6925 •7054 7180 ■7304 •7426 •7546 •7664 7779 7891 •8002 •8110 •8215 •8318 •8418 •8516 •8611 •8704 •8794 •8881 8966 •9048 •9127 •9203 50 10 When the Declination is North the sign is - When the Declination is South the sign is + 81 ALT-AZIMUTH TABLES. Under Altitude in head-line, and abreast of Latitude in Margin, take out the tabular quantity and mark it + or according' as the Latitude is N. or S. TRUE ALTITUDE. Lat. 10 10 20 30 40 50 11 10 20 30 40 50 12 10 20 30 II" 12 13 14 IS i6° i8 19 20 21° 22 23 24 2S 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 51° 52 53 54 55 56° 57 58 59 60 61° 62 63 65 •0000 •0031 •0062 •0092 •0123 •0154 •0184 •0215 •024s ■0276 •0306 •0336 ■0367 •0397 •0427 •0456 •0486 0516 •OS45 ■0574 •0603 •0632 •0661 •0689 ■0717 ■o>4S ■0773 •0801 •0828 •08SS •0882 •0908 ■0934 ■0960 •0986 •loii •1036 •1061 •1086 •mo ■1133 •IIS7 •I 180 •1203 •1225 •1247 •1268 ■1290 ■1310 ■1331 •1351 •1370 •1389 ■1408 •1427 •1444 ■1462 •1479 •149s •1511 •1527 •1542 •I5S7 •1571 •1585 •1598 10 •0000 •0031 •0063 ■0094 •0125 •0156 •0187 ■0219 ■0250 •0281 ■03 1 1 •0342 ■0373 •0403 ■0434 '0464 •0494 ■0524 ■0SS4 •0584 ■0613 •0643 ■0672 •0701 •0729 •0758 •0786 •0814 •0842 •0869 •0897 •0924 ■0950 •0977 ■1003 •1029 ■1054 •1079 ■I 104 •I 129 •IIS3 •1175 ■1200 •1223 •1246 •1268 ■1290 ■1312 •1333 •I3S3 •1374 ■1394 •1413 •1432 •1451 •1469 ■1487 ■1504 •1521 ■IS37 •ISS3 ■1568 •1583 •1598 ■;^I2 ■I62| 10 •0032 •0064 •009s •0127 •0159 •0191 •0222 •0254 •0285 ■0317 •0348 •0379 ■0410 ■0441 •0472 •0503 •0533 ■0563 •0594 0624 ■0653 •0683 ■0712 •0742 •0771 •0799 ■0828 •0856 •0884 •0912 ■0939 •0966 •0993 •1020 •1046 ■1072 •1097 •I 123 ■1147 •I 172 •I 196 •1220 ■1244 •1267 •1289 •1312 •1333 ■I3SS •1376 •1397 •1417 •1437 •1456 •I47S •1494 •1512 •1529 •1546 •1563 ■1579 •IS9S •1610 ■1625 ■1639 •1652 20 •0000 •0032 •0065 •0097 ■0129 ■0162 •0194 ■0226 •0258 •0290 •0322 •0354 •0385 •0417 ■0448 •0480 •0511 •0542 ■0573 •0603 ■0634 '0664 •0694 •0724 •07S4 ■0783 •0812 •0841 •0870 ■0899 •0927 •095s ■0982 •1009 •1036 •1063 •1089 •HIS ■1141 •1166 •1191 •1216 ■1240 •1264 ■1287 •1311 •1333 •I3SS •1377 •1399 •1420 •1440 •1460 •1480 •1499 •1518 •IS37 •ISS4 •1572 ■1589 •1605 •1621 1636 ■1651 •1666 •1680 •0000 •0033 •0065 •0099 •01 3 1 •0164 •0197 •0230 •0262 •029s ■0327 ■03S9 •0392 0424 •0456 •0487 ■0519 •OSS I •0582 ■0613 •0644 •067s •0706 •0736 •0766 ■0796 •0826 ■o8ss •0884 •0913 ■0942 •0970 •0998 •1026 •1053 •1080 •I 107 ■I 134 •I 160 ■ii8s •1211 •1236 •1260 •128s •1308 ■1332 •I3SS ■1378 •1400 •1421 ■1443 •1464 •1484 ■1504 ■1524 •1543 ■1561 •1580 ■1597 ■1614 •1631 •1647 •1663 •1678 •1693 ■1707 40 •0000 ■0033 •0067 •0100 •0133 •0167 0200 ■0233 '0266 0299 •0332 •036s ■0398 •0430 ■0463 •049s •0S27 •OSS9 •0591 •0623 •o6ss •0686 •0717 •0748 •0778 •0809 •0839 •0869 ■0898 •0928 •0957 ■0986 •1014 •1042 ■1070 •1098 •II2S ■IIS2 •1178 •1204 •1230 •I2SS •1280 •130s •1329 •1353 •>377 •1400 •1422 •1444 •1466 •1487 •1S08 •1S28 •1548 •1568 •1586 •I 60s •1623 •1640 •1657 •1674 •1690 •170S •1720 •1734 50 •0000 •0034 •0068 •0102 •0136 •0169 •0203 •0237 •0271 •0304 ■0338 •0371 •0404 •0437 •0470 •0S03 •0536 •0568 •0601 •0633 ■0665 •0697 •0728 •0760 •0791 •0821 •o8S2 •0882 •0913 ■0942 ■0972 •lOOI •1030 •IOS9 •1087 •HIS "43 •1170 •1197 •1223 •1249 •127s •1301 •1326 •I3SO ■1374 •1398 •1422 •I44S •1467 •1489 •iSii •1532 ■1552 •1573 ■1592 •1611 ■1630 •1648 •1666 •1683 ■1700 •1716 •1732 •1747 •1762 11 •0000 ■0034 •0069 •0103 •0138 •0172 •0206 •0241 ■0275 •0309 ■0343 ■0377 •0410 •0444 •0478 •OS 1 1 •OS44 ■0577 •0610 •0643 •067s •0707 •0739 ■0771 •0803 •0834 •oS6s •0896 •0927 •09S7 •0987 •1017 •1046 •I07S •1104 ■1132 •1160 ■1188 ■1215 ■1242 •1269 •129s •1321 •1346 •1371 •1396 •1420 •1444 •1467 •1490 •1512 •IS34 •1556 •1577 •1S97 •1617 •1637 •1656 •1674 •1692 •1710 ■1727 •1743 •17S9 •1774 •1789 •0000 •003s •0070 •oios •0140 •0175 •0244 ■0279 •0314 ■0348 ■0382 •0417 •0451 •048s •OS 19 ■0552 ■0586 •0619 •0653 •068s ■0718 •0751 •0783 •08 IS •0847 •0879 •0910 •0941 •0972 •1002 •1032 •1062 •1092 •II2I •iiSo •II78 •1206 •1234 ■I26I •1288 •I3I5 •I34I ■1367 •1392 •I4I7 •1442 •1466 •1489 ■I5I3 •'535 •1558 •IS79 •1601 •1621 •1642 •1662 •1681 •1700 •1718 •1736 •I7S3 •1770 •1786 ■1801 •1816 10 20 •0000 •0036 •0071 ■0106 •0142 ■0177 •0213 •0248 •0283 •0318 ■03S3 •0388 •0423 •04S8 •0492 •OS27 ■0561 •059s 0629 ■0662 •0696 ■0729 •0762 •079s •0828 ■0860 •0892 ■0924 •09SS •0986 •1017 •1048 •1078 •I 108 •I 138 •I 167 •1196 ■1224 ■I2S3 •1280 •1308 •133s •1361 •1388 •1413 •1439 •1464 •1488 ■1512 ■IS3S •1SS9 •iS8i •1603 ■1625 ■1646 •1667 •1687 •1706 ■172s ■1744 •1762 •1779 ■1796 ■1813 ■1829 •1844 30 ■0000 •0036 •0072 •0108 •0144 •0180 •0216 ■0252 •0287 ■0323 •0359 •0394 •0429 ■0464 ■0500 •0534 •0569 •0604 •0638 ■0672 ■0706 •0740 •0774 •0807 •0840 •0873 •090s •0937 •0969 •looi •1032 •1063 •1094 •II2S •II55 •1184 •1214 •1243 •1271 •1299 •1327 •1355 ■1382 •1408 •1434 1460 •1712 •1732 •1751 •1770 •1788 •1806 •1823 •1840 ■1856 •1871 40 •0000 •0037 ■0073 OHO •0146 •0183 •0219 •0255 0292 •0328 •0364 •0400 •0436 •0471 ■0507 •0542 •0578 •0613 •0647 •0682 •0717 •07s 1 •0785 •0819 •o8s2 ■0885 •0918 •0951 •0984 •1016 •1048 •1079 •mo •1141 •1172 •1202 •1232 •1261 •1290 •1319 ■1347 •1375 •1402 •1429 •1455 •1482 148s •1507 1510 •1532 153 r •1557 1558 •1581 1582 •160S 1 60s •1628 1627 •1651 1649 •1673 1670 •169s 1691 •1716 ■1737 •I7S7 ■1777 •1796 •1814 •1832 •i8so ■1857 •1S83 50 •0000 .•0037 •0074 ■cm •0148 •0186 •0222 ■0259 •0296 ■0333 ■0369 ■0406 •0442 •0478 •0514 •0550 •0586 ■0621 ■0657 •C692 0727 •0762 ■0796 ■0831 ■086s ■0898 •0932 •096s 0998 •1030 •1063 •1095 •I 126 •iiS8 •I 189 •1219 •1249 •1279 •1309 ■1338 •1366 •1394 •1422 •1450 •1477 ■1503 •1529 ■1555 •1580 •1604 •1628 •i6s2 •1675 ■1698 •1720 •I 741 •1762 •1783 •1803 •1822 •1841 ■1859 ■1877 ■1894 •1910 •1926 12 ■0000 •0038 •007s •0113 •01 so •0188 •022s •0263 ■0300 •0337 ■0374 •041 1 ■0448 ■0485 •OS22 •0558 ■0594 ■0630 •0666 •0702 •0737 •0773 •0808 •0842 •0877 •0911 •0945 ■0979 •IOI2 •I04S •1078 •mo •I 142 •1174 •1206 ■1237 •1267 ■1298 ■1327 •1357 •1386 ■1414 ■1443 •1470 •1498 ■1525 •1551 •1577 •1602 1627 •1652 •1676 •1699 •1722 •1744 •1766 •1787 •1808 •1828 •1848 •1867 •1886 •1904 •1921 •1938 •1954 10 ■0000 •0038 •0076 0114 ■0153 •019 1 •0229 •0266 •0304 ■0342 •0380 ■0417 ■0455 •0492 •0529 •0566 •0603 ■0639 ■0676 •0712 •0748 •0784 ■0819 ■0854. •0889 •0924 •0958 •0993 •1026 •1060 •1093 •I 126 •IIS9 ■1191 ■1223 •1254 •128s •1316 •1346 •1376 •'40s •1434 ■1463 •1491 •1519 •1546 •1573 •1599 •162s •i6so •167s •1699 ■1723 •1746 •1769 •1791 ■<8i3 •1834 •1854 •1874 •1894 ■1912 •1931 •1948 •196s •1982 •0000 0039 ■0077 •01 16 •015s •0193 •0232 •0270 •0309 ■0347 •0385 •0423 •0461 •0499 ■0536 ■0574 •061 1 •0648 •068s •0722 ■0758 •0794 •0830 •0866 •0902 •0937 •0972 •1006 ■1041 ■1075 •I 108 ■I 142 ■"75 ■1207 •1240 ■1272 ■1303 •1334 •1365 •1395 •1425 •1454 •1483 •1512 •1540 •1568 •IS9S '1621 •1648 •1673 •1698 •1723 •1747 •1771 •1794 •1816 •1838 •1859 •1880 •1900 •1920 •1939 •1957 •1975 ■1993 •2009 20 30 When the Latitude is North the sign is + When the Latitude is Soutif the sign is — ALT-AZIMUTH TABLES. 82 Under Altitude and abreast of Deelination, take out the tabular quantity and mark it + or — . according as Declination is S. or N. Add Algebraically E and F. Dec- lina- tion. TRUE ALTITUDE. I 2 3 4 S 6° 7 8 9 10 11° 12 13 14 IS i6° 17 i8 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 51° 52 53 54 55 56' 57 58 60 61° 62 i^ 6s 10 ■0000 •0177 ■0354 •0531 0708 ■0885 1061 •1237 ■1413 •1588 •1763 •193S ■21 1 1 ■2284 •2457 ■2628 ■2799 •2969 ■313S •3306 ■3473 ■3639 •3804 ■3968 •4130 ■4291 ■4451 ■4610 ■4767 •49.23 ■5077 •5230 •5381 •5530 •5678 •5824 •5969 ■61 1 1 •6252 ■6390 •6527 •6662 ■679s ■692s •7054 •7180 •7304 ■7426 •7546 ■7664 •7779 •7891 •8002 •8 1 10 ■82 IS ■8318 •8418 ■8516 •86 1 1 ■8704 •8794 •8881 8966 ■9048 ■9127 ■9203 10 20 0000 •OI77 •0355 0532 •0709 •0885 •1062 •123S •1414 •1589 ■1764 •1939 ■2112 •2285 ■2458 •2629 •2800 •2970 •3139 •3308 •3475 ■3641 ■3S06 ■3970 •4132 ■4294 •4454 •4612 •4770 •4925 •5080 •5233 •5384 •5533 ■5681 •5827 •5972 •61 14 •6255 •6394 •6530 •6665 •6798 •6929 •7057 ■7184 •7308 •7430 •7550 ■7667 •7783 •789s •8006 •81 14 ■8219 •8322 •8423 •8520 •8616 ■8708 ■8798 •8886 ■8970 •9052 ■91 3 1 •9208 10 30 •0000 •0177 •0355 •0532 ■0709 ■0886 •1063 •1239 •141S •1590 •1765 •1940 •2113 •2287 •2459 •2631 •2802 ■2972 •3141 •3309 •3477 •3643 •3808 •3972 ■4134 •4296 •4456 •4615 •4772 •4928 •5082 ■5235 •5387 •5536 •5684 •5830 •5975 •61 17 ■6258 •6397 •6534 •6669 •6802 ■6932 ■7061 •7188 ■7312 •7434 ■7554 •7672 •7787 •7900 ■8010 ■8118 ■8224 •8327 •8427 •8525 •8620 •8713 •8803 •8890 •897s ■9057 •9136 •9212 10 40 20 •C3000 •0177 •0355 ■0532 •0709 ■0886 •1063 •1239 •I415 ■1591 •1766 ■1941 •2115 •2288 ^460 •2632 •2S03 ■2974 •3143 33II •3(78 •3645 ■3810 •3974 •4137 •4298 •4458 •4617 •4775 •4931 •5085 •5238 •5389 •5539 •5687 •5833 •5978 •6121 •6261 •6400 •6537 •6672 6805 ■6936 ■7065 •7191 ■7316 •7438 •7558 •7676 ■7791 •7904 •8014 •8122 ■8228 •8331 •8432 •8530 •8625 •8718 •8808 •8895 •8980 •9062 •9141 •9217 50 0000 •0178 ■0355 •0533 •0710 •0887 •1064 •1240 ■1416 •1592 ■1767 •1942 •21 16 •2289 •2462 •2634 •2805 •2975 •3145 •3313 •3480 •3647 ■3812 •3976 •4139 •4300 •4461 •4620 •4777 •4933 •5088 •5241 •5392 •5542 •5690 •5837 •5981 •6124 ■6265 •6404 •6541 •6676 •6809 •6940 •7069 •7195 7320 ■7442 •7562 •7680 •7795 •7908 •8019 ■8127 ■8232 •8336 •8436 •8534 •8630 •8722 ■8813 ■8900 •8985 •9067 •9146 ■9222 30 11 ■0000 •0178 ■0355 •0533 •0710 •0887 •1064 ■1241 •1417 •1593 •1768 •1943 •2117 •2290 •2463 •2635 •2806 •2977 •3146 •3315 ■3482 •3649 •3814 •3978 •4141 •4303 •4463 ■4622 •4780 •4936 •5091 •5244 •5395 •5545 •5693 •5840 •5985 •6127 •6268 •6407 6545 ■6680 •6813 •6944 •7073 ■7199 •7324 •7446 •7566 •7684 •7799 •7912 •8023 ■8131 •8237 •8340 •8441 •8539 •8634 •8727 •8817 •8905 •8990 •9072 •9151 •9228 40 ■0000 ■0178 ■0356 •0533 •07 1 1 •088S ■1065 •1242 •1418 •1594 •1769 •1944 •2118 •2292 ■2464 •2637 •2808 •2978 •3148 •3317 ■3484 •3651 ■3816 •3980 •4143 •4305 •4466 •4625 •4782 •4939 •5094 ■5247 •5398 •5548 •5697 •5843 •5988 ■6131 •6272 ■64H •6548 •6683 •6817 10 •7077 ■7203 7328 ■7450 •7571 •7688 7804 •7917 ■8028 •8136 •8242 •8345 •8446 •8544 8639 ■8732 •8822 •8995 ■9077 ■9156 •9233 50 20 •0000 •0178 •0356 •0533 •0711 •0888 •1065 •1242 ■1419 •1595 ■1770 •1945 •21 19 •2293 •2466 •2638 ■2810 •2980 •3150 •3319 •3486 •3653 •3818 •3983 •4146 •4308 •4468 •4628 •478s •4942 •5096 •5250 •54 I •5551 •5700 •5846 •5991 •6134 •6275 ■641 5 •6552 •6687 •6820 ■6952 ■7081 •7208 •7332 •7455 •7575 ■7693 ■7808 •7921 •8032 ■8140 ■8246 •8350 •8450 •8549 •8644 •8737 •8827 ■891 5 •9000 •9082 •9161 •9238 11 30 40 •0000 •0178 ■0356 ■0534 •07 1 1 ■0S89 •io65 •1243 ■1419 •1595 1771 •1946 ■2120 •2294 ■2467 ■2640 •2811 ■2982 •3152 •332:1 •3488 •3655 •3821 •3985 ■4148 •4310 •4471 •4630 ■4788 •4945 •5099 •5253 •5405 •5555 •5703 •5850 •5995 •6138 •6279 •6418 •6556 •6691 •6824 ■6956 •7085 •7212 •7336 •7459 •7579 •7697 •7813 ■7926 •8037 •8145 •8251 •8354 •8455 •8553 ■8649 •8742 •8832 ■8920 •9005 ■9087 ■9167 •9243 10 •0000 •0178 •0356 •0534 ■0712 •0889 •1067 •1244 ■1420 •1596 ■1772 •1947 ■2122 ■2296 ■2469 •2641 •2813 •2984 •3153 ■3322 •3490 ■3657 •3823 •3987 •4151 •4313 •4474 •4633 •4791 •4947 •5102 ■5256 •5408 •5558 •5705 •5853 •5998 6141 ■6283 ■6422 •6560 •6695 •6828 •6960 •7089 •7216 •7341 •7463 •7584 ■7702 ■7817 ■7931 ■8042 ■8150 •8256 8359 ■8460 •8559 •8654 •8747 •8925 ■9010 ■9093 ■9172 ■9249 20 50 ■0000 ■0178 •0356 •0534 •0712 •0890 •1067 •1244 •I42I •1597 •1773 •1948 ■2123 •2297 •2470 •2643 •28 IS ■298s •3155 •3324 •3492 •3659 •3825 ■3990 •4153 •4315 •4476 •4636 •4794 •4950 •510S •5259 •S4II •5561 •5710 ■5857 •6002 •6145 ■6286 •6426 6563 •6699 •6832 •6964 •7093 ■7220 •7345 •7468 ■7588 •7706 •7822 •7935 •8046 •8155 •8261 ■8364 •8465 •8564 •8659 •8752 ■8843 ■8931 ■9016 ■9098 •9178 •9254 30 12 10 20 •0000 •0178 •0357 •0535 •0713 •0890 •1068 •1245 •1422 •1598 •1774 •1950 •2124 •2298 ■2472 ■2644 •2816 •2987 •3157 •3326 •3494 ■3661 •3827 •3992 •4156 •4318 •4479 •4638 •4797 •4953 ■5109 ■5262 ■54 '4 •5565 ■5713 •5860 •600S •6149 •6290 ■6430 •6567 ■6703 •6837 ■6968 •7097 •7225 •7350 •7472 •7593 •7711 •7827 •7940 •8051 •8160 •8266 •8369 •8470 •8569 •8758 40 •8936 •9021 ■9104 •9183 ■9260 ■0000 •0178 •0357 •053s ■0713 ■0891 •1069 •1246 •1423 •1599 •1775 •195' •2126 •2300 •2473 ■2646 •2818 •2989 •3159 •3328 •3497 ■3664 •3830 •3995 •4158 •4321 •4482 •4641 •4800 •4956 •5112 •5265 •5418 •5568 •5717 •5864 •6009 •6153 ■6294 ■6434 •6571 •6707 •6841 •6972 •7102 •7229 •7354 •7477 •7597 ■7716 ■7832 •7945 •8056 •816s 8271 ■837s •8476 ■8574 ■8670 ■8763 •8854 •9027 •9109 •9189 •9266 50 •0000 ■0179 •0357 •0535 ■0714 •0892 •1069 •1247 ■1424 •1600 •1776 •1952 •2127 ■2301 •2475 •2648 •2820 •2991 •3x61 •3330 •3499 •3666 •3832 ■3997 •4161 •4323 •4484 •4644 •4803 •4959 •5115 •5269 •5421 •5572 •5720 •5868 •6013 •6156 •6298 ■6438 •6576 •67 II •684s •6977 ■7106 •7234 •7359 ■7482 •7602 •7721 •7836 ■7950 •8061 •8170 •8276 •8380 , 8481 •8579 •8675 •8769 •8859 •8947 ■9032 •9115 •9194 •9271 12 ■0000 •0179 •0357 •0536 •0714 ■0892 •1070 •1247 •1425 •1601 •1778 •1953 •2128 •2303 •2476 •2649 ■2821 •2993 •3163 •3333 •3501 •3668 •3835 ■4000 •4163 ■4326 •4487 •4647 •4806 •4963 •5118 •5272 •5424 •5575 ■5724 •5871 •6017 ■6160 •6302 •6442 •6580 •6716 ■6849 •6981 ■7111 ■7238 •7363 •7486 ■7607 •7725 •7841 •7955 •8066 •817s •8281 •8385 ■8486 •8585 •868i •8774 •8865 •8953 •9038 •9121 •9200 •9277 10 30 ■0000 •0179 ■0357 •0536 •07 1 5 •0893 •1071 •1248 ■1426 •1602 •1779 •1954 •2130 •2304 ■2478 ■2651 •2823 •2995 •316S •3335 •3503 •3671 •3837 •4002 •4166 •4329 •4490 •4650 •4809 •4966 •5121 •5275 ■5428 ■5579 •5728 ■5875 •6021 ■6164 •6306 '6446 •6584 •6720 •6854 •6986 •7115 •7243 •7368 ■7491 ■7612 •7730 ■7846 ■7960 •8071 •8180 •8287 •8390 •8492 ■8590 •8686 •8780 •8871 •8959 •9044 •9126 •9206 •9283 20 30 When the Deelination is North the sign is - When the Deelination is South the sign is + 83 ALT~AZiMUTH TABLES. Under Altitude in head-line, and abreast of Latitude in margin, take out the tabular quantity and marls it + or according as the Latitude is N. or S. TRUE ALTITUDE. Lat. 12 30 40 50 13 10 20 30 40 50 14 10 20 30 40 50 15 9 10 11° 12 13 14 IS 16° 'Z i8 19 20 21° 22 23 24 25 26° 28 29 30 31° 32 33 34 35 36° 37 38 39 40 41° 42 43 44 45 46° 47 48 49 SO 51° 52 53 54 55 56° 57 58 £0 61° 62 64 65 •0000 •0039 •0077 •0116 •015s •0193 •0232 •0270 ■0309 •0347 •0385 •0423 •0461 •0499 •0536 'OS74 ■06 n ■0648 •0685 •0722 •0758 •0794 ■0830 •0866 ■0902 ■0937 •0972 •1006 ■1041 •I07S ■I 108 •I 142 •"75 •1207 •1240 •1272 •1303 ■1334 •1365 •139s •1425 •I4S4 •1483 •1512 •1540 ■1568 •IS9S •1621 •1648 ■1673 •1698 •1723 ■1747 •1771 •1794 •1816 ■1838 •1859 ■1880 ■1900 •1920 •1939 •I9S7 •1975 •1993 ■2009 12 30 ■0039 •0078 ■01 18 •0157 ■0196 •0235 •0274 •0313 •0352 •0390 •0429 •0467 •0506 ■0544 ■0582 •0619 •0657 •069s •0732 •0769 •0805 •0842 •0878 •0914 •0950 •0985 •1020 •loss •1090 •I 124 ■1158 •1191 ■1224 •I2S7 •1289 . •1321 •1353 ■1384 •1414 •1445 •1474 •1504 ■IS33 ■1561 •1589 •1617 ■1644 •1670 •1696 •1722 •1747 •I 77 1 •1795 •1818 •1841 •1863 •1885 •1906 •1926 •1946 •1966 •1984 •2003 •2oao •2037 » 40 0000 •0040 •0080 •01 19 •0159 V199 •0238 ■0278 •0317 •0356 '0396 •043s •0474 ■OS 1 2 •0551 ■0590 •0628 •0666 •0704 •0742 •0779 •0816 •0853 •0890 ■0927 •0963 •0999 •1034 •1069 •I 104 •I 139 •1173 •I207 •I24I •1274 ■1307 •1339 •137I •1403 •1434 •1464 •1495 •1524 •I 554 •1582 ■1611 •1639 •1666 •1693 •1719 •1745 •1770 ■ •1795 ■1819 •1843 •1866 •1889 •1911 •1932 ■1953 •1973 •1992 ■201 1 •2030 •2048 •2065 50 •0040 •0081 •0121 ■0161 •0201 ■0241 •0281 •0321 ■0361 •0401 •0441 •0480 •0519 ■OSS9 •0598 ■0636 ■0675 •0713 •0752 •0790 •0827 •086s ■0902 ■0939 •0976 •1012 •1048 •1084 •1119 ■1154 •I 189 •1223 •1257 ■1291 •1324 •1357 •1389 •1421 •1453 •1484 •1515 •1545 •1575 ■1604 •1632 •1661 •1688 ■1716 •1742 ■1769 •1794 •1819 ■1844 ■1868 •1891 ■1914 •1936 ■1958 •1979 •1999 •2019 ■203S ■2057 ■2075 •2092 •oooo •0041 ■0082 •0122 •0163 •0204 ■0244 •028s •0326 ■0366 •0406 •0446 •0486 •0526 ■0566 •0605 •0645 •0684 ■0723 ■0762 •0800 •0838 ■0876 •0914 •09s I ■0989 •1025 •1062 ■1098 •1134 ■II70 ■1205 •1240 •1274 •1308 •1342 •137s •1408 ■1440 •1472 •1504 •IS35 •1565 •1595 •1625 •1654 •1683 ■1711 ■1738 •1766 ■1792 ■1818 •1843 •1868 •1893 •1916 •1939 ■1962 1984 •200s •2026 •2046 •2066 •2084 •2103 ■2120 13 10 •0041 •0083 ■0124 •0165 •0207 ■0248 ■0289 ■0330 ■0371 •0412 •0452 •0493 •0533 •0573 •0613 •0653 •0693 ■0732 •0772 •0811 •0849 •0888 •0926 ■0964 •1039 •1076 ■1113 •I 149 •118S ■1221 •1256 •1291 •1325 •1359 •1393 •1426 •1459 •1492 •1523 •1555 •1586 ■1616 •1646 ■1676 ■'70s •1733 ■1761 ■1789 ■1816 •1842 •1868 •1893 •1917 •1941 •1965 •1988 ■2010 2032 ■2053 •2073 •2093 •2II2 •2130 ■2148 20 •0042 •0084 ■0126 ■0167 •0209 •0251 ■0293 •0334 •0376 •0417 ■0458 ■0499 •0540 •0581 ■0621 '0662 ■0702 ■0742 •0782 •0821 ■0860 •0899 •0938 ■0976 •1015 •1052 •1090 ■1127 •I 164 •1200 ■1236 •1272 ■1308 •1343 •1377 ■1411 •1445 •1478 •IS" •1543 ■IS7S •1606 •1637 •1668 •1698 ■1727 •1756 •1784 ■1812 •1839 •I 865 ■1892 ■1917 •1942 •1967 •1990 •2013 •2036 ■2058 •2079 •2100 •2120 •2139 •2158 •2176 •0000 ■0042 ■0085 •0127 •0170 ■0212 •0254 •0296 •0338 •0380 •0422 •0464 •0506 •0547 •0588 •0629 •0670 •07 1 1 •0751 •0792 •0832 ■0871 •09 1 1 ■0950 0989 •1028 ■1066 ■I 104 ■I 142 •1179 •1216 ■I2S2 •1289 •1324 ■1360 ■1395 •1429 •1463 •1497 •1530 •1563 ■1595 ■J 627 •1658 •1689 •1719 •1749 •1778 ■1807 •1835 •1863 •1890 •1916 •1942 ■1967 •1992 •2016 •2039 ■2062 •2084 •2106 ■2127 ■2147 ■2167 •2185 ■2204 30 40 •0000 ■0043 •0086 •0129 ■0172 •0215 •02S7 •0300 •0343 •0385 ■0428 •0470 •0512 ■0554 ■0596 •0637 •0679 ■0720 ■0761 ■0802 •0842 ■0882 ■0922 ■0962 •1002 ■1041 •1079 •1118 •iiS5 •1194 ■1231 •1268 •1305 •1341 •1377 •1412 ■1447 ■1482 •1516 •1550 •1583 ■1615 ■1648 •1679 •1711 •1741 ■1771 •1801 •1830 •1858 ■1886 •1914 •1940 •1967 •1992 •2017 •2041 •2065 •2088 ■2111 •2133 ■2154 •2174 ■2194 ■2213 •2232 50 •0000 •0044 ■0087 •0130 ■0174 •0217 ■0261 0304 •0347 ■0390 •0433 •0476 •0518 •0561 •0603 ■0645 :o687 ■0729 ■0770 •08 1 2 ■0853 •0894 •0934 ■0974 •1014 •1054 •1093 ■1132 •1171 •1209 •1247 •1284 ■1321 ■1358 ■1394 ■1430 •1466 ■1500 •1535 •1569 ■1603 •1636 •1668 •1700 •1732 •1763 ■1794 •1823 •1853 •1882 •1910 •1938 •1965 •1991 •2017 •2042 •2067 •2091 ■2114 •2137 •2159 •2i8i •2201 ■2222 •2241 •2260 •0044 ■0088 ■0132 ■0176 ■0220 ■0264 •0308 ■0351 •0395 •0438 •0482 •052s •0568 ■061 1 ■0653 •0696 •0738 •0780 •0822 ■0863 •0905 •0946 •0986 •1027 ■1067 •I 107 •I 146 •ii8s •1224 •1262 •1300 •1338 •1375 ■1412 •1448 •1484 •1519 •1554 •1589 •1623 •1656 ■1689 ■1722 •1753 •1785 •1816 •1846 ■1876 •1905 •1934 ■1962 •1989 ■2016 •2042 •2068 •2093 •2117 ■2141 •2164 •2186 •2208 ■2229 •2249 •2269 •2288 14 10 •0000 •0045 ■0089 ■0134 ■0178 •0223 •0267 •03 1 1 •0356 ■0400 •0444 •0488 ■0531 •0575 •0618 ■o56i •0704 •0747 •0790 •0832 •0874 •0916 •0957 •0998 ■1039 ■1080 •I 120 •I 160 •1200 •1239 •1278 ■1316 •1354 •1392 •1429 •1466 •1502 •1538 •1573 ■1608 •1642 •1676 •1710 •1743 ■1775 •1807 ■1838 ■1869 •1899 •1928 •1957 •1986 •2013 ■2041 •2067 ■2093 •2n8 •2143 •2167 •2190 •2213 •223s •2256 •2277 •2297 ■2316 20 0000 ■0045 ■0090 •0135 •0180 •0225 •0270 ■0315 •0360 ■0405 ■0449 ■0493 ■0538 ■0582 ■0626 •0669 •0713 •0756 •0799 •0842 ■088s ■0927 •0969 •lOIO ■1052 •1093 ■1134 ■II74 •I2I4 •1254 •1293 ■1332 ■1370 •1409 •1446 •1483 •1520 •1556 ■1592 ■1628 •1662 •1697 •1730 •1764 ■1797 •1829 •i860 •1891 ■1922 •1952 •1981 ■2010 •2038 •2065 ■2092 •2118 •2144 •2169 •2193 •2217 •2240 •2262 •2283 •2304 •2324 •2344 30 •0000 •0046 •0091 •0137 •0183 •0228 ■0274 •0319 •0364 •0409 ■0454 •0499 ■0544 ■0589 •0633 ■0677 •0721 •076s ■0809 ■0852 •089s •0938 •0980 •1023 •1065 •I 106 •I 147 •I 188 ■1229 •1269 •1309 ■1348 ■1387 •1425 •1464 ■1501 •1538 •1575 •1611 •1647 ■1682 •1717 •1751 •1785 •1818 •1851 •1883 ■1914 •1945 •1975 •2005 •2034 •2062 •2090 •2117 •2144 ■2170 •2195 •2220 •2243 •2267 •2289 •2311 •2332 •2352 •2372 40 0000 0046 •0092 •0139 •0185 •0230 •0277 •0323 •0369 ■0414 •0460 ■0505 •0551 •0596 •064 c ■0685 •0730 •0774 •0818 •0862 •0906 •0949 •0992 •1035 •1077 ■1119 •1161 •1202 •1243 •1284 ■1324 •1364 •1403 •1442 •1481 •1519 •1557 ■1594 •1630 •1667 •1702 •1737 ■1772 •1806 •1840 ■1873 ■1905 •1937 •1968 •1999 •2029 •2058 •2087 •2115 •2143 •2169 •2195 •2221 ■2246 ■2270 •2294 ■2316 •2338 •2360 •2380 •2400 50 •0000 •0047 •0094 •0140 •01S7 •0234 ■0280 ■0327 •0373 •0419 ■0465 •05 1 1 •0557 ■0603 •0648 ■0694 •0739 •0783 •0828 •0872 •0916 •0960 •1004 •1047 •1090 •1132 •II7S •1216 •1258 •1299 •1340 •1380 •1420 ■1459 ■1498 •1537 •1575 •1613 •1650 •1686 •1722 •1758 •1793 •1827 •1861 •1895 •1927 •i960 •1991 ■2022 ■2053 •2082 •21 1 1 •2140 •2168 •2195 •2221 •2247 •2272 •2297 •2321 •2344 ■2366 •2387 ■2408 '2428 15 When the Latitude is North the sign is + When the Latitude is South the sign is - ALT-AZIMUTB TABLES. 84 Under Altitude and abreast of Deelination, take out the tabular quantity and mark it + or t- , aaoording' as Declination Is S. or N. Add Algebraically E and F. Dec- lina- tion. TRUE ALTITUDE, 12 30 40 50 13 10 20' 30 40' 50' 14 10' 20' 30 40' 50 15 0° ■0000 •0000 •0000 •0000 •CXXX) ■0000 •0000 •0000 ■0000 ■0000 •0000 •0000 •0000 0000 •0000 ■0000 I •0179 •0179 •0179 •0179 •0179 ■0x79 •0179 •0180 •0180 •0180 ■0180 •0180 •0180 •0180 •0181 •0181 2 ■03S7 ■0358 •0358 ■03S8 ■0358 •0359 •0359 ■0359 •0359 ■0360 ■0360 •0360 •0360 ■0361 •0361 •0361 3 •0536 •0536 •OS37 ■OS37 •OS37 •0538 •0538 •0539 •0539 ■0539 ■0540 •0540 •0541 •0541 •0541 •0542 4 •07 1 5 ■07 IS •07 IS •0716- •07x6 ■0717 •0717 •07x8 •0718 ■0719 •0719 •0720 ■0721 ■0721 •0722 •0722 5 •0893 •0893 ■0894 ■0894 •089s •0896 •0896 •0897 •0898 ■0898 ■0899 •0900 •ogoo •ogoi 0902 •0902 6° •1071 ■1071 •1072 •X073 •1074 •X074 •1075 •1076 •1077 •1077 •1078 ■1079 ■1080 •1080 •loSx •X082 7 ■1248 •1249 ■1250 ■125X •X252 •1252 •1253 ■1254 ■1255 •1256 •1257 •1258 ■1259 •1260 •1261 •1262 8 •1426 •1426 ■1427 •1428 •1429 •1430 •1431 •1432 •1433 •1434 •143s ■1436 •1438 •1439 •1440 •1441 9 ■1602 •1603 •1604 •x6os •1607 •x6o8 •1609 •x6io •1611 •XbI2 •1613 •1615 ■1616 •1617 •i6x8 ■1620 10 ■1779 •1780 ■178: •1782 ■1783 •178s ■1786 •1787 •1788 ■1790 ■1791 •1792 •1794 •1795 •1796 •1798 11° •I9S4 •1956 •I9S7 •X9S8 .i960 •1961 •1962 •1964 •196s •1967 •1968 •1969 ■1971 •1972 •1974 •1975 12 ■2130 •2131 ■2132 •2134 •213s •2137 •2138 •2140 •214X •2143 •2144 •2146 •2148 •2149 •21SX •2152 13 •2304 •2306 •2307 ■2309 •2310 ■2312 •2313 •2315 ■2317 ■2318 •2320 •2322 ■2324 •2325 •2327 •2329 14 •2478 •2480 •2481 ■2483 •248s •2486 •2488 •2490 •2491 ■2493 •2495 •2497 •2499 ■2501 •2503 •2505 IS •2651 ■2653 •26S4 •26S6 •2658 ■2660 •2662 •2664 •2666 •2667 •2669 ■267 X ■2673 ■267s •2677 •2679 i6° •2823 •2825 •2827 •2829 ■283 X •2833 •2835 •2837 •2839 •284X ■2843 •284s •2847 ■2849 •28SX •2854 17 •2995 •2997 •2999 •3001 •3003 ■3005 ■3007 •3009 •30 IX •3013 ■301 S ■3018 •3020 •3022 •302s •3027 i8 •3165 ■3167 •3169 •3171 •3174 ■3176 •3178 •3180 •3182 ■3185 •3187 •3189 •3192 •3194 •3197 •3199 19 •333s ■3337 •3339 •3341 •3344 •3346 ■3348 •3351 •3353 •3355 •3358 ■3360 ■3363 •3365 •3368 •3371 20 •3503 •3506 •3508 •3510 •3SI3 ■35 'S •3517 •3520 ■3522 ■3525 •3527 •3530 •3533 •3535 •3538 •3541 21° •3671 •3673 •367s •3678 •3680 •3683 •36S6 •3688 •3691 •3693 ■3696 •3699 •3702 ■3704 •3707 ■37'2 22 •3837 •3840 •3842 •384s •3847 ■3850 •3853 •3855 •3858 ■386 X •3864 ■3866 •3869 ■3872 •387s •3878 23 •4002 •400s ■4007 •4010 •4013 •4016 ■4018 •4021 •4024 ■4027 •4030 •4033 •4036 •4039 •4042 •4045 24 ■4166 ■4169 ■4172 ■4174 •4177 •4x80 •4183 •41S6 •4189 ■4192 •4195 •4198 •4201 ■4204 •4208 •42 1 1 25 •4329 •4332 ■4334 ■4337 •4340 ■4343 •4346 •4349 ■4352 •4356 •4359 •4362 •4365 •4369 •4372 •4375 26° •4490 ■4493 •4496 ■4499 •4502 •4505 •4508 •45 II •4515 •4518 •4521 ■4525 ■4528 •4531 ■^Pl •4538 27 •4650 •4653 ■4656 •4659 •4662 •4666 •4669 •4672 •4676 •4679 ■4682 ■4686 •4689 •4693 •4696 •4700 28 ■4809 •4812 •48 1 5 •4818 ■4821 •4825 •4828 •4832 •4835 •4838 •4842 •4846 ■4848 •4853 •4857 •4860 29 •4966 •4969 •4972 ■4976 •4979 •4982 •4986 •4989 •4993 ■4997 •50CX) ■5004 •5008 •50 1 1 •5015 •5019 30 •5121 ■512s •5x28 •S'32 •5135 •5139 •5142 •5146 •5149 ■5153 •5157 •Si6i •5165 •5x68 ■5172 •5176 31' •5275 ■5279 •S282 ■5286 ■5289 ■5293 •5297 •5300 •5304 •5308 •5312 •5316 •5320 ■5324 ■5328 Vl% 32 •5428 ■5431 ■S43S "5439 •S442 ■5446 ■5450 •5454 •5457 •546 X •5465 •5469 ■Sft •5478 •5482 •5486 33 5579 •5582 ■5586 •5590 •SS93 •S597 •5601 ■5605 ■5609 •5613 •5617 •5621 •5626 •5630 '^%^ ■5639 34 •5728 •5731 •S73S •S739 ■5743 •S747 •5751 •5755 •5759 •5763 •5767 ■5772 •5776 •5780 •5785 ■5789 ■5938 35 •5875 •5879 •5883 •5887 •5891 •5895 ■5899 •5903 •5907 ■5911 •5916 •5920 •5924 •5929 ■5934 36° •6021 •6024 •6028 ■6032 ■6037 ■604 X •6045 •6049 •6053 •6058 •6062 ■6067 ■6071 •6076 •6080 ■608s •6164 •616S •6172 •6176 •6x8x •6185 ■6189 •6194 ■6198 ■6202 •6207 •6212 •62x6 •6221 •6226 ■6230 og ■6306 ■6310 ■6314 •6319 •6323 •6327 •6332 •6336 •6341 •6345 •6350 •6354 •6359 •6364 •6369 6374 39 ■6446 ■6450 ■64S4 ■64S9 •6463 •6468 ■6472 •6477 •6481 •6486 •6491 •6495 tl°° tl°5 1l'° 'lt\ 40 •6584 ■6588 •6593 •6597 •660 X •6606 ■661 X ■66 IS •6620 •6625 •6629 ■6634 ■6639 •6644 •6649 ■6655 41° ■6720 •6724 •6729 ■6733 •6738 •6742 •6747 •6752 •6757 •676 X •6766 •6771 •6776 ■6782 •6787 •6792 42 6854 ■6858 •6863 •6867 •6872 ■6877 •6881 ■6886 •689 X •6896 •690 X •6906 •691 1 •69x7 ■6922 ■6927 •7061 43 •6986 •6990 ■6995 •6999 •7004 •7009 •70x4 •7019 •7024 ■7029 •7034 •7039 •7044 •7050 •7181 •7055 •7x86 44 ■7115 •7120 ■7x25 ■7129 ■7134 ■7139 •7144 •7149 ■7154 ■7'59- •7164 •7170 ■7175 •7192 45 •7243 •7247 •72S2 ■7257 •7262 •7267 •7272 •7277 ■7282 ■7288 •7293 •7298 ■7304 ■7309 •73 '5 ■7321 46° •7368 ■7373 •7378 ■7383 •7388 •7393 •7398 •7403 ■740S ■7414 •7419 •7425 7430 ■7436 •7560 •7682 •7441 •7566 •768S ■7447 % ■7491 •7612 ■7496 ■7617 •7501 •7622 •7506 ■7627 •7SIX •7632 •75x6 •7637 •752X ■7643 ■7527 •7648 •7532 •7653 •7537 ■7659 •7543 ■766s •7549 ■7670 •7676 •7572 •7694 •7813 49 •7730 ■773'i / •7740 •7746 ■7751 •7756 •7762 ■7767 •7773 •7778 •7784 ■7790 ■7795 •7801 •7807 50 •7846 •7852 •7857 •7862 ■7867 •7873 •7878 ■7884 ■7889 •789s ■790X •7907 •7912 •7918 ■7925 ■7931 51° 52 53 54 55 •7960 ■8071 •8180 •8a87 ■8390 •7965 ■8077 •8x86 •8292 •8396 •7971 ■8082 ■8191 •8297 •84OX ■7976 •8087 •8196 •8303 ■8407 •7981 •8093 •8202 •8309 •8413 •8098 •8208 •8314 •8418 ■7992 •8104 •8213 ■8320 •8424 •7998 •81 10 ■8219 •8326 ■8430 •8004 ■81 IS ■8225 ■8332 ■8436 •8009 ■8121 ■8231 •8338 ■8442 •801S •8127 ■8237 ■8344 ■8448 ■802I •8133 •8243 •8350 •8455 •8027 •8139 8249 •8356 •8461 •8033 •8146 •8255 'W •8467 •8039 •8x52 ■8262 •8369 •8474 •8046 •8x58 •8268 ■8376 ■8480 S6' i •8492 ■S590 •8686 •8780 ■8871 •S497 ■8596 •8692 •878s ■8876 •8503 •8602 •8698 •8791 •8882 ■8508 •8607 •8704 •8797 •8888 •8S14 •86x3 •8709 •8803 ■8894 •8520 ■8619 ■8715 •8809 •8900 •8526 •8625 ■8721 ■8815 •8906 •7532 ■8631 ■8728 ■8821 8913 •85 ;8 •8637 •8734 •8828 ■8919 •8544 ■8643 •8740 •8834 •892s •8550 ■8650 •8746 •8841 •8932 •8557 •8656 •8753 ■8847 •8938 •8563 •8663 •8759 •8854 ■8945 •8570 •8669 •8766 8S60 •8952 •8576 ■8676 •8773 •8867 ■8959 •«583 ■8683 •8780 •8874 •8966 61° 62 65 ■89S9 ■9044 •9126 •9206 •9283 ■8964 •9050 •9132 •9212 9289 ■8970 •9056 •9x38 ■9218 •9295 •8976 •9062 •9144 •9224 •930 ' ■8982 •9068 •9x51 923' •9308 •8988 •9074 ■9157 ■9237 ■93 '4 •8995 ■9080 •9163 ■9243 9321 ■9001 •9087 ■9170 •9250 •9327 ■9007 •9093 ■9176 9256 ■9334 •9014 ■9100 ■9183 ■9263 •9341 •9021 •9106 •9190 •9270 •9347 •9027 •9113 •9196 •9277 •93S4 •9034 ■9120 •9203 •9284 ■9361 •9041 ■9127 •9210 ■9291 •9368 ■9048 •9134 ■9217 ■9298 •9376 ■905s 9141 ■9224 •930s •9383 12 30 40' 50' 13 10 •20' 30' 40 50 14 10' 20 30' 40' 50' 16 When the Deelination is North the sign is - When the Deelination is South the sign is + . 85 ALT-AZIMUTH TABLES. Under Altitude in head-line, and abreast of Latitude in Margin, talce out the tabular quantity and mark it + or according* as the Latitude is N. or S. Lap. TRUE ALTITUDE. 15 10' 20 30 40 50 16 10 20 30 40 50' 17 10 20 30 0° •0000 •0000 •0000 •0000 •0000 •0000 ■oocxi ■0000 ■0000 •0000 •0000 •0000 •0000 •0000 •0000 •0000 I •CXD47 •0047 •0048 •0048 •0049 •0049 ■0050 •0051 •0051 ■0052 ■0052 ■0053 •0053 •C054 ■0054 ■0055 2 •0094 ■0095 ■0096 •0097 . •oogS ■0099 •0100 •OI02 ■0102 •0103 0104 •0106 0107 •0108 0109 •Olio 3 ■0140 ■0142 •0144 •0145 •0147 •0148 •0150 •0152 ■0153 ■015s •0157 •0158 ■0160 ■0162 0163 0165 4 •0187 •0189 •01 91 •0193 •0196 •0198 •0200 •0202 •0204 •0207 •0209 0211 •0213 ■0215 0218 •0220 5 ■0234 •0236 ■0239 •0242 •0244 •0247 •0250 •0253 •0255 •0258 ■0261 ■0264 •0266 •0269 •0272 •0275 6° •0280 •0283 ■0287 •0290 •0293 •0296 ■0300 •0303 •0306 •0310 •0313 •0316 ■0320 •0323 ■0326 •0330 7 •0327 •0330 •0334 •0338 ■0342 ■0346 •0349 •0353 •0357 ■0361 •0365 •0369 0373 •0376 •0380 ■0384 8 ■0373 •0377 •0382 ■0386 •0390 •0395 ■0399 •0403 •0408 ■0412 ■0417 ■0421 ■0425 •0430 •0434 ■0439 9 •0419 •0424 •0429 •0434 •0439 •0444 •0449 ■0453 •0458 ■0463 •0468 •0473 ■0478 •0483 •0488 •0493 10 •046s ■0471 •0476 •0482 •0487 •0492 •0498 ■0503 •0509 ■0514 •0520 •0525 •0531 •0536 •0542 ■0548 11° ■05 1 1 •0517 ■0523 •0529 •0535 ■0541 •0547 •0553 ■0559 •0565 •0571 •0577 •0583 •0589 •0596 ■0602 12 ■OSS7 •0564 •0570 •0577 •0583 •0590 ■0596 ■0603 •0609 •06 1 6 ■0622 •0629 •0636 •0642 •0649 ■0656 13 •0603 •0610 •0617 •0624 •0631 •0638 ■0645 •0652 ■0659 ■0666 ■0673 •0681 •0688 ■0695 ■0702 ■0709 M •0648 •0656 ■0663 ■0671 •0678 •0686 ■0694 •0701 ■0709 •0717 ■0724 •0732 •0740 ■0747 •0755 ■0763 IS •0694 •0702 ■0710 ■0718 •0726 •0734 ■0742 ■0750 ■0758 ■0767 •0775 •0783 •0791 •0800 •0808 •0816 i6° ■0739 •0747 •0756 ■0764 •0773 •0782 ■0790 ■0799 ■0808 ■0816 ■0825 •0834 •0843 •0851 •0860 •0869 '2 ■0783 •0793 •0802 •08 1 1 •0820 0829 ■0838 •0848 •0857 ■0866 ■087s •0885 •0894 ■0903 •0913 •0922 i8 •0828 0838 •0847 •0857 ■0867 •0876 •0886 •0896 ■0906 ■0915 •0925 •0935 •0945 •0955 •0964 •0974 19 0872 •0883 •0893 •0903 ■0913 •0923 •0934 •0944 ■0954 •0964 ■0975 •0985 ■0995 •1006 •1016 1027 20 ■0916 •0927 •0938 •0949 ■0959 •0970 ■0981 •0992 ■1002 ■1013 ■1024 ■1035 •1046 •1057 •1067 •1078 21° •0960 •0971 •0983 •0994 •1005 •1016 •1028 •1039 •1050 ■1062 •1073 •1084 •1096 ■I 107 •1118 ■I 130 22 •1004 ■1015 •1027 •1039 •1051 •1062 •1074 •1086 •1098 •IIIO •1121 •1133 •I 145 •I 157 •1169 •ii8i 23 ■1047 •1059 •107 1 ■1084 •1096 •I 108 •I 120 •1133 •I 145 •1157 •1170 •1182 ■1195 •1207 •1219 •1232 24 ■1090 •I 103 •ins •I 128 •I 141 •"54 ■1166 •1179 •1192 ■1205 •I2l8 •1231 •1244 •1256 •1269 ■1282 25 1132 •I 146 •"59 •II 72 •1185 •I 199 I2I2 ■1225 ■1238 ■1252 •1265 •1279 •1292 •1306 •1319 ■1333 26° •II7S •1188 •1202 •1216 •1229 ■1243 ■I2S7 •1271 •1285 •1299 ■I3I2 •1326 •1340 •1354 •1368 •1382 27 •1216 •1231 •1245 •I 259 •1273 •12S8 •1302 ■1316 •1330 •1345 •1359 •1374 •1388 ■1402 •1417 ■'43' 28 •1258 ■1273 •1287 •1302 •1317 •1331 •1346 ■1361 •1376 •1391 •1406 •1420 •1435 •1450 •1465 ■1480 29 ■1299 •1314 •1329 •1344 •1360 •1375 •1390 •1405 •1421 •1436 ■I45I •1467 •1482 •1498 •1513 ■1529 3° •1340 •1355 •1371 •1387 •1402 •1418 •1434 •1449 •1465 •1481 •1497 •1513 •1529 •1545 ■1561 •1576 31° •1380 ■1396 •1412 ■1428 •1444 •1461 •1477 •1493 •1509 •1526 ■1542 •1558 •1575 •1591 •1607 ■1624 32 ■1420 •'436 •1453 •1470 •i486 •1503 ■1520 •1536 •1553 •1570 ■1586 •1603 •1620 •1637 •1654 •1671 33 •I4S9 •■476 •1493 ■1510 •1527 •1545 •1562 •1579 ■1596 •1613 •I63I •1648 •1665 •1682 •1700 •1717 34 •1498 •1516 •'533 ■iSSi •J568 •1586 •1603 •1621 ■1639 ■1656 •1674 •1692 •1710 •1727 •1745 •1763 35 •IS37 ■^sss •1573 ■1591 •1609 •1627 •1645 •1663 •1681 •1699 •I7I7 •1735 •1754 •1772 •1790 ■1808 36° ■ISIS •1593 •1612 •1630 •1649 •1667 •1685 •1704 •1723 •1741 •1760 •1778 •1797 •1816 •1834 ■1853 37 •1613 •1631 ■'^l» ■1669 •1688 •1707 •1726 ■1745 •1764 ■1783 •IS02 •1821 •1840 •1859 •1878 •1898 38 ■'^g •1669 •1688 •1707 •1727 •1746 ■1765 ■1785 •1804 •1824 •1843 •1863 •1882 •1902 •1922 •1941 39 ■1686 •1706 •1726 •1745 •1765 •1785 •I80S •1824 •1844 '•1864 •I8S4 •1904 •1924 •1944 •1964 •1984 40 •1722 •1742 •1762 ■1783 •1803 •1823 •1843 •1863 ■1884 ■1904 •1924 •1945 •1965 •1986 ■2006 •2027 41° ■1758 •1778 •1799 •1819 •1840 •1861 •I88I •1902 •1923 •1943 •1964 •1985 ■2006 •2027 ■2048 ■2069 42 •1793 •1814 ■1835 •1856 ■1877 •1898 •1919 •1940 ■1961 ■1982 •2003 •2024 ■2046 •2067 •2088 •2110 43 •1827 •1849 •1870 •1891 •1913 •1934 •1956 ■1977 •1999 ■2020 ■2042 •2063 ■2385 •2107 •2129 •2150 44 •1861 ■1883 •1905 ■1926 •1948 •1970 •1992 •2014 •2036 ■2058 •2080 ■2102 •2124 •2146 •2i68 •21-qo 45 •1895 •1917 •'939 •1961 ■1983 •2005 •2028 •2050 ■2072 ■2095 •2II7 •2139 •2162 ■2184 •2207 7** •2229 46° •1927 •1950 •1972 ■1995 •2017 ■2040 •2063 •2085 ■2108 •2131 •2154 •2176 •2199 ■2222 •2245 ■2268 % •i960 •1982 •2005 •2028 ■2051 •2074 •2097 •2120 •2143 •2166 •2190 •2213 •2236 ■2259 •228^ •2TO6 48 •1991 •2014 •2038 •2061 ■2084 ■2108 •2I3I •2154 ■2178 •220I •2225 •2248 •2272 ■2296 •2319 •2343 49 •2022 •2046 ■2069 •2093 •2117 •2140 •2164 •2188 •2212 -2236 •2259 •2283 •2307 ■2331 ■2355 •2380 50 •2053 •2077 ■2100 ■2124 •2148 •2173 ■2197 •2221 •2245 •2269 •2293 •2318 •2342 •2366 •2391 •2415 Sr° •2082 •2107 ■2131 •2155 •2180 •2204 ■2228 •2253 ■2277" •2302 •2327 •2351 ■2376 •2401 •2426 •2450 52 "2111 •2136 •2l6l •2185 •2210 ■2235 •2260 •2284 •2309 ■2334 •2359 •2384 •2409 ■2434 •2459 •2485 53 '2140 •2168 •2165 •2190 •2215 •2240 ■2265 •2290 •2315 •2340 ■2366 ■2391 ■2416 ■2442 ■2467 •2493 •2518 54 •2193 •2218 •2244 ■2269 ■2294 •2320 •2345 •2371 ■2396 •2422 •2448 •2473 •2499 •2525 ■2551 55 •2195 '2220 •2246 •2272 •2297 •2323 •2349 •2375 •2401 •2426 •2452 •2478 •2504 •2530 •2557 •2583 56° •2221 •2247 •2273 •2299 •2325 •2351 ■2377 •2403 •2430 •2456 ■2482 •2508 •2535 •2561 •2587 •2614 !i •2247 ■2273 •2300 •2326 •2352 •2378 •2405 ■2431 •2458 •2484 •2511 •2537 •2564 ■2591 •2618 •2644 •2272 ■2299 •2325 ■2352 •2378 •2405 •2432 ■2458 ■2485 •2512 •2539 •2566 •2593 •2620 •2647 •2674 59 60 •2297 •2324 •2350 •2377 •2404 •2431 •2458 ■24S5 •2512 •2539 •2566 •2593 •2621 •2648 •2675 •2703 ■2321 •2348 •2375 ■2402 •2429 •2456 •2483 ■251 1 ■2538 •2565 •2593 •2620 ■2648 •2675 •2703 •2731 61° 62 64 6s ■2344 •2371 •2398 •2426 •2453 •2480 •2508 •2535 •2563 •2591 •2618 •2646 •2674 •2702 ■2730 2758 •2366 •2393 •2421 •2449 ■2476 •2504 •2532 ■2560 •2587 •2615 ■2643 •2671 •2699 •2728 ■2756 ■2784 ■2387 •2415 •2443 ■2471 ■2499 •2527 •255s ■2583 •261 1 •2639 •2667 ■2696 •2724 •2752 •2781 ■2809 •2408 •243fi» •2464 •2493 •2521 •2549 ■2577 ■2606 •2634 •2662 •2691 •2719 •2748 •2777 •2805 •2834 •2428 •2457 V 2485 •2513 •2542 •2570 •2599 •2627 •2656 •2685 •2713 •2742 •2771 •2800 •2829 ■2858 15" 10 20 30 40 50 16 10 20 30 40 50 17 10' 20 30 When the Latitude is North the sign is + When the Latitude is South the sign is — . ALT-AZIMUTH TABLES. 86 Under Altitude and abreast of Declination, take out the tabular quantity and mark it + or — . according as Declination is S. or N. Add Algebraically E and F. Dec- . LI NA- TION. TRUE ALTITUDE. iS 10' 20 30 40 50 16 10' 20' 30 40' 50 17 10 20 30' 0° •GOOD ■0000 •cxioo 0000 •0000 ■0000 •0000 •0000 ■0000 •0000 •0000 •0000 •0000 ■0000 ■0000 •0000 I •oi8i •0181 •0I8I •01 8 1 ■oi8i •0181 •0182 ■0182 •0182 •0182 •0182 •0182 •0182 •0183 •0183 •0183 2 ■0361 •0362 ■0362 •0362 ■0362 •0363 •0363 ■0363 •0364 •0364 •0364 •036s •0365 •0365 •0366 •0366 3 •0542 •0542 ■0543 •0543 •0544 •OS44 ■0544 •0545 •0545 •0546 •0546 ■0547 •0547 •0548 •0548 ■0549 4 •0722 •0723 ■0723 •0724 •0724 ■0725 •0726 •0726 ■0727 ■0728 ■0728 • •0729 •0729 •0730 •0731 ■0731 5 ■0902 ■0903 ■0904 •0904 •0905 •0906 •0907 •0907 •0908 •0909 ■0910 •091 1 •091 1 •0912 •0913 ■0914 6° •1082 •1083 •1084 •1085 ■1086 ■1087 •1087 •1088 •1089 •1090 •1091 •1092 ■1093 •1094 •1095 •1096 7 ■1262 •1263 •1264 •1265 •1266 •1267 •1268 •1269 •1270 ■1271 •1272 •1273 •1274 •1276 •1277 •1278 8 •1441 •1442 •1443 •1444 •1445 •1447 ■1448 ■1449 •1450 •1452 •1453 •1454 ■1455 •1457 •1458 •1459 9 10 ■1620 •1621 •1622 •1623 •1625 ■1626 •1627 ■1629 •1630 ■1632 •1633 •1634 •1636 •1637 •1639 •1640 •1798 •1799 •I80I •1802 •1803 •180S •1806 •1808 •1810 .1811 •1813 •1814 •1816 •1817 •1819 •1821 11° •197s •1977 •1979 •1980 •1982 •1983 •1985 •1987 •1988 •1990 •1992 •1994 •1995 •1997 •1999 •2001 12 •2152 •2154 ■2156 •2158 •2159 •2161 ■2163 ■2165 •2167 •2168 •2170 •2172 ■2174 •2176 •2178 ■2180 13 •2329 •2331 •2333 •2334 ■2336 •2338 •2340 •2342 •2344 •2346 •2348 ■2350 ■2352 ■2354 ■2357 ■2359 14 •2505 •2507 •2509 •25 II •2513 •2515 •2517 •2519 •2521 •2523 •2525 •2528 •2530 •2532 •2534 ■2537 IS •2679 •2682 •2684 •2686 •2688 •2690 ■2692 •269s •2697 •2699 •2702 •2704 •2706 •2709 •27 1 1 •2714 16° •2854 •2856 •2858 •2860 •2863 •286s •2867 •2870 •2872 •2875 •2877 •2880 •2882 •2885 •2888 •2890 •3066 17 ■3027 •3029 •3032 ■3034 •3037 •3039 •3042 •3044 •3047 •3049 •3052 •3055 •3057 •3060 •3063 18 ■3199 •3202 •3204 •3207 •3209 •3212 ■3215 ■3217 •3220 •3223 ■3226 •3229 •3231 •3234 ■3237 •3240 19 20 •3371 ■3373 •3376 •3379 •3381 •3384 •3387 •3390 •3393 •3396 •3398 •3401 •3404 •3407 •341 1 ■3414 •3586 •3541 •3544 •3546 •3549 •3552 •3SSS ■3558 •3561 •3564 •3567 ■3570 •3573 •3576 •3580 •3583 21° ■3710 •3713 ■3716 •3719 •3722 •3725 •3728 •3731 •3734 •3738 •3741 •3744 •3747 •3751 •3754 •3758 •3928 22 •3878 •388? •3884 •3887 •3891 •3894 •3897 •3900 •3904 •3907 ■3910 •3914 ■3917 •3921 •3924 23 24 25 ■4045 ■4048 ■4052 4055 •4058 •4061 •4065 ■4068 •4072 •4075 ■4079 •4082 •4086 •4089 •4093 •4097 ■4265 ■42 II •4214 •4217 •4221 •4224 •4228 •4231 •423s •4238 ■4242 •4246 •4249 ■4253 •4257 ■4261 •4375 ■4379 ■4382 •4386 •4389 •4393 •4396 •4400 •4404 •4408 ■4412 •4415 •4419 •4*23 •4427 •4431 26° ■4538 ■4542 •4546 •4549 •4553 •4557 •4560 •4564 •4568 •4572 •4576 •4580 •4584 •4588 •4592 •4756 •4918 •5079 •5238 •4596 •4760 29 30 ■4700 ■4704 •4707 •47 II •4715 ■4719 •4723 ■4727 •4731 ''•m •4739 •4743 •4747 ■4752 •4860 •5019 •5176 •4864 •5023 •5180 ■4868 •5027 •5185 •4872 ■5031 •5189 ■4876 •5035 •5193 •4880 •5039 ■5197 ■4884 •5043 •5201 ■4888 ■5048 •5206 •4892 •5052 •5210 ■4896 •5056 •521S •4901 •5061 •5219 •4905 •5065 •5224 •4909 ■5070 •5228 •4914 •5074 ■5233 ■4923 •5083 ■5243 32 33 34 35 •5332 •5486 ■5639 •5789 ■5938 ■5336 ■5490 •5643 •5794 •5943 •5340 •5495 •5647 •5798 •5947 •5345 ■5499 ■5652 •5803 •5952 •5349 ■5504 •5957 •S3S3 •5508 •5661 •5812 •5962 •5358 •5513 •5666 •5817 •5967 •5362 •5517 •5671 •5822 •5972 ■5367 •5522 •5675 •5827 •5977 •5372 •5527 •5680 ■5832 •5982 •5376 •5532 •5685 ■5837 •5987 ■5381 •5536 •5690 •5842 •5993 •5386 ■5541 •5695 •5847 •5998 •5391 •5546 •5700 •5853 •6003 •5395 •5551 ;57oS ■6009 ■5400 ■5556 •57 1 1 ■5863 •6014 36° 39 40 ■608s ■6230 •6374 •6515 •66SS •6090 •6235 •6379 •6520 ■6660 •6095 •6240 ■6384 ■6100 •6245 ■6389 ■6531 •6670 •610S •6250 •6394 •6536 •6676 •61 ID •625s •6399 •6541 •6681 ■611S •6261 ■640s •6547 ■6687 •6120 ■6266 •6410 •6552 •6693 •6125 •6271 ■6416 ■6558 •6698 •6130 •6277 •6421 •6563 ■6704 •6136 ■6282 ■6427 •6569 ■6710 •6141 •6288 •6432 •6575 •6716 ■6146 •6293 •6438 ■6581 •6722 •6152 •6299 ■6444 •6587 ■6728 •6157 •6304 •6450 •6593 •6734 •6163 6310 •6455 •6599 •6740 41° 42 43 44 45 •6792 •6927 •7061 •7192 ■7321 •6797 •6933 ■7066 •7197 •7326 •6803 6938 ■7072 •7203 •7332 •6808 ■6944 •7077 •7209 7338 ■6814 •6949 •7083 •721 5 •7344 ■6819 •695s •7089 •7221 735° •682s •6961 ■7095 •7227 7356 •6831 ■6967 7101 7233 •7362 •6836 ■6973 •7107 •7239 •7368 •6842 •6979 7113 •724s 7375 ■6848 •698s •7 1 19 •7251 •7381 •6854 ■6991 7125 •7258 ■7388 •6860 •6997 •7132 7264 •7394 •6866 •7003 7138 •7270 •7401 ■6873 •7010 7144 7277 ■7407 •6879 •7016 •7284 •7414 46° % 49 SO ■7447 •7572 •7694 , 7813 •7931 •7453 •7577 •7700 •7819 •7937 7459 ■7583 •7706 •7826 •7943 •7465 ■7590 •7712 •7832 •7950 •7471 7596 ■7718 •7838 ■7956 ■7477 7602 ■7725 •784s ■7963 7731 7851 •7969 ■7490 ■7615 •7737 •7858 ■7976 •7496 ■7621 •7744 •7864 7983 •7502 •7628 7751 •7871 •7989 •7509 •7634 •7757 •7878 •7996 ■7641 •7764 •788s ■8003 7522 •7648 •7892 •8010 7529 7655 7778 •7899 •8018 •7661 778s •7906 •8025 7542 •7668 •7792 •7913 •8032 51° 52 S3 54 55 ■8046 ■8158 •8268 ■8376 •8480 •8052 •8164 •827s •8382 •8487 •8058 •8171 ■8281 •8389 •8494 •806s •8178 •8288 •8396 •8501 ■8071 •8184 •8295 •8402 •8508 •8078 •8191 •8301 ■8409 •8515 •8085 •8198 •8308 •8416 •8522 •8091 •8205 •831S . ^8423 •8529 •8098 •8212 •8322 ■8430 •8536 •8105 •8219 •8329 ■8438 •8543 ■8 1 12 •8226 •8337 •8445 •8551 ■81 19 ■8233 •8344 •8558 ■8127 •8240 •8460 •8566 ■8134 •8248 •8359 •8467 •8573 •8I4I •8255 •8366 •847s •8581 •8149 •8263 •8374 •8589 56° i •8583 •86S3 ■8780 •8874 •8966 •8590 ■8689 •8787 •8881 ■8973 ■8596 •8696 •8793 •8888 •8980 •8603 •8703 •8801 •889s •8987 ■8610 ■8710 •8808 •8902 ■8994 ■8617 •8717 •881S •8910 ■9002 ■8624 •8725 •8822 •8917 ■9009 •8632 ■8732 ■8830 •8925 •9017 •8639 •8739 •8837 •8932 •9024 •8646 •8747 884s •8940 ■9032 •8654 •8754 •8852 •8948 •9040 •8662 8762 •8860 •8955 ■9048 •8669 •8770 •8868 •8963 •9056 •8677 •8778 •8876 •8971 •9064 •868s ■8786 •8884 •8979 •9072 •8693 •8794 •8892 •8988 •9081 61° 62 63 •90SS •9141 ■9224 •9062 •9148 •9232 •9069 •9155 •9239 •9076 ■9163 •9246 •9084 ■9170 ■9254 ■9091 ■9178 •9261 •9099 ■9185 ■9269 •9350 •9428 •9106 •9193 ■9277 •9358 •9436 ■91 14 ■9201 •9285 •9366 •9122 ■9209 ■9293 ■9374 •9130 •9217 •9301 •9382 •9138 •9225 •9309 •9390 •9146 •9233 ■9317 •9399 •9154 •9241 •9326 •9407 •9162 •9250 •9334 •9416 •9171 •9258 •9342 ■9424 ^4 6s •930s •9383 •9312 •9390 •9320 ■9398 •9327 •9405 •9335 •9413 •9342 •9420 •9444 •9452 •9461 •9469 •9477 •9486 •9494 ■9503 15 10 20' 30 40 50 16 10' 20 30' 40' 50' It 10' 20' 30 , When the Declination is North the sign is When the Declination is South the sign is -f 87 ALT-AZIMUTH TABLES. Under Altitude in head-line, and abreast of Latitude in margin, take out the tabular quantity and mark It + or according as the Latitude is N. or S. Lat. TRUE ALTITUDE, 17 30 40 50' 18' 10' 20' 30 40' 50 19 10 20 30 40' 50 20 0° •0000 ■0000 •0000 •0000 •0000 •0000 •0000 ■0000 ■0000 ■0000 ■0000 ■0000 ■0000 ■0000 ■0000 •0000 I ■o°SS •0056 •0056 •0057 ■0057 ■0058 •0058 ■0059 •0060 ■C060 ■0061 ■006 1 •0062 •0062 •0063 ■0064 2 '01 10 ■01 1 1 •01 12 ■01 13 •01 1 5 •0116 ■0117 0118 ■01 1 9 •0120 •0121 •0122 ■0124 ■0125 •0126 •0127 3 4 ■0165 •0167 •0168 ■0170 •0172 •0173 •017S •0177 ■0179 ■0180 ■0182 •0184 ■0185 •0187 •0189 •0190 •OZ20 •0222 ■0224 •0227 •0229 •0231 ■0233 •0236 ■0238 •0240 ■0242 ■0245 •0247 •0249 '0252 •0254 5 ■027s •0278 •0280 •0283 ■0286 ■0289 •0292 ■0294 ■0297 •0300 •0303 •0306 ■0309 •03 1 1 •0314 •0317 6° •0330 ■0333 ■0336 ■0340 ■0343 •0346 ■0350 •0353 •0357 •0360 ■0363 •0367 •0370 •0374 •0377 •0380 7 •0384 •03B8 ■0392 •0396 •0400 •0404 •0408 •0412 •0416 •0420 ■0424 ■0428 •0432 •0436 •0440 ■0444 8 ■0439 •0443 •0448 •0452 •0457 •0461 ■0466 •0470 •0475 ■0479 ■0484 •0488 ■0493 ■0497 •0502 •0507 9 •0493 ■0498 •0503 •0508 "0513 •0518 •0523 •0528 ■0534 •0539 ■0544 •0549 •0554 •0559 '°ti •0569 10 •0548 •0SS3 ■0559 ■0564 •0570 •0575 •0581 •0587 •0592 ■0598 ■0604 •0609 ■0615 •0621 '0626 ■0633 11° •0602 •0608 •0614 0620 •0626 •0632 ■0638 •0645 ■0651 ■0657 •0663 •0669 ■0676 ■0682 •0688 •0694 12 •0656 ■0662 ■0669 •0676 ■o68z ■0689 •0696 •0702 •0709 •0716 •0723 ■0729 •0736 •0743 •0750 ■0757 13 ■0709 ■0716 •0724 •0731 ■0738 •0745 •0753 ■0760 ■0767 ■0775 ■0782 •0789 •0797 •0804 ■08 II •0819 ^4 •0763 •0771 •0778 •0786 ■0794 •0802 •0809 ■0817 ■0825 •0833 ■0841 ■0849 ■0857 •0865 "0873 •0881 IS •0816 •0824 ■0833 •0841 •0849 •0858 •0866 •0874 •0883 ■0891 •0900 ■0908 ■0917 •0925 •0934 ■0942 16° •0869 ■0878 •0887 ■0896 ■0904 •0913 •0922 •0931 ■0940 •0949 ■0958 •0967 ■0976 •0985 -0994 '1003 17 •0922 •C931 •0941 •0950 •0959 •0969 ■0978 ■0988 ■0997 ■1007 ■1016 •1026 •1035 •1045 •loss •1064 i8 •0974 ■0984 •0994 •1004 ■1014 ■1024 •1034 •1044 ■1054 •1064 •1074 ■1084 •1094 •1104 •ins •I 125 19 1027 •1037 ■1047 •1058 •1068 •1079 •1089 •I 100 •1110 ■1121 •ii32 •1142 •1153 ■I 164 •I 174 ■I 185 20 ■1078 ■1089 •I 100 ■nil ■1122 ■1133 •1144 •"55 ■1166 ■1177 •1189 •1200 •1211 ■1222 •1234 •1245 21° •1130 •1141 ■"53 •1164 •1176 •1188 ■1199 ■1211 ■1222 ■1234 •1246 •1257 •1269 •1281 •1293 •1304 22 •II8I •1193 •I 20s •1217 •1229 •1241 •1253 ■1266 •1278 •1290 •1302 •1314 •'1327 ■1339 •1351 •1363 23 •1232 •1244 ■1257 •1270 •1282 •1295 •1307 •1320 •1333 •1345 •1358 •1371 ■1384 •1396 •1409 ■1422 24 •1282 •129s •1308 •1322 •1335 •1348 •1361 •1374 •1387 •I4OI •1414 •1427 ■1440 •1454 •1467 ■1480 25 •1333 ■1346 ■1360 •1373 •1387 ■1400 •1414 •1428 •1441 •1455 •1469 ■1483 •1497 ■1510 •1524 •1538 26° •1382 •1396 ■1410 ■1424 •1438 ■1453 ■1467 •1481 •1495 •1509 •1524 •1538 ■'552 ■1567 ■1581 ■1596 27 ■I43I ■1446 •1461 •1475 •1490 •1504 •1519 ■1534 •1548 •1563 •1578 •1593 ■1608 •1623 •1637 •1652 28 •1480 •I49S ■1510 •1525 ■1541 •1556 •1571 •1586 ■1601 ■1617 •1632 •1647 ■1662 ■1678 •1693 ■1709 29 •1529 ■IS44 1560 •"575 ■1591 •i6o5 •1622 •1638 ■1654 ■1669 •1685 •1701 •1717 •1733 ■1749 -1765 30 •1576 •1592 •1609 ■1625 1641 •1657 ■1673 •1689 ■1705 ■1722 •173S ■1754 •1771 •1787 •1803 'I82Q 31° 'I624 •1640 ■1657 •1673 •1690 •1707 •1723 •1740 •1757 •1773 •1790 •1807 •1824 •1841 •1858 •187s 32 •I67I •1688 ■I 70s •1722 •1739 •1756 ■1773 ■1790 •1807 ■1825 •1842 •1859 ■1877 ■1894 •1911 •1929 33 •I7I7 ■I73S •1752 ■1770 ■1787 •1805 •1822 ■1840 •1858 •1875 ■1893 •1911 •1929 ■1947 ■1964 •1982 34 ■1781 •1799 •1817 •183s •1853 •1871 ■1889 •1907 •1925 ■1944 •1962 •1980 •1999 ■2017 •203s 35 •1808 •1827 •1845 •1864 •1882 •1901 •1919 ■1938 •1956 •1975 •1994 ■2012 •2031 •2050 •2069 ■2088 36° ■'fS3 •1872 ■1891 •1910 •1929 •1948 •1967 •1986 ■2005 •2024 ■2043 •2062 ■208 1 •2101 •2120 ■2139 37 •1898 ■1917 •1936 ■1955 •1975 •1994 •2014 •2033 ■2053 •2072 •2092 ■2111 •2131 •2151 ■2171 •2190 38 •1941 •1961 •1981 ■2000 •2020 •2040 •2060 •2080 ■2100 ■2120 ■2140 ■2160 ■2180 ■2200 •2221 ■2241 39 •1984 •2004 ■2025 ■2045 •2065 ■2085 •2106 ■2126 •2146 •2167 •2187 •2208 ■2229 •2249 ■2270 •2291 40 ■2027 •2047 ■2068 •2o8g •2109 ■2130 •2151 ■2172 •2192 •2213 ■2234 •2255 •2276 •2297 ■2318 •2340 41° ■2069 ■2090 •2111 •2132 •2153 ■2174 ■2195 ■2216 •2238 ■2259 ■22S0 •2302 •2323 •2345 •2366 •2388 42 •21 10 •2131 •21 S3 ■2174 •2196 ■2217 ■2239 ■2261 ■2282 •2304 ■2325 •2348 ■2370 •2391 •2413 •2435 43 •2150 ■2172 •2194 ■2216 •2238 ■2260 ■2282 •2304 •2326 •2348 ■2371 •2393 •2415 ■2437 •2460 ■2482 44 •2190 •2212 •2235 •2257 •2279 ■2302 •2324 ■2347 •2369 •2392 •2415 •2437 •2460 •2483 ■2505 •2528 45 ■2229 •2252 •2275 •2298 •2320 •2343 ■2366 •2389 •2412 •2435 •2458 ■2481 ■2504 •2527 •2550 '2574 46° ■2268 •2291 •2314 •2337 •2360 •2384 •2407 •2430 •2454 ■2477 •2500 •2524 •2547 ■2571 •2595 ■2618 "^l •2306 •2329 ■2353 •2376 ■2400 •2423 ■2447 •2471 •2494 •2518 •2542 •2566 •2590 ■2614 •2638 ■2662 48 •2343 •2367 ■2391 •2415 ■2439 ■2463 ■2487 ■2511 •2535 •2559 •2583 ■2607 •2632 •2656 •2680 •2705 49 ■2380 ■2404 ■2428 ■2452 •2476 •2501 •2525 •2550 •2574 •2599 •2623 ■2648 ■2673 ■2697 ■2722 •2747 50 •241S •2440 •2464 •2489 •2514 ■2538 •2563 •2588 ■2613 •2638 •2663 ■2688 •2713 •2738 •2763 •2788 51° •24S0 •247s ■2500 •2525 •2550 •2575 •2600 ■2625 •2651 •2676 •2701 •2727 •2752 '2777 •2803 •2829 52 •248s •25:0 •2S3S •2560 •2586 •261 1 •2637 •2662 ■2688 ■2713 •2739 •2765 •2790 •2816 ■2842 ■2868 53 •2518 •2544 •2569 •2595 •2621 •2646 ■2672 •2698 ■2724 •2750 •2776 ■2802 •2828 •2854 ■2881 ■2907 54 •2SSI •2S77 •2603 •2629 •2655 •2681 •2707 ■2733 •2759 •2786 •2812 •2838 •2865 •2891 •2918 •2945 55 •2583 ■2609 •263s •2662 ■2688 •2714 •2741 ■2767 ■2794 •2821 •2847 •2874 ■2901 •2928 •29SS ■2981 56° •2614 •2640 •2667 ■2694 •2720 •2747 •2774 •2801 •282S •2855 ■2882 ■2909 •2936 •2963 •2990 •3017 5^ •2644 •2671 •2698 •2725 •2752 •2779 ■2806 •2833 •2861 •2888 •291 5 ■2942 •2970 ■2997 •3025 •3053 •2674 •2701 •2728 •2755 ■2783 •2810 ■^f38 •2865 •2S92 ■2920 ■2948 •2975 •3003 •3031 •3059 •3087 ^ ■2703 ■2730 ■^758 •2785 •2813 •2840 ■2868 ■2896 •2924 •2951 •2979 •3007 •303s •3063 •3092 •3120 •2731 •2758 •2786 •2814 •2842 ■2870 ■2898 ■2926 •2954 •2982 •3010 •3038 •3067 •3095 •3124 •3152 61° 62 6s •2758 •2786 •2814 •2842 •2870 ■2898 •2926 •2955 •2983 •3012 •3040 •3069 .3097 •3126 •3>SS •318S •3>83 •2784 •2812 ■2841 •2869 •2897 •2926 •2954 •2983 ■3012 •3040 ■3069 •3098 •3127 •3156 ■3214 ■2809 •2838 •2866 •2895 ■2924 •2952 •2981 •3010 ■3039 ■3068 •3097 •3126 •31SS •3184 ■3214 •3243 •2834 ■^fo3 •2891 , •2920 •2949 •2978 •3007 •3036 ■3066 •309s •3124 •3153 •3183 •3212 ■3242 •3271 •2858 •2887 •2916 •2945 ■2974 •3003 •3032 •3062 •3091 •3I2I •3150 •3180 •3209 •3239 •3269 •3299 17 3d 40' 50' W 10' 20' 30' 40' 50' 19 10 20' 30' 40' 50' 20 When the Latitude is North the sign Is + When the Latitude is South the sign is - ALT-AZIMUTH TABLES. 88 Under Altitude and abreast of Declination, take out the tabular quantity and mark it + op — , according as Declination is S. or N. Add Algebraically E and F. Dec- lina- tion. TRUE ALTITUDE. 17 30 6° 7 8 9 10 11° 12 13 14 IS i6° 17 i8 19 20 21° 22 23 24 25 26° 27 28 29 30 31° 32 33 34 35 36° 37 38 39 40 4»° 42 43 44 45 46° 47 48 49 50 51° 52 53 54 55 S6° 57 58 60 61° 62 65 ■0000 •0183 •0366 ■0549 ■0731 ■0914 "1096 ■1278 ■I4S9 •1640 •1S21 •2001 ■2180 ■2359 •2537 ■2714 ■2890 •3066 •3240 •3414 ■3S86 •3758 •3928 •4097 ■4265 ■4431 •4596 •4760 •4923 ■S°83 •5243 •5400 •5556 •57" •5863 •6014 •6163 ■6310 •64SS •6S99 •6740 ■6879 •7016 7151 •7284 ■7414 •7542 •7668 •7792 ■7913 ■8032 ■8149 •8263 •8374 ■8483 •8589 •8693 •8794 40 50 18 10 •9081 •9I7I •9258 •9342 •9424 •9503 11 z6 •0000 •0183 ■0366 •OS49 •0732 ■091 S •1097 •1279 •1461 •1642 ■1822 •2003 •2182 ■2361 •2S39 •2716 •2893 •3068 •3243 •3417 •3589 •3761 •3931 •4101 •4269 ■4435 •4601 •4765 •4927 ■5088 •5247 •5405 •5561 •5716 •5869 •6020 •6169 ■6316 •6461 ■6605 •6746 -688s •7023 ■7158 ■7290 •7421 •7549 ■7676 •7799 •7921 •8040 •8156 ■8270 •8382 •8491 •8597 ■8701 ■8802 •8900 •8996 •9089 ■9179 •9267 ■9351 •9433 ■9512 40 •0000 ■0183 •0367 ■0550 •0733 •0916 •1098 ■1280 ■1462 ■1643 •1824 •2004 •2184 •2363 •2541 •2719 •289s ■3071 •3246 •3420 •3593 •3765 •393s •4105 •4273 •4439 •4605 •4769 •4932 •5093 •5252 •5410 •5567 •5721 •5874 ■6025 ■617s ■6322 ■6467 •661 1 •6752 •6892 •7029 •7164 ■7297 •7428 •7556 •7683 •7807 •7928 •8047 •8164 ■8278 •8389 ■8499 •8605 •8709 •8810 •8909 ■9004 •9097 •9188 •927s •9360 •9442 •9521 •0000 •0184 •0367 ■0550 •0733 •0916 •1099 ■J 28 1 •1463 •1645 •1826 •2006 •2186 •2365 ■2544 •2721 ■2898 ■3074 •3249 ■3423 •3596 •3768 •3939 •4108 ■4277 •4444 •4609 •4774 •4936 ■5098 •5257 •5415 •5572 ■5727 •5880 •6031 •6180 ■6328 ■6473 ■6617 ■6759 50 ■7036 •7171 '7304 ■7435 •7564 •7690 •7814 •7935 •8055 •8171 •8286 •8397 ■8507 ■8613 •8717 •8818 ■8917 •9013 •9106 •9196 •9284 ■9369 •9450 ■9529 20 o 18 •0000 •Q184 ■0367 •0551 ■0734 0917 •iioo •1283 •1465 •1646 •1828 •2008 •2188 •2368 •2546 •2724 ■2901 ■3077 •3252 ■3426 •3600 •3772 ■3943 4112 •4281 •4448 ■1614 •4778 •4941 •5102 •5262 ■5421 •5577 ■5732 •5885 •6037 ■6186 •6334 •6480 •6623 •6765 ■6905 •7042 •7178 •73" ■7442 •7571 •7697 •7821 •7943 •8062 ■8179 ■8294 •8405 •8515 ■8621 ■8725 ■8827 •8925 ■9021 ■9"5 ■9205 •9293 ■9378 •9459 •9539 30 10 •0000 •0184 •0368 •0551 ■0735 ■09 1 8 •iioi ■1284 ■1466 •1648 •1829 •2010 •2190 •2370 •2549 ■2727 ■2904 •3080 •3255 •3430 •3603 ■3775 •3946 •41 16 •4285 ■4452 •4618 ■4783 ■4946 •5107 •5267 •5426 •5583 •5738 •5891 •6042 6192 •6340 ■6486 ■6630 •6772 •691 1 •7049 •7185 •7318 •7449 •7578 •7705 •7829 •7951 •8070 •8187 ■8301 •8413 •8523 ■8630 •8734 •883s ■8934 •9030 •9123 •9214 •9302 •9387 ■9469 ■9548 40 20 ■coco •0184 ■0368 •0552 •0736 •0919 •I 102 ■1285 •1468 •1650 •1831 •2012 •2192 •2372 •2551 ■2729 •2907 •3083 •3259 ■3433 •3607 •3779 ■3950 •4120 ■4289 ■4456 •4623 •4787 •4951 ■5112 •5272 ■5431 •5588 •5743 •5897 •6048 ■6198 ■6346 ■6492 ■6636 ■6778 •6918 •7056 ■7192 •7325 •7456 •7585 •7712 •7836 •7958 ■8078 •8195 ■8310 •8422 •8531 •8638 •8742 ■8844 •8943 •9039 •9132 ■9223 •93" •9396 •9478 ■9557 50 •0000 •0184 •0368 •0552 ■0736 •0920 •1103 ■1286 ■1469 •1651 ■1833 ■2014 •2195 •2374 ■2554 •2732 •2909 •3086 •3262 •3436 •3610 •3783 •3954 •4124 •4293 •4461 ■4627 •4792 ■4955 ■5117 •5278 •5436 •5593 •5749 •5902 •6054 ■6204 •6352 •6458 ■6643 •6785 •6925 ■7063 •7199 ■7332 •7464 •7593 ■7720 •7844 •7966 •8086 •8203 •8318 •8430 ■8539 •8646 •8751 •8852 •8951 •9048 •9141 •9232 ■9320. ■9405' •9487 ■9566 30 19 ■0000 •0184 ■0369 •0553 ■0737 •0921 ■1104 ■1288 ■1470 •1653 •1835 ■2016 •2197 •2377 ■2556 •2735 •2912 ■3089 ■3265 •3440 •3614 •3786 •3958 •4128 •4297 •4465 ■4632 •4797 •4960 •5122 •5283 •5442 •5599 ■5754 •5908 •6060 •5210 ■6359 •6505 •6649 •6791 ■6932 •7070 •7206 ■7340 ■7471 •7600 •7727 •7852 •7974 •8094 •821 1 •8326 •8438 •8548 •865s •8759 •8861 •8960 •9057 ■9150 ■9241 ■9329 •9414 •9496 •9576 40 •0000 •0185 ■0369 •0554 •0738 •0922 •iio5 •1289 •1472 •1654 •1837 •2018 •2199 •2379 •2559 •2737 •2915 •3092 •3268 •3443 ■3617 •3790 •3962 ■4132 •4302 ■4470 •4636 •4801 ■4965 •5127 ■5288 •5447 •5605 •5760 •5914 •6066 ■6217 •6365 •65 II •6656 •6798 •6939 •7077 ■7213 ■7347 •7479 ■7608 •7735 ■7860 ■7982 ■8102 •8219 •8334 •8447 •8556 •8664 ■8768 •8870 10 50 •9066 •9159 •9250 •9338 •9423 ■9506 •958S ■0000 ■0185 •0369 ■0554 ■0739 •0923 1 107 •1290 ■1473 •1656 •1838 ■2020 ■2201 •2382 ■2561 •2740 •2918 •3095 ■3272 •3447 •3621 •3794 '3966 ■4137 •4306 •4474 •4641 ■4806 ■4970 ■5133 ■5293 ■5453 •5610 •5766 ■5920 •6072 •6223 •5371 •6518 6563 •6805 •6946 •7084 •7220 ■7354 •7486 •7616 ■7743 ■7868 •7990 •81 10 •8228 •8343 ■8455 ■8565 •8672 ■8777 ■8879 ■8978 ■9075 ■9168 ■9259 ■9348 ■9433 •9515 ■9595 20 30 •0000 ■0185 ■0370 0555 ■0739 •0924 1 108 ■1292 •1475 •1658 ■1840 "2022 •2203 •2384 ■2564 ■2743 •2921 •3098 ■3275 ■3450 ■3625 ■3798 •3970 •4I4I •4310 ■4479 •4646 •48 1 1 ■4975 ■5138 ■5299 ■5458 •5616 •5772 . ^5926 •6079 •6229 •6378 •6525 •6669 •6812 ■6953 •7091 •7228 •7362 ■7494 •7623 •7751 ■7876 ■7998 ■8118 •8236 •8351 •8464 •8574 •8681 ■8786 8987 •9084 ■9178 •9269 •9357 ■9443 ■9525 ■9605 40 0000 0185 ■0370 ■0555 •0740 ■0925 •nog •1293 ■1476 •1660 ■1842 •2024 ■2206 ■2386 •2566 ■2746 ■2924 •3102 •3278 ■3454 •3628 ■3802 •3974 ■4145 ■4315 ■4483 •4650 •4816 ■4980 ■5143 ■5304 ■5464 •5622 •5778 ■5932 ■6085 •6236 ■6384 6531 •6676 ■6819 ■6960 ■7098 ■7235 ■7369 ■7501 ■7631 ■7759 •7884 •8006 ■8127 •8244 •8360 ■8472 ■8582 ■8690 ■8795 •8897 19 10 •9093 •9187 •9278 •9367 ■9452 ■9535 ■9615 •0000 ■0185 ■0371 ■0556 ■0741 ■0926 •IIIO •1294 •1478 •I66I ■1844 •2026 •2208 ■2389 •2569 •2749 •2927 ■3105 •3282 ■3457 •3632 ■3806 ■3978 ■4149 ■4319 ■4488 ■4655 •4821 50 •5148 5310 ■5469 ■5627 ■5784 •5938 ■6091 •6242 ■6391 ■6538 •6683 ■6826 •6967 •7106 •7242 ■7377 ■7509 ■7639 •7767 ■7892 ■8015 ■8135 ■8253 ■8368 •8481 •8591 20 30 •8804 •8906 •9006 ■9103 •9197 •9288 ■9376 •9462 ■9545 •9625 ■0000 ■0186 •0371 •0555 •0742 •0927 •mi •1296 ■1479 ■1663 ■1846 •2028 •2210 •2391 ■2572 ■2751 •2930 •3108 •3285 •3461 ■3636 ■3810 •3982 •4154 •4324 ■4493 •4660 40 ■4991 ■5154 ■5315 •5475 ■5633 ■5790 ■5945 ■6097 •6248 •6398 ■6545 ■6690 •6833 •6974 ■7113 •7250 ■7385 •7517 ■7647 ■7775 ■7900 ■8023 •8143 •8262 ■8377 •8490 •8600 •8708 •8813 ■8916 ■9015 •91 12 •9206 •9298 •9386 •9472 ■9555 ■9635 20 •0000 •0186 •0371 •0557 ■0742 •0927 •1112 •1297 •1481 •1665 •2031 ■2213 ■2394 ■2574 ■2754 •2933 •31 1 1 •3288 •3465 •3640 •3814 •3986 ■4158 •4328 •4497 •4665 •4831 •4996 ■5159 •5321 ■5481 •5639 ■5796 ■5951 •6104 •6255 ■6404 •6552 ■6697 ■6840 ■6982 ■7121 •7258 ■7392 •7525 ■7655 ■7783 •7908 •8031 ■8152 •8270 •8386 •8499 •8609 •8717 •8822 ■8925 ■9025 •9122 •9216 •9308 ■9396 ■9482 ■9565 ■9645 50 20 When the Declination is North the sign is - When the Declination is South the sign is + 89 ALT-AZIMUTH TABLES. Under Altitude in head-line, and abreast of Latitude in Margin, take out the tabular quantity and mark it + or - , according' as the Latitude is N. or S. Lai'. TRUE ALTITUDE. 20 10' 20 30 40 50 21 10 20 30 40 50 22 10' 20' 30 0° I 2 3 4 5 ■0000 •0064 •0127 •0190 ■0254 •0317 ■0000 ■0064 •0128 •0192 •0256 •0320 •0000 •0065 •0129 •0194 ■0258 •0323 ■0000 •0065 ■0130 •0196 •0261 ■0326 •0000 •0066 •0132 •0197 •0263 ■0329 •0000 •oo65 •0133 •0199 ■0265 ■0332 ■0000 ■0067 ■0134 ■0201 •0268 ■0335 ■0000 •0068 •0135 ■0203 •0270 ■0337 0000 •0068 0136 •0204 •0272 •0340 •0000 ■0069 ■0137 •0206 •0275 ■0343 •0000 •0069 •0139 •0208 •0277 •0346 •0000 •0070 ■0140 ■0210 •0279 ■0349 •0000 ■0071 •0141 ■021 1 •0282 ■0352 ■0000 •0071 •0142 ■0213 •0284 •0355 •0000 ■0072 •0143 ■0215 •0287 ■0358 •0000 •0072 0145 •0217 ■0289 •0361 6° I 9 10 ■0380 •0444 ■0507 •0569 •0632 •0384 •0448 •05 1 1 •057s •0638 •0387 •0452 ■0516 ■0580 •0643 ■0391 •0456 ■0520 •0585 •0649 •0394 •0460 ■0525 •0590 ■0655 ■0398 •0464 ■0530 •0595 •0661 ■0401 ■0468 ■0534 •0600 •0667 ■0405 ■0472 ■0539 •0672 •0408 •0476 •0544 •061 1 •0678 •0412 •0480 ■0548 •0616 •0684 •041S •0484 ■0553 •052I •0690 •0419 •0488 ■0558 0627 ■0696 •0422 •0492 •0562 •0632 •0702 •0426 ■0497 •0567 ■0637 •0707 •0429 ■0501 ■0572 •0643 •0713 •0433 •0505 ■0576 •0648 •0719 11° 12 13 M IS ■0694 ■07S7 •0819 •0S81 ■0942 •0701 •0764 •0826 ■0889 •0951 •0707 ■0770 ■0834 ■0896 •09S9 •0713 ■0777 ■0841 ■0905 •0968 •0720 •0784 •0849 •0913 •0976 •0726 ■0791 ■0856 0921 •0985 ■0732 ■0798 •0864 •0929 •0994 •0739 •0805 ■0871 •0937 •1002 ■0745 ■0812 •0879 •0945 •lOII •0752 •0819 •0886 ■0953 •1020 ■0758 •0826 •0894 ■0961 •1028 ■0764 •0833 •0901 •0969 •1037 ■0771 •0840 •0909 •0977 •1046 ■0777 •0847 •0916 •0986 ■1054 •0784 ■0854 •0924 •0994 ■1063 •0790 •0861 •0932 •1002 •1072 i6° 17 i8 19 20 •1003 •1064 ■II2S •ii8s •1245 ■IOI2 •1074 •H3S •I 196 •1256 ■102 1 •1083 ■I 14s •1206 ■1267 •1031 ■1093 •1155 •1217 •1279 ■1040 •I 103 •1166 •1228 ■1290 •1049 ■1113 •1176 •1239 ■[301 •1058 •1122 ■I 186 •1250 ■1313 •1067 •1132 •I 197 •1261 •1324 •1077 •1142 •1207 •1272 •1336 •1086 •1152 •1217 •1282 ■1347 •1095 •I 162 •1228 •1293 •1359 •I 104 •1171 •1238 •1304 •1370 •1114 ■1181 •1249 •1315 •1382 •1123 •1191 ■1259 •1326 •1393 ■1132 •I 201 •1269 ■1337 ■1405 •1142 •1211 •1280 •1349 •1417 21° 22 23 24 25 •1304 ■1363 •1422 ■1480 •1538 •1316 •1376 ■I43S ■1494 •1552 •1328 •1388 •1448 •1507 •1566 •1340 •1401 •1461 •1521 ■1580 •1352 ■1413 •1474 ■1534 •1594 •1364 •1425 •1487 ■1548 •1608 •1376 ■1438 ■1500 •1561 •1622 •1388 ■1450 ;isi3 •1636 •1400 ■1463 ■1526 ■1589 ■1651 •1412 •1476 ■1539 •1602 •1665 •1424 •1488 •I6I6 •1679 •1436 •1501 •1565 •1630 •1693 ■1448 •1514 ■1579 ■1643 •1707 ■1460 •1526 •1592 •1657 •1722 •1472 ■1539 •1605 •1671 •1736 •1484 •1552 •1618 •1685 ■1751 26° 29 30 •1596 ■1652 •1709 •176s •1820 •1610 ■1667 •1724 •1781 •1836 ■1624 •1682 ■1740 •1797 ■1853 •1639 •1697 ■1755 •1813 ■1869 ■1654 •1712 ■1771 •1829 •1886 •1668 •1728 •1786 ■1845 ■1903 •1683 •1743 •1802 •1861 •1919 •1697 •1758 •1818 •1877 •1936 •1712 •1773 ■1834 •1893 •1953 •1727 •1788 •1849 •1910 •1970 •1742 •1804 •1865 •1926 •1986 •1756 •1819 •1881 •1942 •2003 •1771 ■1834 ■1897 ■1959 •2020 •1786 ■1850 •1913 ■1975 •2037 •1801 •1865 •1929 •1992 ■2054 •1816 •1880 ■1945 •2008 •2071 31° 32 33 34 35 ■187s ■1929 •1982 •203s •2088 •1892 •1946 ■7,oon ■2054 •2107 •1909 •1964 ■2018 ■2072 •2126 •1926 •1981 ■2036 ■2091 ■2145 ■1943 ■1999 ■2054 ■2109 •2164 •i960 •2017 •2073 ■2128 ■2183 •1977 •2034 ■2091 ■2147 •2202 •1994 ■2052 •2109 •2165 •2221 •2012 ■2070 •2127 •2184 •2240 •2029 ■2087 ■2145 ■2203 ■2259 •2046 •2105 •2164 •2222 •2279 •2063 •2123 •2182 •2240 ■2298 •2081 •2141 •2200 ■2259 •2317 •2098 •2159 •2219 •2278 •2337 •21 16 ■2177 •2237 ■2297 ■2356 •2133 •2195 •2256 •2316 •2376 36° 39 40 •2139 •2190 ■2241 •2291 ■2340 •2IS9 •2210 ■2261 •23 1 1 ■2361 ■2178 •2230 •2281 •2332 ■2382 •2198 •2250 •2302 ■2353 •2403 •2217 •2270 ■2322 ■2374 ■2425 •2237 ■2290 ■2343 ■2395 ■2446 •2256 •2310 ■2363 ■2415 •2467 •2276 •2330 ■2384 ■2437 ■2489 •2296 ■2350 •2404 •2458 ■2510 ■2315 •2371 •2425 ■2479 •2532 ■2335 ■2391 •2446 •2500 ■2554 ■2355 •241 1 •2467 •2521 ■2575 ■2375 •2431 ■2487 ■2543 ■2597 •2395 ■2452 ■2508 ■2564 •2619 ■2415 •2472 •2529 ■2585 •2641 •2435 •2493 •2550 •2663 41° 42 43 44 45 •2388 •243s •2482 ■2528 ■2S74 ■2409 •2458 •250s ■2551 •2S97 ■2431 ■2480 •2527 ■2574 •2620 ■2453 •2502 •2550 ■2597 •2644 •2475 •2524 ■2573 •2620 •2667 •2497 •2546 •2595 ■2643 ■2691 ■2518 •2569 •2618 •2667 ■2714 ■2540 •2591 •2641 •2690 •2738 •2562 ■2613 •2664 •2713 ■2762 •2584 •2636 •2686 ■2736 ■2785 •2606 •2658 •2709 •2760 •2809 •2628 •2681 •2732 •2783 •2833 •2651 ■2703 ■2755 ■2807 ■2857 •2673 •2726 •2779 •2830 •2881 •2695 ■2749 •2802 •2854 •2905 •2717 •2772 •2825 •2877 •2929 46° % 49 50 •2618 ■2662 •270s •2747 •2788 •2642 ■2686 ■2729 •2772 •2813 ■2666 •2710 •2754 ■2797 •2839 ■2690 •2734 •2779 •2822 •2864 •2713 ■2759 •2803 •2847 ■2890 ■2737 •2783 ■2828 •2872 •2915 ■2761 •2807 •2853 •2897 •2941 ■2785 •2832 •2877 •2922 •2966 •2809 •2856 •2902 •2948 •2992 •2834 •2881 •2927 •2973 •3018 ■2858 •2905 •2952 •2998 •3043 •2882 •2930 •2977 •3024 •3069 ■2906 ■2955 ■3003 ■3049 ■3095 •2931 •2980 •3028 •307s •3121 •2955 •3004 •3053 •3100 •3147 ■2980 ■3029 •3078 •3126 •3173 51° 52 53 54 55 •2829 ■2868 •2907 ■2945 •2981 •2854 ■2894 •2933 ■2971 •3008 •2880 •2920 •2960 ■2998 •3036 •2906 •2946 ■2986 •3025 ■3063 ■2931 •2972 •3012 ■3052 •3090 ■2957 ■2999 ■3039 •3079 •3117 •2983 ■3025 •3066 •3106 •3144 •3009 •3051 •3092 •3133 •3172 ■3035 •3078 ■31 19 •3160 ■3199 •3061 •3104 ■3146 ■3187 ■3227 •3087 ■313I •3173 ■3214 •3254 •3 "4 ■3157 •3200 •3241 ■3282 •3140 ■3184 •3227 ■3269 ■3310 •3166 •3210 •3254 •3296 ■3337 •3193 •3237 •3281 •3324 •3365 •3219 •3264 •3308 •3351 •3393 56° i •3017 ;30S3 •3120 •3152 ■304s •3080 •311S •3148 ■3181 •3072 •3108 •3143 •3176 •3209 •3100 •3136 ■3171 ■3205 ■3238 ■3127 ■3163 •3199 •3233 •3267 ■3155 •3191 ■3227 ■3262 ■3295 •3182 •3219 •3255 ■3290 •3324 •3210 •3247 •3284 ■3319 ■3353 ■3238 ■3275 ■3312 •3348 ■3382 •3266 •3304 •3341 •3376 ■341 1 •3294 ■3332 •3369 •3405 ■3440 •3322 ■3360 •3398 ■3434 3470 ■335° ■3388 •3426 ■3463 ■3499 •3378 •3417 •3455 •3492 ■3528 •3406 •3445 ■3484 ■3521 •3558 •3434 •3474 •35J3 •3551 •3587 6i° 62 65 •3183 •3214 •3243 •3271 ■3299 •3212 •3243 •3272 •3301 •3329* ■3241 •3272 •3302 •3331 •3359 •3270 •3301 ■3331 ■3360 . ■3389 •3299 •3331 •3361 ■3390 •3419 •3328 •3360 •3391 •3420 •3449 •3357 ■3389 •3420 •3450 •3479 •3387 ■3419 •3450 ■3480 ■3509 ■3416 ■3448 ■3480 •3510 ■3540 ■3445 ■3478 ■3510 ■3540 ■3570 •3475 •3508 •3540 •3571 ■3601 ■3504 ■3537 ■3570 •3601 ■3631 ■3534 •3567 •3600 112 •3563 •3597 Si2 •3692 ■3593 •3660 •3692 ■3723 •3623 •3657 •3691 •3723 •3754 20' 10 20' 30 40 50 21 10 20 30 40 50 22 10' 20' 30' When the Latitude is North the sign is + When the Latitude is South the sign is - . ALT-AZIMUTH TABLES. 90 F Under Altitude and abreast of Declination, take out the tabular quantity and mark it + or — , aecording as Declination Is S. or N. Add Algebraically E and F. Dec- . LI NA- TION. TRUE ALTITUDE. 26 10' 20' 30 40' 50 21 10 20' 30' 40' 50' 22 10 20 30' 0° I •0000 •0186 •0000 •0186 •0000 •0186 ■0000 ■0186 •0000 0187 •0000 •0187 0000 •0187 •0000 •0187 ■0000 ■0187 •0000 ■0188 •0000 ■oi88 •0000 •0188 •QOOO •0188 •0000 •0188 ■0000 ■0189 •0000 •0189 2 3 4 5 •0371 •OSS7 ■0742 ■0927 •0372 •0558 •0743 •0928 •0372 ■0558 •0744 •0929 •0373 •0559 •0745 •0930 ■0373 •0559 •0746 •0931 •0373 •0560 •0746 •0933 •0374 •0561 •0747 •0934 •0374 0561 •0748 •0935 •0375 ■0562 •0749 •0936 •0375 •0562 •0750 •0937 •0376 •0563 •0751 ■0938 •0376 •0564 •0751 •0939 •0376 •0564 •0752 •0940 ■0377 ■0565 ■0753 •0941 •0377 •0566 •0754 •0942 •0378 ■0566 •0755 •0943 6° •1112 ■1114 •1115 •1116 •1117 •iu8 ■I 120 •1121 ■II22 •1123 •1125 ■I 126 •I 127 •I 129 •I 130 •1131 I 9 10 ■1297 •1481 •i66s -1848 •1298 •1483 ■1667 •1850 •1300 •1484 •1668 •1852 •1301 •i486 •1670 •1854 •1303 ■1487 •1672 •1856 •1304 •1489 •1674 •1858 ■1305 •1491 •1676 •i860 •1307 ■1492 •1678 •1862 •1308 ■1494 •1679 •1864 ■1310 ■1496 •1681 •1866 •1311 •1498 •1683 •1868 ■1313 •1499 •1685 •1871 •I3I4 •I5OI •1687 •1873 •1316 •1503 ■1689 •1875 •1318 •1505 ■1691 •1877 •1319 •1506 •1693 •1880 11° 12 13 14 IS •2031 •2213 •2394 ■2574 •2754 •2033 ■2215 •2396 •2577 •2757 •2035 •2217 •2399 •2580 •2760 ■2037 •2220 •2402 •2583 ■2763 ■2039 •2222 •2404 •2586 •2766 •2042 •2225 •2407 •2588 •2769 •2044 •2227 •2410 •2591 ■2772 •2046 ■2230 •2412 •2594 •2775 ■2048 •2232 ■2415 •2597 ■2779 •2051 •2235 •2418 •2600 •2782 •2053 •2237 •2421 2603 •2785 ■2056 •2240 •2423 •2606 ■2788 •2058 •2242 •2426 •2609 •2791 •2060 •2245 •2429 ■2612 •2795 ■2063 •2248 ■2432 •2615 •2798 •2065 •2250 •2435 •2619 •2801 i6° % 20 ■2933 ■311 1 •3288 •346S •3640 •2936 •3"5 •3292 •3468 •3644 •2940 •31 18 ■3296 •3472 •3647 •2943 •3121 •3299 ■3476 •3651 •2946 •3125 •33°3 •3480 •3655 •2949 •3128 ■3306 ■3483 ■3659 •2952 ■3132 •3310 •3487 ■3664 ■2956 •3135 •3314 ■3491 •3668 •2959 •3139 •3317 •3495 •3672 •2963 •3142 ■3321 •3499 •3676 •2966 ■3146 •3325 •3503 •3680 ■2969 •3150 •3329 •35^7 •3684 ■2973 •3153 •3333 ■35" •3689 •2976 •3157 •3337 •3516 •3693 •2980 ■3161 •3341 •3520 •3698 •2983 •3165 ■3345 •3524 •3702 21° 22 23 24 25 •3814 ■3986 •4158 ■4328 •4497 •3818 •3991 •4162 •4333 •4502 •3822 •3995 •4167 •4338 •4507 •3826 ■3999 ■41 7 1 ■4342 •4512 •3830 •4004 •4176 •4347 ■4517 •3834 •4008 •4181 •4352 •4522 •3839 •4013 •4185 •4357 •4527 ■3843 •4017 •4190 •4362 •4532 •3847 •4022 ■4195 •4367 •4537 •3852 •4026 •4200 •4372 •4542 •3856 •4031 •4204 ■4377 •4547 ■3861 •4035 ■4209 •4382 •4553 •3865 •4040 •4214 •4387 •4558 3870 •4045 ■4219 •4392 •4563 •3874 •4050 •4224 •4397 •4569 •3879 •4055 •4229 •4402 •4574 26° 29 30 •4665 ■4831 •4996 ■5159 ■5321 •4670 •4836 •5001 •516s •5327 ■467s •4842 ■5007 •5170 ■5332 •4680 •4847 •5012 •5176 •533S •46S5 •4852 •5018 •5:82 •5344 ■4690 •4857 •5023 ■5187 ■5350 •4696 ■4863 •5029 •5193 •5356 •4701 •4868 •5034 •5199 •5362 ■4706 •4874 ■5040 •5205 •5368 •4712 ■4879 •5046 •521 1 •5374 ■4717 •4885 •5052 •5217 •5380 •4722 •4S91 •5057 •5223 ■5386 •4728 •4896 •5063 •5229 •5393 •4734 •4902 •5069 ■5235 •5399 •4739 •4908 ■5075 •5241 •5405 •4745 ■4914 •5082 •5248 •5412 31° 32 33 34 35 •5481 •5639 •5796 ■5951 •6104 •5487 •5645 •5802 •S9S7 ■6 no ■5493 ■5808 •5964 ■61 17 ■5499 •5657 •5815 ■5970 •6124 •5505 ■5664 •5821 •5977 •6130 •55" •5670 •5827 •5983 •6137 •5517 •5676 •5834 •5990 •6144 •5523 •5683 ■5840 •5996 •6151 ■5529 •5689 •5847 •6003 •6158 •5536 •5695 •5854 •6010 •6165 •5542 •5702 •5860 •6017 •6172 •5548 •5709 •5867 •6024 •6179 •5555 •5715 •5874 •6031 •6186 •5561 •5722 •5881 •603S •6194 •5568 •5729 ■5888 •6045 •6201 •5575 •5736 ■5895 •6053 •6208 36° 39 40 •625s ■6404 ■6552 •6697 •6840 •6262 •641 1 •6559 •6704 •684S •6268 6418 ■6566 •67 II •68S5 ■6275 ■6425 •6573 •6719 •6862 •6282 •6432 •6580 •6726 •6870 •6289 •6439 •6587 •6733 •6878 ■6296 ■6446 •6595 ■6741 •6885 •6303 •6454 •6602 ■6748 6893 ■6310 •6461 •6610 •6756 ■6901 •6317 ■6468 ■6617 •6764 •6909 •6325 ■6476 •6625 •6772 ■6917 •6332 ■6483 ■6632 •6780 •6925 ■6339 •6491 •6640 •6787 •6933 ■6347 •6498 ■6648 •6795 •6941 •6355 •6506 •6656 •6804 •6949 •6362 •6514 ■6664 •6812 •6957 41° 42 43 44 45 ■6982 •7121 ■7258 7392 •7525 •6989 •7128 -7265 •7400 7533 •6997 •7136 7273 7408 7541 •7004 7144 •7281 •7416 ■7549 •7012 7152 •7289 ■7424 7557 •7020 •7159 •7297 •7433 •7566 •7027 •7167 7305 •7441 •7574 •7035 7175 ■7313 ■7449 •7583 •7043 ■7184 ■7322 •7458 7591 •7051 ■7192 •7466 •7600 ■7059 •7200 •7338 •7475 ■7609 •7068 •7208 7347 •7483 •7617 •7076 •7217 •7356 •7492 ■7626 •7084 •7225 •7364 •7501 •7635 •7093 7234 7373 7510 •7644 •7101 •7243 •7382 7519 •7654 46° % 49 50 •76SS 7783 7908 •S031 •8152 •7663 7791 •7917 •8040 •8161 •7671 •7800 •7925 •8049 ■8170 •7680 •7808 •7934 ■8057 •8178 '7688 •7817 ■^943 •8066 ■8187 •7697 •7825 7951 •8075 •8196 7705 •7834 7960 •8084 •8205 •7714 ■7843 •7969 •8093 •8215 7723 7852 •7978 •8102 •8224 •7731 •7860 ■7987 8112 •8233 •7740 •7870 •7996 •8121 •8243 7749 •7879 •8006 •8130 •8252 7758 •7888 ■8015 •8140 •8262 •7767 •7897 •8025 •8149 •8272 7777 ■7907 •8034 •8159 •8282 •7786 •7916 •8044 •8169 ■8292 52 S3 54 55 •8270 ■8386 ■8499 ■8609 •8717 ■8279 •8508 •8619 •8727 ■8288 •8404 ■8517 •8628 •8736 ■8297 •8413 •8526 •8637 •8745 •8306 •8422 •8536 •8647 •8755 •8315 ■8431 ■8545 ■8656 ■8765 •8324 •8441 •8555 ■8666 •8774 •8334 •8450 ■85O4 •8675 •8784 ■8.;43 •8460 ■8574 •8685 •8794 •8469 •8584 •8695 •8804 ■8362 ■8479 •8594 •8705 •8814 •8372 •8489 ■8603 •87 1 5 •8825 ■8382 •8499 ■8614 ■8726 •8835 •8392 •8509 •8624 •8736 ■8845 •8402 •8519 •8634 •8746 •8856 •8412 •8529 •8644 •8757 •8866 56° •8822 •892s •9025 •9122 •9216 •8832 ■8934 ■9034 ■9131 •9226 •8841 •8944 •9044 •9141 •9236 •8851 •8954 ■9054 •9151 •9246 •8861 •8964 •9064 •9161 •9256 ■8870 •8973 •9074 •9171 •9266 •8S80 ■8983 •9084 ■9182 •9276 •8890 •8993 •9094 •9192 •9287 ■8900 •9004 ■9104 ■9202 ■9297 •8910 •9014 •911S •9213 ■9308 •8921 •9024 •9125 •9223 •9319 •8931 •9035 •9136 •9234 •9329 ■8941 •9015 ■9146 •9245 •9340 •8952 •9056 ■9157 •9256 •9351 •8963 ■9067 •9168 ■9267 •9363 •8973 •9078 •9179 •9278 •9374 61° 62 6s •9308 •9396 •9482 •9565 ■964s ■9317 •9406 •9492 ■9575 •965s •9327 ■9416 •9502 ■9665 ■9338 •9426 •9512 ■9596 •9676 •9348 ■9437 •9606 ■9686 •9358 •9447 •9533 •9617 •9697 ■9368 •9458 •9544 •9627 •9708 •9379 ■9468 ■9555 •9638 •9719 •9390 •9479 •9565 ■9649 •9730 •9400 ■9490 ■9576 •9660 ■9741 •941 1 •9501 •9587 ■9671 •9752 •9422 •9512 •9599 ■9682 •9763 •9433 ■9523 ■9610 •9694 •9775 •9444 •9534 •9621 •9705 •9786 •9455 •9545 ■9633 ■9717 9798 ■9467 ■9557 •9644 •9728 •9810 26 10 20 30' 40' 50' 21 10 20' 30 40 50 22 10' 20' 30 When the Declination is North the sign is - When the Declination is South the sign is + 91 ALT-AZIMUTH TABLES. Under Altitude In head-line, and abreast of Latitude in margin, talte out the tabular quantity and mark it + or according as the Latitude is N. or S. TRUE ALTITUDE. Lat. 22 30 40 50 23 10 20 30 40 50 24 10 20 30 40 50 25 o" I 2 3 4 5 6° 7 8 9 10 Il- ia 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 51° 52 53 54 55 56° 57 58 60 61° 62 65 •0000 •0072 ■014s ■0217 •0289 •0361 •0433 •0505 •0576 ■0648 •0719 •0790 •0861 ■0932 •1002 •1072 •1142 •1211 1280 •1349 ■1417 •1484 ■1552 ■1618 ■1685 •1751 •1816 •1880 •194s •2008 •2071 ■2133 ■2I9S •2256 •2316 ■2376 ■243s •2493 •2550 •2607 •2663 ■2717 •2772 •2825 •2877 ■2929 •2980 ■3029 •3078 •3126 •3173 •3219 •3264 •3308 ■3351 ■3393 •3434 •3474 ■3513 ■3551 ■3587 •3623 •3657 ■3691 ■3723 •3754 22 30 •0000 ■0073 •0146 ■0219 •0291 •0364 ■0437 ■0509 •0581 •0653 •0725 •0797 •0868 •0939 •loio •1081 •1151 ■1221 •1291 •1360 •1428 ■1497 •1564 •1632 •1699 ■176s ■1831 •1895 •1961 •2025 •2088 •2151 ■2213 •2275 •2335 ■239s ■24SS ■2513 •2571 ■2628 ■2684 •2740 •2794 ■284S •2901 ■29S3 ■3004 ■3054 •3104 ■3152 ■3199 ■3246 ■3291 •333s •3379 •3421 •3462 ■3503 •3542 ■35S0 •3617 •3653 ■3687 •3721 •3754 •3785 40 •CXMO ■0073 ■0147 •0220 •0294 •0367 •0440 ■0513 ■0586 •0659 •0731 ■0803 ■087s •0947 ■IOI9 ■1090 •ii5i ■1231 ■1301 •1371 •1440 ■1509 •1577 ■164s ■1713 •1779 ■1846 ■1912 ■1977 •2041 •2105 ■2169 ■2231 ■2293 •23S4 •2415 ■2475 •2534 •2592 •2650 •2706 •2762 •2817 •2872 •2925 •2977 •3029 •3079 ■3129 ■3178 •3225 •3272 ■3318 ■33B3 •3406 ■3449 •3491 •3531 •3571 •3609 •3646 •3683. •3718 •3752 ■3784 ■3816 50 ■0000 ■0074 ■0148 0222 •0296 ■0370 •0444 •0517 •0591 •0664 ■0737 0810 ■0883 ■09SS •1027 •1099 ■I 170 •:24i ■13:2 ■1382 •1452 •1521 •1590 •1659 •1726 ■1794 •1861 •1927 •1993 •2058 •2122 •2186 ■2249 •2312 •2374 •2435 ■2495 •2555 ■2613 •2671 •2728 •278s •2840 •289s •2949 ■3001 •3053 ■3104 ■3154 •3204 •3252 •3299 •3345 ■3390 •3434 •3477 •3519 •3560 •3600 •3638 ■3676 •3713 •3748 •3782 '381S ■3847 •0000 •0075 ■0149 0224 •0298 •0373 •0447 ■0521 ■0596 •0669 •0743 •0816 •0890 •0963 ■103s •I 108 •1179 ■I 25 1 ■1322 ■1393 •1464 •1533 ■1603 ■1672 •1740 ■1808 •1876 •1943 •2009 •2075 •2140 •2204 •2268 •2331 •2393 •2454 ■2515 •2S7S •2634 •2693 •2751 •2807 •2S63 ■2918 •2973 •3026 •3078 ■3130 •3180 •3229 •3278 ■3326 ■3372 •3417 •3462 •3505 •3548 •3589 •3629 •3668 •3706 •3743 ■3778 ■3813 •3846 •3878 ■0000 ■0075 •0151 •0226 ■0301 •0376 •0451 ■0526 •0600 •0675 ■0749 •0823 •0897 •0970 •1044 •1116 •I 189 •1261 ■1313 •1404 ■1475 •1546 ■1616 •1685 ■I7S4 •1823 •1891 ■1958 ■2025 •2091 •21 57 ■2222 •2286 ■2349 •2412 •2474 ■253s ■2596 ■2655 •2715 •2773 •2830 ■2S86 ■2942 •2996 •3050 ■3103 ■315s ■3206 •3256 3304 •3352 •3399 •344s •3490 '3533 ■3576 ■3618 •365S ■3697 ■3736 •3773 ■3809 ■3843 •3877 •3909 23 10 20 •0000 •0076 ■0152 ■0228 ■0303 ■0379 ■045 s •0530 ■0605 •0680 ■0755 •0830 ■0904 •0978 ■1052 ■1125 •1199 •1271 ■1344 •1416 •1487 •1558 •1629 ■1699 ■1769 ■1838 •1906 •1974 ■2041 ■2108 •2174 ■2239 •2304 •2368 ■2431 •2494 •2556 •2617 •2677 •2736 •2795 ■2853 ■2909 ■2965 ■3020 •3075 ■3128 •3180 ■3231 ■3282 •3331 •3379 •3426 •3473 •3518 ■3562 •3605 ■3647 •3687 •3727 •3766 •3803 •3839 •3874 ■3908 •3941 ■0000 •0076 •0153 •0229 •0306 •0382 ■0458 ■0534 ■0610 ■0686 •0761 ■0836 •09 1 1 •0986 •1060 ■1134 •1208 ■1281 ■ "1354 •1427 •1499 ■1571 •1642 1712 •1783 ■1852 •1921 •1990 •2058 •2125 ■2191 ■2257 •2323 •2387 • •2451 ■2514 •2576 •2638 •2698 •2758 •2817 •2875 ■2933 ■2989 •304s •3099 ■3153 ■320s •3257 •3308 ■3357 ■3406 •3454 •3500 ■3546 ■3590 •3633 ■3676 ■3717 •3757 ■3796 ■3833 •3870 ■3905 ■3939 ■3972 30 40 •0000 ■0077 •0154 •0231 •0308 •0385 •0462 ■0538 ■0615 ■0691 •0767 ■0843 ■0918 •0994 •1069 •1143 •1218 •1292 •1365 •1438 •1511 ■1583 •1655 •1726 •1797 ■1867 ■1936 •2005 •2074 •2142 •2209 •2275 •2341 •2406 •2470 ■2534 •2597 •2659 •2720 •2780 ■2839 ■2898 ■2956 •3013 •3069 ■3124 •3178 •3231 •3283 •3334 •3384 ■3433 ■3481 ■3528 •3574 •3619 •3662 ■3705 •3746 •3787 ■3826 ■3864 ■3900 ■3936 ■3970 •4004 50 •0000 ■0078 ■0155 ■0233 •0311 ■0388 •0465 •0543 •0620 •0696 •0773 •0850 ■0926 ■1002 •1077 •1152 •1227 ■1302 ■1376 ■1450 ■1523 •1596 •1668 •1740 •1811 ■1882 •1952 ■2021 ■2090 •2159 ■2226 •2293 •2359 •2425 •2490 •2554 •2617 •2679 •2741 ■2802 •2862 •2921 •2979 •3036 ■3093 ■3148 •3203 ■3256 •3309 ■3360 ■341 1 •3460 •3508 ■3556 ■3602 ■3647 •3691 •3734 ■3776 ■3816 •3856 •3894 •3931 •3967 ■4002 ■4035 24 ■0000 ■0078 ■0157 •0235 •0313 •0391 ■0469 •0547 •0624 ■0702 •0779 ■0856 •0933 ■1009 •1086 •1161 •1237 ■1312 •1387 •1461 •1535 •1608 •1681 ■1753 •1825 •1967 ■2037 •2107 ■2175 ■2244 ■2311 •2378 •2444 •2509 ■2574 •2638 ■2701 •2763 •2824 •2884 •2944 •3003 ■3060 •3117 ■3173 ■3228 •3282 '3335 •3387 ■3437 •3487 •3536 •3584 •363a ■3676 •3720 •3763 •3805 •3846 •3886 ■3925 ■3962 •3998 ■4033 •4067 10 ■0079 •0158 •0237 ■0315 0394 •0473 •0551 •0629 ■0707 •0785 •0863 •0940 •1017 •1094 •I 170 •1246 ■1322 •1397 •1472 •1547 •1621 •1694 •1767 ■1839 •1911 ■1982 •2053 •2123 •2192 •2261 ■2329 •2396 •2463 •2529 •2594 •2658 •2722 •2784 •2846 ■2907 •2967 •3026 •3084 •3141 •3198 •3253 •3307 •3361 ■3413 •3464 •3514 •3564 •3612 ■3659 •3704 ■3749 ■3793 ■383s •3876 •3916 •3955 •3993 ■4029 •4065 •4098 20 •0000 •0080 •0159 •0239 ■0318 ■0397 •0476 0555 ■0634 ■0713 •0791 ■0870 •0948 ■1025 •1103 •I 180 •1256 •1332 ■1408 •1484 •1559 •1633 •1707 •1781 ■1854 •1926 •1998 ■2069 •2140 ■2209 •2279 •2347 •2415 •2482 •2548 '2614 •2679 •2743 •2806 •2868 •2929 •2990 ■3049 ■3108 ■3166 •3222 •3278 •3333 •3387 •3439 •3491 •3542 •3591 •3640 ■3687 •3733 •3778 •3822 •3865 •3906 ■3947 •3986 ■4024 •4061 •4096 •4130 •0000 •0080 ■0160 •Q240 •0320 ■0400 •0480 ■0560 •0639 ■0718 ■0797 •0876 •095s •1033 'iiii •I 189 •1266 ■1343 •1419 •1495 •1571 •1646 •1720 •1794 •I 868 •1941 •2013 •2085 •2156 '2226 ■2296 •2365 ■2434 •2501 •2568 •2634 ■2699 •2764 •2827 •2890 ■2952 •3013 •3073 •3132 •3190 •3247 •3304 ■3359 ■3413 •3466 •3518 ■3569 •3619 •3668 •3715 •3762 •3807 •3852 •389s •3936 ■3977 •4017 •405s •4092 •4128 4162 30 40 ■0000 •0081 ■0162 •0242 ■0323 •0403 ■04S4 •0564 ■0644 ■0724 •0804 •0883 •0962 •1041 ■I 120 •I 198 ■1276 ■1353 •1430 •1507 •1583 ■1658 ■1734 •1808 •1882 ■1956 •2029 •2101 •2173 •2244 ■2314 ■2383 ■2452 •2520 ■2588 •2654 •2720 •2785 •2849 ■2912 •2975 •3036 •3097 •3156 •3215 •3272 •3329 •3384 ■3439 ■3493 ■3545 •3596 •3647 •3696 •3744 •3791 •3S37 •3881 ■3925 ■3967 •4008 •4047 •4086 •4123 ■4159 ■4194 ■0000 •0081 •0163 '0244 •0325 •0406 ■0487 ■0568 ■0649 •0729 •08 10 •0890 0970 •1049 •1128 •1207 •1285 ■1363 •1441 •1518 ■I 595 •1671 •1747 •1822 •1897 ■1971 '2044 •2117 •2189 •2261 t ■2332 •2402 •2471 •2540 •2608 •2675 •2741 ■2806 •2871 •2935 •2997 •3059 ■3120 •3180 ■3239 •3297 •3354 •3410 •3465 ■3519 •3572 ■3624 ■3675 •3724 •3773 ■3820 •3866 •391 1 •3955 •3997 •4038 •4078 •41 17 •415s •4191 '4226 50 25 When the Latitude is North the sign is + . When the Latitude is South the sign is — . ALT-AZIMUTH TABLES. 92 Under Altitude and abreast of Declination, take out the tabular quantity and mark it + or — , aeeordingr as Declination is S. or N. Add Algebraically E and F. Dec- lina- tion. TRUE ALTITUDE. 22 30 9 ID 11° 12 13 M IS i6° 17 i8 19 20 21° 22 23 24 25 26° 27 28 29 30 31° 32 33 34 35 36° 37 38 39 40 42 43 44 45 46° 42 48 49 50 51° 52 S3 54 55 56° 57 58 60 6i° 62 65 40 •0000 •0189 •0378 •0566 •07SS •0943 •1131 •1319 •1506 •1693 ■1880 •2065 •2250 ■243s •2619 •2801 •2983 •3165 ■334s J3524 •3702 •3879 •4055 ■4229 •4402 •4574 ■4745 •4914 •5082 •5248 •5412 ■5575 •5736 •5895 •6053 •6208 •6362 •6514 •6664 ■6812 •6957 •7101 •7243 73S2 •7519 •7654 •7786 •7916 •8044 •8169 •8292 •8412 ■8529 ■8644 •8757 ■8866 •8973 •9078 •9179 •9278 •9374 •9467 ■9557 •9644 ■9728 ■9810 50 23 22 30 •0189 •0378 •0567 ■0756 •0945 •1133 •1321 •1508 ■169s •1882 •2068 ■2253 •2438 •2622 ■2805 •2987 •3168 •3349 •3528 •3706 •3884 •4060 •4234 •4408 •4580 ■4751 •4920 ■508S ■5254 ■5419 •5581 •5743 •5902 6060 ■6216 •6370 •6522 •6672 •6820 •6966 •7 no •7251 ■7391 •7528 •7663 ■7796 •7926 ■8053 ■8179 •8302 •8422 •8540 •8655 ■8767 •8877 •8984 ■9089 •9190 •9385 ■9478 ■9569 •9656 •9740 ■9822 •0000 •0189 ■0379 ■0568 ■0757 •0946 •II34 •1322 •1510 •1697 ■1884 •2070 •2256 •2441 •2625 •2808 •2991 •3172 •3353 •3532 •37 1 1 •3888 ■4065 •4240 ■4413 ■4586 •4756 •4926 •5094 ■5260 ■5425 ■5588 ■5750 •5909 •6067 •6223 •6378 ■6530 ■6680 •6828 .6974 •7118 •7260 •7400 •7537 ■7672 •7805 •7935 •8063 •81S9 •8312 •8432 ■8550 •8665 •8778 40 •8995 •gioo •9202 •9300 •9397 ■9490 ■9580 •9752 •9834 10 20 ■0000 ■0000 •0190 •0190 ■0379 •0380 ■0569 •0569 •075S •0759 ■0947 •0948 •II36 •II37 ■1324 •1326 •I5I2 •I5I4 ■1699 •1702 •1886 •1889 •2073 •2075 •2259 •2261 •2444 •2447 •2628 •2631 •2812 ■2815 •2994 •3176 ■3357 •3537 ■3716 ■3893 •4070 •4245 ■4419 ■4591 •4762 •4932 •5100 ■5267 ■5432 •5595 ■5757 •5917 ■6075 •6231 ■6385 •6538 •6688 ■6837 •6983 •7127 •7269 ■7409 •7546 •7682 •7815 •7945 ■8073 •8199 •8322 ■8443 •8561 •8676 •8789 ■8899 •9006 ■91 II •9213 •9312 •9408 •9502 •9592 •9680 ■9764 ■9846 50 23 •3180 •3361 ■3541 •3720 •3898 ■4075 ■4250 •4424 •4597 •4768 •4938 ■5106 •5273 •5439 •5602 •5764 •5924 •6082 •6239 •6393 •6546 •6697 ■6845 •6992 •7136 •7278 •7418 •7556 •7691 •7824 •7955 •8083 ■8209 •8332 ■8453 ■8571 ■8687 •8800 •8910 ■9018 •9122 ■9224 ■9323 •9420 •9513 ■9604 ■9692 •9776 •9858 30 40 50 24 10 ■0190 •03S0 ■0570 ■0760 •0949 ■1138 •1327 ■1516 •1704 •1891 •2078 •2264 •2450 ■2635 •2819 •3002 •3184 ■3365 •3546 •3725 •3903 ■4080 •4255 ■4430 ■4603 •4774 •4944 •5113 ■5280 •5445 ■5609 •5771 ■5931 •6090 ■6247 •6401 ■6554 •6705 •6854 ■7000 •7145 •7287 ■7427 •7565 •7701 ■7834 ■7965 •8093 •8219 •8343 •8464 •8582 ■881 1 •8921 •9029 ■9134 •9236 •9335 ■9432 •9525 •9616 •9704 ■9788 •9870 20 •0000 0190 •0381 •0571 •0761 ■0950 •I 140 ■1329 ■1518 •1706 •1894 ■2081 ■2267 •2453 •2638 •2822 •3006 ■3188 •3370 ■3550 •3730 ■3908 •4085 •4261 ■4435 ■4608 •4780 ■4950 ■5119 ■5287 •5452 •5616 •5778 •5939 ■6098 •6255 •6409 •6562 •6713 •6862 ■7009 •7154 •7296 ■7437 •7575 ■7711 •7844 ■7975 •8104 ■8230 •8353 ■8474 •8593 ■8709 ■8822 •8932 9040 •9145 •9247 •9347 •9443 ■9537 •9628 •9716 ■9801 •9883 ■0000 •0191 •0381 •0571 •0762 ■0952 ■1141 •1331 •1520 •1708 •1896 •20S3 •2270 •2456 •2641 •2826 •3009 ■3192 ■3374 •3555 •3734 •3913 •4090 •4266 •4441 •4614 •4786 •4957 •5126 ■5293 •5459 •5623 ■5786 •5947 ■6105 •6262 •6418 •6571 ■6722 •6871 •7018 •7163 •7306 •7446 •7584 •7720 •7854 •7985 •81 14 •8240 •8364 •8485 •8604 •8720 •8833 •8944 ■9052 ■9157 •9259 •9359 •9455 •9549 •9640 •9728 ■9813 •9895 30 •0000 •0191 •0382 •0572 •0763 •0953 ■I 143 •1332 •1521 ■1710 ■1898 •2086 ■2273 •2459 ■2645 •2829 ■3013 •3196 ■3378 •3559 •3739 ■3918 •4095 ■4272 •4447 •4620 •4792 •4963 •5132 •5300 •5466 •5631 ■5793 •5954 •6113 •6270 •6426 •6579 ■6731 •6880 •7027 ■7172 •731S •7456 •7594 ■7730 ■7864 •7995 ■8124 •8251 •8375 ■8496 •8615 •8731 40 •8955 •9063 •9169 ■9271 •9371 •9468 ■9562 •9653 ■9741 •9826 10 0000 oigi 0382 ■0573 •0764 •0954 ■I 144 •1334 •1523 •1712 ■1901 ■2089 ■2276 ■2462 •2648 •2833 •3017 •3200 •3383 ■3564 •3744 ■3923 ■4101 •4277 ■4452 ■4626 •4799 •4970 ■5139 ■5307 ■5473 •5638 ■5801 •5962 •6121 ■6279 •6434 ■6588 ■6739 ■7036 ■7181 •7325 •7465 •7604 ■7740 ■7874 ■8006 •8135 •8261 •8385 •8507 •S626 •8742 •8856 ■8967 •9075 .9180 •9283 ■9383 •9480 •9574 ■9665 ■9753 •9839 ■9921 50 24 20 ■0191 •0383 •0574 •0765 •0955 ■1146 •1336 •1525 •1715 •1903 ■2091 •2279 •2466 •2652 •2837 •3021 ■3205 •3387 •3568 •3749 •3928 •4106 •42S3 •4632 •4805 •4976 ■5146 •5314 •5480 •5645 ■5808 •5970 •6129 ■6287 ■6442 ■6596 •6748 ■6898 •7045 •7191 ■7334 ■7475 •7614 •7750 •7884 •8016 •8145 ■8272 •8396 •8518 ■8637 •8754 •8867 •8978 ■9087 •9192 9295 •9395 •9492 •9586 •9678 30 •9851 ■9934 •0000 •0192 •0383 •0574 ■0766 •0957 •1147 •1338 •1527 ■1717 •1906 ■2094 •2282 ■2469 •2655 •2841 •3025 •3209 •3391 ■3573 •3754 •3933 •411 1 ■4288 •4464 •4638 ■48 1 1 •4983 ■5152 ■5321 •5487 •5553 •5816 •5977 ■6137 ■6295 •6451 ■6605 ■6757 •6907 •7055 ■7200 •7344 ■7485 •7624 •7760 •7895 •8027 •8156 •8283 ■8407 •8529 •8648 •876S •8879 •8990 •9099 ■9204 •9307 •9407 •9505 •9599 •9690 •9779 10 40 50 •9947 •0000 ■0192 •0384 •0575 ■0767 •0958 •I 149 •1339 •1529 •1719 •1908 ■2097 •2285 •2472 •2659 ■2844 •3029 ■3213 •3396 •3578 •3759 •3938 •41 17 •4294 •4170 ■4644 •4817 •4989 ■5159 •5328 ■5495 •5660 ■5824 ■5985 •6145 ■6303 •6459 ■6614 ■6766 ■6916 •7064 •7210 •7353 •7495 •7634 ■7771 ■7905 •8037 ■8167 •8294 ■8418 •8540 ■8860 •8777 •8891 •9002 •91 1 1 •9217 •9320 •9420 •9517 •9612 •9703 •9792 •9877 •9960 •0000 ■0192 ■0384 ■0576 •0768 •0959 •1150 ■1341 •1531 •1721 ■1911 •2100 ■2288 ■2475 •2662 •2848 ■3033 •3217 ■3400 •3583 ■3764 ■3944 •4122 •4300 •4476 •4651 •4824 ■5166 ■5335 •5502 •5668 •5831 ■5993 •6153 ■6312 •6468 •6622 •6775 •6925 •7073 •7219 •7363 ■7505 ■7644 •7781 ■7916 •8178 •8305 •8430 •8552 •8671 •8903 •9014 •9123 •9229 9332 •9432 •9530 ■9624 ■9716 •9805 •9890 •9973 •0000 •0192 ■0385 •0577 •0769 •0960 •1152 •1343 •1534 •1724 •1913 •2103 •2291 •2479 •2666 •2852 ■3037 •3222 •3405 •3587 ■3769 •3949 •4128 •4305 •4482 •4657 •4830 •5002 ■5173 •5342 •5509 •5675 •5839 •6001 ■6162 •6320 •6477 •6631 •6784 •6934 •7083 •7229 •7373 •7515 •7654 ■7792 ■7926 •8059 •8189 •8316 •8441 •8563 •8683 •8800 ■8914 •9026 •913s ■9241 •9345 ■9445 •9543 ■9637 •9729 •9818 ■9904 20 30 40 25 •0193 •0385 •0577 •0770 •0962 •1153 •1345 •1536 •1726 •1916 •2105 •2294 ■2482 •2669 •2856 •3041 ■3226 •3410 ■3592 •3774 •3954 ■4133 ■4311 •448S •4663 •4837 •5009 •5180 •5349 ■5517 •5683 •5847 •6009 •6170 ■6329 •6485 •6640 •6793 •6944 •7092 •7239 •7383 •7525 •7665 •7802 •7937 •8070 •8200 •8327 •8452 •8575 •8695 •8812 ■8927 •9038 •9147 •9254 ■9357 •9458 •9556 •9650 •9742 ■9831 •9917 I -0000 50 25 When the Declination is North the sign is - When the Declination is South the sign is + 93 ALT-AZIMUTH TABLES. Under Altitude in head-line, and abreast of Latitude in Margin, take out the tabular quantity and mark it + or according as the. Latitude is N. or S. Lat. TRUE ALTITUDE. 25 10 20 30 40' 50 26 10 20 30 40 50' 27 10' 20' 3d 0° •0000 •0000 •0000 ■coco •0000 •0000 •coco ■0000 •0000 •0000 •0000 •0000 •0000 •0000 •0000 •0000 I •0081 •0082 •0083 •0083 ■0084 •0084 •0085 •0086 •0086 ■0087 ■0088 •0088 •0089 ■0090 •oogo •0091 2 ■0163 •0164 ■0165 •0166 •0168 •0169 •0170 •01 7 1 •0173 •0174 •0175 ■0177 •0178 •0179 •0180 •0182 3 ■0244 0246 •0248 ■0250 •0252 •0253 •0255 •0257 •0259 •0261 •0263 ■0265 •0267 •0269 •0271 •0272 4 ■0325 ■0328 •0330 ■0333 •0335 ■0338 •0340 •0343 ■0345 ■0348 •0350 •0353 ■0355 ■0358 •0361 ■0363 , S ■0406 •0410 •0413 ■0416 •0419 •0422 •0425 •0428 •0431 ■0435 ■0438 •0441 •0444 ■0447 •0450 •0454 6° ■0487 •0491 ■0495 •0499 •0502 ■0506 •0510 ■0514 •0517 ■0521 •0525 •0529 •0533 ■0536 •.0540 ■0544 ! 7 •0568 ■0573 ■OS77 •0581 •0586 •0590 ■0594 •0599 •0603 ■0608 •0612 •0616 •0621 ■0625 •0630 •0634 8 •0649 •0654 •0659 •0664 ■0669 ■0674 •0679 •0684 •0689 •0694 •0699 •0704 •0709 •0714 •0719 • •0724 9 •0729 ■0735 •0741 ■0746 ■0752 •07S7 ■0763 •0769 •0774 •0780 •0786 •0791 ■0797 •0803 ■0809 ■0814 10 ■0810 •0816 ■0822 •0828 •0834 •0841 •0847 •0853 •0859 ■0866 •0872 •0878 •0885 •0891 •0898 •0904 H" •0890 •0897 •0903 ■0910 •0917 •0924 •0931 •0938 •0944 ■0951 •0958 •0965 •0972 •0979 •0986 •0993 i 12 •0970 ■0977 •0984 •0992 ■0999 •1007 •IOI4 •1022 •1029 •1037 •1044 •1052 •1059 •1067 •1075 •1082 i 13 •1049 •1057 •1065 •1073 ■io8i ■1089 •1097 •1105 •1113 •1122 •I 130 •1138 •I 146 ■1154 •1163 •II71 ' 14 •I 128 •1137 •I 14s ■I 154 •I 163 ■1171 •I 180 •1189 •1197 •1206 •1215 •1224 ■1233 •1242 ■1250 •1259 ! IS •1207 ■1216 •1225 ■1235 •1244 •1253 •1262 •1272 •I 28 1 •1290 •1300 •1309 •1319 •1328 •1338 ■1347 ' i6° •1285 •I 29s •1305 •1315 •1325 •1334 •1344 •1354 •1364 •1374 •1384 •1394 •1404 •1415 •1425 ■1435 ' % •1363 ■1374 •1384 ■139s ■1405 •1415 ■1426 ■1437 •1447 •1458 •1468 •1479 •1490 •1500 •15J1 •1522 i8 ■1441 ■1452 •1463 ■1474 ■1485 ■1496 ■1507 •1518 •1529 •1541 •1552 •1563 ■1575 •1586 •1597 •1609 19 ■1518 •1530 •1541 •ISS3 •156S ■1576 •1588 •1600 •1611 •1623 •1635 •1647 •1659 •1671 •1683 ■1695 20 ■IS9S •1607 •1619 •1631 •1644 •1656 •1668 •1680 ■1693 •1705 •1718 ■1730 ■1743 •1755 •1768 ■1780 21° •1671 •1684 •1697 •1709 ■1722 •1735 •1748 •1761 •1774 •1787 •1800 •1813 •1826 •1839 •1852 •1866 22 •1747 •1760 •1773 •1787 •1800 •1814 •1827 •1841 •1854 •1868 •1881 •1895 •1909 •1922 •1936 •1950 23 •1822 •1836 ■1850 •1864 •1878 •1892 ■1906 •1920 •1934 •1948 •1962 •1977 ■199' •2005 •2020 ■2034 24 •1897 •1911 •1926 ■1940 •1955 ■1969 ■1984 •1998 •2013 •2028 •2043 •2058 •2072 •2087 ■2102 •2II7 25 ■1971 ■1986 •2001 •2016 •2031 ■2046 ■2061 •2076 ■2092 •2107 •2122 ■2138 •2153 •2169 •2184 •2200 26° •2044 •2060 •2075 ■2091 •2107 •2122 ■2138 •2154 •2170 •2186 •2202 •2218 •2234 •2250 •2266 •2282 ' Vz ■2117 •2133 •2149 2165 ■2182 •2198 •2214 •2231 •2247 ■2264 •2280 •2297 ■2313 •2330 ■2347 •2363 •2189 •2206 •2223 •2239 •2256 •2273 ■2290 •2307 •2324 •2341 •2358 2375 •2392 •2409 •2427 ■2444 29 •2261 ■2278 ■2295 •2312 •2330 •2347 •2365 •2382 •2400 ■2417 •2435 •2452 •2470 •24S8 •2506 •2524 3° "2332 ■2349 •2367 •2385 ■2403 •2421 ■2439 ■2457 •2475 •2493 •25 1 1 '2529 ■2548 ■2566 •2584 •2603 31° •2402 •2420 •2438 ■2457 •2475 •2493 •2512 •2531 ■2549 •2568 •2587 •2605 •2624 •2643 •2662 •2681 32 •2471 •2490 •2509 •252S •2547 •2566 ■2585 •2604 ■2623 •2642 •2661 •2681 •2700 •2720 •2739 ■2759 33 •2540 ■2559 •2578 •2598 •2617 ■2637 •2656 •2676 •2696 •2715 •2735 •2755 •2775 •2795 ■2815 •2835 34 •2608 •2627 •2647 •2667 •2687 •2707 •2727 •2748 •2768 •2788 •2808 •2829 •2849 •2870 •2890 ■291 1 35 ■267s ■269s •2715 •2736 •2756 •2777 ■2798 •2818 •2839 •2860 •2881 •2902 •2923 ■2944 ■2965 •2986 36° •2741 •2762 •2783 •2804 •2825 •2846 •2867 •2888 ■2909 •2931 •2952 ■2973 ■2995 •3016 •3038 •3060 ■ 38 •2806 ■2S28 •2849 •2871 •2892 •2914 •2935 •2957 ■2979 ■3001 •3022 ■3044 •3066 •3088 •3111 •3133 •2871 •2893 •291S •2937 •2959 •2981 ■3003 •3025 •3047 •3070 •3092 ■3114 •3137 •3160 •3182 •3205 39 ■293s ■2957 •2979 •3002 •3024 •3047 •3069 •3092 •3115 •3138 •3161 ■3184 •3207 •3230 "3253 •3276 40 ■2997 •3020 •3043 •3066 •3089 •3112 •3135 •3158 •3182 ■3205 •3228 •3252 ■3275 •3299 •3322 •3346 41° •3059 ■3083 •3106 •3129 •3153 •3176 •3200 ■3223 •3247 •3271 •3295 ■3319 •3343 ■3367 3391 '3415 42 •3120 •3180 •3144 •3168 ■3192 •3216 •3240 •3264 •3288 •3312 •3336 •3361 •3385 •3409 ■3434 •3459 ■3483 43 ■3204. •3229 •3253 •3277 •3302 ■3326 •3351 •3376 ■3400 •3425 ■3450 ■3475 •3500 •3525 ■3550 44 •3239 •3264 •3289 •3313 •3338 •3363 •3388 •3413 •3438 ■3463 ■3489 ■3514 ■3539 •3565 •3591 •3616 45 ■3297 •3322 ■3348 ■3373 •3398 •3423 •3449 •3474 •3500 •3526 ■3551 •3577 •3603 •3629 ■3655 •3681 46° •33S4 •3380 •3405 ■3431 •3457 •3483 •3508 •3534 •3560 •3586 •3613 •3639 •3665 •3692 •3718 •3745 % •3410 •3436 •3462 ■3488 •351S •3541 •3567 •3593 ■3620 •3646 •3673 •3700 •3726 •3753 •3780 •3807 •3465 •3492 •3518 •3S4S •3571 •3598 •3625 •3651 •3678 ■3705 •3732 ■3759 ■3787 •3814 •J' •3841 •3869 49 ■3519 •3546 •3573 •3600 •3627 •3654 •3681 •3708 •3735 •3763 •3790 •3818 •3845 •3873 •3901 ■3929 50 •3572 •3599 ■3627 •3654 • ^3681 •3709 ■3736 •3764 •3792 •3819 ■3847 ■3875 •3903 •3931 •3959 •3988 51° ■3624 •3651 •3679 ■3707 •373S •3762 •3790 •3818 •3847 •3875 •3903 ■3931 •3960 •3988 •4017 •4046 52 ■367s •3702 •3731 •3759 ■3787 •3815 •3843 •3872 ■3900 ■3929 •3918 •3986 •4015 •4044 •407^ •4102 S3 •3724 •3752 •3781 •3809 '^lil •3866 •3895 •3924 ■3953 •3982 . ^401 1 •4040 •4069 •4099 •4128 •4157 54 ■3773 •3820 •3801 ■3^30 •3859 •3888 •3917 •3946 •3975 ■4004 •4034 •4063 ■4093 •4122 •4152 •4182 •42 I I 55 •3849 •3878 •3907 •3936 •3966 ■3995 •4025 •4054 •4084 •41 14 •4144 •4174 •4204 •4234 ■4264 56° ■3866 •389s •3925 •3954 •3984 ■4014 •4043 •4073 •4103 ■4133 •4164 •4194 ■4224 ■4255 •4285 ■4316 ■391 1 •39SS •3941 •3985 •3970 ■4015 •4000 •4045 •4030 •4075 •4060 •4106 •4090 •4136 •4121 •4167 •4151 •4197 4181 •4228 •4212 •4259 ■4243 •4290 •4273 •4321 •4304 ■4352 •4335 ■4383 •4366 ■4415 ■3997 ■4038 •4027 •4069 •4058 ■4088 ■41 19 •4150 •4181 •4212 •4243 •4274 •4305 •4336 •4367 ■4399 •4430 •4462 •4100 ■4131 ■4162 •4193 •4224 ■4255 •4286 •4318 •4349 •4381 •4413 •4444 •4476 •4508 61° 62 65 •4078 •4109 ■4141 •4172 •4203 •4234 ■4266 •4297 •4329 •4361 •4393 •4424 •4456 •4489 ■4521 •4553 •4117 ■4149 •4186 ■4180 ■42 1 1 •4243 •4275 ■4306 •4338 •4370 ■4402 •4434 •4467 ■4499 •4531 •4564 •4596 ■41 ss ■4218 ■4250 •4282 •4S14 •4346 •4378 •4410 •4442 ■4475 •4507 •4540 •4573 •4605 •4638 •4I9I •4226 •4223 •4258 . •425s •4287 •4319 '"^m •4384 •4416 ■4449 •4481 ■45 H •4547 •4580 •4613 •4646 •4679 •4291 •4323 •4355 •4388 •4420 ■4453 •4486 ■4519 •4552 •4585 •4618 •4651 •4684 •4718 25 10 20 30 40 50 26 10 20 30 40 50 27 id 20 3d When the Latitude is North the sign is + . WheQ the Latitude is South the sign is — . ALT-AZIMUTH TABLES. 94 Under Altitude and abreast of Declination, take out the tabular quantity and mark it + or — , accordingr as Declination is S. or N. Add Algebraically E and F. Dec- lina- tion. TRUE ALTITUDE. o" I 2 3 4 5 6° I 9 10 n' 12 13 14 IS 16° 17 i8 19 20 21° 22 23 24 2S 26° 27 28 29 30 31° 32 33 34 35 36° H 38 39 40 41° 42 43 44 45 46° 47 48 49 SO SI" 52 S3 M 55 52 58 60 61° 62 65 25 •0000 •0193 •0385 •0577 ■0770 •0962 •1IS3 •1345 ■1536 •1726 •1916 ■2105 •2294 •2482 •2669 ■2856 •3041 ■3226 •3410 •3592 •3774 ■39.54 •4133 •43" •4488 •4663 •4837 ■5009 •5180 •5349 •5517 •S683 •5847 •6009 •6170 ■6329 ■6485 •6640 ■6793 •6944 •7092 •7239 •7383 •7525 •766s •7802 •7937 ■8070 •8200 •8327 •8452 •857s •869s •8812 ■8927 •9038 •9147 •9254 •93S7 ■9458 ■9556 ■9650 •9742 •9831 •9917 i-oooo 10 20 25 •CXX)0 •0193 •0386 •0578 •0771 ■0963 •115s •1347 •1538 •1728 •I9I9 •2108 •2297 ■2485 •2673 ■2860 ■304s •3230 ■3414 •3S97 •3779 •3960 •4139 •4317 •4494 •4669 •4843 •5016 •5.87 ■53S7 •5524 •5691 •58SS •6018 •6178 ■6337 ■6494 •6649 •6802 •6953 ■7102 •7249 •7393 •7S3S •7675 •7813 •7948 •8081 •821 1 •8339 •8464 8587 •8707 ■8824 •8939 •90S' •9160 •9266 •9370 ■9471 •9569 '9664 ■9756 •984s ■9931 I -0014 30 40 50 10 ■CXXDO •0193 ■0386 •0579 •0772 •0964 •II57 •1348 ■1540 •1731 ■I92I •2300 •2489 ■2677 •2864 •3050 •323s •3419 •3602 •3784 •396s •4145 •4323 ■4500 •4676 •4850 •5023 •5194 •5364 ■5532 •5698 •5863 •6026 •6187 ■6346 ■6503 •6658 •6812 •6963 •7112 •7259 •7403 •7546 ■7686 ■7823 •7959 •8092 •8222 •8350 •8476 •8598 •8719 •8836 •8951 ■9063 •9172 •9279 •9383 •9484 •9582 •9677 •9769 •9858 •9944 1-0027 20 •OI93 ■0387 •0580 •0773 •0966 •1158 •135° •1542 •1733 •1924 •2114 •2304 •2492 •2680 •2868 •3054 •3239 •3424 ■3607 ■3789 •3970 •4150 ■4329 •4506 ■4682 •4857 •5030 •5201 •5371 •5540 ■5706 ■5871 ■6034 •6195 •6355 •6512 ■6668 •6821 •6972 •7122 ■7269 •7413 •7556 •7696 •7834 •7970 •8103 ■8234 •8362 •8487 •8610 •8731 ■8963 •9076 •918s •9292 •9396 ■9497 ■959s •9690 •9782 ■9872 •9958 I •0041 26 30 •0000 ■0194 •0387 ■0581 •0774 ■0967 •I 160 •1352 ■1544 •1736 ■1927 •2117 •2307 ■2496 ■2684 ■2872 ■3058 •3244 •3428 •3612 •379s •3976 •4156 •4335 •4513 •4689 •4864 •5037 •5209 •5379 •5547 •5714 ■5879 •6043 ■6204 ■6364 •6521 •6677 •6831 •6982 ■7132 •7279 ■7424 ■7567 •7707 ■7845 •7981 •81 14 •824s •8373 •8499 ■8622 '8743 •8861 •8976 ■9198 •9305 •9409 •9510 •9608 •9704 •9796 •9885 •9972 i-ooss •0000 •0194 •0388 •0581 ■0775 •0968 •1161 •1354 •1546 •1738 •1929 •2120 •2310 ■2499 •2688 •2876 •3062 •3248 •3433 •3617 •3800 ■3982 •4162 ■4341 •4519 •469s •4870 •5044 •5216 •5386 ■ssss •5722 40 •6051 •6213 ■6373 ■6530 •6686 •6840 •6992 •7142 •7289 •7434 •7577 •7718 •7856 •7992 •8126 •8257 •8385 ■8511 •8634 •875s •8873 •9101 •92 1 1 ■9318 •9422 ■9523 •9622 •9717 ■9810 •9899 ■9986 1-0069 10 50 •0194 •0388 ■0582 ■0776 •0970 •I 163 •1356 •1548 •1740 •1932 •2123 •2313 •2503 ■2692 •2880 •3067 •3253 •3438 •3622 ■3805 •39S7 ■4168 ■4347 ■4525 •4702 •4877 •5051 ■5223 •5394 •5563 •5730 •5896 •6060 •6222 •6382 •6540 •6696 •6850 •7002 •7152 •7299 •7445 •7588 •7729 •7867 •8003 •8137 •8268 •8397 •8523 •8647 •8767 •8886 •9001 •9 1 14 •9224 ■9331 ■9435 •9537 ■963s •9731 ■9824 •9913 i-oooo I '0084 20 •0000 •0194 •0389 •0583 ■0777 •0971 ■1165 ■1358 •1551 •1743 •1935 •2126 •2317 •2506 •2695 •2884 •3071 •3258 •3443 •3627 •381 1 •3993 •4174 ■4353 •4532 •4709 •4884 •5058 ■5231 •5402 •5571 •5738 •5904 ■6068 ■6230 •6391 ■6549 •6705 •6860 ■7012 •7162 •7310 ■7455 •7599 •7740 •7878 •801 s ■8149 •8280 •8409 ■8535 ■8659 ■8780 26 •9014 •9127 •9237 •9344 •9449 •955° ■9649 •9745 ■9838 •9927 I -0014 1-0098 30 40 •0000 -OI9S ■0389 •0584 •0778 ■0972 •1166 ■1360 ■1553 •1745 •1938 •2129 •2320 ■2510 ■2699 ■2888 -3076 •3262 •3448 •3633 •3816 •3999 •4180 •4360 ■4538 •4716 •4891 •5066 •5238 ■5409 ■5579 •5747 ■5913 ■6077 •6239 -6400 •6558 •67 1 5 •6869 •7022 •7172 -7320 •7466 •7610 •77S'i •7890 •8026 •8160 -8292 ■8421 •8547 -8671 •8793 •89 II ■9027 -9140 •9250 •9358 -9462 •9564 ■9663 ■9759 •9852 •9942 I -0029 I -01 12 10 50 20 0000 ■0195 ■0390 ■0585 ■0779 ■0974 •I 168 •1362 •I5SS •1748 -1940 ■2132 •2323 ■2514 •2703 •2892 •3080 •3267 ■3453 •3638 -3822 •4004 •4186 •4366 ■4545 -4722 -4898 •5073 ■5246 ■5417 ■5587 ■5755 •5921 •6086 ■6248 •6409 6568 ■6725 •6879 •7032 ■7183 ■7331 ■7477 •7621 •7762 ■7901 ■8038 ■8172 ■8304 •8433 ■8560 -8684 ■880s -8924 •9040 ■9153 •9264 ■937 « ■9476 ■9578 -9677 •9773 •9866 •9956 1-0043 I '0127 •0000 •019s •0391 ■0586 •0781 ■0975 •1170 •1364 ■1557 •1751 •1943 ■2135 ■2327 ■2517 •2707 •2896 •3084 •3272 •3458 •3643 •3S27 •4010 •4192 •4372 ■4551 •4729 •4905 ■5080 ■5254 •5425 •5595 ■5763 ■5930 ■6095 ■6258 -6418 •6577 ■6734 •7042 •7193 •7341 •7488 •7632 •7773 •7913 •8050 ■8184 •8316 •844s ■8572 •8696 •8818 •8937 •9053 •9167 -9277 •9385 -9490 9592 ■9691 •9787 •9880 •9971 I 0058 I "0142 30 0000 •0196 -0391 ■0587 ■0782 -0977 •1171 •1366 •1560 •1753 •1946 ■2138 ■2330 ■2521 •271 1 •2901 ■3089 ■3277 ■3463 •3649 •3833 •4016 •4198 ■4379 ■4558 ■4736 •4913 •5088 •5261 •5433 •5603 •5772 •5939 ■6104 •6267 •6428 ■6587 •6744 ■6900 •7053 •7204 •7352 •7499 ■7643 •778S •7924 •8061 •8196 •8328 •8458 •858s •8709 •8831 •8950 •9066 •9180 •9291 •9399 •9504 •9606 •9705 •9802 •9895 •9985 10073 I ■0157 27 40 •0000 •0196 -0392 ■0587 •0783 ■0978 ■1173 ■1368 •1562 •1756 ■1949 •2141 ■2333 ■2525 ■2715 •2905 •3094 •3281 -3468 ■3654 •3839 •4022 •4204 •4385 ■4565 •4743 •4920 •5095 •5269 ■5441 •5612 ■5780 •5947 ■61 13 ■6276 •6437 •6597 ■6754 •6910 ■7063 •7214 ■7363 •7510 •7654 •7796 •7936 •8073 •8208 •8341 •8470 •8598 •8722 •8844 ■8963 •9080 •9194 •9305 •9413 ■9518 •9620 ■9720 •9816 •9910 I'OOOO I 0087 1-0172 10 -0000 •0196 •0392 -0588 •0784 •0980 ■1175 •1370 •1564 ■1758 •1952 ■214s ■2337 ■2528 ■2719 •2909 •3098 ■3286 ■3473 •3659 •3844 -4028 •42 1 1 •4392 •4572 •4750 •4927 •5103 •5277 •5449 •5620 •5789 •5956 -6122 ■6285 ■6447 •6607 •6764 •6920 ■7074 ■722s •7374 ■7521 ■7666 •7808 ■7948 •8085 ■8220 ■8353 •8483 ■8610 ■8735 •88S7 •8977 •9093 •9207 •9318 -9427 •9532 •9635 •9734 •9831 •9924 I -0015 I^0I02 I '0187 20 50 27 •0000 •0196 •0393 •0589 •0785 ■0981 ■1177 ■1372 •1567 •1761 •1955 -2148 -2340 ■2532 -2723 •2913 •3103 -3291 ■3479 ■366S •3850 ■4034 •4217 •4398 •4579 •4757 •4935 •5 1X0 •5285 ■5457 ■5628 ■5798 ■5965 •6131 •629s •6457 •6617 •6775 ■6930 ■7084 ■7236 •7385 •7532 ■7677 ■7820 •7960 •8097 •8233 •8365 •8496 ■8623 ■8748 •8870 •8990 ■9107 •9221 •9332 ■9441 •9546 •9649 •9749 •9845 •9939 I ^0030 I "01 18 I '0202 10 30 •0000 0197 •0393 •0590 •0786 ■0983 -1178 ■1374 •1569 ■1764 •1958 •2151 ■2344 ■2536 ■2727 •2918 •3107 •3296 •3484 •3670 •3856 ■4040 •4223 •4405 •4585 •4765 •4942 •5118 ■5293 ■5466 ■5637 •5806 •5974 •6140 ■6304 •6466 -6627 ■6785 •6941 •7095 •7247 ■7396 •7544 •7689 •7831 •7972 •81 10 •8245 •8378 ■8508 •8636 •8761 20 •9004 •9121 ■9235 •9346 •9455 ■9561 •9664 •9763 •9860 •9954 1-0045 1-0133 I -0218 30 When the Declination is North the sign is -. When the Declination is South the sign is + • 95 ALT-AZIMUTH TABLES. Under Altitude in head-line, and abreast of Latitude in margin, take out the tabular quantity and mark it + or - , aeeording as the Latitude is N. or S. TRUE ALTIT UD E. Lat, 27 30 40 50 28 10 20 30 40' 50' 29 10 20 30 40 50' 3tf 0° I 2 •nooo ■0091 •0182 ■nnoo ■0091 •0183 ■0274 ■0366 ■0457 •0000 •0092 0184 •0276 •0368 •0460 •0000 •0093 •0186 •0278 ■0371 •0463 ■0000 ■0093 ■0187 ■0280 •0000 0094 •0188 ■0282 •0000 •0095 •0189 ■0284 •0000 ■0095 •0191 ■0286 •0000 •0096 •0192 ■0288 •0000 •0097 ■0193 •0290 •0000 •0097 •0195 ■0292 •0000 •0098 •0196 •0294 •0000 •0099 •0197 •0296 ■0000 •0099 ■0199 •0298 •0000 ■0100 ■0200 •0300 •0000 •0101 •0201 ■0302 3 4 S •0272 •0363 ■04S4 •0374 •0467 •0376 ■0470 •0379 •0473 ■0381 ■0477 •0384 ■0480 •0387 ■0483 •0389 •0486 ■0392 •0490 ■0395 •0493 •0397 ■0496 ■0400 •0500 •0403 •0503 6° I 9 10 •0544 •0634 •0724 •0814 ■0904 ■0548 •0639 •0730 •0820 ■0910 ■0552 •0643 •0735 •0826 ■0917 0648 •0740 ■0S32 ■0923 •0560 •0653 •0745 ■0S38 ■0930 •0564 •0657 ■0750 •0843 •0936 •0568 •0662 •0756 •0849 •0943 ■0571 •0666 •0761 •0855 •0949 •0575 •0671 •0766 •0861 •0956 ■0579 ■0676 •0771 •0867 •0963 ■0680 •0777 •0873 •0969 •0587 •0685 ■0782 •0879 •0976 •0591 •0690 •0787 •0885 ■0982 •0595 •0694 •0793 ■0891 ■ ■0989 •0599 •0798 •0897 ■0996 •0603 •0704 ■0804 •0903 •1003 11° 12 13 14 IS •0993 •1082 ■1171 •I2S9 ■1347 •1000 •1090 ■1179 •1268 ■1357 •1007 •1098 •1188 •1277 •1367 ■1015 ■I 105 •1196 ■1286 •1376 •1022 •1113 •1204 •1295 •1386 •1029 •1121 •1213 •1304 •1396 •1036 •I 129 •1221 •1314 •1405 •1043 •I 1 37 •1230 •1323 •1415 •1050 •I 145 •1238 •1332 •1425 ■1058 •1152 •1247 •1341 •1435 ■1065 •I 160 ■1255 •1350 •1445 •1072 •1168 ■1264 •1359 •1454 •1080 •I 176 •1273 ■1369 •1464 •1087 •1184 •1281 •1378 ■1474 •1094 •1192 •1290 •1387 •1484 •I 102 •1200 •1299 •1397 •1494 i6° 19 20 •1435 •1522 ■1609 ■1695 •1780 •1445 •1533 1620 •1707 •1793 •1455 ■1544 •1632 •1719 •1806 •1466 •1555 •1643 •1731 ■1819 •1476 •1565 •1655 •1743 •1831 •i486 •1576 ■1666 •1755 •1844 •1497 •1587 , -1678 •1768 •1857 •1507 •1598 •1689 •1780 ■1870 •1517 •1610 ■I 701 •1792 •1883 ■1528 •1621 •1713 •1805 •1896 •1538 ■1632 •1725 •1817 •1909 •1549 •1643 •1736 •1829 •1922 :i559 ■1654 •1748 •1842 •1935 •1570 •1665 ■1760 •1854 •1948 -1581 •1677 •1772 •1867 •1961 •1591 •1688 •1784 •1880 •1975 21° ■1866 •1879 •1892 ■1905 •1919 •1932 •1946 •1959 •1973 ■1986 •2000 •2014 •2028 •2041 •2055 •2148 •2241 •2069 •2163 •2256 •2348 22 23 24 25 •1950 •2034 •1964 •2048 •1978 •2063 •1992 •2078 •2006 •2092 •2020 •2107 ■2034 •2I2I •2048 ■2136 •2062 ■2151 ■2076 ■2166 •2091 •2181 ■2105 ■2196 •21 19 •221 1 •2134 •2226 ■2117 •2I'!2 ■2148 ■2163 ■2178 •2193 ■2208 •2224 •2239 •2255 •2270 ■2286 •2301 ■2317 •2333 ■2200 •2216 ■2231 ■2247 ■2263 •2279 •2295 •231 1 •2327 •2343 •2359 ■2375 ■2391 •2407 ■2424 •2440 26° ■2282 •2298 ■2315 •2331 •2347 •2364 •2380 •2397 •2413 •2430 •2447 •2463 •2480 VM, •2514 •2531 ■2363 •2380 •2397 ■2414 ■2431 •2448 •2465 •2482 •2499 •2517 •2534 ■^I^J •2569 ""If • •2604 •2621 •2444 •2461 •2479 •2496 •2514 •2531 •2549 •2567 •2585 •2602 ■2620 ■2638 •2656 •2674 •2692 ■2710 20 2524 -2542 •2560 •2578 •2596 ■2614 •2632 •2651 •2669 •2687 •2706 •2724 •2743 ■2762 ■2780 •2799 30 •2603 ■2621 •2640 •2659 •2677 ■2696 •2715 •2734 ■2753 •2772 ■2791 •2810 ■2829 •2848 ■2867 ■2887 31° ■2681 ■2700 ■2719 •2739 •2758 •2777 •2796 •2816 •2835 •2855 •2875 •2894 •2914 •2934 ■2954 •2974 32 ■2759 •2778 ■2798 •2818 •2837 ■2857 ■2877 •2897 •2917 •2937 •2958 •2978 •2998 •3019 •3039 •3059 33 •2835 •2855 ■2876 •2896 •2916 •2937 •2957 ■2978 ■2998 •3019 •3040 ■3061 •3081 ■3102 •3>23 •3144 34 ■291 1 •2932 ■2952 •2973 •2994 •3015 •3036 •3057 •3078 •3100 •3121. •3142 •3164 •3185 •3207 •3229 3S •2986 ■3007 •3028 •3050 •3071 •3093 ■3114 •3136 •3158 •3179 •3201 •3223 •3245 •3267 •3289 •3312 36° •3060 ■3082 •3103 •3125 •3147 ■3169 ■319I •3214 •3236 •3258 •3281 •3303 •3326 •3348 •3371 •3394 ■3133 •3ISS •3177 •3200 •3222 •3245 •3268 •3290 •3313 •3336 •3359 ■3382 3405 •3428 •3451 •3475 28 ■3205 ■3251 •3274 •3297 •3320 •3343 •3366 •3389 ■34i3 •3436 •3460 •3483 • •3507 •3531 •3555 39 ■3276 •3299 •3323 •3346 •3370 •3393 ■3417 •3441 •3464 •3488 ■35i? •3536 •3561 ■3|§S •3609 •3633 40 •3346 ■3370 ■3394 •3418 •3442 •3466 •3490 •3514 •3539 •3563 •3588 '3512 •3637 •3661 •3686 •371 1 4*° ■3415 •3440 •3464 •3488 •3513 •3537 •3562 •3587 •3612 •3637 •3662 •3687 •3712 •3737 •3762 ■3^f 42 ■3483 •3508 ■3533 •3558 •3583 ■3608 ■3633 ■3658 •3684 •3709 •3735 •3760 •3786 •3811 •3837 •3863 43 "355° ■3576 ' '3601 •3626 •3652 •3677 •3703 ■3729 ■3754 •3780 •3806 •3832 •3859 •3885 •391 1 •3938 44 •3616 •3642 •3668 •3694 •3720 •3746 •3772 •3798 •3824 •3851 ■3877 •3904 •3930 ■3957 •3984 •4011 45 •3681 ■3707 ■3733 •3760 •3786 •3813 •3839 ■3866 ■3893 •3920 •3946 ■3974 ■4001 •4028 •4055 •4082 46° •3745 •3771 •3798 •3825 •3852 •3879 •3906 •3933 •3960 •3987 •4015 •4042 •4070 •4097 •4125 ■4153 47 •3807 •3834 •3861 •3889 •3916 •3943 •3971 •3999 •4026 •4054 •408a •4 1 10 •4138 •4166 •4194 •4222 48 •3869 •3896 ■3924 •3951 ■3979 •4007 •4035 •4063 •4091 ■4119 •4148 •4176 •4205 ■4233 •4262 ■4291 49 ■3929 •3957 •3985 •4013 ■4041 •4069 ■4098 •4126 •4155 •4183 •4212 ■4241 ■4270 •4299 •4328 •4357 50 ■3988 •4016 •4045 •4073 •4102 •4130 ■4159 •4188 ■4217 •4246 •427s •4305 •4334 •4364 ■4393 •4423 51° ■4046 •4074 ■4103 •4132 •4161 •4190 •4220 •4249 ■4278 •4308 •4337 •4367 •4397 •4427 •4457 •4487 52 •4102 •4I3I •4161 ■4190 •4219 •4249 •4279 •4308 •4338 •4368 ■4398 •4428 •4458 •4489 •4519 •4550 S3 •4157 ■4187 -4217 ■4246 •4276 •4306 ■4336 •4366 •4397 •4427 •4457 •4488 ■4518 •4549 •4580 •461 1 54 •42 1 1 •4241 •4271 •4302 ■4332 ■4362 •4393 •4423 •4454 ■4484 •4515 •4546 ■4577 •4608 •4640 •4671 55 •4264 •1295 •4325 •4356 ■4386 •4417 •4448 •4479 •4510 •4541 •4572 •4603 ■4635 •4666 •4698 •4729 56° •4316 •4346 •4377 •4408 •4439 •4470 •4501 •4533 •4564 •4595 •4627 •4659 •4690 •4722 •4754 •4785 •4366 ■4397 •4428 •4459 ■4491 •4522 •4554 ■4585 •4617 •4649 •4681 •4713 •4745 •4777 •4810 •4842 58 ■441S •4446 •4478 ■4509 •4541 •4573 •4605 •4637 •4669 •4701 •4733 ■4766 ■4798 •4831 •4863 •4895 |9 •4462 •4494 •4526 •4558 ■4590 •4622 ■4654 •4686 •4719 •4751 ■4784 •4817 •4850 •4883 •4916 •4949 fio •4508 •4540 •4572 •4605 •4637 •4670 •4702 •4735 •4768 ■4800 •4833 •4867 •4900 •4933 ■4956 •5000 61° •4S53 •4585 •4618 •4650 •4683 •4716 •4749 •4782 •481S •4848 ■4881 •4915 ■4948 ■4982 •5016 •5050 62 •4596 •4629 •4662 •4695 •4728 •4761 '"^V^i •4827 •4861 •4894 •4928 •4962 •4995 •5029 •5064 •5098 63 •4638 '4671 •4704 •4738 ■4771 •4804 •4838 •4871 •4905 •4939 •4973 •5007 ■5041 •5075 ■51 10 ■5144 ^4 •4679 ■4712 •4745 •4779 •4813 •4846 ■4880 ■4914 •4948 •4982 ■5016 •5051 ■5085 •5120 •5154 •5189 65 •4718 ■4751 •4785 ■4819 •4853 •4887 •4921 ■4955 •4989 •5024 •5058 •5093 •5128 •5163 ■5197 •5233 27° 3d 40 50' 28 10' 20 30' 40' oO' 29 10 20' 30' 40 50 30" When the Latitude is North the sign is + . When the Latitude is South the sign is - . ALT-AZIMUTH TABLES. 96 Under Altitude and abreast of Declination, take out the tabular quantity and mark it -f or — . according as Declination is S. or N. Add Algebraically E and F. Dec- lina- tion. TRUE ALTITUDE. 2730 40' 50' 28 10' 20' 30' 40 50' 29 10 20' 30 40 50' 30 0° •0000 0000 -0000 ■0000 0000 ■0000 ■ooco •0000 -0000 ■0000 -0000 -0000 -0000 •0000 •0000 -0000 I •0197 •0197 -0197 •0198 ■0198 -0198 •0199 •0199 -0199 -0200 •0200 -0200 •0201 -0201 -0201 -0202 2 ■0393 ■0394 •0395 ■0395 •0396 •0396 ■0397 -0398 •0398 ■0399 ■0400 -04C0 -0401 •0402 •0402 -0403 3 •0590 •0591 ■0592 •0593 •0594 •0595 -0596 -0596 •0597 •0598 ■0599 •0600 -0601 •0602 -0603 -0604 4 ■0786 •07S8 ■0789 ■0790 0791 •0793 ■0794 •0795 -0796 -0798 •0799 -oSoo •0801 ■0803 -0804 •0805 S •0983 ■0984 -0986 •0987 ■0989 ■0990 -0992 •0993 -0995 -0996 -0998 -1000 •lOOI -1003 -1005 •1006 6° •1178 •I 180 -1182 ■1184 •1186 -1188 -II89 •1191 -1193 -1195 -1 197 -1199 -1 201 -1203 ■1205 •1207 7 ■1374 •1376 -1378 •1380 ■1382 •1385 ■1387 -1389 -1391 •1393 -1396 -1398 -1400 ■1403 -1405 -1407 8 ■1569 ■1571 •IS74 ■1576 •1579 -1581 -1584 -1586 •1589 •1591 ■1594 -1596 •1599 ■1602 -1604 •1607 9 ■1764 ■1766 -1769 -1772 -1774 •1777 •1780 •1783 -1786 -1789 -1791 •1794 -1797 -1800 -1803 •1806 10 ■1958 •I96I -1964 -1967 -1970 ■1973 ■1976 -1979 -1982 •1985 -1989 ■1992 •1995 ■1998 •2002 -2005 IX° •2151 ■2IS4 -2158 ■2161 -2164 -2168 ■2171 •2175 •2178 -2182 -2185 •2189 -2192 -2196 -2200 •2203 12 ■2344 •2348 ■2351 •2355 •2358 -2362 ■2366 -2370 •2373 •2377 •2381 •2385 -2389 •2393 -2397 -2401 13 •2536 ■2540 -2S44 ■2548 ■2552 •2556 -2560 -2564 •2568 -2572 •2576 -2580 -2585 -2589 •2593 ■2598 14 •2727 •2732 -2736 ■2740 ■2744 ■2748 •2753 •2757 -2762 -2766 •2771 -2775 -2780 -2784 -2789 •2793 IS ■2918 ■2922 -2927 -2931 ■2936 •2940 -2945 -2950 ■2954 -2959 •2964 -2969 -2974 •2979 •2984 ■2989 i6° •3107 •3II2 -3117 -3122 -3127 •3132 •3136 •3141 •3146 •3152 ■3157 •3162 -3167 -3172 •3177 •3183 17 •3296 •3301 -3306 •331 1 •3316 ■3322 ■3327 •3332 •3337 •3343 •3348 •3354 •3359 •3365 •3370 •3376 i8 •3484 •3489 •3494 •3500 •3505 ■351 1 •3516 •3522 •3527 •3533 •3539 •3545 •3550 •3556 •3562 -3568 19 ■3670 •3675 -3682 •3687 •3693 •3699 •3705 ■3710 -3716 -3722 -3728 •3735 •3741 •3747 •3753 •3759 20 •3856 •3862 -3868 •3874 •3880 •3886 -3892 •3898 -3904 -391 1 ■3917 •3923 •3930 •3936 •3943 •3949 21° •4040 •4046 •4053 •4059 •4065 •4071 -4078 •4084 -4091 -4097 •4104 ■4111 •4117 •4124 •4131 •4138 22 ■4223 •4230 -4236 •4243 •4249 •4256 -4263 •4269 ■4276 •4283 -4290 -4297 -4304 •43" •4318 •4326 23 •4405 •4412 •4418 ■4425 ■4432 •4439 -4446 •4453 -4460 -4467 •4475 •4482 -4489 •4497 -4504 •4512 24 •4585 ■4592 •4599 -4607 -4614 •4621 -4628 •4636 ■4643 -4650 -4658 •4666 ■4673 -4681 -4689 •4697 25 •476s •4772 •4779 -4786 •4794 ■4801 -4809 •4817 •4824 •4832 -4840 -4848 ■4856 -4864 -4872 -4880 26° ■4942 ■4950 •49S7 •4965 ■4973 •4980 •4988 •4996 -5004 ■5012 ■5020 •5028 •5037 •5045 •5053 •5062 •5118 •5126 •5134 •5142 -5150 •5158 -5166 •5174 -5182 •5191 -5199 -5208 •5216 •5225 •5233 •5242 28 ■5293 •5301 •5309 '5317 ■5325 •5334 •5342 •5351 •5359 •5368 •5376 •538s •5394 -5403 •5412 •5421 29 ■5466 "5474 •5482 •5491 •5499 •5508 •5517 ;S525 •5534 •5543 •5552 •5561 -5570 •5579 •5589 •5598 30 •5637 •5645 ■5654 ■5663 •5672 •5681 -5689 •5708 -5717 ■5726 ■5735 •5745 •5754 •5764 •5774 31° •5806 •5815 -5824 •5833 •5842 •5851 •5861 •5870 •5879 ■5889 ■|^f ■5908 •5918 •5927 •5937 •5947 J" 32 33 34 35 ■5974 ■5983 ■5992 ■6002 ■601 1 -6020 -6030 -6039 -6049 -6059 ■6069 -6079 -6089 -6099 •6109 •6119 •6140 •6150 ■6314 •6159 ■6168 6178 •6188 •6197 -6207 -6217 -6227 -6237 -6247 -6258 -6268 •6278 •6289 •6304 -6323 ■6333 ■6343 •6353 •6363 •6373 •6383 ■6394 •6404 -6414 •6425 1^^? •6446 ti^l •6466 •6476 -6486 -6496 -6506 •6516. -6527 •6537 •6547 •6558 -6569 -6579 •6590 •6601 •6612 •6623 36° 39 40 •6627 •6637 ■6795 -6647 •6657 •6667 •6678 •6688 -6699 -6710 -6720 -6731 ■6742 -6753 ■6765 -6776 •6787 ■6785 -680s -6816 -6827 ■6837 ■6848 -6859 -6870 •6881 -6892 ■6903 •6915 •6926 •7085 -6938 •6949 •6941 •6951 ■6962 •6973 •6984 •6995 -7006 •7017 •7028 •7039 ■7051 •7062 -7074 ■7097 -7109 -7267 •7422 ■709s ■7247 ■7106 •7258 •7117 -7269 ■7127 -7280 •7139 -7291 •7150 •7303 -7161 •7314 -7172 •7326 ■7184 •7338 -7195 •7349 ■7207 -7361 ■7219 ■7373 -7231 ■7385 •7243 •7398 •7255 -7410 41° 42 43 44 45 •7396 7S44 •7689 •7831 ■7972 •7408 75SS ■7700 •7843 •7984 ■7419 -7567 -7712 •78SS -7996 •7430 •7578 •7724 •7867 ■8008 -7442 ■7590 •8Q2I •7454 •7602 •7748 -7892 ■8033 •7465 -7614 -7760 -7904 -8046 •7477 •7626 •7773 -7917 -8059 ■7489 •7638 •7785 •7930 -8072 -7501 ■7651 •7798 •7942 -8085 •7663 -7810 •7955 -8098 •7525 -7675 •7823 -7968 -81 1 1 •7538 -7688 -7836 -7981 -8124 •7550 -7701 -7849 ■7995 -8138 •7563 •7714 -7862 -8008 •8151 •7576 - 7726 -7875 -8021 -8165 46° % 49 50 •8 no ■824s •8378 •8508 ■8636 •8122 •8258 •8391 •8521 •8649 ■8134 -8270 -8404 •8S34 ■8663 •8147 ■8283 •8417 ■8548 •8676 -8160 ■8296 •8430 -8561 •8689 -8172 •8309 •8443 •8574 •8703 -8185 -8322 -8456 -8588 -8717 -8198 •8335 •8470 •8601 •8731 -82 II -8349 -8483 -8615 •8745 •8225 -8362 •8497 -8629 •8759 •8238 •8376 •851 1 •8643 ■8773 ■8251 •8389 •8524 8b57 ■8787 -8265 -8403 -8802 •8279 -8417 •8553 -8686 -8816 -8292 •8431 •8567 -8700 •8831 •8306 •8445 -8581 -8715 -8846 51° 52 53 54 55 •8761 ■8884 •9004 •9121 ■923s •877s ■8897 •9017 •913s •9249 -8788 -8911 •9031 -9149 •9263 ■8802 -8925 •904s •9163 ■9277 •88IS •8939 ■9059 ■9177 ■9292 -8829 ■8953 ■9073 -9191 -9306 -8843 -8967 -9088 -9206 •9321 •8857 -8981 -9102 '9220 •9336 -8871 •8995 -91 1 7 •9235 •9351 -8886 -9010 -9131 •9366 -8900 ■9024 -9146 •9265 ■9381 -8914 -9039 -9161 •9280 •9396 -8929 -9054 ■9176 ■9295 ■9412 -8944 •9069 -9191 •93" -9427 •8959 -9084 -9206 ■9326 •9443 -8974 •9099 •9222 •9342 •9459 56° 57 58 i2 •9346 •94SS •9664 •9763 •9361 •9469 ■9S7S •9678 •9777 •9375 •9484 •9590 •9693 •9793 •9389 •9499 -960s ■9708 ■9808 •9404 •9513 •9620 •9723 •9824 -9419 •9528 ■963s •9738 •9839 •9434 •9543 -9650 •9754 •9854 •9449 •9558 •9665 •9769 •9870 ■9464 •9785 •9886 •9479 •9696 -9800 -9902 •9494 ■9605 -9712 •9816 ■9918 •9510 •9620 -9728 -9832 ■9934 •9525 -9636 ■9744 -9848 •9950 •9541 •9652 •9760 •9865 -9967 ■9|S7 -9668 •9776 -9881 •9983 •9573 -9684 ■9792 -9898 I -0000 61° 62 65 ■9860 •9954 1-0045 I -0133 I '0218 •987s ■9969 I -0060 I ■0148, 1-0233 -9890 0-9985 I -0076 I -0164 I -0249 -9906 I -0000 I -0091 I -0179 I -0265 ■992 1 1-0016 I -0107 I 0195 I -0281 •9937 1-0031 I -0123 I -021 1 1-0297 -9952 1-0047 I -0139 I -0227 1-0313 •9968 1-0063 I -015s I 0244 I -0329 •9984 I -0079 1-0171 I -0260 10346 I -0000 I -0095 I -0187 I -0276 I -0362 I -0016 I -0112 1 0204 I -0293 1-0379 1-0033 I -0128 I '0220 I -0310 1-0396 I -0049 I -0145 1-0237 10327 1-0413 I -0066 1-0161 I 0254 I -0344 I -0430 I 0082 I -0178 I -027 1 1-0361 I -0448 I 0099 I 0195 I -0288 10378 1 -0465 2730 40',. 50: 28 id 20' 30 40 50' 29 10 20' 30' 40 50 30 When the Declination is North the sign is - When the Declination is South the sign is + . 97 ALT-AZIMUTH TABLES. Under Altitude in head-line, and abreast of Latitude In Mar^^n, talie out the tabular quantity and mark it + or accordingr as the Latitude is N. or S. Lat. TRUE ALTITUDE. 30 10 20' 30 40 50 31 10 20 3d 4d 5d 32 id 2d 3d 0° ■0000 •0000 •0000 0000 •0000 •0000 •0000 ■0000 ■0000 ■0000 •0000 •0000 •oooo ■0000 ooco ■0000 I ■oioi ■OIOI ■0102 •0103 0103 •0104 •0105 0106 ■0106 •0107 ■0108 ■0108 •0109 •Olio ■Olio ■01 1 1 2 ■0201 ■0203 ■0204 ■0206 ■0207 ■0208 ■0210 ■02 1 1 ■0212 ■0214 •0215 ■0217 •0218 •0219 0221 ■0222 3 •0302 ■0304 •0306 ■0308 •0310 •0312 •0314 •0317 ■0319 •0321 ■0323 •0325 ■0327 ■0329 •0331 •0333 4 ■0403 ■0405 ■0408 ■04 1 1 •0414 ■0416 ■0419 ■0422 ■0425 ■0427 •0430 ■0433 •0436 ■0439 •0442 ■0444 5 •0503 ■0507 ■0510 •0513 •0517 ■0520 •0524 ■0527 ■0531 •0534 •0538 ■0541 •0545 ■0548 •0552 •0555 6° •0603 ■0608 ■06 1 2 ■0616 •0620 •0624 ■0628 •0632 •0636 •0641 •0645 ^-•0649 •0653 •0657 ■0662 ■0666 7 •0704 ■0708 ■0713 •0718 ■0723 ■0727 ■0732 ■0737 •0742 •0747 •0752 •0757 0762 ■0766 ■0771 •0776 8 •n8n,) •0809 •0814 •0820 •0825 •0831 ■0836 •0842 •0847 ■0853 ■0858 ■0864 ■0870 •0875 •0881 ■0887 9 ■0903 ■0909 ■0915 •0921 ■0928 ■0934 ■0940 ■0946 ■0952 •0959 •0965 •0971 ■0978 •0984 ■0990 ■0997 10 ■1003 ■1009 •IOI6 •1023 1030 ■1037 •1043 ■1050 ■1057 ■1064 •I07I •1078 •108s •1092 •1099 ■I 106 11° •I 102 •I 109 •II16 ■I 124 •1131 •1139 •I 146 •1154 ■I 162 ■1169 •II77 ■1185 •II92 •1200 •1208 ■1216 Ji2 •1200 ■1208 •I217 •1225 ■1233 •1241 •1249 ■1258 •1266 ■1274 •1282 •1291 ■1299 •1308 ■I3I6 •1325 13 •1299 ■1307 •I316 •132s •1334 •1343 ■1352 ■1361 •1370 ■1379 ■1388 •1397 •1406 ■I4I5 •1424 •1433 14 ■1397 •1406 •1416 •1425 ■1435 •1444 •1454 ■1463 •1473 •1482 •1492 •1502 •I5I2 •I52I •1531 •1541 IS •1494 •1504 •I514 •1525 •153s •1545 ■155s ■1565 •1576 ■1586 •1595 ■1607 •I6I7 •I62S ■1638 ■1649 i6° •1591 •1602 •1613 ■1624 •1634 •1645 •1656 ■1667 •1678 ■1689 ■1700 ■1711 •1722 ■1734 •1745 ■1756 '2 •1688 •1699 ■I71I ■1722 •1734 ■1745 •1757 •1768 •1780 ■1792 •1803 •1815 ■1827 •1839 •I85I ■1863 i8 ■1784 •1796 ■1808 ■1820 •1832 •1845 •1857 •1869 •1881 •1894 •1906 •1918 •I93I •1943 •1956 •1969 19 •1880 •1892 ■1905 ■1918 ■1931 •1943 •1956 ■1969 •1982 •1995 •2008 ■2021 •2034 ■2048 •2061 •2074 20 ■1975 ■1988 ■2001 ■201 s •2028 •2042 •2055 •2069 •2082 •2096 ■21 10 •2123 •2137 •2151 •2165 ■2179 21° ■2069 •2083 ■2097 •21 1 1 •2125 ■2139 ■2153 ■2168 ■2182 •2196 •2210 •2225 ■2239 •2254 •2268 ■2283 22 ■2163 ■2177 •2192 •2207 ■2221 ■2236 ■2251 •2266 ■2281 ■2296 •23 1 1 •2326 ■2341 •2356 •2371 •2387 23 •2256 ■2271 ■2286 •2302 •2317 •2332 •2348 •2363 •2379 •2394 •2410 •2426 •2442 ■2457 •2473 ■2489 24 ■2348 ■2364 •2380 •2396 ■2412 ■2428 •2444 •2460 •2476 •2492 •2509 •2525 ■2542 ■2558 •2575 •2591 25 •2440 ■2456 •2473 •2489 •2506 •2523 •2539 •2556 ■2573 •2590 •2607 •2624 •2641 •2658 •2675 ■2692 26° •2531 •2548 '""l^l ■2582 ■2599 ■2617 •2634 •2651 •2669 ■2686 ■2704 ■2722 ■2739 •2757 ■2775 •270-1 27 •2621 ■2639 ■2656 •2674 ■2692 ■2710 •2728 •2746 ■2764 ■2782 •2800 ■2819 ■2837 •2855 •2874 ■2892 28 ■2710 •2729 •2747 •2765 •2784 ■2802 ■2821 2839 ■2858 •2877 •2896 •2915 ■2934 •2953 •2972 ■2991 29 •2799 ■2818 •2837 •2856 ■2875 ■2894 •2913 ■2932 ■2952 •2971 •2990 ■3010 •3029 •3049 ■3069 •3089 30 ■2887 ■2906 •2926 ■2945 ■2965 •2985 •3004 ■3024 ■3044 •3064 •3084 •3104 •3124 •3145 •3165 •3185 31° •2974 ?^v- •3014 •3034 •3054 •3074 ■3095 ■3115 ■3136 •3156 •3177 •3198 •3218 •3239 •3260 •3281 32 •3059 ■3080 •3IOI ■3121 •3142 •3163 ■3184 ■320s ■3226 •3247 •3269 •3290 ■33" •3333 •3354 •3376 33 ■3144 •3166 •3187 ■3208 ■3230 •3251 ■3273 •3294 •3316 •3338 •3359 ■3381 ■3403 ■3425 •3448 JJl " •3470 34 •3229 •3250 •3272 •3294 ■3316 •3338 ■3360 ■3382 ■3404 ■3427 •3449 ■3472 ■3494 '3517 ■3540 ■3562 ■3654 35 ■3312 •3334 •3356 •3379 •3401 ■3424 •3446 ■3469 ■3492 •3515 •3538 •3561 •3584 ■3607 •3631 36° •3394 •3416 ■3498 •3439 •3462 ■3485 •3509 ■3532 •3555 •3578 •3602 ■3626 ■3649 •3673 ■3697 •3721 •3745 •3834 •3922 •4009 •4095 3^ *347S •3521 ■3545 ■3569 •3592 •3616 •3640 ■3664 ■3688 •3712 ■3736 ■3761 •3785 ■3809 "3555 ■3633 •37 1 1 ■3578 •3602 ■3627 •3651 •3675 ■3699 •3724 ■3748 •3773 •3797 •3822 •3847 •3872 •3897 39 40 •3658 •3736 •3682 •3761 ■3707 ■3786 •3732 •3812 ■3756 ■3837 ■3781 ■3862 ■3806 ■3888 ■3831 ■3913 ■3856 •3939 •3882 •3965 ■3907 ■3991 •3932 •4017 •3958 •4043 •3984 •4069 41° •3788 •3863 •3938 ■401 1 •4082 •3889 •3964 ■4038 ■41 10 •3839 •3864 ■3890 ■3916 ■3942 ■3968 •3994 ■4020 ■4047 ■4073 •4100 •4126 ■4153 •4180 42 43 44 45 •3915 •3991 ■4065 •4138 ■3941 ■4017 •4092 ■416s ■3968 •4044 ■41 19 •4193 ■3994 •4071 •4146 •4221 •4021 ■4098 ■4174 ■4249 •4047 ■4125 ■4201 ■4277 •4074 •4152 ■4229 •4305 •4100 ■4179 •4257 •4333 •4127 •4207 •4285 •4361 ■4154 ■4234 •4313 •4390 •4I8I ■4262 •4341 ■4418 •4208 •4289 •4369 •4447 •4236 •4317 '4397 •4476 •4263 •4345 •4425 •4505 46° % 49 SO ■4153 •4222 •4291 •43S7 •4423 •4181 •4251 •4319 •4387 •4453 ■4209 •4279 •4348 ■4416 •4482 •4237 •4308 •4377 ■4446 ■4512 •4265 •4337 ■4407 •4475 ■4542 ■4294 •4366 •4436 •4505 •4573 •4322 ■4394 ■4465 •4535 ■4603 •4351 ■4423 ■4495 •4565 •4633 •4379 •4453 ■4524 •4664 •4408 ■4482 •4554 •4625 ■4694 •4437 •45 1 1 •4584 •465s •4725 ■4466 •4540 ■4614 ■4685 •4756 •4495 •4570 •4644 •4716 •4787 •4524 ■4600 ■4674 •4747 ■4818 •4553 ■4629 •4704 •4777 •4849 •4583 •4659 •4734 ■4808 ■4880 SI" S2 S3 S4 SS •4487 •455° •46 1 1 •4671 •4729 •4517 ■4580 •4642 ■4702 •4761 •4547 ■46 1 1 •4673 •4734 ■4793 ■4578 •4642 •4704 •4765 ■4825 ■4608 •4673 ■4736 •4797 •4857 ■4639 ■4704 •4767 ■4829 •4890 •4670 ■4735 ■4799 •4861 •4922 •4700 ■4766 •4830 •4893 •4954 •4731 •4797 ■4862 •4925 ■4987 •4762 •4829 •4894 •4958 •5020 ■4794 •4861 ■4926 ■4990 •5°53 ■4825 •4892 •4953 •5023 •5086 •4856 •4924 •4990 •5055 ■5119 •4888 •4956 '5023 •5088 •5152 •4919 ■4988 ■5055 •5121 •5185 •4951 •5020 •5088 •5154 •5219 56° 1 •4786 •4842 •4896 •4949 ■5000 ■4819 ■4875 ■4929 ■4982 •5034 •4851 •4907 •4962 •5016 •5067 ■4883 •4940 •4995 •5049 ■5101 •4916 ■4973 •5029 •5083 •5135 •4949 •5006 ■5062 ■5117 •5169 •4981 •5039 ■5096 •5150 ■5204 ■5014 •5073 ■5129 •5184 •5238 •5047 ■5106 •5163 ■5218 •5272 ■5080 •5139 •5197 ■5253 •5307 •5II4' •5173 •5231 ■5287 •5342 ■5147 •5207 •5265 •5322 ■5377 •5180 ■5241 ■5299 ■5356 •5412 ■5214 •5275 •5334 •5391 •5447 •5248 ■5426 •5482 •5282 ■5343 •5403 •5461 •5517 6i° 62 65 ■5050 •5098 •5144 •S189 ■5233 ■5084 •5132 ■5179 ■5^24 ■5268 •5118 •5166 •5214 •5259 •5303 •5152 ■5201 •5248 •5294 •5339 •5186 •5236 •5283 ■5330 ■ ■5374 •5221 ■5270 ■5318 ■5365 •5410 •5255 •5305 ■5354 ■5400 ■5446 •5290 •5340 •5389 •5436 •5482 ■5325 •5375 •5425 •5472 •5518 •5360 ■54 1 1 •5460 •5508 •5554 •5395 ■5446 •5496 •5544 •5590 •5430 •5482 •5532 •5580 •5627 •5465 ■5517 ■5568 •5616 •5663 •5501 ;5553 •5653 •S70O •5536 ■5589 •5640 •S689 •5737 •5572 •5625 ■5676 •5726 •5774 30 10 20' 30 40 50' 31 10 20 3d 4d 5d 32 10' 2d --i — 3d When the Latitude is North the sign is + When the Latitude is South the sign is — . ALT-AZIMUTH TABLES. F 98 Under Altitude and abreast of Declination, take out the tabular quantity and mark it + op — , according- as Declination is S. or N. Add Algebraically E and F. Dec- lina- tion TRUE ALTITUDE. 3tf 10' 20 30 40 50 31 10' 20' 30 40' 60 32 10' 20 3d 0° •0000 ■0000 •0000 -0000 •0000 •0000 •0000 -0000 -0000 •0000 •0000 •0000 -0000 -0000 -0000 -0000 I ■0202 -0202 •0202 -0203 •0203 ■0203 -0204 -0204 -0204 •0205 •0205 -0205 -0206 -0206 •0207 0207 2 ■0403 •0404 ■0404 -0405 -0406 -0406 -0407 •0408 •0409 •0409 •0410 -041 1 -0412 ■0412 •0413 •0414 3 •0604 •0605 ■0606 ■0607 -0608 -0610 •06 1 1 -0612 •0613 •0614 -0615 -0616 •0617 •0618 •0619 -0621 4 •080s •0807 •0808 -0810" -08 II -0812 -0814 -0815 •0817 -0818 ■0820 ■0821 •0823 •0824 -0826 •0827 5 ■1006 •1008 •lOIO -1012 •1013 -1015 -1017 1019 -1020 -1022 -1024 -1026 -1028 ■1030 -1031 -1033 6° •1207 ■1209 •I2H -1213 •1215 •1217 ■1219 ■1222 -1224 •1226 •1228 -1230 ■1233 •1235 •1237 -1239 I •1407 •1410 -I4I2 ■1414 •1417 •1419 •1422 •1424 -1427 •1429 ■1432 ■1434 ■1437 ■1440 •1442 ■1445 •1607 •1610 •1612 •i6is •1618 •1621 •1624 •1626 •1629 -1632 ■1635 -1638 •1641 •1644 -1647 -1650 9 •1806 ■1809 •1812 •1816 ■1819 •1822 •1825 ■1828 •183I ■1835 ■1838 -1841 -1845 •1848 •1851 •1855 10 ■2005 •2008 •2012 -2015 -2019 -2022 •2026 -2029 •2033 •2037 -2040 ■2044 •2048 •2051 •2055 •2059 11° •2203 •2207 •2210 ■2215 •2218 ■2222 •2226 •2230 ■2234 •2238 •2242 •2246 •2250 •2254 ■2258 ■2262 12 ■2401 •2405 •2409 •2413 ■2417 •2421 ■2426 •2430 ■2434 -2438 ■2443 -2447 -2452 •2456 •2461 •2465 13 •2598 •2602 •2606 •26 1 1 •2615 •2620 •2624 -2629 •2634 -2638 •2643 ■2648 -2653 •2657 •2662 •2667 '4 •2793 •2798 •2803 ■2808 •2813 •2817 •2822 •2827 •2832 ■2837 •2842 -2848 •2853 •2858 •2863 •2868 IS •2989 •2994 ■2999 •3004 •3009 •3014 •3019 -3025 •3030 •3036 •3041 •3046 •3052 •3058 •3063 •3069 16° •3183 •3188 ■3194 ■3199 •3205 •3210 •3216 ■3221 •3227 •3233 ■3239 •3244 •3250 •3256 •3262 -3268 17 ■3376 ■3382 ■3387 -3393 •3399 •3405 ■3411 ■3417 ■3423 •3429 ■3435 •3441 •3448 •3454 •3460 "^f^ i8 •3568 •3574 ■3580 -3586 •3593 ■3599 •3605 •36 u -3618 •3624 ■3631 •3637 ■3644 "^%^\ •3657 •3664 19 •3759 •3766 •3772 ■3779 •3785 ■3792 ■3798 ■380s •3812 •3818 •3825 •3832 ■3839 •3846 •3853 •3860 20 •3949 •3956 •3963 ■3969 •3976 •3983 •3990 ■3997 •4004 •401 1 •4018 •4026 ■4033 •4040 •4048 •405s 21° •4138 •4145 •4152 •4159 •4166 •4174 •4181 ■4188 •4196 •4203 -42 II •4218 ■4226 •4234 -4241 •4249 22 •4326 •4333 ■4340 •4348 •4355 •4363 ■4370 •4378 •4386 •4393 •4401 •4409 •4417 •4425 ■ 4433 •4442 23 ■4512 •4519 •4527 •4535 •4543 •4550 •4558 •4566 •4574 •4583 ■4591 •4599 ■4607 •4616 •4624 ■4633 24 •4697 •470s •4712 '4721 •4729 •4737 ■4745 -4753 •4762 •4770 -4779 •4787 ■4796 •4805 •4814 •4823 25 •4880 •4888 •4897 •4905 ■4913 •4922 ■4930 ■4939 •4948 ■4957 •4965 •4974 ■4983 •4993 ■5002 •501 1 26° •5062 ■5070 •5079 •5088 •5096 •5105 •5114 •5123 •5132 ■5141 ■5151 •5160 •5169 •5179 •5188 ■5198 •5242 •5251 •5260 ■5269 •5278 •5287 ■5296 •53°6 •5315 ■5325 ■5334 •5344 •5353 •5363 ■5373 '"^1 28 ■5421 ■5430 •5439 •5449 ■5458 •5467 •5477 •5487 •5496 ■ss?^ "^f\ •5526 ■5536 •5546 •5556 -5566 29 •5598 •5608 •5617 -5627 •5636 •5646 •5656 •5666 •5676 •5686 ■5696 ■5796 •5717 ■5727 ■5738 -5748 30 ■5774 •5783 •5793 •5803 •5813 •5823 •5833 ■5843 •5854 -5864 •5875 •5885 •5896 •5907 •5918 •5928 31° •5947 '5957 •5967 •5977 •5988 ■5998 •6009 •6019 •6030 •6041 ■6051 •6062 •6073 ■6084 •6095 •6107 32 33 34 35 '61 19 -6129 •6140 •6150 ■6161 ■6171 •6182 •6193 ■6204 •6215 -6226 -6237 -6249 •6260 -6272 •6283 ■6289 ■6300 •6310 •6321 -6332 ■6343 ■6354 ■6365 •6376 ■6388 •6399 ■641 1 •6422 -6434 -6416 11^8 ■6457 •6468 •6479 •6490 •6501 •6512 •6524 ■6535 •6547 ■6558 -6570 •6582 ■6594 ■6606 ■6618 -6630 •6623 •6634 •6646 ■66S7 ■6658 ■6680 •6692 ■6703 •6715 •6727 ■6739 ■6751 ■6763 •6776 •6788 •6801 36° ■6787 •6799 •6810 •6822 •6834 -6845 ■6857 •6869 -6881 -6894 -6906 •6918 ■6931 •6944 •6956 -6969 •6949 •6961 •6973 •6985 -6997 •7009 ■7021 ■7033 •7046 ■7058 ■7071 •7084 -7096 ■7109 •7122 ■7136 38 •7109 ■7121 •7133 •7145 •7158 ■7170 ■7183 ■719s ■7208 •7221 ■7234 -7247 -7260 •7273 •7286 •7300 . •7462 -7621 39 •7267 ■7279 •7291 •7304 ■7316 -7329 •7342 ■7355 ■7368 -7381 ■7394 -7407 •7421 •7434 -7448 40 ■7422 •743S •7447 •7460 •7473 •7486 •7499 •7512 •7525 ■7539 •7552 •7566 ■7580 •7593 •7607 4X° 42 43 44 45 ■7576 •7726 •7875 ■8021 •8165 •7588 •7739 •7888 •8035 •8179 •7601 •7753 •7902 •8048 •8193 ■7614 ■7766 •791S •8062 •8207 -7627 •7779 •7929 •8076 •8221 •7640 -7793 -7943 •8090 -8235 ■7654 •7806 ■7956 ■8104 -8249 •7667 •7820 •7970 •81 18 •8264 •7681 •7834 •7984 ■8133 •8278 ■7694 -7848 •7999 •8147 ■8293 •7708 •7862 ■8013 •8162 •8308 •7722 •7876 •8027 •8176 •8323 •7736 •7890 •8042 -8 19 1 ■8338 •7750 -7905 -8057 ■8206 •8353 -7764 -7919 -8071 -8221 •8369 -7779 ■7934 -8086 -8236 -8384 46° % 49 SO ■8306 •8445 •8581 •87 IS •8846 •8320 •8459 ■8596 ■8729 ■8860 •8334 •8474 •8610 •8744 ■88j;s •8349 •8488 -862s 1^59 •8891 -8363 -8503 •8640 •8774 •8906 -8377 •8517 ■8655 •8789 •8921 -8392 ■8532 ■8670 ■880s •8937 •8407 ■8547 ■8685 •8820 ■8953 ■8422 •8562 ■8700 -8836 •8968 -8437 •8578 ■8716 •8851 -8984 •8452 ■8593 -8731 -8867 •9000 •8467 ■8608 •8747 -8883 •9017 -8482 •8624 •8763 -8899 •9033 ■8498 •8640 •8779 •8916 •9050 •8513 ■8656 •8795 -8932 •9066 -8529 •8672 •881 1 ■8949 •9083 51° 52 53 54 55 ■8974 •9099 •9222 •9342 ■9459 -8989 •911S ■9237 ■9357 •9475 •9004 •9130 •9253 -9373 •9491 •9019 •9146 •9269 •9389 -9507 •903s •9161 ■928s •9406 •9523 ■9051 ■9177 •9301 •9422 •9540 •9066 ■9>93 ■9317 •9438 •9557 ■9082 •9209 -9334 •9455 -9573 •9098 •9226 -9350 •9472 -9590 •9IIS •9242 ■9367 -9488 -9607 •9131 ■9259 ■9383 ■9505 ■9624 •9147 •9275 •9400 •9522 •9642 -9164 -9292 ■9417 ■9540 ■9659 -9181 •9309 •9435 •9557 -9677 •919.8 •9326 •9452 •9575 •9695 . -9215 ■9343 •9469 -9592 •9713 56° 60 •9792 ■9898 I'OOOO •9589 •9700 ■9809 ■9914 I -0017 •9605 ■9717 •9826 ■9931 1-0034 •9622 •9734 •9842 ■9948 1-0051 •9638 •9750 •9859 ■9965 1-0068 -9655 •9767 ■9876 ■9983 I -0086 -9672 •9784 ■9894 I '0000 I -0103 •9689 •9801 ■9911 I -0018 I -01 21 ■9706 ■9819 •9928 1-0035 I -0139 ■9723 •9836 -9946 1-0053 I -0X57 •9741 -9854 •9964 1-0071 I-0I7S •9758 •9872 •9982 I -0089 I 0193 •9776 •9889 i-oooo I 0107 I 0212 ■9794 •9907 I 0018 I '0126 I -0231 •9812 •9926 1-0037 I -0145 I -0249 -9830 •9944 1-0055 I -0163 1-0268 61° 62 P 65 I -0099 I -0195 I -0288 1-0378 I 0465 1 -oi 16 I 0213 I -0306 I -0356 I 0483 I -0133 I -0230 1-0323 I 0413 I -0501 1-0151 1-0247 1-0341 I -0431 1-0519 I -0168 I -0265 10359 I -0449 1-0537 I -0186 1-0283 1-0377 I -0467 I '0555 I -0204 I -0301 I -0395 1-0486 10573 I -0222 1-0319 1-0413 I -0504 I -0592 I -0240 1-0337 1-0431 I 0523 I -061 1 I -0258 1-0355 I -0450 I 0541 I 0629 I -0276 I -0374 I -0468 I "0560 I -0648 I -0294 I 0392 I -0487 1-0579 I -0667 IO313 1-0411 I -0506 I -0598 I -0687 I -0332 I -0430 1-0525 1-0617 I -0706 1-0351 I -0450 I -0545 1-0637 I -0726 I -0370 I 0469 1-0565 1-0657 I 0746 30" 10' 20 30 40 50 31 10 20 30 40' 50' 32 10 20 3d V 11. ^1. _ _S S When the Declination is North the sign is - . When the' Declination is South the sign is + 99 ALT-AZIMUTH TABLES. Under Altitude in head-line, and abreast of Latitude in margin, take out the tabular quantity and mark it + or according as the Latitude is N. or S. TRUE ALTITUDE. Lat. 32 3d 40 50 33 10 20 30 40 50 34 10 20 30 40 50 35 o' I 2 3 4 S 6° 7 8 9 10 11° 12 13 14 IS 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 SO 51° 52 S3 54 55 56° 57 58 60 61° 62 ^3 65 •0000 •01 1 1 '0222 ■0333 ■0444 •055s •0666 ■0776 •0887 •0997 •I 106 ■I216 ■1325 •1433 •1541 •1649 •1756 •1863 •1969 •2074 •2179 ■2283 ■2387 •2489 •2591 •2692 ■2793 •2892 •2991 •3089 •318s •3281 •3376 •3470 ■3562 •3654 •3745 ■3834 •3922 •4009 •409s ■4180 •4263 ■4345 •4425 ■4505 ^4583 •4659 *4734 •4808 •4880 •4951 •5020 •5088 ■5154 •5219 •5282 "S343 ■5403 •5461 •5517 'SS72 •5625 ■5676 •5726 ■5774 32 30 •0000 •01 12 '0224 •0336 •0447 •OS59 •0670 •0781 ■0892 •1003 •1113 •1223 ■1333 ■1442 ■1551 ■1659 •1767 ■1875 •1981 •2087 •2193 ■2298 •2402 •2505 •2608 •2710 •2811 •29 1 1 •3010 •3108 •3206 •3302 ■3398 •3492 •358s •3678 ■3769 •3859 •3947 •4035 •4121 ■4206 •4290 •4373 •4454 '4534 •4612 ■4689 ■4765 ■4839 ■4912 ■4983 •5052 ■5121 •5187 ■5252 ■5316 •5377 ■5437 •5496 ■5553 •5608 •5661 •5713 ■5^3 •581 1 40 ■0000 •01 13 •0225 •0338 •0450 ■0562 •0675 •0786 •0898 •1009 ■1121 •1231 ■1342 ■1452 ■1561 •1670 •1779 •1887 •1994 •2101 •2207 •2312 ■2417 ■2521 •2625 •2727 •2829 •2930 ■3029 •3128 •3226 •3323 •3419 ■3514 •3608 •3701 •3793 •3883 ■3973 ■4061 •4148 •4233 ■4318 •4401 ■4482 •4563 •4642 ■4719 •4795 •4870 •4943 •5015 •5085 •5153 •5220 •5286 •5350 •5412 •5472 •5531 •5588 •5644 ■5697 •5749 •5800 ' •5848 50 ■01 1 3 0227 ■0340 ■0453 ■0566 •0679 •0791 ■0904 ■1016 •1128 •1239 •1350 •1461 •1571 •1681 ■1790 •1899 ■2007 •2114 '2221 ■2327 •2433 ■2537 '2641 ■2745 •2847 ■2948 •3049 •3148 ■3247 •3345 ■3441 ■3537 •3631 •3725 ■3817 •3908 •3998 ■4087 ■4174 •4260 ■4345 ■4429 ■45 1 1 ■4592 •4671 •4749 •4826 •4901 ■4975 •5047 •5117 •5186 ■5254 •5320 •5384 ■5446 •5507 ■5567 •5624 •5680 ■5734 ■5786 ■5837 ■5886 33 '01 14 ■0228 •0342 '0456 •0570 •0683 •0796 •0910 •1022 •II35 •1247 ■1359 •1470 •1581 •1692 •I 801 •1911 •2020 •2128 •2235 ■2342 •2448 •2554 ■2658 •2762 •2865 •2967 •3068 •3168 ■3268 ■3366 ■3463 •3559 •3655 •3749 •3841 ■3933 •4024 •4113 '4201 •4288 •4373 •4457 •4540 •4621 •4701 •4780 ■4857 ■4932 •5006 ■5079 ■5150 •5219 ■5287 ■5354 •5418 ■5481 ■5542 '5602 •5660 ■5716 ■5771 ■5823 •5874 ■5923 10 •0000 •01 1 5 '0230 ■0344 •0459 •0573 •0687 •0802 ■0915 •1029 •1142 •1255 •1367 ■1480 ■1591 •1702 •1813 •1923 •2032 •2141 •2250 •2357 •2464 •2570 ■2675 •2780 ■2883 ■2986 ■3088 •3189 •3289 •3387 •3485 •3582 •3678 ■3772 •3866 •3958 •4049 •4139 •4228 ■4315 •4401 ■4486 • ■4569 ■4651 '4731 •4810 •4964 ■5038 •5112 ■5183 ■5253 ■5321 •5388 •5453 ■5516 ■5578 ■5638 •5696 ■5752 ■5807 •5860 •5911 ■5961 20 •0000 •01 16 ■0231 •0346 •0462 ■0577 0692 •0807 •0921 •1035 ■I 149 ■1263 •1376 •1489 •1601 ■1713 •1824 ■1935 ■2045 •215s •2264 •2372 •2479 •2586 •2692 •2797 ■2902 ■3005 •3107 •3209 •3309 •3409 ■3507 •3605 •3701 ■3796 •3890 ■3983 •4075 •4165 ■4255 ■4342 •4429 •4514 •4598 •4680 •4761 ■4841 •4919 ■4995 •5070 ■5144 •5216 ■5286 •5355 •5422 •5487 •5551 ■5613 ■5673 •5732 •5789 •5844 •5897 ■5949 ■5999 30 •0000 ■01 16 •0232 ■0349 •0465 ■0581 •0696 •0812 •0927 •1042 •1157 ■1271 ■1385 •1498 •1611 •1724 ■1836 ■1947 •2058 •2169 •2278 •2387 •2495 •2603 •2709 •2815 •2920 •3024 •3127 •3229 •3330 •3431 •3530 •3628 ■3725 •3820 ■3915 •4009 •4101 •4192 •4281 ■4370 ■4457 ■4543 •4627 •4710 ■4791 •4871 •4950 ■5027 •5102 ■5176 •5249 ■5320 ■5389 ■5456 •5522 •5586 •5649 •5709 •5768 •5826 ■5881 ■5935 ■5987 •6037 ■0000 •0117 •0234 ■0351 •0468 ■0584 •0701 '0817 ■0933 •1049 •I 164 •1279 •1394 •1508 •1622 •1735 •1848 'i960 •2071 •2182 •2293 •2402 •2511 •2619 •2726 ■2833 •2938 ■3043 •3147 •3250 •3351 •3452 •3552 •3651 ■3748 •3845 ■3940 ■4034 •4127 •4218 ■4309 ■4397 •4485 ■4571 ■4656 ■4740 •4822 •4902 •4981 ■5059* ■5135 •5209 •5282 ■5353 ■5423 ■5491 •5557 •5621 •5684 •5745 •5805 ■5862 •5918 •5972 •6024 •607s 40 50 ■0000 •0118 •0235 ■0353 •0471 ■0588 ■0705 '0822 '0939 •1055 •ii7i •1287 •1402 •1517 •1632 •1746 ■1859 •1972 •2084 ■2196 •2307 •2417 •2527 •2636 •2743 ■2851 ■2957 •3062 •3167 •3270 •3373 •3474 •3574 ■3674 ■3772 •3869 •3965 ■4059 •4153 ■4245 ■4336 ■4425 •4513 •4600 •4686 •4769 •4852 •4933 •5013 •5091 •5167 •5242 •5315 •5387 •5457 ■5525 •5592 •5657 ■5720 •5782 •5841 •5899 ■5956 •6010 •6062 •61 13 34 0000 •0118 •0237 ■0355 ■0473 ■0592 ■0709 '0827 ■0945 '1062 '1 1 79 •1295 •1411 •1527 ■1642 ■1757 •1871 •1984 •2097 •2210 •2321 •2432 ■2543 •2652 •2761 •2869 ■2975 •3081 •3187 •3291 ■3394 ■3496 ■3597 •3697 •3796 ■3893 •3990 •4085 •4179 •4272 ■4363 ■4453 •4542 •4629 •4715 '4799 ■4883 ■4964 ■5044 ■5123 •5200 ■5275 ■5349 ■5421 •5491 •5560 ■5627 •5692 •5756 •5818 ■5878 ■5936 ■5993 •6048 •6101 •6152 10 '0000 '01 19 '0238 ■0357 ■0476 •0595 •0714 •0832 '095I •io68 •1186 •1303 •1420 ■1536 •1652 •1768 ■1883 •1997 •21 1 1 •2224 '2336 ■2448 ■2559 '2669 ■2778 •2887 ■2994 '3101 •3207 ■33 1 1 •3415 ■3518 ■3619 ■3720 •3819 •3918 ■4015 '41 10 ■4205 ■4298 ■4390 •4481 ■4570 ■4658 •4745 •4830 •4913 •4995 •5076 ■5155 ■5232 ■5308 ■5382 •5455 ■5526 ■5595 ■5662 •5728 ■5792 •5855 ■5915 ■5974 '6031 •6086 .6139 •6190 20 •0000 •0120 ■0240 ■0360 •0479 •0599 '0718 •0838 '0957 ■1075 '1 193 •1311 •1429 ■1546 •1663 •1779 •1894 •2009 •2124 '2238 ■2351 ■2463 ■2575 '2685 •2795 •2905 ■3013 '3120 ■3227 •3332 •3436 •3540 3642 •3743 ■3843 ■3942 •4040 ■4136 ■4231 "4325 •4418 •4509 •4599 •4687 ■4774 •4860 ■4944 •5026 •5107 ■5187 ■5265 ■5341 •5416 ■5489 ■5560 •5630 •5698 ■5764 •5828 ■5891 ■5952 •601 1 '6068 '6124 •6177 •6229 30 •0000 ■0121 0241 '0362 '0482 '0603 •0723 •0843 '0962 •1082 '1320 ■1438 ■1556 •1673 ■1790 •1906 '2022 •2137 •2252 ■2365 •2478 •2591 •2702 2813 •2923 ■3032 •3140 ■3247 •3353 ■3458 •3562 •3665 ■3767 ■3867 ■3967 ■4065 •4162 •4258 4352 •4445 ■4537 •4628 •4717 '4804 ■4890 ■4975 ■5058 •5139 •5219 ■5298 ■5375 •5450 ■5523 ■5595 ■5665 •5733 •5800 ■586s ■5928 •5989 •6049 •6106 •6162 •6216 •6268 40 0000 •0121 •0243 ■0364 •0485 ■0607 •0727 •0848 •0968 •1089 •1208 •1328 ■1447 ■1565 ■1683 •1801 •1918 ■2035 '2150 •2266 •2380 •2494 •2607 •2719 '2830 ■2941 •3051 •3159 •3267 •3374 •3479 ■3584 •3688 •3790 •3891 ■3991 '4090 4188 •4284 ■4379 ■4473 •4565 •4656 •4746 ■4834 ■4921 •5006 ■5089 ■5171 ■5252 ■5331 •5408 •5484 ■5558 ■5630 ■5700 ■5769 •5836 •5901 •5965 •6027 '6086 •6144 '6200 ■625s •6307 •0000 '0122 ■0244 ■0366 •0488 •0610 '0732 ■0853 •0975 •109s •1216 •1336 •1456 •1575 •1694 •1812 •1930 •2047 •2164 •2280 •2395 •2509 •2623 •2736 •2848 ■2959 •3070 ■3179 •3287 •3395 •3501 •3606 •371 1 •3814 •3916 •4016 ■41 16 •4214 ■431 1 •4407 •4501 ■4594 •4685 •4775 •4864 ■4951 ■5037 ■5121 •5204 ■5285 ■5364 ■5442 ■5518 •5592 5665 ■5736 ■5805 •5872 •5938 •6002 ■6064 •6124 ■6182 '6239 •6293 '6346 50 35 When the Latitude is North the sign is + • When the Latitude is South the sign is — . ALT-AZIMUTH TABLES. 100 Under Altitude and abreast of Declination, take out the tabular quantity and mark it + or — , according as Declination is S. or N. Add Algebraically E and F. Dec- lina- tion. TRUE ALTITUDE, 3230 40 50 33 10 20 30 40 50 34 10 20 30 40 50 35 3 4 5 6' I 9 10 11° 12 13 14 IS 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 SO 51° 52 53 54 55 56° 57 58 59 60 61° 62 ■0000 ■0207 •0414 '062 1 ■0827 ■1033 •1239 •1445 •1650 •185s •2059 •2262 ■2465 •2667 ■2868 •3069 •3268 •3467 •3664 •3860 •40SS •4249 •4442 •4633 ■4823 •50 II •5198 •5383 •SS66 •5748 •5928 ■6107 ■6283 •6458 •6630 •6801 •6969 ■7136 ■7300 •7462 •7621 ■7779 •7934 ■80S6 •8236 •8384 •8529 •8672 •88 1 1 •8949 •9083 •92 IS ■9343 •9469 •9592 •9713 •9830 •9944 i-ooss I 0163 I '0268 I '0370 1 '0469 10565 I 0657 I '0746 32 30 •0000 •0207 •0415 •0622 •0829 ■103s •1242 •1448 •1653 •1858 •2063 ■2267 •2470 •2672 ■2874 •3074 •3274 •3473 •3671 •3867 •4063 •4257 •4450 •4641 •4832 •5020 •5207 •5393 ■5577 •5759 •5939 ■61 18 ■6295 ■6470 ■6643 •6813 •6982 •7149 •7313 •7476 •7636 •7793 •7949 •8101 •8252 •8400 •8545 ■8688 •8828 •896s •9100 •9232 •9361 •9487 •9610 •9731 •9848 •9963 I -0074 I 0182 I '0287 I -0390 1-0488 I -0584 1-0677 I -0766 40 •0000 ■0208 •0415 -0623 •0830 ■1037 •1244 •1450 ■1656 •1862 •2067 •2271 -2474 -2677 -2879 •3080 ■3280 •3480 ■3678 •3875 •4070 •4265 •4458 ■4650 -4841 •5030 •5217 •5403 ■5587 •5770 •5951 •6130 -6307 •6482 •665s •6826 -6995 •7162 •7327 -7490 -7650 •7808 •7963 -81 17 -8267 •8415 -8561 ■8704 •8844 •9117 •9249 •9378 •9505 -9628 •9749 ■9867 •9981 I '0093 I -0201 I -0307 I -0409 I -0508 1 -0604 I -0697 1-0786 50 -0000 0208 •0416 ■0624 •0832 •1039 •1246 •1453 ■1659 •1865 •2071 •2275 •2479 •2682 •288s •3086 •3287 ■3486 •3685 ■3882 •4078 •4273 ■4467 •4659 •4850 ■5039 •5227 •5413 ■5598 ■5781 5962 -6I4I •6319 •6494 •6668 •6839 •7009 •7176 •7341 •7504 ■7664 ■7823 •7978 •8132 •8283 •8431 •8577 •8720 •8861 •8999 •9134 •9266 •9396 ■9523 ■9646 •9767 •9885 I'OOOO I 01 12 I022I I -0326 I -0429 I -0528 I "0624 1-0717 I -0805 33 •0000 •0208 -0417 •0625 •0833 •1041 •1249 •1456 •1663 •1869 •2074 •2279 -2484 -2687 -2890 •3092 •3293 •3493 •3692 •3889 •4086 ■4281 •4475 -4668 •4859 •5049 •5237 •5423 ■5608 -5792 •5973 •6153 •6331 -6506 •6680 •6852 -7022 •7189 ■7355 •7518 -7679 ■7837 •7994 -8147 -8299 •8447 ■8593 ■8737 -8878 -9016 •91 5 1 ■9284 •9414 •9541 •9665 •9786 •9904 I '0019 1-0131 I -0240 I 0346 I 0448 1-0548 I -0644 I -0737 I ^0827 10 •0209 •0418 •0626 •0835 •1043 •1251 ■1459 •1666 •1872 -2078 •2284 ■2489 •2692 -2896 -3098 •3299 •3499 ■3699 ■3897 -4094 •42S9 •4484 •4677 •4868 •5058 •5247 •5434 -5619 •5803 •5985 -6165 •6343 •6519 •6693 •6865 •7035 •7203 •7369 •7532 -7694 •7852 •8009 ■8163 •8314 ■8463 •8610 •8754 •8895 •9033 •9169 •9302 •9432 •9559 •9683 ■9804 •9923 I 0038 1^0150 I 0259 I '0366 I -0468 I ^0568 I ^0665 ro7S8 1 ^0848 •0000 •0209 •0419 •0628 •0837 •1045 ■1254 •146 1 •1669 •1876 -2082 •2288 •2493 -2698 -2901 -3104 •3305 -3506 •3706 •3904 •4102 •4298 •4492 •4686 •4878 •5068 •5257 •5444 •5630 •5814 •5996 ■6176 •6355 ■6531 •6706 •6878 •7049 •7217 •7383 •7547 •7708 •7867 •8024 •8179 •8330 20 •8626 •8770 -8912 -9051 -9186 •9320 •9450 •9577 •9702 •9823 •9942 I -0057 I '0170 I ^0279 1-0385 ro488 I 0588 I ^0685 I ^0778 I 0868 •0000 •0210 •0419 •0629 •0838 •1047 •1256 •1464 ■1672 •1880 •2086 •2293 •2498 •2703 ■2907 •31 10 •3312 ■3513 •3713 •3912 ■4109 •4306 •4501 •4695 -4887 •5078 •5267 ■5455 •5641 •5825 -6008 -6188 •6367 •6544 •6719 •7062 •7231 •7397 •7561 •7723 •7883 •8040 •8194 ■8346 •8496 •8643 •8787 ■8929 •9068 •9204 •9338 •9468 ■9596 •9721 •9842 •9961 I -0077 1^0 1 89 I ^0299 I -0405 I -0509 I '0609 I •0706 1-0799 I 0889 30 •0000 •0210 •0420 •0630 •0S40 •1049 ■1258 •1467 •1675 •1883 •2090 •2297 ■2503 •2708 •2912 -3116 •3318 •3520 -3720 •3919 -4117 •4314 •4510 -4704 -4897 •5088 •5277 ■5465 •5652 •5836 •6019 -6200 •6379 •6557 •6732 -690s -7076 •7245 •7412 •7576 •7738 •7898 •8055 •8210 •8363 •8513 •8660 •8804 40 •9086 •9222 •9356 •9487 •9614 ■9739 •9861 •9980 I •0096 I 0209 I 0319 I '0426 I ^0529 I -0629 I 0726 I 0820 1-0911 50 •0000 •021 1 •0421 •0631 •0841 •1051 •1261 •1470 •1679 •1887 •2095 •2302 •2508 •2713 •2918 •3122 •3325 •3527 •3727 •3927 •4126 •4323 •4519 •4713 •4906 •5098 •5288 •5476 •5663 -5848 •6031 •6212 •6392 •6570 •6745 •6919 •7090 •7259 •7426 •75^1 •7753 •7914 ■8071 •8226 ■8379 •8529 ■8677 •8822 •8964 ■9103 ■9240 •9374 •9505 •9633 •9759 •9881 I •oooo i^oii6 I -0229 I -0339 I 0446 1-0550 I -0650 1-0747 I -0841 I -0932 34 •0000 •021 1 •0422 •0633 •0843 •1053 ■1263 ■1473 •1682 •1891 •2099 •2306 •2513 •2719 •2924 ■3128 •3331 ■3534 •3735 •3935 •4134 •4331 •4527 •4722 •4916 •5108 •5298 •5487 •5674 •5859 •6043 •6225 •6405 •6582 •6758 •6932 •7104 •7274 ■7441 •7606 •7769 •7929 •8087 •8243 •8396 •8546 •8694 •8839 •8982 •9121 •9258 •9393 •9524 •9652 •9778 •9900 I ^0020 I -0136 I -0249 I 0360 I -0466 1-0571 I -067 1 I -0769 I -0863 1-0954 •0000 •02 II •0423 •0634 •0845 •1055 •1266 •1476 ■1685 -1894 •2103 -23 1 1 •2518 •2724 ■2930 •3134 •3338 •3541 •3742 ■3943 -4142 •4340 •4536 •4732 -4926 •5118 •5309 •5498 •5685 •5871 •6055 -6237 -6417 •6596 •6772 •6946 •7118 •7288 •7456 ■7621 -7784 •7945 •8103 ■8259 •8412 •8563 •87 1 1 -8857 ■8999 ■9139 •9277 •941 1 •9543 •9671 •9797 •9920 I ^0040 I 0156 I -0270 I -0380 I -0487 I -0592 I 0692 I -0790 I -0884 10975 10 20 •0000 •0212 ■0423 -0635 -0846 -1058 •1268 •1479 •1689 -1898 -2107 •2315 •2523 •2730 •2935 •3141 •3345 •3548 •3750 •3950 •4150 •4348 •4546 ■4741 •4935 •5128 •5319 •5509 •5697 •5883 •6067 •6250 •6430 •6609 ■6785 •6960 •7132 •7302 -7470 •7636 •7800 •7961 •8u9 •8275 •8429 •8580 •8729 •8874 •9017 •9158 •9295 ■9430 ■9562 •9691 •9817 •9940 I •0060 1-0176 I '0290 I 0401 I -0508 I -0613 1-0714 I 0812 I 0906 1-0997 •0000 0212 •0424 •0636 •0848 •1060 •1271 •1482 •1692 •1902 •21 1 1 •2320 •2528 •2735 •2941 •3147 •3351 •3555 •3757 •3958 •4158 •4357 •4555 •4751 •4945 •5138 •5330 •5520 •5708 •5895 •6079 •6262 •6443 •6622 •6799 •6974 •7147 •7317 •7485 •7652 •7815 •7977 •8136 ■8292 •8446 ■8597 •8746 30 •9035 •9176 •9314 •9449 •9581 •9710 -9836 -9960 I -ooSo I -0197 I -031 1 I 0422 I -0530 I ^0634 I '0735 I ^0833 I -0928 1-1019 •0000 •0213 •0425 •0638 •0850 -1062 •1273 -1485 ■1696 •1906 •2116 •2325 •2533 •2741 •2947 ■3153 •3358 •3562 •3765 •3966 •4167 •4366 -4564 •4760 •4955 •5149 •5341 ■5531 ■5720 •5906 •6091 •6275 •6456 ■6635 •6813 •6988 •7161 •7332 •7501 •7667 •7831 •7993 •8152 •8309 •8463 •861 s -8764 8910 -9054 -9195 •9333 -9468 -9600 ■9730 •9856 ■9980 I'OIOO I -0218 I -0332 I 0443 I '0551 I '0655 I -0757 1-0855 I -0950 I "1042 40 •0000 •0213 ■0426 •0639 •0852 •1064 •1276 •1488 •1699 1910 •2120 •2329 ■2538 •2746 ■2953 -3160 ■3365 ■3569 •3772 •3974 •4175 •4375 •4573 •4770 •4965 •5159 •5352 ■5542 ■5731 •5918 •6104 •6287 •6469 •6649 •6826 •7002 •7176 •7347 •7516 •7683 ■7847 ■8009 ■8169 -8326 •S480 •8632 •8782 -8928 -9072 9213 ■9352 ■9487 -9620 -9750 -9876 I 0000 I-0I2I I -0238 I -0353 I -0464 I -0572 1 -0677 I 0779 10877 I 0972 I -1064 50 35 When the Declination is North the sign is - . When the Declination is South the sign is + . 101 ALT-AZIMUTH TABLES. Under Altitude in head-line, and abreast of Latitude in Margin, take out the tabular quantity and mark It + oi^ according' as the Latitude is N. or S. LAT. TRUE ALTITUDE. 35 10 20 30 40' 50 36 10 20 30 40 50 37 10 20' 30 0° ■0000 ■0000 ■0000 •0000 •0000 •0000 ■0000 ■0000 •0000 •0000 •0000 •0000 •0000 ■0000 •0000 •0000 I ■01 22 •0123 ■0124 •0124 •0125 ■0126 •0127 •0128 •0128 •0129 •0130 ■01 3 1 •0132 •0132 •0133 •0134 2 •0244 ■0246 ■0247 •0249 •0250 •0252 ■0254 •0255 •0257 ■0258 •0260 •0261 ■0263 •0265 •0266 •0268 3 ■°3^6 ■0369 •0371 •0373 •0376 •0378 •0380 •0383 •0385 •0387 •0390 ■0392 •0394 ■0397 •0399 •0402 4 •0488 •0491 •0495 •0498 •0501 ■0504 •0507 ■0510 ■0513 ■0516 ■0519 •0522 ■0526 •0529 •0532 ■0535 5 •0610 •0614 •0618 •0622 ■0626 •0629 •0633 ■0637 •0641 ■0645 ■0649 •0653 •0657 ■0661 ■0665 •0669 6° •0732 •0736 •0741 ■0746 ■0750 •075s ■0759 •0764 •0769 •0773 ■0778 •0783 •0788 •0792 •0797 •0802 7 •0853 •0859 ■0864 ■0869 ■0875 •0880 •0885 •0891 •0896 ■0902 ■0907 ■0913 •0918 •0924 •0930 ■0935 8 •0975 ■0981 •0987 •0993 •0999 •1005 •lOII ■1017 •1024 •1030 •1036 •1042 ■1049 ■1055 •1061 •1068 9 •I09S •I 102 •I 109 ■1116 ■1123 •I 130 •II37 ■I 144 •II5I •I 1 58 ■1165 •1172 ■1179 •I 186 •I 193" •1200 10 •1216 •1223 •1231 •1239 •1246 •1254 •1262 •1269 •1277 •1285 •1293 •1301 •1309 •1316 •1324 ■1332 11° •1336 ■1344 •1353 ■1361 •1369 ■1378 •1386 •1395 •1403 •1412 •1421 •1429 •1438 •1447 •1455 •1464 12 •1456 •1465 •1474 •1483 •1492 ■1501 •iSii •1520 •1529 •1538 •1548 •1557 •1567 •1576 ■1586 •1595 13 •IS7S •1585 •1595 •160S •1614 ■1624 ■1634 •1644 •1654 •166s •1675 •168s •1695 •1705 ■1716 •1726 14 •1694 •1704 •171S •1726 ■1736 •1747 •1758 ■1768 •1779 ■1790 ■1801 •1812 •1823 •1834- •1845 •1856 IS •l8l2 •1824 •1835 •1846 •1858 •1869 ■1880 •1892 •1904 •1915 •1927 •1939 •1950 •1962 •1974 •1986 i6° •1930 •1942 •1954 •1966 •1978 •1990 ■2003 •2015 •2027 •2040 •2052 •2065 •2077 •2090 •2102 •21 15 % ■2047 ■2060 •2073 •2085 •2098 •21 1 1 •2124 •2137 •2150 •2163 •2177 •2190 •2203 •2217 •2230 •2243 i8 •2164 •2177 •2191 •2204 •2218 ■2231 •2245 •2259 •2273 •2287 •2301 •2315 •2329 •2343 •2357 •2371 19 ■2280 •2294 •2308 •2322 •2337 •2351 •2365 •2380 •2394 •2409 •2424 •2439 •2453 ■2468 •2483 •2498 20 •2395 •2410 ■2425 •2440 •2455 •2470 •2485 ■2500 •2515 •2531 •2546 ■2562 •2577 •2593 •2609 ■2624 21° •2509 •2525 •2541 ■2556 •2572 •2588 •2604 ■2620 •2636 •2652 •2668 •2684 •2700 •2717 ■2733 •2750 22 •2623 •2639 •2656 •2672 ■2689 •2705 •2722 •2738 •2755 •2772 ■2789 •2806 ■2823 •2840 •2857 •2874 23 ■^736 •2753 •2770 ■2787 •2804 ■2821 ■2839 •2856 •2874 •2891 •2909 •2927 •2944 ■2962 •2980 •2998 24 •2848 •2866 •2883 •2901 •2919 •2937 •2955 •2973 •2991 •3010 ■3028 •3046 •3065 •3084 •3102 •3121 25 •29S9 ■ -2978 •2996 ■3015 •3033 •3052 ■3071 •3089 •3108 •3127 •3146 •3165 •3185 •3204 •3223 •3243 ' 26° •3070 •3089 •3108 ■3127 •3146 •3166 ■3185 •3204 •3224 •3244 ■3264 •3283 •3303 •3323 •3344 •3364 ^ •3179 •3199 ■3218 •3238 ■3258 •3278 ■3298 •3319 •3339 •3359 •3380 •3400 ■3421 •3442 ■3463 •3484 28 •3287 •3308 •3328 •3349 ■3369 •3390 ■341 1 •3432 •3453 •3474 ■3495 ■3516 •3538 •3559 ■3581 •3602 29 •3395 •3416 ■3437 •3458 ■3479 •3501 ■3522 •3544 •3566 •3587 •3609 •3631 •3653 •3675 •3698 •3720 30 •3501 •3523 •3545 •3566 •3588 •361 1 •3633 •365s •3677 •3700 •3722 •3745 •3768 •3791 •3814 •3837 31° ■3606 •3629 •3651 •3674 •3696 •3719 ■3742 •3765 •3788 •3811 •3834 •3858 •3881 •3905 •3928 •3952 32 •37" •3734 •3757 •3780 •3803 •3827 •3850 •3874 •3897 •3921 •3945 ■3969 •3993 •4017 •4042 •4066 33 •3S14 •3837 ■3861 ■3885 •3909 ■3933 •3957 •3981 •4006 •4030 ■4055 •4079 •4104 •4129 •4154 •4179 34 •3916 •3940 •3964 •3989 •4013 •4038 ■4063 ■4088 •4113 •4138 •4163 •4188 •4214 ■4239 •4265 •4291 35 •4016 •4041 •4066 •4091 •4117 •4142 •4167 •4193 •4218 •4244 ■4270 •4296 ■4322 •4348 •4375 •4401 36° •41 16 •4141 •4167 •4193 ■4218 ■4244 •4271 ■4297 ■4323 •4349 ■4376 •4403 •4429 •4456 ■4483 •4510 3^ •4214 •4240 •4266 •4293 •4319 •4346 •4372 •4399 •4426 ■4453 ■4480 ■4508 •4535 ■4563 ■4590 ■4618 •431 1 •4338 •4365 ■4391 •4419 ■4446 ■4473 •4500 ■4528 •4556 •4583 ■461 1 ■4639 •4667 ■4696 •4724 39 •4407 •4434 •4461 •4489 •4517 •4544 •4572 •4600 •4628 •4657 •4685 •4714 ■4742 ■4771 •4800 •4829 40 •4501 •4529 •4557 •4585 •4613 •4642 •4670 •4699 •4728 •4756 ■4785 •4815 •4844 •4873 •4903 ■4932 41' •4594 •4622 •4651 •4680 •4708 •4737 ■4767 ■4796 •4825 •485s •4884 •4914 ■4944 ■4974 •5004 •5104 •5202 •5034 •5134 •5233 42 •4685 •4714 ■4744 ■*?I3 •4802 •4832 •4862 •4891 •4921 ■4951 •4981 •5012 ■5042 •5073 43 ■4775 •4864 •480s ■4835 •4865 •4895 •4925 •4955 •4985 •5016 •5047 •5077 •5168 •5139 ■5170 44 ■4894 •4925 •4955 •4986 •S016 •5047 •5078 •5109 •5140 •5172 •5203 •5235 •5266 ■5298 •5330 45 ■4951 •4982 •5013 •5044 ■5075 •5106 •5137 •5169 •5201 ■5232 •5264 ■5296 •5328 •5361 •5393 •5426 46° ■5037 •5068 ■fi? •5131 •5163 ■5194 •5226 •5258 •5291 •5323 •5355 •5388 ■5421 '5453 '5487 •5520 % •5121 ■5153 Hi - '5217 •5249 ■5281 •5314 •5346 •5379 •541 z •5445 •5478 •5511 •5545 ■5756 •5843 •5612 •5702 ■5878 •5204 •5236 •5268 •5301 •5333 •5366 •5399 •5432 •5466 •5499 ■5533 •5566 •5600 •5634 49 •5285 •5317 •5350 •5383 •5416 ■5450 •5483 •5517 •5551 •5585 •5619 •5653 •5687 •5722 50 •5364 ■5397 •5431 •5464 •5498 •5532 •5566 •5600 •5634 •5668 •5703 •5738 •5773 ■5808 51° •5442 ■5475 •5509 •5543 ■5578 •5612 ■5646 •5681 •5716 •5751 •5786 ■5821 ■5856 ■5892 •5927 •6010 •5963 •6047 •6128 52 •5518 •5552 ■^If •5621 ■5655 ■5690 •5725 •5760 •5796 •5831 ■5867 •5902 ■5938 ■5974 S3 ;^ii? ■5627 ■5662 •5697 •5732 •5767 •5802 •5838 •5874 ■5910 ■5946 •5982 •6018 •6055 ■6133 •6091 •6170 •6248 54 t^i •5700 •5735 •5771 ■5806 •5842 •5878 •5914 •5950 •5986 •6023 •6060 •6096 •6208 55 •5736 •5771 •5807 •5843 ■5879 •591S •5951 •5988 •6025 •6061 •6098 •6135 •6173 •6210 •6286 56° 1 ■580s •5872 ■5938 •6002 •6064 •5841 •5909 •5975 •6039 ■6102 •5877 •5945 ■6012 •6077 •6139 •5913 •5982 ■6049 •61 14 •6177 •5950 ■6019 •6086 •6152 •6215 •5987 •6056 ■6124 •6190 •6254 •6023 •6093 ■6161 ■6228 ■6292 •6060 •6131 ■6199 •6266 ■6331 •6097 •6168 •6237 •6304 •6369 t'3S •6206 •6275 ■6343 •6408 •6172 •6244 •6313 •6381 •6447 •6210 •6282 ■6352 •6420 •6487 •6247 ■6320 •6391 ■6459 •6526 •6285 •6358 •6429 •6498 •6566 •6323 •6397 •6468 •6538 •660s •6361 •643s •6507 •6577 •664s 61° 62 65 ■6124 •6182 ■6239 ■6293 •6346 •6162 ■6221 ■6278 •633* ■6385 . •6200 •6259 ■6316 •6372 •642s •6239 •6298 •6355 •641 1 •6465 ■6277 ■6337 •639s •6451 •6504 •6316 •6376 ■6434 •6490 •6545 •6354 •641S ■6474 ■6530 •6585 •6393 ■6454 •6513 •6570 ■6623 •6433 •6494 •6610 •6666 •6472 •6583 •6706 •6511 •6573 •6691 •6747 •6551 •6613 •6674 •6732 •6788 •6591 •6653 ■6714 •6631 ■6694 •6755 •6814 •6871 •6671 ■6734 ■6796 ■6855 ■6913 •671 1 1" •6897 •6954 35 10 20 30 40 50 36 10 20 30 40 50' 37 10' 20 30' When the Latitude is North the sign is + . When the Latitude Is South the sign is — . ALT-AZIMUTH TABLES. 102 Under Altitude and abreast of Declination, take out the tabular quantity and mark it + or — , according as Declination is S. or N. Add Algebraically E and F. Dec- lina- tion TRUE ALTITUDE. 35 10' 20 3d 4d 5d 36 id 2d 3d 4d 5d 37 irf 2d 30 0° •0000 •0000 •0000 -0000 -0000 -0000 •0000 -0000 ■0000 •onnn •noon •0000 -0000 •0000 •0000 •0000 I •0213 ■0213 ■0214 •0214 -0215 0215 0216 -0216 •0217 •0217 -0218 •0218 -0219 •0219 -0219 -0220 2 •0426 •0427 •0428 -0429 ■0430 -0430 -0431 ■0432 •0433 -0434 ■0435 •0436 ■0437 •0438 •0439 •0440 3 •0639 -0640 ■0642 -0643 -0644 •0646 •0647 ■0648 •0650 -0651 -0652 •0654 •065 s -0657 -0658 -0660 4 •0852 ■0853 ■0855 ■0857 -0859 •0860 •0862 ■0S64 ■0866 ■0868 ■0870 ■0872 ■0873 ■0875 •0877 •0879 5 •1064 •1066 ■1068 •1071 ■1073 ■1075 -1077 -1080 -10S2 •1084 -1087 •1089 -109 1 •1094 •1096 -1099 6° •1276 ■1279 •1281 •1284 -1287 •1289 •1292 -1295 -1298 -1300 ■1303 •1306 -1309 -1312 ■1315 •1318 I ■1488 -1491 •1494 •1497 •1500 •1503 ■1506 -1510 -1513 ■1516 •1519 •1523 -1526 -1529 •1533 •1536 •1699 •1702 •1706 ■1710 ■1713 •1717 •1720 •1724 -1728 -1731 ■1735 •1739 •1743 -1746 •1750 •1754 9 ■1910 •1914 •1918 -1922 -1926 •1930 -1934 •193S -1942 •1946 ■1950 •1954 -1959 -1963 -1967 •1972 10 •2120 •2124 •2129 ■2133 •2137 •2142 ■2146 -2151 •2156 •2160 •2165 -2170 •2174 •2179 , ■2184 •2189 11° 2329 ■2334 •2339 •2344 •2349 ■2354 ■2359 ■2364 •2369 -2374 •2379 -2384 ' -2389 •2394 ■2400 ■2405 12 •2538 ■2543 •2549 ■2554 •2559 •2565 -2570 •2575 •2581 ■2586 •2592 •2598 •2603 •2609 •2615 •2621 13 •2746 •2752 •2757 •2763 -2769 •2775 -2781 -2786 -2792 •2798 -2804 ■281 1 -2817 •2823 -2829 •2835 '4 •2953 •2959 -2965 -2972 •2978 •2984 •2990 •2997 •3003 -3010 •3016 •3023 •3029 •3036 ■3043 •3049 IS ■3160 •3166 •3173 ■3179 •3186 •3192 ■3199 •3206 ■3213 •3220 ■3227 •3234 -3241 •3248 •325s -3262 16° •3365 ■3372 •3379 ■3386 •3393 •3400 ■3407 •3414 •3422 •3429 •3436 •3444 •3451 ■3459 ■3467 •3474 17 •3569 •3576 •3584 ■3591 •3599 •3606 ■3614 •3622 -3629 •3637 •3645 •3653 •3661 •3669 -3677 •3685 18 •3772 ■3780 •3788 ■3796 -3804 -3812 ■3820 •3828 •3836 •3844 •3852 •3861 -3869 -3878 -3886 •3895 19 •3974 •3983 ■3991 •3999 -4007 •4016 ■4024 -4033 •4041 •4050 ■4059 -4068 •4077 •4086 -4095 -4104 20 ■4>7S •4184 •4192 -4201 •4210 -4219 •4228 •4237 -4246 •4255 •4264 •4273 -4283 •4292 •4301 •4311 21° ■4375 ■4384 •4393 -4402 -441 1 -4420 •4430 •4439 •4449 ■4458 •4468 •4477 •4487 ■4497 ■4507 ■4517 22 ■4573 •4582 •4592 -4601 •4611 •4621 •4630 -4640 •4650 ■4660 •4670 •4680 -4691 •4701 •47 1 1 •4722 23 ■4770 -4780 -4790 •4799 •4809 ■4820 -4830 •4840 -4850 -4861 -4871 •4882 -4892 ■4903 •4914 •4925 24 •4965 •4975 •4986 •4996 •5006 ■5017 ■5028 •5038 -5049 -5060 ■5071 -5082 •5093 ■5104 -511S •5127 25 ■5159 •5170 -5180 •5 19 1 -5202 ■5213 ■5224 -5235 -5246 •5257 •5269 •5280 •5292 ■5303 ■531S •5327 26° ■5352 •5362 •5374 •538s •5396 •5407 •5419 •5430 •5^42 -5453 ■5465 •5477 -5489 ■5501 •5513 •5526 27 ■5542 ■5554 ■5565 •5576 •5588 •5600 -5612 •5624 •5636 -5648 •5660 -5672 •5685 -5697 ■5710 ■5722 •5918 28 ■5731 ■5743 ■5755 •5767 -5779 •5791 -5803 •5815 -5828 ■5840 ■5853 •5866 •5878 •5891 •5904 29 •5918 ■5931 •5943 •5955 •5967 •5980 •5993 ■6005 ■6018 -6031 -6044 -6057 •6070 -6084 ■6097 -61 1 1 30 '6104 ■6 116 •6129 -6142 •6154 •6167 •6180 •6193 •6207 ■6220 -6233 -6247 -6261 •6274 •6288 •6302 31° ■6287 •6300 ■6313 -6326 •6340 •6353 •6366 -6380 - •6393 •6407 -6421 •6435 -6449 tf^ •6477 -6492 -6679 -6865 •7048 32 •6469 •6482 •6496 -6509 -6523 •6536 -6550 ■6564 -6578 •6592 -6606 -6621 -6635 -6650 -6665 33 •6649 ■6662 -6676 -6690 -6704 •6718 -6732 -6746 -6761 •6775 •6790 -6805 -6820 -6835 -6850 34 ■6826 -6840 -6855 •6869 ■6883 -6897 -6912 6927 ■6941 -6956 -6971 '^^11 -7002 -7017 •7033 35 ■7002 •7016 •7031 •7045 •7060 •7075 -7090 ■7105 -7120 ■7135 -7151 ■7166 •7182 •7198 •7214 •7230 36° •7176 -7190 -7205 •7220 •7235 •7250 •7265 ■7281 -7296 •7312 •7328 -7344 •7360 -7376 •7392 •7569 -7409 -7586 -7760 i ■7347 •7362 ■7377 ■7392 •7408 ■7423 •7439 •7455 -7471 ■7487 •7503 •7519 •7536 •7552 ■7516 •7531 •7547 •7562 •7578 ■7594 •7610 -7626 ■7642 •7659 •7675 -7692 ■7709 •7726 '1743 39 40 •7683 •7847 -7698 •7863 -7714 -7879 •7730 ■7896 •7746 •7912 •7762 ■7929 •7779 •7945 ■7795 -7962 •7812 •7979 -7829 ■7996 -7846 ■8014 -7863 •8031 ■7880 •8049 -7897 -8066 . •7915 -8084 •7932 . -8102 41° 42 43 44 45 ■8009 ■8169 ■8326 •8480 ■8632 •8025 ■8185 •8343 •8498 ■8650 •8042 ■8202 •8360 •8668 •8059 •8219 •8377 •8533 ■8686 •8075 •8236 •8395 •8550 •8704 ■8092 ■8254 •8412 •8568 •8722 •8109 -8271 -8430 •8586 ■8740 •8127 -8288 -8448 -8605 ■8759 •8144 •8306 -8466 •8623 -8778 ■8161 •8324 •8484 •8642 ■8796 -8179 •8342 -8502 ■8815 -8197 •8360 -8521 -8679 -8835 -8215 -8378 -8540 -8698 -8854 -8233 -8397 •8558 -8717 •8873 •8251 •8415 •8577 •8737 •8893 -8269 •8434 -8596 •8756 ■8913 46° 49 50 •8782 ■8928 •9072 ■9213 ■9352 •8799 •S946 •9091 •9232 •9371 -8818 •8965 -9109 -9251 •9390 •8836 •8983 ■9128 ■9270 •9410 -8854 •9002 •9147 -9290 •9429 -8873 -9021 ■9166 •9309 •9449 ■8892 ■9040 -9186 ■9329 -9469 ■8910 ■9059 ■9205 •9349 -9489 -8929 •9079 -9225 •9368 •9509 •8949 -9098 ■9245 •9389 •9530 -8968 -9118 -9265 •9409 ■9550 •8987 •9138 -9285 -9429 •9571 -9007 -9158 ■9305 -9450 -9592 -9027 •9178 •9326 •9471 -9613 -9047 ■9198 •9346 •9492 •9634 -9067 -9219 •9367 •9513 •9656 51° 52 S3 54 55 •9487 •9620 •9750 •9876 I -0000 •9507 ■9640 -9769 •9896 1-0020 ■9526 -9659 -9790 -9917 1-0041 •9546 •9679 •9810 •9937 1-0062 •9566 •9700 •9830 •9958 1-0083 •9586 •9720 ■9851 ■9979 I -0104 •9606 ■9740 -9872 I -0000 I -0125 •9626 -9761 •9893 I 002 1 I -0147 -9647 -9782 •9914 I 0043 I -0168 -9668 •9803 •9935 J -0064 1 0190 -9689 -9824 ■9957 1-0086 I -0212 •9710 •9845 •9978 i-oio8 1-0235 •9731 -9867 1-0000 I -0130 1-0257 •9752 -9889 I -0022 1-0152 1 -0279 •9774 -991 1 1-0044 1-OI75 1-0302 -9796 ■9933 1-0067 1-0197 I -0325 56° 60 I -0121 I -0238 i^o3S3 I -0464 1-0572 I 0141 I -0259 1^0374 1-0485 l'OS94 I -0162 I -0280 1^0395 1-0507 I 0616 I •0183 I -0302 I -0417 I -0529 10205 1*0323 10439 1-0551 1-0660 I -0226 1-0344 I -0460 1-0573 1-0683 I -0247 1-0367 I -0482 1^0595 1 -0705 I -0269 1-0389 1-0505 I -0618 I -0727 I -0291 I -041 1 1-0527 1-0640 I -0750 ro3i3 I 0433 I -0550 I -0663 10773 1-0336 I -0456 1-0573 I -0686 I -0797 1-0358 I -0478 1-0596 1-0709 1 -0820 I -0381 I -0501 I -0619 10733 1 -0844 I -0404 1-0524 1 -0642 1-0757 I -0868 1-0427 1 -0548 10666 1 -0780 I -0892 I -0450 1-0571 I 0689 1-0804 1-0916 61° 62 1-0677 1-0779 1-0877 1-0699 I -0801 10899 I -0721 I -0823 I -0922 I -0743 1-0845 1-0944 1-0766 1-0868 1 -0967 1-1063 1-1156 1-0788 1-0891 I -0990 I -1086 1-1179 I -081 1 I 0914 I -1013 I 'IIIO 1-0834 1-0937 I -1037 I-II33 1-1226 1-0857 1 -0960 1-1060 1-1157 1 -0880 1 0984 1 -1084 i-ii8i 1 -0904 i-ioo8 I -1108 1-1205 I -0928 1-1032 1-1132 1-1230 1-0951 1-1056 1-1157 1-1254 1-0976 1 1080 11181 I -1279 i-iooo 1-1105 I -1206 1-1304 I -1024 I-I129 1-1231 1-1329 ^4 65 I 0972 I -1064 1-0995 I -1087 I -1017 I -1 109 I -1040 1-1132 I -1203 I -1250 I -1274 1-1289 1-1323 1-1348 1^1373 1-1398 1-1424 35' 10 20'. 3d 4d 5d 36 id 2d 3d 4d 5d 37' id 20 3d When the Declination is North the sign is - . When the Declination is South the sign is + 103 ALT-AZIMUTH TABLES. Under Altitude In head-line, and abreast of Latitude In marg-in, take out the tabular quantity and mark It + or according as the Latitude is N. or S. Lat. TRUE ALTITUDE. 37 3d 40 50 38 10' 20' 30 40' 50 39 10 20' 30 40 50' 40 0° •0000 •0000 •0000 •0000 •0000 ■0000 •0000 •0000 ■0000 •0000 •0000 •0000 ■0000 ■0000 0000 •0000 I •0134 •0135 •0136 •0136 ■0137 •0138 •0139 •0140 •0140 •0141 •0142 •0143 •014; •OI4S •0146 •0146 2 ■0268 ■0269 •0271 •0273 ■0274 •0276 •0278 •0279 ■0281 •0283 •0284 •0286 •0288 •0289 •0291 •0293 3 •0402 ■0404 •0406 •0409 •04 n •0414 •0416 ■0419 •0421 ■0424 ■0426 •0429 •0431 •043 1 •0437 •0439 4 •0535 •0538 •0542 •054s •0548 •0552 •0555 •0558 ■0562 •0565 •0568 ■0572 •057s ■0578 •0582 •0585 5 •0669 •0673 ■0677 ■0681 •0685 •0689 ■0693 •0697 ■0702 •0706 •0710 •0714 •0718 •0723 ■0727 •0731 6' •0802 •0807 ■0812 •0817 •0822 ■ •0827 •0831 •0836 ■0841 •0846 •0852 •0857 ■0862 •0867 •0872 •0877 I ■0935 •0941 •0946 ■0952 •0958 •0964 •0969 ■0975 ■0981 •0987 •0993 •0999 •1005 •Id I •1017 •1023 •1068 ■1074 •1081 •1087 •1094 •I 100 ■I 107 ■1114 ■1120 •I 1 27 •1134 •I 140 •I 147 •I 154 ■1161 •1168 9 •1200 •1208 •121S ■1222 •1230 •1237 •1244 ■1252 •1259 ■1267 ■1274 •1282 •1290 •1297 •130S •1313 10 •1332 •1340 •1349 •1357 •1365 •1373 •1381 •1390 •1398 '1406 •1415 •1423 •1431 •1440 •1448 ■1457 11° •1464 •1473 •1482 •1491 •1500 •1509 ■1518 •1527 •1536 •1545 •1554 •1564 •1573 •1582 •1592 •1601 12 •1595 •1605 •1615 ■1624 •1634 •1644 •1654 •1664 ■1674 •1684 •1694 •1704 •1714 •1724 •1734 •1745 13 ■1726 ■•^37 ■1747 •1758 •1768 ■1779 •1789 •1800 •1811 •1822 •1832 •1843 •1854 •1865 •1876 ■1888 14 •1856 •1S68 ■1879 ■1890 ■1901 •1913 ■1924 •1935 •1947 ■1959 •1971 ■1982 •1994 ■2006 •2018 •2030 IS •1986 •1998 ■2010 •2022 •2034 •2046 ■2059 ■2071 •2083 •2096 ■2108 •2121 •2134 •2146 •2159 •2172 i6° ■21 15 •2128 ■2141 •2154 •2166 •2179 •2193 •2205 •2219 •2232 •2245 •2259 •2272 •2286 •2299 •2313 '2 ■2243 •2257 ■2271 ■2284 •2298 ■2312 ■2326 •2340 •2354 •2368 •2382 •2396 •2410 •2424 ■2439 ■2453 i8 •2371 •238s ■2400 •2414 •2429 ■2443 •2458 •2473 ■2488 ■2502 •2517 ■2532 •2547 •2562 •2578 •2593 19 ■2498 •2513 ■2528 •2544 '^^it •2574 ■2590 ■2605 •2621 •2636 ■2652 •2668 •2684 •2700 ■2716 •2732 20 •2624 •2640 •2656 •2672 •2688 •2704 •2721 •2737 •2753 •2770 •2786 •2803 •2819 ■2836 •2853 •2870 21° •2750 •2766 •2783 ■2800 •2817 •2834 ■2851 ■2868 •2885 ■2902 •2919 •2937 •2954 •2972 •2989 •3007 22 •2874 ■2892 ■2909 •2927 ■2944 ■2962 ■2980 ■2998 ■3016 ■3034 •3052 •3070 •3088 •3106 •3125 ■3143 23 ■2998 •3016 ■3034 •3053 •3071 •3090 ■3108 ■3127 •3145 •3164 •3183 ■3202 •3221 •3240 •3259 •3279 24 •3121 •3140 •3159 •3178 •3197 ■3216 •3235 •3255 •3274 •3294 •3313 •3333 •3353 •3373 •3393 •3413 25 •3243 •3262 ■3282 •3302 •3322 •3342 •3362 •3382 ■3402 •3422 •3443 •3463 •3484 •3504 •3525 •3546 26° •3364 •3384 •3404 •3425 •3446 ■3466 •3487 •3508 •3529 •3550 •3571 ■3592 •3614 •3635 •3657 •3678 27 •3484 •3505 •3526 ■3S47 •3568 •3590 •36 1 1 •3633 •3655 •3676 •3698 ■3720 •3742 3765 •3787 •3809 28 •3602 •3624 •3646 ■3668 •3690 •3712 •3734 •3757 •3779 •3802 •3824 •3847 •3870 •3893 •3916 ■3939 29 •3720 '^li^ •3765 ■3788 •381 1 •3833 •3856 •3879 •3903 •3926 •3949 •3973 •3996 •4020 •4044 •4068 30 ■3837 •3860 •3883 •3906 •3930 •3953 •3977 •4001 •4025 •4049 •4073 •4097 •4122 •4146 •417 1 •4195 31° '.i?^l •3976 ■4000 •4024 •4048 •4072 •4097 •4I2I •4146 •4171 •4196 •4221 •4246 •4271 •4296 •4322 32 ■4060 •4091 •4115 •4140 •4165 •4190 •421S •4240 •4266 •4291 •4317 •4342 •4368 •4394 •4420 ■4447 33 •4179 •4204 ■4230 •4255 •4281 •4306 ■4332 •4358 •4384 ■4410 •4437 •4463 •4490 •4516 •4543 ■4570 34 ■4291 •4317 : •4343 •4369 •4395 •4422 •4448 •4475 •4501 •4528 •4555 •4582 ■4610 •4637 •4665 ■4692 35 •4401 ■4428 •4454 ■4481 •4508 •4535 •4562 •4590 •4617 •4645 •4672 •4703 •4728 •4756 •4785 •4813 36° •4510 '"^1.^1 •4565 •4592 •4620 •4648 •4675 •4703 •4732 •4760 •4788 •4817 •4845 •4874 •4903 •4932 ^l ■4618 •4646 •4674 •4702 •4730 •4759 •4787 •4816 •4844 •4873 •4902 ■4932 •4961 •4990 •5020 ■sow 38 ■4724 ■4753 •4781 •4810 •4839 •4868 •4897 •4927 •4956 •4986 ■5015 ■5045 •5075 •5105 •5136 ■5166 39 •4829 •4858 •4887 •4917 •4946 •4976 •5006 •5036 •5066 •5096 •5127 •5157 •5188 •5219 •5250 •5281 40 ■4932 •4962 •4992 •5022 •5052 •5083 •5113 •5144 •5174 ■5205 •5236 ■5267 ■5299 •5330 •5362 •5394 41° •5034 •5065 •5095 ■5126 •5156 ■5187 •5219 •5250 •5281 ■5313 •5344 •5376 •5408 ■5440 '5473 •5505 42 ■5134 ■5165 ■5197 ■5228 •5259 •5291 •5323 ■5354 ■5386 •5419 ■5451 •5483 •5516 •5549 •5582 ■')6i5 43 ■5233 ■5265 •5296 ■5328 •5360 •5393 •5425 •5457 •5490 •5523 •5556 •5589 ■5622 •5655 •5689 ■5723 44 ■5330 •5426 ■5362 •S39S •5427 •5460 •5493 •5526 •5559 •5592 •5625 •5659 •5692 •5726 •5760 •5795 •5829 •5933 45 •5459 •5491 •5525 •5558 •5591 •5625 •5658 ■5692 •5726 •5760 •5794 •5829 •5864 •5898 46° •5520 •5612 •5553 ■5646 ■5586 •5680 •5620 •5654 •5748 •5688 •5783 •5722 •5817 •5756 •5852 •5791 •5887 •5825 •5922 •5860 •5958 •5895 "5993 ;S93o •5965 •6065 ■6162 •6000 •6101 •6036 •6137 •6236 •6333 •6428 •5702 '^Pl '^V •5806 •5841 •5876 ■591 1 •5947 •5982 ■6018 ■6054 •6090 •6126 ■6199 •629s •6390 49 SO ■5791 ■5878 ■5826 •5914 •5861 •5949 ■5896 •5985 •5932 •6021 •5967 •6057 ■6003 ■6093 ■6039 ■6130 •6075 •6166 •6112 •6203 •6148 ■6240 ■618s •6277 '6221 •63 1 5 •6258 •6352 51° 52 S3 54 55 •5963 •6047 •6128 •6208 ■6286 •5999 •6083 •6165 ■6245 ■6324 •603s •6120 ■6202 •6283 ■6362 •6072 •6157 •6240 •6321 •6400 ■6108 •6194 •6277 •6359 •6438 ■6145 •6231 •6315 •6397 ■6477 ■6182 •6268 •6353 ■643s ■6516 ■6219 ■6306 •6391 ■6474 •655s •6256 •6343 •6429 ■6512 •6594 •6293 •6381 •6467 •6633 •6331 •6419 •6506 •6368 •6457 •6545 ■6630 ■6713 •6406 •6496 •6583 •6669 •6753 •6444 •6534 •6623 •6709 •6793 •6483 •6573 ■6662 •6748 ■6833 ■6521 •66i2 •6701 •6788 •6874 56° i •6361 ■643s •6507 •6577 •664s •6400 ■6474 •6547 •6617 •6685 •6438 •6513 •6586 •6657 •6726 •6477 •1il6 •6697 ■6766 •6516 ■6592 •6665 •6737 ■6807 11^5 ■6631 ■6705 ■6778 ■6848 •6594 •6671 •6746 •6818 ■6889 •6634 •67 1 1 •6786 •6859 •6930 •6674 •6751 •6827 ■6900 •6971 •6713 •6791 •6867 •6941 •7013 •6753 •6832 •6908 •6983 7055 •6794 •6873 ■6949 •7024 •7097 •6834 •6913 •6991 •7066 •7139 •6875 •6955 •7032 •7108 •7181 ■6915 •6996 •7074 •7150 •7224 •6956 •7037 7116 •7192 •7267 61° 62 65 •67 1 1 ■6775 •6837 •6897 •6954 •6752 ■6816 •6878 . •6996 , •6792 •6857 ■6920 •6980 •7038 ■6833 •6898 ■6961 ■7022 •7081 •6874 •6940 •7003 •7064 •7123 •6916 •6981 ■7045 •7107 ■7166 •6957 •7023 •7087 •7149 •7209 •6999 ■7065 •7130 ■7192 •7252 •7041 •7108 •7172 •723s •7296 •7083 ■7150 •7215 ■7278 •7339 •7125 •7193 •7258 •7322 •7383 •7167 •7235 ■7301 •7365 •7427 •7210 •7278 ■734S •7409 •7471 •7253 •7322 •7389 •7453 •7515 •7296 •7365 •7432 •7497 •7560 •7339 •7409 •7476 •7542 •760s 37 30 40' 50' 38" 10' 20 30' 40' 50' 39 10 20' 30' 40' 50' 40" When the Latitude is North the sign is + When the Latitude is South the sign is - ALT-AZIMUTH TABLES. 104 Under Altitude and abreast of Declination, take out the tabular quantity and mark it + or — . according as Declination is S. or N. Add Algebraically E and F. Dec- lina- tion. TRUE ALTITUDE, 0" I 2 3 4 5 6° 7 8 9 10 11° 12 13 14 IS i6° % 19 20 21° 22 23 24 25 26° 27 28 29 30 31° 32 33 34 35 36° H 38 39 40 41° 42 43 44 45 46° 47 48 49 50 Si° 52 S3 54 55 56° 58 60 61° 62 64 65 37 30 •0000 •0220 •0440 •0660 •0879 •1099 •1318 ■1536 •1754 •1972 ■2189 ■2405 •2621 ■283s •3049 ■3262 •3474 •3685 •389s •4104 •431 1 •4517 ■4722 ■4925 •5127 ■5327 ■5526 •5722 ■5918 •6111 ■6302 •6492 •6679 •686s •7048 ■7230 •7409 •7586 •7760 •7932 ■8102 •8269 •8434 •8596 ■8756 •8913 •9067 •9219 ■9367 ■9513 ■9656 ■9796 •9933 I 0067 I '0197 I 0325 I -0450 10571 I -0689 I -0804 1-0916 I '1024 I-II29 I 1231 1-1329 I -1424 40 50 3730 ■0000 -0220 •0441 -066 1 •0881 •iioi •1321 •1540 -1758 -1976 -2194 ■2410 -2627 •2842 •3056 •3270 ■3482 ■3694 •3904 ■41 1 3 •4321 •4527 •4732 •4936 •5138 •5339 •5538 •5735' •5931 •6125 •6316 -6506 -6694 -6880 •7064 -7246 •7425 •7603 •7778 ■7950 8288 •8453 •8616 •8776 ■8933 -9087 •9239 -9388 ■9534 -9677 -9818 •9955 I -0089 I -0220 I 0348 I -0473 10595 10713 I -0829 I 0940 I -1049 I IIS4 I -1256 I -1354 I -1449 38 10 40 -0000 •0221 -0442 •0663 ■0883 •I 104 ■1323 •1543 •1762 -1981 ■2199 ■2416 -2632 •2848 •3063 •3277 •3490 •3702 •3913 •4122 •4330 •4537 •4743 ■4947 •5150 ■5351 ■5550 •5748 •5944 •6138 •6331 ■6521 •6710 -6896 •7080 •7262 ■7442 -7620 ■7795 •7968 •8139 ■8307 -8472 •863s •8795 ■8953 -9108 •9260 -9409 ■9556 •9699 •9840 •9977 I 0112 I 0243 1-0372 I -0497 I 0619 10738 1-0853 I 0965 I -1074 I -1 179 I-I28I 1-1380 I -1475 50 -0000 -0221 •0443 •0664 -0885 -1106 •1326 •1547 -1766 •1985 -2204 -2421 •2638 •2855 •3070 •3284 •3498 •3710 •3921 -4132 ■4340 •4548 ■4754 •4958 •5162 •5363 •5563 -5761 •5958 -6152 ■6345 -6536 -6725 ■6912 •7096 •7279 7459 •7637 •7813 •7986 •8157 •8326 •8491 ■8655 -8815 -8973 •9129 -9281 ■9431 •9577 -9721 •9862 I 0000 I 0135 I -0267 I ^0395 1 0521 I 0643 I -0762 I 0878 I 0990 I -1099 1-1205 1-1307 1-1406 1-1501 20 30 38 -0000 -0222 -0444 -0666 -0887 -1109 •1330 •1550 -1770 •1990 -2209 -2427 •2644 •2861 ■3077 •3292 •3506 •3719 •3930 •4141 •4350 •4558 •4765 •4970 •5173 •5375 •5576 •5774 -5971 -6166 ■6360 •6551 -6740 •6927 -7112 7295 •7476 •7655 •7831 -8004 -8176 •834s ■85 1 1 -8674 •8835 •8994 ■9149 -9302 ■9452 •9599 ■9743 -988s 1-0023 1 0158 I "0290 I -0419 1^0545 I -0667 1-0786 I -0902 1-1015 I-II24 1-1230 ri333 IT432 1-1527 ■oooo ■0222 •0445 -0667 10 •1333 •1554 ■1774 •1994 -2214 ■2432 ■2651 •2868 •3084 •3300 •3514 ■3727 •3939 •4150 •4360 •4569 •4776 •4981 •5185 •5388 ■5589 •5788 •5985 •6i8i ■6374 •6566 ■6756 •6943 -7129 •7312 •7493 ■7672 •7849 •8023 •8194 -8364 •8530 -8694 •8856 -9014 ■9170 -9324 ■9474 ■9621 -9766 -9907 I -0046 1-0181 1-0314 I 0443 I 0569 I -0692 I -081 1 I 0927 I -1040 i'ii50 1-1256 I -1359 I -1458 i^i554 40 20 -0000 •0223 -0446 •0669 0891 •1114 •1336 ■ISS7 •1778 •1999 -2219 •2438 -2657 ■2874 -3091 -3307 ■3522 ■3736 •3949 -4160 ■4370 ■4579 ■4787 •4993 ■5197 ■5400 •5601 •5801 ■5999 •6195 •6389 •6581 -6771 ■6959 7145 ■7329 75" -7690 •7867 •8041 •8213 ■8383 ■8550 •8714 -8876 ■9035 •9192 •9345 -9496 •9644 ■9788 ■9930 I 0069 I -0205 1-0337 I -0467 I -0593 I -0716 I -0836 I -0953 I -1066 1-1176 I -1282 1-1385 1-1485 1-1581 -0224 •0447 -0670 ■0893 -1116 •1339 -1561 -1782 •2004 -2224 •2444 •2663 -2881 -3098 •3315 •3530 •3745 •3958 •4170 -4380 -4590 •4798 •5004 -5209 •5413 ■5614 •5814 •6013 -6209 -6404 •6596 -6787 •6975 •7162 •7346 -7528 -7708 •7885 ■8060 •8232 •8402 -8570 •8735 50 30 -9056 -9213 •9367 -9518 -9666 ■9811 •9953 I -0092 I -0229 I -0361 1-0491 I -0618 I -0741 I -0861 I -0978 I -1092 I -1202 1-1308 1-1412 1-1511 I -1608 0224 ■0448 •0672 ■0895 •1119 •1342 ■1564 •1787 -2008 •2229 •2449 •2669 •2888 •3106 •3323 •3538 •3753 •3967 •4179 •4391 •4601 ■4809 •5016 •5221 •5425 •5628 •5828 -6027 ■6224 •6419 •6612 -6803 •6992 •7179 7363 •7546 •7726 •7903 -8079 -8252 39 -8590 •875s ■8918 •9077 •9234 •9389 •9540 40 ._ •9834 •9977 I 01 16 I 0252 I -0386 I -0516 I -0643 I -0766 1-0887 I -1004 I-III8 1-1228 I-I335 1-1438 1-1538 I •1635 •0000 -0225 ■0449 -0673 -0898 ■II2I -1345 ■1568 •1791 -2013 •2234 ■2455 •2675 •2895 ■31 13 ■3330 ■3547 -3762 •3976 -4189 -4401 -461 1 •4820 ■5028 •5234 ■5438 •5641 -5842 •6041 •6238 -6434 •6627 -6819 -7008 -7195 7381 ■7563 •7744 -7922 10 50 -8271 ■8442 •8610 ■8776 •8939 •9099 -9256 •9411 •9562 -971 1 •9857 I -0000 1-0140 I -0277 I -0410 I -0541 I -0668 I -0792 1-0912 I -1030 I -1 144 I -1254 1-1361 1-1465 1-156S 1-1662 39 20 30 •0000 •0225 •0450 •0675 -0900 •1124 -1348 •1572 •1795 -2018 -2240 -2461 -2682 -2901 ■3120 •3338 •3555 •3771 ■3986 •4199 •4411 •4622 ■4832 •5040 ■5246 •5451 •5654 •5856 ■6055 ■6253 •6449 -6643 •6835 •7025 -7212 7398 •7581 ■7762 7941 -811 7 -8291 •8462 •8630 •8796 -8960 -9120 •9278 •9433 •9585 •9734 •9880 1 -0024 I -0164 I 0301 1-0435 1-0565 I -0693 1-0817 I 0938 I -1056 1-1170 I-I28I 1-1388 I -1492 I -1593 1-1690 •0000 -0226 -0451 -0677 -0902 •1127 -1351 •1576 -1799 -2022 •2245 •2467 •2688 -2908 -3128 •3346 •3564 •3780 •3995 •4209 •4422 •4633 •4843 •5052 •5259 •5464 •5668 •5870 •6070 •6268 -6464 ■6659 ■6851 •7041 -7230 •7416 -7599 •7781 •7960 •8136 -8310 40 •8651 -8817 •8981 •9142 ■9300 •9455 •9608 •9757 •9904 I -0048 I -0188 I -0325 I -0460 I -0591 1-0718 I -0843 I -0964 I -1082 I -1 197 1-1308 1-1415 1-1520 I -1620 1-1717 10 •0000 -0226 ■0452 -0678 -0904 •1130 •1355 •1579 •1804 -2027 -2250 -2473 ■2694 -2915 •3135 ■3354 -3572 •3789 -4005 -4219 •4432 •4644 •4855 •5064 •5271 •5477 -5681 •6084 -6283 •6480 -6675 •6868 -7058 -7247 -7433 -7618 7799 -7979 -8156 •8330 -8502 -8672 20 -9003 -9164 9322 •9478 •9631 •9781 ■9928 I -0072 I -0212 I -0350 I -0485 I -0616 I -0744 I 0869 I -0990 1-1109 I -1223 I -1335 1-1443 I -1547 1-1648 1-1745 50 -0000 -0227 ■0453 -0680 -0906 -1132 •1358 •'583 -1808 -2032 -2256 -2479 -2701 -2922 •3143 ■3362 •3581 •3798 •4014 •4229 ■4443 •4656 •4866 •5076 •5284 •5490 •5695 •5898 •6099 -6298 -6495 ■6691 •6884 •7075 •7264 7451 -7636 •7818 -7998 ■8175 •8350 •8523 •8693 •8860 -9024 •9186 -9345 -9501 •9654 -9804 •9952 I -0096 1 -0237 1^0375 1-0510 1 -0641 1-0770 1 0895 1-1017 fii35 1-1250 1-1362 1-1470 1-1575 1-1676 1-1774 •0000 •0227 •0454 -0682 -0908 •"35 •1361 •1587 •1812 •2037 -2261 •2485 •2707 -2929 •3150 •3370 •3589 -3807 •4024 •4240 •4454 •4667 •4878 •5088 •5297 •5503 •5709 •5912 ■6114 •6313 •65 1 1 •6707 -6901 •7092 •7282 •7469 •7654 •7837 -8017 -819s ■8371 ■8543 -8714 -8881 •9046 •9208 •9367 •9524 •9677 •9828 ■9976 I -0120 I -0262 I -0400 1^0535 I -0667 1 -0795 1 -0921 1 -1044 1-1162 1-1278 1-1390 I- 1498 1-1603 I -1704 I -1802 30 40 40 ■0000 -0228 •0456 ■0683 ■0911 ■1138 •I36S -1591 •1817 -2042 -2267 •2491 -2714 -2937 •3158 •3379 •3598 •3817 •4034 •4250 -4465 ■4678 •4890 -5101 •5310 •5517 ■5723 •5926 -6129 -6329 •6527 -6723 •6918 -7110 -7300 •7488 7673 7856 •8037 -8215 •8391 •8564 •8735 -8903 -9068 •9231 •9390 •9547 •9701 •9852 I -0000 I -0145 I -0287 1 -0425 1-0561 I -0693 1 -0822 I -0948 1-1070 1-1190 1-1305 1-1417 1-1526 1-1631 1^1733 1-1831 50 40 When the Declination is North the sign is - . When the Declination is South the sign is -f . 105 ALT-AZIMUTH TABLES. Under Altitude In head-line, and abreast of Latitude in margin, take out the tabular quantity and mark it + op according as the Latitude is N. or S. Lat. TRUE ALTITUDE. 40' 10' 20 30' 40' 50' 41 10' 20' 30 40 50' 42° 10 20' 30' 0° •0000 •0000 ■0000 0000 •0000 •noon •0000 •0000 ■0000 •0000 •0000 •0000 •0000 •0000 ■0000 •0000 I •0146 •0147 •0148 •0149 •0150 •0151 •0152 •0153 ■0154 ■0154 •0155 •0156 •0157 •0158 •0IS9 •0160 2 •0293 •0295 •0296 •0298 •0300 ■0302 •0303 •0305 ■0307 •0309 . ■03 1 1 •0312 •0314 ■0316 •0318 •0320 3 •0439 •0442 •0444 •0447 ■0450 •0452 •0455 ■0458 •0460 •0463 •0466 •0468 •0471 •0474 •0477 •0480 4 ■0SS5 •0589 •0592 ■0596 •0599 •0603 •0606 •0610 •0614 ■0617 •0621 •0624 ■062S •0632 •0635 •0639 5 •0731 •0736 •0740 •0744 •0749 •0753 ■0758 0762 •0767 •0771 •0776 •0780 •0785 •0789 •0794 ■0799 6° ■0877 •0882 •0888 •0S93 •0898 •0903 •0909 •0914 •0919 ■0925 •0930 •0936 •0941 ■0947 •0952 •0958 7 ■1023 •1029 ■103s •1041 •1047 •1053 ■1059 •1066 •1072 •1078 •1085 1091 •1097 •1104 •I 1 10 ■1117 8 •I 168 •1175 •1182 •1189 •1196 •1203 ■1210 •1217 •1224 ■1231 ■1239 •1246 ■1253 ■1260 •1268 •1275 9 ■1313 •1320 •1328 ■1336 •1344 ■1352 ■1360 •1368 •1376 •1384 ■1392 •1400 •1409 •1417 •1425 •1433 10 •I4S7 •1466 •"474 ■1483 •1492 •1501 •1510 •1518 •1527 •1536 ■IS4S •ISS4 ■1564 •1573 •1582 •1591 n° •1601 ■161 1 •1620 ■1630 •1639 •1649 ■1659 ■1668 •1678 •1688 •1698 •1708 •1718 •1728 ■1738 •1748 12 •1745 •I75S •1765 •1776 •1785 •1797 ■1807 •1818 ■1829 •1839 •1850 ■i86i •1872 •1883 •1894 •1905 13 •1888 •1899 •1910 •1921 •1933 •1944 •1955 •1967 •1979 •1990 •2002 •2014 •2025 •2037 •2049 •2061 14 •2030 •2042 •2054 ■2066 •2078 •2091 •2103 •2115 ■2128 •2140 ■2153 •2166 •2178 ■2191 •2204 •2217 15 •2172 ■2185 •2198 •2211 ■2224 ■2237 •2250 •2263 •2276 •2290 ■2303 •2317 •2330 •2344 •2358 •2372 i6° •2313 •2327 •2340 •23S4 •2368 •2382 •2396 •2410 •2424 •2439 •2453 ■2467 •2482 •2496 •25 1 1 •2526 17 •2453 •2468 •2482 •2497 ■2512 •2527 •2542 •2557 •2572 •2587 •2602 •2617 •2633 •2648 •2663 •2679 i8 •2593 •2608 •2624 •2639 ■265s •2671 •2686 •2702 •2718 •2734 ■2750 •2766 •2782 •2799 ■281S •2832 19 •2732 ■2748 ■2764 .2781 •2797 •2814 •2830 •2847 •2864 •2880 •2897 •2914 •2931 •2949 ■2966 •2983 20 •2870 •2887 •2904 •2921 •2938 •2956 •2973 •2991 •3008 •3026 ■3044 ■3062 •3080 ■3098 •31 16 •3134 21° •3007 •3025 •3043 ■3061 •3079 •3097 •3115 •3134 ■3152 ■3171 ■3189 •3208 •3227 •3246 •3265 •3284 22 •3 '43 •3162 ■3181 •3199 •3218 •3237 •3256 •3276 ■3295 ■3314 •3334 •3353 •3373 •3393 •3413 •3433 23 •3279 •3298 •3318 •3337 ■3357 •3377 ■3397 •3417 •3437 ■3457 •3477 •3498 •3518 •3539 •3560 •3580 24 •3413 •3433 •3453 •3474 •3494 •3515 •3536 •3557 ■3577 ■3599 •3620 •3641 •3662 •3684 '3705 •3727 25 •3546 •3567 •3588 •3610 •3631 •3652 •3674 ■3695 ■3717 - ^3739 •3761 •3783 •3805 •3828 •3850 •3873 26° •3678 •3700 •3722 •3744 •3766 •3788 ■38 1 1 ■3833 ■3856 ■3878 •3901 •3924 •3947 ■3970 •3994 •4017 27 •3809 •3832 •3855 ■3877 •3900 •3923 •3946 •3970 ■3993 •4017 •4040 ■4064 •4088 •41 12 •4136 •4160 28 •3939 •3963 •3986 •4010 •4033 ■4057 ■4081 ■4105 •4129 ■4154 •4178 ■4202 ■4227 •4252 •4277 •4302 29 •4068 •4092 ■41 16 ■4141 ■4165 •4190 ■4214 ■4239 •4264 •4289 ■4314 •4340 ■4365 •4391 •4417 •4442 30 ■419s •4220 •4245 •4270 •4296 •4321 •4346 •4372 ■4398 •4424 •4450 ■4476 •4502 •4528 •4555 ■4582 31° ■4322 •4347 •4373 •4399 •4425 •4451 ■4477 •4504 •4530 •4557 •4583 ■4610 •4637 •4665 •4692 •4719 . 32 ■4447 •4473 •4499 ■4526 •4553 •4580 ■4607 •4634 •4661 •4688 •4716 •4744 •4771 •4799 ■4828 •4856 33 •4570 •4597 •4624 •4652 •4679 •4707 •4734 •4762 •4790 •4819 •4847 ■487s •4904 •4933 •4962 •4991 34 •4692 •4720 •4748 •4776 •4804 •4833 •4861 ■4890 •4918 •4947 •4976 ■5006 •S°35 •5065 •5094 •S'24 35 •4813 •4841 •4870 •4899 •4928 •4957 •4986 •5015 •5045 •507s •5104 ■5134 •5165 •519s •5225 •5256 36° ■4932 ■4961 •4991 •5020 •5050 •50S0 ■5110 •5140 •5170 •5200 •5231 ■5262 ■5292 ■5323 •S3SS •5386 37 ■5050 ■5080 •5110 ■5140 •5170 •5201 •5231 ■5262 ■5293 •5324 ■5356 •5387 ■5419 •5451 •5482 •5515 38 5166 •5197 •5227 •5258 ■5289 ■5321 •5352 ■5383 ■5415 •5447 •5479 ■55" ■5543 •5576 •5609 •5641 39 •5281 •5312 •5343 ■5375 •5407 ■5439 ■^47! •5503 ■5535 •5568 ■5600 •5633 ■5666 •5700 •5733 ■5767 40 •5394 •5426 ■5458 ■5490 •5522 •5555 •5588 •5621 •5654 •5687 •5720 •5754 ■5788 ■5822 ■5856 •5890 41° ■5505" '^V-l ■5|^° •5603 •5636 •5670 •5703 •5737 •5770 •5804 •5838 •5873 ■5907 ■5942 5977 •6012 42 ■56 IS •5648 •5681 •57 1 5 •5749 •5783 •5817 ■5851 ■588s •5920 •5955 •5990 •6025 •6060 •6096 •6131 43 •5723 •5757 •5791 •5825 •5859 •5894 •5929 ■5963 ■5999 •6034 ■6069 •6105 •6141 •6177 •6213 •6249 44 •5829 ■5863 •5898 "5933 •5968 ■6003 6039 •6074 ■61 10 ■6146 ■6182 ■6218 ■6255 •6291 •6328 •6442 •6365 ■6479 45 •5933 •5968 •6004 •6039 •607s ■61 1 1 •6147 •6183 ■6219 •6256 •6293 ■6330 ■6367 ■6404 46° ■6036 ■6072 •6108 •6144 •6180 •6216 •6253 ■6290 •6327 •6364 •6402 •6439 •6477 •6515 •6553 ■6592 % t'^l ■6173 ■6210 •6246 ■6283 •6320 •6358 •639s ■6433 ■6470 •6508 ■6547 ■6585 •6624 •6663 ■6770 •6702 ■6236 ■6273 -6310 •6347 ■^3^5 •6422 •6460 •6498 ■6536 •6575 •6613 •6652 ■6691 •6731 •6810 49 50 6333 6428 ■6370 •6466 •6408 •6504 •6446 ■6543 ■6484 6581 ■6522 ■6620 •6561 ■6659 ■6599 •6698 ■6638 ■6738 ■6677 •6777 •6716 •6817 ■6756 ■6857 •679s •6897 s ■6875 •6979 •6916 •7020 51' 52 S3 54 55 •6521 •6612 •6701 •6788 •6874 •6560 •6651 ■6829 ■6914 •6598 •6691 •6781 •6869 •6955 ■6637 ■6730 •6821 •6910 ■6996 •6677 •6770 ■6861 ■6950 •7038 ■6716 ■6810 •6902 •6991 •7079 •6756 ■6850 ■6942 ■7033 •7121 •6795 •6890 ■6983 •7074 ■7163 ■683s ■6931 ■7024 •7116 ■7205 ■6876 •6972 ■7066 •7158 ■7247 •6916 ■7013 •7107 •7200 ■7290 ■6957 ■7054 •7149 ■7242 •7333 ■6997 ■709s •7191 •7284 •7376 •7038 •7137 •7233 •7327 •7419 ■7080 7179 •7276 ■7370 •7462 •7121 •7221 •7318 •7413 ■7506 56° 12 ■6956 •7037 ■7116 •7192 •7267 ■6998 •7079 •71^8 ■723s •7039 •7121 •7200 •7278 •7081 ■7163 •7243 •7321 ■7122 •7364 •7164 •7248 •7329 •7408 •7207 •7290 •7372 ■7451 •7249 •7333 ■7415 •7495 •7292 •7377 •7459 ■7539 ■7335 •7420 ■7503 ■7584 •7378 •7464 ■7547 •7628 ■7421 ■7507 ■7591 ■7673 •746s •7SSI •7636 •7718 7508 •7681 ■7763 ■7SS2 ■7640 •7726 •7809 •7597 •768s •7771 ■7854 •7310 •7353 •7397 •7440 •7484 ■7528 •7573 •7617 •7662 ■7707 •7752 ■7798 •7843 •7889 •7936 6i» 62 6s •7339 ■7382 •7426 •7470 •7514 ■7558 •7603 •7648 ■7693 •7738 •7783 •7829 •7875 •7921 •7968 •8014 •7409 •7476 •7453 ■7497 •7565 •7541 •7586 •7630 •7675 •7721 •7766 •7812 •7858 •7904 ■7950 ■7997 17 •8044 •8091 •7521 •7586 •765a ■7610 •7655 •7700 ■7745 •7791 ■7837 ■7883 ■7929 •7976 •8023 •8070 ■8117 ■8i6s ■7542 ■7605 'liK , 7676 •7722 •7767 ■7813 •7859 ■7905 ■7952 ■7999 •8046 •8093 •8140 •8188 •8236 •769s •7741 •7786 •7832 •7878 •7925 •7971 •8018 •806S ■81 13 •8160 •8208 •8256 ■830s 40' 10' 20 3d 40' 50 41 id 20' 3d 40' 50' 42° 10' 20' 30 When the Latitude is North the sign is + . When the Latitude is South the sign is >- . ALT-AZIMUTH TABLES. 106 Under Altitude and abreast of Deellnation, take out the tabular quantity and mark it + or — . according: as Declination is S. or N. Add Algebraically E and F. ripr- TRUE ALTITUDE. LI NA- TION 40° 10' 20 30 40 50 41 10 20 30 40 50' 42 10' 20 3d 0° •0000 •0000 -0000 -0000 •0000 •0000 •0000 -0000 -0000 -0000 -0000 •0000 -0000 -0000 -0000 ■0000 I •0228 ■0228 •0229 ■0230 -0230 •0231 -0231 •0232 -0232 •0233 •0234 •0234 •0235 •0235 •0236 -0237 2 •0456 •04S7 •0458 -0459 •0460 0461 -0462 •0464 -0465 ■0466 •0467 •0468 •0470 ■0471 •0472 -0473 3 •0683 •0685 •0687 -0688 -0690 -0692 -0693 -0695 •0697 •0699 -0701 -0702 -0704 •0706 •0708 -0710 4 •091 1 •0913 •0915 •0917 •0920 •0922 •0924 -0927 -0929 •0931 •0934 •0936 ■0939 •0941 -0944 •0946 5 •II38 •1141 •I 143 •1146 -1149 •1152 •"55 •1158 -1161 -1164 •I 167 •1170 •1173 •1176 •1179 •1182 6° •1365 •1368 -1371 -1375 -1378 •1382 -1385 •1389 -1392 •1396 •1399 •1403 •1407 •1410 -1414 •1418 ^8 •1591 -159s ■1599 •1603 •1607 •1611 -1615 ■1619 -1623 -1627 -1631 •1636 ■1640 •1644 •1649 •1653 •I8I7 •1821 •1826 •1830 •1835 •1839 -1844 •1849 •1853 •1858 •1863 ■1868 •1873 •1878 •1883 •188S 9 ■2042 •2047 ■2052 ■20S7 -2062 •2068 •2073 •2078 -2083 -2089 -2094 -2100 •2105 •21 11 •2116 -2122 10 •2267 ■2272 -2278 -2284 •2289 •2295 -2301 -2307 ■2313 -2319 •2325 •2331 •2337 -2343 •2349 -2355 11° •2491 •2497 •2503 -2509 •2516 •2522 -2528 •2535 -2541 •2548 •2554 -2561 -2568 ■2574 •2581 -25S8 12 •2714 •2721 -2727 -2734 -2741 -2748 •2755 -2762 -2769 ■2776 •2783 •2790 -2798 •2805 -2813 •2820 13 •2937 •2944 ■2951 ■2958 ■2966 -2973 •2981 •2988 •2996 •3004 -3011 •3019 -3027 -303s -3043 •3051 -3281 14 •3158 •3166 ■3174 •3181 •3189 •3197 ■3205 •3214 -3222 •3230 •3238 •3247 -3255 •3264 -3273 IS •3379 -3387 •339s •3404 •3412 •3421 -3429 •3438 •3447 •3456 •3465 •3474 -3483 •3492 -3501 •3510 16° •3598 •3607 •3616 •3625 •3634 •3643 •3652 •3662 -3671 -3680 •3690 •3699 ■3709 •3719 •3729 -3739 -3966 17 ■3817 •3S26 ■383s -3845 -3855 •3864 -3874 -3884 -3S94 •3904 •3914 •3924 -3934 •3945 ■3955 -4180 18 ■4034 •4044 •4054 -4064 •4074 -4084 ■4095 •4105 •41 15 -4126 •4 '37 •4147 -4158 •4169 •4191 •4416 •4639 19 20 •4250 •4260 ■4271 •4282 -4292 ■4303 ■4314 •4325 -4336 •4347 •4358 •4370 -4381 •4392 -4404 ■4465 •4476 •4487 -4498 •4509 •4520 •4532 •4543 -4555 •4567 •4578 •4590 ■4602 •4614 -4627 21° ■4678 ■4690 •4701 •4713 -4725 •4736 -4748 •4760 -4773 •4785 •4797 •4810 -4822 •4835 •4848 -5067 -5286 •4861 •5081 22 ■4890 •4902 ■4914 -4926 -4939 •4951 -4964 •4976 -4989 -5002 -5015 •5028 -5041 -5258 •5054 23 24 25 ■5IOI -■illS •5126 -5138 -5151 ■5'64 -5177 •5190 •5204 -5217 •5230 -5244 •5272 •5488 •5300 •IJSIO -5323 -553° ■5 336 -5349 ■5362 -5376 •5389 -5403 •5417 ■5431 -5445 -5459 -5473 •5502 •55 '7 •SSI7 •SS44 -5558 -5572 -5586 -5600 ■5614 ■5628 -5643 -5657 •5672 -5687 •5702 -5717 •5732 26° 29 30 •5723 ■5926 •6129 ■6329 ■6527 •S737 •5941 •6144 •6344 ■6543 -S7SI ■5956 -6159 •6360 ■6559 -5765 -5970 -6174 -6376 -6575 -5779 -5985 -6189 -6392 -6592 -5794 -6000 •6205 -6408 -6608 •5808 ■6015 -6221 -6424 -6625 •5823 -6031 •6236 -6440 -6642 •6046 -6252 ■6457 -6659 -6062 -6268 -6473 -6676 •5868 -6077 •6285 •6490 •6693 -5883 -6093 -6301 ■6507 •6711 •5899 •6109 -6317 -6524 -6728 •5914 •6125 -6334 •6541 -6746 •5930 •6141 -6351 •6558 •6764 •5946 -6158 ■6368 -6576 -6782 31° 32 33 34 35 ■6723 •6918 •7 1 10 •7300 •7488 •6740 -693s •7127 •7318 •7506 •6756 •6952 •714s -7336 •7524 -6773 •6969 -7162 -7354 -7543 •6790 ■6986 ■7180 -7372 •7562 -6807 •7004 -7198 -7391 •7581 -6824 •7021 •7217 -7409 •7600 -6842 -7039 -7235 •7428 -7619 •6859 •7057 •7253 •7447 •7639 ■6877 -7075 -7272 -7466 -7658 •6895 -7094 •7291 •7486 •7678 -6912 -7112 •7310 •7505 •7698 ■6931 •7131 •7329 •7525 -7718 -6949 •7150 -7348 -7544 -7739 •6967 •7168 •7368 •7564 •7759 -6986 -7188 •7387 ■7585 •7780 36° 39 40 ■7673 •7856 ■8037 •8215 ■8391 •7692 •7875 •8057 ■823s •8412 •771 1 ■7895 -8076 •8256 -8432 -7730 •7914 ■8096 •8276 -8453 •7749 -7934 -81 17 •8297 -8474 •7769 -7954 •8137 •8318 -8496 -7788 -7974 •8158 •8339 -8517 ■7808 •7994 •8178 ■8360 •8539 •7828 •8015 -8199 -8381 -8560 -7848 ■8035 -8220 ■8403 •8582 ■7868 -8056 -8242 •8424 -8605 •7889 ■8077 ■8263 -8446 •8627 ■7909 -8098 •8285 -8468 -8650 •7930 -8120 -8306 -8491 •8672 •7951 •8141 •8328 •8513 •8695 •7972 -8163 -8350 •8536 -8718 41° 42 43 44 45 •8564 •S73S Si ■9231 •8756 ■892s •9090 ■9253 -8606 -8778 ■8947 •9113 ■9276 •8628 -8800 •8969 -9135 -9299 -8649 -8822 -8991 •9158 -9322 •8671 -8844 -9014 •9181 -9346 -8693 -8866 -9037 -9204 -9369 •8715 •8889 •9060 •9228 •9393 -8737 ■891 1 -9083 -9251 -9417 •8760 -8934 •9106 -9275 •9441 -8782 •8957 •9130 •9299 •9466 ■8805 •8981 •9153 •9323 -9490 •8828 -9004 -9177 •9348 ■9515 •8851 -9028 ■9201 •9372 •9540 -8875 -9052 -9226 -9397 -956S -8898 -9076 •9250 -9422 -9591 46° 48 49 50 •9390 .•9S47 •9701 •9852 i-oooo -9413 •957 1 •9725 •9876 1-0025 -9437 ■9594 •9749 •9901 1-0049 •9460 -96 r 8 -9773 -9925 1-0074 -9484 •9642 •9797 •9950 I 0099 •9507 -9666 -9822 ■9975 I -01 25 -9531 -9691 -9847 1 -0000 1-0150 •9556 •9715 -9872 1-0025 10175 -9580 ■9740 •9897 1-0051 I -0202 -9605 -9765 •9922 I -0077 1-0228 •9629 •9790 -9948 1-0103 1-0255 -9654 •9816 -9974 1 0129 I -0281 -9680 -9841 1-0000 1-0156 1 0308 •9705 -9867 I -0026 1-0182 1^0335 ■9731 •9893 1-0053 I -0209 1-0363 -9757 -9920 1-0080 1-0236 1-0390 51° 52 S3 S4 55 I -0145 I 0287 10425 1-0561 1-0693 I -0170 I 0312 1-0451 1-0587 I -0719 I -0195 10337 10477 I 0613 I -0746 I -0220 I 0363 I -0503 I o639n 10773 1 -0246 I -0389 I -0529 1-0666 1 -0799 1-0271 I -041 5 1-0554 1 -0693 1-0827 1 -0297 1 0441 10582 1 -0720 1-0854 I 0323 1-0468 1 -0609 1-0747 1-0881 I -0350 1 -0495 I 0636 I -0774 1 0909 1-0376 1-0521 1 0663 1 -0S02 1-0937 1 -0403 I -0549 1-0691 I -0830 1 -0966 1 •0430 I -0576 I 0719 I -0858 1-0994 1 -0458 1 0604 10747 1-0886 1-1023 I -0487 I -0632 1-0775 1-0915 1-1052 1-0513 I -0660 I -0803 1-0944 I -1081 I -0541 I -0688 1 -0832 1-0973 I'lIlO 56° 1 I 0822 I -0948 I -1070 I "1 190 I 1305 1 -0849 1-0975 1-1098 1-1217 I -1333 I -0876 I -1002 III25 I -1245 1-1361 1-0903 I 1029 1-1153 1-1272 1-1389 I -0930 1-1057 1-1180 1-1301 1-1417 1-0957 1-1085 I 1208 I 1329 1-1446 1-0985 I-1I12 I -1237 11358 I -1475 1-1013 1-1141 I -1265 1-1386 1-1504 1-1041 1-1169 1-1294 1-1415 1-1533 1-1069 I -1198 1-1323 I -1445 1-1563 1-1098 1-1227 1-1352 1-1474 I -1593 I -1 127 1-1256 1-1382 1-1504 1-1623 1-1156 1-1285 1-1412 1^1534 1-1654 1-1185 1-1315 1-1442 1-1565 1-1684 ri2iS 1^1345 1-1472 1-1595 1-1715 I -1245 1-1375 1-1502 1-1626 1-1746 61° 62 6S i'i4i7 1-1526 I 1631 I -1733 1-1831 I -1445 I -1660 1-1762 i-i86o I -1474 1-1583 I -1689 1-1791 I -1889 1-1502 1-1612 1-1718 1-1820 1-1919 1-1531 1-1640 1-1747 1-1849 I -1948 1-1560 I 1670 1-1776 I -1879 1-1978 1-1589 11699 1-1806 I -1909 I -2009 1-1618 1-1729 1-1836 I -1939 1 2039 1-1648 1-1759 1-1866 I -1970 I -2070 1-1678 I -1789 1-1897 I -2001 I-2IOI I -1708 1-1820 1-1927 I -2032 1-2132 1-1738 1-1850 1-1958 I -2063 1-2164 1-1769 1-1881 1-1990 1 -2094 1-2196 11800 1-1912 I -2021 1-2126 I -2228 ri83i 1-1944 1-2053 1-2158 I -2260 1-1863 1-1976 1-2085 I -2191 1'2293 40' 10 20 30 40 50 41 10 20 30 40 50 42 10 20 30 _ When the Declination is North the sign is - . When the Declination is South the sign is + 107 ALT-AZIMUTH TABLES. Under Altitude In head-line, and abreast of Latitude in Margin, talie out the tabular quantity and mark it + or aecording as the Latitude is N. or S. Lat. TRUE ALTITUDE. 42 30 40 50' 43 10 20 30 40' 50 44 10 20' 3d 40 50 45° 0° •0000 •0000 •0000 •0000 •0000 •0000 •0000 •0000 •0000 •CXXX3 •0000 ■0000 •CX30O •0000 ■CXXX3 •CX30O I ■0160 •0161 •0162 •0163 •0164 •0165 ■0166 •0167 ■0168 •0169 •0170 ■0171 ■0172 •0173 •0174 •0175 2 3 4 S •0320 •0480 •0639 ■0799 0322 0482 •0643 ■0803 •0324 ■0485 •0647 ■0808 •0325 •0488 •0650 •0813 •9327 •0491 ■0654 •0817 •0329 ■0494 ■0658 ■0822 ■0331 •0497 •0662 ■0827 •0333 •0500 •0666 ■0832 •0335 •0502 0670 •0837 •0337 •0505 •0674 •0842 •0339 •0508 •0678 •0847 •0341 •0511 •0682 •0852 •0343 ■0514 •068s •o8s6 ■0345 ■0517 •0861 •0347 •0520 ■0694 ■0867 •0349 ■0872 6° I 9 10 •0958 ■1117 ■I27S •1433 •1591 •0963 ■1123 •1283 ■1442 •1601 •0969 ■1130 ■1290 •1450 1610 •097s ■1136 •1298 •1459 •1619 0980 •I 143 •1305 •1467 •1629 •0986 •1150 •1313 ■1476 •1638 •0992 •I 156 •1321 •1485 •1648 ■0998 ■1163 •1328 •1493 •1657 ■1004 ■I 170 •1336 '1 502 •1667 •1009 •II77 •1344 •IS" •1677 ■1015 •1184 ■1352 •1519 •1687 ■1021 ■1191 •1360 •1528 •1697 1027 •1198 ■1368 •1537 •1706 ■1033 ■1205 •1376 •1546 •1716 •1039 •I2I2 •1384 •1555 ■1726 •1045 ■1219 ■1392 •1564 •1736 11° 12 13 14 IS . -1748 •190S ■2061 •2217 •2372 •1759 •1916 ■2073 •2230 •2386 •1769 ■1928 •2086 ■2243 •2399 ■1779 •1939 •2098 •2256 •2414 ■1790 •1950 •2110 •2269 •2428 •1800 •1962 •2122 •2282 •2442 ■i8n •1973 ■2135 •2296 •2456 •1821 ■1985 •2147 •2309 ■2470 ■1832 •1996 •2160 •2323 •2485 •1843 •2008 •2172 ■2336 ■2499 •1853 ■2020 ■2185 •2350 ■2514 •1864 •2031 ■2198 •2364 •2S29 •1875 •2043 •22 II •2377 •2543 •1886 •205s •2223 •2391 •2558 ■1897 •2067 •2236 •2405 ■2573 ■1908 ■2079 ■2250 ■2419 ■2588 16° 17 18 19 20 •2526 •2679 ■2832 •2983 •3134 •2541 ■269s ■2848 •3001 •3152 ■2555 •27 1 1 •286s •3018 •3171 •2570 •2726 •2882 •3036 •3189 •258s ■2742 •2898 •3054 ■3208 •2601 •2758 ^ •29 IS ■3072 •3227 •2616 ■2775 •2932 •3090 ■3246 •2631 •2791 •2950 ■3108 •3265 •2646 •2807 •2967 •3126 •3284 •2662 •2823 •2984 ■3144 •3303 •2677 •2840 •3002 ■3162 •3322 •2693 •28S6 •3019 •3I8I •3342 •2709 ■2873 •3037 •3199 •3361 •2724 •2890 ■3054 •3218 ■3381 •2740 •2907 ■3072 •3237 •3400 •27s6 ■2924 •3090 •3256- ■3420 21° 22 23 24 25 •3284 •3433 ■3580 ■3727 •3873 •3303 •3453 ■3601 •3749 •3895 •3322 •3473 ■3622 •3771 ■3918 •3342 •3493 •3644 •3793 •3941 •3361 •3665 •3815 •3964 •3381 •3534 •3686 ■3837 •3987 •3401 •3555 •3708 •3860 ■4010 •3421 •3576 •3730 •3882 •4034 •3441 •3597 •3751 •3905 •4057 •3461 •3618 •3773 •3928 •4081 •3481 •3639 •3795 •3951 •4105 •3501 •3660 •3817 •3974 ■4129 ■3840 •3997 •4153 ■3542 ■3703 •3862 ■4020 •4177 •3563 ■37?4 •3885 ■4044 ■4202 ■3584 •3746 . -3907 •4067 •4226 26° 29 30 •4017 •4160 •4302 •4442 ■4582 •4040 •4184 ■4327 •4468 •4608 •4064 •4209 •4352 •4495 ■4635 ■4088 ■4234 •4378 •4521 •4663 •4112 •4258 •4403 •4547 •4690 ■4136 •4283 •4429 •4574 •4717 ■4160 •4308 •4455 •4601 •4745 •4184 ■4333 •4481 •4628 •4773 •4209 ■4359 ■4507 •4655 •4800 •4233 •4384 •4534 •4682 •4828 •4258 •4410 •4560 •4709 •4857 •4283 •4435 •4587 •4737 •488s ■4308 •4461 ■4613 •4764 •4913 •4333 •4487 •4640 •4792 •4942 •4358 •4514 •4667 •4820 •4971 •4384 •4540 •4695 •4848 ■5000 31° 32 33 34 35 •4719 •4856 •4991 •5124 •5256 •4747 •4884 •5020 •5154 •5287 •4775 •4913 •5049 •5184 •5318 •4803 •4942 ■5079 •5215 •5349 •4831 •4970 •5109 ■5245 •5380 •4859 •5000 •5138 •5276 •541 1 •4888 •5029 •5168 •5307 •5443 •4916 •505S •5199 •5338 "5475 •4945 •5088 •5229 •5369 •5507 •4974 •S117 ■5260 •5400 •5539 •5003 •5147 •5290 ■5432 •5571 •5032 •5177 ■5321 •5463 •5604 •5061 •5208 •5352 ■5495 ■5637 •5091 •5238 •5383 ■5|f •5669 •5121 •5268 •5415 •5559 •5702 •5150 •5299 •5446 •5592 •5736 36° 39 40 •5386 •5641 •5767 •5890 •5418 •5547 ■5675 •5800 •5925 •5449 •5579 •5708 •5834 •5959 •5481 •5612 •5741 •5869 •5994 •5513 •5645 •5775 •5903 •6029 •5545 •5678 •5808 •5937 ■6064 •5578 •57 1 1 ■5842 •5972 •6100 •5610 •5744 •5877 •6007 •6135 •5643 ■5778 •591 1 •6042 •6171 •5676 •5812 •5945 •6077 •6207 •5709 •5846 •5980 •61 13 •6244 ■5743 •5880 ■6015 •6148 ■6280 ■5776 ■5914 ■6050 ■6184 •6317 •S8io •5949 ■6085 ■6220 •6354 •5844 •5983 ■6121 •6257 •6391 •5878 •6oi8 ;6i57 ■6428 41° 42 43 44 45 •6012 •6131 •6249 •636s •6479 •6047 •6167 •6286 •6403 •6517 •6082 •6203 •6323 ■6440 •6556" •6ii8 ■6240 •6360 •6478 ■6594 •6154 •6276 •6397 •6516 •6632 •6190 •6313 •6434 •6226 •6350 •6472 •6592 ■6710 •6262 •6387 •6510 •6631 •6749 •6299 •6424 •6548 •6669 •6789 •6462 •6586 •6708 ■6828 •6372 •6499 •6624 ■6747 •6868 ■6410 •6537 •6663 •6787 ■6908 •6447 •6576 ■6702 •6826 •6949 •648s ■6614 ■6741 ■6866 ■6989 •6523 •66s2 •6780 •6906 •7030 •6561 •6691 ■6820 •6947 : ■7071 46° % 49 SO •6592 ■6702 •6810 •6916 •7020- •6630 •6741 •6850 ■6956 ■7061 •6669 •6780 ■6890 ■6997 •7102 •6708 •6820 •6930 •7038 •7143 •6747 •6860 •6970 •7079 •7185 ■6787 •6900 •7011 •7120 ■7227 •6826 •6940 •7052 •7162 •7269 •6866 •6981 •7093 ■7204 •7312 ■6906 •7022 •7135 ■7246 •7355 •6947 •7063 •7176 •7288 •7398 •6987 ■7104 ■7218 •7331 •7441 •7028 ■7145 ■7260 •7373 •7484 •7069 •7187 •7303 •7417 •7528 7110 ■7229 •7345 ■7460 ■7572 •7152 •7271 •7388 ■7503 ■7616 ■7193 •7314 ■7431 •7547 •7660 SI" 52 53 S4 55 •7121 •7221 •7318 •7413 •7506 •7163 •7263 ■7361 •7457 •7550 •7205 •7306 ■7404 •7500 - •7594 •7247 •7348 •7447 •7544 •7639 •7289 •7391 •7491 •7588 ■7683 •7332 •7434 •7535 •7633 •7728 •7375 •7478 •7579 •7677 •7773 •7418 •7522 •7623 •7722 •7819 ■7461 •7566 •7668 •7767 •786s •7505 •7610 •7712 •7813 •7910 •7549 •7654 •7757 •7858 •7957 •7593 •7699 •7803 •7904 •8003 ■7637 ■7744 ■7848 '•7950 ■8050 •7682 •7789 ■7894 •7997 ■8097 •7726 ■7834 ■7940 •8043 •8144 ■7771 •7880 •7986 •8090 ■8192 56" 1 •7597 •7685 •7771 •7854 •7936 •7641 ■7730 •7816 •7900 •7982 ■7686 •7775 •7862 •7947 ■8029 •7731 •7821 •7908 •7993 •8076 •7776 •7866 •7954 •8040 •8123 •7822 •7912 •8001 ■8087 •8171 •7867 •7959 •8048 •8134 ■8218 7913 •8005 •8095 •8182 •8266 •7959 •8052 •8142 •8230 •8315 •8006 •8099 •8190 •8278 •8363 •8053 •8146 •8237 •8326 ■8412 •8100 1't4 •8285 •8374 •8461 •8147 •8242 •8334 •8423 •8510 ■8194 •8290 •8382 •8473 •8560 •8242 •8338 •8431 •8522 ■8610 ■8290 •8387 •8480 ■8572 •8660 6i» 62 65 •8014 •8091 •8165 •8236 •8305 •8061 •8138 ■8212 •8284 •8353 « ■8109 •8186 •8260 •8333 •8402 •8156 ■8234 •8309 •8381 ■8451 ■8204 •8282 ■8357 ■8430 •8501 •8252 •8330 •8406 •8480 •8551 •8300 •8379 •8455 •8529 •8601 •8348 •8428 •8505 •8579 •8651 ■8397 •8477 •8629 '8701 •8446 •8527 •8604 •8680 •8752 ■8495 •8576 ■86SS •8730 •8803 •8626 ■S781 •8855 1|55 •8677 •8756 •8832 •8906 ■8645 •8727 •8807 •8884 •8958 •869s •8778 ■8858 ■8936 ■go 1 1 •8746 •8829 ■8910 ■8988 ■9063 i 12 30 40 50 43 10 20 30 40 50 44° 10 20 30' 40 50' 45 When the Latitude is North the sign is + When the Latitude is South the sign is — ALT-AZIMUTH TABLES. 108 Under Altitude and abreast of Declination, take out the tabular quantity and mark it + or — , according as Declination is S. op N. Add Algebraically E and F. Dec- lina- tion. TRUE ALTITUDE. 4230 40 50' 43 10 20 30 40 50 44 10 20 30 40 50' 45 0" •0000 •0000 •0000 -0000 -0000 -0000 -0000 -0000 -0000 -0000 -0000 -0000 •OGOO •0000 •0000 •0000 I ■0237 •0237 -0238 •0239 •0239 -0240 -0241 -0241 -0242 -0243 -0243 -0244 •0245 -0245 -0246 •0247 2 •0473 •0475 -0476 -0477 -0478 -0480 -0481 •0482 •0484 •0485 -0487 •0488 -0489 -0491 •0492 -0494 3 ■0710 0712 -0714 •0716 -0718 •0720 -0722 -0724 -0726 ■0728 -0730 •0732 -0734 •0736 -0738 •0740 4 •0946 •0949 -0951 -0954 •0956 •0959 •0962 •0964 -0967 -0970 -0972 ■0975 -0978 -0981 •0984 •0987 5 ■1182 •ii8s -1188 ■1192 ■II9S -1198 -1202 •1205 •1208 -1212 -1215 •1218 •1222 •1225 •1229 •1233 6° •1418 •1422 •1425 -1429 •1433 •1437 -1441 -1445 •1449 •1453 -1457 •1461 -1466 •1470 -1474 •1478 7 ■165:5 •1657 ■1662 •1666 •1671 •1675 -1680 •1685 •1689 •1694 -1699 -1704 •1709 •1714 •1719 •1723 8 •1888 ■1893 ■1898 -1903 -1908 -1913 -1919 •1924 •1929 -1935 ■1940 •1946 •1951 •1957 ■1963 •1968 9 2122 •2127 •2133 -2139 •2145 •2151 -2157 ■2163 •2169 •2175 -2181 -2187 •2193 •2200 •2206 •2212 10 •23SS •2362 •2368 ■2374 •2381 •2387 •2394 •2401 •2407 -2414 -2421 ■2428 •2435 •2442 •2449 •2456 11° •2588 •2S9S •2602 •2609 -2616 •2623 -2630 •2638 •2645 -2653 ■2660 -2668 •2675 •2683 •2691 •2698 12 •2820 ■2828 ■283'; ■2843 •2851 •2858 •2866 •2874 •2882 ■2890 -2898 •2907 -2915 •2923 •2932 ■2940 13 ■3051 •3059 -3068 -3076 -3084 •3093 •3101 •3110 •3118 •3127 -3136 •3145 ■3154 •3163 •3172 •3181 14 •3281 •3290 •3299 •3308 •3317 •3326 •3335 •3344 •3354 -3363 •3373 •33S2 •3392 •3402 •34" •3421 IS •3510 •3520 •3529 •3539 •3549 •3558 -3568 •3578 -3588 •3598 -3608 -3618 ■3629 •3639 •3650 •3660 le" •3739 •3749 •3759 -3769 •3779 •3789 •3800 •3810 •3821 •3832 -3843 •3854 •3865 •3876 •3887 •3898 17 •3966 •3976 •3987 •3998 -4009 •4020 •4031 •4042 •4053 •4064 ■4076 •4087 -4099 •4111 •4123 •4135 18 •4191 ■4203 -4214 -4225 •4237 -4248 -4260 •4272 •4284 -4296 •4308 •4320 -4333 •4345 •4358 ■4370 19 •4416 •4428 •4440 •4452 -4464 •4476 -4488 -4501 •4513 ■4526 -4539 -4552 •4565 •4578 •4591 •4604 20 ■4639 •4651 •4664 •4677 •4689 -4702 •47 1 5 •4728 ■4741 •4755 •4768 •4782 -4795 •4809 -4823 •4837 21° ■4861 •4874 •4887 ■4900 •4913 •4927 •4940 ■4954 •4968 •4982 •4996 •5010 •5024 •5039 -5053 •5068 22 ■5081 •5095 ■5108 •5122 •5136 ■5150 •5164 •5179 •5193 •5208 •5222 -5237 •5252 •5267 , •5282 ■5298 23 •5300 •5314 ■5328 •5343 •5357 •5372 •5387 •5402 •5417 •5432 •5447 ■5463 •5478 -5494 -5510 ■5526 24 •SS17 ■SS32 •5546 •5561 •5577 •5592 •5607 •5623 •5638 •5654 •5670 •5686 •5703 •5719 -5735 •5752 25 •5732 •5747 •5763 •5779 •5794 •5810 •5826 -5842 •5859 •5875 •5892 •5908 ■5925 •5942 -5959 •5977 26° ■5946 ■5962 •5978 •5994 -6010 •6027 -6043 •6060 -6077 •6094 -6111 •6129 •6146 •6164 •6182 -6200 27 ■6158 •6174 ■6191 ■6208 -6224 -6242 -6259 •6276 -6294 ■6311 -6329 •6347 ■6365 •6383 ■6402 -6420 28 •6368 •6385 •6402 •6419 ■6437 •6454 -6472 -6490 •6508 •6526 -6545 15^3 ■6582 •6601 ■6620 •6639 29 •6576 •6593 •66 1 1 •6629 -6647 •6665 -6684 ■6702 -6721 •6740 •6759 •6778 ■6797 •6817 ■6836 ■6856 30 •6782 -6800 •6818 ■6837 ■6855 •6874 -6893 •6912 •6931 •6951 •6970 •6990 •7010 •7030 •7051 •7071 31° •6986 •7004 ■7023 ■7042 -7061 •7081 •7100 -7120 •7140 -7160 -7180 •7200 •7221 -7242 •7263 •7284 32 ■7188 ■7207 •7226 ■7246 •7265 •7285 -7305 •7326 •7346 •7367 -7388 •7408 ■^1^5 •7451 •7472 •7494 33 ■7387 ■7407 •7427 •7447 •7467 •7488 •7508 •7529 •7550 •7571 -7593 -7614 •7636 •7658 •7680 •7885 ■7702 34 •7585 •7605 ■7625 •7646 ■7667 •7688 •7709 •7730 •7752 •7774 •7796 •7818 •7840 •7863 •7908 35 •7780 •7800 •7821 •7843 •7864 •7886 •7907 •7929 •7951 ■7974 •7996 •8019 •8042 ■8065 •8088 ■8112 36° •7972 •7994 •801S •8037 ■8059 •8081 •8103 •8126 •8148 •8171 -8194 •8217 •8241 •8265 •8288 •8313 •8163 •8185 •8207 •8229 •8251 •8274 •8297 •8320 •8343 •8366 -8390 •8414 •8438 •8462 •8486 •851 1 38 ■8350 •8373 •8395 ■8418 •8441 •8464 •8488 -8511 •8535 •8559 •8583 •8607 •8632 ■8657 •8682 •8707 39 •8536 ■8559 •sssi ■8605 •8628 -8652 •8676 •8700 ■8724 •8749 -8773 •8798 •8823 •8849 ■8874 ■8900 40 ■8718 •8742 •8765 •8789 •8813 ■8837 •8861 •8886 •8911 •8936 -8961 •8986 •9012 •9038 •9064 -9090 41° ■8898 •8922 •8946 -8970 -8995 -9020 •9044 ■9069 -909s •9120 •9146 •9172 •9198 •9225 •9251 •9436 •9617 •9796 ■9278 •9463 ,9645 •9824 42 43 44 45 •9076 •9250 ■9422 -9100 •9275 ■9447 ■9124 •9300 •9473 •9149 ■9325 •9498 •9174 •9351 •9524 •9199 •9376 •9550 •9225 ■9402 •9577 ■9250 •9428 •9603 •9276 -9454 ■9630 •9302 •9481 •9657 •9328 -9508 •9684 •9355 •9535 •9712 •9381 -9562 •9739 •9408 •9589 -9767 •9591 •9616 •9642 •9668 •9695 •9721 •9748 •9775 •9802 •9830 •9858 •9886 •9914 -9942 •9971 1 "OOOO 46° '9757 •9783 ■9809 •9836 •9863 •9890 •9917 •9944 •9972 1-0000 1-0028 1-0057 1-0085 1-0114 I -0283 1-0144 1^0173 47 ■9920 •9946 •9973 I -0000 I 0027 1-0055 10082 10110 1-0139 1 -0167 I -0196 1 -0225 10254 1-0313 I '0343 49 50 I -0080 I -0107 I -0134 1-0161. I -0189 I -0217 1 -0245 1-0273 1 -0302 1-0331 1 -0360 1 -0389 1-0419 1 0449 1 0479 I -0642 1 -0802 1-0510 1-0673 1-0834 I -0236 1 0390 I -0264 1-0418 I -029 1 I -0446 I 0319 I -0474 1-0347 10503 1-0376 I -0532 1 -0404 1 -0561 1-0433 I -0590 1 -0462 1-0619 1 -0492 1 -0649 I -0521 1-0679 1-0551 1-0710 I 0581 1 -0740 i-o6i2 1-0771 51° 52 I '0541 I -0569 I -OS97 I -0626 fo6s5 1 -0684 1-0714 I -0743 1-0773 I -0804 1 -0834 1-0865 1-0896 1-0927 1 -1080 1-0959 1-0991 I 0688 I -0717 I -0746 I -0775 1-0804 I -0834 1 -0864 1 -0894 I -0924 I ^0955 I -0986 1-1017 1 -1048 1 "1112 1-1262 1 -1408 I-I551 1-1144 53 54 55 I -0832 I 0973 IIIIO I 0861 I -1002 1-1140 I -o8go 1-1032 I -1 170 I 0920 1-1062 I '1200 1-0950 I -1092 1-1231 I -0980 1-1122 1-1262 l-IOIO i^ii53 11293 I -1040 1-1184 I -1324 1-1071 1-1215 1-1356 1-1102 I -1247 11388 I-II34 I -1278 1-1420 1-1165 1-1310 1-1452 1-1197 I -1343 1-1485 1-1229 I -1375 1-1518 1*1294 1-1441 1-1585 56° 59 I -1245 I -1375 I -1502 I '1626 I-I27S i"i4o6 i^i533 I '1657 ri305 1-1436 I 1564 I -1689 I -1336 I -1467 1-1596 1-1720 1-1367 I -1499 i^i627 1-1752 I -1398 1-1530 1-1659 I -1784 1-1429 1-1562 1-1691 1-1817 1-1461 11594 1-1724 1-1850 I -1493 11626 1-1756 1-1883 I 1525 1-1659 1-1789 I -1916 I-1557 1-1692 1-1823 I -1950 1-1590 1-1725 I -1856 I -1984 i'i623 1-1758 1-1890 1-2018 1-1657 1-1792 1-1924 I -2052 1-1690 1-1826 1-1958 1 -2087 1-1724 I -1861 I -1993 1-2122 1-2247 60 1-1746 I -1778 I -1809 I-I84I 1-1874 1 -1906 1-1939 1-1972 1-2005 1-2039 1 -2073 1-2107 1-2142 1-2177 I '2212 61° 1-1863 1-1895 1-1927 I -1959 I -1991 1 -2024 1 -2057 I -2091 I -2125 1-2IS9 1-2193 1 -2228 I 2262 1 -2298 1-2333 1-2369 1-2487 1-2601 I 2711 1-2817 62 I -1976 1-2008 I 2040 1-2073 1-2106 1-2139 1-2172 1 -2206 I -2240 I -2274 I -2309 I 2344 I -2379 1-2415 1 -2528 1-2638 1-2451 1-2564 1-2674 1 -2780 ^3 64 I -2085 1-2191 I-2H7 I -2223 1-2150 I -2256 I -2183 I -2289 I -2216 I 2323 1 -2250 I '2357 I -2283 1-2391 1-2317 1-2425 12352 1 -2460 I -2386 1 2495 1-2421 1-2530 1-2457 1-2566 I -2492 I -2601 65 I 2293 I -2326 1-2359 I -2392 I 2426 1 -2460 1-2494 1-2529 1-2564 1-2599 1-2635 1-2671 1-2707 I -2743 42 30 40 50 43 10 20 30 40 50' 44 10 20 3d 40 50 45' When the Declination is North the sign is — . When the Declination is South the sign is -f . 109 ALT-AZIMUTH TABLES. Under Altitude in head-line, and abreast of Latitude in Margin, take out the tabular quantity and mark it + or according as the Latitude is N. or S. Lat. TRUE ALTITUDE. 45 10 20 30 40 50' 46 10 20 30 40 50 47 10 20 3d 0° ■noon ■0000 •0000 •0000 ■0000 ■0000 "0000 •0000 ■0000 •0000 •0000 •0000 •0000 •0000 ■0000 •0000 I •017s ■0176 •0177 •0178 •0179 •0180 •01 8 1 •0182 ■0183 •0184 •oiSs •0186 •0187 •0188 •0189 •0190 2 ■0349 •0351 •0353 •035s •0357 ■0359 •0361 •0364 ■0366 •0368 ■0370 •0372 ■0374 •0376 •0379 ■0381 3 ■0523 •0526 ■0529 •0533 ■0536 ■0539 •0542 •0545 •0548 ■0552 ■0555 •0558 ■0561 •0565 ■056S ■0571 4 ■0698 •0702 •0706 •0710 •0714 •0718 •0722 '0727 •0731 ■0735 •0739 •0744 •0748 •0752 ■0757 •0761 5 •0872 •0877 •0882 ■0887 ■0892 •0897 •0903 •0908 •0913 ■0918 •0924 •0929 ■0935 •0940 •0946 •0951 6° •1045 •1051 •1058 •1064 •1070 •1076 ■1082 •1089 •1095 •I 102 •I 108 ■1114 •1121 •1127 •1134 •1141 I •1219 '1226 •1233 •1240 •1247 ■I2S5 •1262 •1269 •1277 •1284 •1292 •1299 ■1307 ■1315 •1322 ■1330 •1392 ■1400 •1408 ■1416 •1425 •1433 •1441 •1450 ■1458 •1467 •1475 •1484 ■1492 ■1501 •1510 •1519 9 •1564 ■IS73 •1583 •1592 •1601 •i6ii ■1620 •1629 •1639 •1648 •1658 •1668 •1678 •1687 •1697 •1707 10 •1736 •1747 •1757 •1767 •1777 •1788 •1798 •1809 •1819 •1830 •1841 •1851 •1862 •1873 •1884 ■1895 11* ■1908 •1919 •1930 •1942 •1953 •1964 •1976 •1987 •1999 •201 1 •2022 ■2034 •2046 •2058 •2070 •2082 12 ■2079 •2091 •2103 ■2116 •2128 •2140 •2153 •2166 •2178 •2191 •2204 ■2217 •2230 •2243 •2256 •2269 13 ■2250 •2263 ■2276 ■2289 •2302 •2316 •2329 •2343 •2357 •2370 •2384 •2398 •2412 •2426 •2441 ■2455 »4 ■^"^i? •2433 '2448 •2462 •2476 ■2491 ■2505 •2520 •2535 •2549 •2564 •2579 •2594 •2609 •2625 •2640 IS •2588 •2603 •2618 •2634 •2649 ■2665 ■2680 ■2696 •2712 ■2727 •2743 •2759 •2775 •2792 •2808 •2825 16° •2756 •2772 •2789 •2805 ■2821 •2838 •2854 ■2871 •2888 ■290s •2922 ■2939 ■2956 •2973 •2991 •3008 '2 •2924 •2941 •2958 •2975 •2993 ■3010 ■3028 ■3045 ■3063 •3081 •3099 •31 17 ■3135 •3154 •3 '72 •3191 i8 •3090 •3108 •3126 •3145 •3163 •3181 •3200 •3219 •3237 ■3256 •327s •3295 •3314 •3333 •3353 ■3372 19 •3256 •327s •3294 •3313 •3332 •3352 •3371 ■3391 •341 1 •3431 ■3451 •3471 •3491 •3512 •3532 ■3553 20 ■3420 •3440 •3460 •3480 •3501 ■3521 ■3542 •3562 •3583 •3604 •3625 •3645 •3668 •3689 ■3711 •3732 21° •3584 •3605 •3626 •3647 •3668 •3689 •37 1 1 ■3733 •3754 •3776 ■3798 •3821 •3843 ■3866 •3888 •39" 22 ■3746 •3768 •3790 •3812 •3834 •3857 •3879 •3902 •3925 •3948 •3971 ■3994 •4017 •4041 •4064 •4088 23 •3907 ■3930 ■39S3 •3976 •3999 •4023 •4046 •4070 •4094 •41 1 7 •4142 •4166 •4190 •4215 •4239 •4264 24 •4067 ■4091 •41 15 ■4139 ■4163 •4187 •4212 ■4236 •4261 •4286 •43 1 1 ■4336 •4362 •4387 •4413 ■4439 25 •4226 •4251 •4276 •4301 ■4326 •4351 •4376 •4402 •4428 •4453 •4479 •4506 ■4532 ■4559 •4585 •4612 26° ■4384 •4409 •4435 •4461 •4487 ■4513 •4539 ■4566 •4593 ■4619 ■4646 , •4674 •4701 •4728 •4756 ■4784 27 •4540 •4566 •4593 ■4620 •4647 •4674 •4701 •4729 •4756 •4784 •4812 •4840 •4868 •4897 •4926 '4954 28 '"^t^i •4722 •4750 •4777 ■480s •4833 ■4862 •4890 •4918 ■4947 •4976 •5005 •5034 •5064 ■5094 ■5123 29 •4848 •4876 •4905 •4933 ■4962 •4991 ■5020 ■5050 •5079 ■5109 •5139 •5169 •5199 ■5229 ■5260 ■5291 30 •5000 •5029 •5°59 •5088 •5118 •5148 ■5178 •5208 ■5238 •5269 ■5300 •5331 •5362 ■5393 •5425 ■5457 31° •S150 •5180 •S2II •5241 •5272 •5302 •5333 •5365 •5396 •5427 •5459 •5491 •5523 ■5555 •5588 •5621 32 •5299 •533° •5361 ■5392 ■5424 •5456 •5487 •5520 •5552 •5584 ■5617 ■5650 •5683 ■5716 •5749 ■5783 33 •5446 •5478 ■5510 ■5542 •5575 ■5607 ■5640 •5673 •5706 •5739 •5773 •5807 •5841 •587s ■5909 ■5944 34 •5592 •5625 •5657 •5690 ■5724 •5757 •5791 ■5824 •5858 •5893 •5927 •5962 ■5997 ■6032 •6067 •6103 35 ■5736 •5769 •5803 •5837 •5871 •5905 ■5940 •5974 •6009 •6044 •6080 ■611S •6151 ■6187 •6223 •6259 36° •S878 •5912 •5947 •5981 •6016 •6051 •6087 •6122 •6158 •6194 ■6230 •6267 •6303 •6340 ■6377 •6415 37 ■6018 •6053 ■6089 •6124 •6160 ■6196 •6232 •6268 •6305 ■6342 ■6379 •6416 ■6454 •6491 ji 1 •6529 ■6568 38 •6157 •6193 •6229 ■6265 •6302 •6338 ■6375 •6413 •6450 •6488 •6526 •6564 ■6602 •6641 •6680 •6719 39 •629; ■6330 ■6367 ■6404 •6441 •6479 •6517 ■6555 ■6593 •6632 •6670 •6709 •6749 •6788 •6828 ■6868 40 •642 J •6465 •6503 •6541 ■6579 •6618 •6656 •6695 •6734 ■6774 •6813 •6853 •6893 •6933 •6974 •7015 41" 'it ■6599 •6637 •6676 ■^^'5 '^Joi'^ •6794 •6833 ■6873 ■6913 ■6954 ■6994 7035 •7077 •7118 •7160 42 •6691 ■6730 •6770 ■6809 •6849 ■6889 ■6929 •6970 •7010 ■7051 •7092 7134 •7176 •7218 •7260 •7302 43 •6820 •6860 •6900 •6940 ■6981 ■7021 •7062 •7104 7145 •7187 ■7229 •7271 7314 •7356 ■7399 ■7443 44 •6947 •6987 •7028 •7069 ■7110 •7152 7193 7235 7278 ■7320 •7363 •7406 ■7449 7493 '7537 •7581 45 •7071 •7112 7154 •7196 •7238 •7280 •7322 •7365 ■7408 ■7451 7495 •7539 7583 •7627 •7672 ■7717 46° •7193 723s •7278 ■7320 7363 •7406 •7449 •7492 7536 7580 •7625 •7669 7714 ■7759 •7805 •7850 % •7314 7356 ■7399 ■7442 ■7486 7529 7573 7618 •7662 •7707 7752 7797 ■7843 •7889 •7935 •7981 ■7431 747S •75 '8 •7562 ■7606 •7651 •7695 •7740 7786 7831 7877 •7923 •7969 ■8oi6 ■8063 •81 ID 49 7S47 •7660 7591 •7635 ■7680 ■7725 •7770 •7815 ■7861 •7907 •7953 7999 •8046 •8093 ■8141 •8188 •8236 50 •7705 •7750 7795 •7841 7887 •7933 •7979 •8026 ■8072 •8120 •8167 •8215 •8263 •83 1 1 •8360 51° •7771 7817 ■7862 ■7908 'W. ■8001 •8048 •809s •8142 ■8189 ■8237 ■828s '8334 •8383 •8432 •8550 •8665 •8777 •8481 52 •7880 •7926 •7972 •8019 •8066 ■8113 •8160 •8208 •8256 •8304 ■8352 •8401 •8450 •8500 •8600 53 •7986 •8033 ■8080 •8127 ■8174 •8222 ■8270 •8318 •8367 •8416 ■8465 •8515 ■8564 ■8614 •8716 •8829 54 •8090 ■8137 •8185 •8233 •8281 ■8329 •8378 ■8427 •8476 ■8525 •8575 •862s •8676 •8726 55 '8192 •8239 ■8287 •8336 ■8384 •8433 •8483 •8532 ■8582 •8632 •8683 •8733 •8784 •8836 •8887 ■8939 56° •8290 1^3? V^^ •8436 ■8486 •8535 •8585 ■8635 •8685 •8736 •8787 •8839 •8890 •8942 ■8995 •9099 •9201 •9300 •9396 •9047 •9152 ■9255 ■9354 ■9451 i l3f7 ■8480 ■8572 •8660 •8436 •8530 ■8622 •8711 •8485 •8580 ■8672 •8762 •8534 •8630 ■8723 ■8813 ■8584 •8680 ■8774 ■8864 •8634 •8731 •8825 •8916 •8685 ■8782 •8876 •8968 ;8735 ■8928 •9020 •8786 •8885 •8980 •9073 •8838 •8937 ■9033 ■9126 •8889 •8989 •9085 ■9179 ■8941 •9041 ■9139 •9233 •8994 •9094 •9192 •9287 •9046 •9147 •9246 •9341 61° 62 •8746 ■8829 •8910 ■8988 ■9063 ■8797 •8881 •8962 •8849 •8933 •8900 •8985 •8952 •9037 ■9004 •9090 •9057 •9143 •91 10 •9197 •9163 ■9250 ■9217 ■9304 •9270 ■9359 •9325 ■9413 •9379 •9468 •9434 ■9524 •9489 •9580 ■9545 •9636 "^ 1 ■9014 •9067 •9120 ■9173 . -9227 ■9281 •9335 ■9389 ■9444 •9499 ■9555 •96 1 1 •9667 •9724 65 •9040 •91 16 ' ■9093 ■9146 ■9200 •9253 •9307 •9362 ■9416 •9471 •9527 •9582 ■9638 •9695 •9752 •9809 •9169 •9223 ■9276 •9331 ■9385 ■9440 •9495 •9550 •9606 •9662 •9719 •9776 •9833 •9891 45 10. 20 30 40 50 46 10 20 30 40' 50' 47 10' 20 30 When the Latitude is North the sign is + When the Latitude is South the sign is — . ALT-AZIMUTH TABLES. no Under Altitude and abreast of Deellnation, take out the tabular quantity and mark it + or — , aeeordingr as Declination is S. or N. Add Algebraically E and F. TRUE ALTITUDE. LINA- TION. 45 10 20 30 40 50 46 10' 20 3d 40' 50 47 10 20 30' 0° ■0000 •0000 •0000 ■0000 •0000 -0000 -0000 •0000 -0000 •0000 -0000 0000 -0000 •0000 -0000 •0000 I 2 3 4 S •0247 •0494 •0740 •0987 •1233 •0248 ■0495 •0742 ■0989 •1236 •0248 ■0496 •0744 -0992 •1240 -0249 -0498 -0747 -0995 -1243 •0250 -0499 -0749 -0998 -1247 •0250 •0501 ■0751 -lOOI -I25I -0251 -0502 •0753 •1004 -1255 -0252 -0504 -0756 -1007 ■1258 -0253 -0505 -0758 -1010 -1262 -0254 -0507 -0760 •1013 -1266 •0254 •0509 •0763 -1017 -1270 •0255 -0510 -0765 -1020 -1274 -0256 -0512 -0767 -1023 -1278 •0257 -0513 •0770 -1026 -1282 -0258 -OS'S -0772 -1029 -1286 -0258 -0517 -0775 -1033 -1290 I 9 10 •1478 •1723 •1968 •2212 •2456 -1483 •1729 •1974 •2219 ■2463 •1487 -1734 •1980 •2225 -2470 -1491 -1739 -1986 •2232 -2477 -1496 ■1744 •1992 ■2239 •2485 -1500 -1749 -1997 -2245 •2492 -1505 •1754 •2003 -2252 -2500 -1509 -1760 ■2010 •2259 -2507 •1514 -1765 -2016 -2266 -2515 •1519 •1770 -2022 -2273 ■2523 •1523 -1776 -2028 -2280 -2530 -1528 •1781 -2034 -22S7 -2538 -1533 -1787 -2041 -2294 -2546 •1537 •1793 -2047 •2301 •2554 •1542 •1798 -2054 -2308 -2562 ■1547 -1804 -2060 •2316 •2570 11° 12 13 14 IS ■2698 •2940 •3181 •3421 •3660 •2706 -2949 •3191 ■3431 ■3671 -2714 -2958 •3200 •3441 -3682 -2722 •2966 •3209 •3452 •3693 -2730 -2975 -3219 -3462 -3704 -2739 •2984 -3229 •3472 ■3715 -2747 •2993 •3238 ■3483 -3726 •2755 -3002 -3248 -3493 -3737 -2763 -3011 -3258 •3504 •3748 ■2772 -3020 -3268 -3514 -3760 -2780 -3030 -3278 •3525 -3772 -2789 -3039 -3288 •3536 •3783 -2798 •3049 •3298 -3547 -3795 •2807 •3058 •3309 •3558 •3807 •2815 •3068 •3319 •3570 •3819 -2824 •3077 •3330 •3581 •3831 i6° % 19 20 •3898 •413s ■4370 •4604 •4837 •3909 -4147 -4383 •4618 -4851 •3921 ■4159 •4396 -4631 •4865 -3933 •4171 ■4409 •4645 •4880 •3944 •4184 •4422 ■4659 -4894 •3956 •4196 •4435 •4673 -4909 •3968 -4209 ■4448 •4687 -4924 -3980 •4222 -4462 -4701 -4938 ■3992 -4234 -4476 -4715 •4953 •4004 -4247 -4489 •4730 •4969 -4017 -4260 -4503 -4744 -4984 -4029 -4274 -4517 -4759 -4999 -4042 -4287 -4531 -4774 -5015 -4054 -4300 •4545 •4789 •5031 •4067 -4314 -4560 -4804 -5047 •4080 -4328 •4574 •4819 -5063 21° 22 23 24 2S •5068 •5298 •5526 •5752 •5977 •5083 •5313 -5542 •5769 •5994 •5098 ■5329 •5558 -5786 ■6012 -5113 -5345 •5575 -5803 •6030 •5128 •5360 •5591 -5820 •6047 •5143 ■5377 -5608 -5838 -6066 -5159 •5393 -5625 -6084 -5175 -5409 -5642 •5873 •6102 •5190 •5425 •5659 •5891 -6121 •5206 -5442 •5676 ■5909 -6140 -5222 -5459 •5694 •5927 -6158 ■5238 •5476 •57" •5945 -6178 •525s -5493 -5729 -5964 ■6197 •5271 -5510 •5747 •5983 -6216 -5288 •5527 •5765 -6001 -6236 •5305 •5545 •5784 •6020 -6256 26° 29 30 •6200 •6420 •6639 •6856 •7071 •6218 •6439 -6659 •6876 •7092 •6236 -6458 •6678 •6896 ■7113 -6254 ■6477 -6698 -6917 -7134 ■6273 -6496 -6718 -6937 -7155 •6292 •6516 •6738 -6958 -7176 -6311 -6535 -6758 -6979 ■7198 •6330 •655s •6779 -7000 -7220 -6349 -6575 -6799 -7022 -7242 -6368 -6595 ■6S20 •7043 •7264 •6388 -6616 -6841 -7065 -7286 -6408 -6636 -6862 •7087 7309 -6428 6657 •6884 ■7109 ■7331 -6448 -6678 -6905 •7131 •7354 -6468 -6699 -6927 •7153 ■7378 -6489 -6720 •6949 •7176 •7401 31° 32 33 34 35 •7284 •7494 ■7702 •7908 •81 12 -7305 -7516 ■7725 -7931 -8135 -7326 -7538 -7748 -7955 -8159 -7348 -7560 -7770 ■7978 ■8183 •7370 -7583 •7794 -8002 -8208 -7392 •7606 -7817 ■8026 -8232 •7414 -7628 •7840 -8050 -8257 -7437 -7652 -7864 -8074 •8282 -7459 -7888 -8099 •8307 ■7482 •7698 •7912 -8124 -8333 •7505 •7722 •7937 -8149 ■8358 •7528 •7746 •7961 •8174 •8384 ■7552 ■7770 •7986 ■8199 -8410 -7576 -7794 -801 1 •8225 •8437 •7599 ■7819 -8036 -8251 •8463 -7624 -7844 -8062 -8277 •8490 36° 39 40 •8313 •8511 •8707 •8900 ■9090 -8337 •8536 •8732 •8926 •91 17 -8361 •8561 •8758 -8952 •9144 -8386 •8586 ■8784 ■8979 -9171 •84 1 1 -8612 -8810 -9005 •9198 -8436 -8637 -8836 •9032 -9226 •8462 •8663 -8863 -9059 ■9253 -8487 -8690 •8890 -9087 -9281 •8513 -8716 -8917 •9114 -9310 -8539 -8743 -8944 -9142 •9338 •8565 -8770 -8971 •9171 •9367 •8592 -8797 •8999 -9199 •9396 -8619 -8824 -9027 •9228 -9425 -8646 -8852 -9056 -9257 •9455 -8673 -8880 •9084 •9286 •9484 -8700 -8908 -9113 •9315 ■9514 4X° 42 43 44 45 •9278 •9463 •9645 •9824 i-oooo •9305 •9491 -9673 •9853 1-0029 •9333 -9518 •9702 ■9882 1-0059 -9360 -9547 •9730 •9911 I -0088 -9388 -9575 -9759 -9940 I -01 18 ■9416 -9604 •9788 -9970 1 0149 -9444 -9633 -9818 1 -0000 I -01 79 •9473 •9662 •9847 1 -0030 1 0210 -9502 -9691 -9877 I -0061 I -024 1 -9531 ■9721 -9908 1 -0092 I -0272 -9560 -9751 -9938 1-0123 1-0304 -9590 -9781 -9969 1-0154 1 -0336 -9620 -9811 i-nnnn I 0186 I -0368 -9650 -9842 I 0031 1-0218 1 -0401 -9680 •9873 1-0063 1 -0250 ro433 -9711 -9904 I -0095 I -0282 I -0466 46° % 49 50 I -0173 I -0343 I 0510 10673 1-0834 I -0203 1-0373 I -0540 I -0704 I 0865 1-0233 I -0404 1-0571 1-0736 1-0897 1 -0263 I 0434 1 -0603 1 -0768 1 0929 I -OZ93 1 0465 1 -0634 I -oSoo 1 -0962 1 -0324 1-0497 1 0666 1 -0832 1 -0995 1-0355 1 -0528 I -0698 1 -0864 1-1028 1-0387 1 -0560 1-0730 10897 1-1061 I -0418 10592 1 -0763 1-0931 1-1095 1-0450 I 0625 I 0796 I 0964 1-1129 I -0482 1-0657 I -0829 1 -0998 1-1163 1-0515 I -0690 1-0863 1-1032 1-1197 I -0548 1-0724 I 0897 1-1066 I -1232 I -0581 1-0757 1-0931 I-lIOl 1-1268 I -0614 1-0791 1-0965 1-1136 1-1303 I -0648 I 0825 1 -1000 11171 I -1339 51° 52 S3 54 55 I '0991 I -1 144 I -1294 1-1441 1-1585 1-1023 1-1177 1-1327 I 1475 i-i6i8 I -1055 I-12I0 1-1361 1-1508 1-1653 1-1088 1-1243 1-1394 1-1542 1-1687 1-1121 I 1276 1 -1428 1-1577 1-1722 1-1154 1-1310 1-1462 11611 I-I7S7 1-1187 I -1344 1-1497 1-1646 1-1792 1-1221 1-1378 1-1532 I -1681 1-1828 1-1255 1-1413 I -1567 1-1717 1-1864 11290 I -1448 1-1602 11753 1-1900 1-1325 I -1483 I -1638 1-1789 I -1937 1-1360 1-1519 1-1674 1-1826 ri974 I -1395 1-1554 1-1710 I -1862 I -2011 1-1431 1-1591 I -1747 1-1900 1 2049 I -1467 1-1627 1-1784 1-1937 I -2087 1-1664 I 1821 I 1975 1-2125 56° I -1724 I -1861 I -1993 I -2122 1-2247 I -1759 1-1895 I -2028 1-2158 I -2283 I -1793 I -1930 I -2064 1-2193 1-2319 I -1828 1-1965 I -2099 I -2229 12356 1-1863 1 -2001 I 2135 1 -2266 1-2392 1-1899 1-2037 1-2172 1 -2302 1 -2430 ri934 1-2073 1 -2208 1-2339 12467 1-1971 I -21 10 1 2245 1-2377 I -2505 1-2007 1-2147 I -2282 1-2414 1-2543 1 -2044 I -2184 1-2320 I -2452 1-2581 1 -2081 1-2221 I 2358 I -2491 1 -2620 1-2118 1-2259 I -2396 1 -2529 1-2659 1-2156 1-2297 1-2435 1-2568 1-2698 I -2194 1-2336 1^2474 1-2608 1-2738 1-2233 1-2375 I -2513 I -2648 1-2778 1-2271 I -2414 ;:^2ii 1-2819 61° 62 65 1-2369 1-2487 I -2601 1-2711 1-2817 I 240s 1-2523 1 -2638 1 -2748 1-2855 I -2442 1 -2560 1-2675 1-2785 I -2892 1-2478 I -2597 1-2712 1 -2823 I 2930 1-2515 1-2635 I 2750 1-2861 1 -2969 1-2553 1 -2672 1-2788 I -2900 1-3008 1-2591 1-2711 1-2827 1-2939 1-3047 I -2629 1 -2749 1 -2865 I -2978 1 -3086 1 -2667 1-2788 I -2905 I 3017 1-3126 I -2706 1-2827 1 -2944 1-3057 1-3166 1-2745 1-2866 1 -2984 1-3097 1-3207 1-2785 1 -2906 1-3024 1-3138 1-3248 1-2824 I -2946 1-306S 1-3179 1-3289 1-2865 1 -2987 1-3106 I -3220 1-3331 1-2905 1-3028 1-3147 1-3262 1-3373 1 -2946 1-3069 1-3189 I •3304 1^3415 45 10' 20 30' 40' 50 46 10 20 30 40 50 47 10' 20 30 When the Declination is North the sign is — . When the Declination is South the sign is + ■ Table G. Missing Page Missing Page 115 ALT-AZIMUTH TABLES. Enter with Latitude in 1 margin, and over the algebraic sum of E + F will be found the Azimuth in the head-line. Lat. TRUE AZIMUTH. o| 1° ll 2° 2| 3° 3| 4" 4 5° 5| 6° el 7° Ti 0° I 2 3 4 S I -0000 •9998 •9994 •9986 •997S •9962 •9998 ■9997 ■9992 •998s •9974 •9960 •9997 •9995 ■9990 ■9983 ■9972 •9959 ■9994 •9992 ■9988 ■9980 ■9970 •9956 ■9990 ■9989 •9984 ■9977 •9966 •9952 ■9986 ■9985 ■9980 ■9973 •9962 •9948 ■9981 •9980 •9975 ■9968 •9957 ■9943 •9976 •9974 •9970 ■9962 •9951 •9938 •9969 •9968 •9963 •9956 •9945 •9931 •9962 •9960 •9956 •9948 •9938 ■9924 •9954 ■9952 ■9948 •9940 •993° •9916 •9945 •9944 ■9939 •9933 •9921 •9907 •9936 •9934 •9930 , •9922 •99 J2 •9898 •9925 •9924 •9919 •9912 ■9901 •9888 •9914 •9913 •9908 •9901 •9890 •9877 6° I 9 10 •994S •992s ■9902 •9877 •9848 •9944 •9924 •9901 •987s •9847 ■9942 •9922 •9899 •9873 •984s •9939 •9919 •9897 •9871 •9842 •9936 •9916 •9893 •9867 •9839 ■9932 •9912 •9889 •9863 •983s •9927 ■9907 •9884 •9858 ■9830 •9921 •9901 •9879 •9853 -9824 •9915 •989s ■9872 ■9846 •9818 •9907 •9888 •986s •9839 •9811 •9899 •9880 ■9857 •9831 •9803 •9891 •9871 •9848 •9823 •9794 ■9881 ■9862 •9839 •9813 •9785 •9871 •9852 ■9829 •9803 •9775 •9860 •9841 •9818 •9792 •9764 H° 12 13 14 IS •9816 •9781 •9743 •9703 •9659 ■98IS •9780 •9742 •9701 ■96S8 •9813 •9778 •9740 •9700 ■9656 ■9810 •9776 •9738 •9697 ■9653 •9807 •9772 •9734 •9694 ■9650 •9803 •9768 •9730 •9690 •9646 •9798 •9763 •9726 •9685 ■9641 •9792 •9758 •9720 •9679 •9636 •9786 •9751 ■9714 •9673 •9629 ■9779 •9744 •9707 •9666 •9623 •9771 ■9736 •9699 •9658 •961 s •9762. •9728 •9690 •9606 •9753 •9719 •9681 ■9641 •9597 •9743 •9709 •9671 •9631 ■9587 ■9732 •9698 •966J •9620 •9577 16° 11 19 20 •9612 9563 •9510 •94SS •9397 •961 1 •9562 •9509 •94S4 •939S ■9609 •9560 •9507 •9452 •9394 •9607 •9557 •9505 ■9449 •9391 ■9603 •9554 •9502 ■1% •9599 •9550 •9498 ■9442 •9384 •9595 •9545 •9493 •9438 •9379 •9589 •9540 •9487 •9432 •9374 •9583 •9534 ■9481 •9426 •9368 •9576 ■9527 •9474 •9419 •9361 •9568 •9519 •9467 •9412 •9354 •9560 •95" ■9458 •9403 •9345 •9S5> •9502 •9449 •9394 •9337 •9541 •9492 •9440 •9385 •9327 ■9530 •9481 •9429 •9374 •9317 21° 22 23 24 25 ■9335 •9271 •9205 •9 '35 •9063 ■9334 •9270 •9204 •9134 •906a •9333 •9269 •9202 •913a ■9060 •9330 •9266 •9199 •9130 •9058 •9327 ■9263 ■9196 •9127 •9054 ■9323 •9259 •9192 ■9123 •9051 •9318 •9255 ■9188 •91 18 •9046 ■9313 •9249 •9183 •91 13 •9041 •9307 •9243 •9177 •9107 •9935 •9300 •9237 ■9170 •9101 •9029 •9293 •9229 •9163 •9093 ■9021 •928s •9221 •9155 •9085 •9013 ■9276 •9212 •9146 ■9077 •9005 •9266 •9203 •9136 •8996 •9256 •9193 •9126 26° 29 30 ■8988 •8910 •8829 •8746 •8660 •8987 •8909 ■8828 •8659 ■898s ■8907 ■8826 •8743 •86S7 •8982 a •8741 •8655 •8979 •8902 •8821 •8738 ■8652 ■8976.. •8898 •8817 " •8734 ■8648 •8893 •8813 •8730 •8644 ■8966 ■8888 •8808 •872s ■8639 •8960 .•8883 . ■8802 •8719 •8634 ■8954 •8876 ■8796 •8713 •8627 •8947 •8869 •8789 ■8706 •8620 ;8939 •8781 •8698 •8613 ■8930 •8853 •8773 •8690 •8605 •8921 •8844 •8764 •8681 •8596 •8911 •8834 •8754 •8671 •8586 31° 32 33 34 35 •8571 •8480 •8386 •8290 •8191 •8570 '^^^^ ■8289 •8190 ■IS lit •8189 •8566 •8475 •8382 ■828s •8187 •8564 •8472 ■8184 •8560 •8469 •837s •8279 ■8180 •8556 • -8465 •8371 ■8275 ■8176 ■8460 •8366 •8270 •8172 •854s •8454 •8361 •8265 •8166 •8539 •8448 •8355 8532 •8441 •8348 •8252 •8154 •8525 •8434 •8341 ■8245 •8147 •8426 •8333 ■8237 ■8139 •8508 •8417 '8324 ■8229 •8130 •8498 •8408 •8315 •8219 •8121 36° 39 40 •7880 •7771 ■7660 •8089 •7985 •7879 •7770 •7659 •8087 ■7984 •7877 •7769 •7658 ■808s •7981 •787s •7767 •7656 •8082 •7979 •7873 •7764 ■7653 •8079 •7975 •7869 ■7761 ■7650 •807s •7971 •7865 •7757 ■7646 •8070 •7967 •7861 •7753 •7642 •8065 •7962 •7856 •7748 •7637 •8059 •7956 •7850 •7742 •7631 •8053 ■7950 •7844 •7736 •7625 •8046 •7943 •7837 •7729 •7618 •8038 •7935 •7829 •7722 •761 1 •8030 •7927 •7821 •7714 •7603 •8021 •7918 •7813 •770s •7595 41° 42 43 44 45 7S47 •7431 •7313 •7193 •7071 •7546 •7430 •7312 •7192 ■7070 ■7S4S •7429 •73" ■7191 ■7069 •7543 •7427 •7309 •7189 •7067 •7540 •7424 •7307 •7187 •7064 •7S37 •7421 •7304 ■7184 ■7061 •7S33 •7418 ■7300 •7180 ■7058 ■7529 •7413 •7296 •7176 ■7054 •7524 ■7409 •7291 •7171 •7049 •7518 •7403 •7286 •7166 ■7044 •7512 •7397 ■7280 •7160 •7039 •7506 •7391 •7273 •7154 •7032 •7499 •7384 •7267 •7147 •7026 •7491 •7376 •7259 •7140 •7018 •7483 •7368 •7251 •7132 •701 1 46° tl 49 SO •6946 •6820 •6691 •6560 •6428 •6946 •6819 •6690 •6560 •6427 •6944 ■6818 •6689 •6426 6942 ■6816 •6687 ■6557 •6424 •6940 ■6813 ■668s •6SS4 •6422 •6937 •681 1 •6682 •6553 •6419 ■6934 •6807 •6679 •6548 •6416 ■6930 •6803 •6675 •6545 •6412 •6925 •6799 •6671 •6540 ■6408 •6920 •6794 •6666 •6536 •6403 •6789 ■6661 •6530 •6398 •6909 •6783 •6655 •6525 •6393 •6902 ■6776 •6648 •6518 •6387 •6769 •6641 •6512 •6380 •6887 •6762 •6634 •6504 •6373 51° 52 S3 54 55 •6293 •6156 •6018 •5878 ■5736 '6292 •6156 •6017 ■5877 •S73S ■6291 •6016 •5876 •5734 •6289 •6153 ■6014 ■5874 •5732 ■6287 •6151 •6012 •5872 •573° •628s •6148 ■6010 •5870 •5728 •6281 ■614s ■6007 ■5867 •5725 •6278 ■6142 •6003 •5864 •5722 •6274 •6138 •6000 •5860 •5718 •6269 •6133 •5995 •S855 •5714 •6264 •6128 •5990 •5851 ■5709 ■6259 •6123 ■5846 •5704 •6253 •61 17 •5840 •5699 •6246 6111 •5973 •5834 •5693 ■6239 •6104 •5967 •5828 •5687 56° 57 58 11 ■5592 •5446 •5299 •5150 •5000 ■SS9I •5446 •5298 • •5150 •4999 •SS90 •S445 •5297 •S149 ■4998 •5589 •5443 •5296 •5147 •4997 •5587 •5441 •5294 ■5145 •4995 •5584 •5439 •5292 •5143 •4993 •5581 •5436 •5289 •5141 •4991 •5578 •5433 •5286 •S138 •4988 •5575 •5430 •5283 •513s •4985 •5571 •5426 ;5279 •4981 •5566 •5421 •527s •5127 •4977 •5561 ■5417 •5270 ■5122 •4973 •5556 ■54" •5265 •5550 •5406 •5260 •5112 ■4963 •5544 *S400 •5254 •5106 •4957 61° 62 P 65 •4848 •469s ■4540 •4384 ■4226 •4847 ■4694 •4539 •4383 •4226 « •4846 •4693 ■4538 •4382 •4225 •484s •4692 •4537 •4381 •4224 •4843 •4690 •4536 •4380 '4222 •4841 •4688 •4534 •4378 .4220 •4686 •4531 •4376 •4218 •4836 •4683 •4529 •4373 •4216 •4833 •4680 •4526 ■4370 •4213 ■4830 •4677 •4523 •4367 ■4210 •4826 •4673 •4519 •4364 •4207 ■4822 •4669 •4515 •4360 •4203 •4817 •4665 •45 1 1 •4356 •4199 •4812 ■4660 ■4506 •4351 •4195 •4807 •4655 •4501 •4346 •4190 o| I'- 1| 2° 2| 3° 3| 4' 4 5° 5h° 6° 6J° 7° 7i When the sign is + the Azimuth is to be reckoned from the South. When the sign is - the Azimuth is to be reckoned from the North. ALT-AZIMUTH TABLES. 116 ] Enter with Latitude in margin, and over the algebraic snm of E + F will be found the Azimuth in the head-line. Lat. TRUE AZIMUTH. 8° 8| 9° 9| 10° 10| 11' Ill 12° 12i 13° 13| 14° 14| 15° 0° I 2 3 4 5 ■9903 •9901 ■9897 •9889 •9879 •986s •9890 •9889 •9884 •9877 •9866 •9853 •9877 ■987s •9871 ■9863 ■9853 •9839 •9863 •9861 •9857 •9849 ■9839 •9825 •9848 •9847 •9842 •983s •9824 ■981 1 •9833 •9831 •9827 ■9819 •9809 •9795 ■9816 •9815 ■9810 •9803 •9792 •9779 •9799 ■9798 •9793 ■9786 •9775 •9762 •9781 •9780 •9776 •9768 •9758 •9744 ■9763 •9761 ■9757 •97 '^o ■9737 ■9726 •9744 •9742 •9738 •9730 •9720 •9707 •9724 •9722 ■9718 •9710 •9700 ■9687 •9703 •9701 ■9697 •9690 •9679 •9666 •9681 •9680 •9676 •966S •9658 •9645 •9659 •9658 •9646 •9636 •9623 6° 1 9 10 •9848 ■9829 •9806 •9781 •9752 •9836 •9816 •9794 •9768 •9740 •9823 •9803 •9781 •97SS •9727 ■9809 •9789 •9767 •9741 •9713 ■9794 •9775 •9752 •9727 •9698 •9779 •9759 •9737 •97 1 1 ■9683 •9762 •9743 •9721 ■9695 ■9667 ■9746 •9726 •9704 •9679 ■9650 ■9728 •9709 •9686 ■9661 •9633 •9709 •9690 •9668 •9643 •961s •9690 , 9671 •9649 •9624 ■9596 •9670 •9651 •9629 •9604 •9576 •9650 •9631 •9609 •9583 •9556 •9628 •9609 •9587 •9562 •9534 •9606 ■9587 •9565 •9540 •9513 11° 12 13 14 IS •9721 •9686 •9649 •9609 •9565 •9708 •9674 •9637 •9596 •9553 •969s -9661 •9624 •9583 ■9540 •9682 •9647 ■9610 •9570 •9527 •9667 ■9633 •9596 ■9556 •9513 •9652 •9618 •9581 •9540 •9498 •9636 •9602 •9565 •9525 •9482 •9619 •9585 •9548 ■9508 •9465 ■9602 •9568 •9531 •9491 •9448 •9584 •9550 •9513 •9473 •9430 •9565 •9531 •9494 •9454 •9412 •9545 ■95" ■9474 ■9435 •9392 •9525 •9491 •9454 •9415 •9372 •9504 ■9470 ■9433 ■9394 •9352 •9482 •9448 ■9412 •9372 •9330 i6° 'I 19 20 •9519 •9470 ■9418 •9363 ■9305 ■9507 ■9458 •9406 •9351 •9294 ■•9494 ■9445 ■9393 •9339 •9281 •9481 •9432 •9380 •9326 •9268 •9467 ■9418 •9366 •9312 •9254 •9452 •9403 •9351 •9297 •9240 •9436 •9387 •9336 •9281 •9224 •9420 •9371 •9320 •9265 ■9208 •9403 •9354 •9303 •9249 ■9192 •9385 •9336 ■9285 •9231 •9174 •9366 •9318 •9267 •9213 ■9156 •9347 ■9299 •9248 •9194 •9137 ■9327 •9279 •9174 •91 18 •9306 •9258 •9208 •9154 ■9098 •9285 •9133 •9077 21° 22 23 24 25 •924s •9182 •911S •9047 •897s •9233 •9170 •9104 •903s •8964 •9221 •9158 •9092 •9023 •8951 •9208 •9145 •9079 ■go 10 •8939 •9194 ■9131 •9065 •8997 •8925 •9179 •9117 •9051 ■8982 •89 1 1 •9164 •9IOI •9036 •8968 •8897 •9148 •9086 •9020 •8952 •8881 •9132 ■9069 •9004 •8936 •8865 •9115 •9052 •8987 •8919 •8848 ■9097 •9034 •8969 •8901 •8831 ■9078 •9016 •8951 •8883 •8813 ■9058 •8996 ■8932 •8864 •8794 •9038 •8977 •8912 •8844 •8774 •9018 •8891 •8824 •8754 26° 29 30 •8900 ■8823 •8744 •8661 •8576 •8889 ■8812 •8732 •8650 ■8565 •8877 •8800 •8721 •8639 •8554 •8865 ■8788 •8708 •8626 •8541 ■8851 •8775 •8695 •8613 •8529 •8837 ■8761 ■8682 •8600 •8515 •8823 •8746 •8667 •8586 •8501 •8808 •8731 •8652 •8571 •8486 ■8792 •871S •8637 •8555 •8471 •8775 •8699 •8620 ■8539 •8455 •8758 •8682 •8603 •8522 •8438 •8740 •8664 •8586 •8505 •8421 •8721 •8645 •8567 •8486 •8403 •8702 ■8626 •8548 •8468 •8384 ■8682 ■8606 •8529 ■8448 •8365 31° 32 33 34 35 •8488 •8398 •830s •8210 •8112 •8478 •8387 •8295 •8199 ■8102 •8466 •8376 •8283 ■8188 •8091 •8454 •8364 •8272 •8177 •8079 •8441 •8352 •8259 •8164 ■8067 •8428 ■8338 ■8246 •8152 ■8054 ■8414 •8325 •8233 •8138 •8041 •8400 •8310 •8218 •8124 •8027 •8384 •8295 •8203 •8109 •8013 •8368 ■8279 •8188 •8094 •7997 ■8172 •8078 •7982 s lol? •7965 •8317 •8229 ■8138 ■8044 •7948 •8299 ■8210 ■8120 •8026 •7931 •8280 •8192 ■8IOI •8008 •7912 36° 39 40 •Son •7909 ■7803 •8001 ■7899 •7794 •7686 •7576 •7783 •7676 •7566 •7979 ■7877 7772 •7665 7555 •7967 •7865 •7760 7653 •7544 7955 •7853 •7748 •7641 7532 •7942 •7840 •7735 •7629 •7520 •7928 •7826 ■7722 •7615 •7507 •7913 •7812 •7708 •7602 •7493 •7898 7797 7693 •7587 ■7479 7883 •7782 •7678 7572 ■7464 7867 •7766 •7662 7557 •7449 •7850 •7749 7646 •7541 •7433 •7832 7732 •7629 •7524 •7416 •7815 •7714 •7612 •7507 7399 41° 42 43 44 45 •7474 73S9 •7242 •7123 •7002 •7464 ■7350 ■7233 •7114 •6993 7454 •7340 7223 •7105 •6984 •7444 •7330 •7213 •7095 •6974 •7432 •7319 •7202 ■7084 •6964 •7421 •7307 •7191 7073 •6953 •7408 •7295 7179 •7061 ■6941 •7396 ■7282 ■7167 ■7049 •6929 •7382 •7269 7154 •7036 •6917 •7368 •7255 ■7140 •7023 •6903 7354 ■7241 •7126 •7009 •6890 •7339 ■7226 •7111 •6995 •6876 7323 •7211 •7096 •6980 ■6861 •7307 7195 •7081 ■6964 •6846 7290 •7178 7064 •6948 •6830 46° tl 49 50 •6879 •6754 •6626 •6497 •636S •6870 •6745 •6618 •6489 ■6357 •6861 ■6736 •66og •6480 •6349 •6851 •6726 •66cx) •6471 •6340 •6841 •6716 ■6590 •6461 •6330 •6830 ■6706 •6579 •6451 •6320 ■6819 •6695 •6568 •6440 •6310 •6807 •6683 •6557 •6429 ■6299 •6795 •6671 •6545 •6417 •6287 •6782 •6658 •6533 •6405 •6276 •6769 •6645 ■6520 •6392 ■6263 •6755 •6632 •6506 •6379 •6250 •6740 •6617 •6493 •6366 •6237 ■6725 •6603 •6478 •6352 •6223 •6710 •6588 •6463 •6337 •6209 51° 52 53 54 55 ■6232 •6097 •5960 •5821 •5680 •6224 •6089 •5952 •5813 •5673 •6216 •6081 •5944 •5805 •5665 •6207 •6072 •5936 •5797 •5657 ■6198 •6063 •5927 •5789 •5649 •6188 •6054 •5917 •5779 •5640 •6178 •6044 •5908 •5770 ■5630 ■6167 •6033 •5897 •5760 •5621 •6156 •6022 •5887 •5749 •5610 •6144 •601 1 •5875 •5739 •S6cra •6132 •5999 •5864 •5727 •5589 •61 19 •5987 •5852 •5715 •5577 •6106 •5974 •5839 •5703 •5565 •6093 •5961 •5826 •5691 •5553 •6079 •5947 •5813 •5678 •5540 56° i ■5538 •S393 •5248 •5100 •4951 •5531 ■5387 •5241 •5094 •4945 •5523 •5379 •5234 •5087 •4938 •5515 •5372 •5227 •5080 •4931 •5507 ■5364 •5219 ■5072 •4924 •5498 •5355 ■5210 •5064 •4916 •5489 •5346 •5202 •5056 •4908 •5480 •5337 •5193 •5047 •4900 •5470 •5327 •5183 ■5038 •4891 •5459 •5317 •5174 ■5028 •4881 •5449 •5307 •5163 •5018 •4872 •5437 •5296 ■5008 •4862 •5426 •5285 •5142 •4997 ■4851 •5414 ■5273 •4841 •5401 •5261 •SI 19 •4975 •4830 61° 62 P 65 •4801 •4649 •4496 ■4341 •4185 •479s •4643 ■4490 •4336 •4180 •4788 •4637 •4484 •4330 •4174 •4782 ■4630 •4478 •4324 •4168 •4774 •4623 •4471 •4317 •4162 •4767 •4616 •4464 •4310 ■4155 •4759 •460S •4456 •4303 •4149 •4751 •4600 •4449 •4296 •4141 •4742 •4592 ■4441 •4288 •4134 •4733 •4583 ■4432 •4280 ■4126 •4724 •4574 •4424 •4271 •4118 •4714 •4565 •4414 •4263 •4109 •4704 •4555 •4405 •4253 •4101 •4694 •4545 •4395 •4244 •4092 •4683 •4535 •4385 •4234 •4082 8 8l 9° 9| 10° io| 11° 111 12 12| 13° 13| 14 14| 15° >. When the sign is + the Azimuth is to be reckoned from the South. ■When the sign is - the Azimuth is to be reckoned from the North. 117 ALT-AZIMUTH TABLES. Enter with Latitude in margin, and over the algebraic sum of E + F will be found the Azimuth in the head-line. Lat. TRUE AZIMUTH. - lb\ 16° 16l 17° 17| 18° IQ\ 19° 19| 20° 20| 21" 21; 22° 22| 0° •9636 •9613 ■9588 ■9563 •9537 •951 1 •9483 •9455 •9426 ■9397 •9367 •9336 •9304 •9272 , •9239 I •963s •961 1 ■9587 •9562 •9536 ■9509 '9482 •9454 •9425 •9395 •9365 •9334 •9303 •9270 •9237 2 •9630 •9607 •9582 •9557 ■9531 •9505 •9477 ■9449 •9421 •9391 9361 •9330 •9299 •9266 ■9233 3 •9623 •9S99 •957S •9550 ■9524 ■9498 •9470 •9442 •9413 •9384 •9354 •9323 •9291 •9259 •9226 4 •9613 ■9589 •9565 •9540 •9514 •9487 ■9460 •9432 •9403 •9374 •9344 •9313 •9282 •9249 ■9216 5 •9600 ■9576 ■9552 •9527 •9501 •9474 9447 •9419 •9391 •9361 •9331 9300 ■9269 •9237 •9204 6° •9584 ■9560 ■9536 •95" •9485 •9458 •9431 •9404 •9375 •9345 •9315 •9285 •9253 •9221 •9188 7 ■9564 ■9541 •9517 •9492 •9466 ■9440 •9413 ■9385 ■9356 •9327 •9297 •9266 •9235 •9203 •9170 8 ■9S43 ■9519 ■9495 •9470 •9444 •9418 •9391 •9363 •9335 •9305 •9276 •9245 •9214 •9182 •9149 9 •9518 ■9494 ■9470 •9445 •9420 ■9393 ■9366 •9339 •9310 •9281 •9251 ■9221 ■9190 •9158 ■9125 10 •9490 ■9467 ■9443 ■9418 •9392 ■9366 ■9339 •9312 •9283 •9254 ■9224 •9194 ■9163 •9131 •9098 Il- •9459 •9436 ■9412 ■9387 •9362 •9336 ■9309 •9281 •9253 •9224 •9195 ■9164 9133 ■9101 •9069 ia •9426 •9403 •9379 •9354 •9329 ■9303 •9276 ■9249 ■9220 •9192 •9162 ■9132 •9101 •9069 •9037 13 •9389 •9366 •9342 •9318 •9293 ■9267 •9240 •9213 9185 •9156 •9127 •9097 •9066 •9034 •9002 14 •9350 ■9327 ■9303 •9279 ■9254 •9228 ■9202 •9174 •9146 ■9118 •9088 •9058 ■9028 ■8996 •8964 IS •9308 •928s •9261 •9237 •9212 ■9186 ■9160 •9133 •9105 ■9077 •9048 •9018 •8987 •8956 •8924 i6° •9263 •9240 •9217 •9193 •9168 ■9142 ■9116 •9089 •9061 ■9033 •Q004 •8974 •8944 •8913 •8881 VJ •9215 •9193 •9169 ■9145 •9120 •9095 •9069 •9042 •9015 •8986 •8957 8928 •8898 ■8867 •883s i8 •916s •9142 •9119 •9095 •9070 •S045 •9019 8992 •8965 •8937 ■890S •8879 •8849 •8818 •8787 19 •91 II •9089 •9066 ■9042 •9018 ■8992 •8967 ■8940 •8913 •8885 •8856 ■8827 •8797 •8767 •8735 20 •905s •9033 •9010 •8986 •8962 •8937 •8911 •8885 •8858 •8830 •8802 •8773 •8743 •8713 •8682 21° •8996 •8974 •8951 •8928 •8904 •8879 •8853 •8827 •8800 •8773 •8745 •8716 •8686 •8656 •8625 22 ■!?3s •8913 •8890 ■8867 •8843 ■8818 •8793 •8767 •8740 •8713 •8685 ■8656 •8627 •8597 •8566 23 •8870 ■8848 ■8826 •8803 •8779 •8755 ■8729 ■8704 ■S677 •8650 ■8622 •8594 •8565 ■8535 •8504 24 •8803 ■8782 •8759 ■8736 •8713 ■8688 ■8663 •8638 •861 1 •8585 •8557 •8529 •8500 •8470 •8440 25 •8733 •8712 ■8690 •8667 ■8644 •8619 •8595 ■8569 •8543 ■8517 ■8489 ■8461 •8432 •8403 •8373 26° •8661 •8640 •8618 •8595 •8572 •8548 •8523 ■8498 •8472 •8446 •8419 •8391 •8363 ■8333 •8304 27 1586 •8565 ■8543 •8521 •8498 ■8474 •8450 •8425 •8399 •8373 ■8346 •8318 •8290 •8261 ■8232 28 •8508 •8487 ■S466 ■8444 •8421 •8397 •8373 •8348 ■8323 •8297 ■8270 •8243 •821S •8187 •8157 29 •8428 •8407 ■8386 •8364 •8341 •8318 •8294 •8270 •8245 ■8219 •8192 •8165 •8138 •8109 •8080 30 •834s ■8325 •8304 ■8282 ■8259 •8236 ■S213 •818S •8164 •8138 ■8112 ■8085 ■8058 ■8030 •8001 31° •8260 •8240 •8219 •8197 Vll •8152 •8129 •8105 •8080 •8055 •8029 •8002 7975 •7948 •7919 32 •8172 •8152 •8131 '8110 ■8088 •8065 •8042 ■8018 •7994 •7969 •7943 •7917 •7890 ■7863 •783s 33 •8082 •8062 •8041 ■8020 •7999 7976 •7953 •7930 •7906 •7881 ■7856 •7830 •7803 •7776 •7748 34 ■7989 •7969 7949 •7928 ■7907 7885 ■7862 •7839 •7815 •7790 •7765 •7740 7714 •7687 •7659 35 7894 ■7874 7854 •7834 •7812 ■7791 •7768 •7745 ■7722 •7698 •7673 •7647 •7622 •7595 •756S 36° "'l^^ 7777 77S7 7737 •7716 •7694 ■7672 •7649 •7626 •7602 7578 7553 •7527 •7501 7474 37 •7696 •7677 7657 •7637 •7617 7595 7574 7551 7528 7505 •7481 ■7456 •7431 ■7405 •7378 3" 7S94 7S7S 7556 7536 ■7515 •7494 7473 •7451 •7428 •7405 7381 7357 7332 ■7306 •7280 39 7489 •7470 745 1 •7432 •7412 7391 •7370 •7348 •7326 7303 •7279 7255 •7231 ■7206 •7180 40 ■7382 7364 7345 ■7326 •7306 •7286 •7265 •7243 •7221 ■7198 ■7175 7152 7127 ■7103 •7077 41° 7273 7255 •7236 •7217 •7198 •7178 7157 •7136 ■7114 ■7092 •7069 •7046 •7022 '6998 ■6973 42 •7161 7144 ■7125 ■7107 •7087 ■7068 •7047 ■7027 •7005 ■6983 •6961 •6938 •6914 •6890 •6866 43 7048 ■7030 •7012 ■6994 '^11^ ■6956 •6936 •6915 •6894 •6872 ■6850 •6828 •6805 •6781 •6757 44 •6932 •691s ■6897 ■6879 ■6860 ■6841 ■6822 •6801 •6781 •6760 •6738 •6716 •6693 •6670 •6646 45 •6814 ■6797 ■6780 •6762 •6744 •6725 •6706 •6686 ■6665 •6645 •6623 •6601 •6579 •6556 ■6533 46° ■6694 •6677 •6661 •6643 •6625 •6607 •6588 •6568 •6548 •6528 •6507 •6485 •6463 ■6441 •6418 '"^ ■6572 •6556 ■6539 •6522 •6504 •6486 •6468 ■6448 •6429 •6409 •6388 •6367 •6^41; •6^2 ■? •6TOI 48 ■6448 •6432 •6416 •6399 •6382 ■6364 •6346 •6327 •6308 •6288 •6268 •6247 •6226 •6204. •6182 49 ■6322 •6306 •6290 •6274 •6257 ■6239 •6222 •6203 •6184 •6:65 •6145 •6125 •6104 •6081 •606 1 50 6194 •6179 •6163 •6147 ■6130 ■6113 •6096 •6078 ■6059 ■6040 •6021 •6001 •5981 •5960 ■5939 51° •6064 ■6049 •6034 •6018 ■6002 •5985 'n^i •5950 •5932 •5914 •5895 •587s •5855 •583s •5814 52 ■5933 •5918 •5903 ■5888 •5872 •5855 •5838 •5821 ■ ^5803 •5785 •5767 •5748 •5728 J J3 •5708 ■5688 53 '>1V •5785 •5770 •5755 '^V^l •5724 •5707 •5690 •5673 •5655 ■5637 •5618 •5599 •5580 •«6o 54 •5664 •5650 ■5636 •5621 •5606 ■5590 •5574 •5558 •5541 •5523 •5506 •5487 •5469 '5450 '5430 55 •5527 •SS14 •5500 ■5485 •5470 •5455 •5439 •5423 •5407 •5390 •5373 •5355 •5337 •5318 ■5299 56° •5389 •5248 •5106 ■4963 •4818 •S37S ■5235 ■5094 •4951 •4806 ■5362 •5222 •5081 •4938 •4794 •5348 •5208 •5068 •4925 •4782 •5333 •5194 •5054 •4912 •4769 •5318 •5180 '5249 •4898 •4755 •5303 •5165 •4884 •4742 •5287 •5150 •5010 •4870 •4728 •5271 •5134 •4995 •4855 •4713 •5255 •5118 •4980 •4840 •4698 •5226 •5101 •4964 ■4824 •4683 ■5221 •5085 •4947 •4808 •4668 •5203 •5067 •4930 •4792 •4652 •5185 •5050 •4913 •4775 •4636 ■5166 •5032 •4896 •4758 •4619 61° 62 65 •4672 •4524 •437S •4224 •4072 ■4660 •4513 ■4364 •4214 •4062 •4648 •4501 •4353 •4203 •4052 ■4636 •4490 •4342 •4192 •4042 •4623 •4477 •4330 •4I8I •4031 •4611 •4465 •4318 •4169 •4019 •4598 •4452 •4305 •4157 ■4008 ■4584 •4439 •4293 •4145 •3996 •4570 •4425 •4280 •4132 •3984 •4556 •4412 •4266 •4119 •3971 •4541 •4397 ■4252 •4106 •3959 •4526 •4383 •4238 •4093 •3945 •451 1 •4368 •4224 •4079 •3932 •449S •4353 ■4209 •4065 •3918 •4479 •4337 ■4194 •4050 •3904 16| 16° 16| 17° 17| 18° 18l 19° 19| 20° 20| 21" 2l| 22° 22i When the sign is + the Azimuth is to be reckoned from the South. Wh^n the sign is - the Azimuth is to be reckoned from the North. ALT-AZIMUTH TABLES. 118 Enter with Latitude in margrin, and over the algebraic sum of E + F will be found the Azimuth in the head-line. TRUE AZIMUTH. Lat. 23 23i 24 24^ 25 25i 26 26^ 27 27J 28 28| 29° 29| 30 0° I 2 3 4 S 6° ^8 9 10 11° 12 13 14 15 16° H 18 19 20 21° 22 23 24 25 26° 27 28 29 30 31° 32 33 34 35 36° 32 38 39 40 41° 42 43 44 45 46° 42 48 49 SO 51° 52 53 54 55 56° 57 58 60 61° 62 ^3 65 •920s •9204 •9199 ■9192 •9183 •9170 •915s ■9136 •91 IS •9092 •906s •9036 •9004 •8969 •8932 •8891 •8803 •87SS •8704 •8650 ■8594 •8S3S •8473 •8409 •8343 ■8273 •8202 ■8128 •8051 •7972 ■7890 •7806 •7720 •7631 7S40 ■7447 73SI •7254 ■7154 •7051 •6947 ■6841 •6732 ■6622 •6509 •6394 ■6278 •6159 •6039 •5917 •S793 •5667 ■SS40 •54" •5280 •S'47 •5013 •4878 ■4741 •460J •4463 •4322 •4179 ■403s •3890 •9171 •9169 •9165 •9158 •9148 •9136 •9120 •9102 ■9081 •9058 •9031 •9002 •8970 •8936 23 •8858 •881S •8770 •8722 •8671 •8618 •8561 ■8502 ■8442 •8378 ■83 1 1 -8242 •8171 •8097 ■8021 7942 •7861 •7777 •7691 •7603 7SI2 7419 ■7324 7227 7127 7025 •6921 •681s •6707 ■6597 •648s ■6370 •6254 •6136 •6016 •5895 •5771 •5646 •SS19 •5390 ■5260 •5128 •499s •4860 •4723 •4585 •4446 ■430s ■4163 ■4020 •3876 •913s ■9134 •9130 •9123 •91 13 •9101 •908s •9057 ■9047 ■9023 •8997 ■8968 ■8936 ■8901 •8864 ■8824 •8782 •8736 •8688 •8638 ■8585 8529 •8470 ■8409 •8346 •8280 ■821 1 •8140 ■8c66 7990 7912 •7831 •7747 .7662 •7574 •7483 •7391 7296 7199 7100 •6998 ■689s •6789 •6681 •6571 •6460 •6346 •6230 •61 13 •5993 •5872 •5749 •5624 •5498 •5370 •5240 •5108 •4976 •4841 •470s •4568 •4429 •4289 •4147 ■400s •3861 23^ ■9100 ■9098 ■9094 ■9087 ■9077 •9065 . •9050 •9032 ■901 1 24 ■8961 •8932 •8901 ■8866 •8829 •8790 •8747 •8702 •8654 •8604 ■8551 ■8495 ■8437 •8376 ■8313 •8247 •8179 •8108 •8034 79S9 7880 7800 7717 7632 7544 7454 7362 7267 7171 7072 •6971 ■6868 ■6762 •6655 •6546 •6434 •6321 •6206 ■6089 •5970 •5849 •5727 ■5602 •5476 •5349 •5219 •5088 •4956 ■4822 •4687 •455° ■4412 •4272 •4131 •3989 •3846 •9063 •9062 •9058 •9051 •9041 •9029 •9013 •8996 •897s •8951 ■8925 ■8897 •8865 •8831 ■8794 •8754 ■87 1 2 •8667 •8619 •8569 •8517 ■8461 •8403 •8343 •8280 •8214 ■8146 ■8075 •8002 •7927 7849 •7769 ■7686 ■7631 7514 7424 ■7332 7238 7142 •7043 •6943 ■6840 •673s •6628 ■6519 64-9 •6296 ■6181 ■6064 •5946 ■5826 •5704 •5580 ■5454 •5327 •5198 •5068 ■4936 •4803 ■4668 •4532 •4394 •4255 •41 IS •3973 •3830 ■9026 ■9024 ■9020 ■9013 •9004 ■8992 ■8976 ■8959 •8938 •891S ■8860 24i ■8795 •8758 ■8718 •8676 •8631 •8584 ■8534 •8482 ■8426 •8369 •8308 •8246 •8180 ■811 2 •8042 ■7969 •7894 7817 7737 •7654 7570 •7483 •7394 •7302 7208 •7112 7014 ■6914 ■6812 •6708 ■6601 •6493 ■6382 •6270 ■6156 ■6039 ■5921 •5802 •5680 •5557 ■5432 •5305 •5177 •5047 •4916 •4783 •4649 •4513 •4376 •4237 •4098 •3957 •3814 •8987 •8982 •8976 ■8966 •8954 ■8939 •8921 25 25^ ■8877 •8851 ■8823 •8792 •8758 ■8721 •8682 •8640 •8595 •8548 •8498 ■8446 •8391 ■8333 ■8273 •821 1 •8146 •8078 •8008 •7936 ■7861 7784 ■7704 ■7622 •7538 7451 •7362 ■7271 7178 •7083 ■6985 •688s ■6783 ■6679 •6573 ■6465 •6355 •6244 •6130 •6014 •5897 •5777 •5656 •5534 •5409 •5283 •5155 •5026 •4895 •4763 •4629 •4494 •4357 •4220 •4080 ■3940 •3798 •8949 •8948 ■8944 •8937 •8928 ■8915 ■8900 26 •8862 •8839 ■8813 •8785 ■8754 •8720 •8684 •8644 ■8603 •8558 ■8511 •8462 •8410 •8355 •8298 •8238 •8176 •81 II ■8044 •7974 ■7902 7827 775° •7671 7589 •7So6 •7419 7331 •7240 7147 ■7052 6955 ■6856 •6754 •6651 ■6545 •6438 •6328 •6217 ■6103 •5988 •5871 •5753 •5632 •5510 ■5386 •5260 •5133 •5004 ■4874 •4742 •4609 •4475 •4339 •4201 •4063 ■3923 •3782 •8910 ■8909 •8905 ■8876 •8861 •8844 •8823 •8800 ■'8775 ■8746 •8715 •8682 •8645 •8606 ■8565 ■8521 •8474 •8425 •8373 ■8318 •8261 •8202 •8140 •8075 •8008 •7939 •7867 7793 7716 7637 7556 •7473 •7387 7299 •7208 •7 1 16 •7021 •6924 •6825 6725 •6621 ■6516 •6409 •63CX3 •6189 ■6077 •5962 ■5846 •5727 ■5607 •5486 •5362 •5237 •Sin •4982 ■4853 •4722 •4589 •4455 •4320 •4183 •4045 •3906 •3766 26^ ■8870 •8869 •886s 8836 •8822 •8804 •8784 •8761 •8735 •8707 •8676 •8643 •8607 •8s68 •8526 •8483 •8436 ■8387 •8335 •8281 •8224 •8i6s •8103 •8039 •7972 •7903 7832 7758 ■7682 7603 7522 ■7439 7354 7266 7176 •7084 •6990 •6893 •6795 •6694 •6592 •6487 •6381 •6272 •6162 •6049 •5935 •5819 •S702 •5582 •5461 •5338 •5214 ■5088 •4960 •4831 •4700 ■4568 •4435 •4300 •4164 •4027 27 ■3749 •8829 •8828 •8824 •8817 •8808 •8796 •8781 •8764 •8744 •8721 •8695 •8667 •8637 •8603 •8567 ■8529 •8487 •8444 •8397 •8348 •8297 •8243 •8187 •8128 •8066 ■8002 •7936 7867 7796 ■7722 7647 7568 •7488 •7405 7320 7233 7143 •7052 ■6958 •6862 •6764 •6664 ■6562 •6457 6351 •6243 •6133 •6022 •5908 •5793 ■5675 •5557 •5436 •5314 •5190 •5064 •4937 •4809 ■4679 •4548 •4415 •4281 •4145 •4008 ■3871 ■3731 27^ •8788 •8787 •8783 ■8776 ■8767 •8755 ■8740 •8723 •8703 •8680 •8655 •8627 ■8596 ■8563 •8527 •8489 ■8448 •8404 •8358 •8309 •82S8 •8204 •8148 •8ogo •8028 ■7965 7899 ■7830 7759 7686 •761 1 7533 7453 7370 •7286 7199 •7110 ■7019 •692s •6830 •6732 •6633 •6531 •6427 •6322 ■6214 •610S ■5994 •5880 •S766 ■5649 •5531 ■5411 •5289 •5166 •3041 •4914 •4786 ■4657 •4526 •4394 •4261 •4126 •3990 •3852 •3714 28 •8746 •8745 •8741 •8734 •8725 •8713 •8698 •8681 •8661 •8639 •8613 ■8586 ■8555 •8S22 •8486 •8448 •8407 •8364 •8318 •8270 •8219 .8165 •8109 ■8051 •7990 ■7927 •7861 7793 •7722 ■7650 7574 7497 7417 7335 72s I 7164 •7076 •698S •6892 •6797 ■6700 •6601 •6500 •6397 •6291 •6184 •6076 •5965 •5852 •5738 •5622 •5504 •5385 •5264 •5141 ■5017 •4891 •4764 •4635 •4505 •4373 •4240 •4106 •3971 ■3834 •3696 28t •8704 •8702 •8698 •8692 •8682 •8670 •86s6 ■8639 •8619 ■8596 •8571 ■8544 •8513 •8480 ■8445 •8407 •8366 •8323 •8278 ■8229 •8179 •8125 ■8070 •8012 •7951 •7823 7755 768s •7612 7538 •7460 •7381 ■7299 •7216 7130 •7041 •69s I •68s8 •6764 ■6667 •6S69 •6468 •636S •6261 •6154 •6046 •5936 •5824 •5710 •5595 •5477 •5358 •5238 •5116 •4992 •4867 •4740 •4612 ■4483 •4352 •4220 •4086 •3951 •3815 •3678 29 •8660 •8659 •8655 •8648 •8639 •8627 •8613 •8596 •8576 •8554 •8529 •8soi •8471 •8438 •8403 •836s ■8325 •8282 •8236 •8188 •8138 ■808s ■8030 •7972 •7912 7849 7784 7716 7647 7574 7S0O 7423 7344 7263 7180 •7094 •7006 •6916 •6824 •6730 ■6634 •6536 •6436 •6334 ■6230 •6124 '6016 -•5906 •5795 •5682 •5567 •5450 •5332 •5212 •5090 •4967 ■4843 •4717 •4589 •4460 •4330 •4199 •4066 •3932 •3796 •3660 29| 30" When the sign is + the Azimuth is to be reckoned from the South. When the sign is - the Azimuth is to be reckoned from the North. 119 ALT-AZIMUTH TABLES. G Enter with Latitude in margin, and over the algebraic sum of E . + F will be found the Azimuth in the head-line. Lat. TRUE AZIMUTH. 30l 31° 31| 32° 32| 33° 33| 34° 34| 35° 35| 36° 36| 37° 37°i 0° •8616 •8572 •8526 •8480 •8434 •8387 ■8339 ■8290 ■8241 •8192 •8141 •8090 ■8039 •7986 •7934 I ■8615 ■8570 •8525 ■8479 •8433 •838s •8338 ■8289 •8240 •8190 •8140 •8089 •8037 •7985 7932 2 •861 1 •8566 •8521 ■8475 •8429 •8382 •8334 •828s •8236 •81S7 ■8136 •8085 •8034 ■ ■7981 •7929 3 •8604 •8560 •8515 •8469 ■8422 •837s •8327 •8279 •8230 •8180 •8130 ■8079 ■8028 ■7975 •7923 4 •8595 ■8551 ■8506 •8460 •8413 •8366 ■8319 •8270 ■8221 ■8172 •8121 •8070 ■8019 ■7967 •7914 5 •8584 •8539 ■8494 •8448 •8402 ■8355 •8307 •8259 •8210 •8160 •8110 •8059 8008 ■7956 •7903 6° •8569 •8525 •8480 •8434 •8388 •8341 •8293 •8245 ■8196 ■8147 •8046 ■7995 7943 •7890 7 •8552 •8508 •8463 •8417 •8371 ■8324 ■8277 ■8229 ■8180 ■8130 •8080 •8030 ■7979 7927 ■7874 8 •8532 ■8488 •8443 ■8398 ■8352 •8305 •8258 •82 10 •8161 ■8112 ■8062 •801 1 ■7960 ■7909 ■7856 9 •8510 •8466 ■8421 •8376 •8330 •8283 ■8236 •8188 •8140 •8091 ■8041 •7991 •7940 •7888 •7836 10 •848s •8441 ■8397 •8352 •8306 ■8259 •8212 •S164 •8116 •8067 ■8017 ■7967 •7916 •7865 •7813 11° ■^S8 •8414 •8370 ■8325 •8279 •8233 ■8186 ■8138 ■8090 ■8041 •7992 ■7942 ■7891 •7840 •7788 12 ■8428 •8384 •8340 •829s ■8250 •8203 •8157 ■8109 ■8061 ■8013 •7963 ■7913 ■7863 ■7812 •7760 13 •839s •8352 ■8308 •8263 ■8218 •8172 •8125 •8078 •8030 •7982 •7932 ■78S3 ■7833 ■7782 •7730 14 •8360 •8317 •8273 •8229 •8183 ■8138 •8091 •8044 •7996 •7948 ■7899 •7850 •7800 ■7749 •7698 IS ■8323 •8280 ■8236 •8192 •8147 •8101 •8055 •8008 •7960 ■7912 •7864 ■7815 ■7765 7714 7663 r6° ■8283 •8240 •8196 •8152 •8107 ■8062 •8016 •7969 •7922 •7874 •7826 7777 7727 ■7677 •7626 '2 ■8240 •8197 •8154 ■8110 ■806s •8020 •7974 •7928 •7881 7834 7785 7737 •7687 •7637 ■7587 i8 ■8i9S ■8152 •8109 •806s •8021 •7976 •7931 •7885 ■7838 •7791 •7743 •7694 •7645 7595 ■754s 19 •8147 ■8105 •8062 •8018 7974 •7930 •7885 •7839 •7792 •7745 •7698 •7649 •7601 ■7551 •7501 20 •8097 ■8055 •8012 •7969 7925 ■7881 ■7836 •7790 •7744 •7698 •7650 •7602 7554 •750s •7455 21° ■8044 •8002 •7960 •7917 7874 •7830 •7785 •7740 •7694 •7647 •7600 •7553 ■7505 7456 •7407 22 •7989 •7948 •7906 ■7863 •7820 •7776 •7732 •7687 •7641 •7595 ■7548 7501 •7453 •7405 ■7356 23 •7931 •7890 •7849 •7806 7763 •7720 •7676 ■7631 ■7586 •7540 •7494 •7447 •7400 ■7351 •7303 24 •7871 •7831 •7789 "^W^ 7705 •7662 ■7618 •7574 7529 •7483 •7437 7391 ■7344 •7296 •7248 25 •7809 •7769 •7728 •7686 •7644 •7601 7558 ■7514 •7469 •7424 7378 ■7332 •7285 •7238 •7190 26° •7744 •7704 •7663 •7622 7580 7538 •7495 •7451 •7407 • ■7362 7317 •7271 ■7225 •7178 •7131 27 ■7677 7637 7S97 ■"io 751S •7473 •7430 •7387 •7343 •7299 •7254 •7208 ■7162 ■7116 •7069 28 ■7608 •7568 7528 7488 7447 •7405 •7363 •7320 7277 •7233 •7188 7143 •7098 •7052 •7005 29 •7536 7497 74S7 •7417 7376 7335 •7293 ■7251 ■7208 •7164 •7120 •7076 •7031 ■6985 •6939 30 ■7462 7423 7384 7344 7304 •7263 •7222 •7180 7137 •7094 ■7050 •7006 •6962 ■6916 •6871 31° •7386 7347 •7309 •7269 •7229 •7189 •7148 •7106 •7064 ■7022 ■6978 ■6935 •6890 ■6846 •6800 32 •7307 •7269 •7231 •7192 •7152 •7112 •7072 •7031 ■6989 •6947 •6904 •6861 •6817 •6773 ■6728 33 ■7226 •7189 •71S1 ■7112 7073 •7034 ■6994 •6953 ■6912 •6870 •6828 •6785 •6742 ■6698 •6654 34 7143 •7106 •7069 •7031 •6992 •6953 •6913 •6873 •6832 •6791 •6749 ■6707 •6664 ■6621 ■6577 35 •7058 •7022 •6984 •6947 •6909 ■6870 •6831 •6791 •6751 •6710 ■6669 ■6627 ■6585 ■6542 ■6499 36° •6971 1?3S •6898 •6861 •6823 •6785 ■6746 •6707 ■6667 •6627 ■6586 •6545 ■6503 ■6461 •6418 37 •6881 •6846 •6809 •6773 •6736 •6698 •6660 •6621 •6582 •6542 ■6502 •6461 ■6420 ■6378 •6336 38 ■6790 •67SS •6719 •6683 •6646 ■6609 •6571 •6533 ■6494 •6455 ■6415 •6375 •6334 •6293 •6252 39 •6696 •6661 •6626 t^^l •6554 ■6518 ■6481 •6443 •6405 ■6366 ■6327 ■6287 •6247 •6207 ■6166 40 •6600 •6566 ■6532 •6496 ■6461 •642s •6388 •6351 •6313 •6275 ■6236 •6197 •6158 •61 18 •6077 41° •6503 •6469 •643s ■6400 •6365 •6330 •6293 •6257 ■6220 •6182 •6144 •6106 •6067 •6027 •5988 •5806 42 •6403 •6370 •6336 •6302 •6268 •6233 •6197 ■6161 ■6124 ■6087 •6050 •6012 '5974 •5935 43 •6302 ■6269 ■6236 •6202 •6168 ■6134 •6099 •6063 •6027 •5991 ■5954 •5917 ■5879 J7JJ ■5841 ■';8o2 44 •6198 •6166 •6133 •6100 •6067 •6033 ■5998 •5964 •5928 •5892 ■5856 •5820 ■5782 ■5745 ■';7o7 45 •6093 •6061 •6029 •5997 •5964 •5930 •5896 ■5862 •5827 •5792 ■5757 •5721 •5684 ■5647 •5610 46° '^fi ■5f54 •5923 •5891 •5859 •5826 •5793 ■5759 •5725 •5690 ■5655 •5620 ■5584 ■5548 •5511 ^l •5876 ■5846 •5815 •5784 •5752 •5720 •5687 •5654 •5621 •5587 •5552 ■5517 ■5482 •5447 48 •5765 ■5736 •570s •5675 •5643 •5612 ■5580 •5547 •5514 ■5481 •5447 ■5413 •5379 ■5344 ■5309 49 '.t^l •5624 ■5594 •5564 •5533 •5502 •5471 ■5439 •5407 •5374 •5341 ■5308 •5274 •5240 •5201; 50 •5538 •5510 •5481 ■5451 •5421 ■5391 •5360 ■5329 •5297 •5265 ■5233 ■5200 •5167 •5134 J J •5100 51° •5422 •5394 •5366 •S337 •5308 •5278 •5248 •5217 •S186 ■5155 ■5123 ■5091 ■5059 •5026 •4993 52 •5305 ■5277 ■5249 •5221 •5192 •5163 •5134 ■5104 ■5074 ■5043 •5012 ■4981 ■4949 •4917 •4884 •4775 53 •5185 •5159 •5131 •5104 •SQ76 •5047 •5018 •4989 ■4960 •4930 •4899 •4869 ■4838 ■4806 54 ■5065 •S038 ■5012 •4985 •4957 •4930 •4901 •4873 •4844 •4815 •4785 •4755 ■4725 ■4694 •4663 •4550 55 •4942 ■4917 •4891 ■4864 •4837 ■4810 •4783 ■4755 ■4727 •4698 •4670 •4640 -It J •461 1 ■4581 56° •4818 ''^lll ■4768 •4742 •4716 •4690 •4663 •4636 •4608 •4581 •4552 •4524 ■4495 ■4466 •4436 ■4^21 57 •4693 ■4668 •4644 ■4619 ■4593 •4568 ■4542 ■4515 •4489 ■4461 •4434 •4406 •4378 •4350 S" ■4566 ■ASA^ •4518 •4494 ■4469 •4444 •4419 ■4393 ■4367 ■4341 •4314 •4287 •4260 •4232 •4204 S •4438 'Ki •4391 •4368 ■4344 •4319 ■429s •4270 ■424s ■4219 ■4193 ■4167 •4140 •41 13 ■4086 00 •4308 •4286 •4263 ■4240 •4217 •4193 •4169 •4145 •4121 •4096 ■4071 •4045 •4019 •3993 •3967 6i° •4177 ■4156 •4134 ■41 1 1 •4089 •4066 •4043 •4019 ■3995 •3971 ■3947 •3922 ■3897 •3872 ■3846 62 •404s •4024 •4003 •3981 •3959 •3937 •3915 •3892 •3869 ■3846 •3822 •3798 •3774 ■3749 ■3725 •3602 •3478 •3353 «3 •3912 •3891 •3871 •3850 •3829 ■3807 •3786 •3764 ■3741 ■3719 •3696 •3673 •3649 •3626 «^ •3777 ■3758 •3738 •3718 •3697 •3676 •3656 •3634 ■3613 ■3591 •3569 •3546 •3524 ■3501 65 •3641 •3623 •3603 ■3584 •3564 •3544 •3524 •3504 ■3483 •3462 ■3441 •3419 •3397 •3375 30| 31° 31| 32° 32| 33° 33| 34° 34| 35° 35| 36° 36| 37° 37\ When the sign is + the Azimuth is to be reckoned from the South. When the sign is - the Azimuth is to be reckoned from the North. ALT-AZIMUTH TABLES. G 120 Enter with Latitude in marg-ln, and over the algebraic sum of E + F will be found the Azimuth in the head-line. TRUE AZIMUTH. Lat. 38 38.V 39 39 i 40° 40i 41 41| 42 42^ 43 43i 44 44i 45 o" I 2 3 4 5 6° 7 3 9 10 11° 12 13 14 IS i6° 17 i8 19 21" 22 23 24 25 26° 27 z8 29 30 31° 32 33 34 35 36° 37 38 39 40 41° 42 43 44 45 46° 47 48 49 50 51° 52 53 54 55 56° 57 58 59 60 6i* 62 ^3 64 65 •7880 ■7879 787s •7869 •7861 •7850 ■7837 •7821 •7803 •7783 ■7760 7735 •7708 •7678 •7646 •7612 7S7S 7536 7494 7451 ■7405 73S7 •7306 ■7254 7199 •7142 ■7083 •7021 •6958 •6892 •6824 •67SS ■6683 •6609 ■6533 ■64SS ■6375 ■6293 ■6210 •6124 ■6037 •5947 •5856 •5763 •5668 5572 ■5474 •5374 •5273 •5170 •5065 ■4959 ■4851 •4742 •4632 •4520 •4406 •4292 ■4176 ■4059 •3C40 •3820 •3699 ■3577 •3454 •3330 •7826 7825 ■7821 •781S •7807 •7796 ■7783 ■7768 •7750 •7730 •7707 •7682 ■7655 •7625 7594 7559 7523 7484 7443 •7400 7354 •7306 7256 •7204 7149 7093 •7034 •6973 ■6910 •6845 •6778 •6708 •6637 •6564 •6488 •641 1 •6331 •6250 •6167 •6082 •5995 ■5906 •5816 ■5724 •5630 •5534 •5436 •5337 •5237 ■5134 ■5031 •492s •4818 ■4710 •4600 ■4489 •4376 ■4262 •4147 •4031 ■3913 ■3794 •3674 ■3553 •3431 •3307 38 381 •7771 ■7770 ■7767 •7761 7753 •7742 •7729 7714 ■7696 •7676 7653 •7629 ■7602 7572 7541 ■7507 ■7470 7431 7391 •7348 •7303 •7255 •7206 7154 •7100 ■7043 ■6985 •6924 ■6862 •6797 ■6730 •6661 ■6591 •6518 ■6443 •6366 •6287 •6207 •6124 ■6040 •5953 •586s •5775 •5684 •5590 •5495 •5399 ■5300 •5200 ■5099 ■4995 •4S91 •4785 •4677 •4568 •4458 •4346 •4233 •41 18 •4003 •3886 ■3768 ■3648 •3528 •3407 ■3284 •7716 7715 •7712 •7706 •7697 •7687 •7674 •7659 •7641 •7621 7599 ■7S74 7548 •7518 •7487 •7453 •7417 •7379 7339 •7296 7251 •7204 7154 •7103 •7049 •6993 ■6935 ■6875 •6813 ■6749 ■6682 6614 •6544 •6471 •6397 •6321 •6243 ■6162 •6080 •5997 ■591 1 •5824 ■5734 •5643 ■5551 •5456 •5360 ■5262 •5163 •5062 •4960 •4856 ■4751 •4644 •4535 •4426 ■4315 •4203 39 ■3974 •3858 •3741 •3623 ■3503 •3383 ■3261 39i •7660 •7659 •7656 •7650 •7642 ■7631 •7618 •7603 •7586 ■7566 •7544 7520 ■7493 ■7464 ■7433 •7399 •7364 •7326 •7286 •7243 ■7198 •7152 •7103 •7051 ■6998 ■6943 •6885 ■6826 ■6764 •6700 •6634 •6566 •6496 •6425 •6351 •627s •6197 •61 18 ■6037 •5953 ■5868 •5781 ■5693 ■5602 •5510 •5417 •5321 •5224 ■5126 •5026 •4924 •4821 •4716 ■4610 •4503 •4394 ■4284 •4172 •4059 •3945 •3830 •3714 •3596 •3478 •3358 •3237 •7604 ■7603 •7599 7594 •7586 7575 7562 •7547 ■7530 7510 ■7489 •7464 •7438 •7409 •7378 7345 •7309 •7272 •7232 •7190 7145 •7099 ■7050 ■7000 •6947 •6892 •6834 ■6775 •6714 ■6651 •6585 •6518 •6449 •6377 •6304 •6229 ■6152 •6073 •5992 ■5909 ■5825 •5739 •5651 •5561 •5470 5377 •5282 •5186 •5088 •4989 •4785 •4682 •4576 •4470 ■4362 •4252 •4141 ■4030 •3916 ■3802 •3687 •3570 •3452 ■3333 •3214 40 40| •7547 •7546 •7542 7537 7529 ■7518 •7506 7491 7474 •7454 7432 •7408 •7382 7354 •7323 ■7290 •7255 •7217 •7178 •7136 •7092 •7046 •6998 •6947 ■6895 •6840 •6783 •6725 •6664 ■6601 ■6536 ■6469 •6400 •6330 •6257 ■6182 ■6106 •6027 •5947 •5865 ■5781 •5696 ■5609 •5520 •5429 •5337 •5243 •5147 •5050 •4951 •4851 •4750 ■4646 •4542 •4436 •4329 •4220 •41 10 ■3999 •3887 •3774 •3659 •3543 ■3426 ■3308 •3190 41 ■7490 •7488 •7485 •7479 ■7471 •7461 7449 •7434 •7417 •7397 7376 7352 ■7326 7298 •7267 •7234 •7199 •7162 ■7123 •7082 •7038 •6992 ■6944 •6894 •6842 ■6788 •6732 ■6673 ■6613 •6551 •6486 ■6420 •6352 •6281 ■6209 •6135 •6059 •5981 ■5902 •5820 ■5737 •5652 •5566 •5478 •5388 •5296 •5203 •5108 ■501 1 •4914 ■4814 ■4713 ■461 1 •4507 •4402 •4296 •4188 •4079 •3969 •3857 •3745 •3631 •3S>6 •3400 •3283 ■3165 41i 7431 7430 ■7427 •7421 •7413 •7403 •7391 7376 •7359 •7340 7319 •7295 ■7269 •7241 •7211 ■7178 7144 •7107 •7068 •7027 ■6983 •6938 •68go ■6841 •6789 •6735 •6679 •6621 •6562 •6500 ■6436 •6370 ■6302 •6233 6161 ■6087 ■6012 •5935 ■5856 •5775 •5693 •5609 •5523 •5435 •5346 •5255 •5162 •5068 •4973 •4875 •4777 •4677 •4575 ■4472 •4368 •4263 •4156 ■4047 •3938 •3827 •3716 ■3603 ■3489 ■3374 ■3258 •3141 7373 7372 •7368 •7363 7355 •7345 •7332 ■7318 ■7301 •7282 •7261 •7237 •7212 7184 7154 ■7122 •7087 •7051 ■7012 ■6971 •6928 •6883 •6836 ■6787 •6735 ■6682 ■6627 •6569 •6510 ■6448 •638S •6320 •6252 ■6183 •6112 •6039 •5965 42 •5810 ■5730 ■5648 •5564 •5479 •5392 •5304 ■5213 •5122 •5028 •4933 •4837 ■4739 ■4640 •4539 •4437 •4334 •4229 ■4123 ■4016 •3907 •3797 •3686 ■3574 •3461 •3347 •3232 •3116 7314 •7312 •7309 7304 ■7296 •7286 •7273 •7259 ■7242 •7223 •7202 •7179 7154 •7126 •7096 •7064 •7030 •6994 ■6956 ■6915 ■6872 ■6828 •6781 ■6732 •6681 •6628 ■6573 •6516 ■6457 •6397 ■6334 ■6269 •6202 •6134 •6063 •5991 •5917 •5841 ■5763 •5684 •5602 •5520 •5435 •5349 •5261 •5171 ■5080 •4988 ■4894 •4798 •4701 •4603 •4503 •4401 ■4299 •4195 •4090 •3983 •3876 •3767 •3657 •3546 •3433 ■3320 •3206 •3091 •7254 •7253 •7249 ■7244 •7236 •7226 •7214 •7200 7183 •7164 7144 ■7120 ■7095 ■7068 •7038 •7007 •6973 •6937 •6899 ■6859 •6816 ■6772 ■6726 ■6677 6627 ■6574 ■6520 ■6463 •6405 ■5344 ■6282 •6218 ■6152 ■6084 •6014 •5942 ■5868 •5793 •5716 •5637 •5557 •5474 •5391 •5305 ■5218 •5129 •5039 ■4947 •4854 •4759 •4663 ■4565 •4466 ■4365 '4264 ■4161 ■4056 •3951 •3844 •3736 •3627 •3517 •3405 •3293 •3180 •3066 42^ 43 7193 •7192 •7189 ■7184 ■7176 •7166 7154 •7140 ■7123 7105 •7084 •7061 •7036 ■7009 •6980 ■6948 •6915 •6879 •6841 •6801 ■6760 ■6716 ■6670 •6622 •6571 ■6519 •6465 •6409 •6351 •6291 •6230 •6166 •6100 •6033 •5964 ■5892 •5820 •5745 ■5668 •5590 •5510 •5429 ■5346 •5261 ■5174 •5087 •4997 •4906 •4813 ■4719 •4624 ■4527 •4429 •4329 ■4228 ■4126 '4022 ■3918 •3812 ■3705 •3597 •3487 ■3377 •3266 •3153 •3040 43i 7133 •7132 •7128 •7123 •7115 •7105 •7093 •7079 •7063 •7045 •7024 ■7001 •6977 •6950 •6921 •6889 ■6856 •6821 •6783 •6744 •6702 •6659 ■6613 •6566 ■6516 ■6464 •641 1 •6355 •6298 ■6238 •6177 •6114 ■6049 •5982 •5913 ■5843 •5770 •5696 ■5620 ■5543 ■5464 •5383 •5300 •5216 ■5131 ■5043 •4955 •4864 •4773 •4679 •4585 •4489 •4391 •4292 •4192 •4091 ■3988 •3885 •3780 •3674 •3566 •3458 ■3349 •3238 ■3127 •3014 44 •7071 •7070 •7067 •7061 •7054 ■7044 •7032 •7018 7CX)2 ■6984 •6964 •6941 •6917 •6890 ■6861 •6830 ■6797 ■6762 •6725 •6686 ■6645 •6601 ■6556 ■6509 ■6460 •6409 •6355 •6300 •6243 •6184 •6124 •6061 •5997 •5930 •5862 •5792 ■5721 •5647 ■5572 ■5495 •5417 •5337 •5255 •5171 ■5087 •5000 •4912 ■4822 ■4731 •4639 •4545 •4450 •4353 •4255 •4156 ■4056 •3954 ■3851 •3747 •3642 ■3536 •3428 •3320 •3210 •3100 ■2988 44J 45 When the sign is + the Azimuth is to be Feekoned from the South. When the sign is ~ the Azimuth is to be reckoned from the North. 121 ALT-AZIMUTH TABLES. Enter with Latitude in margin. « r and over the algebraic i Ul sum of E -f F will be found the Azimuth In the head-line. Lat. TRUE AZIMUTH. 45| 46° 46| 47° 47| 48° 48| 49° 4Q\ 50° 50l 51° 51°i 52° 52| 0° •7009 •6947 ■6884 ■6820 ■6756 ■6691 ■6626 •6561 ■6494 •6428 ■6361 ■6293 •6225 ■6157 ■6088 I 7008 •6946 •6883 •6819 ■675s •6690 •6625 •6560 ■6493 •6427 ■6360 •6292 •6224. •6156 •6087 2 700s ■6942 •6879 •6816 •6752 •6687 •6622 ■6557 •6491 ■6424 •6357 •6289 •6221 •6153 •6084 3 ■6999 ■6937 1!l* ■68 1 1 ■6747 ■66S2 ■6617 ■6552 •6486 ■6419 ■6352 •6285 ■6217 •6148 •6079 4 •6992 •6930 •6867 •6803 ■6739 ■6675 •6610 •6545 •6479 •6412 6345 •6278 ■6210 ■6142 •6073 5 ■6982 •6920 ■6857 •6794 •6730 •6666 •6601 ■6536 •6470 •6403 ■6337 ■6269 ■6201 •6 '33 ■6064 6° •6971 •6909 •6846 ■6783 •6719 •6655 ■6590 ■6525 ■6459 ■6393 ■6326 •6259 ■6191 •6123 •6054 I •6957 •689s •6832 •6769 ■6705 •6641 ■6577 •6512 •6446 •6380 •6313 •6246 ■6179 •61 1 1 •6042 8 •6941 ■6879 •6817 ■6754 ■6690 •6626 6562 ■ •6497 ■6431 ■6365 •6299 •6232 ■6165 ■6097 •6029 9 •6923 •6861 •6799 ■6736 •6673 •6609 ■6545 •6480 •6415 ■6349 •6283 ■6216 ■6149 •6081 •6ai3 10 •6903 •6841 ■6779 ■6716 ■6653 •6590 •6526 ■6461 •6396 ■6330 ■6264 •6198 •6131 •6063 •5995 11° ■6880 ■6819 •6757 ■669s ■6632 ■6568 ■6504 ■6440 ■6375 •6310 •6244 •6178 •6111 ■6044 ■5976 12 •6856 vp ■6733 ■6671 •6608 ■6545 ■6481 •6417 •6352 ■6287 •6222 ■6156 ■6089 •6022 •5955 13 •6829 ■6769 •6707 ■664s ■6583 •6520 •6456 ■6392 ■6328 ■6263 ■6198 •6132 ■6066 "5999 •5932 14 ■6801 •6740 •6679 ■6617 ■6555 •6493 •6430 •6366 •6302 •6237 •6172 •6106 •6040 •5974 •5907 IS •6770 •6710 ■6649 •6588 ■6526 •6463 •6400 ■6337 ■6273 ■6209 •6144 ■6079 •6013 •5947 •S880 i6° ■6738 •6677 •6617 •6556 ■6494 •6432 •6369 •6306 •6243 •6179 ■61 14 •6049 •5984 •5918 •5852 17 •6703 •6643 •6583 •6522 •6461 ■6399 ■6337 ■6274 •62 1 1 •6147 •6083 ■6018 ■5953 •5888 ■5822 18 •6666 •6607 •6547 •6486 ■6425 •6364 ■6302 ■6239 •6176 ■6113 •6049 ■5985 ■5920 ■5855 •5790 19 •6627 •6568 •6508 ■6448 •6388 1^27 •6265 •6203 •6141 •6078 •6014 •5950 ■5886 •5821 >• •5756 20 ■6586 •6528 ■6469 •6409 ■6349 •6288 ■6227 •6165 •6103 ■6040 •5977 ■5914 •5850 •5785 ■5720 21° •6544 •6485 ■6426 •6367 ■6307 •6247 •6186 •6125 •6063 •6cx)i •5938 ■5875 •5812 •5748 •5683 22 •6499 ■6441 •6382 •6323 •6264 ■6204 •6144 •60S3 ■6022 •5960 •5898 •5835 •5772 ■5708 ■5644 23 •6452 'P'^i ■6336 •6278 •6219 •6159 •6099 •6039 ■5978 ■5917 •5855 ■5793 ■5730 •S667 •5604 24 •6403 ■6346 ■6288 ■6230 •6172 •61 1 3 ■6053 •5993 ■5933 ■5872 ■58H ■5749 •5687 •5624 •5561 25 6352 ■6296 •6239 •6181 •6123 ■6064 •600s ■5946 •5886 •6826 ■5765 ■5704 •5642 •5580 •5517 26° ■6300 ■6244 •6187 •6130 •6072 •6014 ■5956 ■5897 •5837 •5777 ■5717 ■5656 •5595 ■5534 ■5472 fs ■624s •6189 •6133 ■6077 •6020 •5962 •5904 ■5846 ■5787 •5727 •5667 •5607 ■5547 •5486 •5424 •6189 VH •6078 •6022 •5965 •5908 ■5851 ■5793 •5734 •5675 •5616 •5557 •5497 •5436 •5375 29 •6130 •6076 •6021 ■596s •5909 ■5852 ■5795 ■5738 ■5680 ■5622 •5563 ■5504 ■5445 ■5385 •5325 30 ■6070 •6016 •5961 •5906 •5851 •5795 ■5739 •5682 •5625 ■5567 •5509 •5450 ■5391 •5332 •5272 31° •6008 •5954 ■5i°5 ■5846 ■5791 •5736 •5680 ■5624 ■5567 ■5510 •5452 ■5394 •5336 •5277 •i;2i8 32 •S944 •5891 •5838 •5784 ■5729 •5675 ■5619 ■5564 •5508 ■5451 •5394 •5337 •5279 D t 1 •5221 ■5163 33 •5878 •5826 •5773 •5720 •5666 •5612 ■5557 •5502 •5447 ■5391 •5335 ■5278 •5221 •5163 •mo6 34 •581 1 ■5759 •5707 ■5654 •5601 •5547 ■5493 ■5439 ■5384 ■5329 ■5273 •5217 •5161 ■'1IO4 •5047 35 •5742 •5690 •5639 ■5587 ■5534 •5481 ■5428 ■5374 ■5320 •5265 •5210 ■5155 ■5099 •5043 •4987 36° •5670 •5620 •5569 ■5517 ■5465 ■5413 ■5361 ■5308 •5254 •5200 •5146 •5091 •5036 ■4981 •4925 37 38 ■5598 •5548 •5498 ■5447 •5395 •5344 ■5292 ■5240 •5187 •5134 •5080 •5026 •4972 •4917 •4862 ■5523 •5474 •5424 ■5374 ■5324 •5273 •5222 •5170 •5118 ■5065 ■5012 ■4959 ■4905 ■4851 •4797 39 •S447 ■5399 •5350 ■5300 •5250 ■5200 •5150 •5099 ■5047 ■4995 ■4943 •4891 ■4838 •4785 •4.7^1 40 •5369 •5321 •5273 ■5224 ■5175 •5126 ■5076 •5026 •4975 4924 •4873 •4821 •4769 •4716 ■t6i3 41° ■5290 •5243 •5195 ■5147 •5099 •5050 •5001 •4951 ■4901 •4851 •4801 •4750 •4698 '4646 •4594 •4524 ■4452 ■4379 •4304 42 •5209 •5162 •5115 •5068 ■5021 ■4973 •4924 ■4875 •4826 ■4777 ■4727 •4677 •4626 •4575 •4503 •4429 •4353 43 •5126 •5080 •5034 ■4988 •4941 •4894 •4846 •4798 ■4750 •4701 •4652 •4603 'A'if.% 44 ■5042 •4997 ■4952 •4906 •4860 •4813 •4766 •4719 •4672 •4624 ■4576 ■4527 ■4478 15 ■4956 •4912 •4867 •4822 ■4777 ■4731 ■4685 •4639 ■4592 ■4545 •4498 ■4450 ■4402 46° •4869 ■4780 •4690 •4826 •4738 •4648 ■4782 •4695 •4606 ■4738 ■4651 ■4563 •4693 •4607 •4520 •4648 •4563 ■4477 ■4603 •4519 ■4434 •4557 •4474 ■4390 ■45 1 1 ■4429 ■4346 ■4465 ■4384 •4301 •4419 •4338 ■4256 •4372 •4292 •4211 •4325 •4246 ■4166 •4277 •4199 '4120 •4229 •4152 •4074 •3994 ■3913 49 50 ■4598 ■4505 ■4557 ■4465 •4516 ■4425 ■4474 ■4384 ■4432 ■4343 ■4390 •4301 •4347 ■4259 ■4304 ■4217 •4261 ■4175 4217 •4132 ■4173 ■4089 ■4129 ■4045 •4084 •4001 •4039 •3957 51° •441 1 ■4372 ■4332 •4292 ■4252 •42 u ■4170 ■4129 •4087 ■4045 •4003 ■3960 •3917 •3874 •3790 •3705 •3619 ■3531 ;383i •3664 ■3578 •3492 52 •43 IS •4277 •4238 •4199 •4160 •4120 •4080 ■4039 ■3998 •3957 •3916 ■3874 •3832 '^74.6 53 •4218 •4181 ■4143 •4104 ■4066 •4027 •3988 ■3948 •3908 •3868 •3828 •3787 54 55 •4120 ■4020 •4083 •3984 •4046 •3948 •4009 •3912 ■3971 ■3875 ■3933 •3838 ■3895 ■3801 ■3856 ■3763 •3817 ■3725 •3778 ■3687 ■3739 •3649 •3699 ■3610 ■3659 •3571 56° 1 ■3919 •3817 •3714- •3610 •3505 •3884 ■3783 ■3681 •3578 •3473 ■3849 ■3749 ■3648 •3546 ■3442 ■3814 ■3714 ■3614 ■3513 •3410 •3778 ■3679 ■3580 ■3480 ■3378 ■3742 •3644 •3546 •3446 •3346 •3706 •3609 •3512 •3413 ■3313 •3669 •3573 •3477 ■3379 •3280 •3632 •3537 •3442 •3345 •3247 •3594 ■3501 •3406 ■3311 •3214 •3557 ■3465 ■3371 •3276 •3181 ■3519 ■3428 ■3335 •3241 •3147 ■3481 ■3391 ■3299 ■3206 •3II3 •3443 ■3353 •3263 •3171 •3078 •3404 ■3316 •3226 ■3136 •3044 61° 62 P. •3398 •3291 •3182 •3368 •3261 •3154 ■3337 ■3232 •3125 ■3306 •3202 ■3096 ■3275 •3172 •3067 •3244 •3141 ■3038 ■3213 ■3111 •3008 ■3181 ■3080 •2978 •3149 •3049 •2948 ■3116 ■3018 •2918 •3084 ■2986 •2888 ■3051 ■2954 •2857 •2759 •2660 ■3018 '2922 ■2826 •298s •2890 •2795 •2699 •2602 •2952 •2858 •2764 •2669 ■2S73 64 65 ■3073 ■2962 ■3045 ■2936 • •3018 •2909, ■2990 •2882. •2962 ■2855 ■2933 •2828 ■2905 •2800 •2876 •2773 •2847 ■2745 ■2818 •2717 •2789 •2688 ■2728 ■2631 45| 46° 46| 47° 47i 48° 48| 49° 49| 50° 50| 51° 51| 52° 52i When the sign is + the Azimuth is to be reckoned from the South. When the sign is - the Azimuth is to be reckoned from the North. ALT-AZIMUTH TABLES. 122 Enter with Latitude In margin, and over the algebraic sum of E + F will ba found the Azimuth in the head-line. Lat. TRUE AZIMUTH. 53- 53| 54° 54i 55° 55| 56° 56| 57° 571 58° 58°^ 59 59| 60° 0° •6018 •5948 ■5878 •5807 •5736 •5664 •5592 •5519 •5446 •5373 ■5299 •5225 ■5150 •5075 ■5000 I ■6017 ■5947 •5877 •5806 •5735 •5663 •5591 •5519 •5446 ■5372 •5298 •5224 •5150 •5°7S •4999 2 •6014 •5945 •5874 •5803 •5732 •5661 •5589 •5516 •5443 •5370 ■5296 •5222 •5 '47 •5072 •4997 3 •6010 •5940 ■5870 •5799 •5728 •5656 ■5584 •5512 ■5439 ■5366 ■5292 •5218 •5 "43 •5068 •4993 4 •6003 •5934 ■5864 •5793 •5722 •5650 •5578 •5506 ■5433 ■5360 •5286 •5212 •5138 •5063 ■4988 5 ■5995 ■5926 •5855 •5785 •5714 •5643 •5571 •5498 •5426 ■5353 ■5279 •5205 •5131 •5056 •4981 6° •5985 •5916 •5846 •5775 •5704 ■5633 •5561 •5489 •5417 ■5344 ■5270 •5196 ■5122 •5048 •4973 7 •5973 •5904 •5834 •5764 •5693 •5622 •5550 ■5478 •5406 ■5333 ■5260 •5186 •5112 •5038 •4963 8 •5960 •5891 •5821 •5751 ■5680 ■5609 ■5538 •5466 •5393 ■5321 •5248 •5174 •5100 •5026 ■4951 9 ■5944 •5875 ■5805 •5735 •566s •5594 •5523 •5451 •5379 ■5307 ■5234 •5161 ■5087 •5013 •4938 10 •5927 ■5858 •5789 •5719 •5649 •5578 •5507 •5436 •5364 •5292 ■5219 •5146 •5072 •4998 ■4924 11° •5908 •5839 ■5770 •5700 •5630 •5560 ■5489 •5418 •5346 ■5274 •5202 •5129 ■5056 •4982 •4908 12 ■5887 •5818 •5749 •5680 ■5610 ■5540 ■5470 •5399 •5327 ■525s •5183 •5111 •5038 ■4965 •4891 13 ■5864 •5796 •5727 •5658 ■5589 •5519 •5449 •5378 •5307 ■5235 ■5163 •5091 ■5018 ■4945 •4872 14 •5839 •5771 •5703 •5634 •5565 •5496 •5426 •5356 •5285 •5214 ■5142 •5070 ■4997 •4924 ■4851 IS ■5813 ■5746 •5678 •5609 •5540 •5471 •5401 ■5331 ■5261 ■5190 ■5119 •5047 ■4975 •4903 •4830 16° ■5785 •5718 •5650 •5582 •5514 •5445 •5375 •5305 •5235 •5165 •S094 •5023 ■4951 •4879 ■4806 17 "5755 •5688 ■5621 •5553 •5485 •5417 •5348 ■5278 •5208 ■5138 •5068 •4997 ■4925 •4854 •4782 18 ■5724 •5657 ■5590 ■5523 •5455 •5387 •5318 •5249 •5180 •5110 •5040 •4969 •4898 •4827 •4755 19 •5690 ■5624 ■5558 ■5491 •5423 •5355 •5287 •5219 •5150 •5080 ■5010 ■4940 ■4870 ■4799 •4728 20 •5655 •5589 •5523 •5457 •5390 ■5323 •5255 •5187 •5118 •5049 •4980 •4910 •4840 •4769 •46^8 21° •5618 •5553 •5487 •5421 •5355 •5288 •5221 •5153 •5085 ■5016 •4947 •4878 •4808 ■4738 ■4668 22 •5580 •5515 ■5450 ■5384 ■5318 •5252 ■518s •5118 ■5050 •4982 ■4913 •4844 ■4775 •4706 •4636 23 ■5540 •5476 ■5411 •5346 •5280 •5214 ■5147 •5080 ■5013 •4946 ■4878 •4810 •4741 •4672 ■'^^aI 24 ■5498 •5434 •5370 •5305 ■5240 •5174 •5 108 •5042 •4976 •4909 •4841 •4773 ■'^IS^ ■4637 •4568 25 •S4S4 •5391 •5327 •5263 ■5198 •5133 •5068 •5002 •4936 ■4870 •4803 •4736 •4668 •4600 •4532 26° ■5409 •5346 ■5283 •5219 •5155 •5091 ■5026 •4961 •4895 •4829 ■4763 ■4696 •4629 •4562 •4494 •5362 ■5300 •5237 •5174 ■5111 •5047 ■4982 •4918 •4853 •4788 •4722 ■4656 •4589 •4522 •4455 28 •5314 ■5252 ■5190 •5127 •5064 •5001 ■4937 •4873 •4809 •4744 ■4679 •4614 ■4548 •4482 •4415 29 ■5264 •5203 •5141 ■5079 •5017 ■4954 ■4891 •4828 •4764 ■4700 ■4635 ■4570 ■4505 •4439 ■4373 30 •5212 •5151 •5090 •5029 •4967 •4905 •4843 •4780 •4717 ■4653 •4589 ■4525 •4460 •4395 •4330 31° •5159 •5099 ■5038 •4978 •4917 •4855 •4793 •4731 •4668 •4606 ■4542 •4479 '"^^li •4350 ■4286 32 ■5104 "5044 •4985 •4925 •4864 •4803 •4742 •4681 •4619 •4557 ■4494 •4431 •4368 •4304 •4240 33 ■5047 ■4989 •4930 •4870 •4810 ■4750 •4690 •4629 •4568 ■4506 ■4444 •4382 •4319 ■4257 •4193 34 •4989 ■4931 •4873 •4814 •4755 ■4696 •4636 •4576 •4515 •4454 ■4393 ■4332 ■4270 •4208 •4145 35 •4930 •4873 •4815 •4757 •4698 •4640 •4581 •4521 •4461 •4401 •4341 ■4280 •4219 •4158 •4096 36° •4869 ■4812 "4755 •4698 •4640 •4582 •4524 •446s •4406 ■4347 •4287 •4227 •4167 ■4106 •4045 •4806 ■4750 ■4694 •4638 •4581 •4524 •4466 •4408 •4350 •4291 •4232 •4173 ■4113 ■4053 •3993 38 •4742 ■4687 •4632 •4576 •4520 •4463 •4406 •4349 ■4292 ■4234 ■4176 •4118 •4059 •4000 •3940 •3886 39 •4677 •4623 •4568 ■4513 •4458 •4402 •4346 ■4290 •4233 •4176 •4118 •4061 •4003 •3945 40 •4610 •4557 •4503 ■4449 •4394 •4339 •4284 •4228 •4172 •41 16 •4059 •4002 ■3945 •3888 •3830 41° ■4.S42 •4489 ■4436 •4383 •4329 •4275 ■4220 ■4165 •41 10 •4055 ■3999 ■3943 ■3887 ■3831 •3774 ■37,16 ■3657 42 43 •4472 ■4401 •4420 •4350 ■4368 •4299 •4316 ■4247 •4263 •4195 •4210 •4143 •4156 •4090 ■4102 •4037 •4047 •3983 •3993 •3930 '3938 ■3876 ■3883 •3822 •3827 •3767 ■3772 •3712 44 45 •4329 •4255 •4279 •4206 •4228 •4156 •4177 ■4106 ■4126 •4056 ■4074 •4005 ■4022 •3954 •3970 •3903 •3918 •3851 •3865 •3799 •3812 ■3747 ■3759 •369s •3705 ■3642 ■3651 ■3589 ■3597 •3536 46° 40 •4I8I •4104 •4027 •3948 •3868 •4132 •4057 •3980 •3902 •3823 •4083 •4009 ■3933 •3856 ■4034 ■3961 •3886 •3810 •3984 ■39'? •3838 •3763 •3934 •3863 ■3790 •3716 •3884 •3814 •3742 ■3669 •3834 •3764 ■3693 •3621 •3783 •3714 •3644 ■3573 •3732 •3664 •3595 •3525 •3681 •3&14 •3546 •3477 ■3630 ■3564 ■3496 •3428 ■3578 ■3513 •3446 •3379 ■3526 •3462 ■3396 ■3330 •3473 •3410 ■3346 •3280 50 •3778 •3733 •3687 •3641 •3594 •3548 ■3501 •3454 ■3406 ■3359 "33" ■3263 •3214 51° 52 53 54 55 •3787 ■370s •3622 ■3537 •3452 •3743 •3662 •3580 •3496 •3412 •3699 •3619 •3537 •3455 •3371 •3655 •3575 •3495 •3413 •3331 •3610 •3531 •3452 •3371 ■3290 •3565 •3487 •3409 •3329 •3249 •3519 •3443 •3365 •3287 •3207 •3474 •3398 •3322 •3244 ■3166 •3428 ■3353 •3278 •3201 •3124 •3382 ■3308 •3234 •3158 •3082 •3335 •3263 •3189 •3115 •3039 •3288 •3217 ■3145 ■3071 •2997 •3241 ■3171 ■3100 •3027 •2954 ■3194 ■3125 ■3055 ■2983 •2911 ■3147 •3078 ■3009 •2939 •2868 56° S ■336s •3278 •3189 •3100 •3009 •3326 •3240 •3152 •3064 •2974 •3287 •3201 •3J15 •3027 ■2939 •3247 •3163 '3077 •2991 ■2904 •3207 ■3124 •3039 •2954 •2868 •3167 •3085 •3001 •2917 •2832 •3127 •3046 •2963 •2880 •2796 •3087 •3006 •2925 •2843 •2760 •3046 •2966 •2886 •2805 •2723 ■3005 •2926 •2847 •2767 •2687 •2963 •2886 •2808 •2729 •2650 •2922 •2846 •2769 •2691 •2613 •2880 •2805 •2729 •2653 •2575 •2838 •2764 ■2690 •2614 •2538 •2796 ■2723 •2650 •2575 ■2500 61° £2 65 •2918 •282s •2732 ■2638 •2543 ■2884 •2792 ■2700 •2608 •2514 ■2850 ■2759 . -2668 •2577 •2484 •2816 ■2726 ■2636 •2546 •2454 ■2781 •2693 ■2604 •2514 ■2424 ■2746 ■2659 •2572 •2483 •2394 •271 1 •2625 •2539 ■2451 ■2363 •2676 •2591 •2506 •2420 •2333 •2640 •2557 •2473 •2388 ■2302 •2605 •2523 •2440 •2356 ■2271 ■2569 •2488 •2406 •2323 •2240 •2533 ■2453 •2372 ■2291 ■2208 •2497 ■2418 ■2338 •2258 ■2177 •2461 •2383 •2304 •2225 •2145 •2424 •2347 •2270 •2192 •21 1 3 53° 53| 54° 54| 55° 55| 56° 56| 57° 57| 58° 58°^ 59° 59| 60 When the sign is + the Azimuth is to be reckoned from the South. When the sign is - the Azimuth is to be reckoned from the North. 12S ALT-AZIMUTH TABLES. G Enter with Latitude In margin, and over the algrebraie sum of E + F will be found the Azimuth In the head-line. When the sign is + the Azimuth is to be reckoned from the South. When the sign Is - the Azimuth is to be reckoned from the North. Lat. TRUE AZIMUTH. 60| 61° 61| 62° 62| 63° 63| 64° 64| 65° 65°| 66 66| 67° 67i° 0° I 2 3 4 5 •4924 ■4923 •4921 •4917 •4912 •490s ■4848 •4847 •4845 ■4841 •4836 ■4830 •4772 •4771 •4769 ■4765 •4760 •4753 •4695 •4694 •4692 •4688 •4683 •4677 •4617 •4617 •4615 ■46 1 1 •4606 •4600 •4540 •4539 ■4537 ■4534 ■4529 •4523 ■4462 •4461 •4459 •4456 ■4451 •4445 •4384 ■4383 •4381 ■4378 •4373 ■4367 •4305 •4304' ■4302 •4299 •4295 •4289 •4226 •4226 •4224 ■4220 •4216 ■4210 ■4147 •4146 •4144 •4141 ■4137 •4131 ■4067 •4067 •4065 •4062 •4057 •4052 •3987 •3987 •3985 ■3982 •3978 •3972 ■3907 •3907 •3905 ■3902 ■3898 ■3892 •3827 ■3826 •3825 •3822 ■3818 •3812 6° I 9 10 •4898 •4888 •4876 •4863 •4849 ■4822 •4812 •4801 •4788 •4774 •4746 •4736 •4725 •4713 •4699 •4669 •4660 •4649 •4637 •4623 •4592 •4583 ■4573 •4561 •4547 •4515 •4506 •4496 •4484 •4471 •4438 •4429 ■4419 •4407 •4394 •4360 •4351 ■4341 •4330 •4317 •4282 •4273 •4263 •4252 •4240 •4203 •4195 ■4185 ■4174 ■4162 •4124 •41 16 •4107 •4096 ■4084 ■4045 ■4037 •4028 •4017 •4006 •3966 •3958 •3949 •3938 •3927 ■3S86 ■3878 •3869 ■3859 •3848 •3806 ■3798 •3790 ■3780 ■3769 11° 12 13 H IS ■4834 •4817 ■4798 •4778 •47S7 •4759 ■4742 •4724 •4704 •4683 •4684 •4667 •4649 ■4630 ■4609 •4608 •4592 •4574 ■4555 •4535 ■4532 •4517 ■4499 •4480 •4460 •4456 •4441 •4424 •4405 •4385 •4380 •4365 ■4348 •4329 •4310 •4303 •4288 •4271 ■4253 •4234 •4226 ■421 1 •4195 •4177 •4158 •4149 •4134 •41 18 •4101 •4082 •4071 •4056 •4041 ■4024 ■4006 •3993 •3978 •3963 •3947 •3929 ■391 5 •3900 ■3885 •3869 •3852 •3836 •3822 •3807 •3791 •3774 •3757 •3743 •3729 •3713 •3696 If % 19 20 ■4733 •4709 •4683 •4656 •4627 •4660 •4636 •461 1 •4584 •4556 •4587 •4563 •4538 ■4512 ■4484 ■4513 •4490 ■4465 ■4439 •4412 •4439 •4416 •4392 ■4366 •4339 •4364 •4342 •4318 •4293 •4266 ■4289 •4267 •4244 •4219 •4193 •4214 ■4192 ■4169 •4145 •41 19 •4138 •41 17 ■4094 •4071 •4045 •4062 ■4042 •4019 •3996 ■3971 •3986 •3966 •3944 ■3921 •3897 ■3910 •3890 •3868 •3846 ■3822 •3833 •3814 •3792 •3770 •3747 •3756 ■3737 •3716 •3694 ■3672 •3660 •3640 •3618 •3596 21° 22 23 24 25 •4S97 ■4566 •4533 •4499 •4463 •4526 •4495 •4463 •4429 •4394 •4455 ■4424 •4393 •4359 •4325 •4383 •4353 ■4322 ■4289 •4255 •4311 •4281 •4251 -4218 •4185 •4238 •4209 •4179 ■4147 •4115 •4166 ■4137 ■4107- •4076 •4044 ■4093 •4065 ■4035 ■4005 •3973 •4019 ■3992 •3963 •3933 •3902 •3945 ■3890 •3861 ■3830 •3871 ■3845 •3817 •3789 ■3758 ■3797 •3771 •3744 •3716 •3686 •3723 ■3697 •3671 •3643 •3614 •3648 ■3623 •3597 •3570 ■3541 •3573 •3548 •3523 •3496 •3468 26° 29 30 ■4426 •4388 •4348 ■4312 •426s •4357 •4320 •4281 •4240 •4199 •4289 •4252 •4213 •4173 ■4133 •4220 •4183 •4145 ■4106 •4066 •4150 •41 14 ■4077 •4039 •3999 •4080 •4045 •4008 •3971 ■3932 •4010 •3976 •3940 •3903 •3864 •3940 •3906 •3871 •3834 •3796 •3869 •3836 ■3801 •3765 •3728 •3798 •3766 •3731 •3696 •3660 •3727 •3661 ■3627 •3591 •3656 ■3624 •3591 •3557 •3522 •3584 •3553 •3521 •3487 ■3453 •3512 •3481 •3450 ■3417 •3384 •3440 •3410 ■3379 ■3347 ■3314 31° 32 33 34 3S •4221 •4176 •4130 •4082 •4034 •4156 '41 1 1 •4066 ■4019 •3971 •4090 •4047 •4002 •3956 •3909 •4024 •3981 •3937 •3892 •3846 •3958 •3916 •3873 ■3828 •3783 •3891 •3850 •3807 •3764 ■3719 •3825 •3784 ■3742 •3699 •3655 •3758 •3718 ■3676 •3634 •3591 •3690 ■3651 •361 1 •3569 •3527 •3623 •3584 •3544 •3504 •3462 •3555 ■3517 •3478 •3438 •3397 •3486 •3449 •341 1 •3372 •3332 •341S •3382 •3344 •3306 •3267 •3349 ■3314 •3277 ■3239 •320s' •3280 •3245 ■3209 •3173 •3135 36° 39 40 •3984 ■3933 •3880 •3827 •3772 •3922 •3872 •3820 •3768 •3714 •3860 •381 1 •3760 •3708 •3655 •3798 •3749 •3699 •3648 •3596 •3736 •3688 •3638 ■3588 •3537 •3673 •3626 •3577 •3528 •3478 •3610 •3564 •3516 •3468 •3418 •3546 •3501 ■3454 •3407 •3358 •3483 •3438 •3392 •3346 •3298 •3419 •3375 •3330 ■3284 •3237 •3355 •3312 •3268 ■3223 •3177 •3291 •3248 •3205 •3161 •3116 •3226 •3185 ■3142 •3099 •305s •3161 •3121 •3079 •3037 •2993 •3096 •3057 •3016 ■2974 •2932 41" 42 43 44 45 •3717 •3660 •3602 •3542 •3482 •3659 ■3603 •3546 •3487 ■3428 ■3601 •3546 ■3490 •3432 •3374 "3543 ■3489 •3433 ■3377 •3320 •3485 •3432 •3377 •3322 ■3265 •3426 •3374 •3320 •3266 •3210 •3367 •3316 •3263 •3210 •3155 •3308 •3258 •3206 ■3153 •3100 •3249 ■3200 •3149 ■3097 •3044 •3190 •3141 •3091 •3040 •2988 •3130 ■3082 •3033 •2983 •2932 ■3070 •3023 •2975 •2926 •2876 •3010 •2964 •2917 •2869 ■2820 ■2949 •2904 •2858 •28 1 1 •2763 •2S88 •2844 •2799 •2753 •2706 46° % 49 5Q •3421 ■3358 •329s ■3231 •316s •3368 •3306 •3244 •3181 ■3116 •3315 •3254 •3 '93 •3131 ■3067 •3261 ■3202 •3141 ■3080 •3018 ■3208 •3149 ■3089 •3029 ■2968 •3154 •3096 •3038 •2978 •2918 •3100 •3043 •2986 •2927 ■2868 ■3045 ■2990 •2933 •2876 •2818 ■2991 •2936 ■2881 ■2825 •2768 •2936 •2882 •2828 ■2773 ■2717 •2S81 ' •2828 •2775 •2721 ■2666 •2825 •2774 ■2722 •2668 •2614 •2770 •2720 ■2669 ■2616 ■2563 •2714 ■2665 •2615 •2563 •2512 •2658 ■2610 •2561 ■25 II •2460 51° 52 53 54 55 •3099 •3032 •2964 •289s ■2825 '3051 ■2985 •2918 •2850 •2781 •3006 ■2938 •2872 •2805 •2737 •2954 ■2890 •2825 •2759 ■2693 •2906 •2843 •2779 ■2714 •2649 ■2857 •2795 •2732 •2668 ■2604 •2808 •2747 •2685 •2623 •2559 •2759 •2699 •2638 ■2577 •2514 •2710 ■2651 •2591 •2531 •2469 •2660 ■2602 •2543 •2484 •2424 •2610 ■2553 •2496 •2438 •2379 •2560 •2504 •2448 •2391 •2333 •2510 •2455 •2400 •2344 •2287 •2459 •2406 •2351 ■2297 •2241 •2408 •2356 •2303 ■2250 •2195 56° i •2754 •2682 ■2610 •2536 •2462 •271 1 •2640 ■2569 ■2497 •2424 •2668 •2599 •2529 •2458 •2386 •2625 •2557 •2488 •2418 ■2347 •2582 •2515 ■2447 •2378 •2309 ■2539 •2473 •2406 ■2338 •2270 •2495 •2431 •2365 ■229S ■2231 •2451 •2388 •2323 •2258 •2192 •2407 •2345 •2282 •2218 •2153 •2363 ■2302 ■2240 •2177 ■2113 •2319 •2259 •2198 •2136 •2074 ■2274 •221 s ■2155 •209s •2034 •2230 ■2172 ■2113 •2054 •1994 •2185 •2128 •2071 •2012 •I9S4 •2140- ■2084 •2028 •1971 •1914 61° 62 65 ■2387 ■2312 •2236 •2159 •2081 ■2350 •2276 •2201 ■2125 •2049 •2313 '2240 ■2166 •2092 •2017 •2276 •2204 •2131 •2058 ■1984 •2239 •2168 •2096 •2024 •1951 •2201 •2131 •2061 •1990 •1919 •2163 •2095 •2026 •1956 •1886 •2125 ■2058 •1990 ■1922 •1853 •2087 •2021 •1955 •1888 •1819 ■2049 •1984 •1919 •1853 •1786 •201 1 •1818 •1753 ■1972 ■1910 •1847 •1783 •1719 ■1933 ■1872 •1811 •1748 •1685 •1894 •1834 •1774 •1713 •1651 •185s ■1797 •1738 •1678 •1617 60| 61° 61| 62° 62| 63° 63i 64° 64| 65° 65°J 66 66| 67° 671 ALT-AZIMUTH TABLES. G 124 Enter with Latitude in margin, and over the alerebraie sum of E + F will be found the Azimuth in the head-line. Lat. TRUE AZIMUTH. 68* 68| 69° 69| 70° 70| 71" 71| 72° 72°| 73 73| 74° 74i° 75° 0" •3746 •366s •3584 •3502 ■3420 •3338 •3256 ■3173 •3090 •3007 •2924 •2840 •2756 •2672 •2588 I •374S •3664 •3583 ■3502 •3 (20 •3338 •3255 ■3173 •3090 •3007 •2923 •2840 •2756 •2672 ■2588 2 •3744 ■3663 •3581 ■3500 •3418 ■3335 ■3254 ■3171 •30S8 •3005 •2922 •2838 ■2755 •2671 ■2587 3 ■3741 •3660 •3S79 •3497 ■3416 ■3333 •3251 •3169 •3086 •3003 •2920 ■2836 ■2753 •2669 •2585 4 •3737 •3656 •3575 •3494 ■3412 •3330 •3248 •3165 ■3083 •3000 •2917 ■2833 •2750 •2666 •2582 5 •3732 ■3651 ■3570 •3489 ■3407 •3325 •3243 •3161 ■3078 •2996 •2913 •2829 •2746 •2662 •2578 6° •3726 •364s •3564 •3483 •3401 •3320 •3238 ■3156 ■3073 •2991 •2908 •2825 •2741 •2658 ■2574 i ■3718 ■3638 •3557 •3476 ■3395 •3313 ■3231 •3149 •3067 •2985 •2902 ■2819 •2736 •2653 •2569 •3710 ■3630 •3549 •3468 ■3387 ■3306 •3224 •3142 •3060 ■2978 •2895 ■2813 ■2730 •2647 •2563 9 •3700 •3620 ■3540 •3459 ■3378 •3297 •3216 ■3134 ■3052 ■2970 ■2888 •2805 ■2722 ■2639 •2556 10 •3689 ■3609 ■3529 •3449 ■3368 •3287 ■3206 ■3125 ■3043 •2961 •2879 ■2797 •2714 ■2632 ■2549 11° •3677 ■359S •3518 •3438 •3357 ■3277 •3196 ■311S ■3033 •2952 •2870 •2788 ■2706 •2624 ■2541 12 •3664 •3585 •3505 ■3425 ■3345 •3265 •3185 •3104 •3023 ■2942 •2860 •2778 •2696 •2614 ■2532 13 •3650 ■3571 •3492 •3413 ■3333 •3253 ■3172 ■3092 ■30 1 1 ■2930 ■2849 •2768 •2686 •2604 •2522 M •363s •3556 •3477 ■3398 •3319 •3239 •3159 •3079 •2998 •29 iS ■2837 •2756 ■2674 •2593 •2511 IS •3618 •3540 ■3462 •3383 •3304 ■3225 •3145 •3065 ■2985 •2905 •2824 •2743 •2662 •2581 ■2500 i6° •3601 •3523 •3445 •3367 •3288 •3209 •3130 •3050 ■2970 •2890 ■2810 •2730 •2650 ■2569 •2488 17 •3582 ■3505 •3427 •3349 ■3271 •3192 ■3'i3 ■ -3034 ■2955 •2876 •2796 •2716 •2636 •2556 •2475 i8 ■3563 •3486 •3408 ■3331 •3253 ■3175 •3096 •3018 ■2939 •2860 •2781 •2701 ■2621 ■2542 '2462 19 ■3542 •3465 ■3388 •33" •3234 ■3156 •3078 •3000 •2922 ■2843 •2764 •2685 •2606 ■2527 •2447 20 •3520 •3444 •3368 •3291 •3214 ■3137 •3059 •29S2 •2904 ■2S26 •2747 •2669 •2590 •251 1 ■2432 21° •3497 ■3422 ■3346 •3270 ■3193 •3>i6 •3039 ■2962 •2885 •2808 •2730 •2562 •2573 ■2495 •2416 22 •3473 ■3398 ■3323 ■3247 ■3171 •3095 •3019 •2942 •2865 •2788 •27 1 1 •2634 •2556 ■2478 •2400 23 •3448 ■3374 •3299 ■3224 •314S •3073 •2997 ■2921 ■2845 •2768 •2691 •2614 ■2537 •2460 ■2382 24 •3422 ■3348 ■3274 •3200 ■3125 •3050 ■2974 •2899 •2823 •2747 •2671 •2595 ■2518 •2441 ■2364 25 ■3395 •3322 •3248 ■3174 ■3100 ■3026 ■2951 •2S76 •2801 ■2726 •2650 ■2574 •2498 •2422 ■2346 26° ■3367 •3294 ■3221 •3148 •3074 •3000 ■2926 ■2852 ■2777 ■2703 •2628 •2553 ■2477 •2402 •2326 27 ■3338 ■3266 •3193 ■3120 •3047 ■2974 •2901 •2827 ■2753 •2679 •2605 •2531 •2456 •2381 •2306 28 ■3308 •3236 ■3164 •3092 •3020 ■2948 •2875 ■2802 •2728 •2655 •2581 •2508 ■2434 •2360 •2285 29 •3276 ■3205 •3134 •3063 •2991 •2919 •2847 •2775 •2703 •2630 ■2557 •2484 •241 1 •2338 •2264 30 •3244 ■3174 •3104 ■3°33 ■2962 •2891 •2820 •2748 •2676 •2604 •2532 •2460 ■2387 •2314 •2241 31° •321 1 •3142 •3072 ■3002 •2932 •2861 •2791 •2720 •2649 •2578 •2506 ■2434 •2363 •2291 •2219 32 •3177 •3108 •3039 •2970 •2900 •2831 ■2761 ■2691 •2621 ■2550 •2479 •2409 ■2338 •2266 •2195 33 •3142 ■3074 •3006 •2937 •2868 •2800 •2730 •2661 ■2592 •2522 ■2452 •2382 ■2312 •2241 •2171 34 ■3106 ■3039 •2971 •2903 ■2835 ■2767 ■2699 ■2631 •2562 ■2493 ■2424 ■2355 •2285 •2216 •2146 35 •3069 •3003 •2936 •2869 •2S02 •2735 •2667 ■2599 •2531 •2463 •2395 •2327 ■2258 •2189 •2120 36° ■3031 •2965 •2899 ■2833 •2767 •2701 •2634 •2567 •2500 ■2433 •2365 •2298 •2230 •2162 •2094 g •2992 •2927 •2862 •2797 •2731 ■2666 •2600 ■2534 •2468 •2402 ■2335 •2268 •2201 •2134 ■2067 ■2952 •2888 •2824 ■2760 •2695 ■2631 •2566 •2501 ■2435 ■2370 ■2304 ■2238 •2172 •2 1 06 •2040 39 ■2911 •2848 •2785 •2722 •2658 •2594 ■2530 •2466 ■2402 ■2337 •2272 •2207 •2142 •2077 •2011 40 ■2870 •2808 ■2745 •2683 •2620 •2557 •2494 •2431 •2367 •2304 •2240 •2176 •2112 •2048 •1983 41° •2827 •2766 •2705 •2643 •2581 ■2519 ■2457 ■2395 ■2332 •2270 •2207 •2144 •2080 •2017 ■1953 42 •2784 •2724 •2663 •2603 •2542 •2481 •2419 ■2358 •2296 ■2235 •2173 •21 1 1 •2048 •1986 •1923 43 •2740 •2681 •2621 ■2561 •2501 •2441 •2381 ■2321 •2260 •2199 •2138 •2077 •2016 •1955 •1893 44 •2695 ■2637 ■2578 •2519 •2460 •2401 ■2342 ■2283 •2223 •2163 •2103 •2043 •1983 •1923 •1862 45 •2649 ■2592 •2534 ■2476 •2418 •2360 •2302 •2244 ■2185 •2126 •2067 •2008 ■1949 •1890 •1830 46° •2602 •2546 ■2489 ■2433 •2376 ■2319 ■2262 •2205 ■2147 •2089 •2031 •1973 •1915 •1857 •1798 47 ■255s ■2500 ■2444 ■2389 ■2333 •2277 ■2220 •2164 •2107 •2051 •1994 ■1937 •1880 •1823 •1765 48 •2507 ■2453 ■2398 ■2344 •2289 •2234 •2178 ■2123 •2068 •2012 •1956 •1900 •1844 •1788 •1732 49 •2458 ■2405 ■2351 •2298 •2244 •2190 •2136 ■2082 •2027 ■1973 •1918 •1863 •1808 •1753 •1698 50 •2408 ■2356 •2304 ■2251 •2198 '2146 • ^2093 •2040 ■1986 •1933 •1879 •1826 •1772 •1718 ■1664 51° ■2357 •2306 •225s •2204 ■2152 ■2101 •2049 ■1997 •1945 '•1893 •1840 •1788 •1735 •1682 •1629 52 •2300 •2256 •2206 •2156 •2106 •2055 •2004 ■I9S3 •1902 ■1851 •1800 •1749 ■1697 ■1645 •1593 53 •2254 '2202 ■2206 ■2157 •2108 •2058 •2009 ■1959 •1910 •i860 •1810 •1760 •1710 ■1659 •1609 •1558 54 ■2154 ■2103 ■2106 •2058 •2010 •1962 •1914 •1865 •1816 •1768 •1719 •1670 '1 620 •1571 •1521 55 •2149 ■2056 •2009 ■1962 •1915 •1867 •1820 •1772 •1725 •1677 ■1629 •1581 •1533 ■1485 56° ■2095 •2040 •2050 2004 •1959 •1913 •1867 •1821 ■1775 •1728 •1682 •163s •1588 •1541 •1494 ■1447 ■1996 •1952 •1908 •1863 •1818 ■1773 •1728 •1683 •1638 •1592 •1547 •1501 ■1456 •1410 eg •198S •1929 •1S73 ■1942 •1899 ■1856 •1812 •1769 ■1725 •1682 ■1638 ■1594 •1549 •1505 •1461 ■1417 •1372 59 •1888 •1846 •1804 •1762 •1720 •1677 •163s •1592 ■1549 •1506 •1463 •1420 ■1377 ■1333 60 •1833 •1792 •1751 •1710 •1669 •1628 •1587 •1545 •1504 •1462 '1420 •1378 •1336 •1294 fil" •1816 ■1777 •1737 •1698 ■1658 •1618 •1578 •1538 •1498 ■1458 •1417 •1377 •1336 •1296 •I2SS 62 •I7S9 •I 701 •1721 •1682 ■1644 ■1606 •1567 •1528 •1490 ■145 1 •1412 •1373 •1334 •1294 •1255 •121S 63 ■1664 •1627 ■1590 ■1553 •1516 •1478 •1441 •1403 •1365 •1327 •1289 •1251 •1213 •I 175 64 ■1642 •1607 •1571 ■1535 ■1499 •1463 •1427 •1391 •1355 •1319 ■1282 •1245 •1208 •1172 •1135 65 •1583 •1549 •1515 ■1480 •1445 •1411 ■1376 •1341 •1306 •1271 •1236 •1200 •1165 •1129 •1094 68 68| 69° 69| 70 . 70| 71° 71| 72° 72°J 73° 73| 74° 74 75° When the sign is + the Azimuth is to be reckoned from the South. When the sign is - the Azimuth is to be reckoned from the North. 125 ALT-AZIMUTH TABLES. G Enter with Latitude in margin, and over tlie algebraic sum of E + F will be found the Azimuth in the head-line. TRUE AZIMUTH. Lax. 75l 76' 76| 77° 771 78 78| 79 79^ 80 80J 8i 8U° 82° 82^ I 3 4 S 6° 7 8 9 10 11° 12 13 M 15 i6° 19 20 21° 22 23 24 25 26° 27 28 29 30 31° 32 33 34 35 36° % 39 40 41° 42 43 44 45 46° % 49 50 51° 52 53 54 55 56° 57 58 to 61° 62 ^3 65 •2504 •2503 •2502 •2500 •2498 •2494 ■2490 •248s •2479 •2473 •2466 ■2458 •2449 •2440 ,■2429 - •2418 •2407 •2394 ■2381 •2367 ■2353 •2337 •2321 ■2305 •2287 ■2269 •2250 •2231 ■221 1 -2190 •2168 •2146 •2123 ■2100 •2076 •2051 •2026 •2000 ■1973 ■1946 •1918 •i8go •1861 •1831 ■1801 •1770 •1739 •1708 •1675 •1643 •i6og •1576 ■1541 •1507 •1472 ■1436 •1400 ■1364 •1327 •1290 •1252 •1214 •1175 •I 137 ■1098 ■1058 75J •2419 •2419 •2418 •2416 •2413 •2410 •2406 ■2401 •2396 •2389 ■2382 •237s •2366 •23S7 •2347 •2337 •2326 •2314 ■2301 •2287 •2273 ■2259 •2243 ■2227 •2210 ■2193 ■2174 •2156 •2136 '2Il6 •209s •2074 •2052 •2029 •2006 'I982 •I9S7 •1932 •1906 •1880 •1853 •1826 •1798 •1769 •1740 ■1711 •1681 •1650 •1619 •1587 •isss •1522 •1489 •1456 •1422 •1388 ■I3S3 •1318 ■ •1282 •1246 •1210 ■1173 •1136 •1098 •1061 76 •2334 •2334 •2333 •2331 ■2329 ■2326 ■2322 •2317 •2312 •2306 ■2299 ■2292 ■2283 •2275 ■2265 •22SS ■2244 ■2233 ■2220 ■2207 •2194 ■2180 •2165 ■2149 •2133 '21 16 •2098 •2080 ■2061 '2042 •2022 ■2001 •1980 •1958 ■1936 •I913 •1889 •1865 •1840 •1814 ■1788 •1762 •I73S •1707 •1679 •1651 '1622 ■1592 •1562 •1532 •1501 •1469 •1437 ■140S •1372 ■1339 ■1306 •1272 ■1237 •1203 •I 168 •1132 •1096 ■1060 •1024 •0987 ■2250 •2249 •2248 •2246 •2244 '2241 ■2237 ■2233 •2228 •2222 •221S ■2208 ■2200 -2192 •2183 •2173 •2162 ■2151 ■2139 ■2127 ■21 14 ■2100 •2086 •2071 •2055 •2039 •2022 '2004 •1986 •1967 ^948 •1928 •1908 • •1887 •186s •1843 •1820 •1797 •1773 •1748 ■1723 •1698 •1672 •164s •1618 •1591 ■1563 ■I 534 •1505 •1476 ■1446 •1416 •1385 •1354 ■1322 ■1290 •1258 •1225 •I 192 ■1159 ■I 125 •1091 •1056 •1021 ■0986 •0951 76i 77 ■2164 ■2164 •2163 •2161 •2IS9 •2156 •2153 •2149 •2144 ■2138 •2132 ■2125 •21 1 7 ■2109 •2100 •2091 ■2081 •2070 ■2058 •2047 •2034 •2021 •2007 ■1993 •1977 ■1962 •1946 •1929 ■1911 ■1893 ■1874 •1855 •1836 •181S ■1795 •1773 •1751 •1729 •1706 ■1682 •1658 ■1634 ■1609 ■1583 ■1557 •1530 ■1504 •1476 ■1448 •1420 •1391 ■1362 ■1333 •1303 ■1272 •1242 ■1179 ■1147 •1115 •1083 •1050 ■1016 ■0983 •0949 •0915 77i ■2079 •2079 •2078 ■2076 •2074 ■2071 ■2068 ■2064 •20S9 •2054 •2048 '2041 •2034 '2026 •2017 •2008 •1999 ■1988 ■1977 •1966 •1954 •1941 •1928 •1914 ■1899 •1884 •1869 ■1853 •1836 •1818 •1801 •1782 •1763 ■1744 •1724 ■1703 •1682 ■1660 •1638 •1616 •1593 •1569 ■1545 •1521 •1496 ■1470 •'444 •1418 ■1391 ■1364 •1336 ■1308 •1280 •1251 ■1222 •I 193 •I 163 •1132 ■I 102 •1071 •1040 •1008 •0976 •0944 •091 1 •0879 78° •1994 •1993 ■1992 •1991 ■1989 •1986 •1983 •1979 •1975 •1970 •1964 •1957 •1950 •1943 •1934 •1926 ■1917 •1907 •1896 •1885 •1874 ■1861 •1849 •1835 •1821 •1807 •1792 •1777 ■1761 •1744 •1727 ■1709 •1691 •1672 •1653 •1633 •1613 •1592 •1571 •1550 •1528 ■1505 •1482 •1458 •1435 •1410 •1385 ■1360 •1334 •1308 ■1281 •1255 •1228 •1200 ■1172 •I 144 •1115 •1086 •1057 •1027 •0997 •0967 •0936 •0905 •0874 •0843 78| ■1908 •1908 ■1907 •1905 •1903 •1901 •1898 •1894 •1890 •1885 ■1879 •1873 ■1866 •1859 •1851 •1843 •1834 ■1825 •1815 ■1S04 •1793 •1781 •1769 ■1756 •1743 ■1729 •1715 ■1700 ■1685 ■1669 •1652 •1636 •1618 •1600 •1582 •1563 •1544 •1524 •1504 •1483 •1462 •1440 ■1418 ■1395 •1373 •1349 •1325 •1301 •1277 •1252 '1 226 •1201 •1175 •I 148 '1122 •1094 •1067 •1039 ■loii ■0983 ■0954 •0925 •0896 ■0866 •0836 •0806 79° •1822 ■1822 •1821 ■1820 ■1818 •1815 ■1813 ■1809 •1805 •1800 •1795 ■1789 •1783 •1776 •1768 ■1760 •1752 . •1743 •1733 ■1723 •1713 •1701 •1690 ■1677 •1665 ■1652 •1638 '1 624 •1609 •1594 •1578 •1562 •«54S •1528 •1511 •1493 •1475 •1456 •1436 '1416 •1396 •1376 •1354 •1333 •1311 •1289 •1266 •1243 •1220 •I 196 •1171 •1147 '1122 •1097 •1072 •1045 •1019 ■0993 •0966 •0939 •091 1 ■0884 ■0856 •0827 •0799 •0770 79| •1736 •1736 •1735 •1734 •1732 •1730 •1727 •1724 ■1720 •1715 •1710 •1705 •1699 •1692 ■1685 •1677 •1669 •1661 •1651 •1642 ■1632 ■I 62 1 •1610 •1598 ■1586 •1574 •1561 •1547 •1533 •1519 •1504 •1488 •1473 •1456 •1440 •1422 •1405 •1387 •1368 •1349 •1330 •13H '1290 ■1270 •1249 •1228 •1206 •1184 •I 162 •1139 '1116 ■1093 •1069 •1045 •102 1 •0996 •0971 •0946 •0920 •0894 •0868 •0842 •0815 •0788 •0761 •0734 80 •1656 •1650 •1649 •1648 •1646 •1644 ■1642 •1639 •1635 •1630 •1626 ■1621 ■1615 •1608 •1602 .•1594 ■1587 •1579 •1570 •1561 •1551 •1541 •1530 ■1519 •1508 •1496 •1484 •1471 •1457 •1444 •1430 ■1415 •1400 •1384 •1369 •1352 •1336 •1318 •1301 •1283 •1264 '1 246 •1227 •1207 •1187 ■1167 •I 147 ■1126 •1105 •1083 •1061 •1039 •1016 •0993 •0970 •0947 •0923 •0899 •0875 •0850 •0825 •0800 •0775 •0749 •0724 •0698 8OI ■1564 •1564 •1563 •1562 . •1561 •1558 •1556 •1553 •1549 •1545 •1541 •1536 •1530 ■1524 •1518 •IS" •1504 •1496 •1488 •1479 ■1470 ■1460' •1450 •1440 ■1429 •1418 ■1406 ■1394 ■1381 •1368 •'355 •1341 •1327 •1312 •1297 •1281 •1266 •1249 ■1233 •1216 •I 198 •1181 •I 163 •1144 •1125 •I 106 •1087 •1067 •1047 •1026 •1006 ■0984 •0963 •0941 •0919 •0897 •0875 ■0852 ■0829 •0806 •0782 •0758 •0734 •0710 •0686 •0661 81 ■1478 •1478 •1477 •1476 •1474 •1472 •1470 •1467 ■1464 •1460 •1456 •145 1 ■1446 •1440 ■1434 •1428 •1421 •1414 •1406 ■1398 ■1389 ■1380 •1370 ■1361 •1350 •1340 ■1329 •1317 •130S ■1293 •1280 •1267 •1253 ■1240 '1 226 •1211 ■I 196 •I 180 •I 165 •I 149 •I 132 •I 1 16 •1099 •1081 •1063 •1045 •1027 •1008 •0989 •0970 •0951 •0930 ■0910 •0890 •0869 •0848 •0827 •0805 •0784 •0762 •0739 •0717 •0694 •0671 •0648 •0625 81i •1392 •1392 •1391 ■1390 •1388 •1386 •1384 •1381 •1378 •1375 •1371 •1366 •1361 •1356 •1350 ■1344 •1338 •1331 ■1324 •1316 ■ •1308 •1299 ■1290 •1281 •1271 •1261 •1251 •1240 •1229 •1217 '1 205 •1193 •1180 •I 167 •'154 •I 140 •1126 •iiii •1097 •1082 •1066 •1050 •1034 •1018 •1001 •0984 •0967 •0949 •0931 ■0913 •0895 ■0876 •0857 •0838 •o8i8 •0798 •0778 •0758 •0738 •0717 •0696 •067s •0653 •0632 •0610 •0588 82 ■1305 ■1305 •1304 •1303 •1302 •1300 •1298 ■1296 •1293 •1289 •1285 •1281 •1277 •1272 •1266 •1261 •1255 •1248 ■1241 •1234 ■1227 •1219 •1210 •1201 ■I 192 •1183 •1173 •I 163 •1152 •I 142 •I 130 •1119 •1107 •1095 •1082 •1069 •1056 '1042 '1029 •1014 •1000 •0985 •0970 ■0955 •0939 •0923 ■0907 ■0890 •0873 •0856 •0839 •0821 •0804 ■0786 •0767 •0749 •0730 •0711 •0692 •0672 •0653 ■0633 •0613 •0593 •0572 •0552 82J When the sign is + the Azimuth is to be reckoned from the South. When the sign is - the Azimuth is to be reckoned from the North. ALT-AZIMUTH TABLES. G 126 Enter with Latitude in margin, and over the algebraic sum of E + F will be found tlie Azimuth in the head-line. TRUE AZIMUTH. Lat. 0° I 2 3 4 S 6° 9 10 ii' 12 13 M 15 i6° 17 i8 19 20 21"" 22 23 24 25 26* 27 28 29 30 31° 32 33 34 35 36° 37 38 39 40 4X° 42 43 44 45 46° 48 49 50 51° 52 S3 54 55 56° 58 60 6i° 62 i^ 65 83 •1219 •1219 •1218 •1217 ■1216 •1214 •1212 •1210 •1207 •1204 ■1200 •1196 •1192 •I 187 ■1182 •1177 •1171 •1165 •IIS9 •1152 •"45 •I 1 38 •1130 •1122 •1113 •I 105 •109s •1086 •1076 •1066 ■loss •I04S •1034 •1022 •lOIO •0998 •0986 ■0973 •0960 •0947 •0934 •0920 •0906 •0891 •0877 ■0862 •0847 •0831 •08IS •0800 ■0783 •0767 ■0750 ■0733 ■0716 •0699 ■0681 ■0664 ■0646 •0628 •0609 •0591 •0572 •OSS3 ■OS34 ■0515 83i 84 •1132 •1132 •1131 •I 1 30 •1129 •1128 •1126 ■1124 '1121 •1118 ■mS •mi •I 107 •1103 •1098 ■1094 •1088 •10S3 •1077 •1070 '1064 •I0S7 •1050 •1042 •1034 •1026 ■1Q17 •1009 •1000 •0990 •0980 •0970 •0960 ■0949 ■0938 •0927 •0916 0904 ■08 ;2 •0880 ■0868 •08SS •0842 •0828 ■08 IS ■0800 •0787 •0772 ■0757 •0743 ■0728 ■0713 ■0697 ■0681 ■0665 •0650 •0633 ■0617 •0600 ■0583 •0566 ■0S49 •0531 •0514 •0496 •0478 84 83 831 ■1045 •I04S •104s ■1044 •1043 •1041 •1040 ■1037 •1035 •1032 •1029 ■1026 •1022 •1018 ■1014 •lOIO ■loos •1000 •0994 •0988 ■0982 •0976 •0969 •0962 •09SS ■0947 •0939 •0931 ■0923 •0914 •0905 ■0896 ■0886 •0877 •0867 •0856 •0846 ■083s ■0824 •0812 ■0801 •0789 •0777 •0764 •0752 ■0739 •0726 •0713 •0699 ■0686 ■0672 •0658 ■0644 •0629 •0614 •0600 •0585 •0569 •0SS4 •0538 •0523 •0507 ■0491 ■0475 ■0458 ■0442 85 85l 86 ■0958 ■0958 ■0958 •0957 •0956 ■0955 •0954 ■0951 ■0949 •0947 ■0944 •0941 ■0938 •0934 •0930 ■0926 -0922 •0917 •0912 ■0906 •0901 ■0895 •0889 ■0882 ■0876 •0869 ■0861 •0854 ■0847 •0838 ■0830 0822 •0813 ■0804 •0795 •0785 •0775 •0766 •0756 •074S ■0735 ■0724 ■0713 ■0701 ■0690 •0678 •0666 ■0654 ■0641 ■0629 ■0616 •0603 •0591 •0577 ■0563 ■0550 ■0536 •C522 0508 •0494 ■0479 ■0465 ■0450 ■043s ■0420 ■0405 •0872 •0871 •0871 •0870 •0869 •0868 •0867 ■0865 •0863 ■0861 •0858 •0855 ■0853 ■0849 ■0846 ■0842 ■0838 •0833 •0829 ■0824 •0819 ■0814 •0808 •0802 ■0796 •0790 •0783 •0777 ■0770 0762 ■075s ■0747 •0739 •0731 0723 ■0714 ■0705 0696 •0687 ■0677 ■0668 •0658 ■0648 •0637 ■0627 ■0616 •0605 •0594 •0583 ■0572 •0560 ■0548 ■0537 ■0525 •0512 •0500 •0487 •0475 ■0462 ■0449 0436 ■0423 •0409 0396 ■0382 •0368 84 QQh 87 •0785 •0784 •0784 ■0784 •0783 •0782 •0781 ■0779 •0777 ■0775 ■0773 •0770 •0768 •0765 •0762 ■0758 ■0755 •0750 ■0746 ■0742 •0738 •0733 •0728 •0722 •0717 •07 1 1 ■0705 •0700 •0693 ■0686 •0680 •0673 •0665 •0658 •0650 •0643 ■0635 ■0627 •0619 •0610 •0601 •0592 •0583 •0574 •0565 ■0555 •0545 ■0535 •0525 •0515 •0504 •0494 ■0483 •0473 ■0461 •0450 ■0439 •0428 •0416 •0404 •0392 ■0380 •0368 •0356 ■0344 ■0332 84i 85 85i •0698 •0697 •0697 ■0697 ■0696 •0695 •0694 •0692 •0691 •0689 •0687 •0685 •0682 ■0680 •0677 •0674 •0671 •0667 •0663 •0660 •0656 •0651 •0647 •0642 ■0637 •0632 •0627 •0622 •0616 •0610 •0604 •0598 •0592 •0585 •0578 •0571 •0564 •0557 •0550 •0542 ■0534 •0526 ■0518 •0510 •0502 •0493 •0485 •0476 •0467 •0458 •0448 ■0439 •0429 •0420 ■0410 ■0400 ■0390 •0380 •0370 •03S9 •0349 •0338 •0327 •0317 •0306 •0295 ■0610 •0610 •0610 ■0610 ■0609 ■0608 •0607 •0606 •0605 •0603 •0601 •0600 ■0597 •0595 •0593 •0590 •0587 ■0584 •0581 •0578 •0574 •0570 •0566 •0562 ■0558 •0553 •0549 •0544 ■0539 ■0534 •0529 ■0523 •0518 ■0512 •0506 ■0500 •0494 •0488 ■0481 •0475 •0468 •0461 •0454 •0447 •0439 •0432 ■042s •0417 •0409 ■0401 •0392 •0384 ■0376 •0368 ■0359 ■0350 •0342 •0333 •0324 ■0315 ■0305 •0296 •0287 •0277 •0268 •0258 86 87^ 8§ 88i ■0523 ■0523 ■0523 •0523 •0522 ■0521 ■0520 •0519 ■0518 •0517 •051S •0514 •0512 •0510 •0508 ■0506 •0503 ■0500. •0498 ■0495 •0492 •0489 ■0485 •0482 ■0478 •0474 •0470 •0466 •0462 ■0458 . ^0453 •0449 •0444 ■0439 ■0434 •0429 ■0423 •0418 •0412 ■0407 ■0401 ■0395 •0389 ■0383 •0376 •0370 •0364 ■0357 ■0350 •0343 ■0336 ■0329 ■0322 •0315 ■0308 ■0300 •0293 •0285 ■0277 ■0270 •0262 •0254 •0246 •0238 ■0229 •0221 86| •0436 •0436 :o436 •0436 •0435 •0435 ■0434 •0433 ■0432 •0431 ■0430 ■0429 ■0427 ■0425 •0424 •0422 ■0419 •0417 •0415 •0413 •0410 ■0408 ■0405 •0402 •0399 •0395 ■0392 •0389 •038s •0382 •0378 •0374 •0370 •0366 •0362 •0357 •0353 ■0349 •0344 •0339 ■0334 •0329 •0324 ■0319 •0314 •030S •0303 ■0298 •0292 •0286 •0280 •0275 •0269 •0263 •0257 •0250 •0244 •0238 •0231 •0225 •0218 •021 1 •0205 •0198 •0191 •0184 87 ■0349 •0349 ■0349 •0349 •0348 ■0348 ■0347 •0346 ■0346 ■0345 ■0344 •0343 ■0341 •0340 •0339 •0337 ■0335 ■0334 •0332 •0330 ■0328 •0326 ■0324 •0321 •0319 •0316 •0314 ■031 1 •0308 •0305 •0302 •0299 •0296 ■0293 •0289 ■0286 •0282 •0279 •0275 •0271 •0267 ■0263 •0259 ■0255 •0251 ■0247 •0242 •0238 •0234 •0229 •0224 •0220 •0215 •0210 •0205 •0200 ■0195 ■0190 •0185 •0180 •0174 ■0169 ■0164 •0158 ■0153 ■C147 89 89| 87i •0262 0262 •0262 0261 •0261 •0261 •0261 •0260 •0260 •0259 •0258 •0257 ■0256 •0255 ■0254 •0253 •0252 •0251 •0249 ■0248 •0246 •0245 •0243 ■0241 •0239 •0237 •0236 •0234 •0231 •0229 •0227 ■0224 •0222 •0220 ■0217 •0214 ■0212 •0209 ■0207 •0204 ■020I •0198 •0195 •0192 •0189 •0185 0182 •0179 •0176 ■0172 ■0168 •0165 •OI6I •0158 •0154 •0150 ■0147 •0143 •0139 •013s •OI3I •0127 ■0123 01x9 •0115 •01 II 88 ■0175 ■0174 •0174 •0174 •0174 ■0174 •0174 •0173 •0173 •0172 ■0172 ■0171 •0171 •0170 ■0169 ■0169 ■0168 •0167 •0166 ■0165 •0164 •0163 •0162 •0161 •0159 •0158 •0157 •0156 •0154 •0153 •0151 •0150 •0148 •0146 •0145 •0143 •0141 •0139 •0138 ■0136 •0134 •0132 ■0130 •0128 •0126 •0123 '0121 •0119 •01 17 •01 14 '0112 •Olio •0107 •0105 •0103 •0100 •0098 •0095 0092 •0090 ■0087 ■0085 •0082 •0079 •0077 •0074 •0087 •0087 ■0087 •0087 •0087 •0087 ■0087 •0087 ■0086 •0086 •0086 •0086 •0085 •0085 ■0085 •0085 •0084 ■0084 •0083 •0083 •0082 •0082 •0081 •0081 ■0080 •0079 ■0079 •0078 •0077 •0077 •0076 •0075 •0074 ■0073 •0072 •0071 •0071 •0070 •0069 ■C068 •0067 •0066 •0065 •0064 •0063 •0062 •0061 ■0060 •0059 •0057 •0056 •0055 ■0054 •0053 •0052 ■0050 •0049 •0048 •0046 •0045 •0044 •0042 •0041 •0040 •0038 ■0037 88^ 89 90 ■0000 ■0000 •0000 •0000 •0000 •0000 •0000 •0000 •0000 •0000 •0000 •0000 •0000 ■0000 •0000 •0000 •0000 •0000 •0000 •0000 ■0000 •0000 •0000 •0000 •0000 •0000 ■0000 •0000 •0000 •0000 •0000 ■0000 •0000 ■0000 . •0000 •0000 •0000 •0000 •0000 •0000 •0000 •0000 ■cooo ■0000 ■0000 ■0000 ■0000 ■0000 •0000 ■0000 ■0000 •0000 ■0000 ■0000 •0000 •0000 •0000 •0000 •0000 •0000 •0000 ■0000 ■0000 •0000 •0000 •0000 89i 90 When the sign is + the Azimuth is to be reckoned from the South. When the sign is - the Azimuth is to be reckoned from the North.