THE 
 
 AMERICAN 
 
 UNIVERSITY 
 
 LIBRARY 
 
 ARTEMAS MARTIN, PH. D. 
 WASHINGTON, D. C. 
 
 ^ 
 
\\ 
 
L. 
 
Ajironomical & Geographical 
 
 ESSAYS: 
 
 CONTAINING, 
 
 I. 
 A FULL AND COMPREHENSIVE VIEW, ON A NEW PLAN, 
 
 OF THE 
 
 General f&rinciples of %ftxm\mi^. 
 
 II. 
 
 THE USE OF THE 
 
 CELESTIAL AND TERRESTRIAL 
 
 GLOBES, 
 
 Exemplified in a greater Variety of Problems ^ than are to be 
 found in any other Work. 
 
 III. 
 THE DESCRIPTION AND USE 
 
 OF THE MOST IMPROVED 
 
 PLANETARIUM, TELLURIAN, 
 
 AND 
 
 LUNARIUM. 
 
 IV. 
 
 AN INTRODUCTION TO 
 
 PRACTICAL ASTRONOMY. 
 
 BY THE LATE 
 
 GEORGE ADAMS, 
 
 MATHEMATICAt INSTRUMENT MaKER TO HiS MaJESTY, AND 
 
 Optician to the Princi of Wales. 
 
 JTourt!) coition. 
 
 If^itt the Author's lajl Improvementi, Illufirated ivitb elegant Copper-platet. 
 
 WHITEHALL : 
 
 miNTBD FOR WILLIAM TOUNG, bookseller and 
 
 STATIONE R -^^sTiftt^ SOUTH 2''. STREET, 
 PHILADELPHIA. 
 1800. 
 
(X'Mt 
 
 At I 
 
Pr^izfr 
 
 PREFACE. 
 
 THE conneclion of aflronomy with 
 geography is fo evident, and both 
 in conjun61ion fo neceffary to a liberal 
 education, that no man will be thought 
 to have deferved ill of the republic of 
 letters, who has applied his endeavours 
 to diffufe more univerfally the know- 
 ledge of thefe ufeful fciences, or to ren- 
 der the attainment of them eafier ; for as 
 no^ branch of literature can be fully 
 comprehended without them, fo there is 
 none which impreffes more pleafing ideas 
 on the mind, or that affords it a more 
 rational entertainment. 
 
 The fifth edition of my father's treat- 
 ife on the globes being out of print, I 
 was folicited to reprint it. To obviate 
 feveral objeftions to the form in which 
 he had difpofed the problems, I was in- 
 duced to undertake the prefent work, in 
 which they are arranged in a more me- 
 thodical manner, and a great number 
 added to them. Such fa6ls are alfo oc- 
 cafionally introduced, fuch obfervations 
 interfperfed, and fuch relative informa- 
 
 
iv PREFACE. 
 
 tion communicated, as it is prefumed will 
 excite curiofity, and fix attention. 
 
 Having proceeded fo far in this work, 
 I found that it was eafy to render it fub- 
 fervient to my plan of publifhing, from 
 time to time, " Essays, describing 
 THE Use of Mathematical and 
 Philosophical Instruments ;" for 
 the defcription of thofe which have been 
 contrived to fmooth the path to the 
 fcience of aftronomy, or to facilitate the 
 pradice of the arts depending on it, could 
 no where be introduced with fo much 
 propriety, as in a work which treated of 
 it's elementary principles. 
 
 To further this defign, it was necef- 
 fary to prefix an introduction to aitrono- 
 my. This is divided into three parts. 
 In the firft, the pupil is fuppofed to be 
 placed in the fun, the center of the folar 
 fyftem : from this fituation he confiders 
 the motion of the heavenly hoft, and finds 
 that all is regular and harmonious. In the 
 fecond part, his attention is direfted to 
 the appearances of the planetary bodies, 
 as obferved from the earth. It were to 
 be wifiied that the tutor would at this part 
 exhibit to his pupil the various phenom- 
 ena in the heavens themfelves : by teach- 
 ino^ him thus to obferve for himfelf, he 
 
PREFACE. V 
 
 would not only raife his curiofity, but fo 
 fix the impreflions which the objecls have 
 made on his mind, that by proper culti- 
 vation they would prove a fruitful fource 
 of ufeful employment ; and he would 
 thereby alfo gratify that eager defire af- 
 ter novelty, which continually animates 
 young minds, and furnifli them with ob- 
 jefts on which to exercife their natural 
 aftivity. In the third part of this intro- 
 du61ion, the received, or Copernican fyf- 
 tem is explained : by this fyftem the va- 
 rious phenomena of the heavens are ra- 
 tionally accounted for ; it fliews us how 
 to reconcile the real ftate of things with 
 the fallacies arifing from the fenfes ; and 
 teaclies us that the irregularities obferv- 
 able in the motion of the heavenly bodies, 
 are for the mofl part to be attributed to 
 the fituation from which they are obferv- 
 ed. Aftronomy, in common with other 
 branches of the mathematics, while it 
 flrengtheris the powers of the mind, re- 
 ffrains it from rafli prefumption, and dif- 
 pofes it to a rational affent. 
 
 The principles of the Copernican fyf- 
 tem are further elucidated in the third 
 effay ; in which the moft improved plan- 
 etarium, lunarium, and tellurian, are 
 defcribed. Thefe inftruments, though 
 lefs complicated in their conflru6lion. 
 
vi PREFACE. 
 
 and lefs expenfivc to the purchafer, than 
 thofe large ones heretofore made for the 
 fame purpofe, are equally, perhaps bet- 
 ter, adapted to explain the general prin- 
 ciples of aflronomy. In defer ibing them, 
 it was necefiary to re-confider many fub- 
 jefts which had been previoufly treated ; 
 but as they are here placed in another 
 point of view, prefented to the mind 
 under a different form, are generally 
 defcribed in other words, and often with 
 the addition of new matter, it is hoped 
 that thefe repetitions, fo far from being 
 an objeft of complaint, will be found to 
 contribute to the main intention of this 
 work, by conveying further inftruftion, 
 fixing it more deeply in the mind, and 
 rendering that obvious which before 
 might be found difficult. 
 
 One part feemed wanting to an intro- 
 ductory treatife on pradical aftronomy ; 
 fomething that would gently lead the 
 pupil to a knowledge of the pra6lical 
 part of this fcieoce, a branch of aftron- 
 omy to which we arc indebted for our 
 prefent knowledge of the heavens, by 
 which geography has been improved, 
 and by which the paffage of fliips over 
 the tracklefs ocean is facilitated. 
 
PREFACE. 
 
 There is no part of mathematical 
 fcience more fimple and eafy, than the 
 meafurement of the relative pofitions 
 and diflances of inacceflible obje6ts ; yet, 
 to the uninftrufted, to determine the 
 diflance of a fhip on the ocean, to af- 
 certain the height of the clouds and 
 meteors that float in the atmofphere, to 
 fix the latitude and longitude of places 
 &c. are problems that have ever appear- 
 ed to be above the reach of human art - 
 they are therefore particularly calculated 
 to engage the attention of young minds, 
 and may be ufed to encourage dilicrence, 
 and reward application. 
 
 To introduce the pupil to this branch 
 of aftronomy, I have defcribed two in- 
 flrumcnts, each of which is fimple in it's 
 conftruaion, and of fmall expence. By 
 thefe he may find the diftance of any in- 
 acceffible objea, the height of a fpire, 
 a mountain, or any other elevation- 
 learn to plot a field ; afcertain the alti- 
 tude of a cloud, a fire-ball, or any other 
 meteor; determine with accuracy the 
 hour of the day, the latitude or longi- 
 tude of a place, with many other curio'us 
 problems. In the felection of thefe, for the 
 firft edition, I have to acknowledge the af- 
 fifiancc I received from an ingenious friend. 
 
i 
 
 N. B. The different EfTays in this 
 
 firft American Edition are printed fo as 
 to be bound or purchafed in one volume, 
 or feparately, as may be moft agreeable ; 
 therefore the folios are arranged accord- 
 ingly ; viz. the numbers on the top of 
 the page, to fuit thofe who wifh to bind 
 or purchafe feparately ; the numbers at 
 the foot, thofe who chufe the whole in 
 one volume : of courfe the references 
 and contents refer always to the number 
 at xh^foot of xh^page. 
 
 The Binder 
 
 Will ohferve that the figures following 
 the Signatures f ferve as a guide to collate 
 the xoork. 
 
TABLE OF CONTENTS. 
 
 PAGE 
 
 12 
 14 
 
 \J F the Solar Syftem, as Teen from the S;in 3 
 Of the Cflcftial Signs and Conftellations 6 
 
 Of the Planets, as feen from the Sun 
 Of the Paths of the Planets 
 Of the Motion of the Planets round their Axis 15 
 
 Of the Phenomena of the Heavens, as feen from the 
 
 S"n - - . ,8 
 
 or the Apparent Motion of the Sun 18 
 
 Of the Apparent Phenomena of the Moon 
 
 'Of the Apparent Motion of the Stars 
 
 The Appearance of the Phnets 24. 
 
 Of the Copernican Syftem 28 
 
 Of the Sun 
 
 Of Mercury . - 96 
 
 Of Venus 
 
 Of the Earth 
 
 Of the Moon 
 
 Of Mars 
 
 21 
 22 
 
 38 
 42 
 
 43 
 48 
 Of Jupiter , . ^Q 
 
 Of Saturn . , . *- 
 
 Of the Georgium Sidu8 56 
 
 b 
 
X CONTENTS. 
 
 PAGE. 
 
 Of the Figure of the Earth 62 
 
 Of the Diurnal Motion of the Earth 69 
 
 Of the Annual Motion of the Earth 79 
 Of tl)c Apparent jMotlon of the Sun, arifmg from the 
 
 Earth's Annual Motion round it 82 
 
 Of the Phenomena occafioned by the Annual and 
 
 Diurnal Motions of the Earth 86 
 
 Of the Seafons of the Year yl 
 
 Of Solar and Siderial time 10 1 
 An Explanation of the Phenomena which arife from 
 the Motion of the Earth, and of the inferior 
 
 Planets, Mercury and Venus 107 
 
 Of the Inferior Planets 1 10 
 
 Of the Phafes of Venus j20 
 
 Of the Superior Planets 124. 
 
 Of the Secondary Planets 129 
 
 Of the Moon 1 30 
 
 Of the Phafes of the Moon 136 
 
 Of the Satellites of Jupiter, &c. 140 
 
 Of Eclipfes 1 44 
 
 Of Eclipfes of the Moon 146 
 
 Of Eclipfes of the Sun 152 
 
 Of the Period of Eclipfes 156 
 
 Of Parallax and Refiaftion 159 
 
 Of the fixed Stars 166 
 
 Hcifchcl on the Conftruftion of the Univerfe, &c. 173 
 
 Of Comets - - 179 
 
 Of the Telefcoplc Appearance of the Planets 186 
 
 Of the Ufe of the Qlobes 195 
 
 Advantacjes of Globes 195 
 
CONTENTS. xi 
 
 PAGB 
 
 V 
 
 Dcfcrlption of the Globes 20+ 
 
 Of the Terreftrial Globe 2 1 4 
 
 Of Latitude and Longitude 2 i + 
 
 PROB 
 
 1. To find the Longitude of any Place 219 
 
 2. To find the Difference of Longitude between any 
 
 two Places - 221 
 3 To find all thofe Places where it is _Noon at any 
 
 given Hour of the Day, in another Place 222 
 
 4. When it is Noon at any Place, to find what 
 
 Hour it is at any other place 223 
 
 5. At any given Hour where you are, to find the 
 
 Hour at a Place propofed 224. 
 
 Of Latitude - - 225 
 
 6. To find the Latitude of any Place 227 
 
 7. To find all thofe Places which have the fame La- 
 
 titude with any given Place 227 
 
 8. To find tht Difference of Latitude between any 
 
 two Places - - 228 
 
 9. The Latitude and Longitude being known, to 
 
 find the place - 228 
 
 Of finding the Longitude 229 
 
 10. To find the Diilance of one Place froni another 239 
 
 11. To find the Angle of Pofition of Places 240 
 I 2. To find the Bearings of Places 240 
 Of the Twilight - 241 
 To reaify the Globe - 245 
 13. To redlify for the Summer SoUlicc 247 
 
 14. for the Winter Solftice 249 
 
 15* f'Jr the Times of Equinox 250 
 
 i6. To exemplify the Sun's Altitude 253 
 
xM CONTENTS. 
 
 PROB. PAGE 
 
 17. Of the Sun's Meridian Altitude 254 
 
 18. To find the Sun's Meridian Altitude univerfally 255 
 
 19. Of the Sun's Azimuths 256 
 Of the Zones and Climates 258 
 
 20. To find the Climates - 260 
 
 21. To iiluftrate the Diftinftion of Afcii, &c. 264 
 i2. To find the AntcEci, &c. - 267 
 
 23. To fiiid thofe Places over which the Sun is 
 
 vertical - - 26S 
 
 24. To find the Sun's Place - 269 
 
 25. To find the Sun's Declination 272 
 
 26. To find the two Days on which the Sun is in the 
 
 Zenith of any given Place, Sec. 273 
 
 27. To find where the Sun is vertical on a given 
 
 Day and Hour ^ - 273 
 
 28. At a given Time of the Dayinone Place, to find 
 
 at the fame Inftant thofe Places where the 
 
 Sun is n'fing, fetting, &c. 274 
 
 29. To find all thofe Places within the Polar Circles, 
 
 on which the Sun begins to fhine, &c. 276 
 
 30. To make Ufe of the Globe as a Tellurian 277 
 3 I . To rectify the Globe to the Latitude and Hoi izon 
 
 of any Place - 280 
 
 32. To reftify for the Sun's Place 281 
 
 33. To rectify for the Zenith of any Place 2S2 
 Of expofing the Globe to the Sun 285 
 
 34. To obfcrve the Sun's Altitude 286 
 ■35. To place the Globe, when expofed to the Sun, 
 
 that It may reprefcnt the natural Pofiticns of 
 
 the Earth - 288 
 
CONTENTS. adtt 
 
 l>ROB. PAGE 
 
 36. To find naturally the Sun's Declination 290 
 
 37. To find naturally the Sun's Azimuth 291 
 
 38. To fhew where the Sun will be twice on the 
 
 fame Azimuth in the Morning, and twice ia 
 
 the Afternoon - 2f 8 
 
 39. To find the hour by the Sun 294 
 (Bf Dialling - - 298 
 
 40. To conftruA an Horizontal Dial 303 
 
 41. To delineate 3 South Dial 307 
 
 42. To make an ereA Dial - 308 
 Of Navigation - - 312 
 
 43. Given the Difference of Latitude, and Difference 
 
 of Lon<ritude, to find the Courfc and Dif- 
 tance failed - 3^* 
 
 44. Given the Difference of Latitude and Courfc, 
 
 to find the Difference of Longitude and Dif- 
 tance failed - 3^9 
 
 45. Given the Difference of Latitude and Diftance 
 
 run, to find the Difference of Longitude, and 
 Angle of the Courfe 320 
 
 4.6. Given the Difference of Longitude and Courfc, 
 to find the Difference of Latitude, and Dif- 
 tance failed $2i 
 
 47. Given the Courfe and Diftance, to find the 
 
 Difference of Longitude and Latitude 322 
 
 48. To ftcer a Ship upon the Arch of a great Circle, 
 
 &c. - - 323 
 
 Of the Cclcftial Globe - 337 
 
 Of the Precefllon of the Equinoxes 343 
 
ilv CONTENTS. 
 
 ^K.OB. PAGE 
 
 2- To rcftify the Ctleftlal Globe 34.9 
 
 3. To find the Deciiiiati.>n aiid Right Afcenfion of 
 
 the Sua - - 3^0 
 
 4. To find the Sun's oullque Arcenfion, Sec. 351 
 
 5- the Sun's meridian Ahitudc 352 
 
 6. the Length of the Day in Latituuts un- 
 der 66' Decrees - 3531, 
 
 7- the I^ength of the longed and fnorUfl: 
 
 Day in Latitudes under 66' Degrees 352 
 
 8. To find the Latitude where tlie longed Day may 
 
 be of any given Length between twelve and 
 
 twenty-four hours - 353 
 
 9. the time of Sun-rifing, Sec. 354 
 
 10. how long, &c. the Sun fliines in any 
 
 Place within the Polar Circles 356 
 
 1 1. To illuftrate the equation of Time, &c. 360 
 
 12. To find the Right Afcenfion, &c. of a Star 362 
 
 13. the Latitude and Longitude of a Star 363 
 
 14. the place of a Star on the Globe by, &ic. 363 
 
 15. at what hour a given Star tranfits the 
 
 Meridian - - 364 
 
 16. On what Day a Star will come to the Meridian 365 
 
 1 7. To reprefcnt the face of the Heavens for any 
 
 given Day and Hour - 365 
 
 18. To trace the Circles of the Sphere in the Heavens 368 
 
 19. To find the Circle of perpetual Apparition 374 
 
 20. the Sun's Amplitude 375 
 
 2 [. the Sun's Altitude at a given Hour 376 
 
 22. when the Sun is due Eaft in' a given La- 
 titude ■ - « .379 
 
CONTENTS. XV 
 
 f ROB. 
 
 PA Gl 
 
 23. To find the Rifing, Setting, Culmmating, &,c. 
 
 of a Star . . ^^^ 
 
 24. the Four of the Day, the Altitude and 
 
 Azimuth of a Star being given ^gj 
 
 25. the Altitude and Azimuth of a Star, Sec, 382 
 
 ^^- t^^it Azimuth, Sec. at any hour of the 
 
 Night - . ^3^ 
 
 27- the Sun's Altitude, and the Hour, from 
 
 the Latitude, Sun's Place, and Azimuth 383 
 
 28. the Hour, the Latitude and Azimuth 
 
 29. a Star, the Latitude, Sun's Place, Hour, 
 
 ^c. given _ . ^g^ 
 
 30. To find the Hour by Data from two Stars that 
 have the fame Azimuth 
 
 31. the Hour by Data from two Stars that 
 
 have the fame Altitude 
 
 32- the Latitude by Data from two ttars 387 
 
 33. the Latitude by other Data from two 
 
 Stars . „ 
 
 34. when a Star rlic? or fcts cofmically 389 
 
 35- when a Star rifes or fcts achronically 390 
 
 3^- when a Star will rife heliacally 392 
 
 37- when a Star will fct heliacally 
 
 Of the Correfpondence between the Celcftial and 
 
 Tenefl rial Spheres ,g- 
 
 38. To- find the Place of a Planet, Sic. 398 
 
 39- what Planets are above the Horizon 399 
 
 '^°- ^'i'-' f'g'it Afcenfion, &c. of a Planet 400 
 
 385 
 386 
 
 393 
 
 41. .. the Moon's Place 
 
 407 
 
xvi CONTENTS. 
 
 »ROB. FACE 
 
 42. To find the Moon's Declination 407 
 
 43. the Moon's greateft. and lead Meridian 
 
 Altitudes - - 408 
 
 44. To illuftrate the Harveft Moon 409 
 
 45. To find the Azimuth of the Moon, and thence 
 High Water, &c. 414 
 
 Of Comets - - 415 
 
 46. To reaify the Globe for the Place of Obferva- 
 
 tion - - 417 
 
 47. To determine the Place of a Comet 4 1 8 
 
 48. To find the Latitude, Sec. of a Comet 418 
 
 49. To find the Time of a Comet's Rifing, &c. 419 
 
 50. To fisd the fame at London 420 
 
 51. To determine the Place of a Comet from an Ob- 
 fervation made at London 420 
 
 52. From two given Places to aflign the Comet's 
 Path - - 421 
 
 53. To eftimate the Velocity of a Comet 422 
 
 54. To reprefent the general Phenomena of a Comet 423 
 A Defcription of the moft improved Planetarium, 
 
 Tellurian, and Lunarium 425 
 
 Defcription of the Planetarium 427 
 
 Defcription of the Tellurian 445 
 
 Defcription of the Lunarium * 460 
 An Introduftion to Pradtical Aftronomy, in which 
 
 is introduced a Variety of curious Problems, from 473 
 
 to the End of the Work. 
 
ASTRONOMI CAL 
 
 ESSAYS. 
 
 ESSAY I. 
 PART I. 
 
 MANKIND have in all ages been defirous 
 of forming rational conceptions of the 
 nature and motion of thofe bodies that appear 
 in the vaft: concave above their heads. Amidil 
 the infinite variety of objedls which furround 
 them on every fide, the heavenly bodies mud 
 have been amongfl thofe which firrt: attracted 
 their attention. They are of all objefts the mod 
 confpicuous, tlie moil important, and the molt 
 beautiful. 
 
 Aftronomy inflrudls us in the laws, or 
 rules, that govern and dired the motions of 
 the heavenly hoft. It weighs and confidcrs the 
 powers by which they circulate in their orbs. 
 It enables us to difcover their fize, determine 
 C I 
 
2 ASTRONOMICAL ESSAYS. 
 
 their diflance, explain their various phenomena, 
 and correct the fallacies of the fenfes by the 
 light of truth. 
 
 Aftronomy is not merely a fpeculative fci- 
 ence j it's ufe is as extenfive, as it's refearches 
 are fublime. Navigation owns it for it's guide : 
 by it commerce has been extended, and geogra- 
 phy improved. It is aftronomical obfervations 
 that form the bafis of geography. Thus it has 
 co-operated with other caufes in the greateft of 
 all works, the diffufion of knowledge, and the 
 civilization of man. 
 
 As in order to attain an accurate idea of 
 any piece of mechanifm, it is bed to begin 
 our inveftigations by an examination of thofe 
 parts which give motion to the reft, the pri- 
 mary caufes of thofe effet^ls for which the ma- 
 chine was made ; fo the young pupil will more 
 eafily gain a juft idea of the motion of the 
 heavenly bodies, by confidering them as feen 
 from the fun, the center of our fyftem, and 
 the principal agent ufed by the Lord of na- 
 ture, for conducting and regulating the plan- 
 etary fyftem. 
 
 It will not be difficult, after this, to inform 
 him how thofe appearances are to be accounted 
 for, that arife from his particular fituation ; 
 •whence he views the heavens from a point 
 which is not in the center of the fyftem, and 
 is confequcntly the fource of many apparent 
 
ASTRONOMICAL ESSAYS. 3 
 
 irregularities. This knowledge attained, it 
 will then be eafy to prove to him, that the real 
 and apparent motions of the heavenly bodies 
 are frequently the reverfe of each other. For 
 being by this means put into pofTeflion of the 
 univerfals of this fcience, the knowledge of par- 
 ticulars will be rendered facile and clear. 
 
 Of the Solar System, as seen by a Spec- 
 tator SUPPOSED TO BE PLACED IN THE 
 
 Sun. 
 
 As the center of the fydem is the only 
 place from which the motion of the planets 
 can be truly feen, let us fuppofe an obferver 
 placed in the center of the fun. In this fitua- 
 tion he will fee at one view all the heavens, 
 which will appear to him perfedly fpherical, 
 the flars being fo many lucid points in the 
 concave furface of the fphere, whofe center is 
 the fun, or, in the prefent inftance, the eye 
 of the obferver. 
 
 Our fpedator will not, however, immedi- 
 ately conclude from appearances, either that 
 the heavens are really fpherical, or tluic the 
 fun is in the center of that fphere, or that the 
 ftars are all at an equal diftance from him ; 
 having been previoufly taught by experience 
 and obfervation, that while he remains in the 
 fame place, he cannot judge properly of the 
 
 3 
 
4 ASTRONOMICAL ESSAYS. 
 
 diftance of furrounding objects, at lead of thofe 
 which are placed beyond the ordinary reach of 
 his view. When objects are removed beyond 
 the diftances we are accuftomed to, the princi- 
 ples by which we form our general judgment 
 fail us ; and we can only tell which is neareft, 
 or which is furthefl, either by our own motion, 
 or that of the objects. 
 
 To illuftrate this, let us fuppofe a number 
 of lamps to be placed irregularly, at different 
 diftances from the eye, in a dark night. Now 
 if in this cafe we fuppofe the darknefs to be 
 fo complete, that no intermediate objects 
 could be feen, no difference in colour dif- 
 cerned, nor any convergence towards the point 
 of fight be perceived ; our judgment could 
 not afTift us in diftinguilhing the diftance of 
 one from the other, and they would therefore 
 all feem to be at an equal diftance from the 
 fpe£tator. 
 
 For the fiime reafon, the fun and moon, 
 the flars and planets, appear to be all at an 
 equal diftance from us ; though it is highly 
 probable, that fome of the ftars are many mil- 
 lions of times nearer to us than others. The 
 fun is demonftrated to be nearer than any of 
 the ftars. The moon and fome of the planets 
 are known by occular proof to be nearer to us 
 than the fun, becaufe they fometimes come be- 
 tween it and our eye, and hide the whole, or 
 
 4 
 
ASTRONOMICAL ESSAYS. 21 
 
 a great part of his diik, from our view. They 
 all, however, appear equally diftant, and as If 
 placed in the farface of a fphere, whereof our 
 eye is the center. In whatever place, there- 
 fore, the fpedator refides, whether it be on 
 this earth, in the fun, or in the regions of Sa- 
 turn, he will confider that place as the middle 
 point of the univerfe, and the center of the 
 world ; for it will be to him the center of a 
 fpherical furface, in which all diftant bodies 
 appear to be placed. 
 
 Thefe things being rendered plain, the 
 pupil may proceed to confider the obfervations 
 of the folar fpeftator ; to whom, as we have 
 already obferved, the heavens will appear as the 
 furface of a concave fphere, concentrical to his 
 eye : in this furface he will difcover an innumer- 
 able hoft of fixed ftars, which will for fome 
 time engage his attention, before he difcovers 
 that they may be diftinguiflied into two kinds ; 
 the one difperfed through the whole heavens, 
 differing in their degree of brightnefs, but re- 
 maining always at the fame relative diftancc 
 from each other. Thefe he will therefore call 
 Jixed Jiars, ox on\y Jiars. Befides thefe, he will 
 find fome others moving among the foregoing 
 with different velocities, which he will call 
 wandering Jiars, or planets. 
 
22 ASTRONOMICAL ESSAYS. 
 
 Of the Celestial Signs and Constella- 
 tions. 
 
 Having proceeded thus far, our fpedator 
 will endeavour to find out fome method of 
 diftiiiguifliing the (lars from each other; con- 
 cluding, that as they do not change their re- 
 lative pofitions one to the other, he may eafily 
 make an exa6l defcription of them, and by re- 
 peated obfervations determine the pofition and 
 order which fubfift among them. 
 
 That he may avoid confufion in defcrip- 
 tion, and be able to point out any particular 
 ftar, without being obliged to give a name to 
 each, he will divide them into feveral parcels ; 
 to each of thefe parcels he will affign a figure 
 at pleafure ; thefe aflemblages, or groupes of 
 ilars, he will call conjiellations. Thus a num- 
 ber of ftars near the north pole is called the 
 bear, becaufe the (lars which compofe it are 
 at fuch diilances from each other, that they 
 may fall within the figure of a bear. Ano- 
 ther conftellation is called the fhip, becaufe 
 that collection of ftars, which compofe it, is 
 reprefented upon a cleleftial globe as com- 
 prized within fome part of the figure of a 
 fhip. 
 
 As the fixed ftars will appear to our ob- 
 ferver of different degrees of magnitude and 
 fplendor, he will divide them into different 
 6 
 
ASTRONOMICAL ESSAYS. 23 
 
 claiTes. Thofe which feem the largefl and 
 brighteft, he will call ftars of the firfl: magni- 
 tude ; the fmallefl that we can fee with the na- 
 ked eye, are called ftars of the fixth magnitude ; 
 and the intermediate ones, according to their 
 different apparent fizcs he will call of the 
 fecond, third, fourth, or fifth magnitudes. 
 Thofe flars, which cannot be feen without the 
 afliftance of a telefcope, arc not reckoned in 
 any of thefe clafTes, and are called telefcopic 
 Jiars. 
 
 By a knowledge of the fixed ftars and their 
 pofirions, our obferver will obtain fo many 
 fixed points, by which he may obferve the 
 motions of the planets, and the relation of 
 thefe motions to each other ; he will ufe them 
 as fo many landmarks, (if the word may be 
 allowed) by which the fituations of other ce- 
 leftial bodies may be afcertained, and the va- 
 rieties to which they are fubjeO: be obferved. 
 For from the fame place, the motions of the 
 neavenly bodies can only be eftimated by the 
 angle formed at the fpedlator's eye by the fpace 
 which the moving body pafTes over. 
 
 To meafure the fpaces, the (tars muft be 
 ufed, and confidered as fo many luminous 
 points fixed in the concavity of a fphere, 
 whofe radius is indefinite, and of which the 
 obferver's eye is the center. We may learn 
 from hence the neceflity of forming an exad 
 
 7 
 
24 ASTRONOMICAL ESSAYS. 
 
 catalogue of the Jlars, and of determining their 
 pofitions with accuracy and care. With fuch 
 a catalogue, the fcience of aftronomy begins. 
 
 Although to thofe who are unacquainted 
 with the nature of celeftial obfervation, it might 
 at firfl fight appear almoft impoflible to number 
 the ftars ; yet their relative fituations have 
 been fo carefully obferved by aftronomers, that 
 they have not only been numbered, but even 
 their places in the heavens have been afcer- 
 tained with greater accuracy, than the relative 
 fituation of mod places on the furface of the 
 earth. 
 
 The greateft number of ftars that are vifi- 
 ble to the naked eye, are to be feen on a win- 
 ter's night, when the air is clear, and no 
 moon: appears. But even then a good eye can 
 fcarce diftinguifh more than one thoufand at 
 a time in the vifible hemifphere : for though 
 on fuch a night they appear to be almoft in- 
 numerable, this appearance is a deception, 
 that arifes from our viewing them in a tran- 
 fient and confufed manner ; whereas, if we 
 view them diftindly, and only confider a fmall 
 portion of the heavens at a time, and after 
 fome attention to the fituation of the remark- 
 able ftars contained in that portion, begin to 
 count, we ftiall be furprized at the fmallnefs of 
 their number, and the eafe with which they may 
 be enumerated. 
 
 S 
 
ASTRONOMICAL ESSAYS. 2^ 
 
 The number of the ancient conflellations 
 was 48 ; in thefe were included 1022 ftars. 
 Many confteilations have been added by mo- 
 dren aftronomers ; fo that the catalogues of 
 Flamfleed and De la Caille, when added to- 
 gether, are found to contain near five thou- 
 fand ftars. The names of the confteilations, 
 their fituation in the heavens, with other par- 
 ticulars, arc beft learned by ftudying the arti- 
 ficial reprefentation of the heavens, a celeftial 
 globe. 
 
 The galaxy or milky way muft not be ne- 
 gle£ted ; it is one of the moft remarkable ap- 
 pearances in the heavens ; it is a broad circle 
 of a whitifti hue, in fome places it is double, 
 but for the moft part confifts of a fingle path fur- 
 rounding the whole celeftial concave. The great 
 Galileo difcovered by the telefcope, that the por- 
 tion of the heavens which this circle pafles 
 through, was every where filled with an infinite 
 multitude of exceeding fmall ftars, too f mall to 
 be difcovered by the naked eye ; but by the 
 combination of their light diffufing a fliining 
 whitenefs through the heavens. Mr. Brydone 
 fays, that when he was at the top of mount Etna, 
 the milky way had the moft beautiful effeft, ap- 
 pearing like a pure flame that ftiot acrofs the 
 heavens. 
 
 The ftars appear of a fenfible magnitude 
 to the naked eye, becaufe the retina is not 
 
 9 
 
26 ASTRONOMICAL ESSAYS. 
 
 only afFeded by the rays of light which are 
 emitted diredly from them, but by many thou- 
 fands more, which, falling upon our eyelafhes, 
 and upon the vifible serial particles about us, are 
 reflefted into our eyes fo ftrongly, as to excite 
 vibrations, not only in thofe points of the retina, 
 where the real images of the ftars are formed, 
 but alfo in other parts round about it. This 
 makes us imagine the ftars to be much bigger, 
 than they would be if we faw them only by the 
 few rays which come dire£lly from them to our 
 eyes, without being intermixed with others. 
 Any one may be made fenfible of this, by looking 
 at a ftar of the firft magnitude, through a long 
 narrow tube ; which, though it takes in as much 
 of the fky as would hold a thoufand of fuch ftars, 
 icarce renders that one vifible. 
 
 The number of the ftars almoft infinitely 
 exceeds what we have yet been fpeaking of. 
 An ordinary telefcope will difcover, in feveral 
 parts of the heavens, ten times as many ftars 
 as are vifible to the naked eye. Hooke, in his 
 Micrographia, fays, that with a telefcope of 
 twelve feet he difcovered fcventy-eight ftars 
 among the Pleiades, and with a more per- 
 fect telefcope, many more. Galileo reckoned 
 eighty in the fpace between the belt and the 
 fword of Orion, and above five hundred more 
 in another part of the fame conftellation, with- 
 
 to 
 
ASTRONOMICAL ESSAYS. 27 
 
 in the compafs of one or two degrees fquare. 
 Antonfa Maria de Rheita counted in the fame 
 conftellation above two thoufand ftars. Fu- 
 ture improvements in telefcopes may enable us 
 to difcover numberlefs flars that are now in- 
 vifible ; and many more there may be, which 
 are too remote to be feen through telefcopes, 
 even when they have received their uhimate 
 improvement. Dr. Herfchel, to whofe inge- 
 nuity and afTiduity the aftronomical world is 
 fo much indebted, and whofe enthufiaftic 
 ardor has revived the fpirit of difcoveries, of 
 which we (hall fpeak more largely in another 
 part of this effay, has evinced what may be 
 effeded by improvements in the inflruments 
 of obfervation. In fpeaking here of his dif- 
 coveries, I fhall ufe the words of M. de la 
 Lande.* "In pafling rapidly over the hea- 
 vens with his new telefcope, the univerfe in- 
 creafed under his eye ; 44000 ftars, feen in the 
 fpace of a few degrees, feemed to indicate 
 that there were feventy-five millions in the 
 heavens." He has alfo fhewn that many ftars, 
 which to the eye, or through ordinary glafles, 
 appear fmgle, do in fad confift of two or 
 more ftars. The galaxy or milky way owes 
 it's light entirely to the multitude of fmall 
 ftars, placed fo clofe as not to be difcoverable 
 even by an ordinary telefcope. The nebulas. 
 
 *Mcmoircsde 1' Academic dc Dyon, 1785. 
 II < 
 
28 ASTRONOMICAL ESSAYS. 
 
 or fmall vvhitifh fpecks, difcernei by means of 
 telefcopes, owe their origin to the fame caufe ; 
 former aftronomers could only reckon 103, 
 Dr. Herfchel has difcovered upwards of 1250 
 of thefe clufters, befides a fpecies which he calls 
 planetary nebulce. But what are all thefe, when 
 compared to thofe that fill the whole expanfe, 
 the boundlefs fields of ether ! Indeed, the im- 
 menfity of the univerfe mufl contain fuch num- 
 bers, as would exceed the utmoft ftretch of the 
 human imagination. For who can fay, how 
 far the univerfe extends, or where are the lim- 
 its of it ? where the Creator flayed " his rap- 
 pid wheeh ;'* or where he " fixed the golden 
 compafles ?** 
 
 Of the Planets, as seen from the Sun. 
 
 Our folar obferver having attained a com- 
 petent knowledge of the fixed flars, will now 
 apply himfelf to confider the planets : thefe, 
 as we have already obferved, he will foon dif- 
 tinguifti, by their motion, from the fixed 
 ftars ; the ftars always remaining in their 
 places, but the planets will be feen paffing by 
 them with unequal velocities. Thus on ob- 
 ferving the earth, for inftance, he will find it 
 moving among the fixed ftars, and approach- 
 ing nearer and nearer to the more eaftern 
 ones ; in a year's time it will complete it's 
 revolution, and return to the fame place again. 
 
 12 
 
ASTRONOMICAL ESSAYS. 13 
 
 He will find /even of thefe bodies revolving 
 round the fun, to each of which he will affian 
 a name, calhng the fwifteft IV'ercury^ denomi- 
 nating the others in order, according to their 
 velocities, as Veniu^ then the Earthy and after- 
 wards Marj, Jupiter, Saturn, and the Georgium 
 Sidus. 
 
 Proceeding with attention in thus explor- 
 ing and examining ths heavens, he will perceive 
 that the earth is always accompanied by a fmall 
 ftar, Jupiter by four, Saturn by feven, and the 
 Georgium Sidus by two : thefe fometimes pre- 
 cede, at others follow ; now pafs before, and 
 then behind the pUnets they refpedlively attend. 
 Thefe fmall bodies he will call fecondary planets, 
 fatellites, or moons. 
 
 The obferver, by remarking the exad time 
 when each planet pafles over fome fixed ftar, and 
 the time they employ from their fetting out, to 
 their return to the fame ftar again, will find the 
 times elapfing between each fuccefTive return of 
 the fame planet to the fame ftar, to be equal j 
 and he would fay, that the feveral planets defcribe 
 circles in ditFerent periods ; but that each of 
 them always completes it's own circle in the fame 
 fpace of time. 
 
 He will further obferve, that there are cer- 
 tain bodies, which at their firft appearance are 
 fmall, obfcure, ill defined, and that move very 
 flow, but which afterwards increafe ia magni- 
 E 13 
 
14 ASTRONOMICAL ESSAYS. 
 
 tude, light, and velocity, until they arrive at a 
 certain fize, when they lofe thefe properties, and 
 diminifli in the fame manner as they before aug- 
 mented, and at laft difappear. To thefe bodies, 
 which he will find in all the regions of the 
 heavens, moving in different directions, he will 
 give the name of comets* 
 
 Of the Paths of the Planetf. 
 
 Our obferver will take notice, that the 
 planets run fuccelTively through thofe con- 
 flellations which he has denominated, Aries, 
 Taurus, Ge?nim, Cancer, Leo, Virgo, Libra, 
 Scorpio, Sagittarius, Capricornus, Aquarius, Pif- 
 ces ; and that they never move out of a certain 
 fpace, or zone, of the heavens, which we will 
 call the zodiac. 
 
 He will find, by proceeding in his obferva- 
 tion, that the orbits of the planets are not all 
 in the fame plane, but that they crofs each 
 other in different parts of the heavens j fo 
 that if he makes the orbit of any one planet a 
 ftandard, and confiders it as having no obli- 
 quity, he would judge the paths of all the reft 
 to be inclined to it ; each planet having one 
 half of it's path on one fide, and the other 
 half on the oppofite fide of the flandard path, 
 or orbit. Aflronomers generally affume the 
 earth's orbit, as the flandard from which to 
 
 14 
 
ASTRONOMICAL ESSAYS. I5 
 
 compute the inclination of the others, and cal 
 it the ecliptic. The points, where the orbits 
 interfedt each other, are called the nodes. 
 
 This inclination of the orbits to each other, 
 may be rendered more familiar to the imagina- 
 tion,* by taking as many hoops as there are 
 planets, with a wire thruft: through each, and 
 thereby joined to that hoop which reprefents the 
 ecliptic ; the other hoops may be then fet more 
 or lefs obliquely to the reprefentativc of the 
 ecliptic. 
 
 The feveral orbits do not crofs or interfeft 
 the ecliptic in the fame point, or at the fame 
 angles ; but their nodes, or interfedions, are 
 at different parts of the ecliptic. 
 
 It fhould, however, be obferved here, that 
 in fpeaking of the orbits of the planets, nothing 
 more is meant by this term, than the paths they 
 pafs through in the open fpace in which they 
 move, and in which they are retained by a ce- 
 leftial but continuous mechanifm. 
 
 Of the IVIoTioN OF THE Planets round 
 THEIR Axis. 
 
 By attentively confidering, with a telefcope, 
 the furface of the primary planets, our folar ob- 
 ferver will find, that fome parts, or fpots, are 
 more obfcure than others. By continued obfer- 
 vation he will find, that thefe fpots change their 
 
 * Dr. Watts's Aftronomy. 
 
iS ASTRONOMICAL ESSAYS. 
 
 places, and move from one fide of the planet to 
 the other ; then difappear for a certain fpace 
 of time ; after which, they again, for a while, 
 become vifible on the fide where they were firft: 
 feen, always continuing the fame motion nearly 
 in an uniform manner. The diftance between 
 the fpots grows wider as they advance from the 
 edge towards the middle of the planet, and then 
 grows narrow again as they pafs from the mid- 
 dle to the other edge. '1 he time they are feen 
 on the planet's difk, is fomewhat lets than the 
 time of their difappearance. 
 
 From thefe circumftances he will conclude, 
 firft, that thefe fpots adhere to the body of the 
 planet; and fecondly, that each planet is a globe 
 turning on it's axis, and has confequentiy two 
 motions, one whereby it is moved round it's 
 axis in a fhort time, the other by which it re- 
 volves round the fun. Thefe motions may be 
 eafily conceived, by only imagining a fmall ball 
 to roll round a large fphere. The firft of thefe 
 motions, or that of a planet round it's axis, is 
 called the diurnal motion ; and the fecond, or 
 it's revolution round the fun, is called the annual 
 motion. 
 
 The tutor may in fome meafure realize to 
 his pupil the foregoing heliocentric pheno- 
 mena, by plate I. fig. i, of the folar fyftem ; 
 or ftill much better, by means of a planeta- 
 rium ; for by fuppofing himfelf on the brafs ball 
 which reprefents the fun, he will fee that all 
 
 i6 
 
ASTRONOMICAL ESSAYS. I7 
 
 the planets move round him in beautiful and 
 harmonious order. If on account of their dif- 
 tance he refers their motions to the fixed ftars, 
 he will fee how readily the periods of their revo- 
 lutions may be obtained, by obfervlng the time 
 that elapfes between their fctting out from any 
 fixed point, or ftar, and their returning to the 
 fame again. He will alfo fee, that if the paths 
 of the planets were in one plane, as in the in- 
 ftrument, they would all be transferred to one 
 circle in the heavens. 
 
 When he underftands thefe particulars, the 
 tutor may proceed to fhew him that the mo- 
 tions, which are fo regular when viewed from the 
 fun, become intricate and perplexed when view- 
 ed from the earth ; and infer from thence that 
 whenever "we examine the works of the Dei^y 
 at a proper point of diftance, fo as to take iij 
 the whole of his defign, we fee nothing but 
 uniformity, beauty, and precifion." Thus the 
 heavens prefent us with a plan, which, though 
 inexpreflibly magnificent, is yet regular beyond 
 the power of invention ; and the volume of the 
 univerfe will be found to be as perfedl as it*6 
 Author, containing mines of truth for ever 
 opening, fountains of good for ever flowing, an 
 endlefs fucceffion of bright, and ftill brighter 
 exhibitions of the glorious Godhead, anfwering 
 to the nature and idea of infinite fulnefs and 
 perfedion. 
 
 ^7 
 
( »8) 
 
 ESSAY I. 
 
 PART II. 
 
 Of the Phenomena of the Heavens, as 
 
 SEEN FROM THE EarTH. 
 
 THE various appearances of the celeftial 
 bodies, as feen from the earth, are the 
 /ads which lay the foundation of all aftrono- 
 mical knowledge. To account for, and ex- 
 plain them, is it*s principal bufmefs : a true 
 idea of thefe phenomena is therefore a necef- 
 fary ftep to a knowledge of aftronomy. Let 
 XLS therefore fuppofe ourfelves in the open air, 
 contemplating the appearances that occur in 
 the heavens. 
 
 Of the apparent Motion of the Sun. 
 
 The firfl: and moft obvious phenomenon is 
 the daily rifmg of the fun in the eaft, and his 
 fetting in the weft ; after which the moon and 
 itars appear, ftill keeping the fame wefterly 
 
 i8 
 
ASTRONOMICAL ESSAYS. I9 
 
 courfe, till we lofe fight of them altogether. 
 Thefe appearances give rife to what is called 
 the apparent diurnal motion of the heavens. 
 
 This cannot be long obferved, before we muft 
 alfo perceive, that ihtfun does not always rife 
 exa£tly at the fame point of the heavens, his mo- 
 tions deviating confiderably at particular feafons 
 from thofe they perform at other times. Some- 
 times we perceive him very high in the heavens, 
 as if he would come diredly over our heads ; at 
 other times he is almoft funk in the fouthern part 
 of the heavens. If we commence our obferva- 
 tions of the fun, for inftance, in the beginning 
 of March, we fhall find him appear to rife more 
 to the northward every day, to continue longer 
 above the horizon, to be more vertical, or high- 
 er, at mid-day ; this continues till towards the 
 end of June, when he moves backward in the 
 fame manner, and continues this retrograde mo- 
 tion till near the end of December, when he be- 
 gins to move forwards, and fo on. 
 
 It is this change in the fun*s place, that occa- 
 fions him to rife and fet in different parts of the 
 horizon, at different times of the year. It is 
 from hence that his height is fo much greater in 
 fummer, than in winter. In a word, the change 
 of the fun's place in the heavens is the caufe of 
 the different length in the days and nights, and 
 the vicillitudes of the feafons. 
 
 As the knowlege of the fun's apparent mo- 
 19 
 
20 ASTRONOMICAL ESSAYS^, 
 
 tion is of great importance, and a proper con- 
 ception of it abfolutely neceflary, in order to 
 form a true idea of the phenomena of the hea- 
 vens, the reader will excufe my dwelling fome- 
 thing longer upon ir. If on an evening we take 
 notice of fome fixed ftar near the place where 
 the fun fets, and obferve it for feveral fucceflive 
 evenings, w^ fliiU fiad that it approaches the 
 fun from day to day, till at lafl; it will difappear, 
 being effaced by his light, though but a fe^v days 
 before it was at a fufficient diltance from him. 
 That it is the fun which approaches the ftars, 
 and not the flars the fun, is plain, for this rea- 
 fon; the Itars always rife and fet every day at the 
 fame points of the horizon, oppofite to the fame 
 terreifrial objeds, and are always at the fame dif- 
 tance from each other j whereas the fun is con- 
 tinually changing both the place of it*s rifing 
 and fetting, and it's diftance from the ftars. 
 
 The fun advances nearly one degree every- 
 day, moving from weft to eaft ; fo that in ^6^ 
 days we fee the fame ftar near the fetting fun, 
 as was obferved to be near him on the fame day 
 in the preceding year. In other words, the 
 fun has returned to the place from whence he 
 fet out, or made what we call his annual revolu- 
 tion. 
 
 We cannot indeed obferve the fun's motion 
 among the fixed ftars, becaufe he darkens the 
 heavens by his fplendor, and effaces the feeble 
 
 20 
 
ASTRONOMICAL ESSAYS. 29 
 
 from manhood to old age, will find him ever 
 bufy in endeavouring to find fome reality, to 
 fupply the place of the falfe appearances, by 
 which he has hitherto been deceived. 
 
 It is the bufmefs of the prefent part of this 
 eflay to corred the errors arifing from appear- 
 ances, and to point out truth by a brief detail 
 of the principal parts of the Copernican fyf- 
 tem, which is now univerfally received, be- 
 caufe it rationally accounts for, and accords 
 with, the phenomena of the heavens. 
 
 " At the appointed time, when it pleafed 
 the fupreme Difpenfer of every good gift to 
 reftore light to a bewildered world, and more 
 particularly to manifefl his wifdom in the 
 fimplicity, as well as in the grandeur of his 
 works, he opened the glorious fcene with a 
 revival of found aftronomy ;"* and raifed up 
 Copernicus to difpel the darknefs in which it 
 was then involved. 
 
 The Copernican fyjiem confifts of the fun, 
 feven primary, fourteen fecondary planets, and 
 the comets. 
 
 The feven planets. Mercury, Venus, the 
 Earth, Mars, Jupiter, Saturn, and the Geor- 
 gium Sidus, move round the fan, fin orbits 
 included one within the other, and in the 
 
 * Pringle's Six Difcourfes to the Royal Society. 
 
 \ The fun is not abfolutely at re l, bein^ fubjeft to a 
 fmall degree of motion, which is confidered in larger works 
 on aftronomy. 
 
 G 20 
 
30 ASTRONOMICAL ESSAYS. 
 
 order here ufed in mentioning their names, 
 Mercury being that which is ncareft the fun. 
 
 The feven, which revolve round the fun as 
 their center, are called primary planets. 
 
 The fourteen planets, which revolve round 
 the primary ones as a center, and are at the 
 fame time carried round the fun with them, are 
 called fecondjvy planets^ moons ^ or fatellites. 
 
 The Georgium Sidus is attended by two 
 moon's, Saturn by feven, Jupiter by four, and 
 the Earth by one ; all of thefe, excepting the 
 lad, are invifible to the naked eye, on account 
 of the fmallnefs of their fize, and the greatnefs 
 of their diflance from us. 
 
 Mercury and Venus being within the 
 Earth's orbit, are called inferior planets ; but 
 Mars, Jupiter, Saturn, and the Georgium Si- 
 dus, being without it, are called y^^mor pla- 
 nets. 
 
 The orbits of all the planets are elliptical ; 
 but as the principal phenomena of the Coper- 
 nican fyflem may be fatisfaclorily illuftrated, 
 by confidering them as circular, the latter 
 fuppofition is ufually adopted in giving a gene- 
 ral idea of the difpofition and motion of the 
 heavenly bodies. 
 
 Before we enter into a defcription of the 
 folar f)(lem, it may be neceifary to define what 
 is meant by the axis of a planet ; left the pupil 
 fhould conceive them to turn on fuch material 
 
 30 
 
ASTRONOMICAL ESSAYS. 31 
 
 axes, as are ufed in the machines which are con- 
 trived to reprefent the planetary fyftem. 
 
 The axis of a planet is a line conceived to 
 be drawn through it's center, and about which 
 it is conceived to turn, inthecourfe of it's revo- 
 lution round the fun : the extremities of this 
 line terminate in oppofite points of the furface 
 of the planet, and are called it's poles; that 
 which points towards the northern part of the 
 heaven, is called the «or/^/>o/^/ that which points 
 towards the fouthern, the fouth pole. A ball 
 whirled from the hand into the open air, turns 
 round upon a line within itfelf, while it is mo- 
 ving forward ; fuch a line as this is meant, when 
 we fpeak of the axis of a planet. 
 
 Fig. I, plate I. reprefents the folar fyflem, 
 wherein O denotes the fun ; A B the circle 
 which the neareft planet. Mercury, defcribes in 
 moving round it ; CD that in which Venus 
 moves ; F G the orbit of the earth ; H K that 
 of Mars J I N that of Jupiter ; OP that of 
 Saturn ; and Q^R that of the Georgium Sidus. 
 Beyond this are the ftarry heavens. 
 
 The fun and the planets are fometimes ex- 
 prcffed by marks or characters, inftead of writ- 
 ing their names at length. The charaders are 
 as follow : O the fun, 5 Mercury, 9 Venus, 
 © the Earth, % Mars, 2/ Jupiter, h Saturn, 
 ¥ Georgium Sidus. 
 
32 ASTRONOMICAL ESSAYS. 
 
 Of the Sun. 
 
 The fun is the center of the fyftem, round 
 which the reft of the planets revolve. It is the 
 firft and greateft objtdl of aflronomical kncw- 
 ledge, and is alone enough to itamp a value on 
 the fcience, lo which the ftudy of it belongs. 
 The fun Is the parent of the feafons ; c'ay and 
 night, fummer and winter, are among it'^s fur- 
 prifing efftd?. h\\ the vegetable crtationare 
 the offspring of it's beams ; our own lives are 
 fupported by it's influence. Nature revives, 
 and puts on a new face, when it approaches near- 
 er to us in fpring ; and fmks into a temporary 
 death at his departure from us in the winter. 
 
 Hence the fun was, with propriety, called 
 by the ancients cor cceli, the heart of heaven ; for 
 as the heart is the center of the animal fyftem, 
 fo is the fun the center of our univerfe. As the 
 heart is the fountain of the blood, and the center 
 of heat and motion ; fo is the fun the life and 
 heat of the world, and the firft mover of the 
 mundane fyftem. When the heart ceafes to 
 beat, the circuit of life is at an end ; and if the 
 fun Ihould ceafe to a£t, a total ftagnation would 
 take place throughout the whole frame of na- 
 ture. 
 
 The fun is placed near the center of the orbits 
 of all the planets, and turns round his axis in 
 twenty-five ^ days. His apparent diameter, at 
 a mean diftance from the earth, is about thirty- 
 two minutes, twelve feconds. 
 
 32 
 
ASTRONOMICAL ESSAYS. QQ 
 
 Thofe who are not accuflomed to aftrono- 
 mical calculation, will be furprized at the real 
 magnitude of this luminary ; which, on ac- 
 count of it's diftance from us, appears to the 
 eye not much larger than the moon, which 
 is only an attendant on our earth. When 
 looking at the fun, they are viewing a globe, 
 whofe diameter is 890,000 Englilh miles ; 
 whereas the earth is not more in diameter 
 than 7970 miles : fo that the fun is about 
 1,392,500 times bigger than the earth. Thus 
 as it is the fountain of light and heat to all the 
 planets, fo it alfo far furpafles them in it's 
 bulk. 
 
 If the fun were every where equally bright, 
 his rotation on his axis would not be percep- 
 tible ; but by means of the fpots, which are 
 vifible on his pure and lucid furface, we are 
 enabled todifcover this motion. 
 
 When a fpherical body is near enough to 
 appear of it's true figure, this appearance is 
 owing to the (hading upon the different parts 
 of it's furface : for as a flat circular piece of 
 board, when it is properly fhaded by painting, 
 will look like a fpherical body ; fo a fpherical 
 body appears of it's true fhape, for the fame 
 reafon that the plane board, in the prefent in- 
 flance, appears fpherical. But if the fpherc 
 be at a great distance, this difference of ihad- 
 ing cannot be difcerned by the eye, and con- 
 
 33 
 
34 ASTRONOMICAL ESSAYS. 
 
 fequently the fphere will no longer appear of 
 it*s true fhape ; the fliading is then loft, and it 
 icems like a flat circle. 
 
 It is thus with the fun ; it appears to us 
 like a bright flat circle, which flat circle is termed 
 the furies dijk. By the afliftance of telefcopes 
 dark /pots have been obferved on this difli, 
 and found to have a motion from caft to weft ; 
 their velocity is greater when they are at the 
 center, than when they are near the limb. 
 They are feen firft on the eaftern extremity, 
 by degrees they come forwards towards the 
 middle, and fo pafs on till they reach the wef- 
 tern edge ; ihey then difappear ; and after they 
 have lain hid about the fame time that they 
 continued vifible, they appear again as at 
 firft. By this motion we difcover not only the 
 time the fun employs in turning round his axis, 
 ■^but alfo the inclination of his axis to the plane 
 of the ecliptic* 
 
 The page of hiftory informs us, that there 
 have been periods, when the fun has wanted 
 
 * Tlie young obferver may view the fpots of the fun with 
 a refracting telefcope of two or three feet, or a reflefting 
 one of 12 inches, i8 inches, or two feet, taking care to 
 guard the eye with a dark glafs, to take off the glaring light : 
 or the image or picture of the fun, with his fpots, may be 
 thrown into a dark room, through a telefcope, and received 
 upon a piece of paper placed nearer or further from the glafs 
 at pleafure. 
 
 34 
 
ASTRONOMICAL ESSAYS. Q^ 
 
 of it's accuftomed brightnefs, fhone with a dim 
 and obfcure light for the fpace of a whole year. 
 This obfcurity has been fuppofed to arife from 
 his furface being at thofe times covered with 
 fpots. Spots have been feen that were much 
 larger than the earth. 
 
 The fun is fuppofed to have an atmo- 
 fphere, which occafions that appearance which 
 is termed the zodiacal light. This light is 
 feen at fome feafons of the year, either a little 
 after fun-fet, or a little before fun-rife. It is 
 faintly bright, and of a whitifh colour, refem- 
 bling the milky way. In the morning it" be- 
 comes brighter and larger, as it rifes above 
 the horizon, till the approach of day, which 
 diminifhes it's fplendor, and renders it at lafl 
 invifible. It's figure is that of a flat or lentic- 
 ular fpheroid, feen in profile. The diredion of 
 it's longer axis coincides with the plane of the 
 fun's equator. But it's length is fubjed to great 
 variation, fo that the diflance of it's fummit 
 from the fun, varies from 45 to 1 20 degrees. It 
 is feen to the bed advantage about the folftices. 
 It was firft defcribed and named by Caflini, in 
 1683 ; it was noticed by Mr. Childrey, about 
 the year 1650. 
 
 ZS 
 
36 ASTRONOMICAL ESSAYS. 
 
 Of the iNFERioEi Planets, Mercury and 
 Venus. 
 
 Of Mercury. 5 
 
 Of all the planets, Mercury is the leart: ; at 
 the fame time, it is that which is neareft the fun. 
 It is from his proximity to this globe of light, 
 that he is fo feldom within the fphere of our ob- 
 fervation, being loft in the fplendor of the folar 
 brightnefs ; yet it emits a very bright white 
 light. It is oftener feen in thofe parts of the 
 world, which are more fouthward than that 
 which we inhabit ; and oftener to us than to 
 thofe who live nearer the north pole ; for the 
 more oblique the fphere is, the lefs is the planet's 
 elevation above the horizon. 
 
 Mercury never removes but a few degrees 
 from the fun. The meafure of a planet's 
 feparation, or diftance, from the fun, is called 
 it's elongation. His greateft elongation is 
 little more than 28 degrees, or about as far as 
 the moon appears to be from the fun, the 
 fecond day after new moon. In fome of it's 
 revolutions, the elongation is not more than 18 
 degrees. 
 
 Mercury is computed to be '^'j millions 
 of miles from the fun, and to revolve round 
 him in 87 days, 23 hours, and nearly 16 mi- 
 nutes, which is the meafure of it's year, about 
 one-fourth of our's. As from the nearnefs of 
 
 36 
 
ASTRONOMICAL ESSAYS. 37 
 
 this planet to the fun, we neither know the 
 time it revolves round it*s axis, nor the incli- 
 nation of that axis to the plane of it's orbit, 
 we are neceflfarily ignorant of the length of it's 
 day and night, or the variety of feafons it may 
 be liable to. Mercury is 3000 miles in dia- 
 meter. Large as Mercury, when thus con- 
 fiJered, appears to be, it is but an atom, when 
 compared With Jupiter, whofe diameter is 
 90,000 miles. It's apparent diameter, at a 
 mean diftancefrom the earth, is 20 feconds. 
 
 Mercury is fuppofed to move at the rate 
 of iio,53o miles per hour. The fun is above 
 26,ODO,ooo times as big: as Mercury ; fo that 
 it would appear to the inhabitants of Mercury 
 nearly three times larger than it does to us ; 
 and it's dilk, or face, about feven times the 
 (ize we fee it. As the other five planets are 
 above Mercury, their phenomena will be 
 nearly the fame to it as to us. Venus and the 
 earth, when in oppofition to the fun, will fliine 
 with full orbs, and afford a brilliant appearance 
 to the Mercurian fpedator. 
 
 Mercury, like the moon, changes it's 
 phafes, according to it's feveral pofitions with 
 refpeft to the fun and earth. He never ap- 
 pears quite lound or full to us, becaufe his 
 enlightened fide is never turned diredly to- 
 wards u^, except when he is fo near the fun, 
 as to become invifible. The times for making 
 H 37 
 
38 ASTRONOMICAL ESSAYS. 
 
 the mod favourable obfervations on this pla- 
 net, are, when it paiTes before the fun, and is 
 feen traverfing his diik, in the form of a black 
 fpot. This paiTage of a planet over the face 
 of the fun, is called a tranfit. It happens in 
 it*s lower conjundion, at a particular fituation 
 of the nodes ; which leads us to mention their 
 place in the ecliptic. 
 
 The angle formed by the inclination of 
 the orbit of Mercury with the plane of the 
 ecliptic, is 6" 59' ; the node from which Mer« 
 cury afcends northward, above the plane of 
 the ecliptic, is 16° 1' 30''' ; in Taurus, the op- 
 pofite one, 14" 1' 24''; in Sagittarius, it's 
 nodes move forward about c^o'^ per year. 
 
 If Mercury, at his inferior conjundion, 
 comes to either of his nodes about thefe times, 
 he will appear to iranfit over the di(k of the 
 lun. But in all other parts of his orbit his 
 conjundions are invifible, becaufe he either 
 goes above or below the fun. 
 
 Of Venus. 9 
 
 Venus is the brighteft and largeft, to appear- 
 ance, of all the planets, diftinguifhed from them 
 all by a fuperiority of luftre ; her light is of a 
 white colour, and fo confiderable, that in a duf- 
 ky place (he projeds a fenfible fliade. 
 
 38 
 
ASTRONOMICAL ESSAYS. 39 
 
 The diameter of Venus is 7,699 miles ; her 
 diftance from the fun is 69,500,000 miles ; (he 
 goes round the fun in 224. days, 16 hours, 49 
 minutes, moving at the rale of 80,995 mi'^s 
 per hour. Her motion round har axis has been 
 fixed by fome at 23h. 22m. ; by others at above 
 24 days. She, like Mercury, conftantly at- 
 tends the fun, never departing from him above 
 47 or 48 degrees. Like Mercury, (lie is never 
 feen at midnight , or in oppofition to the Jun^ be- 
 ing vifible only for three or four hours in the 
 morning, or evening, according as (he is before 
 or after the fun. 
 
 One would not imagine that this planet, 
 which appears fo much fuperior to Saturn in 
 the heavens, is fo inconfiderable when com- 
 pared to it ; for the diameter of Saturn is 
 nearly 78,000 miles ; while, on the other hand, 
 one would fcarce imagine that Venus, which 
 appears but as a lucid fpangle in the heavens, 
 was fo large a globe as (lie truly is, her diameter 
 being 7,699 miles. It is the dijlance which 
 produces thefe effefts ; which gives and takes 
 away the magnitude of things. Her apparent 
 fize varies with her diftance ; at fome feafons 
 (he appears nearly 32 times larger than at 
 others. 
 
 When this planet is in that part of it's or- 
 bit which is weft of the fun, that is, from 
 her inferior to her fuperior conjundion, fhe 
 
 39 
 
40 ASTRONOMICAL ESSAYS. 
 
 rifes before him in the morning, and is called 
 fbofphorus^ or lucifer, or the mornhig Jiar, 
 When fhe appears eall: of the fun, that is, from 
 her fuperior to her inferior conjundtion, (he fets 
 in the evening after him; oi, in other words, 
 {liines in the evening after he fets, and is cal- 
 led he/perns, or vefper, or the evening Jiar, 
 
 The inhabitants of Venus fee the planet 
 Mercury always accompanying the fun ; and 
 he is to them, by turns, an evening or a morn- 
 ing (lar, as Venus is to us. To the fame in- 
 habitants, the fun will appear almoft twice as 
 large as he does to us. 
 
 Venus, when viewed through a telefcope, 
 is feldom feen to fhine with a full face ; but 
 has phafcs, jull like the moon, from the fine 
 thin crefcent to the enlightened hemifphere. 
 Her illuminated part is conftantly turned to- 
 wards the fun ; hence it's horns are turned to- 
 wards the eaft when it is a morning ftar, and 
 towards the weft when it it an evening ftar. 
 Sofue aftronomers have thought they perceived 
 a fatellite moving round Venus; but as fuc- 
 ceeding obfervers have not been able to verify 
 their obfervations, they are fuppofed to have 
 originated in error. In obferving the tranfit 
 of Venus, Mr. Dunn, and other gentlemen, 
 faw a penumbra which took place about live 
 feconds before the contad, precceding the 
 cgrefs of the planet ; and from thence they 
 
 40 , 
 
ASTRONOMICAL ESSAYS. 4I 
 
 concluded, that it had an atmofphere of about 
 50 geographical miles in height. 
 
 We are told, that, when Copernicus firfl; 
 publilhed his account of the folar fyftem, it 
 was objeded to him that it could not be true, 
 becaufe, if it was, the inferior planets muit 
 have different phafesy according to their dif- 
 ferent fituation with refpedl to the fun and 
 earth ; whereas they always appear round to 
 us. The anfwer faid to be made by him, is, 
 that they appear round to the eye by reafon of 
 their diflance ; but if we could have a nearer, 
 or more diftind view of them, we jhould fee in 
 them the fame phafes we do in the ?Jwon. The 
 invention of telefcopes is faid to have verified 
 this prediction of Copernicus. But it is nei- 
 ther probable, that a defender of the Ptole- 
 maic fyftem fliould make fuch an objeftioa, 
 or Copernicus fuch an anfwer ; fmce in the 
 Ptolemaic, as well as in the Copernican fyf- 
 tem, the fliape of thefe planets ought to 
 change, juft as the moon does ; confequently, 
 the mer£ change of Jhape in the inferior planets 
 is an argument, which, in the common way 
 of urging it, proves nothing at all as to the 
 truth or falftiood of the Copernican fyftem. 
 If, befides the changes of fliape made in the 
 inferior planets, we confider the fituation of 
 the planets with refped to the fun, when 
 thefe changes happen ; this, indeed, will (hew 
 
 41 
 
42 ASTRONOMICAL ESSAYS. 
 
 US, that the Ptolemaic fyftem is falfe,* as will be 
 feen in a fubfeqiient part of thefe effays. 
 
 Venus is fometimes feen palTing over the 
 difk of the fun, as a round dark fpot. Thefe 
 appearances, which are called tranfits, happen 
 very feldom ; though there have been two with- 
 in thefe few years, the one in June 1761, the 
 other in June 1769; the next will be in the 
 year 1874. 
 
 Of the Earth, e 
 
 The next planet that comes before us is 
 the earth that we inhabit ; fmall as it really is 
 when compared to fome of the other planets, 
 it is to us of'the highefl importance : we wifh 
 only to attain knowledge of others, that we 
 may find out their relation to this, and from 
 thence learn our connexion with the univerfe 
 at large. But when viewed with an eye to 
 eternity J it's value to us is heightened in a 
 manner that exceeds expreffion, and furpaffes 
 all the powers of the human mind. He alone 
 can form fome idea of it, who in the regions 
 of celeflial blifs is become a partaker of the 
 length and breadth, the depth and height, of 
 divine love. 
 
 * Rutherford's Syftem of Natural Philofophy, vol. 2^ 
 p. 78r. 
 
 42 
 
ASTRONOMICAL ESSAYS. 43 
 
 The orbit of the earth is placed between 
 thofe of Venus and Mars. The diameter of 
 the earth is 7970 miles ; it's diftance from the 
 fun is 96 millions of miles, and goes round him 
 in a year, or ;^65 days, 6 hours, 9 minutes, mov- 
 ing at the rate of 68,856 miles per hour. It's 
 apparent diameter, as feen from the fun, is about 
 21 feconds. 
 
 It turns round it's axis, from wf/^ to eajl, in 
 24 hours, which occafions the apparent diur- 
 nal motion of the fun, and all the heavenly bod- 
 ies round it, from (f///? to wejl^ in the fame time ; 
 it is, of courfe, the caufe of their rifmg and 
 fetting, of day and night. 
 
 The axis of the earth is inclined 23^ degrees 
 to the plane of it's orbit, and keeps in a direc- 
 tion parallel to itfelf, throughout it's annual 
 courfe, which caufes the returns of fpring and 
 fummer, autumn and winter. Thus his diurnal 
 motion gives us the grateful viciUlrude of night 
 and day, and his annual moixQn the regular fuc- 
 ceflions of feafons. 
 
 Of THE Moon, c 
 
 Next to the fun, the moon is the moil 
 fplendid aiid fhining globe in the heavens, the 
 fatellite, or infeparable companion of the 
 earth. By difTipating, in fome meafure, the 
 darknefs and horrors of the night ; fubdividing 
 
 43 
 
44 ASTRONOMICAL ESSAYS. 
 
 the year into months ; and regulating the flux 
 and reflux of the Tea ; flie not only becomes a 
 pleafing, but a welcome objeft ; an objeft af- 
 fording much for fpecuhition to the contempla- 
 tive mind, of real ufe to the navigator, the trav- 
 eller, and the hufliandman. i he Hebrews, the 
 Greeks, the Romans, and, in general, all the 
 ancients, ufed to aflemble at the time of new 
 moon, to difcharge the duties of piety and grat- 
 itude for ic's manifold ufes. 
 
 That the moon appears fo much larger than 
 the other planets, is owing to her vicinity to us ; 
 for to a fpeftator in the fun {he would be fcarce- 
 ly vifible, without the afli tance of a telefcope- 
 Herdiflance is but fmali from us, when compa- 
 red with that of the ocher heavenly bodies ; for 
 among thefe, the leal abfolute difliance, when 
 put down in numbers, will appear great, and the 
 fmalleil magnitude immenfe. 
 
 The moon is 2161 miles in diameter ; her 
 bulk is about -V of the earth's ; her difl-ance 
 from the center of the earth 240,000 miles ; 
 file goes round her orbit in 27 days, 7 hours, 
 43 minutes, moving at the rate of 2299 irii'es 
 per hour. The, time in going round the earth, 
 reckoning from change to change, is 29 days, 
 12 hours, 44 minutes. Her apparent diameter 
 at a mean difl:ance from the earth is 31' 16^"^ ; 
 but as viewed from the fun, at a mean diftance 
 about G". 
 
 44 
 
ASTORNOMICAL ESSAYS. 45 
 
 Her orbit is inclined to the ecliptic, in an 
 angle of 5 degrees, 18 minutes, cutting it in 
 two points, which are diametrically oppofite 
 to each other ; thefe points are called her nodes. 
 Her nodes have a mntion ivejiward, or contrary 
 to the order of the fiiins, making a complete re- 
 volution in about 19 years ; in which time, each 
 node returns to tha!: point of the ecliptic whence 
 it before receded. 
 
 If the moon were a body poflefling native 
 light, we fliould not perceive any diverfity of 
 appearance ; but as (he fhines entirely by light 
 received from the fun, and reflecled by her fur- 
 face, it follows, that, according to the fituatioa 
 of the beholder with refpeft to the illuminated 
 part, he will fee more or lefs of htr reflecled 
 beams, for only one half of a globe can be enlight- 
 ened at once. 
 
 Hence, while fhe is making her revolution 
 round the heavens, fhe undergoes great changes 
 in her appearance. She is fometimes on our 
 meridian at midnight, and therefore in that part 
 of the heavens which is oppofite to the fun ; in 
 this fituation (he appears as a complete circle, 
 and it is faid to be full moon. As fhe moves 
 eallward, flie becomes deficient on the weft 
 fide, and in about y\ days comes to the meri- 
 dian, at about fix in the morning, having the 
 appearance of a femicircle, with the convex 
 fide turned towards the fun ; in this ftate, her 
 
 I 45 
 
4^ ASTRONOMICAL ESSAYS. 
 
 appearance is called the half moon. Moving on 
 ftill eaftward, (he becomes more deficient on 
 the weft, and has the form of a crefcent, with 
 the convex fide turned towards the fun ; this 
 crefcent becomes continually more flender, till 
 about fourteen days after the full moon (he is 
 fo near the fun, that (lie cannot be feen, on ac- 
 count of his great fplendor. About four days 
 after this difappearance, file is feen in the even- 
 ing, a little to the eafiward of the fun, in the 
 form of a fine crefcent, with the convex fide 
 turned from the fun ; moving fi:ill to the eafl:- 
 ward, the crefcent becomes more full ; and when 
 the moon comes to the meridian, about fix in 
 the evening, flie has again the appearance of a 
 bright femicircle ; advancing ftill to the eaftward 
 file becomes fuller on the eafl: fide ; at laft, in 
 about 29]- days, flie is again oppofite to the fun, 
 and again full. 
 
 It frequently happens, that the mcon is ecHp- 
 fed when at the full ; and that the fan is eclipfecl 
 fome time between the difappearance of the moon 
 in the morning on the weft fide of the fun, and 
 her appearance in the evening on the eaft fide of 
 the fun. The nature of thefe phenomena will 
 be more fully confidered, when we come to treat 
 particularly of eclipfes . 
 
 In every revolution of the moon about the 
 earth, flie turns once round upon her axis, and 
 therefore always prefents the fame face to our 
 
 46 
 
ASTRONOMICAL ESSAYS. 47 
 
 view ; and as, during her courfe round the 
 earth, the fun enh'ghtens fuccefTively every part 
 of her globe only once, confequently (he has 
 but one day in all that time, and her day and 
 night together are as long as our lunar month. 
 As we fee only one fide of the moon, we are 
 therefore invifible to the inhabitants on the 
 oppofite fide, without they take a journey to 
 that fide which is next to us, for which pur- 
 pofe fome of them mufl: travel more than 1500 
 miles. 
 
 As the moon illuminates the earth by a light 
 reflected from the fun, (lie is reciprocally en- 
 lightened, but in a much greater degree, by the 
 earth ; for the furface is above thirteen times 
 greater than that of the moon ; and therefore, 
 fuppofing their, power of refle>^"ling light to be 
 equal, the earth will reflect thirteen times more 
 light on the moon than fhe receives from it. 
 When it is what we call new moon, we fhall 
 appear as a full moon to the Lunnrians ; as it 
 increafes in light to us, our's will decreafe to 
 them : in a word, our earth will exhibit to them 
 the fame phafes as fhe does to us. 
 
 We have already obferved, that from one 
 half of the moon the earth is never feen ; from 
 the middle of the other half, it is always feen 
 over head, turning round almofl thirty times 
 as quick as the moon does. To her inhabi- 
 
 47 
 
48 ASTRONOMICAL ESSAYS. 
 
 tants, the earth feems to be the largefl body 
 in the univerfe, about thirteen times as large 
 to them, as fhe does to us. As the earth turns 
 round it's axis, the feveral continents and 
 iflands appear to the Lunarians as fo many 
 fpots, of different forms ; by thefe fpots, they 
 may determine the time of the earth's diurnal 
 motion j by thefe fpots, they may, perhaps, 
 meafure their time, — they cannot have a better 
 dial. 
 
 Of the superior Planets. 
 
 Mars, 'Jupiter, Saturn, and the Georgium 
 Sidus, are called fuperior planets, becaufe they 
 are higher in the fyftem, or farther from the 
 center of it, than the earth is. 
 
 They exhibit feveral phenomena, which are 
 very different from thofe of Mercury and Venus ; 
 among other things, they come to our meridian 
 both at noon and midnight, and are never feen 
 croffmg the fun's dilk. 
 
 Of Mars. S 
 
 Mars is the leaft bright and elegant of all 
 the planets ; it's orbit lies between that of the 
 earth and Jupiter, but very diftant from both. 
 He appears of a dufky reddilli hue ; from the 
 dullnefs of his appearance, many have con- 
 
 48 
 
ASTRONOMICAL ESSAYS. 49 
 
 jedured that he is encoinpafled with a thick 
 cloudy atmc/phere ; his light is not near fo bright 
 as that of Venus, though he is fometimes near- 
 ly equal to her in fize. 
 
 Mars, which appears fo inconfiderable in 
 the heavens, is 5,309 miles in diameter. It's 
 dillance from the fun is 146.000,000 mile«. 
 It goe^ round the fun in one year, 321 days, 23 
 hours, moving at the rate of 55,287 miles per 
 hour. It revolves round it's axis in about 24 
 hours, 40 minutes. I'o an inhabitant in Mars, 
 the fun would appear one-third lefs in diameter 
 than it does to us. It's apparent diameter, as 
 viewed at a mean diflance from the eanh, is 
 30 feconds. 
 
 Mars, when in oppofition to the fun, is five 
 times nearer to us than when in conjunftion. 
 This has a very vifible tfitdl on the appearance 
 of the planet, caufmg him to appear much lar- 
 ger at fome periods than at others. 
 
 The analogy between Mars and the earth is 
 by far the greatell in the whole folar fydem ; 
 their diurnal motion is nearly the fame ; the 
 obliquities of their refpedive ecliptics not very 
 dilierent. Of all the fuperior planets, that of 
 Mars is by far the nearefl: like the earth : nor 
 will the Martial year appear fo diffimilar to 
 our's, when we compare it with the long dura- 
 tion of the years of Jupiter, Saturn, and the 
 Georgium Sidus. It probably has a con- 
 
 49 
 
50 ASTRONOMICAL ESSAYS. 
 
 fiderable atmofphere ; for befides the permanent 
 fpots on it's fur face, Dr. Herfchel has often per- 
 ceived occafional changes of partial bright belt*, 
 and alfo once a darkifli one in a pretty high lat- 
 titude ; alterations which we can attribute to no 
 other caufe than the variable difpofition of 
 clouds and vapours floating in the atmofphere of 
 the planet. 
 
 A fpedator in Mars will rarely, if ever, fee 
 Mercury, except when he fees it paffing over the 
 fun's difk. Venus will appear to him at about 
 the fame diftance from the fun, as Mercury ap- 
 pears to us. The earth will appear about the 
 fize of Venus, and never above 48 degrees from 
 the fun ; and will be, by turns, a morning and 
 evening flar to the inhabitants of Mars. It ap- 
 pears, from the mofl accurate obfervations, that 
 Mars is a fpheroid, or flatted fphere, the equa- 
 torial diameter to the polar being in the pro- 
 portion of about 131 to 127 ; and there is rea- 
 fon to fuppofe that all the planets are of this 
 figure. 
 
 Of Jupiter. % 
 
 Jupiter Is fituated fl;ill higher In the fyflem, 
 revolving round the fun, between Mars and 
 Saturn. It is the largeft of all the planets, and 
 eafily diftinguiflied from them by his peculiar 
 magnitude and light. To the naked eye it ap- 
 
 50 
 
ASTRONOMICAL ESSAYS. 5I 
 
 pears almoft as large as Venus, but not altoge- 
 ther fo bright. 
 
 Jupiter revolves round it's axis in 9 hours, 
 56 minutes ; it's revolution in it's orbit to the 
 fame point of the ecliptic is 1 1 years, 314 days, 
 10 hours. The difproportion of Jupiter to 
 the earth, in fize, is very great ; viewing him 
 in the heavens, we confider him as fmall in 
 magnitude; whereas he is in reality 90,228 
 miles in diameter ; his diftance from the fun is 
 494,750,000 miles ; he moves at the rate of 
 rather more than 29,083 miles per hour. It's 
 apparent diameter, as feen at a mean diftance 
 from the earth, is 39''. 
 
 To an eye placed in Jupiter, the fun would 
 not be a fifth part of the fize he appears to us, 
 and his difk be 25 times lefs. Though Jupiter 
 be the largeft of all the planets, yet it's revolu- 
 tion round it's axis is the fwifteft. The polar 
 axis is fhorter than the equatorial one, and his 
 axis perpendicular to the plane of his orbit. 
 
 Jupiter, when in oppofition to the fun, is 
 much nearer the earth, than when he is in con- 
 jundion with him ; at thofe times he appears 
 alfo larger, and more luminous than at other 
 times. 
 
 In Jupiter, the days and nights are of an 
 equal length, each being about five hours long. 
 We have already obferved, that the axis of his 
 diurnal rotation is nearly at right angles to the 
 
 51 
 
^2 ASTROI^JOMICAL ESSAYS. 
 
 plane of his annual one, and confequently there 
 can be fcarce any difierence in the leafons ; and 
 here, as far as we may reafon from analogy, 
 we may difcover the footfteps of wifdom : for 
 if the axis of this planet were inclined by any 
 confiderable number of degrees, jull fo many 
 degrees round each pole would, in their turn, 
 be almoft fix years in darknefs ; and as Jupiter 
 is of fuch an amazing fize, in this cafe immenfe 
 regions of land would be uninhabitable. 
 
 Jupiter is attended by four fatellites, or 
 moons ; thefe are invifible to the naked eye ; 
 but through a telefcope they make a beautiful 
 appearance. As our moon turns round the 
 earth, enlightening the nights, by rcfieding 
 the light fhe receives from the fun j fo thefe 
 alfo enlighten the nights of Jupiter, and move 
 round him in different periods of times, pro- 
 portioned to their feveral diftances ; and as the 
 moon keeps company with the earth in it's an- 
 nual revolution round the fun, fo thefe accom- 
 pany Jupiter in it's courfe round that luminary. 
 
 In fpcaking of the fatellites, we diftinguifh 
 them according to their places ; into the firfl:, 
 the fecond, and fo on ; by the firft, we mean 
 that which is neareft to the planet. 
 
 The outermoft of Jupiter's fatellites will 
 appear almoft as big as the moon does to us ; 
 five times the diameter, and twenty-five times 
 the difK of the fun. The four fatellites mufl 
 
 52 
 
ASTRONOMICAL ESSAYS. 53 
 
 afford a pleafing fpedacle to the inhabitakts 
 of Jupiter ; for fometimes they will rife 
 all together, fometimes be all together on 
 the meridian, ranged one under another, 
 befides frequent eclipfes. Notwiihl^anding the 
 diftance of Jupiter and his fatellites from us, 
 the eclipfes thereof are of confiderable ufe, for 
 afcertaining with accuracy the longitude of 
 places. From the four fatellites the inhabitants 
 of Jupiter will have four different kinds of 
 months, and the number of them in their year 
 not lefs than 4,500. 
 
 An aftronomer in Jupiter will never fee Mer- 
 cury, Venus, the Earth, or Mars ; becaufe, 
 from the immenfe diftance at which ne is placed, 
 they muft appear to accompany the fun, and rife 
 and fet with him ; but then he will have for 
 the objefts of obfervation, his own four moons, 
 Saturn, his ring and fatellites, and probably 
 the Georgium SiJus. 
 
 Of Saturn, k 
 
 Before the difcovery of the Georgium 
 Sidus, Saturn was reckoned the moft remote 
 planet in our fyftem ; he fhines but with a pale 
 feeble light, Ms bright than Jupiter, though 
 lefs ruddy than Mars. The uninformed eye 
 imagines not, whe;i it is dire£led to this little 
 fpeck of light, that it is viewing a large and 
 glorious globe, one of the moft ftupenduous of 
 
 K 53 
 
^4 ASTRONOMICAL tSSAYS. 
 
 the planets, whofe diameter is nearly 78,000 
 miles. Wd need not, however, be furprized 
 at the vad: bulk of Saturn, and it's dilpropor- 
 tion to it's appearance in the heavens ; i^r we 
 are to coniider that all objcfts decreafe in 
 their apparent magnitude, in. proportion to 
 their dillance^ but the diflance of Saturn is 
 immenfe ; that of the earth from the fun is 
 96,000,000 i^iile.s J of Sjaturn, 916,500,000 
 miles. 
 
 The length of a planet's year, or the time 
 of it's revolution round it's orbit, is propor- 
 tioned to it's dillance from the fun. Saturn 
 goes round the fun in 29 years, \6'j days, 
 6 hours, moving at the rate of rather more 
 than 12^1^'^ miles per hour. His apparent 
 diameter at a mean di (lance from the earth 
 is i6^ 
 
 It has not yet been afcertainedwwith cer- 
 tainty by aflronomical obfervation,- whether 
 Saturn revolves or not upon his axis. 'I he 
 fun's difls. will appear ninety times lefs to an 
 inhabitant of Saturn, than it does -to us ; but 
 Dotwlthftanding the fun appears fo fmall to the 
 inhabitants of the regions of Jupiter and Sa- 
 turn, the light that he will afford them f-g 
 much more than would be at firfl: fuppofed : 
 and calculations have been made, from which 
 it is infeired, that the fun will afford 500 
 times as much light to Saturn, as the full moon 
 to us ; and 1600 times as much to Jupiter. 
 
ASTRONOMICAL ESSAYS. 55 
 
 To eyes like our's, unaffifted by inftruments 
 Jupiter and the Georgium Sidus would be the 
 oniy planets Teen from Saturn, to whom Jupiter 
 would fometimes be a morning, fometimes an 
 evening Itar. 
 
 One oH the fird difcoveries of the telefcope, 
 when brought to a tolerable degree of perfec- 
 tion, was, that Saturn did not appear like other 
 planets. Galileo, in 161c, fuppofed it com- 
 pofed of 3 (tars, or globes, a larger in the mid- 
 dle, :ind a fmallsr on each fide ; and he con- 
 tinued his obfcrvaticns till the two lefTer ftars 
 di^iappeared, and tliis planet looked like the 
 others. Further obfervation fliewed that what 
 Galileo took for two (lars, were parts of a ring. 
 'Jhis fingular and curious appendage to the 
 planet Saturn, is a thin, broad, opake ring, 
 encompalfing the body of the planet, without 
 touching it, Hke the horizon of an artificial 
 globe, appearing double when viewed through 
 a good telefcope. The fpace between the ring 
 and the globe of Saturn, is fuppofed to be ra- 
 ther more than the breadth of th^ ring, and the 
 greated diameter of the ring to be in propor- 
 tion to that of the globe, as 7 to 3 ; the plana 
 of the ring is inclined to the plane of the 
 ecliptic, in an angle of 30 , and is about 21,000 
 miles in breadth. It puts on different ap- 
 pearances to us, fometimes being feen qui'e 
 open, at others only as a line upon the equator. 
 
 55 
 
^6 ASTRONOMICAL ESSAYS. 
 
 It is probable, that it will at times cafl: a fhadow 
 over vaft regions of Saturn's body. The ring 
 of Saturn confidered as a broad flat ring of folid 
 matter, fufpended round the body of the planet, 
 and keeping it's place without any connection 
 with the body, is quite different from all other 
 planetary phenomena with which we are acquain- 
 ted. Of the nature of this ring, various and un- 
 certain were the conjeftures of the firft obferv- 
 ers ; though not more perplexed, than thofe 
 of the lateft. Of it's ufe to the inhabitants of 
 Saturn, we are as ignorant as of it's nature : 
 though there are reafons for fuppofmg that it 
 would appear to them as little more than a white 
 or bright-coloured cloud. Some of the pheno- 
 mena of Saturn's ring will be treated of more par- 
 ticularly in another part of this effay. 
 
 Saturn is not only furnifhed with this beau- 
 tiful ring, but it has alfo feven attendant moons. 
 
 Of the Georgium Sidus. ^ 
 
 From the time of Huygens and Caflini, to 
 the difcovery of the Georgium Sidus by Dr. 
 Herfchel, though the intervening fpace was 
 long, though the number of aflronomers vv^as 
 increafed, though alfiduity in obferving was 
 aflifted by accuracy and perfeftion in the in- 
 (Iruments of obfervation, yet no new difcovery 
 was made in tke heavens, the boundaries of 
 
 56 
 
ASTRONOMICAL ESSAYS. C7 
 
 our fyftem were not enlarged. The inquifitive 
 mind naturally enquires, why, when the num- 
 ber of thofe that cultivated the fcience was 
 increafed, when the fcience itfelf was fo much 
 improved, in practical difcoveries it was fo 
 deficient ? A fmall knowledge of the human 
 mind will anfwer the queflion, and obviate the 
 difficulty. The mmd of man has a natural 
 propeniity to indolence ; the ardour of it's pur- 
 fuits, when they are unconneded with felfifh 
 views, are foon abated, fmall difficulties dif- 
 courage,' little inconveniences fatigue it, and 
 reafon foon finds excufes to juflify, and even 
 applaud this weaknefs. In the prefent inftance, 
 the unmanageable length of the telefcopes that 
 were in ufe, and the continual expofure to the 
 cold air of the night, were the difficulties the 
 aftronomer had to encounter with ; and he foon 
 perfuaded himfelf, that the fame effeds would 
 be produced by fliorter telefcopes, with equal 
 magnifying power ; herein was his miftake, and 
 hence the reafon why fo few difcoveries have 
 been made fince the time of Caffini. A fimilar 
 inftance of the retrogradation of fcience occurs 
 in the hiftory of the microfcope, as I have fhewn 
 in my eflays on that inftrument. 
 
 The Georgium Sidus was discovered by 
 Dr. Herfchel, in the year 1781 : for this dif- 
 covery he obtained from the Royal Society the 
 
 S7 
 
53 ASTRONOMICAL ESSAYS. 
 
 honorary recompence of Sir Godfrey Copley's 
 medal. He named the planet in honour of 
 his INLijefly King George III. tiie Patron of 
 fcience, who has taken Dr. Herfchel under his 
 patronage, and granted him an annual falary, 
 / By this munificence he has given fcope to a 
 very uncommon genius, and enabled him to 
 profecute his favourite ftudies with unremitted 
 ardour. 
 
 In fo recent a difcovery of a planet fo dif- 
 tant, many particular-; cannot be expefted. It's 
 year it fuppofed to be more than 80 fiderial 
 years ; it's diameter 34,299 miles ; the inclina- 
 tion of it's orbit 43' 35''''; it's diameter, com- 
 pared to that of the earth, 35431,769 to i ; in 
 bulk it is 8,049,256 times as large as the earth. 
 It's light is of a blueifli white colour, and it's 
 brilliancy between that of the moon and Venus. 
 Though the Georgium Sidus was not known 
 as a planet till the time of Dr. Herfchel, yet 
 there are many reafonS to fuppofe it had been 
 feen before, but had then been confidered as a 
 fixed ftar. Dr. Herfchel's attention was firft 
 engaged by the fteadinefs of it's light ; this in- 
 duced him to apply higher magnifying powers 
 to his telefcope, which increafed the diameter 
 of it : in two days he obferved that it's place 
 was changed; he then concluded it was a 
 com=;t ; but in a little time he, with others, de- 
 
 58 
 
ASTRONOMICAL ESSAYS. 59 
 
 termined that it was a planet, from it's vicinity 
 to the ecliptic, the direftion of it's motion, 
 being ilationary in the lime, and in fuch cir- 
 cumftances as correfpond with fimilar appear- 
 ances in other planets. 
 
 With a telefcope, which magnifies about 
 300 times, it appears to have a very well-de- 
 fined vifible diflv ; but with inftrumenis of a 
 fmaller power it can hardly be diftinguifiied 
 from a fixed ftar between the fixth and fevenih 
 magnitude. When the moon is abfent, it may 
 alio be feen by the naked eye. 
 
 Dr. Herfchel has frnce difcovered that it is 
 attended by two fatellites : a difcovery which 
 gave him confiderable pleafure, as the little 
 fecondary planets feemed to give a dignity to 
 the primary one, and raife it into a more con^ 
 fpicuous fituation among the great bodies of 
 our folar fyftem. 
 
 As the diftances of the planets, when 
 marked in miles, are a burden to the memory, 
 aftronomers often exprefs their mean diflances 
 in a fliorter w-ay, by fuppofing the diftance of 
 the earth from the fun to be divided into ten 
 parts. Mercury may then be eftimated at four 
 of fuch parts from the fun, Venus at feven, the 
 earth at ten. Mars at fifteen, Jupiter at fifty- 
 two fuch parts, Saturn at ninety-five, and the 
 Georgium Sidus 190 parts. 
 
 By comparing the periods of the planets, or 
 59 
 
60 ASTRONOMICAL ESSAYS. 
 
 the time they take to finifh their revolutions, 
 with their diflance from the fun, they zre 
 found to obferve a wonderful harmony and 
 proportion to each other ; for the nearer any 
 planet is to the fun, the fooner does he finifh 
 his revolution. And in this there is a conllant 
 and immutable law, which all the bodies of the 
 univerfe inviolably obferve in their circula- 
 tions ; namely. That the fquares of their periodi- 
 cal times are as the cubes of their dijlances from 
 the center of the orbits about which they regu- 
 larly perform their motions. We are indebted to 
 the fagacity of Kepler for the difcovery of this 
 law ; he was indeed one of the firft founders of 
 modern aftronomy. 
 
 I cannot conclude this general furvey of 
 the folar fyflera better than in the words of 
 that excellent mathematician, Mr. Maclaurin. 
 " The viev^ of nature which is the immediate 
 objed of fenfe, is very imperfeft, and of 
 fmall extent ; but by the afTillance of art, and 
 the aid ofreafon, becomes enlarged, till it lofes 
 itfelf in infinity. As magnitude of every 
 fort, abftracledly confidered, is capable of being 
 increafed to infinity, and is alfo divifible with- 
 out end ; fo we find, that in nature the limits of 
 the greatefl and leaft dimenfions of things are 
 actually placed at an immenfe diflance from 
 each other. 
 
 " We can perceive no bounds of the vafl 
 60 
 
ASTRONOMICAL ESSAYS. 6l 
 
 expanfe, in which natural caufes operate, and 
 fix no limit, or termination, to the univerfe. 
 The objects we commonly call great, vanifli, 
 when we contemplate the va(l body of the earth. 
 Tlie terraqueous giobe itfelf is loil in the folar 
 fyftem ; the fun itfelf dvvindlesinto a (tar; 
 Saturn's vaft orbit, and all the orbits of the 
 comets, crowd into a point, when viewed from 
 numberlefs places beiween the earth and the 
 nearelt fixed ftirs. Other fun's kindle to illu- 
 minate other fyftems, where our fun's rays are 
 unperceived ; but they alfo are fwallowed up in 
 the vaft expanfe. When we have rifen fo high, 
 as to leave all definite meafures far behind us, we 
 find ourfelves no nearer to a term, or limit. 
 
 " Our views of nature, however imperfeft, 
 ferveto reprefent to us, in a moftfenfible man- 
 ner, that mighty Power which prevails through- 
 out, acting with a force and efficacy that fufFers 
 no diminution from the greateft diftances of fpace 
 or intervals of time ; and to prove that all things 
 are ordered by infinite wifdom, and perfect good- 
 nefs : fcenes which (hould excite and animate 
 us to correfpond with the general harn^ony of 
 nature."* 
 
 * Maclaurin. 
 
 L 6i 
 
62 ASTRONOMICAL ESSAYS. 
 
 An Explanation of various Phenomena, 
 
 AGREE^iBLE TO THE CoPERNICAN SySTEM. 
 
 Having given a general idea of the Coper- 
 nican fyflcm, and the bodies of which it is 
 compofed, it will be neceflary to enlarge thefe 
 ideas by a more minute defcription of the par- 
 ticular parts, which form this great whole ; and 
 to (Irengthen them by the force of that evi- 
 dence, on which the fyftem is founded. 
 
 Of the Figure and Magnitude of the 
 Earth. 
 
 The places of the heavenly bodies could 
 not be fettled with accuracy from obfervations 
 made on the furface of the earth, unlefs it's 
 figure and magnitude were previoufly known ; 
 and without this knowledge, computations 
 from the obfervations of the heavenly bodies, 
 for afcertalning the fituation of places on the 
 earth, could not be depended on. 
 
 I have already obferved, that the appear- 
 ance of the heavenly bodies is not the fame to 
 the inhabitants of various parts of the earth ; 
 that the fun, the moon, and the ftars, rife and 
 fet in Greenland in a manner very different 
 from what they do in the Eaft Indies, and In 
 both places very different to what they do in 
 
 62 
 
ASTRONOMICAL ESSAYS. 6^ 
 
 England: an J as it was natural to attribute 
 the caufe of this change in the apparent face 
 of the heavens, to the figure of the earth, (for 
 appearances mud ever anfwer to the form and 
 fl:ru£lure of the things) the nature of this 
 figure was, therefore, one of the firfl; objects 
 of inquiry among philofophers and aftrono- 
 mers. 
 
 Some of the fages of antiquity concluded, 
 that the earth muft neceffarily be of a fpherical 
 figure, becaufe that figure was, on many ac- 
 counts, the mofl convenient for the earth, a& 
 an habitable world ; they alfo argued, that this 
 figure was the m^d natural, becaufe any body 
 expofed to forces, which tend to one common 
 center, as is the cafe with the earth, would 
 necefTarily alTume a round figure. The affent, 
 however, of the modern philofopher to this 
 truth, was not determined by fpeculative rea- 
 foning ; but on evidence, derived from fads 
 and aiftual obfervation. From thefe I fliall fe- 
 left thofe ar>^riiinents, that I think will have the 
 greated weight with young minds. 
 
 It is* known, from the laws of optics and 
 perfpetftive, that if any body, in all fituations, 
 and under all circum fiances, project a circular 
 JhadoWy that body muft be a globe. 
 
 It is alfo known, that eclipfes of the moon 
 are caufed by the fiiadow of the earth. 
 
 And we find, that whether the Jhadow be 
 
 63 
 
64 ASTRONOMICAL ESSAYS. 
 
 projected towards the eafl, or the weft, the 
 north, or the fourh, under ev-ery circumltance 
 it is circular: the body, therefore, that caits 
 the fhadow, which is the earth, mad be of a 
 globular figure. 
 
 We fliall obtain another convincing proof 
 of the globular fhipe of tha earth, by inquiring 
 in what mmner a perfoa ftanding upon the 
 coafl of the fea, and waiting for a vefTel which 
 he knows is to arrive, fees that veffel. We 
 fli III find, that he firft of all, and at the greatefl 
 diftance, fees the top of the mail rifing out of 
 the water ; and the appearance is, as if the 
 fhip was fwallowed up in the water. As he 
 continues to obferve the obje£l, more and 
 more of the maft appears ; at length he begins 
 to fee the tip of the deck, and by degrees the 
 whole body of the vefTel. On the other hand, 
 if the fhip be departing from u-, »ve firft lofe 
 fight of the hull, at a greater diftance the 
 main-fails difappear, at a ftill greater the top- 
 fail. Bat if the furface of the fea were a plane, 
 the body of the (hip. being the largeft part of 
 it, would be itQW firft, and from the greatefl 
 diftance, and the malts would not be vifible 
 till it came nearer. 
 
 To render this, if pofTible, ftill clearer, let 
 us confider two fhips meeting at fea, the top- 
 maft of each are the parts firft difcovered by 
 both, the hull, &c. being concealed by the 
 
 64 
 
ASTRONOMICAL ESSAYS. 65 
 
 convexity of the globe which rifes between them. 
 The {hips may, in this inltance, be refembled to 
 two men, who approach each other on the op- 
 pofite fides of a hill ; their heads will be firll 
 feen, and gradually, as they approach, the body 
 will come entirely in view. From hence is de- 
 rived a rational method of eflimating the dif- 
 tance of a (hip, which is in ufe among fca-faring 
 people, namely, of ob'erving how low they can 
 bring her down^ that is to fay, the man at the mad- 
 head fixes his eyeson the veflel ia fight, and 
 flowly defcends by the flirouds, till (he becomes 
 no longer vifible. The lefs the diflance, the 
 lower he may defcend before (he difappears. If 
 obfervations of this kind be made with a tele- 
 fcope, the etfed is (till more remarkable ; as 
 the didanc^ increafes or diminidies, the fliip in 
 fight will appear to become more and more im- 
 merfed, or to rife gradually out of the water. 
 
 This truth is fully evinced by the following 
 confideration ; that fnips have failed round the 
 earth, have gone out to the wellward, and have 
 come home from the eaftward ; or in other 
 words, the (hips have kept the fame courfe, and 
 yet returned from the oppofite fide into the 
 harbour whence they firft failed. Now we are 
 certain that this could not be the cafe, if the 
 earth were a plane ; for then a perfon, who 
 fhould fet out for any one point, and go on 
 
 65 
 
66 ASTRONOMICAL ESSAYS. 
 
 llrait forward, without flopping, would be con- 
 tinually going further from the point from which 
 he fet out. This argument may be much eluci- 
 dated, by referring the pupil to a terreftrial 
 globe, on which he may follow the tracks of an 
 Anfon and a Cook round the world. 
 
 Fig. I and 2, plate II. are illuflrationsof the 
 foregoing principles. Fig. i, (hews that if the 
 earth was a plane, the whole of a fliip would 
 be feen at once, however diftant from the fpecla- 
 tor, and that whether he was placed at the top 
 or bottom of a hill. From fig. 3, it appears, 
 that the rotundity of the earth, reprefentcd by 
 the circle ABC, conceals the lower part of the 
 fhip d, while the top-maft is ftill vifible ; and 
 that it is not till the (hip comes to e, that the 
 whole of it is vifible. 
 
 The following remarks evince the fame truth. 
 Obferve any ftar nearer the northern part of the 
 horizon, and if you travel to the fouth, it will 
 feem to dip farther and farther downwards, till 
 by proceeding, it will defcend entirely out of 
 ijfrht. In the mean time, the flars to the fouth- 
 
 o 
 
 ward of our traveller will feem to rife higher and 
 higher. The contrary appearances would hap- 
 pen, if he went to the northward. This proves 
 that the earth is not a plane furface, but a curve 
 in the dire(5lion fouth and north. By an obferva- 
 on nearly fim ilar to this, the traveller may prove 
 the curvature of the earth, in an eafl and weft 
 direction. 
 
 66 
 
ASTRONOMICAL ESSAYS. Sj 
 
 The globular figure of the earth may be al- 
 fo inferred from the operation of levelling, or the 
 art of conveying water from one place to ano- 
 ther ; for in this procefs, it is found neceffary 
 to make an allowance between the true and ap- 
 parent level ; or in other words, for the figure 
 of the earth. For the true level is not a ftrait 
 line, but a curve which falls below the ftrait line 
 about eight inches in a mile, four times ei^^ht 
 in two miles, nine times eight in three miles, fix- 
 teen times eight in four miles, always increafing 
 as the fquare of the diftance. 
 
 What the earth lofes of it's fphericity by 
 mountains and vallies, is very inconfiderable ; 
 the higheft eminence bearing fo little propor- 
 tion to it's bulk, as to be fcarcely equivalent to 
 the minuteft protuberance on the furface of a 
 lemon. 
 
 It is proper, however, to acquaint the young 
 pupil, that though we call our earth a globe, 
 and that when fpeaking in general terms, it 
 may be confidered as fuch ; yet in the ftriclnefs 
 of truth, it muft be obferved, that it is not ex- 
 adlly and perfedly a fphere, but a fpheriod, fat- 
 tened a little towards the poles, and Jewelling at the 
 equator ; the equatorial diameter being about 
 thirty-four miles longer than the diameter from 
 pole to pole. This difference bears, there- 
 fore, too fmall a proportion to the diameter, to 
 be reprefented on globes. M. Caffini, from 
 
 67 
 
68 ASTRONOMICAL ESSAYS. 
 
 PIcart*s meafure of a degree, aflcrted, that the 
 earth was an oblong or prolate fpheriod, flat- 
 tened at the equator, and protuberant at the 
 poles ; while Newton and Huygens, from a 
 confideration of the known laws and the 
 diurnal motion of the earth, concluded that the 
 fifTure of the earth was that of an opiate fphe- 
 roid, flattened at the poles, protuberant at the 
 equator. To decide this important queftion, 
 Louis XIV. ordered two degrees of tie me- 
 ridian to be meafured, one ui;der the equator, 
 the other as near the pole as polTible. For this 
 purpofe, the Royal Academy of Sciences fent 
 Mefl". Maupertuis, Clairault, Camus, and Le 
 Monnier, to Lapland : they fet out from France 
 in 1735, and returned in the fpring of the 
 vear 1736, having fatisfaftorlly accomplifhed 
 the purpofe for which they were fent. Mefl". 
 Godin, Condamine, and Bouguer, were fent 
 on the fouthern expedition : to thefe the King 
 of Spain joined Don George Juan, and Don 
 Anthony de Ulloa, who left Europe in the 
 year 1735, and after encountering innumera- 
 ble hardfhips and difliculties, returned to Eu- 
 rope in different times, and by different ways, 
 in 1744, 1745, 1746. The refult of this ardu- 
 ous tafli was a complete confirmation of New- 
 ton's theoretical invefligation. The differ- 
 ence between the equatorial and polar dimen- 
 fions, when compared with the earth's femi- 
 diameter, is but an inconfiderable quantity, 
 
 68 
 
ASTRONOMICAL ESSAYS. 69 
 
 amounting in the whole to an elevation of little 
 more than 16^ of 3970 ; that is, to lefs than a 
 240th part of the diltance from the furface of 
 the earth to the center. If a meridional feiStion 
 of fuch a fpheroid were laid down upon paper, 
 
 the eye would not diftinguifli it from a perfect 
 circle. 
 
 Of the Diurnal Motion of the Earth. 
 
 Though it is this motion which gives us the 
 grateful viciffitudes of day and night, adjuftcd 
 to the times of labour and reft ; yet young peo- 
 ple generally find fome difficulty in conceiving 
 that the earth moves ; the more fo, becaufe, in 
 order to allow it, they muft give up, in a great 
 meafure, the evidence of their exterior fenfes, 
 of which the impreflions are at their age ex- 
 ceeding ftrong and lively. It will, therefore, 
 be neceflary for the tutor to prove to them, that 
 they can by no means infer that the earth h at 
 reft, becaufe it appears fo, and convince them 
 by a variety of fads, that reafon was given to 
 correct the fallacies of the fenfes. 
 
 To this end we fliall here point out fome 
 inftances, where apparent motion is produced in 
 a body at reft, by the real motion of the fpecla- 
 tor. Let us fuppofe a man in a ftiip to be car- 
 ried along by a brifk gale, in a direction pa- 
 rallel to a ftiore, at no great diftance from him ; 
 while he keeps his eye on the deck, the maft, 
 M 69 
 
'J^ ASTRONOMICAL ESSAYS. 
 
 the fails, or any thing about the fliip, that is to 
 fay, while he fees nothing but fome part of the 
 veffel on board of which he is, and confequently 
 every part of which moves with him, he will 
 not perceive that the fliip moves at all. Let 
 him, after this, look to the (bore, and he will 
 fee the houfes, trees, and hills, run from him in 
 a direction contrary to the motion of the veffel ; 
 and fuppofmg him to have received no previ- 
 ous information on the fubjeft, he might natu- 
 rally conclude, that the apparent motion of 
 thefe bodies was real. 
 
 In a fimilar fituation to this, we may con- 
 ceive the inhabitants of the earth ; who, in 
 early times, knew nothing of the true ftru£lure 
 or laws of the univerfe, faw the fun, the liars, 
 and the planets, rife and fet, and perform an 
 apparent revolution about the earth. They 
 had no idea of the motion of the earth, and 
 therefore all this appearance feemed reality. 
 But as it is highly reafonable to fuppofe, that 
 as foon as the flighteft hint fliould be given to 
 the man, of the motion of the veffel, he would 
 begin to form a new opinion, and conceive it 
 to be more rational, that fofmall a thing as the 
 fhip fhould move, rather than all that part of the 
 earth which was open to his view ; fo, in the 
 fame manner, no fooner was an idea formed of 
 the vaft extent and greatnefs of the univerfe, 
 
 70 
 
ASTRONOMICAL ESSAYS. 7I 
 
 with refpe^l to this earth, than mankind began 
 to conceive it would be more rational that the 
 earth fliould move, than the whole fabric of 
 the heavens. 
 
 By another familiar inftance it will be eafy 
 to fhew the young pupil, that as the eye does 
 not perceive its own motion, it always judges 
 from appearances. Let a perfon go into a com- 
 mon windmill, and dcfire the miller to turn 
 the mill round, while he is fitting within it 
 with his eyes fixed on the upright pofl: in the 
 center thereof ; this pofl, though at reft, will 
 appear to him to turn round with confiderable 
 velocity, the real motion of the mill being the 
 caufe of the apparent motion of the fwivel pod. 
 Sea-faring people are furniflied with various 
 inftances to illuftrate this fubjeifl ; thofe who 
 are bufy in the hold of a (hip at anchor, 
 cannot by any perception determine whether 
 the (hip has fwung round or not by the turn of 
 the tide. When a (hip firfl gets undcr-way 
 with a light breeze, flie m^y be going at a good 
 rate before thofe whj are between decks can 
 perceive it. Having thus obviated the ob- 
 je£lions which arife from the teftimony of the 
 fenfes, we may now proceed to confider the 
 arguments which tend more directly to prove 
 the motion of the earth. 
 
 All the celeftial motions will, on this fuppo- 
 
 7» 
 
72 ASTRONOMICAL ESSAYS. 
 
 fition, be incomparably more fimple and mode- 
 rate. 
 
 This opinion is much more agreeable to our 
 notions of final caufes, and our knowledge of 
 the ceconomy of nature ; for if the earth be at 
 refl, and the ftars, &c. move round it once in 
 24 hours, their velocity murt: be immenfe ; and 
 it is certainly more agreeable to rea'.on, that 
 one fingle body, and that one of the fmalleft , 
 fhould revolve on its own axis in 24 hours, 
 than that the whole univerfe fhould be carried 
 round it in the fame time, with inconceivable 
 velocity. 
 
 The rotation of the earth round it's axis 
 is analagous to what is obferved in the fun, and 
 moft of the planets ; it being highly probable, 
 that the earth, which is itfelf one of the pla- 
 nets, fhould have the fame motion as they have, 
 for producing the fame effeft : and it would be 
 as abfurd in us to contend for the motion of 
 the whole heavens round us in 24 hours, rather 
 than allow a diurnal motion to our globe, as it 
 would be for the inhabitants of Jupiter to in- 
 fifl that our globe and the whole heavens, mufl 
 revolve round them in ten hours, that all it's 
 parts might fucceffively enjf^y the light, rather 
 than grant a diurnal motion to their habita- 
 tion. 
 
 All the phenomena relative to this fubjed. 
 
ASTRONOMICAL ESSAYS. 73 
 
 are as as eafily folved on the fuppofition of the 
 earth's motion, as on the contrary hypothefis. 
 
 Befides the foregoing confiderations, there 
 are feveral arguments to be deduced from the 
 higher parts of ajironomy, which demonjlrably 
 prove the diurnal motion of the earth. 
 
 Before we enter into a further explanation 
 of phenomena, It will be neceflary to define 
 fome of the principal circles of the globe. Ihe 
 reader will comprehend more fully thefe defi- 
 nitions, and attain more accurate ideas of thefe 
 circles, by placing, while he is reading them, 
 a terreftrial globe or armillary fphere before 
 him. It may, however, be neceifary to pre- 
 mife, that we are at liberty to fuppofe as many 
 circles as we pleafe, to be defcribed on the 
 earth ; and the plane of any of thefe to be con- 
 tinued from the earth until it marks a corref- 
 ponding circle in the concave fphere of the 
 heavens. 
 
 Among thefe circles, the horizon Is the mofl 
 frequently named. Properly fpeaking, there 
 are two circles by this name, but diftinguifhed 
 from each other by added epithets, the one 
 being called the fenfible^ the other the rational 
 horizon* 
 
 In general terms, the horizon may be de- 
 fined to be an imaginary circle, that feparates 
 the vifible from the invifible part of the 
 heavens. 
 
 n 
 
74 ASTRONOMICAL ESSAYS. 
 
 If a fpedator fuppofes the floor or plane on 
 which he ftands, to be extended every way, till 
 it reach the ftarry heavens, this plane is his 
 fenftble horizon. 
 
 The rational horizon is a circle, whofe plane 
 is parallel to the former, but paffing through the 
 center of the earth. 
 
 The rational horizon divides the concave 
 fphere of the heavens into two equal parts, or 
 hemifpheres ; the objeds that are in the upper 
 hemifphere will be vifible ; fuch as are in the 
 lower hemifphere will be invifible to the fpcc- 
 tator. 
 
 Though the globe of the earth appears fo 
 large to thofe who inhabit it, yet it is fo mi- 
 nute a fpeck, when compared to the immenfe 
 fphere of the heavens, that at that diftance the 
 planes of the rational and fenfible horizons coin- 
 cide : or in other words, the diflance between 
 them in the fphere of the heavens, is too fmall 
 for admeafurement. 
 
 To illuflrate this, let A B C D, fig. i, plate 
 III. reprefent the earth ; z h n o the fphere of 
 the ftarry heaven. If an inhabitant of the 
 earth ftand upon the point A, his fenfible hori- 
 zon is s e, his rational one ho; the diflance be- 
 tween the planes of thefe two horizons is AF, 
 the femidiameter of the earth, which is mea- 
 fared in a great circle upon the fphere of the 
 heaven, by the angle eY o, or the arc e o; this 
 
 74 
 
ASTRONOMICAL ESSAYS. 75 
 
 arc in fo fmall a circle, zhno, would amount 
 to feveral degrees, and confequently the dif- 
 ference between the fenfible and rational horizon 
 would be great enough to be meafured by ob- 
 fervation. If we reprefent the fphere of the 
 heaven by a larger circle, the femidiameter of 
 the earth A F, meafured in this circle, will 
 amount to fewer degrees ; for the arc E O is lefs 
 than the arc e ; and the larger the fphere of 
 the heaven is, in proportion to the globe of the 
 earth, the lefs fenfible is the difference between 
 the two horizons. Now as the fphere of the 
 earth is but a point, when compared to the 
 ftarry heaven, the difference between the fen- 
 fible and rational horizon will be infenfible. 
 
 From what has been faid, it appears that the 
 only diftindtion between the fenfible and the ra- 
 tional horizon, arifes from the diftance of the 
 objedl wc are looking at. 
 
 The fenfible h9nzon is an imaginary circle, 
 which terminates our view, when the objedls 
 we are looking at are upon the earth's furface. 
 
 The rational horizon is an imaginary circle, 
 which terminates our view, when the objecls 
 we are looking at are as remote as the heavenly 
 bodies. 
 
 As the rational horizon divides the apparent 
 celeftial fphere into two equal hemifpheres, 
 and ferves as a boundary, from which to mea- 
 fure the elevation or depreffion of celeftial ob- 
 
 75 
 
7" 
 
 ASTRONOMICAL ESSAYS. 
 
 jeds ; thofe in the upper, or vifible hemilphere, 
 are faid to be high, or elevated above the hori- 
 zon ; and thofe in the other hemifphere are called 
 low, or below the horizon. 
 
 The earth being a fpherical body, the ho- 
 rizon, or limits of our view, muft change as we 
 change our place ; and therefore every place up- 
 on the earth has a different horizon. Thus, if 
 a man lives at ^, fig. 2, plate III. his horizon is 
 G C -, if he lives at />, his hinizon is H D ; if at 
 C, it is A E. From hence we obtain another 
 proof of the fphericity of the earth ; for if it were 
 flat, all the inhabitants thereof would have the 
 fame horizon. 
 
 The point in the heavens, which is dired- 
 ly over the head of a fpeclator, is called the 
 xenith. 
 
 That point which is direQly under his feet, 
 is called the nadir. 
 
 If a man lives at a^ fig. 2, plate 111. his 
 zenith is A, his nadir E . if he lives at b, his 
 zenith is B, his nadir F. Confequently the zenith 
 and horizon of an obferver remains fixed in the 
 heavens, fo long as he continues in the fame 
 place ; but he no fooner changes his pofition, 
 than the horizon touches the earth in another 
 point, and his zenith anfwers to a different point 
 in the heavens. 
 
 The o.xis of the earth is an imaginary line, 
 conceived to be drawn through the center 
 
 76 
 
ASTRONOMICAL ESSAYS. ']'] 
 
 of the earth upon which line its revolutions 
 are made. 
 
 The poles of the earth are the extremities 
 of it's axis, or thofe two points on it's furface, 
 where it's axis terminate ; one of thefe is called 
 the norths and the other i\\t fouth pole. The 
 poles of the heavens, or of the world, are thofe 
 two points in the heavens, where the axis of 
 the earth, if produced, would terminate ; fo 
 that the north pole of the heavens is exadly 
 over the north pole of the earth, and the fouth 
 pole of the heavens is diredly over the fouth pole 
 of the earth. 
 
 The equator is an imaginary circle, which 
 is fuppofed to be drawn round the earth's fur- 
 face, in the mid.^le between the two poles. It 
 divides the earth into two equal parts, one of 
 which is called the northern^ the other the fouth- 
 em hemifphere. 
 
 If we fujpofe the plane of the earth's 
 equator to be extended all ways, as far as the 
 heavens, it will mark there a circle, that will 
 divide the heavens into two equal parts ; this 
 circle is called fometimes the equinodia I, feme- 
 times the celejiial equator. 
 
 The meridian of any place is a circle fup- 
 pofed to pafs through that place and the poles 
 of the earth ; we may therefore imagine as 
 many meridians as there are places upon the 
 earth, becaufe any place that is ever fo little to 
 N yy 
 
78 ASTRONOMICAL ESSAYS. 
 
 the cart or the weft of another place, has a dif- 
 ferent meridian. 
 
 By the foregoing definition, we fee that the 
 meridian of any place is immoveably fixed to 
 that place, and carried round along with it by 
 the rotation of the earth. The meridian marks 
 upon the plane of the horizon the north and 
 fouth points. 
 
 The circle which the fun appears to de- 
 fcribe every year, in the concave fphere of the 
 heavens, is called the ecliptic. It is thus de- 
 nominated, becaufe in all eclipfes the moon is 
 either in or near the plane of it. But as the 
 earth moves round the fun, in the plane of the 
 ecliptic, it is Ukewife the plane of the earth's 
 orbit. 
 
 If we conceive a zone, or belt, about fix- 
 teen degrees broad, in the concave fphere of 
 the heaven, with the ecliptic pafling through 
 the middle of it, this zone is called the zodiac. 
 The ftars in the zodiac were divided by the 
 ancients into twelve equal parts or figns, to 
 correfpond with the months of the year j and 
 becaufe the number twelve with them was al- 
 ways exprefiive of fulnefs or completion, it is 
 ufed in that fenfe in facred writ. The figns 
 are named, Aries, Taurus, Gemini, Cancer, 
 Leo, Virgo, Libra, Scorpio, Sagittarius, Capri- 
 cornus, Aquarius, Pifces. 
 
 We may imagine as m.any circles as we 
 78 
 
ASTRONOMICAL ESSAYS. 
 
 79 
 
 pleafe drawn on a globe, parallel to the equa- 
 tor, and thefe will decreafe in their diameter, 
 as they approach nearer the poles. The tropics 
 are two lefTer circles of this kind, parallel to 
 the equator, and 2 3^- degrees diftant from it j 
 one in the northern hemifphere, which is 
 called the tropic of Cancer ; the other in the 
 fouthern, which is called the tropic of Capri- 
 corn. If we conceive the planes of thefe cir- 
 cles expanded, till they reach the flarry hea- 
 ven, the fun will be {cqw to move in that circle 
 which correfponds to the tropic of Cancer on 
 the longed funimer's day, and in that circle 
 which anfwers to the tropic of Capricorn on the 
 fhortefl: winter's day. 
 
 The polar circles are two lefler circles, con- 
 ceived to be defcribed at 23^ degrees diftance 
 from each pole. 
 
 The axis of the earth is inclined to the 
 plane of the ecliptic, and makes with it an 
 angle of 66\ degrees ; therefore the plane of 
 the earth's equator cannot coincide with the 
 plane of the ecliptic, but thefe two planes 
 make with one another an angle of 23-1- de- 
 grees. 
 
 Of the Annual Motion of the Earth, 
 
 The foregoing definitions being undcrflood, 
 we may now proceed in the defcription of the 
 79 
 
8o ASTRONOMICAL ESSAYS. 
 
 phenomena of our fyftem. It is owing to the 
 induftry of modern aflronomers, that the an- 
 nual motion of the earth has been fully evinced; 
 for though this motion had been known to, 
 and adopted by many among the ancient phi- 
 lofophers, yet they were not able to give their 
 opinions that degree of probability, which is 
 attainable from modern difcoveries, much lefs 
 the evidence arifmg from thofe demonftrative 
 proofs of which we are now in poffcffion. We 
 fhall, therefore, enumerate fome of the reafons 
 which induce aflronomers to believe that the 
 earth moves round the fun^ and then explain 
 further the nature of this motion, calculated to 
 afford us the ufeful and delightful vaiiety of 
 the feafons, the mutual allay of immoderate 
 heat and cold, as alfo for the fucceflive grow^th 
 and recruit of vegetation. 
 
 The celeftial motions become incomparably 
 more fimple, and free from thofe looped con- 
 tortions which muft be fuppofed in the other 
 cafe, and which are not only extremely improb- 
 able, but incompatible with what we know of 
 motion. 
 
 This opinion is alfo more reafonable, on 
 account of the extreme minutenefs of the earth, 
 when compared with the immenfe bulk of the 
 fun, Jupiter and Saturn ; and there are no 
 known laws of motion, according to which fo 
 
 80 
 
ASTRONOMICAL ESSAYS. 8l 
 
 grea a body as the fun can revolve about fo fmall 
 a one as the earth. 
 
 The fun is the fountain of light and heat, 
 which it darts through the whole fydem ; it 
 ought, therefore, to be in the center, that it's 
 influence may be regularly difFufed through the 
 whole heavens, and communicated in jult gra- 
 dations to the whole fyftem. 
 
 When we confider the fun as the center of 
 the fyftem, we find all the bodies moving round 
 it, agreeable to the univerfal laws of gravity ; 
 but upon any other confideration we are left in 
 the dark. 
 
 The motion of the earth round the fun ac- 
 cords with that general harmony, and univerfal 
 law, which all the other moving bodies in the 
 fyftem obferve, namely, that the fquarcs of the 
 periodic times are as the cubes of the diftances ; but 
 if the fun moves round the earth, that law is 
 deftroyed, and the general order of fymmetry in 
 nature interrupted. 
 
 It is inconteftibly proved by obfervation, a 
 motion having been difcovered in all the fixed 
 ftars, which arifes from a combination of the 
 motion of light with the motion of the earth in 
 it's orbit. 
 
 It will be clearly fliewn in it's place, that 
 
 Venus and Mercury move round the fun in orbits 
 
 that are between it and the earth ; that the 
 
 orbit of the earth is fituated between that of 
 
 8i ^ 
 
82 ASTRONOMICAL ESSAYS. 
 
 Venus and Mars ; and that the orbits of Mars^ 
 Jupiter, &c. are exterior to, and include the 
 other three. 
 
 Of the apparent Motion of the Sun, art- 
 sing FROM THE Earth's ANNUAL Motion 
 
 ROUND IT. 
 
 As when a perfon fails along the fea coafl, 
 the fliore, the villages, and other remarkable 
 places on land, appear to change their fitua- 
 tion, and to pafs by him ; fo it is in the hea- 
 vens. To a fpedator upon the earth, as it 
 moves along it's orbit, or fails as it were 
 through celeftial fpace, the fun, the planets, 
 and the fixed ftars, appear to change their 
 places. 
 
 Apparent change of place is of two forts ; 
 the one is that of bodies at reft, the change of 
 whofe place depends folely on that of the fpec- 
 tator ; the other is that of bodies in motion, 
 whofe apparent change of place depends as well 
 on their own motion, as on that of the fpec- 
 tator. 
 
 We Ihall firft confider only that apparent 
 change which takes place in tliofe which are at 
 reft, and which is owing wholly to the motion 
 of the earth, and (hew that the fun, when feen 
 from the earth, will appear to move in the 
 fame manner, whether it revolves round the 
 earth, or whether the earth revolves round the 
 82 
 
ASTRONOMICAL ESSAYS. ^Q 
 
 fun. Let us fuppofe the earth at re/i, without 
 any motion of it's own, and let the fun be fup- 
 pofed to revolve rounl it in the orbit A B C D, 
 fig. I, plate IV ; aaJ let E F G H be a circle in 
 the concave fphere of the (tarry heavens ; as 
 the fun moves in the order of the letters A B 
 CD in it's orbit, it will appear to a fpedator 
 on the earth to have d^fcribea the circle E F G 
 H. When the fa:i is at A, it will appear as if 
 it was among the fixed ftars that are at E ; 
 when ft is at B, it will appear among the 
 fixed ftars at F ; when at C, among thofe at G ; 
 and when it is at D, it will appear among the 
 fixed ftars at H. Indeed, the fixed ftars and the 
 fun are not {etn at the fame time ; but we have 
 fliewn, that we may tell in what part of the 
 heavens the fun is, or what fixed ftars it is near, 
 by knowing thofe which are oppofite to it, or 
 come to the fouth at midnight. Therefore, if 
 we find that any fet of Itars, as thofe at H for in- 
 ftance, come to the fouth at midnight, we may 
 be fure that they are oppofite to the fun ; and 
 confequently, if we could fee the ftars in that 
 part of the heavens where the fun is, we (liould 
 find them to be thofe at F. 
 
 Secondly, let us fuppofe that S is the /««, 
 having no motion of it's own, that it refts within 
 the orbit A B C D, in which we (hall now fup- 
 pofe the earth to move, in the order of the letters 
 ABCD. Upon this fuppofition, when the 
 83 
 
84 ASTRONOMICAL ESSAYS. 
 
 earth is at A, the fun will appear in that part of 
 the heavens where the ftars G are ; when the 
 earth is at B, the fun will appear in that part of 
 the heavens where the (tars H are ; when the 
 earth is at C, the fun will appear in that part of 
 the heavens where the ftars E are ; and as the 
 earth revolves round the fun, in the orbit ABC 
 D, tbefun will appear to a fpedtator on the earth 
 to defcribe the circle G H E F. 
 
 Thus whether the earth be at reji, and the 
 fun revolves in the orbit A B C D j or the fun 
 be at reji, and the earth revolves in the fame 
 orbit, a fpedator on the earth will fee the fun 
 defcribe the fame circle E F G H, in the concave 
 fphere of the heavens. 
 
 Hence if the plane of the earth's orbit be 
 imagined to be extended to the heavens, it 
 would cut the ftarry firmament in that very cir- 
 cle, in which a fpeclator in the fun would fee 
 the earth revolve every year : while an inhabi- 
 tant of the earth would obferve the fun to go 
 through the fame circle, and in the fame fpace 
 of time, that the folar fpedator would fee the 
 earth defcribe it. 
 
 The inhabitants of all the other planets will 
 obferve juft fuch motions in the fun as we do, 
 and for the very fame reafons ; and the fun will 
 be fcen from every planet to defcribe the fame 
 tircle, and in the fame fpace of time, that a 
 fpe6tator in the fun would obferve the planet to 
 
 84 
 
ASTRONOMICAL ESSAYS. 8^ 
 
 do. For example, an inhabitant of Jupiter 
 would think that the fun revolved round him, 
 defcribing a circle in the heavens in the fpacc 
 of twelve years : this circle would not be the 
 fanie with our ecliptic, nor would the fun 
 app>.-ar to pafs through the fame ftars which he 
 does to us. On the fame account, the fun, 
 feen fron Saturn, will appear to move in 
 another circle, diftind from cither of the for- 
 mer ; and will nor f em to finifh his period in lefs 
 time than thirty years. Now as it is impoffible 
 that the fun can have all thefe motions really in it- 
 f'f, we may fafely affirm, that none of them are 
 re d, but that they are all apparent, and arife 
 from the motions of the refpedive planets. 
 
 One phenomenon arifing from the annual 
 motion of the earth, which has already been 
 (lightly touched upon, may now be more fully 
 explained ; for as from this motion, the fun 
 appears to move from wefl: to eaft in the hea- 
 vens, if a (lar rifes or fets along with the fun 
 at any time, it will in the courle of a few days 
 rife or fet before it, becaufe the fun's appa- 
 rent place in the heavens will be removed to 
 the ea(l ward of that flar. Hence thofe (lars 
 which at one time of the year fet with the fun, 
 and therefore do not appear at all, (hall at 
 another time of the year rife when the fun fets, 
 andfhineall the night. And as any one ftar 
 O 8^ 
 
86 ASTRONOMICAL ESSAYS. 
 
 fhifts it's place with refpe£t to the fun, and in 
 confequence of that with refped: to the hour of 
 the night, fo do all the reft. Hence it is that 
 all thofe ftars, which at onetime of the year ap- 
 pear on any one fide of the pole ftar in the even- 
 ing, (hall in half a year appear on the contrary 
 fide thereof. 
 
 Of Phenomena occasioned by the annual 
 
 AND DIURNAL MoTIONS OF THE EaRTH. 
 
 Firft, of thofe that arife from the diurnal 
 motion. As the earth is of a fpherical figure, 
 that part of it, which comes at any time under 
 the confined view of an obferver, will feem to be 
 extended like a plane ; and the heavens will ap- 
 pear as a concave fpherical fuperfices, divided by 
 the aforefaid plane into two equal parts,* one of 
 which is vifible, the other concealed from us by 
 the opacity of the earth. 
 
 Now the earth, by it's revolution round 
 it's axis, carries the fpednior and the afore/aid 
 flane from wejl to cjl ; therefore all thofe 
 bodies to the eaft, which could not be feen 
 becaufe they were below the plane of the hori- 
 zon, will become vifible, or rife above it, 
 when, by the rotation of the earth, the hori- 
 zon finks as it were below them. On the other 
 hand, the oppofite part of the plane, towards 
 the weft, rifing above the ftars on that fide, 
 
 • Sec page 74 of thcfc Eflays. 
 
 86 
 
ASTRONOMICAL ESSAYS. 87 
 
 will hide them from the fpedator, and they will 
 appear to fet, or go below the horizon. 
 
 As the earth, together with the horizon of 
 the fpeftator, continues moving to the eaft, and 
 about the fame axis, all fuch bodies as are fepa- 
 rated from the earth, and which do not partake 
 of that motion, will feem to move uniformly in 
 the fame time, but in an oppofite diredlion, that 
 is, from eaft to wejl ; excepting the celeftial poles, 
 which will appear to be at reft. Therefore, 
 when we fay, that the whole concave fphere of 
 the heavens appears to turn round upon the axis 
 of the world, whilft the earth is performing one 
 rotation round it's own axis, we muft be un* 
 derftood to except the two poles of the world, 
 for thefe do not partake of this apparent mo- 
 tion. 
 
 It is, therefore, on account of the revolu- 
 tion of the earth round it's axis, that the fpeda- 
 tor imagines the whole ftarry firmament, and 
 every point of the heaven, (excepting the two 
 celeftial poles) to revolve about the earth from 
 call to weft every tvi^enty-four hours, each 
 point defcribing a greater or lefler circle, ^s it is 
 more or lefs remote from one of the celeftial 
 poles. 
 
 The earth is made to revolve on it's axis, in 
 order to give alternate night and day to every part 
 of it's furface. 
 
 Although every place on the furface is 
 
 87 
 
83 ASTRONOMICAL ESSAYS. 
 
 illuminated by all the ftars which are a^ove 
 the horizon of that place ; yet when theyi/w is 
 above the horizon, his light i> fo flrong, that 
 it quite extinguifhes the faint light of the ftars, 
 and produces day. When the fun goes below 
 the horizon, or more properly, when our hori- 
 zon gets above the fun, the ftars give their 
 light, and we are in that ftate which is called 
 night. 
 
 Now as the earth is an opakefpherical body, 
 ata great diftance from the fun, one halfoVw. will 
 always be illuminated thereby, while the other 
 half will remain in darknefs. 
 
 The circle which difiinguiflies or divides the 
 illuminated face of the earth from the dark fide, 
 and is the boundary between lit];ht and darknefs, 
 is generally called the terminator. A line drawn 
 from the center of the fun to the center of the 
 earth, is perpendicular to the plane of this 
 circle. 
 
 It is plain, that when any given place on the 
 globe firft gets into the enlightened hemifphere, 
 thefunisjufl: rifen to that part ; when it gets 
 half-way, or to it's greateft diftance from the ter- 
 minator, it is then noon ; and v/hen it leaves the 
 enlightened hemifphere, it is xhenfun-fet. 
 
 Here it will be neceftary to premife a few 
 confiderations : Firft, that on account of the 
 immenfe diftance of the fun from the earth. 
 
ASTRONOMICAL ESSAYS. Si) 
 
 the rays which proceed from it mav be con- 
 fidered as parallel to each other. Secondly, 
 that only one-half of a globe can be illuminated 
 by parallel rays, and therefore o«/y one half of 
 the earth will be enlightened by the fun at one 
 time. 
 
 Thefe confiderations will be rendered more 
 forcible, by an attentive furvey of fig. i, 
 plate V ; in which S reprefents the fun, from 
 whom we fjppofe parallel rays to flow in all 
 direftions. At A, B, C, are reprefented three 
 different pofitions of the globe of the earth 
 the bright part being that which is illuminated 
 by the rays proceeding fro.ii the fun, the 
 Ihaded part, the portion of the globe which is 
 in darknefs ; of courfe the line T I is the ter- 
 minator, or boundary of light and darknefs. 
 
 In the globe at C, the poles coincide with 
 the terminator. 
 
 In the globe at A, the north pole is in the 
 enlighted portion, and the fouth pole in the 
 dark hemifphere : while in the oppofite globe 
 at B, the fouthern pole is in the illuminated 
 part, and the north pole in obfcurity. 
 
 It is evident, that it is day in any given 
 place on the globe, fo long as that place con- 
 tinues in the enlightened hemifphere ; but 
 when, by the diurnal rotation of the earth on 
 it's axis, it is carried into the dark hemifphere, 
 it becomes night to that place. 
 89 
 
go ASTRONOMICAL ESSAYS. 
 
 The length of the day and the night depend 
 therefore on the pofttion of the terminator^ with 
 refpe6i to the axis of the earth. 
 
 If the poles of the earth be fituated in the 
 terminator, as at c, every parallel will be 
 divided into two equal parts ; and as the uni- 
 form motion of the earth caufes any given 
 place to defcribe equal parts of it's parallel in 
 equal times, the day and the night would be 
 equal on every parallel of latitude, that is, all 
 over the globe, except at the poles, where the 
 fun would neither rife nor fet, but continue in 
 the horizon. 
 
 But if, as at A and B, the axis be not in the 
 plane of the terminacor, the terminator will 
 divide the equator into two equal parts, but all 
 the circles parallel to it into unequal parts ; 
 thofe circles that are fituated towards the en- 
 lightened pole, will have a greater part of 
 their circumference in the enlightened than 
 in the dark hemifphere ; while fimilar parallels 
 towards the other pole will have the greater 
 part of their circumference in the dark hemi- 
 fphere. Whence it follows, that the firft- 
 Hientioned parallels will enjoy longer days than 
 nights ; and the contrary will happen to the 
 latter, where the days will be the fhorteft, and 
 the nights the longed ; while at the equator, 
 the days will always be of the fame length. 
 
 Having ftiewn that the viciffitudes in the 
 90. 
 
ASTRONOMICAL ESSAYS. Qi 
 
 length of the days and nights are occafioned by 
 the pofition of the ierminutor with refped to the 
 axis of the earth, I have now only to explain 
 what occ.fions thefe various pofitions ; which 
 is the more important, as on thefe depend the 
 diverfity in the feafons of the year. 
 
 Of the Seasons of th£ Year. 
 
 In confidering this fubjeft, you will find 
 further proofs of that divine wisdom which 
 pervades all the works of God, and fee, that no 
 other conformation of the fyflem could have 
 given fuch commodious diftributions of light 
 and heat, or imparted fertility and pleafure to 
 fo great a part of the revolving globe. 
 
 The changes in the pofition of the termi- 
 nator are occafioned, ,. By the inclination of 
 the earth's axis to the plane of the ecliptic, or 
 orbit in which it moves. 2. Becau/e through the 
 whole of it's annual ccurfe, the axis of the earth 
 preferves it's pofition, or continues parallel to it- 
 felf; that is, if a line be conceived as drawn 
 parallel to the axis, while the earth is in any one 
 point of it's orbit, the axis will in every other 
 pofition of the earth be parallel to the faid Hne. 
 ^ It mud be evident to you, that the paral- 
 lelifm of the axis mud occafion confiderable 
 differences. By a bare infpedion of the globes 
 A, B, fig. 1, plate V, you will fee that when 
 91 
 
92 ASTRONOMICAL ESSAYS. 
 
 the earth is In one pofitlon of it*s orbit, the 
 north pole will be turned towards the fun, but 
 in the oppofite part will be turned from him. 
 But the abfence of the fun's light produces a 
 proportionable degree of cold ; hence the 
 feafons are, in the northern and fouthern 
 parts of the globe, diftindlly marked by different 
 degrees of heat and cold. It is this annual turn- 
 ing or the poles towards the fun, that occafions 
 the very long days in the northern and fouthern 
 part*:. It is owing to the fame caufe, that the fun 
 feems to rife higher in the heavens during fum- 
 mer than in W'inter ; and this alternate finking 
 and rifing is perceptible over the whole globe. 
 
 If the axis of the earth were perpendicular 
 to the plane of it's orbit, the equator and the 
 orbit (or ecliptic) would coincide ; and as the 
 fun is always in the plane of the ecliptic, it would 
 in this cafe be always over the equator, as in 
 fig. 3, and the tzuo poles would be in the ter- 
 minator, and there would be no diverfity in the 
 days and nights, and but one feafon of the 
 year ; but as this is not the cafe, we may fairly 
 infer, that the axis of the earth is not perpen- 
 dicular to the plane of it's orbit. 
 
 But if the earth's axis be inclined to the 
 plane of the ecliptic, when the earth is in the 
 fituation reprefented at fig. i, plate V, the pole 
 N will be towards the fun, and the pole S will 
 be turned from it j but juft the contrary will 
 
 92 
 
ASTRONOMICAL ESSAYS. 
 
 9^ 
 
 happen, when the earth, by going half round the 
 fun, has arrived at the oppofite point in it's or- 
 bit. Hence the fun wiil not always be in the 
 equator, but at one time of the year it will appear 
 nearer to one of the poles, and at the oppofite 
 feafon it will appear nearer to the other. Here 
 then you find a caufe f )r the change of the fea- 
 fons ; for when the (an leaves the equator, and 
 approaches to one of the poles, it will be fum- 
 ner on that fide of the equator, and when the lun 
 departs from [hence, and approaches to the other 
 pole, it will be winter. 
 
 Thefc ideas may be ftrengthened, and a clearer 
 notion obtained of the effed produced by the 
 inclination of the earth's axis, by confidering 
 fig. 2, plate V, in which the elli;>/ts is fuppofed 
 to reprefent the earth's orbit, the eye fome- 
 what elevated above the plane thereof. The 
 earth is here rcprefented in the firft point of each 
 of the 12 figns of the ecliptic, as marked in the 
 figure with the 12 corrcfponding months an- 
 nexed ; P the nortn pole of the globe, P m it'* 
 axis, round which the earth performs it's diur- 
 nal revolution from weft to eaft ; this axis is ex- 
 hibited as parallel to itfelf in every part of the 
 orbit J P C £ (hews the angle of it's inclination, 
 e the pole, e d the axis of the ecliptic, perpendi- 
 cular to the plane of the orbit. 
 
 In Marfb, when the earth is in the firfl point 
 P 93 
 
94 ASTRONOMICAL ESSAYS. 
 
 oi Libra, the fun appears in the oppofite point 
 of the ecliptic at Aries. In September, when the 
 earth is in the firft point oi Aries, the fun will be 
 in Libra. At thefe times the terminator pafTes 
 through the poles of the world, and divides every 
 parallel into two equal parts, (fee c, fig. i,) con- 
 fequently the ncdlurnal and diurnal arches, or 
 the length of day and night, will be equal in all 
 places over ^he world. 
 
 Conceive the earth to have moved from Libra 
 to Capricorn in June, the axis P m preferving 
 it's parallelifm by this motion, the north pole 
 will have gradually advanced into the enlighten- 
 ed hemifphere ; fo that the whole northern po- 
 lar circle will be therein, ■while the fouthern 
 polo is immerged in obfcurity ; the northern 
 parts of the world will enjoy long days, while 
 they are fliort in the fouthern parts. While the 
 earth is moving from Libra through Capricorn to 
 Aries, the north pole remains in the illuminated 
 hemifphere, and will therefore have fix months 
 continual day. 
 
 But in the other half year, while the earth is 
 moving from Aries through Cancer to Libra, the 
 north pole is turned from the fun, and therefore 
 in darknefs, but the fouth pole is in the il- 
 luminated hemifphere. When the earth is at 
 Cancer, the fun is at Capricorn ; at this feafon 
 the nights to us will as much exceed the days, 
 
 •94 
 
ASTRONOMICAL ESSAYS. 
 
 95 
 
 as the days exceeded the nights, when the earth 
 was in the oppofite point of her orbir. 
 
 From the foregoing explanation it is eafy to 
 perceive, that the inhabitants of the fouthern 
 hemifphere have the fame viciffitudes with thofe 
 of the northern, though not at the fame time, it 
 being winter in one hemifphere, when it is fum- 
 mer in the other. 
 
 From what has been faid, you mud have per- 
 ceived, that during the courfe of the earth through 
 her orbit, theie are four days particularly to 
 be remarked ; thefe aftronoraers have diilin- 
 guiHied by the names oHht foljlitial and equinoc- 
 tial d^^s. The fohlitial days are thofe on which 
 the fun appears moft to the northward and the 
 fouthward : the equinodial days are thofe on 
 which he appears in the equator, and the days 
 are equal to the nights. 
 
 The annual motion of the earth occafions a 
 daily apparent change in the declination of the 
 fun. Thus about the 22d of December, when 
 the earth is in Cancer, the fun will be over the 
 tropic of Capricorn ; and confequently by the 
 earth's rotation on it's axis, the inhabitants of 
 every part of this circle will fucceffively have 
 the fun in their zenith, or in other words, 
 he will be vertical to them that day at noon. 
 
 About the 2iftof March, the earth is at 
 Libra, and the fun will then appear in Aries ; 
 a central folar ray will terminate upon the fur'- 
 95 
 
9^ ASTRONOMICAL ESSAYS. 
 
 face of the earth, in the equator ; and therefore 
 the fun appears to be carried round in the celef- 
 tial equator, and is fucceflively verticz^l to thofe 
 who live under that circle. 
 
 About the 21ft of June, when the earth is in 
 Capricorn, a central folar ray terminates on the 
 furfaceof the earth, in the northern tropic, and 
 for that day the (un appears to be carried round 
 in the tropic of Cancer, and is vertical to thofe 
 who live under that circle. About the 22nd of 
 September, the earth is in Aries, and the fun in 
 Libra, and the central folar ray again terminates 
 at the equator ; confequently the lun again ap- 
 pears in the celeftial equator, and is vertical to 
 thofe who live under it. 
 
 We have feen, that as the fun moves in the 
 ecliptic, from the vernal equinox to the tropic 
 of Cancer, it gets to the north of the equator, 
 or it's declination towards our pole increafes. 
 Therefore, from the vernal equinox, when the 
 days and nights are equal, till the fun comes to 
 the tropic of Cancer, our days lengthen, and 
 our nights fhorten ; but when the fun comes to 
 the tropic of Cancer, it is. then in it*s utmoft 
 northern limit, and returns in the ecliptic to 
 the equator again. During this return of the 
 fun, it*s declination towards our pole de- 
 creafes, and confequently the days dccreafe, 
 and the nights increafe, till the fun is arrived 
 in the equator again, and is in the autumnal 
 95 
 
ASTRONOMICAL ESSAYS. ^7 
 
 equinoctial point, when the days and nights 
 will again be equal. As the fun moves from 
 thence towards the tropic of Clapricorn, it 
 gets to the fouth of the equator ; or it's decli- 
 narion towards the fouth pole increafes. There- 
 fore, at that time of year, our days fhorten, 
 and our nights lengthen, till the fun arrives at 
 the tropic ot Capricorn ; but when the fun is 
 arrived there, it is then at it's urmoft fouthern 
 limit, and returns in the ecliptic to the eqja- 
 tor again. During this return, it's diftance from 
 our pole leffens, and confequently the days will 
 lengthen, as the nights will fliorren, till they 
 become equal, when the fun is come round to 
 the vernal equino^ial point. 
 
 Our fummer is nearly eight Hays longer than 
 the winter. By fummer is meant here the 
 time that pafles between the vernal and autum- 
 nal equinoxes ; by winter, the time between 
 the autumnal and vernal equinox. 1 he eclip- 
 tic is divided into fix northern, and fix fourhern 
 figns, and interfeds the equator at the firft of 
 Aries, and the firft of Libra. In our fummer, 
 the fun's apparent motion is through the fix 
 northern, and in winter through the fix fouth- 
 ern figns ; yet the fun is i86 days, 1 1 hours, 51 
 minutes, in pafling through the fix firft ; and 
 Only 178 days, 17 hours, 58 minutes, in paiTing 
 through the fix laft. Their difference, 7 days, 
 
 97 
 
gS ASTRONOMICAL ESSAYS. 
 
 ly hours, 53 minutes, is the length of time by 
 which our lummer exceeds the winter. 
 
 In fig. I, plate VI, AB C D reprefents the 
 earth's orbit ; S the fun in one of its foci ; 
 when the earth is at B, the fun appears at H, 
 in the firfl point of Aries ; and whilfb the earth 
 moves from B through C to D, the fun appears 
 to run through the fix northern figns, from T 
 through c5 to =:. at F. When the earth is at 
 D, the fun appears at F, in the firfl: point of 
 Libra ; and as the earth moves from D through 
 A to B, the fun appears to move through the fix 
 fouthern figns, from =2= through vs to Aries at H. 
 
 Hence the line FH, drawn from the firfl 
 point of Aries through the fun at S. to the firfl 
 point of :i=, divides the ecliptic into two equal 
 parts ; but the fame line divides the earth's 
 elliptical orbit into two unequal parts. The 
 greater part B C D is that which the earth de- 
 fcribes in the fummer, while the fun appears in 
 the northern figns. The leffer part is DAB, 
 which the earth defcribes in winter, while the 
 fun appears in the fouthern figns. C, the earth's 
 aphelion, where it moves flowefl, is in the 
 greater part ; A, it's perihelion, is in the leffer 
 part, where the fun moves fafleft. 
 
 There are, therefore two reafons why our 
 fummer is longer than our winter ; firfl, be- 
 caufe the fun continues in the northern figns, 
 while the earth is defcribing the greater part 
 
 98 
 
ASTRONOMICAL ESSAYS. 99 
 
 of it*s orbit; and fecondly, becaufe the fun's 
 apparent motion is flower while it appears in the 
 northern figns, than whilft it appears in the 
 fouthern ones. 
 
 The fun's apparent diameter is greater in 
 our winter than in fummer, becaufe the earth 
 is nearer to the fun when at A in the winter, 
 than it is when at C in the fummer. The fun's 
 apparent diameter, in winter, is 32 minutes, 47 
 feconds ; in fummer, 31 minutes, 40 feconds. 
 
 But if the earth is farther from the fun in 
 fummer than in winter, it may be afked, why 
 our winters are fo much colder than our fum- 
 mers. To this it may be anfwered, that our 
 fummer is hotter than the winter, firfl:, on ac- 
 count of the greater height to which the fun 
 rifes above our horizon in the fummer : fecond- 
 ly, the greater length of our days. The fun is 
 much higher at noon in fummer than in win- 
 ter, and confequently, as it's rays in fummer 
 are lefs oblique than in winter, more of them 
 will fall upon the furface of the earth. In the 
 fummer, the days are very long, and the nights 
 very (hort ; therefore the earth and air are heated 
 by the fun in the day-time, more than they are 
 cooled in the night ; and upon this account, the 
 heat will keep increafing in the fummer, and for 
 the fame reafon will decreafe in wioter, when 
 the nights lengthen. 
 
 99 
 
 
lOO ASTRONOM^ICAL ESSAVS. 
 
 I fhould exceed the limits of this eflay, iff 
 were to enquire into the feveral concurring" 
 caufes of the temperatures that obtain in various 
 climates ; it may be lufBcient, therefore, to ob- 
 ferve what a remarkable provifion is made in the 
 world, and the feveral part:, of it, to keep up a 
 perpetual change in the degrees of heat and 
 cold. Ihefe two are antagonifts, or, as Lord 
 Bacon calls them, the very hands of nature with 
 which jhe chiefly workeih ; the one expanding, 
 the other contrading bodies, fo as to maintain 
 an ofcillatory motion in all their parts ; and f(5 
 ferviceable are thefe changes in the natural 
 worki, that they are promoted every year, every 
 hour, every moment. From the oblique pofi- 
 tion of the ecliptic, the earth continually pre- 
 fents a different face to the fun, and never re- 
 ceives his rays two days together in the fame 
 direftion. In the day and night, the differences 
 are fo obvious, that they need not be mentioned, 
 though they are mofl remarkable in thofe cli- 
 mates, where the fun at his fetting makes the 
 greateft angle with the horizon. Every hour of^ 
 the day, the heat varies with the fun's altitude, 
 is altered by the interpofition of clouds, and the 
 action of winds ; and there is little room to 
 doubt, but what the various changes that thuff 
 take place, concur in producing many of the 
 fmaller and greater phenomena of nature. 
 
 Be this however as it may, it is certain that 
 
 lOO 
 
ASTRONOMICAL ESSAYS. IQl 
 
 the various irregularities and intemperature of 
 the elements, which feem to defiroy nature in 
 one feafon, ferve to revive it in another : the 
 immoderate heats' of fummer, and the excef- 
 five, cold of winter, prepare the beauties of the 
 fpring, and the rich fruits of autumn. Thefe 
 viciffitudes, which feem to fuperficial minds 
 the effedls of a fortuitous concourfc of irregular 
 caufes, are regulated according to weight and 
 meafure, by that sovereign wisdom, who weighs 
 the earth as a grain of /and, thefea as a drop of 
 water. 
 
 Of Solar and Siderial Time. 
 
 I have already fhewn, that the daily motion 
 of the fun from eafl to weft, is not a real, but 
 an apparent one, which is owing to the rotation 
 of the earth round it's axis. Now if the fun 
 had no other motion but this apparent one, it 
 would feem to go once round the earth, in the 
 time of one complete rotation, or in 23 hours, 
 c,6 minutes ; which is the cafe with any of the 
 fixed ftars, and is therefore the length of a 
 ftderial day. But the fun is found to take up 
 a longer time to complete it's apparent revolu- 
 tion ; for if it is in the fouth of any particular 
 place at twelve o'clock at noon to-day, it will 
 not complete an apparent revolution, fo as to 
 return to the fouth of that place again, till 
 Q^ 101 
 
102 ASTRONOMICAL ESSAYS. 
 
 twelve o'clock at noon on the next day, and 
 confequently the time of this apparent revolu- 
 tion is twenty-four hours. 
 
 Let us endeavour to render this fubje£t 
 clearer, by defining in other words the nature 
 of the folar and fiderial day. 
 
 The folar day is that fpace of time which 
 intervenes between the fun's departing from 
 any one meridian, and it's return to the fame 
 circle again ; which fpace is alfo called a natu- 
 ral day ; or it is the time from the noon of one 
 day to the noon of the next. 
 
 T\\t fiderial day h the fpace of time which 
 happens between the departure of a ftar from, 
 and it's return to the fame meridian again. 
 
 I am now to fhevv why thefe dnys differ in 
 length, or why the time, that the fun takes up 
 to complete one revolution, is longer than the 
 time that the earth takes to revolve once upon 
 it's axis. 
 
 This difference arifes from the fun's annual 
 motion. For the fun does not continue always 
 in the fame place in the heaven, as the fixed 
 ftars do : but if it is feen at M, fig. 2, pi. IV, 
 one day, near the fixed flar R, it will have 
 fhifted it's place the next day, and will be near 
 to fome other fixed flar L. This motion of 
 the fun is from weft to eaft, and one entire re- 
 volution is completed in a year. Suppofe, 
 therefore, that the fun, when it is at-M, near 
 102 
 
ASTRONOMICAL ESSAYS. lO.Q 
 
 to the fixed ftar R, appears in the fouth of any 
 particular place S ; and then imagine the earth 
 to turn once round upon it's axis from weft to 
 enft, or in the diredion S T V W, fo thar the 
 place may be returned to the fame fituation ; 
 after this rotation is completed, the ftar R will 
 be in the fouth of the place as before ; but ihe 
 fun. having, in the meantime, moved call wards, 
 and being near to the ftar L, or to the eaft of 
 R, will not be in the fouth of the place S, but 
 to the eaftward of it : upon this account, the 
 place S muft move on a little farther, .and muft 
 come to T before it will be even with the fun 
 again, or before the fun will appear exactly in 
 the fouth. 
 
 This may be illuftrated by an inftance. 
 The two hands of a watch are clofe together, or 
 even with one another at twelve ; they both 
 turn round the fame way, but the minute hand 
 turns round in a fliorter time than the hour 
 hand; when the minute hand has completed 
 one rotation, and is come round to twelve, the 
 hour hand will be before it, or will be at one ; 
 fo that the minute hand muft move more than 
 once round, in order to overtake the hour hand, 
 and be even with it a<rain. 
 
 As this fubjed is of fome importance, we 
 
 fliall endeavour to render it more clear, by 
 
 placing it in a different point of view : the 
 
 more fo, and it may accuftom the young pupil 
 
 103 
 
104 ASTRONOMICAL ESSAYS. 
 
 to reafon on both hypothefes, namelv, the mo- 
 tion of the fun, and that of the earth. 
 
 The diameter of the earth's orbit is'" but a 
 phyfical point in proportion to the diflancfe of 
 the ftars ; for which reafon, and the earth's 
 uniform motion of it's axis, any given meridian 
 will revolve from any ftar to the fame ftar 
 i^gain, in every abfolute turn of the earth upon 
 it's axis, without the leaft perceptible differ- 
 ence of time being fnewn by a clock which goes 
 exactly true. 
 
 If the earth had only a diurnal, without an 
 annual motion, any given meridian would re- 
 volve from the fun to the fun again, in the 
 fame quantity of time as from any flar to the 
 fame ilar. again j becaufe the fun would never 
 change his place with refped to the ftars. But 
 as the earth advances almofl a degree eaftward 
 in It's orbit, in the time that it turns eaft- 
 ward raund it's axis, whatever ftar pafles over 
 the meridian on any day with the fun, will 
 pafs over the fame meridian on tlie next day, 
 when the fun is almofl: a degree (liort of it, that 
 is, 3 min. 56 feconds fooner. If the year con- 
 tained only 360 days, the fun's apparent place, 
 fo far as his motion is equable, would change 
 a degree every day, aiid then the fiderial days 
 would be juft four minutes fiiorter than the 
 fqlar. 
 
 Let A B C D E F G H, fig. 3, plate IV, be 
 104 
 
ASTRONOMICAL ESSAYS. IO5 
 
 the earth's orbit, in which it goes round the 
 fun every year, according to the order of the 
 letters, that is, from weft to eafl, and turns 
 round it's axis the fame way, from the fun 
 to the fun again in every twenty-four hours. 
 Let S be the fun, and R a fixed frar, at fuch 
 an inimenfe difrance, that the diameter G G 
 of the earth's orbit bears no fenfible pro- 
 portion to that dirtance ; N m n the earth 
 in different points of it's orbit. Let N m be 
 any particular meridian of the earth, and N 
 a given point, or place, lying under that me- 
 ridian. 
 
 When the earth is at A, the fun S hides the 
 ftar R, which would always be hid if the earth 
 never moved from A ; and confequently as 
 the earth turns round it's axis, the point N 
 would always come round to the fun and the 
 liar at the fame time. 
 
 But when the earth has advanced through 
 an eighth p^rt of it's orbit, or from A to B, it's 
 motion round it's axis will bring the point 
 N an eighth part of a day, or three hours, 
 fooner to the (tar than to the fun. For the 
 ftar will come to the meridian in the fame 
 time as though the earth had continued in 
 it's former fituation at A, but the point N 
 mult revolve from N to N, before it can have 
 the fun upon it's meridian. The arc N n be- 
 ing therefore the fame part of a whole circle, 
 
 105 
 
106 ASTRONOMICAL ESSAYS. 
 
 as the arc A B, it is plain that any (lar which 
 comes to the meridian at noon, -wiih the fun, 
 when the earth is at A, will come to it at nine 
 o'clock in the forenoon, when the earth is at B. 
 When the earth has paffed from A to C, one- 
 fourth part of it's orbit, the point N will have 
 the ftar upon it*s meridian, or at fix in the 
 morning, fix hours fooner than it comes round 
 to the fun ; but the point N muft revolve 
 fix hours more before it has mid-day by the 
 fun : for now the angle A S D is a right angle, 
 and fo is N D n ; that is, the earth has ad- 
 vanced 90 degrees on it's axis, to carry the 
 point N from the ftar to the fun ; for the ftar 
 always comes to the meridian when N m is 
 parallel to R S A ; becaufe D S is but a point in 
 refpeft to R S. When the earth is at D, the 
 flar comes to the meridian at three in the morn- 
 ing at E, the earth having gone half round it's 
 orbit ; N points to the ftar at midnight, it be- 
 ing then diredly oppofite to the fun ; and, 
 therefore, by the earth's diurnal motion, the 
 ftar comes to the meridian tv/elve hours before 
 the fun, and then goes on, till at A it comes to 
 the meridian with the fun again. 
 
 Thus it is plain, that one abfolute revolu- 
 tion of the earth on it's axis (which is alw^ays . 
 completed when any particular ftar comes to 
 be parallel to it's fituation at any time of the 
 day before) never brings the fame meridian 
 106 
 
ASTRONOMICAL ESSAYS. IO7 
 
 round from the fun, to the fun again ; but 
 that the earth requires as much more than one 
 turn on it's axis, to finifli a natural day, as it 
 has gone forward in that time, which, at a mean 
 Aate, is a 365th part of a circle. 
 
 From hence we obtain a method of knowing 
 by the ftars, whether a clock goes true or not. 
 For if through a fmall hole in a window-fliut- 
 ter, or in a thin plate of metal fixed to a 
 window, we obferve at what time any ftar 
 difappears behind a chimney, or corner of a 
 houfe, at a little diflance ; and if the fame flar 
 difappears the next night, 3 rnin. ^6 feconds, 
 fooner by the clock ; and on the fecond, 7 
 minutes, 52 feconds fooner ; the third night, 
 1 1 minutes, 48 feconds fooner, and fo on every 
 night ; it is an infallible fign that the machine 
 goes true ; otherwife it does not, and mull; be 
 regulated accordingly. This method may be 
 depended on to nearly half a fecond. 
 
 An Explanation of the Phenomena which 
 
 ARISE FROM THE MoTION OF THE EarTH, 
 AND OF THE INFERIOR PlANETS, MeRCURY 
 
 AND Venus. 
 
 It will be neceflary in this place to define 
 more exadly feme words which have been 
 nightly explained before, and recall the read- 
 107 
 
108 ASTRONOMICAL ESSAYS. 
 
 er*s attention to fome definitions that have been 
 already given ; and it is prefumed, that thefe 
 repetitions will not be an objed of comphiint, 
 becaufe they will anfwer the beneficial purpofe 
 of grounding the reader more firmly in the 
 knowledge of the fcience, to which this eflay is 
 intended as an introdudlion. 
 
 When two planets are feen together in the 
 fame fign of che zodiac, and equally advanced 
 therein, they are faid to be in conjundion. But 
 when they are in oppofite figns of the zodiac, 
 they are faid to be in cppofjion. Thus a planet 
 is faid to be in oppofition to the fun, when the 
 earth is between the fun and the planet. 
 
 The elongation of a planet is it's apparent 
 diftance from the fun. When a planet is in 
 conjunclion with the fun, it has no elongation; 
 when in oppofition, it's elongation is 180 de- 
 grees. 
 
 The nodes of a -planet's orbit are thofe two 
 points where the orbit cuts the plane of the 
 ecliptic. I before obferved, that the orbits 
 of all the planets are inclined to the plane of 
 the ecliptic, and confequently crofs this plane. 
 In fig. 3, plate III, A B C D is the plane of the 
 ecliptic; EBFD is the orbit of a planet, in 
 which the points 3 and D are the two nodes. 
 
 The line of the nodes is a line B D, fuppofed 
 to be drawn through the fun from one node to 
 the other. The limits of a planet's orbit are 
 108 
 
ASTRONOMICAL ESSAYS. IO9 
 
 two points in the middle between the two nodes. 
 The point E is called the greateft northern 
 limit, F the greateft fouthern limit. 
 
 The greatefl dillance of the earth, or of any 
 planet from the fun, it called it's aphelion, or 
 higher apfis; it's lead diftance is called the peri- 
 helion, or lower aphs. 
 
 '1 hus in fig. 4, plate III, A is the place of the 
 aphelion, P that of the perihelion. 
 
 '1 he axis, P A, fig. 4, of any planet's ellipfis 
 is called the line of the apfides : the extreme 
 points of it's (horteft diameter T V are the places 
 of it's mean diftance from the fun, and S T, or 
 S V, the line of it's mean dijiance. 
 
 When a planet moves according to the order 
 of the figns, it's motion is faid to be dire6l, or 
 in confequentia ; but when it's motion is contrary 
 to the order of the figns, it is faid to be retrograde, 
 or in anttcedentia. 
 
 The place in the flarry heavens that any 
 planet appears in, when feen from the center of 
 the earth, is called it's geocentric place. The 
 place where it would be feen in the celeflial 
 fphere, by an obferver fuppofed to be in the fun, 
 is called it's heliocentric place. 
 
 R 109 
 
110 ASTRONOMICAL ESSAYS. 
 
 Of the Conjunctions and Elongations of 
 THE inferior Planets, Venus and Mer- 
 
 CURY. 
 
 There are two different fituations, In which 
 an inferior planet will appear in conjundlion with 
 the fun ; one when the planet is between the fun 
 and the earth, the other when the fun is between 
 the earth and the planet. Let A, fig. 2, plate 
 VI, be the earth in it's orbit, E the place of 
 Venus in her orbit E U G, S the fun, I' VFqR 
 TD an arc in the Aarry heavens. In this ntua- 
 tion the fun and Vtnus are on the lame fide of 
 the earth, and will apj-ear in the fame point of 
 the heavens, fo as to be in conjundion. If the 
 earth is at A, and Venus at G, they W'ill alfo 
 appear to be in conjunction. 
 
 If the earth is at A, the fun at S, the planet 
 at E, nearer to the earih than the fun, it is called 
 it's inferior conjuncl'.on. But if the earth is at 
 A, and the planet at G, farther from the earth 
 than the fun, this is called xhQ fuperior conjunc- 
 tion of the planet. 
 
 If an inferior planet is at E, the earth at A, 
 and the fun at S, the elongation is nothing, the 
 planet being then in it's inferior conjunction. 
 As the planet moves from E to y, it's elongation 
 increafes ; for when it is at y, it appears in the 
 line A y P, while the fun appears in the line 
 1 10 
 
ASTRONOMICAL ESSAYS. Ill 
 
 A S Q^; fo that P A Q^ will be it's elongation. 
 When the planet is arrived at x, it appears in 
 the line Ax V^, which is a tangent to it*s orbit ; 
 and then it's elongation is V A C^, which is the 
 greatefl that can be on ihat fide the fun ; for 
 after this, the elongation decreafes. When the 
 planet is at K, it's elongation is P A Q^; when 
 at G, it is nothing, becaufe it is then in ii's fu- 
 perior conjun(ilion ; as the planet moves on 
 from G, it's elongation again increafes ; for 
 when it comes to C, it appears in the line 
 A C R, and it's elongation is R A (^ When 
 the planet comes to H, a line drawn from the 
 earth through the planet is a tangent to the 
 orbit, and the elongation is T A O, the greatefl 
 it can have when it is on the other fide of the 
 fun ; for after this, the elongation again de- 
 creafes. 
 
 Hence it is clear, that the inferior planets 
 can never appear far from the fun, but muft 
 always accompany it in it's apparent motion 
 through the ecliptic. When we fee either 
 Venus or Mercury, it is either in the evening 
 in the weft, foon after the fun has fet ; or in 
 a morning, a little before the fun rifes. Ve- 
 nus is indeed bright enough fometimes to be 
 feen in the day time,- but then fhe is never far 
 from the fun. The greateft elongation of 
 Venus is about 40, and of Mercury about ^^ 
 degrees. 
 
 Ill 
 
Hi. ASTRONOMICAL ESSAYS. 
 
 If the earth is at A, fig. 2, plate VII, when 
 Venus appears in any part of the arc E x G, (he 
 is weftward from the fun, and therefore rifes be- 
 fore him in the morning, and is called the 
 viorning Jlar, When file appears any-where 
 in the arc G H E, flie is eaflward from the fun, 
 and therefore fcts after him ; is feen in the 
 evening, and is then the evening Jiar. 
 
 From the apparent motions of the inferior 
 planets, we derive an argument to prove the 
 fajfih of the Ptolemaic fyjlem. If the earth was 
 within the orbit of Venus, as the Ptolemaic 
 fyflem fuppofes, flie might be fometimes on 
 one fide of the earth, whilfl: the fun is on the 
 oppofite fide ; or Venus might be fometimes in 
 oppofition to the fun ; but Venus is never feen 
 in oppofition. Therefore the earth is on the 
 outfide of the orbit of Venus, and confequently 
 the Ptolemaic fyflem is not true. The fame is 
 alfo true of Mercury. But this, and feme other 
 circumflances relative to the motions of thefe 
 planets, will be better underflood by a planeta- 
 rium than by any diagram. 
 
 Of the retrograde, direct, akd station- 
 ary Motions of Venus and Mercury. 
 
 It is eafy to explain thefe motions on the 
 Copernican fyflem, it being the natural refult 
 of the refpeftive fituations and motions of the 
 
 I J2 
 
ASTRONOMICAL ESSAYS. 
 
 ^13 
 
 earth and thefe planets. But on the Ptolemaic 
 fyftem they are inexplicable, without calling in 
 ^the aid of a very complicated hypothecs. 
 
 When the inferior planets are pafling from 
 their greatefl: elongation, on one fide of the fun, 
 through their fuperior conjan(5lion, to their 
 greatefl elongation on the other fide, their motion, 
 as viewed from the earth, is dired. In order to 
 explain this propofition, we (hall firfl: fuppofe 
 the earth to be at reft at A, fig. 2, pi. VII ; and 
 corred this fuppofition afterwards, by fiiewing 
 that the apparent motion of Venus, or Mercury, 
 feen from the earth, is the fame in this refpea-, 
 whether the earth moves in it's orbit, or refts 
 at A. 
 
 The propofition to be explained is this ; 
 that as Venus, for inllance, moves from x, it's 
 greateft elongation on one fide of the fun, 
 through G '\t\ fuperior conjundion, to H it's 
 greate'l elongatioii on the other fide, it will ap- 
 pear to a fpeftator upon the earth, to move 
 from weft to eaft according to the order of 
 the figns ; that is, it's geocentric motion will be 
 direft. 
 
 The planets move round the fun from weft 
 to eaft, and confequently if there was a fpeda- 
 tor at the fun, they would appear to him to 
 move through the zodiac, according to the 
 order of the figns ; or in other words, the heli- 
 ocentric motion of Venus is diredl. Now if 
 
114 ASTRONOMICAL ESSAYS. 
 
 the fun and the earth A, are both on the fame 
 fide of the planet, a fpedator at the earth is in 
 the fame fituation, with refpedt to the planet and 
 it*s motion, as if hs had been at the fun : for 
 whilfl: the planet is moving from x, through G, 
 to H, a fpedator either at A or S is on the con- 
 cave fide of the planet's orbit ; and confequent- 
 ly the planet will appear to move in the fame 
 manner from either ; but the apparent motion 
 of the planet, when feen from the fun, is dire6ly 
 and confequsntly it's motion, when feen from 
 the earth, will alfo be direct. 
 
 For when Venus is at x, it appears to a 
 fpedator on the earth at A, to be in the line 
 Ax V, oris feen among the (tars at V; when 
 Venus has moved to K, it is feen among the 
 fixed ftars at P ; when it has moved to G, it 
 is in it's fuperior conjunction j when it has 
 moved to C, it appears among the fixed flars 
 at R ; and when it is come to K, it appears 
 among the fixed ftars at T. Thus whilft: 
 Venus has moved in it's orbit from x, it's 
 greatefl: elongation on one fide of the fun, 
 through G it's fuperior conjunflion, to H it's 
 ' greatefl: elongation on the other fide, it appears 
 to have defcribed the arc VPQ^RT in the 
 concave fphere of the heavens j but the letters 
 X K G C H lie from weft to eaft, becaufe they 
 lie in the fame direction that the planet moves 
 round the fun J and the letters VPQ^RT lie 
 
 H4 
 
ASTRONOMICAL ESSAYS. 
 
 1^5 
 
 in the fame diredlion with x K G C H. There- 
 fore, as the planet feems to a fpedator on the 
 earth, to defcribe the arc V P Q^R T, it's appa- 
 rent motion, feen from the earth, is dired, or 
 from wefl to eaft. 
 
 The fccond propofition is this ; that while 
 the inferior planets move from their greateft 
 elongation on one fide of the fun, through their 
 inferior conjundion, to their greateft elonga- 
 tion on the other fide, their geocentric motion is 
 retrograde. 
 
 In other words, whilft Venus is moving from 
 it*s greateft elongation H, plate VII, fig. 3, 
 through it's inferior conjundion E, to it's other 
 greateft elongation x, it appears to a fpedator 
 upon the earth at A, to move backwards, or 
 from eaft to weft, contrary to the order of the 
 figns. 
 
 A fpedator at the fun is on the concave fide 
 of the planet's orbit, viewing it from within fide. 
 But whilft Venus is moving from it's greateft: 
 elongation H on one fide, through E it's infe- 
 rior conjundion, to X it's greateft elongation on 
 the other fide, a fpedator upon the earth is on 
 the convex fide of it's orbit, viewing it from 
 without. 
 
 Therefore, if a fpe£lator at the fun S would 
 fee the planet move one way, a fpedator at 
 the earth A will fee it move the contrary way ; 
 or the geocentric motion will be contrary to 
 
Il5 ASTRONOMICAL ESSAYS. 
 
 it's helioceniric motion, and therefore retro- 
 grade ; for as feen from. the fun, it's motion is 
 always dired. 
 
 That two fpeclators, one at the earth, the 
 other at the fun, as they are on contrary fides 
 of the arc H E x, will fee the planet apparently 
 move contrary ways, rnay be rendered more 
 plain by the following familiar confideration. 
 If two men (land with their faces towards each 
 other, and a ball is rolled along upon the 
 ground, this ball will move from the right hand 
 of one of the men towards his left, and from 
 the left hand of the other towards his right. 
 In like manner, if one man is at the earth A, 
 and the other at the fun S, then vvhilfl: the 
 planet is defcribing the arc Hex which is 
 between them, it will appear to move from 
 the right hand of the man at S towards his left, 
 and from the left hand of the man at A towards 
 his right. 
 
 Whill: the motion of Venus is direft, or 
 while it is defcribing the arc x G H, it appears 
 to move from V to T, among the fixed ftars. 
 But after it has been carried in it's orbit from 
 H to Q^, it appears in the line A z R, and is 
 ieen among the fixed ftars at R. When it 
 comes to E, it appears at C^; and when at y, 
 it's apparent place in the heavens is at P. Thus 
 as the planet pafles from it's greateft elongation 
 H on one fide of the fun, through it's inferior 
 
 ii6 
 
ASTRONOMICAL ESSAYS. II7 
 
 junction E, t'> it's greatefl: elongation x on the 
 other fide, it apparently runs back from T to V, 
 or it's motion is retrograde. 
 
 Our third propofition is, that Venu> hjiati' 
 o?:ary, or h:i5 no apparent motion for fome time, 
 when it is at itVs greatefl elongation ; that is, 
 vh:n it is at H or x, and it's apparent place is 
 either at 'I' or V. 
 
 When either of the inferior planets, Venus 
 for inflance, is at it's greateft elongation H 
 or X, a line drawn from the earth through the 
 planet, as A H T, or A x V, is a tangent to 
 the orbit. Now though a light line touches a 
 circle but in one point, yet fome part of the 
 circle greater than a point is fo near to the tan- 
 gent, as not to be diflinguiflied from it. Thus 
 the arc b d f o nearly coincides with the tan- 
 gent A H T, that a fpeftator's eye placed at A, 
 could not diflinguifli the tangent from this part 
 of the curve. Confequently, while the planet 
 is defcribing this arc, no other change will be 
 made in it's geocentric place, than if it was to 
 move in the tangent. 
 
 But the geocentric place of the planet 
 would not be altered, if the planet was to move 
 in the tangent. For if it was to move from T 
 towards A, or from A to V, the apparent place 
 of it in the heavens would in one cafe be at T, 
 in the other cafe at V. Therefore, while the 
 planet is at it's greatefl elongation, and is 
 S 117 
 
Il8 ASTRONOMICAL ESSAYS. 
 
 dcfcriblng a fmall arc in it's orbit, that nearly 
 coincides with the tangent, it's geocentric place 
 does not alter, but it appears to conllnue for fomc 
 time in the fame part of the heavens^ or is Jla- 
 tionary. 
 
 1 have hitherto fuppofed the earth to be at 
 reft, and upon that fiippofition have explained 
 the progrcjfs and regrefs, the conjunftions and 
 fLiitions of the inferior planets. If this fuppo- 
 fition was true, V r, or the arc which the pla- 
 Dct at any ti;ne defcribes in it's progrefs, and T 
 V, the arc which it dcfcribes in it's regrefs, 
 would always be in the fiinie part of the hea- 
 vens. The planet, when in conjunclion, would 
 always appear at Q^among the fame fixed ftars ; 
 and at it's elongation, or when it is flationary, 
 it would always appear among the fame fixed 
 flars at T on one fide of the fun, and at V on the 
 other fide. 
 
 But this fuppofition is not true ; for the 
 earth revolves in it's orbit ABO round the 
 fun. Now if the earth is at A, at the time of 
 either conjunction, the planet at this conjunc- 
 tion would appear among the fixed liars at Q^, 
 and the arcs of the greateft elongation Q^V 
 and QJl\ would be on each fide of thofe ftars. 
 But if the earth is at B, at the time of either 
 of the conjunftions, then at the time of this 
 conjuncl'on, the planet will appear in the line 
 BST, and be feen among the fixed fiars at T, 
 
 ii8 
 
ASTRONOMICAL ESSAYS. 1 I9 
 
 and the arcs of the greateft elongation will be 
 on each fide of thefe ftars ; that is, the conjunc- 
 tions and elongations will happen in a difiVrent 
 part of the heavens, when the earth is at B, 
 from what they happen when the earth is at A. 
 In other refpects, the foregoing phenomena will 
 be much the fame, notwithftanding the motion 
 of the earth, only the planet will be more direct 
 in the fartheft part of the orbit, and lefs retro- 
 grade in the neareft. 
 
 The inferior planets always appear very 
 near the fun ; but by the motion of the earth in 
 it's orbit, the fun appears in different parts 
 of the heavens, in different times of the year. 
 Therefore the inferior planets, as they are 
 always very near the fun, will alfo appear in 
 different parts of the heavens, at different times 
 of the year. And confequently their conjunc- 
 tions and greateft: elongations will fometimes 
 happen when they are in one part of the heavens, 
 and fometimes vi'hcn they are In another part- 
 Venus, feen from the earth, will appear to vi- 
 brate in an arc V T, half of which is on one 
 fide of the fun's apparent place, and half on the 
 other fide. 
 
 V/hen an inferior planet, viewed from a fu- 
 perior, moves apparently retrograde, the fuperi- 
 or planet has alfo an apparently retrograde 
 motion. 
 
 When a fuperior planet, viewed from an 
 119 
 
1.20 AST RON O MICA L ESSAYS. 
 
 inferior, appears flationary, the ir:r:;rior p'.^net 
 viewed at the fame time from the luperior, is 
 alfo flationary. 
 
 Of the Phases of Venus. 
 
 That the planets are all opake or dark bo- 
 dies, anrd confequenily fliine only by the light 
 they receive from the fun, is plain, becaufe they 
 are not vifible when they are in fuch parts of 
 their orbits as are between the fun and earth, 
 that is, when their illuminated fide is turned 
 from us. 
 
 The fun enlightens only half a planet at 
 once; the illuminated hemifphere is always 
 that which is turned towards the fun, the other 
 hemifphere of the planet is dark. To fpeak 
 with accuracy, the fun being larger than any 
 of the planets, will illuminate rather more 
 than half; but this difference, on account of 
 the great diftance of the fun from any of the 
 planets, is fo fmall, that it's light may be con- 
 fidered as coming to them in lines phyfically 
 parallel. 
 
 Like other opake bodies, they call a flia- 
 dow behind them, which is always oppofue to 
 the fun. The line in the planet's body, which 
 diftinguifiies the lucid from the obfcure part, 
 appears foiuetimcs (trait, fometimes crooked. 
 The convex part of the curve is fometimes 
 
ASTRONOMICAL ESSAYS. 121 
 
 towards the Tplendid, and the concave towards 
 that which is obfeure, and vice \ crfa, according 
 to the fitua'^ion of the eye with refped: to the 
 planet, and of the fun whicli enlightens the 
 planet. 
 
 . Hence the inferior planets going round 
 the fun in Icfs orbits than our earth does, will 
 fometimes have more, fometimes lefs of their 
 illuminated fide towards us ; and as it is the 
 illuminated part only which is vifible to us. 
 Mercury and Venus will, through a good tele- 
 fcope, exhibit the feveral appearances of the 
 moon, from a fine thin crefcent to the enlight- 
 ened hcmifphere. 
 
 If we view Venus through a telefcope, 
 when flie follows the fun's rays on the eaftern 
 fide, and appears above the horizon after fun- 
 fet, we fliall fee her appear nearly round, and 
 but fmall ; fhe is at that time beyond the fun, 
 and prefents to us an enlightened hemifphere. 
 As file departs from the fun towards the eaR> 
 ihe augments in her apparent fize ; and on 
 viewing her through a telefcope, is feen to alter 
 her figure, abating of her apparent roundnefs, 
 and appearing fucceffively like the moon, in the 
 different ftages of her decreafe. At length, 
 when flic is at her greateft elongation, /lie is 
 like the moon in her firft quarter, and appears 
 as (lie does when from a full, fhe has decreafed 
 to a half moon. 
 
 121 
 
122 ASTRONOMICAL ESSAYS. 
 
 After this, as flie approaclies Cin appear- 
 ance) to the fun, flie appears concave in her 
 illuminated part, as the moon when (lie forms 
 a crefcent ; thus fhe continues till fhe is hid 
 entirely in the fun's rays, and prefents to us 
 her whole dark hemifphere, as the moon does 
 in her conjundiou, no part of the planet being 
 then vifible. 
 
 When flie departs out of the fun*s rays on 
 the weftern fide, we fee her in the morning, 
 jufl before day-break. It is in this fituation 
 that Venus is called the morning flar, as in the 
 other flie is called the evening ftar. She at 
 this time appears very beautiful, like a fine 
 thin crefcent : jufl a verge of filver light is 
 feen on her edge. From this period flie grows 
 more and more enlightened every day, till flie 
 is arrived at her greateil digreflion or elonga- 
 tion, when flie again appears as a half moon, or 
 as the moon in her firfl; quarter ; from this 
 time, if continued to be viewed with a tele- 
 fcope, fhe is found to be more and more enlight- 
 ened, though flie is all the while decrcafing in 
 magnitude, and thus continues growing fmaller 
 and rounder, till fhe is again hid or loft in the 
 fun's rays. 
 
 Fig. I, plate VII, reprefents the orbits of 
 Venus and the earth, with the fun in the cen- 
 ter of them. The planet Venus in drawn in 
 eight different fituations, with it's illuminated 
 
 123 
 
ASTRONOMICAL ESSAYS. 1 23 
 
 hemifpheres towards the fun. If we fuppofe 
 the earth to be at T, when Venus is at A, her 
 dark hemifphere is towards the earth, and (he 
 is therefore invifible, except the conjunclion 
 happens in her node, for then fhe appears like 
 a dark fpot upon the diflc of the fun. When 
 Venus is at B, a little of her enlightened fide 
 is turned towards the earth, and therefore fhe 
 appears fharp-horned ; when (lie is at C, half 
 her enlightened hemifphere is turned towards 
 the earth, and flie appears like an half moon ; 
 at D, more than half her enlightened hemi- 
 fphere is towards us, and fhe appears like the 
 moon about three days before it is full ; 
 at E, the whole enlightened hemifphere is to- 
 wards the earth, Venus is then either behind 
 the fun, or fo very near him, that fhe can 
 hardly be feen ; but if fhe could, flie would 
 appear round, like the full moon. At F fhe 
 is like the moon three days after the full ; at 
 G like a half moon again ; at H like a crefcent, 
 with the points of the horn turned the contrary 
 way to what they were at B. All this is equally 
 applicable to Mercury. 
 
 Fig. 2, plate VIII, exhibits the different 
 appearances of Venus, correfponding to her 
 feveral fituations in the foregoing figure ; thus 
 when Venus is at A, fig. i, flie is quite dark, as 
 at A, fig. 2 ; when fhe is at B, fig. i, fhe ap- 
 pears as at B, fig. 2, &c. 
 123 
 
124 ASTROiNOMlCAL ESSAYS. 
 
 The inferior plar.ets do not fliine brighteft 
 when they are full ; thus Venus dr,es not appear 
 brighteft in her fuperior conjundion, though 
 her illuminated hernifphere be then turned 
 towards us. Her fplendor is more diminilhed 
 by her being at a greater dillance from us, 
 than the confpicuous part of her illuminated 
 difk is increafed. Dr. H alley has iliewn, 
 that Venus is brighteft when hsr elongation 
 from the fun is but 4c". Mercury is in his 
 greateft brightnefs, when very near his utmoft 
 elongation. 
 
 Of THE SUPERIOR PlANETS. 
 
 I have already obferved, that the greateft 
 elongation of either of the inferior planets is 
 lefs than 90', or a quarter of a circle j fo that 
 they are never far from the fun, but conftantly 
 attend it. But the fuperior planets do not 
 always accompany the fun, as I have fhewn 
 that the inferior ones do ; they are indeed 
 fometimes in conjun£lion with it, but then 
 they are alfo fometimes in oppofition to, or 180" 
 from it. 
 
 Let S, fig. 3, plate VI, be the fun ; A B C D 
 the orbit of any fuperior planet, Mars, for in- 
 ilance ; E F G the earth's orbit. If the earth 
 be at E, the fun at S, and the planet at D, the 
 fun and the planet will be both on the fame 
 124 
 
ASTRONOMICAL ESSAYS. 
 
 125 
 
 fide of the earth ; and confequently the planet 
 will appear in conjunaim with the fun. But 
 as the orbit of the earth is between the fun and 
 the orbit of the fuperior planet, it is poffible 
 for the earth to be between the fun and the 
 planet, and confequently for the planet and the 
 fun to be on oppofite fides of the earth, or the 
 planet to be In oppofition ; thus, if when the 
 earth is at E, Mars be at A, he is then in oppofi^ 
 tion to the fun. 
 
 A fuperior planet is in quadrature with the 
 fun, when it's geocentric place is 90" from the 
 geocentric place of the fun. If the earth be at 
 E, and Mars at B or C, he is in quadrature with 
 the fun J for the lines A E, E B, form a right 
 angle, as do alfo the lines E A, E C. 
 
 Of the direct, stationary, and retro- 
 grade Motion of the superior Planets. 
 
 As the earth goes round the fun in lefs 
 time, and in a lefs orbit than any of the fupe- 
 rior planets, it will not be amifs to fuppofe a 
 fuperior planet to ftand flill in fome part of it's 
 orbit, while the earth goes once round the fun 
 in her's, and confider the appearances the pla- 
 nets would then have, which are thefe : i. 
 While the earth is in her moft diftant femi- 
 clrcle, the apparent motion of the planet would 
 be direa, 2. While the earth is in her neareft 
 
 T 125 
 
126 ASTRONOMICAL ESSAYS, 
 
 femicircle, the planet would be retrograde, 3, 
 While the earth is near the poinds of contaft 
 of a line drawn from the planet, fo as to be a 
 tangent to the earth's orbit, the planet would 
 hejiationary. 
 
 To illudrate this, let A B C D E F G H, 
 plare VII, fig. i, be the orbit of the earth, S the 
 fun, PQ^OV the orbit of Mars, L M N T an 
 arc of the ecliptic. Let us now fuppofe the 
 planet Mars to continue at P, while the earth 
 goes round in her orbit, according to the order 
 of the letters A B G, &c. A B C D E F H G 
 may be confidered as fo many (tations, from 
 whence an inhabitant of the earth would view 
 Mars at different times of the year ; and if ilrait 
 lines be drawn from each of thefe (lations, 
 through Mars at- P, and be continued to the e- 
 cliptic, they will point out the apparent place of 
 Mars, at thefe diiTerent ftations. 
 
 Thus fuDpofing the earth at A, the planet 
 will be feen among the (lars at L ; when the 
 earth is arrived at B, the planet will appear at 
 M ; and in the fame manner when at C D and 
 E, it will be {ten among the (lars at N R T ; 
 therefore, while the earth moves over the large 
 part of the orbit A B C D E, the planet will 
 have an apparent motion from L to T, and this 
 motion is from we/i to eaji, or the fame way 
 with the earth ; and the planet is faid to move 
 dired, or according to the order of the figns. 
 126 
 
ASTRONOMICAL ESSAYS. 127 
 
 When the earth is near to A and E, the point 
 of contad of the tangent to the earth's orbit, 
 the planet will be Jiationary for a fhort fpace of 
 time. 
 
 When thd earth moves from E to H, the 
 planet feems to return from T to N ; but while 
 it moves from H to A, it will appear to move ia 
 a contrary direQion, and thus be retrograde 
 from N to L, where it will again ht Jiationary : 
 and fince the part of the orbit which the earth 
 defcribes in parting from A to E, is much grea- 
 ter than the part E H P, though the Ipace '1 L 
 which the planet defcribes in diredl and retro- 
 grade motion is the fame, the dired motion 
 from L to T muft be much flower than the retro- 
 grade motion from T to L. 
 
 When the earth is at C, a line drawn from 
 C through S and P to the ecliptic, (hews that 
 Mars is then in conjun6tion with the fun. But 
 when the earth is at H, a line drawn from H 
 through P, and continued to the ecliptic, would 
 terminate in a point oppofite to S ; therefore in 
 this fituation Mars would be in oppofition to the 
 fun. Thus it appears that the motion of Mars 
 is dired when in conjundion, and retrograde 
 when in oppofition. 
 
 The retrograde motions of the fuperior 
 planets happen oftener, the flower their mo- 
 tions are ; as the retrograde motions of the in- 
 ferior planets happen oftener, the fwifter their 
 127 
 
128 ASTRONOMICAL ESSAYS. 
 
 angular motions. Becaufe the retrograde mo- 
 tions of the iup.rior planets depend upon the 
 motions of the earth ; but thofe of the inferior 
 on their own angular motion. A fupeiior 
 one is retrograde once in each revolution of 
 the earth; an inferior one in every revolution 
 of it's own. 
 
 Other Phenomena of the superior 
 Planets. 
 
 The fuperlor planets are fometimes nearer 
 the earth than at other times ; they alfo appear 
 larger, or fmaller, according to their different 
 diftances from us. Thus fuppofe the earth to 
 be ar C ; if Mars be at P, he is the whole dia- 
 meter of the earth's orbit nearer to us than if 
 he were at V, and confequently his difK mu(l 
 appear larger at V than it would be at P. In 
 other places, the diftances of Mars from the 
 earth are intermediate. 
 
 The diameter of the earth's orbit bears a 
 greater ratio ro the diameter of the orbit of 
 Mars, than it does to the diameter of the orbit 
 of Jupiter ; and a greater to that of Jupiter, 
 than of Saturn ; confequently the difference 
 between the greateft and lead apparent diame- 
 ters is greater in Mars than in Jupiter, and 
 greater in Jupiter than in Saturn. 
 
 The fuperior, like the inferior planets, do 
 not ahvays appear in the ecliptic, their orbits 
 
 128 
 
ASTRONOMICAL ESSAYS. 120 
 
 being inclined alfo to that of the earth ; one 
 half is therefore above the ecliptic, the other 
 half below it, nor are they ever feen in it but 
 when they are in their nodes. 
 
 They alfo move in an ellipfe. They are 
 fometimes nearer to, and fometimes further 
 from the earth. Their apparent diameter va- 
 ries according to the difference in their dif- 
 tance. 
 
 Of the Secondary Planets,or Satellites. 
 
 It has been already obferved, that four of 
 the primary planets, the Earth,- Jupiter, Saturn 
 and the Georgium Sidus, are, in their revolu' 
 tions round the fun, attended by fecondary 
 planets. ^ 
 
 As the moon turns round the earth en 
 h-ghtenincr our night, by refleding the light ih^ 
 receives from the fun, fo do the other fateUites 
 enlighten the planets to which they belong 
 and move round thofe planets at different pt 
 nods of time, proportioned to their feveral dif 
 tances ; and as the moon keeps company with 
 this earth, in it's annual revolution round the 
 fun, fo do they feverally accompany the planets 
 to which they belong in their feveral courfes 
 round that luminary. 
 
 I fhall fpeak here firfl: of the moon, which 
 of all the heavenly bodies, excepting the fun, is 
 129 
 
130 ASTRONOMICAL ESSAYS. 
 
 the mod fplendid and brilliant, the infeparable 
 companion and attendant of our earth. In 
 mythology (he was confidered as Luna, in the 
 heavens the radiant planet of the night, upon 
 earth as the chafte Diana, and as the tremen- 
 dous Hecate in Hell. 
 
 Of the Moon. 
 
 If we imagine the plane of the moon's or- 
 bit to be extended to the fphcre of the heaven, 
 it would mark therein a great circle, which 
 may be called the moon's apparent orbit ; be- 
 caufe the moon appears to the inhabitants of 
 the earth to move in that circle, through the 
 twelve figns of the zodiac, in a periodical 
 month. This pofition is illuflrated by the 
 following figure ; let E F G H I, fig. 3, plate 
 IX, be the orbit of the earth, S the fun, abed 
 the orbit of the moon, when the earth is at E : 
 let A B C D be a great circle in the fphere of 
 the heaven, in the fame plane with the moon's 
 orbit. The moon, by going round her orbit 
 according to the order of letters, appears to an 
 inhabitant of the earth to go round in the 
 great circle A B C D, according to the order 
 of thofe letters : for when the moon is at a, 
 feen from the earth at E, fhe appears at A ; 
 when the moon is got to b, fhe appears at B ; 
 when to c, fhe will appear at C 5 when arrived 
 
 130 
 
ASTRONOMICAL ESSAYS. I31 
 
 at d, {he will appear at D. It is true, when 
 the moon is at b, the vifual line drawn from 
 E, through the moon, terminates in L ; as it 
 does in M, when the moon is at d ; but the 
 lines L M and D B being parallel, and not 
 farther diftant from each other than the dif- 
 tance of the earth's orbit, are as to fenfe coin- 
 cident, their diftance meafured in the fphere 
 of the heaven being infenfible : for the fame 
 reafon, though the earth moves from E to F, 
 in the time that -the moon goes round her orbit, 
 fo that at the end of a periodical month the 
 moon will be at a, and is feen from the earth 
 at F, in the line F N ; the moon will, notwith- 
 (landing, appear at A, the lines FN and E A 
 being parallel, and as to fenfe coincident : in 
 like manner, in whatever part of her orbit the 
 earth is, as at H or I, the moon, by going round 
 in her orbit, will appear to an inhabitant of 
 the earth to go round in the great circle A B 
 C D. 
 
 The plane of the moon's orbit extended to 
 ^he heavens, cuts the ecliptic in two oppofite 
 points. 
 
 The two points where the moon*s apparent 
 orbit thus cuts the ecliptic, arc called the 
 vioon's nodes. 
 
 The point where the moon appears to crofs 
 the ecliptic, as flie goes into north latitude, is 
 called the moon's afcending node, of which 
 
132 ASTRONOMICAL ESSAYS. 
 
 fhis is the character ^ ; the point where 
 the moon goes into fouth latitude is her de- 
 fcending node, and is marked thus is ; the 
 moon's afcending node is olicii called the dra- 
 gon's head ; her defcending node the dragon's 
 tail. 
 
 The line of the moorC s node is a line drawn 
 from one node to the other. 
 
 The extremities of the line of the nodes 
 are not always directed towards the fame 
 points of the ecliptic, but continually fliift 
 their places from eafl; to weft, or contrary to 
 the order of the figns, performing an entire 
 revolution about the earth, in the fpace of 
 fomething lefs than nineteen years. 
 
 The moon appears in the ecliptic only 
 when Ihe is in one of her nodes ; in all other 
 parts of her orbit {he is either in north or fouth 
 latitude, fometimes nearer to, fometimes fur- 
 ther removed from the ecliptic, according as 
 fhe happens to be more or lefs diftant from the 
 nodes. 
 
 When the place, in which the moon ap- 
 pears to an inhabitant of the earth, is the fame 
 with the fun's place, fhe is faid to be in con- 
 jundion. When the moon's place is oppofite 
 to the fun's place, flie is faid to be in oppofi- 
 tion. When fhe is a quarter of a circle diflant 
 from the fun, flie is faid to be in quadrature. 
 
 132 
 
ASTRONOMICAL ESSAYS. I33 
 
 Both the corjiindlion and oppofition of the 
 moon are lermsd /yzigies. 
 
 The common lunar month, or the time 
 rhat pafles between any new moon and the 
 next that follows, is called a fpiodical months 
 or a lunation. '1 his month contains 29 days, 
 12 hours, 44 minutes, 3 feconds. 
 
 A pejiodic ?no!itbh the time the moon takes 
 np to defer ibe her orbit ; or in other words, the 
 time in w'hich the moon performs one entire 
 revolution about the earth, from any point in 
 the zodiac to the fame again ; and contains 27 
 days, 7 hours, 43 minutes. 
 
 If the earth had no revolution round the 
 fun, or the fun had no apparent motion in the 
 ecliptic, the periodical and fynodical month 
 would be the fame ; but as this is not the cafe, 
 the moon takes up a longer time to pafs from 
 one conjundion to the next, than to defcribe 
 it's whole orbit ; or the time between one new 
 moon and the next, is longer than the moon's 
 periodical time. 
 
 The moon revolves round the earth from 
 weft to eaft, and the fun apparently revolves 
 round the earth the fame way. Now at the 
 new moon, or when the fun and moon ar6 in 
 conjundion, they both fet out from the fame 
 place, to move the fame way round the earth ; 
 but the moon moves much fafler than the fun, 
 and confequently v/ill overtake it ; and when 
 
 u 133 
 
134 ASTRONOMICAL ESSAYS. 
 
 the moon does overtake it. it will be a new 
 moon again. If the fun had no apparent mo- 
 tion in the eclipiic, the moon would come up 
 to it, or be in conjun£lion again, after it had 
 gone once round in it's orbit ; but as the fun 
 moves forward in the ecliptic, whilft the moon 
 is going round, the moon mufl move a little 
 more than once round, before it comes even 
 with the fun, or before it comes to conjunction. 
 Hence it is that the time between one conjunc- 
 tion and the next in fucceflion, is fomething 
 more than the time the moon takes up to go 
 once round it's orbit ; or a fynodical month is 
 longer than a periodical one. 
 
 In fig. 3, plate VIII, let S be the fun, C F 
 a part of the earth's orbit, M D a diameter o 
 the moon's orbit when the earth is at A, and 
 m d another diameter parallel to the former, 
 when the earth is at B. Whili'l the earth is at 
 A, if the moon be at D, flie will be in con- 
 jundlion ; and if the earth was to continue at 
 A, when the moon had gone once round it's 
 orbit, from D through M, fo as to return to D 
 ao-ain, it would again be in conjundion. There- 
 fore, upon the fuppofition that the earth has 
 no motion in it's orbit, the periodical and fy- 
 nodical months would be equal to one another. 
 But as the earth does not continue at A, it 
 will move forward in it's orbit, during the 
 revolution of the moon from A to B j and as 
 
 134 
 
ASTRONOMICAL ESSAYS. 135 
 
 the moon's orbit moves with it, the diameter 
 M D will then be in the pofition m d ; there- 
 fore, when the moon his defcribed it's orbit, 
 it will be at d in this diameter md; but if the 
 moon is at d, and the fun at S, the moon will 
 not be in conjundion, confequently the pe- 
 riodical month is completed before the fynodi- 
 cal. The moon, in order to come to conjunc- 
 tion, when the earth is at B, mud be at e, in 
 the diameter e f ; or befides going once round 
 it's orbit, it mufl: alfo defcribe the arc d e. 
 The fynodical month is therefore longer than 
 the periodical, by the time the moon takes up 
 to defcribe the arc d e. 
 
 This may alfo be explained in another 
 manner, by confidering tlie apparent motion of 
 the fun ; a view of the fubjeil, that may render 
 it more eafy to fome young minds than the 
 foregoing. Thus let us fuppofe the earth at rell 
 at E, fig. 4, plate VUl, M the moon in con- 
 junftion with the fun at S, while the moon de- 
 fcribes her orbit ABC about the earth at E, let 
 the fun advance by his apparent annual mo- 
 tion from S to D. It is plain that the moon will 
 not come in conjunftion with the fun again, 
 till, befides defcribing her orbit, flie hath de- 
 fcribed, over and above, the arc M F corref- 
 ponding to the arc S D. 
 
 ^35 
 
136 ASTRONOMICAL ESSAYS. 
 
 Of the Phases of the Moon. 
 
 As the moon goes round the earth in a 
 much fmaller orbit than that in which the 
 earth revolves round the fun, fomeiimes more, 
 fometimes lef=;, and fometimes no part of her 
 enliwi-htened half will be towards us ; hence fhe 
 is inceflantly varying her appearance ; fome- 
 times (lie looks full upon us, and her vifage 
 is all luflre; fometimes fhs (hews only half 
 her enlightened face, foon fhe appears as a ra- 
 diant crefcent, in a little time all her brightnefs 
 vanifhes, and flie becomes a beamlefs orb. 
 
 The full moon, or oppofition, is that ftate 
 in v^'hich her whole difk is enlightened, and 
 we fee it all bright, and of a circular figure. 
 The new moon is when fhe is in conjunction 
 with the fun ; in this flate, the whole furface 
 turned towards us is dark, and is therefore in- 
 vifible to us. 
 
 The firfl quarter of the moon fhe appears 
 in the form of a femicircle, whofe circumfe- 
 rence is turned towards the weft. At the lafl 
 quarter, fhe appears again under the form of 
 a femicircle, but with the circumference turn- 
 ed towards the eaft. 
 
 Thefe phafes may be illuftrated in a very 
 pleafing manner to the pupil, by expofing an 
 ivory ball to the fun, in a variety of pofitions, 
 
 136 
 
ASTRONOMICAL ESSAYS. I37 
 
 by which it may prefent a greater or fmaller 
 part of it*s illuminated furface to the obferver. 
 If it be held nearly in oppofition, fo that the 
 eye of the obferver may be almoft immediately 
 between it and the fun, the greateft part of the 
 enlii^hrened fide will be feen ; but if it be moved 
 in a circular orbit, towards the fun, the vifible 
 enlightened part will gradually decreafe, and at 
 lad diiappear, when the ball is held direftly to- 
 wards the fu;i. Or to apply the experiment 
 more immediately to our purpofe ; if the ball, at 
 any time when the fun and moon are both vifi- 
 ble, be held diredly between the eye of the ob- 
 ferver an J the moon, that part of the ball on 
 which the fun (hines, will appear exactly of the 
 fame figure as the moon itfelf. 
 
 The phafes of the moon, like thofe of Ve- 
 nus, may alfo be illuftrated by a diagram ; thus 
 in fig. I, plate IX, let S be the fun, T the 
 earth, ABCDEFGHthe orbit of the moon. 
 The firll obfervation to be deduced from this 
 figure, is, that the half of the earth and moon, 
 which is towards the fun, is wholly enlightened 
 by it ; and the other half, which is turned 
 from it, is totally dark. When the moon 
 is in conjundion vi^ith the fun at A, her en- 
 lightened hemifphere is turned towards the 
 fun, and the dark one towards the earth ; in 
 which cafe we cannot fee her, and it is faid to 
 
 137 
 
138 ASTRONOMICAL ESSAYS. 
 
 be new moon. When the moon has moved 
 from A to B, a fmall portion a b of her enlight- 
 ened hemifphere will be turned towards the 
 earth ; which portion will appear of the form 
 reprefented at B, fig. 2, plate XI, (a figure which 
 exhibits the phafes as they appear to us). 
 
 As the moon proceeds in her orbit, accord- 
 ing to the order of the letters, more and more 
 of her enlighteae;.l part is turned towards the 
 earth. When fhe arrives at C, in which pofi- 
 tion Ihe is faid to be in quadrature, one half of 
 that part towards the earth is enlightened, ap- 
 pearing as at C among the phafes ; this appear- 
 ance is called a half moon. When fhe comes to 
 D, the greatefl: part of that half which is towards . 
 us is enlightened ; the moon is then faid to be 
 gibbous, and of that figure which is feen at D, in 
 fig. 2. 
 
 When the moon comes to F, (he is in oppo- 
 fition to the fun, and confequenuly turns all her 
 illuminated furface towards the earth, and fhines 
 with a full face, for which reafon (he is called a 
 full moon. As (he pafles through the other half 
 of her orbit, from E by F G, and H to A again, 
 fhe puts on the fame phafes as before, but in a 
 contrary order or pofition. 
 
 As the moon, by refledled light from the fun, 
 illuminates the earth, fo the earth does more 
 than repay her kindnefs, in enlightening the 
 
 «38 
 
ASTRONOMICAL ESSAYS. l^g 
 
 furface of the moon, by the fun's reflex light, 
 which fhe diifufes more abundantly upon the 
 moon, than the moon does upon us ; for the 
 furface of the earth is confidcrably greater than 
 that of the moon, and confequently, if both 
 bodies refled; light in proportion to their fize, 
 the earth will reflect much more light upon the 
 moon, than it receives from it. 
 
 In new moon, the illuminated fide of the 
 earth is fully turned towards the moon, and 
 the Lunarians will have a full earth, as we, in a 
 fjmilar pofirion have a full moon. And from 
 thence arifes that dim light which is obferved in 
 the old and new moons, whereby, befides the 
 bright and fliining horns, we can perceive the 
 reft of her body behind them, though but dark 
 and oblcure. Now when the moon comes to be 
 in oppofition to the fun, the earth, feen from 
 the moon, will appear in conjundion with him, 
 and It's dark fide will be turned towards the 
 moon, in which pofition the earth will be invifi- 
 ble to the Lunarians ; after this, the earth will 
 appear to them as a crefcent. In a word, the 
 earth exhibits the fame appearance to the inhab- 
 itants of the moon, as the moon does to us. 
 
 The moon turns about it's own axis in the 
 fame time that it moves round the earth ; it is 
 on this account that (he always prefents nearly 
 the fame face to us : for by this motion round 
 
 J39 
 
140 ASTRONOMICAL ESSAYS. 
 
 her axis, flie turns jufl: fo much of her furface 
 conftantly towards us, as by her motion about 
 the earth would be turned from us. Ihis 
 motion about her axis is equable and uniform, 
 but that about the earth is unequal and irregular, 
 as being performed in an tllipfis ; confequently 
 the fame precife part of the moon's luriace can 
 never be (hewn conftantly to the earth ; which 
 is confirmed by a telefcope, by which we often 
 obferve a little fegment on the eaitern and weft- 
 ern limb, appear and difappear by turns, as if 
 her body librated to and fro; this phenomenon 
 is called the moon's Hbration. The lunar mo- 
 tions are fubjeft to feveral other irregularities, 
 which are fully difcufled in the larger works on 
 aftronomy. 
 
 Of the Satellites of Jupiter, Saturn, 
 
 AND THE GeORGIUM SiDUS. 
 
 The exiftence of all the fatellites, except the 
 moon, muft: have remained unknown, without 
 the afTiPcance of the telefcope. By the affillance 
 of this inftrument, Jupiter is found to be attend- 
 ed by four, Saturn by feven, and the Georgium 
 Sidus by two. 
 
 The fatellites are difting'uifhed according 
 to their places; into firft, fecond, &c. the 
 Jirji being that which is neareft the planet. 
 They revolve round their refpedive primaries 
 
 140 
 
ASTRONOMICAL ESSAYS. I4I 
 
 in elliptic orbits, the primary planets being 
 in the focus. 
 
 The planes of the orbits of the fecondary 
 planets produced, interfcd the heliocentric 
 orbits of their primaries in two oppofite points, 
 which are called their nodes. 
 
 Again, the planes of the orbits of the fatel- 
 lites produced, interfe£t the ecliptic in two 
 oppofite points ; thefe are called the geocen- 
 tric nodes of the fatellites. 
 
 The orbits of Jupiter's fatellites are nearly, 
 but not exaiftly, in the fame plane. This plane 
 produced makes an angle of about 3" with 
 Jupiter's orbit. The fecond deviates a little 
 from the reft. 
 
 The orbits of Saturn's fatellites, except 
 the 5th, which deviates from the reft feveral 
 degrees, are nearly in the fame plane. They 
 are nearly parallel to the plane of the equa- 
 tor. The orbit of the 5th fatelllte makes an 
 angle with the orbit of it's primary of 1 3 " 8'. 
 
 The fyftem of Jupiter and his fatellites is 
 very large in itfelf ; yet, on account of it's im- 
 menCe diflance from us, it appears to occupy 
 but a fmall fpace in the fphere of the ftarry 
 heavens, and confequently every fatellite of 
 Jupiter appears to us always near it's primary, 
 and to have an ofcillatory motiony like that of 
 a pendulum, going alternately from it's greateft 
 digreflion on one fide the planet, to it's greateft 
 X 141 
 
142 ASTRONOMICAL ESSAYS. 
 
 on the other, fometimes in a flralt line, at 
 oihers in an elliptic curve. 
 
 When a fatellite is in it's fuperior femicir- 
 cle, or that half of it's orbit that is more diftant 
 from the earth, it's motion appears clire£t to 
 us ; when a fatellite is in it's inferior femicir- 
 cle, neareft to the earth, the apparent motion 
 of it is retrograde. Both thefe motions feem 
 quickeft, when the fatellite is neareft the cen- 
 ter of the primary, and flower when they are 
 more diftant ; at the greateft diftance they ap- 
 pear ftationary for a fliort time. 
 
 The fatellites, and their primaries, mutually 
 eclipfeeach other, in the fame manner in which 
 it has been fliewn that the earth and the moon 
 do. But there are three cafes, in which the fa- 
 tellites difappear to us. 
 
 The one is, when the fatellite is dire£tly 
 beyond the body of it's primary, with refpe£l 
 to the ear'th ; this is called an occultaiion of the 
 planet. 
 
 Another Is, when it is direftly behind it's 
 primary, with refped to the fun^ and fo falls 
 into it's fhadow, and fufters an eclipfe, as the 
 moon, when the earth is interpofed between 
 that and the fun. 
 
 The laft is, when it is interpofed between 
 the earth and it's primary ; for then it cannot 
 be diftinguiflied from the primary itfelf. 
 142 
 
ASTRONOMICAL ESSAYS. I43 
 
 It is not often that a fatellite can be difcover- 
 ed upon thedifk of Jupiter, even by the bed lel- 
 efcopes, excepting at it's fir ft entrance, when, 
 by reafon of it's being more dircdly illuminated 
 by the rays of the fun, than the planet itlelf, it 
 appears like a lucid fpot upon it ; fometimes 
 however a fatellite is feen paiTing over the diik 
 like a dark fpot ; this has been attributed to fpots 
 on the furface of the fatellite, and that the more 
 probably as the fame fatellite has been known to 
 pafs over the dilk at one time as a dark fpot, and 
 at another time to be fo luminous, as only to be 
 diftinguiflied from the planet at it's ingrefs and 
 egrefs. The beginnings and endings of thefe 
 eclipfes are eafily feen by a telefcope, when the 
 planet is in a proper fituation ; but when it is 
 in conjundlion with the fun, the brightnefs of 
 that luminary renders both the planet and fatel- 
 lite invifible. 
 
 By obferving the eclipfes of Jupiter's fatel- 
 lites, it was difcovered that light is not propaga- 
 ted inftantaneoully, though it moves with an 
 incredible velocity ; fo that light reaches from 
 the fun to us in the fpace of eleven minutes of 
 time, at more than the rate of 100,000 miles in 
 a fecond. 
 
 The orbits of all the fatellites of Saturn, 
 except the fifth, are nearly in the fame plane, 
 which plane makes an angle v/ith that of Sa- 
 
 143 
 
144 ASTRONOMICAL ESSAYS. 
 
 turn's orbit, of about 31"; this inclination is fo 
 great, that they cannot pafs either acrofs Saturn 
 or behind it, with refped to the earth, except 
 when they are very near their nodes, fo that 
 their ecHpfes are not near fo frequent as thofe 
 of Jupiter. An occultation of the fourth behind 
 the body of Saturn has been obferved, and Caf- 
 fini once faw a ftar covered by the fouith fa- 
 teUite, fo that for 13 minutes they appeared as 
 one. 
 
 Of Eclipses. 
 
 Thofe phenomena, that are termed eclipfes, 
 where in former ages beheld with terror and 
 amazement, and looked upon as prodigies that 
 portended calamity and mifery to mankind. 
 Thefe fears, and the erroneous opinions which 
 produced them, had their fource in the hiero- 
 glyphical language of the firft inhabitants of the 
 earth. We do not, however, imagine that even 
 the mod ancient of thefe knew any more of the 
 laws and motions of the heavenly bodies, than 
 what could be djfcovered from immediate fight ; 
 or that they knew enough of the lunar fyitem 
 to calculate an eclipfe, or even that , they ever 
 attempted it. 
 
 The word eclipfe is derived from the Greel^, 
 and fignifies dereliction, a fainting away, or 
 fwooning. Now as the moon falls into the 
 144 
 
ASTRONOMI CAL ESSAYS. 14^ 
 
 lliadov/ of the earth, and is deprived of the fun's 
 enlivening rays, at the time of her greatell 
 brighmefs, and even appears pale and languid 
 before her obfcuration, lunar eclipfes were called 
 lun(2 laborcs, the flruggles or labours of the 
 moon ;• to relieve her from thefe imagined dif- 
 treffes, fuperftition adopted methods as impo- 
 tent as they were abfurd. 
 
 When the moon, by pafling between us and 
 the fun, deprived the earth of it's light and 
 heat, the inn. was thought to turn away his 
 face, as if in abhorrence of the crimes of man- 
 kind, and to threaten everlafling night and 
 deftrutflion to the world. But thanks to the 
 advancement of fcience, which, while it has 
 delivered us from the foolifh fears and idle ap- 
 prehenfions of the ancients, leaver us in poffef- 
 fion of their reprefentative knowledge, enables 
 us to explain the appearances on which it was 
 founded, and points out the perverfion and 
 abufe of it. 
 
 Any opake body, that is expofed to the light 
 of the fun, will cait a fliadow behind it. This 
 fhadow is a fpace deprived of light, into which 
 if another body comes, it cannot be feen for want 
 of light ; the body thus falling within tlie flia- 
 dow, is faid to be ecHpfed^ 
 , The earth and moon being opake bodir?, 
 and deriving their light from the fun, do each 
 of them call a fhadow behind, or towards the 
 hemifphere oppofed to the fun. Now when 
 
 M5 
 
145 ASTRONOMICAL ESSAYS, 
 
 either the moon or the earth pafTes through 
 the other's (hadow, it is thereby deprived of 
 illumination from the fun, and becomes invifi- 
 ble to a fpe£tator on the body from whence the 
 fhadow comes ; and fuch fpe£lator will ob- 
 ferve an eclipfc of the body which is paffing 
 through the fliadow ; while a fpedator on the 
 body which pafTes through the (hadow, will 
 obferve an eclipfe of the fun, being deprived of 
 his light. 
 
 Hence there mufl be three bodies concerned 
 in an eclipfe ; i. the luminous body ; 1. the opake 
 body that cafts the fhadow j and, 3. the body 
 involved in the fhadow. 
 
 Of Eclipses of the Moon. 
 
 As the earth is an opake body, enlightened 
 by the fun, it will caft a fhadow towards thofe 
 parts that are oppofite to the fun, and the axis 
 of this fhadow will always be in the plane of 
 the ecliptic, becaufe both the fun and the earth 
 are always there. 
 
 The fun and the earth are both fpherical 
 bodies ; if they were, therefore, of an equal fize, 
 the fhadow of the earth would be cylindrical, 
 as in in fig. 5, plate VIII; and would continue 
 of the fame breadth at all diftances from the 
 earth, and would confequently extend to an 
 infinite diftance, fo that Mars, Jupiter, or 
 Saturn, might be eclipfed by it j but as the 
 146 
 
ASTRONOMICAL ESSAYS. I47 
 
 planets are never eclipfed by the earth, this 
 is not the fliape of the fhadow, and confe- 
 quently the earth is not equal in fize to the 
 fun. 
 
 • 
 
 If the fun were Icfs than the earth, the fha- 
 dow would be wider the farther it was from the 
 earth, fee fig. 6, plate VIII, and would there- 
 fore reach to the orbits of Jupiter and Saturn, 
 and eclipfe any of thefe planets when the earth 
 came between the fun and them ; but the earth 
 never cclipfes them, therefore this is not the 
 fhape of it's fhadow, and confequently the fun 
 is not lefs than the earth. 
 
 As we have proved that the earth is neither 
 larger nor equal to the fun, we may fairly con- 
 clude that it is lefs ; and that the fhadow of the 
 earth is a cone, which ends in a point at fome 
 diftance from the earth, fee fig. 7, plate Vllt. 
 
 The axis of the earth's fhadow falls always 
 upon that point of the ecliptic that is oppofite 
 to the fun's geocentric place ; thus if the fun 
 be in the firft point of Aries, the axis of the 
 earth's fliadow will terminate in the firfl point 
 of Libra. It is clear, therefore, that there can 
 be no eclipfe of the moon but when the earth is 
 interpofed bct'ween it and the fun, that is, at the 
 time of it's oppofition, or when it is full ; for 
 unlefs it is oppofite to the fun, it never can be 
 in the earth's fhadow : and if the moon did 
 always move in the plane of the ecliptic, fhe 
 would every full moon pafs through the body 
 
 147 
 
148 ASTRONOMICAL ESSAYS. 
 
 of the fiiadow, and there would be a total 
 eclipfeofthe moon. 
 
 We have already obferved, that the moon's 
 orbit is inclined to the plane of the ecliptic, and 
 only coincides with it in two placer, which are 
 termed the nodes. It may therefore be full 
 moon * without her being in the plane of the 
 ecliptic ; fhe may be either on the north or the 
 ft)Uth iide of it ; in either of thefe cafes {he will 
 not enter into the {hadow, but be above it in the 
 one, below it in the other. 
 
 To illuftrate this, let H G, fig. i, plate X, 
 reprefent the orbit of the moon, EF the plane 
 of the ecliptic, in which the center of the 
 earth's fliadow always moves, and N the node 
 of the moon's orbit ; A B C D four places of 
 the (hadow of the earth in the ecliptic. When 
 the Ihadow is .at A, and the moon at I, there 
 will be no eclipfe : when the full moon is 
 nearer the node, as at K, only part of her globe 
 paffes through the fhadow, and that part be- 
 coming dark, it is called a partial eclipfe ; and 
 it is faid to be of fo many digits as there are 
 tivelfih -parti of the moon's diameter darken- 
 ed. W^'hen the full moon is at M, fhe enters 
 
 * A planet may be in oppofition to, or conjunftion with the 
 fun, without being in a right h'ne that pafles through the fun 
 and the earth. Aftronomers term it in conjunftion with the 
 fun, if it be in the fame part of the zodiac ; in oppcfition, if 
 it be in the part of a zodiac, i 80 ' from the fun. 
 
 148 
 
ASTRONOMICAL ESSAYS. I49 
 
 into the ffiadow C ; and paiTing through it, 
 becomes wholly darkened at L, and leaves the 
 fhadovv at O : as the whole body of the moon 
 is here immerfed in the fliade, this is called a 
 total eclipfe ; but when the moon's center pafles 
 through that of the (hadow, which can only 
 happen when fhe is at the node at N, it is 
 called a total and central eclipfe. There will 
 always be fuch eclipfes, when the center of the 
 moon and axis of the fhadow meet in the 
 nodes. 
 
 The duration of a central eclipfe is fo long, 
 as to let the moon go the length of three of it's 
 diameters totally eclipfed, which (lay in the 
 earth's Ihadow is computed to be about four 
 hours ; whereof the moon takes one hour, 
 from its beginning to enter the fliadow, till 
 quite immeri'ed therein ; two hours more (he 
 continues totally dark ; and the fourth hour is 
 taken up from her firfl: beginning to come ou^ 
 of ttie fiiadow, till fhe is quite out of it. 
 
 In the beginning of an eclipfe, the moon 
 enters the weilern part of the fliadow with the 
 eaftern part of her limb ; and in the end of it, 
 fhe leaves the eaflern part of the fliadow with 
 the weflern part of her limb. All the inter- 
 mediate time, from her entrance to her quit- 
 ting the fliadow, is reckoned into the eclipfe ; 
 but only fo much into the total immerfion, as 
 paffes while the moon is altogether obfcured. 
 Y 149 
 
150 ASTRONOMICAL ESSAYS. 
 
 From the magnitude of the fun, the fize of 
 the earth, their diftance from each other, the 
 retni6lion of the atmofphere, and the diftance 
 of the moon from the earth, it has been cal- 
 culated that the fhadow of the earth termi- 
 nates in a point, which does not reach fo far 
 as the moo!\'s orbit. The moon is not, there- 
 fore, echpfed by the fliadow of the earth alone. 
 1 he atmofphere, by refradling fome of the rays 
 of the fun, and refledling others, cafts a flia- 
 dow, though not fo dark a one as that which 
 arifes from an opake body : when, therefore, 
 we fav that the moon is ech'pfed, by palTrng 
 into the fliadow of the earth, it is to be under- 
 ftood of the fiiadow of the earth, together with 
 it's atmofphere. Hence it is that the moon 
 is vifible in eclipfes, th*? (hadow cafh by the 
 atmofphere not being fo dark as that caft by 
 the earth* The cone of this fliadow is larger 
 than the cone of the earth's fliadow, the bafe 
 thereof broader, the axis longer. There have 
 been eclipfes of the moon, in which the moon 
 has entirely difappeared : Hevelius mentions 
 one of this kind, which happened in Auguft 
 1647, when he was not able to diftinguiHi the 
 place of the moon, even with a good telefcope, 
 although the fky was fufliciently clear for him 
 to fee the flars of the fifth magnitude. 
 
 All opake bodies ; when illuminated by the 
 rays of the fun, caft a ftiadow from them, which' 
 
 150 
 
ASTRONOMICAL ESSAYS. 
 
 151 
 
 is encompafled by a penumbra, or thinner 
 fhadow, which every where furrounds the for- 
 mer, growing larger and larger as we recede 
 from the body : in other words, the penumbra 
 is all that ipace furrounding the fhadow, into 
 which the rays of light can only come from 
 fome part of that half of the globe of thj fun 
 which is turned towards the planet, all the rcll 
 being intercepted by the intervening body. 
 
 Let S, fig. 2, plate X, be the fun, E the 
 planet, then the penumbral cone is F G H. 
 The nearer any part of the penumbra is to the 
 fhadow, the lefs light it receives from the fun ; 
 but the further it is, the more it is enli^jhr- 
 ened ; thus the parts of the penumbra near M 
 are illuminated by thofe rays of light which 
 come from that part of the fun near to I, all 
 the red being intercepted by, the planet E. 
 In like manner, the parts about N can only 
 receive the light that comes from the part of 
 the fun near to L ; whereas the parts of the 
 penumbra at P and Q^ are enlightened in a 
 much fj;reater degree : for the planet intercepts 
 from P only thofe rays which come from the 
 fun near L, and hides from Q^onlv afmall part 
 of the fun near I. 
 
 The moon palTes through the penumbra 
 before fhe enters into the fliadow of the atmo- 
 fphere. Ihis caufes her gradually to lofe her 
 light, which is not fenfible at firft ; but as fhe 
 
 151 
 
152 ASTRONOMICAL ESSAYS. 
 
 goes into the darker part of the penumbra, 
 (he grows paler. The penumbra, where it is 
 contiguous to the fliadow, is fo dark, that it is 
 difficult to diltinguifli one from the orher. If 
 the atmofpherc be ferene, every ecHple of the 
 moon is vifible at the fame inflant to all the 
 inhabitants of that fide of the earth to which 
 flie is oppofite. 
 
 The moon in a total eclipfe, generally ap- 
 pears of a dufl^y reddifli colour, efpecially 
 towards the edges ; but of a darker towards 
 the middle of the ftiadow. 
 
 Of Eclipses of the Sun. 
 
 The moon, when in conjundion, if near 
 one of her nodes, will beinterpofed between us 
 and the fun, and will confequently hide the 
 fun, or a part of him, from us, and cads a flia- 
 dow upon the earth : this is called an edipfc of 
 the fun ; it may be either pariial or total. 
 
 An eclipfe of any lucid body is a deficiency 
 or diminution of light, which would otherwife 
 come from it to our eye, and is caufed by the 
 interpofition of fome opake body. 
 
 The eclipfes of the fun and moon, though 
 exprelTed by the fame word, are in nature very 
 different ; the fun, in reality, lofes nothing of 
 it's native luflre in the greateft eclipfes, but is 
 all the while incefiantly fending forth flreams 
 152 
 
ASTRONOMICAL ESSAYS. 153 
 
 of light every way round him, as ccpioufly as 
 before. Some of thefe ftreams are, however, 
 intercepted in their way towards our earth, by 
 the moon coming between the earth and the 
 fun :• and the moon having no light of her 
 own, and receiving none from the fun on that 
 half of the globe which is towards our eye, 
 mud appear dark, and make'fo much of the 
 fun's dilk appear fo, as is hid from us by her 
 interpofition. 
 
 What is called an eclipfe of the fun, is 
 therefore, in reality, an eclipfe of the earth, 
 which is deprived of the fun's light, by the 
 moon's coming between, and calling a fhadow 
 upon it. The earth being a globe, only that 
 half of it, which at any time is turned towards 
 the fun, can be enlightened by him at that 
 time ; it is upon fome part of this enlightened 
 half of the earth, that the moon's fliadow, or 
 penumbra, falls in a folar eclipfe. 
 
 The fun is always in the plane of the 
 ecliptic ; but the moon being inclined to this 
 plane, and only coinciding with it at the nodes, it 
 will not ^over either the whole or a part of the 
 fun ; or in other words, the fun will not be 
 cclipfed, unlefs the moon at that time is in or 
 near one of her nodes. 
 
 The moon, however, cannot be direftly be- 
 tween the fun and us, unlefs they are both in 
 the fame part of the heavens ; that is, unlefs 
 
 ^53 
 
1^4 ASTRONOMICAL ESSAYS. 
 
 they are in ccnjiin£lion. Therefore, the fun 
 can never be eclipfed but at the new moon, 
 nor even then, unlefs the moon at that time is 
 in or near one of her nodes. 
 
 From hence it is eafy to fhew, that the 
 darknefs of our Saviour* s crucifixion ivas not 
 owing to an eclipfe of the fun. For the cruci- 
 fixion happened at the time of t'-e Jewifh paii- 
 over, and the paflbver, by the appointment of 
 the law, was to be celebrated at the full moon j 
 the fun could not, therefore, be eclipfed at the 
 time of the paffover. Ar\ intelligent tutor will 
 find many opportunities of obierving to his 
 pupil, that nature, and philofophy, which ex- 
 plains the phenomena of nature, do always 
 agree with divine revelation. 
 
 The moon being much fmaller than the 
 earth, and having a conical fhadow, becaufe fhe 
 is lefs than the fun, can only cover a Imall jjart 
 of the earth by her fliadow ; though, as we 
 have obferved before, the whole body of the 
 moon may be involved in that of the earth. 
 Hence an eclipfe of the fun is vifible but to a 
 few inhabitants of the earth ; whereas an 
 €clipfe of the moon may be feen by all thofe 
 that are on that hemifphere which is turned 
 towards it. In other words, as the moon can 
 never totally eclipfe the earth, there will be 
 many parts of the globe that will fuffer no 
 eclipfe, though the fun be above their hori- 
 zon, 
 
 IS4 
 
ASTRONOMICAL ESSAYS. 
 
 ^55 
 
 An eclipfe of the fun always begins on the 
 weftern, and ends on the eaftern fide ; becaufe 
 the moon moving in her orbit from weft to eaft, 
 neceflarily firit arrives at and touches the fun's 
 weflern limb, and goes off at the eaftern. 
 
 It is not necelfary, in order to conftitute a 
 f^w/r^/ eclipfe of the fun, that the moon fliould 
 be exaftly in the line of the nodes, at the time 
 of it's conjundion ; for it is fufiicient to deno- 
 niinare an eclipfe of the fun central, that the 
 center of the moon be diredly between the 
 center of the fun, and the eye of the fpeftator ; 
 for to him, the fun is then centrally eclipfed. 
 But as the fliadow of the-moon can cover but 
 a fmall portion of the earth, it is obvious this 
 may happen when the moon is not in one of 
 her nodes. Further, the fun may be eclipfed 
 centrally, totally, partially, and not at all, at the 
 fame time. 
 
 A total eclipfe of the fun is a very curious 
 fpedacle : Clavius fays that, in that which he 
 obferved in Portugal, in 1650, the obfcurity 
 was greater, or more fenfible than that of the 
 night : the largeft ftars made their appearance 
 for about a minute or two, and the birds were 
 fo terrified, that they fell to the ground. 
 
 Thus in fig. 3, plate X, let A B C be the 
 fun, MN the moon, h 1 g part of the cone of 
 the moon's ftiadow, f d the penumbra of the 
 moon : from this figure it is eafy to perceive, 
 
 I. That thofe parts of the earth that are 
 
 J 55 
 
153 ASTRONOMICAL ESSAYS. 
 
 within the circle reprefented by gh, are cover- 
 ed by the fliadow of the moon, fo that no rays 
 can come from any part of the fun into that 
 circle, on account of the interpofition of the 
 moon. 
 
 2. In thofc parts of the earth where the pe- 
 numbra falls, only part of the fun is vifible ; 
 thus between d and g, the parts of the fun near 
 C cannot be feen, the rays coming from thence 
 towards d or g being intercepted by the moon ; 
 whereas at the fame time, the parts between f 
 and h are illuminated by rays coming from C, 
 but are deprived by the moon of fuch as come 
 from A. 
 
 3. The nearer any part of the earth, with- 
 in the penumbra, is to the fiiadow of the moon, 
 
 as in places near g, I, or h, the lefs portion of 
 the fun is vifible to it's inhabitants ; the nearer 
 it is to the outfide of the penumbra, as towards 
 d, e, or f, the greater portion of the fun may be 
 feen. 
 
 4. Oat of the penumbra, the entire difk of 
 the fan is vifible. 
 
 Of the Limits of Solar and Lunar 
 Eclipses. 
 
 The diftance of the moon in degrees and 
 minutes, above or below the ecliptic line, is 
 called her latitude. If flie be above the eclip- 
 
 .56 
 
ASTRONOMICAL ESSAYS. I57 
 
 tic, fhe is faid to have north ; if below it, fouth 
 latitude. 
 
 If the latitude at any time exceed the fum 
 of the femi-diameter of the moon, equal to 
 16-^ minutes, and the earth's fhadow equal to 
 45 1; minutes, the moon at that time cannot be 
 eclipled ; but will either pafs under or over the 
 fhadow, according as flie happens to be above 
 or below the ecliptic line. 
 
 The diftance from the node, either before 
 or after it, correfponding to the above extent, 
 is about I 2 degrees, which is confequently the 
 limit of lunar eclipfes : for when a full moon, 
 happens within 12 degrees of the nodes, fhe 
 will be eclipfed ; and the nearer to the nodes, 
 the greater will the eclipfe be. 
 
 If at the new moon, the latitude of the 
 moon exceeds the time of the femi-diameters 
 of the fun i64- min. and of the moon i6\ min. 
 we fliould fee no eclipfe of the fun from the 
 center of the earth. But as we view the lumi- 
 naries from the furface, which is much higher, 
 we are obliged to take in the femi-diameter of 
 the earth as feen from the moon. Then, if 
 the latitude of the moon be greater than the 
 fum of thefc three numbers, 94^ minutes, the 
 fun will not be eclipfed ; for the moon will 
 pafs either over or under his difk, according as 
 fhe is above or below the ecliptic line. The 
 diftance from the node on either lide agreeing 
 Z 157 
 
158 ASTRONOMICAL ESSAYS. 
 
 to the above ment'oned extent, is the 18 de- 
 grees, which is the utmofl limit of folar 
 eclipfes ; whence it follows, that if the fun 
 and moon, at the time of new moon, happen 
 to be within 18 degrees of the node, the fun 
 will be eclipfed. 
 
 Of the Period of Eclipses. 
 
 If the places of the moon's nodes were 
 fixed, eclipfes would always happen nearly at 
 the fame time of the year ; but as they have a 
 motion of about 3 min. 11 fee. every day 
 ■backwards, or contrary to the order of the 
 figns, the fucceeding eclipfe muff recede like- 
 wife ; and in one revolution of the nodes, 
 which is completed in 18 years, 224 days, 3 
 hours, they will revolve in a retrograde man- 
 ner through the year, and return to the fame 
 place again. 
 
 But there is a more correal period, called 
 the Chaldean Saros, which is 18 years, 11 days? 
 7 hours, 43 min. for in that time the fun and 
 moon advance jufl as far beyond a complete 
 direct revolution in the ecliptic, as the nodes 
 v/ant of completing their retrograde one : con- 
 fequently, as the fun and moon meet the nodes 
 at the end of that period, the fame folar and 
 lunar afpecls, which 'happened 18 years, 11 
 days, 7 hours, 43 min. ago, will return, and 
 
ASTRONOMICAL ESSAYS. 1 r^g 
 
 produce ecHpfes of both luminaries, for many 
 ages, the fame as before. 
 
 Of ancient aftronomieal obfervations much 
 has been faid, with very little foundation, bv 
 many modern writers : the oldeft ecliples of the 
 moon that Hipparchus could make any ufe of, 
 went no higher than the year before C!iii;l 721, 
 Whatever obfervations, therefore, the Chal- 
 deans had before this, were probably very rude 
 and imperfect.* 
 
 Of Parallax and Refraction. 
 
 Aflronomy is fubjecl to many difficulties, 
 befides thofe which are obvious to eveiy eye. 
 When we look at any ftar in the heavens, we 
 do not fee it in it's real place ; the fays coming 
 from it, when they pafs^ out of the purer 
 etherial medium, into our coarfer and more 
 denfe atmofphere, are refraded^ or bent in 
 fuch a manner, as to fluw the ftar hlnrh;:r 
 than it really is. Hence we fee all the flars 
 before they rife, and after they fet ; and never, 
 perhaps, fee any one in it's true place in the 
 heavens. There is another difference in tlie 
 apparent fituation of the heavenly bodies, 
 which arifes from the flations in which an ob- 
 ferver views them. This difference in fituation 
 is called the parallax of an objed. 
 
 * Coftard's Hiftory of Aftronomy. 
 
 ^S9 
 
l60 ASTRONOMICAL ESSAYS. 
 
 Of Parallax. 
 
 The parallax of any objed is the difference 
 between the places that the objett is referred 
 to in the celeftial fplierc, when feen at the 
 fame time from two different places wiihin 
 that fphere. Or, it is the angle under which 
 any two places in the inferior orbits are {ten 
 from a fuperior planet, or even the fixed 
 flars. 
 
 The parallaxes principally ufed by aftro- 
 nomers, are thofe which arife from confidering 
 the object as viewed from the centers of the 
 earth and the fun, from the furface and center 
 of the eaith, and from all three compounded. 
 
 The difference between the place of a 
 planet, as feen from the fun, and the fame as 
 feen from the earth, is called the parallax of 
 the annual orbit ; in other words, the angle at 
 any planet, fubtended between the fun and the 
 earth, is called the parallax of the earth's or 
 annual orbit. 
 
 The diurnal parallax is the change of the 
 apparent place of a fixed ftar, or planet, of any 
 celeflial body, arifmg from it's being viewed 
 on the furface, or from the center of the 
 earth. 
 
 The annual parallax of all the planets is 
 very confiderable, but that of the fixed ftars is 
 imperceptible. 
 
 160 
 
ASTRONOMICAL ESSAYS. i6i 
 
 The fixed flars have no diurnal parallax 
 the moon a confidtrable one ; that of the 
 planets is greater or kls, according lo their 
 diltances. 
 
 To explain the parallaxes with refpccl to 
 the earth only, let H S W, fig. 2, plate VII, 
 reprefent the earth, T the center thereof, 
 o R G part of the moon's orbit, Prg part of 
 a planet's orbit, Z a A part of the flarry hea- 
 vens. Now to a fpedator at S, upon tlie fr.r- 
 face of the earth, let the moon appear in G, 
 that is, in the fenfible horizon of S, and it will 
 be referred to A ; but if viewed from the cen- 
 ter T, it will be referred to the point D, which 
 is it's true place. 
 
 The arc A D will be the moon's parallax ; 
 theangleSGT the paralladic angle; or the 
 parallax is expreffed by the angle under which 
 the femi-diameter T S of the earth is feen from 
 the moon. 
 
 If the parallax be confidered with refped 
 to different planets, it will be greater or lefs as 
 thofe objeas are more or lefs diilant from the 
 earth ; thus the parallax A D of G i-? ^reater 
 than the parallax a d of g. 
 
 If it be confidered with refpecl to the fame 
 planet, it is evident that the horizontal parallax 
 (or the parallax when the cbjea h in the ho- 
 rizon) is greateft of all, and diminiHies gra- 
 dually, as the body rifes above the horizon, 
 161 
 
l62 ASTRONOMICAL ESSAYS. 
 
 until it comes to the zenith, where the parallax 
 vanifhes, or becomes equal to nothing. Thus 
 AD and a d, the horizontal parallaxes of G 
 and g, are greater than a B and a b, the pa- 
 rallaxes of R and r ; but the objedls O and P, 
 feen from S or T, appears in the fame place Z, 
 or the zenith. 
 
 By knowing the parallax of any celeflial 
 objeft, it's diftance from the center of the 
 earth may be eafily obtained by trigonometry. 
 Thus if the diftance of G from T be fought, in 
 the triangle S T G, ST being known, and the 
 angle S T G determined by obfervation, the 
 fide T G is thence known. 
 
 The parallax of the moon may be deter- 
 mined by two perfons obferving her from dif- 
 ferent ftations at the fame time ; fhe being 
 vertical to the one, and horizontal to the other. 
 It is generally concluded to be about 57'. 
 
 But the parallax mod wanted, is that of 
 the fun, whereby his abfolute didance from the 
 earth is known ; and hence the abfolute dif- 
 tances of all the other planets would be alfo 
 known, from the fecond Keplerian law. But 
 the parallax of the fun, or the angle under 
 which the femi-diameter of the earth would 
 appear at that diflance, is fo exceeding fmall, 
 that a midake of a fecond will caufe an error of 
 feveral millions of miles. 
 
 162 
 
• ASTRONOMICAL ESSAYS. 163 
 
 Of Refraction. 
 
 As one of the principal objefts of agrono- 
 my is to fix the fituari .n of the feveral heaven- 
 ly bodies, it is neceflT.iry, as a firft Oep, to under- 
 ftand the caufes which occafion a falfe appear- 
 ance of the place of f hofe objeds, and make us 
 fuppofe them in a different fituation from that 
 which they really have. Amonoj thefe caufes 
 refradion is to be reckoned. By this term is 
 meant the bending of the rays of light as they 
 pafs out of one medium into another. 
 
 The earth is every where furrounded by an 
 heterogeneous fluid, a mixture of air, vapour, 
 and terreftrial exhalations, that extend to the 
 regions of the flvy. '1 he rays of light from the 
 fun, moon, and (tars, in pafTing to a fpedator 
 upon earth, come through this medium, and are 
 fo refracted in their pnfiage through it, that their 
 apparent altitude is greater than their true alti- 
 tude. 
 
 Let A C, fig. 3, plate VII, reprefent the 
 furface of the earth, T it's center, B P a part 
 of the atmofphere, H E K the fphere of the 
 fixed ftars, A F the fenfible horizon, G a 
 planet, G D a ray of light proceeding from 
 the planet to D, where it enters our atmo- 
 fphere, and is rtfrafted towards the line D T, 
 163 
 
164 ASRTONOMICAL ESSAYS. 
 
 which is perpendicular to the furface of the 
 atmofphere ; and as the upper air is rarer than 
 that near the earth, the ray is continually en- 
 tering a denfer medium, and is every moment 
 bent towards T, which caufes it to defcribe a 
 curve, as D A, and to enter a fpectator's eye at 
 A, as if it came from E,apoinr above G. And 
 as an object always appears in that line in which 
 it enters the eye, the planet will appear at E, 
 higher than it''s true place, and frequently above 
 the horizon A F, when it's true place is below 
 it, at G. 
 
 This refraction is greateft at the horizon, 
 and decreafes very fad as the altitude in- 
 creafes, infomuch that the refradion at the 
 horizon differs from the refradlion at a very 
 few degrees above the horizon, by about one 
 third part of the v/hole quantity. At the ho- 
 rizon, in this climate, it is found to be about 
 33'. In climates nearer to the equator, where 
 the air is purer, the refraftion is lefs ; and in 
 the colder climates, nearer to the pole, it 
 increafes exceedingly, and is a happy provifion 
 for lengthening the appearance of the light at 
 thofe regions fo remote from the fun. Gaf- 
 fendus relates, that fome Hollanders, who 
 wintered in Nova Zembla, in latitude 75", 
 were furprized with a fight of the fun feven- 
 teen days before they expefted him in the 
 . horizon. This difference was owing to the 
 
 164 
 
ASTRONOMICAL ESSAYS. 165 
 
 refradlion of the atmofphere in that latitude. 
 To the fame caufe, together with the peculiar 
 obliquity of the moon's orbit to the ecliptic, 
 fome of thefe very northern regions are indebt- 
 ed for an uninterrupted light from the moon 
 much more than half the month, and fometirnes 
 almoil as long as it is capable of affording any 
 light to other parts of the earth. 
 
 Through this refraction we are favoured 
 with the fight of the fun about three minutes 
 and a quarter before it rifes above the horizon, 
 and alfo as much every evening after it fets 
 below it, which in one year amounts to more 
 than 40 hours. 
 
 It is to this property of refra£lion that we 
 are alfo indebted for that enjoyment of light 
 from the fun when he is below the horizon, 
 which produces the morning and evening 
 twilight. The fun's rays, in falling upon the 
 higher part of the atmofphere, are reflected 
 back to our eyes, and form a faint light, which 
 gradually augments till it becomes day. It is 
 owing to this, that the fun illuminates the 
 whole atmofphere at once : deprived of the at- 
 mofphere, he would have yielded no light, but 
 when our eyes weredirefted towards him ; and 
 even when he is in meridian fplendor, the 
 heavens would have appeared dark, and as full 
 of ftars as on a fine winter's night. The rays of 
 light would have come to us in ftrait lines, 
 A a 165 
 
l66 ASTRONOMICAL ESSAYS. 
 
 the appearance and difappearnnce of the fun 
 would have been inftanraneous ; we fhould 
 have had a fudden tranfition from the brightert: 
 fiin-fliine to the moft profound darknefs, and 
 from thick darknefs to a blaze of light. 'J hus 
 by refraOion we are prepared gradually for the 
 light of the fun, the duration of it's light is 
 prolonged, and the (hades of darknefs foft- 
 ened. 
 
 To it we muft attribute another curious 
 phenomenon, mentioned by Pliny ; for he re- 
 lates, that the moon had been eclipfed once in 
 the weft, at the fame time that the fun ap- 
 peared above the horizon in the ealh Mceflli- 
 rus, in Kepler, fpeaks of another iriftance of 
 the fame kind, which fell under his own ob- 
 fervation. 
 
 Of the Fixed Stars. 
 
 No part of the univerfe gives fuch enlarged 
 ideas of the lirufturc and magnificence of the 
 heavens, as the confideration of the number, 
 magnitude, and diftance of the fixed flars. 
 We admire indeed, with propriety, the vail 
 bulk of our own globe ; but when \vt confider 
 how much it is furpaffed by moft of the hea- 
 venly bodies, what a point it degenerates into, 
 and how little more even the vafl: orbit in 
 which it revolves would appear, when feen 
 i66 
 
ASTRONOMICAL ESSAYS. iSj 
 
 from feme of the fixed (lars, we begin to con- 
 ceive more juft ideas of the extent of the uni- 
 verfe, and of the boundaries of creation. 
 
 The nion: confpicuous and brightefl of the 
 fixed rtars of our horizon is Sirius. The earth, 
 in moving round the fun, is 190 millions of 
 miles nearer to this (lar in one part of it's orbit, 
 than in the oppofire ; yet the magnitude ot the 
 ftar does not appear to be in the lead altered, or 
 it's diftance affected by it; fo that the diftance 
 of the fixed flars is great beyond all compu- 
 tation. The unbounded fpace appears hlled, 
 at proper diilances, with tl.efe liars ; each of 
 which is probably a fun, with attendant pla- 
 nets rolling round it. In this view, what, 
 and how amazing, is the ftruclure of the uni- 
 verfe ! 
 
 Though the fixed flars are the only marks 
 by which aflronomers are enabled to judge of 
 the courfe of the moveable ones, and we have 
 alferted their relative pofitions do not vary ; 
 yet this affertion mufl: be confined within feme 
 limits ; for many of them are found to undergo 
 particular changes, and perhaps the whole are 
 liable to fome peculiar motion, which conne<^s 
 them with the univerfal fyftem of created na- 
 ture. Dr. Herfchel even goes fo far as to fup- 
 pofe, that there is not, in ftridnefs of fpeak- 
 ing, one fixed fiar in the heavens ; but that 
 there is a general motion of all the (tarry fyf- 
 167 
 
l68 ASTRONOMICAL ESSAYS. 
 
 terns, and confequently of the folar one, among 
 the reft. 
 
 There are fome ftars, whofe fituation and 
 place were heretofore known, and marked with 
 precifion, that are no longer to be feen : new 
 ones have alfo been difcovered, that were un- 
 known to the ancients, while numbers feeni 
 gradually to vanilh. There are others which 
 are found to have a periodical increafe and de- 
 creafe of magnitude ; and it is probable that 
 the inftances of thefe changes would have been 
 more numerous, if the ancients had polfcfled 
 the fame accurate means of examining the hea- 
 vens as are ufed at prefcnt. 
 
 New ftars offer to the mind a phenomenon 
 more furprizing, and lefs explicable, than al- 
 mofl any other in the fcience of aftronomy. I 
 {hall felect a few indances of the more remark- 
 able ones, for the inftrutlion ot the young pu- 
 pil : a confideration of the changes that take 
 place, at fo immenfe a diftance as the ftars are 
 known to be from him, may elevate his mind 
 to confider the immenfity of his power, who 
 regulates and governs all thele wide extended 
 motions ; " who hath meafured the waters in the 
 hollow of his hand, and nuted out heaven with a 
 /pan." 
 
 It was a new ftar difcovered by Hippar- 
 chus, the chief of the ancient aftronomers, 
 that induced him to compofe a catalogue of 
 
 :63 
 
ASTRONOMICAL ESSAYS. 169 
 
 the fixed ftars, that future obfervers mieht 
 learn from his labours, whether any of the 
 known (tars diiappeartd, or new ones were 
 produced. The iame motives engaged the il- 
 lulfrious Tycho Brahe to form, with unremit- 
 ting labour and afliduity, another new cata- 
 logue of the Itars. 
 
 Of new itars, the firfl: of which we have a 
 good account, is that which was difcovered in 
 the conlleliation Cailiopea, in the month of 
 November of the year 1572, a time when 
 aflronomy was fufficiently cultivated, to enable 
 the aitronomers to give the account with pre- 
 cifion. It remained vifible about fixteen months; 
 during this time, it kept it's place in the heav- 
 ens, without the lealf variation. It had all the 
 radiance ot the fixed ffars, and twinkltd like 
 them ; and was in all refpedls like Sijftis, except- 
 ing thiit it furpafifed it in brightnefs and magni- 
 tude. It appeared larger than Jupiter, who was 
 at that time in his perigee ; and v»as fcarce lefs 
 bright than Venus. 
 
 It was not by degrees that it acquired this 
 diameter, but (lione forth at once of it's full 
 lize and brightnefs, as if of inftantaneous crea- 
 tion. It continued about three weeks in full 
 and entire fplendor, during which time it 
 might be feen even at noon day, by thofe who 
 had good eyes, and knew where to look for it. 
 Biifore it had been feen a month, it became 
 169 
 
/ 
 
 lyO ASTRONOMICAL ESSAYS. 
 
 vifibly fmaller, and from thence continued di- 
 minifliing in magnitude till March, 1574, 
 when it entirely difappeared. As it dccreafed in 
 fize, it varied in colour ; at fin'l, it's light was 
 white, and extremely bright ; it then became 
 yeilowifh, afterwards of a ruddy colour, like 
 Mars; and fi lifhed with a pale livid white, 
 refembling that ot Saturn. 
 
 In Augufl 1596, Fabricius obferved a new 
 ftar in the neck of the Whale. In 163-', Pho- 
 cyllides Holwarda, obferved it again, and not 
 knowing that it had been feen before, took it 
 for a new difcovery : he watched it's place in 
 the heavens, and faw it appear again the fuc- 
 ceeding year, nine months after it's difappear- 
 ance. It has been fince found to be every year 
 very regular In it's period, except that in 1672 
 it was miffed by Hevelius, and not feen again 
 till 1676. Bullialdus determined the periodi- 
 cal time between this ftar's appearing in it's 
 greateft brightnefs, and returning to it again, 
 to be about 333 days ; obferving further, that 
 this ftar did not appear at once in it's full 
 magnitude and brightnefs, but by degrees ar- 
 rived at them. 
 
 Three changeable, or re-apparent Ifars 
 have been difcovered in the conftellation of 
 the Swan ; the firfl was feen by Janfonlus, in 
 1600 ; the fecond was difcovered in 1670 ; the 
 third by Kirchius, in 1686. 
 170 
 
ASTRONOMICAL ESSAYS. 171 
 
 In the latter end of Seprember, 1604, anew 
 ftar was dilcovered near the heel of the right 
 foot of Serpentarius. Kepler, in defcribing it, 
 fays, that it was precifely round, without any 
 kind of hair, or tail ; that it was exaftiy like 
 one of the (tars, except that in the vividnefs of 
 it's luil'-e, and the quicknefs of it's fparkling, 
 it exceeded ar.y thing he had ever feen before. 
 It was every moment changing into fome of 
 the colours of the rainbow, as yellow, orano-e 
 purple, and red ; thou jjh it was generally white, 
 when ir was at fome dillance from the vapours 
 of the horizon. Thofe in general who faw it, 
 agreed that it was larger than any other fixed 
 flar, or even any of the planets, except Venus : 
 it preferved it's luftre and fize for about three 
 weeks ; from this time it grew gradually fmall- 
 er. Kepler fuppofes that it difappeared fome 
 time between Oaober, 1605, and the February 
 following, but on what day is uncertain. 
 
 Befides thefe feveral re-apparent ftars, fo 
 well characterized and eftablifhed by the earli- 
 efl among the modern aftronomcrs, there have 
 been many difcovered fince, by CalTini, Maral- 
 di, and others; Mr. Montanere fpeaks of hav- 
 ing obferved above one hundred changes among 
 the fixed ftars. 
 
 The ftar Algol, in Medufa's head, has been 
 obferved long fince to appear of different mag- 
 nitudes, at difterent times. Ihe period of it 
 171 
 
172 ASTRONOMICA L ESS AYS. 
 
 has been lately fettled by J. Goodrick, Efq. of 
 York. It periodically changes from the firfl: to 
 the fourth magnitude; the time employed from 
 one greateft diminution to the other, was, anno 
 1783, at a mean 2 days, 20 hours, 49 minutes, 
 3 feconds. 
 
 The caufes of thefe appearances cannot be 
 affigned at prefent with any decree of proba- 
 bility; perhaps they have fome analogy to the 
 fpots on the fun, which at fome times appear 
 in greater numbers than at others, fome of them 
 bigger than the whole earth ; or perhaps they 
 are owing to fome real motions of the flars them- 
 felves. 
 
 There are feveral ftars that appear fingle to 
 the naked eye, which are, on examination with 
 a telefcope, found to confift of two, three, &c. 
 The number of double (lars obferved before 
 the time of Dr. Herfchel, was but fmall ; but 
 this celebrated aflronomer has noted upwards of 
 four hundred ; among thefe, fome that are 
 double, others that are treble, double double, 
 quadruple, double treble, and multiple ; his 
 catalogue gives the comparative lize of thefe 
 flars, their colour as they appeared to him, 
 with feveral other very curious particulars. 
 
 172 
 
ASTRONOMICAL ESSAYS. 17,3 
 
 Of Nebul/e, and of Herschel's Ideas re- 
 specting THE Construction of the Uni- 
 verse. 
 
 Befides thofe appearances of the fixed flars 
 already noticed, there is another which de- 
 ferves particular attention, namely, ike nebula, 
 or parts of the heavem which appear brighter 
 than the rcjl. The mod remarkable among 
 thefe is, that large irregular zone or band of 
 whitifli light which crofles the ecliptic in 
 Cancer and Capricorn, and is inclined thereto 
 in an angle of about 60 degrees ; it is a circle 
 bifeding the celeftial fphere, irregular in 
 breadth and hrightnefs, and in many places 
 divided into double dreams. 1 he principal 
 part runs through the Eagle, the Swan, CaJJio- 
 pea, Perfeus, and Auriga : it continues it's 
 courfe by the head of Monoccrus, along by the 
 greater Dog, through the Ship, under the Cen- 
 taurs Feet ; till having paffed the Altar, the 
 Scorpion's Tail^ and the Bow of Aquarius, it 
 ends at laft where it began. 
 
 This curious appearance is owing to a 
 multitude of fmall (tars, which are too minute 
 to be diflinguiflied by the naked eye ; yet, 
 blending their light together, form that white- 
 nefs which occupies fo large a trad of the 
 heavens. The milky w^ay may be confidered 
 Bb i73 
 
174 ASTRONOMICAL ESSAYS. 
 
 as a conflellation of the telefcopic (tars ; a fea of 
 " them, of great breadrh, and of a whitifli colour, 
 encompailing the whole heavens : even before 
 aftronoiny reaped any benefit from improve- 
 ments in optics, Democritus confidered it as 
 formed of clufters of Imall Itars. 
 
 Mr. Herfchel's large telefcope completely 
 refoived the whitifh appearance of the milky 
 way into flars. Having viewed and guaged 
 this bric^ht zone in all diredions, he found it 
 compofed of fliining flars, whofe number in- 
 creafes and diminiflies in proportion to it's ap- 
 parent brightnefs to the naked eye. 
 
 The portion of the milky way that he frrfl 
 obferved, was that about the hand and club 
 of Orion. Here he found an aflonifliing mul- 
 titude of flars, which he attempted to number. 
 By eflimating the number contained in the 
 field of his telefcope at once, and computing, 
 from a mean of thefe, how many might be 
 contained in a given portion of the milky 
 way, in the moll vacant places, about that 
 part, he found 6t^ flars ; other fix fields con- 
 tained iio, 60, 70, 90, 70, and 74 fiars : a 
 mean of thefe give5 79 for the number of fiars 
 in each field ; fo that, allowing 15 minutes for 
 the diameter of his field of view^, a belt of fifteen 
 degrees long, and two degrees broad, could 
 not contain lefs than 50,000 flars, large enough 
 to be diftinclly numbered \ befides which, he 
 
 »74 
 
ASTRONOMICAL ESSAYS. I -^ - 
 
 fufpeded twice as many more, which could be 
 feenonly now and then by i^iint glimpfes, for 
 want of fufficient light. 
 
 In the moll crouded parts of the milky 
 way, he has had a field of view of 588 ftars, 
 and thefe continued for many minutes; fo that 
 in one quarter of an hour's time not lefs than 
 116,000 ftars have palTed through the field of 
 his telefcope. He endeavours to fiiew, that 
 the powers of his telefcope arejuch, that it will 
 not only reach the ftars at 497 tinges the dilUnce 
 of Sirius, fo as to diftinguifh them, but that it 
 alfo (liews the united lultre of the accumulated 
 ftars that compofe a milky nebulofity at a far 
 greater diftance. From thefe confiderations, it 
 is highly probable, that as his twenty feet tele- 
 fcope does not fliew fuch a nebulofity in the 
 milky way, it goes already far beyond the extent 
 thereof; and therefore a more powerful indru- 
 ment would remove all doubt, by expofing a 
 milky nebulofiry beyond the (Iratum, which 
 could then no longer be miflaken for the dark 
 ground of the heavens. 
 
 To a fpeclator placed in indefinite fpace, 
 all very remote objects appear to be equally 
 diflant from the eye. To judge of the milky 
 way only from phenomena, we mufl of courfe 
 confider it as a vaH; ring of ilars fcattered 
 promifcuoufly round the celeflial regions ; but 
 a more perfed view of the fubjed will fliew 
 ^7S 
 
 I 
 
1-6 ASTRONOMICAL ESSAYS. 
 
 US, that the appearance, &c. of this beautiful 
 obje£l arife from our eccentric \\c\v. Mr. 
 Wright, in his *' Original 'I'heory of the Uni- 
 verfe, 1750,*' and Dr. llerfchel fince, m " l he 
 Philofophical I ranlaclions," have fhewn, that 
 this appearance may be accounted for, by al- 
 fuming it's figure as much more extended to- 
 wards the apparent zone of illumination, than 
 in any other direction. 
 
 Suppofe, fays Dr. Herfchel, a number of 
 flars arranged between two parallel planes infi- 
 nitely extended every way, but at a given 
 confiderable diflance from each other ; and 
 calling this a fidcrial Jlraium^ an eye placed 
 fomewhere within it, will fee all the flars in 
 the diredions of the planes projeclcd into a 
 great circle, lucid on account of the accu- 
 mulation of flars ; while the reft of the heav- 
 ens, at the fides, will only feem fcattered over 
 with conflellations, more or lefs crowded, ac- 
 cording to the diftance of the planes, or num- 
 bers of the flars contained in the thicknefs or 
 fides of the llratum. 
 
 If the eye be placed without the Oratum, 
 but at no very great diflance, the appearance 
 of the flars within it would form one of the 
 lefT^^r circles of the fphere, which would be 
 more or lefs contra6led, according to the dif- 
 taiice of the 'eye. 
 
 176 
 
ASTRONOMICAL ESSAYS. 177 
 
 He coniklers our fun as placed in that 
 flratuni of flars which forms our milky way, 
 and as not far from the plate where feme 
 fmaller rtratum branches out from it. Fvery 
 (lar in the llratutn has it's own galaxy, only 
 with fuch variations, in form and luflre, as may 
 arife from their particular fituations. 
 
 According to Dr. Herfch.-l, the univerfe 
 confids of nebula:, or immenfe colledions of 
 innumerable flars, each individual of which is 
 a fun, not only equal, but much fuperior to 
 our's : yet none of the celeflial bodies, in our 
 fyffem, are nearer to one another than we are 
 to Sirius, who is fuppofed to be 400,000 times 
 further than the fun from us ; that is, thirty- 
 eight millions of millions of miles. The ex- 
 tent of the nebuliE is fuch in fome places, that 
 the light of a ftar placed at it's extreme boun- 
 dary, fuppofing it to fly with the velocity of 
 twelve mi!lion^ of miles every minute, mufl 
 have taken nearly 3000 years to reach us. 
 
 Not content with thefe conjeilures, our 
 indefatigable ailronomer endeavours to trace 
 the or/^/« of nebulous flars, and gives us hints 
 concerning their antiquity. Suppofing fome 
 to have a greater air of vigour than others, 
 he attempts to fliew that they are at dillant pe- 
 riods feparated and fubdivided, and even decay. 
 Theie compofitions and decompofitions he 
 pretends to account for, and points out fome 
 177 
 
178 ASTRONOMICAL ESSAYS. 
 
 that he confiders as having fullained greater 
 ravages of time than others! k is not here 
 only that even his very conjectures furpafs all 
 human credulity, for you will find him alTign- 
 ing the boundaries of the vafl: periods requifite 
 for forming nebula;, and hazarding conjedures 
 concerning others, as if tiiey were the luba- 
 ratories of the univcrfe I 
 
 If you are attentive to aftronomical writers, 
 you will foon perceive that much of our know- 
 ledge of aftronomy is founded upon conjec- 
 ture, though drefTed up with all the parade 
 of mathematical demonffration. You will find 
 much of their reafoning weak ; and you will 
 often find them arguing in a circle; and this 
 particularly with refpefc to the denfities, 
 magnitudes, diflances, and other afTetlions of 
 the planets. Many of their conclufions are 
 deduced from analogy ; a fpecies of reafoning 
 that in it's beft form amounts only to proba- 
 bility. Many of their ideas are fupported 
 upon an afiumed attractive power, which they 
 modify at pleafure. 
 
 Though in a popular work it is impofTibie 
 to enter into a difcufTion of thefe points, yet it 
 may be ufeful to fay fomething concerning the 
 value of conjecture, &c. in phyfical fciences. 
 The world has been fo long befooled by hypo- 
 thefes in all parts of fcience, that it is now 
 necfffary to treat them with contempt. Con- 
 178 
 
ASTRONOMICAL ESSAYS. 
 
 ^79 
 
 ieaures and hypothefes are the invention and 
 works of men, and mud therefore bear pro- 
 portion to the fkill and capacity of the inventor • 
 and will always be very unlike the works of God, 
 which it is the bufinefs of philofophy to dif- 
 cover. 
 
 It is natural for men to judge of things lefs 
 known, by fome fimihtude they obfcrve, or 
 think they obferve, between them and things 
 more famihar, or better known : in many cafes 
 we have no other way of judging. Analogical 
 reafoning is not therefore to be always lejeded ; 
 but it ought always to be obferved, that this 
 kind of reafoning can only afford probable evi- 
 dence, that it may lead into error, and that it 
 varies in the degrees of it's force according to 
 the nature of the truths from which we reafon, 
 according to their greater or lefs extent, and 
 according as the inftances compared are more or 
 lefs fimilar. 
 
 Of Comets. 
 
 Comets are a kind of ftars appearing at 
 unexpe6led times in the heavens, and of fm- 
 gular and various figures, defcending from far 
 diftant parts of the fy(tem, with great rapi- 
 dity, furprizing us with the fingular appear- 
 ance of a train, or tail ; and after a (hort flay 
 179 
 
l8o ASTRONOMICAL ESSAYS. 
 
 are carried ofF to didant regions, and difap- 
 pear. 
 
 They were imapjined in ancient times to 
 be prodigies hung out by the immediate hand 
 of God in the heavens, afid intended to alarm 
 the world. Their nature being now better 
 underftood, they are no longer terrible : but 
 as there are ftill many who think them to be 
 heavenly warnings, portents of future events, 
 it may not be improper for the tutor to inform 
 his pupil, that the Architeft of the univcrfe 
 has framed every part according to divine 
 order, and fubje6led all things to laws and 
 regulations ; that he does not hurl at random 
 [tars and worlds, and diforder the fyftem oT 
 the whole glorious frame, to produce falfe 
 apprehenfions of diflant events, fears without 
 foundation, and without ufe. Religion glo- 
 ries in the teft of reafon, of knowledge, and of 
 true wifdom ; it is every way connefted with, 
 and is always elucidated by them. From philo- 
 fophy we may learn, that the more the works 
 of the Lord are underflood, the more he mud 
 be adored ; and that his fuperintendancy over 
 every portion is more clearly evinced, and more 
 fully expreffed, by their unvaried courfe, than 
 by ten thoufand deviations. 
 
 Ihe exiftence of an univerfal connexion 
 between all the parts of nature is now gene- 
 i8o 
 
ASTRONOMICAL ESSAYS. l8l 
 
 rally allowed. Comets undoubtedly form a part 
 of this great chain ; but of the part they occupy, 
 and of the ufes for which they exifl, we are' 
 equally ignorant. It is a portion of fcience 
 whofe perfedion is referved for fome diftant 
 day, when thefe bodies, and their vaft orbits, 
 may, by long and accurate obfervation, be ad- 
 ded to the known parts of the folar fyftem; 
 when aftronomy will appear as anew fcience, 
 after all our difcoveries, great as we at prefent 
 imagine them to be. 
 
 The af^ronomy of comets is very imper- 
 fe£l ; for but little can be known with cer- 
 tainty where but little can be feen. Comets 
 afford few obfervations on which to ground 
 conjeaure, and are for the greatelf part 
 of their courfe beyond the reach of human 
 vifion ; but that they are not meteors in the 
 air is plain, becaufe they rife and fet in the 
 fame manner as the moon and (lars. They 
 are called comets from their having a long tail, 
 fomewhat refembling the appearance of hair : 
 fome, however, have appeared without this ap- 
 pendage, as well defined and round as planets. 
 Imperfed: as our knowledge is concerning them, 
 mathematidans have even ventured to calculate 
 the fizes of their orbits, which they have made 
 fo great as to furpafs the ordinary bounds of cre- 
 dulity. 
 
 C c i8i 
 
l82 ASTRONOMICAL ESSAYS. 
 
 It is generally fuppofed that they are plan- 
 etary bodies, making part of our fylteni, re- 
 volving round the fun in extremely long 
 elliptic curves ; that as the orbit of a comet 
 is more or lefs eccentric, the diltance to which 
 they recede from the fun will be greater or 
 lefs. Very great difference has been found by 
 obfervation in this refpe^l ; even fo great, that 
 the fides of the elliptic v)rbit in fome cafes de- 
 generate almoft into right lines. Ihey are very 
 numerous ; 450 are fuppofed to belong to our 
 folar fyftem. 
 
 It is fuppofed, that thofe comets, which go 
 to the greateft diitance from the fun, approach 
 the nearefl to him at their return. 
 
 Their motions in the heavens are not all 
 direct, or according to the order of the figns, 
 like thofe of the orher planets. The number 
 of thofe which move in a retrograde manner, 
 is nearly equal to thofe whofe motion is 
 direft. 
 
 The orbits of mofl of them are inclined in 
 very large angles to the plane of the ecliptic. 
 
 The velocity with which they move is varia- 
 ble in every part of their orbit : when they are 
 near the fun, they mov<^ with incredible fwilt- 
 nefs ; when very remote from him, their motion 
 is inconceivably flow. 
 
 When they appear, they come in a direifl 
 line towards the fun, as if they were going to 
 182 
 
ASTRONOMICAL ESSAYS. 1 83 
 
 fall into his body ; and after having difa; - 
 peared for fonie time, and in confequence of his 
 ex reme brightnefs, they fly olF on the other 
 fide as fait as they came, continually lofing 
 their fplendor, till at lait thev totally difap- 
 pear. Their apparent magnitude is very dif- 
 ferent ; lometimes leeming not bigger than 
 the fixed (lars, at other times equal in dia- 
 merer to Venus. Hevelius obferved one in 
 1652, which was not inferior to the moon in 
 fize, though not lo bright : it's light pale and 
 dim, it's afpecl difmal. 
 
 A greater number of comets are feen in the 
 hemifphere towards the fun, than in the oppo- 
 fite ; and are generally invifible at a fmaller 
 diuance than that of Jupiter. Mr. Brydone 
 obferved one at Palermo, in July 1770, which, 
 in twenty. four hours, defcribed an arch in the 
 heavens upwards of fif y degrees in length ; fo 
 that, if it was far diiiant from the fun, it muft 
 have moved at the rate of upwards of fixiy 
 millions of miles in a day. 
 
 They dilfer alfo in form from the other 
 planets, confiding of a large internal body, 
 which fliines with the rcflcded light of the 
 fun, and is encompalfed with a very large at- 
 mofphere, apparently of a fine matter, much 
 rtfembling that of the aurora borealis : this 
 is called the head of the comet, and the in- 
 ternal part the nucleus. When a comet ar- 
 
 ■83 
 
184 ASTRONOMICAL ESSAYS. 
 
 rives at a certain diftance from the fun, an 
 exhalation arifes from it, which is called the 
 tail. 
 
 The tail is always direfled to that part of 
 the heavens which is diredtly or nearly oppo- 
 fite to the fun, and is greater and brighter after 
 the comet has paffed it's perihelium, than in 
 it*s approach to it ; being greatelt of all when 
 it has ju(l paffed the perihelium. The tail of 
 the comet of 1680 was of a prodigious fize, 
 extending from the head to a diftance fcarcely 
 inferior to that of the fun from the earth. 
 
 No fati factory knowledge has been ac- 
 quired concerning the caufe of that train of 
 light which accompanies the comets. Some 
 plilofophers imagine that it is the rarer at- 
 mofphere of the comet, impelled by the fun*s 
 rays. Others, that it is the atmofphere of the 
 comet rifing in the folar atmofphere, by it's 
 fpecific levity : while others imagine that it is 
 a phenomenon of the fame kind with the au- 
 rora borealis, and that this earth would appear 
 like a comet to a fpedator placed in another 
 planet. 
 
 T he number of the comets is certainly 
 very great, confiderably beyond any eflimation 
 that might be made from the obfcrvations we 
 now poflefs. 
 
 Though ajironomers have beflowed much 
 labour in calculating the periods of comets, 
 184 
 
ASTRONOMICAL ESSAYS. 185 
 
 and much attention to account for their phe- 
 nomena, yet experience bears no teftimony in 
 favour of their opinions, nor have modern cal- 
 culators had better fuccefs. Indeed the im- 
 menfe diftances to which they are iuppofed to 
 run out, are entirely hypothetical. 
 
 There are, who do not think, the prefent 
 aftrpnomy of comets well elUblifhed; and 
 as fo many finall ones are frequently feen, they 
 think that nothing can be determined, with 
 certainty, till fome better marks are difco- 
 vered for dillinguifhing one from another, 
 than any at prefent known ; and that even the 
 accomplifliment of Dr. Halley's prediclion is 
 uncertain ; for it is very fingular, that out of 
 four years, in which three comets appeared, 
 the only one in which no comet was to be feen, 
 fiiould be that very year in which the greateft 
 aftronomers that ever exilted had foretold the 
 appearance of one ; and in accounting for it>'s 
 non-appearance, Mr. Ciairault would have 
 been equally fupported by cometic evidence, 
 whether he had concluded the comet to' have 
 been retarded or accelerated by the a£lion of 
 Jupiter and Saturn. A comet appeared in 
 1757, as well as in 1755 ; and had he deter- 
 mined the retardation of the comet to be twice 
 as great as he did, another appeared in 1760 to 
 have verified his calculations. 
 
 185 
 
l85 ASTRONOMICAL ESSAYS. 
 
 Of 7 he Telescopic Appearance of ihe 
 Planets, 
 
 'I hough by the telefcope we have been led 
 onward in our advances tov,ards a more perfedl 
 knowledge of tne heavenly bodies, and aftro- 
 noniy being railed from linle more than a 
 caialo^Tue of ftars into a fcience ; yet by this 
 inftrument men have been led into errors, 
 and ailronomers have indulged in fpeculations 
 that equally deviate Ironi 1 bund reafon, and 
 the plain dictates of common fcnfe. 
 
 Ihe generality of mankind, in p.11 ages, 
 have confidered the fun as a mafs of pure ele- 
 mentary fire, fubfilling from the creation, and 
 lupported by fome unknown caufe, without any 
 occafion for the grofs fuel neceflary for fup- 
 porting our terreftrial fires. The conjectures 
 of aflronomers have neither been fo fimple nor 
 fo rational ; limited in their conceptions, they 
 have n;.t been able to perceive how fire of any 
 kin J could fubfiit vyithout fuel, and have 
 therefore fuppofed the fun and the earth to be 
 of a fimilar fubftance, and confequently, that 
 the earth itfelf would be a fun if fet on fire. 
 Sir Ifaac Newton has even propofed it as a 
 query, whether the fun and fixed fiars are not 
 great earths made vehemently hot, whofe pirts 
 are kept from fuming away by the vafl weight 
 i86 
 
ASTRONOMICAL ESSAYS. 187 
 
 and denfry of their fiiperincumbent atmo- 
 fphere, and whofe heat is preferved by the 
 proJigious a£lion and re-aclion of their pans ? 
 Others have imagined the fun to be a body of 
 quire a different nature, and have even denied 
 him to be pofleffed of any inherent hear, though 
 they allow him the power of producing it in 
 other bodies. Some have fuppofed, that the 
 main body of tl^e fun has neither h'ght nor 
 hear, but that it confiits ot a vjji dark globe, 
 furrouuded o 1 all fidis with a thin covering 
 of aerial or foggy matter immenfely fplendid, 
 which gives him the power he polfelles, &;c. 
 &c. 
 
 The only foundation for thefe wild con- 
 jectures, is the appearance of the fun ih ough 
 telelcopes. By viewing it through thefe in- 
 (Iruments, his face is found not to be equally 
 br'glit in all it's parts. A flightly fpotted ap- 
 pearance, chiefly on or near the edges, is com- 
 monly taken notice of; and very frequently 
 dark fpors of various fhapes and fizes are per- 
 ceived traverfing the difk from one edge to the 
 other. Thefe fpots appear at uncertain inter- 
 vals, and often change their form while they 
 are paffing over the folar difl-c, or are broken in 
 pieces, enlarge, and diminifli by caufes of which 
 we are ignorant. 
 
 Thofe who adhere to the conjeBures of Sir 
 I. Newton, fuppofe the fpots to be the fmoke 
 
 .87 
 
l83 ASRTONOMICAL ESSAYS. 
 
 of new a'ld immenfe volcanoes breaking out in 
 the body of the fun himfelf ; while thofe who are 
 pleafed with \\\q. fupprjfttions of Profeflor VVilfon, 
 imagine them to be the dark globe reiidered 
 vifible by the difplacement of the fliining and 
 furrovHiding matter. 
 
 Though it would be deviating from our 
 plan, to fpend our time in fpeculations on fub- 
 iefts removed fo far beyond the reach of hu- 
 man inveftlgation ; yet we can fcarce refrain 
 from obferving, that there is no foundation for 
 fuppofing that the fun has any folid body. 
 Meteors^ refembling that glorious luminary in 
 fplendor, have been known to arife in the 
 higher parts of our atmofphere, though their 
 continuance there has been but for a fhort 
 time. No one fuppofes that they have any 
 folid body. It is not therefore unreafonable 
 to fuppofe [he fun to be a vad collection oF 
 elementary fire and light, which being fent out 
 from him, by means unknown to us, and having 
 accomplifhed the purpofes for which they are 
 defigned, perpetually return to him, are fent out 
 again, and fo on. Thus the fun continues to 
 burn unfupported by any terrcftrial fuel, and 
 without the lead tendency to diminution, or pof- 
 fibility of decay. 
 
 Of the Moon. From the appearance of this 
 luminary through a telefcope, it feems prob- 
 able, that there are great inequalities on her 
 i88 ' . 
 
ASTRONOMICAL ESSAYS. i8q 
 
 furface. Viewing her at any time, except 
 when full, we fee one of the fides notched and 
 toothed like a faw. Many fmall points appear 
 like ftars at a fmall diltance from the main 
 luminous body, which join it in a little time. 
 Thefe are confidered as the tops of high moun- 
 tains, which catch the light of the fun fooner 
 than the other parts which are lower. That 
 thefe very (hlaing parts are higher than the 
 reft of the furface, is evident from the appear- 
 ance of their fliadows, which lengthen and 
 fliorten according to their ficuation with re- 
 fpeft to the fun. Some aftronpmers have un- 
 doubtedly made the mountains of the moon 
 extravagantly high ; they have been much re- 
 duced by modern calculators Dr. Herfchel 
 has thought he difcovered volcanoes on her 
 diik. And it is fuppofed fhe has an atmo- 
 fphere, becaufe the limb of the fun has been 
 obferved to tremble jufl: before the beginning 
 of a folar cclipfe, and becaufe the planets be- 
 come oval at the beginning of an occultation 
 behind the moon. 
 
 Mercury being always near the fun, nothing 
 more is di tinguiflied by the telefcope, than a 
 variation of his figure, which is fometimes that 
 of a half moon, fometimes a little more or lefs 
 than half. 
 
 Venus ^ when in the form of a crefcent, and 
 at her brighteit times, affords a very pleafing 
 D d 189 
 
igO ASTRONOMICAL ESSAYS. 
 
 tclefcopic view, her furface being diverfified 
 with fpots like the the moon. The diurnal mo- 
 tion of this planet, both as to it's period and 
 direction, has not hitherto been decidedly af- 
 certained : Dr. Ilcrfchel concludes from his 
 obfervations, that it's atmofphcre is very con- 
 fiderable. He has not been able to find the 
 lead trace of mountains, and ridicules thofe 
 obfervers who have feen fuch as exceed four, 
 five, and even fix times the height of Chimbo 
 Raco, the highefl: of our mountains. 
 
 Afdrs always appears round except at the 
 quadratures, when it's difk is like that of the 
 moon about three days after the full. It*s 
 atmofphere is from the ruddinefs of the planet 
 fuppofed to be very denfe ; fpots are difcovered 
 on his furface, but they do not appear fixed : 
 Dr. Herfchel has obferved two white luminous 
 circles furrounding the poles of this planet, 
 which hefuppofes to arife from the fnow lying 
 about thofe parts. 
 
 The furface of 'Jupiter is diflinguilhed by 
 certain hands or helts^ of a dufkier colour than 
 the red of his furface, running parallel to each 
 other and to the plane of his orbit. They are 
 neither regular nor conflant in their appear- 
 ance, fometimrs more, fometimes fewer being 
 perceived ; their breadth varies, and fometimes 
 one or more fpots are formed between the 
 belts. 
 
 190 
 
ASTRONOMICAL ESSAYS. I9I 
 
 Saturn's diilance does not permit us with 
 common inftruments to diflinguirti many va- 
 rieties on his furface, but his ring is a fruitful 
 fource for aftronomical fpeculation. Dr. Her- 
 fchel, by means of his powerful inftruments, 
 has difcovered a muhiplicity of regular belts, 
 which did not change much during thecourfeof 
 his obfervations. From thefe he has found, that 
 Saturn has a pretty quick rotation upon it's 
 axis, which he has fixed at 10 h. 16 min. o fee. 
 He has alfo fhewn, that the ring of Saturn 
 is divifible into two concentric rings of un- 
 equal dimenfions and breadth, firuated in one 
 plane which is probably not much inclined to 
 the equator of the planet. I'hefc rings are at 
 a confiderable diftance from each other, the 
 fmalleft being much lefs in diameter at the 
 outfide, than the largeft is at the infide : the 
 two rings are entirely detached from each 
 other, fo as plainly to permit the ooen hea- 
 vens to be feen through the vacancy between 
 ihcm. 
 
 Though much has been unfolded to you in 
 the courfe of this eflliy, upon a little confi- 
 deration, you will find the things, of which 
 you remain ignorant, infinitely exceed thofe 
 which you know. It is with us as with a child, 
 that thinks if he could but jufl come to fuch 
 a field, or climb to the top of fuch a hill, he 
 fhould be able to touch the (ky ; but no fooner 
 191 
 
ig2 ASTRONOMICAL ESSAYS. 
 
 is he come thither, than he finds it as far oiF 
 as it was before. 
 
 It may perhaps be u^-ful to point out to 
 you the littlenefs of human knowledge, even 
 in thofe fubjefts of which we have been 
 treating ; and this 1 (hall do principally in the 
 words of a late writer. 
 
 How far docs the univerfe extend, and 
 where are the limits thereof? Where did the 
 Creator " (lay his rapid wheels ?'* where 
 "fix the golden compafles ?" Certainly him- 
 self alone is without bounds, but all his 
 works are finite. He muft therefore have faid, 
 at fome point of fpace, 
 
 . " Be thefe thy bounds ; 
 
 *< This be the juft circumference, O world '.'* 
 
 Here the mathematician mufl be filent, and 
 wave all calculations, as there can be no ratio 
 between bounded and boundlefs fpace, even 
 though the magnitude of the former were 
 taken at the utmoft limit man can conceive, or 
 numbers exprefs. But where are the boun- 
 daries ? Who can tell ? All beyond the fixed 
 flars is utterly hid from the children of men. 
 
 But what do we know of ihe Jixed Jiars ? 
 A great deal, one would imagine ; fmce, like 
 the MOST HIGH, we too tell their numbers^ 
 yea, and call them by their tiames ! But what 
 are thofe that are named, in comparifon with 
 192 
 
ASTRONOMICAL ESSAYS. I03 
 
 thofe which our glaffes difcover ? What are 
 two or three thoufand, to thofe we difcover in 
 the milky way alone ? How many then are 
 there in the whole expanfe ? But to what end 
 do they ferve ? To illuminate worlds, and im- 
 part light and heat to their feveral choirs of 
 planets ? or to gild the extremities of the folar 
 fphere, and minifter to the perpetual circulation 
 of light and fpirit ? 
 
 What are comets? Planets not full formed, 
 or planets deflroyed by conflagration ? or bo- 
 dies of an wholly different nature, of which we 
 can form no idea ? How eofy it is to form a 
 thoufand conjectures ! how hard to determine 
 any thing concerning them ! Can their huge 
 revolutions be even tolerably accounted for on 
 the principles of gravitation and projedtion ? 
 What brings them back, when they have tra- 
 velled fo immenfely far ? or what whirls them 
 on, when, reafoning juftly on the fame powers, 
 they fhould drop into the fo^ar fire ? 
 
 What is the/i/«itfelf ? It is undoubtedly the 
 mod glorious of all the inanimate creatures ; 
 and it's ufe we know. God made it to rule the 
 day. It is 
 
 " Of this great world both eye and foul." 
 
 But who knows of what fubftance it is com- 
 pofed, or even whether it be folid or fluid ? 
 What are the fpots on it's furface ? what it's 
 
 ^93 
 
1^4 ASTRONOMICAL ESSAYS. 
 
 real magnitude ? Here is an unbounded field for 
 conjeBure ; but what foundation for real know- 
 ledge ? 
 
 What do we know of the feebly-ihining 
 bodies the planets^ that move regularly round 
 the fun ? Their revolutions we are acquainted 
 with ; but who ran regularly demonftrate to us 
 either their magnitude or their di fiance, unlefs 
 he affumes it in the ufual way, inferring their 
 magnitude from their diflance, and the dif- 
 tance from the magnitude. What are Jupiter's 
 belts ? What is Saturn's ring ? The honeft 
 ploughman knows as well as the moft learned 
 aftronomer. 
 
 " Sir Ifaac Newton certainly difcovered more 
 of the dependencies, connections, and relations 
 of the great fydem of the univerfe, than had, 
 previous to his time, been conceded to human 
 penetration : yet was he forced to bottom all his 
 reafoning on the hypothefts of gravitation ; of 
 which he could give no other account, than that 
 it was aeceffary to the conclufions he reded up- 
 on it." 
 
 194 
 
AN 
 
 ESSAY, 
 
 ON THE USE OF THE 
 
 Celestial ano Xnxtsttial 
 GLOBES; 
 
 EXEMPLIFIED IN A GREATER VARIETY ot PROBLEMS, THAN ARE 
 TO BE FOUND IN ANY OTHER WORK ; 
 
 Exhibiting the general Principles of 
 
 DIALING AND NAVIGATION. 
 
 BY THE LATE 
 
 GEORGE ADAMS, 
 
 Mathematical Insti'Umcnt Maker to His Majesty, and Optician to ilie Prince of Wale*. 
 
 FIFTH EDITIOjV. 
 
 WITH THE author's LAST IMPROVEMENTS, 
 Illustrstted with Copper Plates. 
 
 PHILADELPHIA: 
 
 PUBLISHED BY WILLIAM W. WOODWARD, 
 
 No. 52, South Second Street. 
 
 1808. 
 
 Dickinson, Printer. 
 
CONTENTS. 
 
 OF the Use of the Globes 
 Advantages of Globes. 
 Description of the Globes 
 Of the Terrestrial Globe 
 Of Latitude and Longitude - 
 
 Page. 
 9 
 
 9 
 
 18 
 
 28 
 28 
 
 Problem. 
 
 1. To find the Longitude of any Place 
 
 2. To find the difference of Longitude between any 
 
 two Places ------ 
 
 3. To find those places where it is Noon at any 
 
 given Hour of the Day, at any given Place 
 
 4. When it is Noon at any Place, to find Avhat 
 
 Hour it is at any other Place . - - 
 
 5. At any given Hour where you are, to find the 
 
 Hour at a Place proposed - - - - 
 Of Latitude 
 
 6. To find the Latitude of any Place - - - 
 
 7. To find all those Places which have the same 
 
 Latitude with any given Places - - - 
 
 8. To find the Difference of Latitude between any 
 
 two Places _----- 
 
 35 
 
 36 
 
 38 
 39 
 41 
 
 41 
 42 
 
IV CONTENTS. 
 
 Problcjn. Page 
 
 9. The Latitude and Longitude being known, to find 
 
 the Place 42 
 
 Of finding the Longitude - - - - . 43 
 
 10. To find the Distance of one Place from another 53 
 
 1 1. To find the Angle of Position of Places - - 54 
 
 12. To find the Bearings of Places - - - 54 
 
 Of the twilight 45 
 
 To rectify the Globe - - - - - 59 
 
 lo. To rectify for the Summer Solstice - - 61 
 
 14. for the Winter Solstice - - - 63 
 
 15. for the Times of E(jUinox - - - 64 
 
 1 6. To exemplify the Sun's Altitude - - - 67 
 
 17. Of the Sun's Meridian Altitude * - - 68 
 
 18. To find the Sun's Meridian Altitude universally 69 
 
 19. Of the Sim's Azimuths - - - - 70 
 Of the Zones and Climates - - - - 72 
 
 20. To find the Climates 74 
 
 21. To illustrate the Distinction of Ascii, &c. - 7t 
 
 22. To find the Antoeci, &c. - - - - 81 
 
 23. To find those Places over which the Sun is verti- 
 
 cial - 82 , 
 
 24. To find the Sun's Place - - - ^ 83 
 
 25. To find the Sun's Declination - - - 86 
 
 26. To find the two Days on winch the Sun is in the 
 
 Zenith of any given Place, 8cc. - - - 87 
 
 27. To find where the Sun is vertical on a given Day 
 
 and Hour ...--- 87 
 
 28. At a given Time of the Day in one Place, to find at 
 
 the same Instant those Places where the Sun is 
 rising, setting, &c. ----- 88 
 
 29. To find all those Places within the Polaf Circles, 
 
 on wi.ich the Sun begins to shine, Sec. - - 9* 
 
 30. To make Use of the Globe as a Tellurian - - 91 
 
 31. To rectify the Globe to the Latitude and Horizon 
 
 of any Place _----- 95 
 
 32. To rectify for the Sun's Place - - - 95 
 
CONTENTS. V 
 
 Problem. Page- 
 
 33 To rectify for the Zenith of any Place - - 96 
 
 Of exposing the Globe to the Sun - - - 97 
 
 34. To observe the Sun's Altitude - - - loo 
 
 35. To place the Globe, when exposed to the Sun, 
 
 that it may represent the natural Positions of 
 the Earth 102 
 
 36. TO find naturally the Sun's Declination - - 104 
 
 37. To find naturally the Sun's Azimuth - - 105 
 
 38. To shew where the Sun will be twice on the 
 
 same Azimuth in the Morning, and twice in 
 the Afternoon .----- 106 
 To find the Hour by the Sun - - - - 108 
 Of Dialling 112 
 
 40. To construct an Horizontal Dial - - - 117 
 
 41. To delineate a South Dial - - - - 121 
 
 42. To make an erect Dial - - - - 122 
 Of Navigation - - - - - • -126 
 
 43. Given the Difference of Latitude, and Difference 
 
 of Longitude, to find the Course and Distance 
 sailed - - - - - - -132 
 
 44. Given the Difference of Latitude and Course, to 
 
 find the Difference of Longitude and Distance 
 sailed - - - - - - -133 
 
 45. Given the Difference of Latitude and Distance 
 
 run, to find the Difference of Longitude, and 
 Angle of the Course - - - - 134 
 
 46. Given the difference of Longitude and Course, to 
 
 find the difference of Latitude, and Distance 
 sailed - - - - - - -135 
 
 47. Given the Course and Distance, to find the 
 
 Difference of Longitude and Latitude - 1 36 
 
 48. To steer a ship upon the Arch of a great Circle, 
 
 &c. 137 
 
 Of the Celestial Globe 151 
 
 Of the Precession of tlje Equinoxes - - - 157 
 
VI CONTENTS. 
 
 Problem. Page. 
 
 2. To rectify the Celestial Globe - - - 163 
 
 3. To find the Declination and Right Ascension of the 
 
 Sun - - - - - - -164 
 
 4. To find the Sun's oblique Ascension, 6cc. - 165 
 
 5. the Sun's meridian Altitude - - 166 
 
 6. the Length of the Day in Latitudes under 
 
 66i Degrees - - - - 166 
 
 7. the Length of the longest and shortest Day 
 
 in Latitudes under 66^ Degrees - - 167 
 
 8. To find the Latitude where the longest Day may 
 
 be of any given Length between twelve and 
 twenty four Hours - - - 167 
 
 9. the time of Sun-rising, See. - - 168 
 
 10. how long, Ecc. the Sun shines in any Place 
 
 within the Polar Circles - - - 170 
 
 11. To illustrate the Equation of Time, Sec. - - 174 
 
 12. To find the Right Ascension, Stc of a Star - 176 
 
 13. the Latitude and Longitude of a Star - 177 
 
 14. the Place of a Star on the Globe by, &c. 177 
 
 15. at what hour a given Star transits the 
 
 meridian - - - - -178 
 
 16. On M^hat Day a Star will come to the Meridian 179 
 
 17. To represent the Face of the Heavens for any 
 
 given Day and Hour - - - 179 
 
 18. To trace the Circles of the sphere in the Heavens 182 
 ly. To find the Circle of perpetual Apparition 188 
 
 20. the Sun's Amplitude - - - 189 
 
 21. the Sun's Altitude at a given Hour - 19Q 
 
 22. when the Sun is due East in a given Lati- 
 tude - - - - - 193 
 
 23. the Rising, Setting, Culminating, 8cc. of a 
 
 Star - - - - - 194 
 
 24. the Hour of the Day, the Altitude and 
 
 Azimuth of a Star being given - - 19S 
 
 9. J. the Altitude and Azimuth of a Star, &c, 196 
 
CONTENTS. Vli 
 
 Fi-oblcin. I'ag"'- 
 
 26. the Azimuth, &c. at any Hour of the 
 
 Night - ' - - - 197 
 
 27. the Sun's Altitude, and the Hour, from 
 
 the Latitude, Sun's Place, and Azimuth 197 
 
 21. the Hour, the Latitude and Azimuth 
 
 given - - - - - 198 
 
 29. • a Star, the Latitude, Sun's Place, Hour, 
 
 &c. given - - - - - 199 
 
 30. To find tlie Hour by Data from two Stars that 
 
 have the same Azimuth - - - - 199 
 
 31. the Hour by Data from two Stars that 
 
 have the same Altitude .... 200 
 
 32. the Latitude by Data from two Stars 201 
 
 33 ■ the Latitude by other Data from two Stars 201 
 
 34. when a Star rises or set cosmically - 203 
 
 35. when a Star rises or sets achronically - 204 
 
 36. when a Star will rise heliacally - 206 
 
 37. when a Star will set heliacally - - 207 
 
 Of the Correspondence between the Celestial and Ter- 
 restrial Spheres ----- 208 
 28. To find the Place of a Planet, kc. - - 212 
 
 39. what Planets are above the Horizon - 213 
 
 40. . the right Ascension, &c. of a Planet - 214 
 
 41. the Moon's Place - . . . 220 
 
 42. the Moon's Declination - - - 221 
 
 43. The Moon's greatest and least Meridian 
 
 Altitudes 222 
 
 ^4. To illustrate the Harvest Moon - - - 223 
 
 45. To find the Azimuth of the Moon, and thence 
 
 High Water, Sec. 228 
 
 Of Comets ----- 229 
 
 46. To rectify the Globe for the Place of Observation 231 
 
 47. To determine the Place of a Comet - - 232 
 
 48. To find the Latitude, Sec. of a Comet - - 23? 
 
 49. To find th^ Time of a Comet's Rising, &r. - 233 
 
vm CONTENTS. 
 
 Problem. Pag'- 
 
 50. To find the same at London - - , . 234 
 
 5 1 . To determine the Place of a Comet from an Obser- 
 
 vation made at London - - - 234 
 
 52. From two given Places to assign the Comet's 
 
 Path 235 
 
 53. To estimate the Velocity of a Comet - - 236 
 
 54. To represent the general Phenomena of a Comet 237 
 
PREFACE 
 
 TO THE ESSAY ON THE GLOBES. 
 
 1 HE connection of astronomy with geography 
 is so evident, and both in conjunction i;o nect;S- 
 sary to a liberal education, that no man will be 
 thought to have deserved ill of the republic of 
 letters, who has applied his end-favours to dif- 
 fuse more universally the knov/ledge of these 
 useful Sciences, or to render the attainment 
 of them easier ; for as no branch of literature 
 can be fully comprehended without them, so 
 there is none which impresses more pleasing 
 ideas on the mind, or that affords it a more ra- 
 tional entertainment. 
 
 In the present work, several objections to 
 former editions are obviated ; the Problems ar- 
 ranged in a more methodical manner, and a 
 great number added. Such facts are also oc- 
 
ii PREFACE. 
 
 casionally Introduced, such observations inter- 
 spersed, and such relative information commu- 
 nicated, as it is presumed will excite curiosity, 
 and fit attention. 
 
 To further the design, the attention is direct- 
 ed to the appearance of the planetary bodies, 
 as observed from the earth. It were to be 
 wished that the tutor would at this part exhi- 
 bit to his pupil the various phenomena in the 
 heavens themselves ; by teaching him thus to 
 observe, for himself, he would not ohly raise his 
 curiosity, but so fix the impressions which the 
 objects have made on his mind, that by proper 
 cultivation they would prove a fruitful source 
 of useful employment ; and he would therby 
 also gratify that eager desire after novelty, 
 which continually animates young minds, and 
 furnishes them with objects on which to exer- 
 cise their natural activity. 
 
PART I. 
 
 A TREATISE 
 
 ON THE USE OF THE TERRESTRIAL AND 
 CELESTIAL GLOBES. 
 
 •F THE ADVANTAGES OF GLOBES IN GENERAL, FOR IL- 
 LUSTRATING THE PRIMARY PRINCIPLES OF ASTRONO- 
 MY AND geography; and PARTICULARLY OF THE 
 ADVANTAGES OF , THE GLOBES, WHEN MOUNTED IN MY 
 father's MANNER. 
 
 UNIVERSAL approbation, the opinion of 
 those that excel in science, and the ex- 
 perience of those that are learning, all concur 
 to prove that the artificial representations of the 
 earth and heavens, on the terrestrial and celestial 
 globes, are the instruments the best adapted to 
 convey natural and genuine ideas of astronomy 
 and geography to young minds. 
 
 This superiority they derive principally 
 from their form and figure, which communi- 
 cates a more just idea, and gives a more ade- 
 B 195 
 
10 - DESCRIPTION AND USE 
 
 quate representation of the earth and heavens, 
 than can be formed from any other figure. 
 
 To understand the nature of the projection 
 of either sphere in piano, requires more know- 
 ledge of geometry than is generally possessed 
 by beginners, it*s principles are more recluse, 
 and the solution of problems more obscure. 
 
 The motion of the earth upon it's axis is 
 one of the most important principles both in 
 geography and astronomy ; on it the greater 
 part of the phenomena of the visible world de- 
 pend : but there is no invention that can com- 
 municate so natural a representation of this 
 motion, as that of a terrestrial globe about it*s 
 axis. By a celestial globe, the apparent mo- 
 tion of the heavens is also represented in a na- 
 tural and satisfactory manner. 
 
 In order to convey a clear idea of the va- 
 rious divisions of the earth, of the situation of 
 different places, and to obtain an easy solution 
 of the various problems in geography, it is 
 necessary to conceive many imaginary circles 
 delineated on it's surface, and to understand 
 their relation to each other. Now on a globe 
 these circles have their true form ; their inter- 
 sections and relative positions are visible upon 
 the most cursory inspection. But in projec- 
 tions of the sphere in piano, the form of these 
 circles is varied, and their nature changed ; 
 they are consequently but ill adapted to convey 
 196 
 
OF THE GLOBES. H 
 
 to young minds the elementary principles of 
 geography. 
 
 On a globe, the appearance of the land 
 and water is perfectly natural and continuous, 
 fitted to convey accurate ideas, and leave per- 
 manent impressions on the most tender minds ; 
 whereas in planispheres one-half of the globe 
 is separated and disjoined from the other ; and 
 those parts, which are contiguous on a globe, 
 are here separated and thrown at a distance 
 from each other. The celestial globe has the 
 same superiority over projections of the heavens 
 in piano. 
 
 The globe exhibits every thing in true propor- 
 tion, both of figure and size j while on a planis- 
 phere the reverse may often be observed. 
 
 Presuming that these reasons sufficiently 
 evince the great advantage of globes over 
 either planispheres or maps, for obtaining the 
 first principles of astronomical and geographi- 
 cal knowledge, I proceed to point out the pre- 
 eminence of globes mounted in my father* s man- 
 ner, over the common, or rather the old and 
 Ptolemaic mode of fitting them up. 
 
 The great and increasing sale of his globes 
 mounted in the best manner, may be looked 
 upon at least as a proof of approbation from 
 numbers ; to this I might also add, the en- 
 couragement they have received from the 
 principal tutors of both our universities, the 
 197 
 
r2 DESCRIPTION AND USE 
 
 public sanction of the university of Leyden,. 
 the many editions of my father's treatise on 
 their use, and its translation into Dutch, &c. 
 The recommendation of Mess. Arden, Walker, 
 Burton, &c. public lecturers in natural philoso- 
 phy, might also be adduced : but leaving these 
 considerations, I shall proceed to enumerate 
 the reasons which give them, in my opinion, 
 a decided preference over every other kind of 
 mounting.* 
 
 * The following note from Mr. Walker's Easy Intro- 
 duction to Geograpliy, in favour of my father's globes, 
 •will not, I hope, be deemed improper. 
 
 " Simplicity and perspicuity should ever be studied by 
 those who cultivate the young mind ; and jarring, oppos- 
 ing, or equivocal ideas should be avoided almost as much, 
 as error or falsehood. Our globes, till of late years, 
 were equipt with an hour circle, which prevented the 
 poles from sliding through the horizon ; hence their rec- 
 tification was generally for the place on the earthy instead 
 ©f the sun's place in the ecliptic ; which put the globe into 
 so unnatural and absurd a position respecting the sun, 
 that young people were confounded when they compared 
 it with the earth's positions during it's annual rotation 
 round that luminary, and considering the horizon as the 
 boundary of day and niglit. Being, therefore, sometimes 
 obliged to rectify for the place on the earth, and some- 
 times for the sun's place in the ecliptic, the two rules 
 clash so unhappily in the pupil's mind, that few re- 
 member a single problem a twelvemonth after the end 
 of their tuition. Globes, therefore, with a horary cir- 
 cle, are but partially described in this treatise ; the 
 gjreat intention of which is, to make the elevations and 
 
 198 
 
OF THE GLOBES. IS 
 
 The earth, by it*s diurnal revolution on it's 
 axis, is carried round from west to east. To 
 represent this real motion of the earth, and to 
 solve problems agreeable thereto, it is necessary 
 that the globe, in the solution of every problem, 
 should be moved from west to east ; and for this 
 purpose, that the divisions on the large brass cir- 
 cle should be on that side which looks westward.* 
 Now this is the case in my father's mode of 
 mounting the globes, and the tutor can thereby 
 explain with ease the rationale of any problem to 
 his pupil. But in the common mode of mount- 
 ing, the globe must be moved from east to west, 
 according to the Ptolemaic system ; and conse- 
 quently, if the tutor endeavours to shew how 
 things obtain in nature, he must make his pupil 
 unlearn in a degree what he has taught him, and 
 by abstraction reverse the method he has instruct- 
 ed him to use ; a practice that we hope will not 
 be adopted by many.. 
 
 depressions of the poles of a terrestrial globe to repre- 
 sent all the situations the earth is in to the sun, for everv 
 day or hour t.aough the year. The globes of Mr. Adains- 
 are the most favourable for the above mode of rectificatiou 
 of any plates we have at present ; and to make a quiescent 
 gl )be to represent all tiie positions of one revolving round 
 the sun, turning on an inclined axis, and keeping that axis 
 altogether parallel to itself, his globes are better adapted 
 than any, I believe, in being." 
 
 * See the Rev. Mr. Hutchin's New Treatise on the Globes.-: 
 199 
 
14 DESCRIPTION AND USE 
 
 The celestial globe being intended to re- 
 present the apparent motion ot the heavens, 
 should be moved, when used, from east to 
 west. 
 
 Of the phenomena to be explained by the 
 terrestrial globe, the most material are those 
 which relate to the changes in the seasons ; all 
 the problems connected with, or depending 
 upon these phenomena, are explained in a 
 clear, familiar, and natural manner, by the 
 globe, when mounted in my father's mode ; for 
 on rectifying it for any particular day of the 
 month, it immediately exhibits to the pupil 
 the exact situation of the globe of the earth for 
 that day ; and while he is solving his problem, 
 the reason and foundation of it presents itself 
 to the eye and understanding. 
 
 The globe may also be placed with ease in 
 the position of a right sphere ; a circumstance 
 exceedingly useful, and which the old con- 
 struction of the globes did not admit of. 
 
 By the application of a moveable meridian, 
 and an artificial horizon connected with it, it 
 is easy to explain why the sun, although he be 
 always in one and the same place, appears to 
 the inhabitants of the earth at different alti- 
 tudes, and in different azimuths, which cannot 
 he so readily done with the common globes. 
 
 On the celestial globe there is a moveable 
 circle of declination, with an artificial sun. 
 200 
 
OF THE GLOBES. 15 
 
 The brass wires placed under the globes, 
 serve to distinguish, in a natural and satisfacto- 
 ry manner, twilight from total darkness, and the 
 reason of the length of it's duration. 
 
 The next point, wherein they materially dif- 
 fer from other globes, is in the hour circle. 
 Now it must be confessed, that to every contri- 
 vance that has been used for this purpose there 
 is some objection, and probably no mods' can 
 be hit upon that will be perfectly free from 
 them. The method adopted by my father ap- 
 pears to me the least exceptionable, and to 
 possess some advantages over every other me- 
 thod I am acquainted with. Agreeably to the 
 opinion of the first astronomers, among others 
 of M. de la Lande, he uses the equator for the 
 hour circle, not only as the largest, but also as 
 the most natural clicle that could be employed 
 for that purpose, and by which alone the solu- 
 tion of problems could be obtained with the 
 greatest accuracy. As on the terrestrial globe, 
 the longitude of different places is reckoned 
 on this circle ; and on the celestial, the right 
 ascension of the stars, &c. it familiarizes the 
 young pupil with them, and their reduction to 
 time. This method does not in the least im- 
 pede the motion of the globe ; but while it 
 affords an equal facility of elevating either the 
 north or south pole, it prevents the pupil from 
 placing them in a wrong position j while the 
 201 
 
16 DESCRIPTION AND USE 
 
 horary wire secures the globe from falling out 
 of the frame. 
 
 Another circumstance peculiar to these globes, 
 is the mode of fixing the compass. It is self- 
 evident, that the tutor, who is willing to give 
 correct ideas to his pupil, should always make 
 him keep the globes with the north pole direct- 
 ed towards the north pole of the heavens, and 
 that, both in the solution of problems, and the 
 explanation of phenomena. By means of the 
 compass, the terrestrial globe is made to supply 
 the purpose of a tellurian, when such an instru- 
 ment is not at hand. I cannot terminate this pa- 
 ragraph, without testifying my disapprobation 
 of a mode adopted by some, of making the globe 
 turn round upon a pin in the pillar on which it 
 is supported; a mode, that, while it can give 
 little but relief to indolence, is less firm in it's 
 construction, and tends to introduce much con- 
 fusion in the mind of the pupil. 
 
 In order to prevent that confusion and per- 
 plexity which necessarily arises in a young 
 mind, when names are made use of which do 
 not properly characterize the subject, my fa- 
 ther found it necessary, with Mr. Hutchins, 
 to term that broad wooden circle which sup- 
 ports the globe, and on which the signs of the 
 ecliptic and the days of the month are engraved, 
 the broad paper circle, instead of horizon, by 
 202 
 
OF THE GLOBES. 
 
 which it had been heretofore denominated. 
 The propriety of this change will be evident to 
 all those who consider, that this circle in some 
 cases represents that, which divides light from 
 darkness, in others the horizon, and some- 
 times the ecHptic. For similar reasons, he was 
 induced to call the brazen circle, in which the 
 globes are suspended, the strong brass circle. 
 
 In a word, many operations may be perform- 
 ed by these globes, which cannot be solved by 
 those mounted in the common manner ; while 
 all that they can solve may be performed by 
 these, and that with a greater degree of perspi- 
 cuity ; and many problems may be performed 
 by these at one view, which on the other globes 
 require successive operations. 
 
 But as, notwithstanding their superiority, 
 the difference in price may make some persons 
 prefer the old construction, it may be proper 
 to inform them, that they may have my father* s 
 globes mounted in the old manner^ at the usual 
 prices. 
 
 C 203 
 
PART II. 
 
 CONTAINING 
 
 A DESCRIPTION OF THE GLOBES MOUNTED IN 
 THE BEST manner; TOGETHER WITH SOME 
 PRELIMINARY DEFINITIONS. 
 
 DEFINITIOKS. 
 
 BEFORE we begin to discribe the globes, 
 it will be proper to take some notice of 
 the properties of a circle, of which a globe may- 
 be said to be constituted. 
 
 A line is generated by the motion of a point. 
 Let there be supposed two points, the one 
 moveable, the other fixed. 
 
 If the moveable point be made to move direct- 
 ly towards the fixed point, it will generate in 
 it's motion a straight line. 
 
 If a moveable point be carried round a fixed 
 point, keeping always the same distance from 
 it, it will generate a circle, or some part 
 204 
 
OF THE GLOBES. 19 
 
 of a circle, and the fixed point will be the 
 center of that circle. 
 
 AH strait lines going from the center to the 
 circumference of a circle, are equal. 
 
 Every strait line that passes through the cen- 
 ter of a globe, and is terminated at both ends 
 by it's surface, is called a diameter. 
 
 The extremities of a diameter are it's poles. 
 
 If the circumference of a semicircle be turned 
 round it's diameter, as on an axis, it will gene- 
 rate a globe, or sphere. 
 
 The center of the semicircle will be the cen- 
 ter of the globe ; and as all points of the gene>- 
 rating semicircle are at an equal distance from 
 it's center, so all the points of the surface of 
 the generated sphere are at an equal distance 
 from it's center. 
 
 DESCRIPTION OF THE GLOBES. 
 
 There are two artificial globes. On the sur- 
 face of one of them the heavens are delineated j 
 this is called the celestial globe. The other, on 
 which the surface of the earth is described, is 
 called the terrestrial globe. 
 
 Fig. 2, plate XIII, represents the celestial, 
 fig. 1 , plate XIII, the terrestrial globe, as mount- 
 ed in my father's manner. 
 205 
 
20 DESCRIPTION AND USE 
 
 In using the celestial globe, we are to consider 
 ourselves as at the center. 
 
 In using the terrestrial globe, we are to 
 suppose ourselves on some point of it's sur- 
 face. 
 
 The motion of the terrestrial globe repre- 
 sents the real motion of the earth. 
 
 The motion of the celestial globe represents 
 the apparent motion of the heavens. 
 
 The motion, therefore, of the celestial globe, 
 is a motion from east to west. 
 
 But the motion of the terrestrial globe is a 
 motion from west to east. 
 
 On the surface of each globe several circles 
 are described, to every one of which may be ap- 
 plied what has been said of circles in page 205. 
 
 The center of some of these circles is the 
 same with the center of the globe ; these are, 
 by way of distinction, called great circles. 
 
 Of these great circles, some are graduated. 
 
 The graduated circles are divided into 360, 
 or equal parts, 90 of which make a quarter of a 
 circle, or a quadrant. 
 
 Those circles, whose centers do not pass 
 through the center of the globe, are called lesser 
 circles. 
 
 The globes are each of them suspended at 
 the poles in a strong brass circle N Z jiE S, and 
 turn therein upon two iron pins, which ar? 
 206 
 
OF THE GLOBES. 21 
 
 the axis of the globe ; they have each a thin brass 
 semicircle NHS, moveable about these poles, 
 with a small thin circle H sliding thereon : it 
 is quadrated each way to 90" from the equator 
 to either pole. 
 
 On the terrestrial globe this semicircle is a 
 ?novcable 7neridian. It's small sliding circle, 
 which is divided into a few of the points of the 
 mariner's compass, is called a terrestrial or 
 •visible horizon. 
 
 On the celestial globe this semicircle is a 
 moveable circle of declination^ and it's small brass 
 circle an artificial sun, or planet. 
 
 Each globe has a brass wire circle, T W Y, 
 placed at the limits of the crcpusculum, or twi- 
 light, which, together with the globe, is mount- 
 ed in a wooden frame. 1 he upper part, B C, 
 is covered with a broad paper circle, whose 
 plane divides the globe into two hemispheres ; 
 and the whole is supported by a neat pillar and 
 claw, w ith a magnetic needle in a compass-box, 
 marked M. 
 
 A DESCRIPTION OF THE CIRCLES DESCRIBED 
 ON THE BROAD PAPER CIRCLES B C ; TO- 
 GETHER WITH A GENERAL ACCOUNT OF 
 IT*S USES. 
 
 It contains four concentric circular spaces, 
 the innermost of which is divided into 3G0% 
 207 
 
22 DESCRIPTION AND USE 
 
 and numbered into four quadrants, beginning at- 
 the east and west points, and proceeding each 
 way to 90% at the north and south points : 
 these are the four cardinal points of the hori- 
 zon. The second circular space contains, at 
 e^qual distances, the thirty-two points of the 
 mariner's compass. Another circular space is 
 divided into twelve equal parts, representing 
 the twelve signs of the zodiac ; these are again 
 subdivided into 30 degrees each, between which 
 are engraved their names and characters. This 
 space is connected with a fourth, which con- 
 tains the calendar of the months and days ; 
 each day, on the eighteen-inch globes being 
 divided into four parts, expressing the four 
 cardinal points of the day, according to the 
 Julian reckoning ; by which means the sun*s 
 place is very nearly obtained for the common 
 years after bissextile, and the intercalary day 
 is inserted without confusion. 
 
 In all positions of the celestial globe, this 
 broad paper circle represents the plane of the 
 horizon, and distinguishes the visible from the 
 invisible part of the heavens ; but in the ter- 
 restrial globe, it is applied to three different 
 uses. 
 
 1. To distinguish the points of the horizon. 
 In this case it represents the rational horizon of 
 any place. 
 
 2. It Is used to represent the circle of 
 
 208 
 
OF THE GLOBES. 23 
 
 Ulwnination, or that circle which separates day 
 from night. 
 
 3. It occasionally represents the ecliptic. 
 
 Of the strong brass circle N iE Z S. Oiie side 
 of this strong brass circle is graduated into four 
 quadrants, each containing 90 degrees. 
 
 The numbers :^n two of these quadrants in- 
 crease from the equator towards the poles ; 
 the other two increase from the poles towards 
 the equator. 
 
 Two of the quadrants are numbered from 
 the equator, to shew the distance of any point 
 on the globe from the equator. The other 
 two are numbered from the poles, for the more 
 ready setting the globe to the latitude of any 
 place. 
 
 The strong brass circle of the celestial globe 
 is called the meridian, because the centre of the 
 sun comes directly under it at noon. 
 
 But as there are other circles on the ter- 
 restrial globe, which are called meridians, we 
 chuse to denominate this the strong brass circle^ 
 or meridian. 
 
 The graduated side of the strong brass circle, 
 that belongs to the terrestrial globe, should face 
 the 'uoest. 
 
 The graduated side of the strong brazen 
 meridian of the celestial globe, should face the 
 east. 
 
 209 
 
24- DESCRIPTION AND USE 
 
 On the strong brass circle of the terrestrial 
 globe, and at about 23\ degrees on each side 
 of the north pole, the da)'S of each month are 
 laid down according to the declination of the 
 sun. 
 
 Of the Horary Circles, and their Indices. 
 When the globes are mounted in my father's 
 manner, we use the equator as the hour circle j 
 because it is not only the most natural, but 
 also the largest circle that can be applied for 
 that purpose. 
 
 To make this circle answer the purpose, a 
 semi-circular wire is placed over it, carrying 
 two indices, one on the east, the other on the 
 west side of the strong brass circle. 
 
 As the equator is divided into 369", or 24 
 hours, the time of one entire revolution of the 
 earth or heavens, the indices will shew in what 
 space of time any part of such revolution is 
 made among the hours which are graduated 
 below the degrees of the equator on either 
 globe. 
 
 As the motion of the terrestrial globe is 
 from west to east, the horary numbers increase 
 according to the direction of that motion : on 
 the celestial globe they increase from the east to 
 the west. 
 
 Of the (luadrant of Altitude, Z A. This is 
 a thin, narrow, flexible slip of brass, that will 
 bend to the surface of the globe ; it has a nut, 
 210 
 
OF THE GLOBES. 25 
 
 Tvith a fiducial iine upon it, which may be 
 readily applied to the divisions on the strong- 
 brass meridian of either globe. One edge of 
 the quadrant is divided into 90 degrees, and 
 the divisions are continued to 1 8 degrees below 
 the horizon. 
 
 OF SOME OF THE CIRCLES THAT ARE DESCRIB- 
 ED UPON THE SURFACE OF EACH GLOBE. 
 
 We may suppose as many circles to be de- 
 scribed on the surface of the earth as we please, 
 and conceive them to be extended to the 
 sphere of the heavens, making thereon con- 
 centric circles : for as we are obliged, in order 
 to distinguish one place from another, to ap- 
 propriate names to them, so are we obliged to 
 use different circles on the globes, to distinguish 
 th^ir parts, and their several relations to each 
 other. 
 
 Of the Equator^ or Equinoctial. This circle 
 goes round the globe exactly in the middle, be- 
 tween the two poles, from which it always 
 keeps at the same distance \ or in other words, 
 it is every where 90 degrees distant from each 
 pole, and is therefore a boundary, separating 
 the northern from the southern hemisphere j 
 hence it is frequently called the line by sailors, 
 and when they sail over it they are said to cross 
 the line. 
 
 D 211 
 
26 DESCRIPTION AND USE 
 
 It is that circle in the heavens in which 
 the sun appears to move on those two days, 
 the one in the spring, the other in the autumn, 
 when the days and nights are of an equal 
 length all over the world ; and hence on the 
 celestial globe it is generally called the cqui- 
 noclial. 
 
 It is graduated into 360 degrees. Upon 
 the terrestrial globe the numbers increase from 
 the meridian of London westward, and pro- 
 ceed quite round to 360. They are also num- 
 bered from the same meridian eastward, by an 
 upper row of figures, to accomodate those 
 who use the English tables of latitude and lon- 
 gitude. 
 
 On the celestial globe, the equatorial degrees 
 are numbered from the first point of Aries east- 
 ward, to 360 degrees. 
 
 Under the degrees on either globe is gra- 
 duated a circle of hours and minutes. On the 
 celestial globe the hours increase eastward, 
 from Aries to XII at Libra, where they begin 
 again in the same direction, and proceed to XII 
 at Aries. But on the terrestrial globe, the 
 horary numbers increase by twice twelve hours 
 westward from the meridian of London to the 
 same again. 
 
 In turning the globe about, the equator 
 keeps always under one point of the strong 
 212 
 
OF THE GLOBES. 27 
 
 brass meridian, from which point the degrees 
 on the said circle are numbered both ways. 
 
 Of the Ecliptic. The graduated circle, which 
 crosses the equator obliquely, forming with 
 it an angle of about 23 ^ degrees, is called the 
 ecliptic. 
 
 This circle is divided into twelve equal parts, 
 each of which contains thirty degrees. The 
 beginning of each of these thirty degrees is 
 marked with the characters of the twelve signs 
 of the zodiac. 
 
 The sun appears always in this circle ; he 
 advances therein every day nearly a decree, and 
 goes through it exactly in a year. 
 
 The points where this circle crosses the 
 equator are called the equinoctial points. The 
 one is at the beginning of Aries, the other at 
 the beginning of Libra. 
 
 The commencement of Cancer and Capricorn 
 are called the solstitial points. 
 
 The twelve signs, and their degrees, are laid 
 down on the terrestrial globe ; but upon the 
 celestial globe, the days of each month are gra- 
 duated just under the ecliptic. 
 
 The ecliptic belongs principally to the celes- 
 tial globe. 
 
 213 
 
PxVIlT III. 
 
 THL USE OF THE TERRESTRIAL GLOBE^ 
 MOUNTED IN THE BEST MANNER. 
 
 OF LONGITUDE AND LATITUDE, OF TERRK.STRIAL MERI- 
 DIANS, AND THE PROBLEMS RELATINCJ TO LONGITUDE 
 AND LATITUDE. 
 
 "l^ypfERIDIANS are circular lines, going over 
 X V Jl the earth's surface, from one pole to the 
 other, and crossing the equator at right angles. 
 
 Whatever places these circular lines pass 
 through, in going from pole to pole, they are 
 the meridians of those places. 
 
 There are no places upon the surface of the 
 earth, through which meridians may not be con- 
 ceived to pass. Every place, therefore, is sup- 
 posed to have a meridian line passing over it's 
 zenith from north to south, and going through 
 the poles of the world. 
 
 Thus the meridian of Paris is one meri- 
 dian ; the meridian of London is another. 
 This variety of meridians is satisfactorily rc- 
 214 
 
OF THE GLOBES. 29 
 
 presented on the globe, by the moveable meri- 
 dian, which may be set to every individual point 
 of the equator, and put directly over any parti- 
 cular place. 
 
 Whensoever we move towards the east or 
 west, we change our meridian ; but we do not 
 change our meridian if we move directly to the 
 north or south. 
 
 The moveable meridian shews that the poles 
 of the earth divide every meridian into two semi- 
 circles, one of which passes through the place 
 whose meridian it is, the other through a point 
 on the earth, opposite to that place. 
 
 Hence it is, that writers in geography and 
 astronomy generally mean by the meridian of 
 any place the semicircle which passes through 
 that place ; these, therefore, may be called the 
 geographical meridians. 
 
 All places lying under the same semicircle, 
 are said to have the same meridian ; and the 
 semicircle opposite to it is called the opposite 
 meridian, or sometimes the opposite part of the 
 meridian. 
 
 From the foregoing definitions, it is clear that 
 the meridian of any place is immoveably fixed 
 to that place, and is carried round along with it 
 by the rotation of the globe. 
 
 When the meridian of any place is by the re- 
 volution of the earth brought to point at the sun, 
 it is noon, or mid-day, at that place. 
 2L7 
 
30 DESCRIPTION AND USE 
 
 Tile plane of the meridian of any place may 
 be imagined to be extended to the sphere of 
 the fixed stars. 
 
 When, by the motion of the earth, the plane 
 of a meridian comes to any point in the heavens^ 
 as the sun, moon, Sec. that point, &c. is then 
 said to come to the meridian. It is in this sense 
 that we generally use the expression of the sun 
 or stars coming to, or passing over the meridian. 
 
 The time which elapses between the noon of 
 any one day in a given place, and the noon of 
 the day following in the same place, is called a 
 natural day. 
 
 All places which lie under the same meridian, 
 have their noon, and every other hour of the 
 natural day, at the same tinv?. Thus when it is 
 one in the afternoon at London, it is also one in 
 the afternoon to every place under the meridian 
 of London. 
 
 In order to ascertain the situation of any 
 point, there must first be a settled part of the 
 earth's surface, from which to measure ; and as 
 the point to be ascertained may lie in any part 
 of the earth's surface, and as this surface is 
 spherical, the place from whence we measure 
 must be a circle. It would be necessary, how- 
 ever to establish two such circles ; one to know 
 how fiir any place may be east or west of ano- 
 ther, the second to know it's distance north or 
 216 
 
OF THE GLOBES. CI 
 
 south of the given point, and thus determine it*j; 
 precise situation. 
 
 Hence it has been customary for geographer>= 
 to fix upon the meridian of some remarkable 
 place, as a first ?ncridiany or slandnrd ; and to 
 reckon the distance of any place to the cast or 
 •west, or it's longitude, by it*s distance from the 
 first meridian. On English globes, this first 
 meridian is made to pass through London. The 
 position of this first meridian is arbitrary, because 
 on a globe, properly speaking, there is neither 
 beginning nor end. The first person (whose 
 works at least are come down to us) who com- 
 puted the distance of places by longitudes and 
 latitudes was Ptolemy, about the year after 
 Christ 14-0. 
 
 The longitude of any place is it's distance from 
 the first meridian, measured by degrees on the 
 equator. 
 
 To find the longitude of a place, is to find 
 what degree on the equator the meridian of that 
 place crosses. 
 
 All places that lie under the same meridian, 
 are said to have the same longitude ; all places 
 that lie under different meridians, are said to 
 have different longitudes ; this difference may 
 be east or west, and consequently the difference 
 of longitude between any two places, is the dis- 
 tance of their meridians from each other measur- 
 ed on the equator. 
 
 217 
 
32 DESCRIPTION AND USE 
 
 Thus if the meridian of any, place cuts the 
 equator in a point, which is fifteen degrees 
 east from that point, where the meridian of 
 London cuts the equator, that place is said to 
 differ from London in longitude 15 degrees 
 eastward. 
 
 Upon the terrestrial globe there are 24 meri- 
 dians, dividing the equator into 24 equal parts, 
 which are the hour circles of the places through 
 which they pass. 
 
 The distance of these meridians from each 
 other is 15 degrees, or the 24th part of S60 
 degrees ; thus 15 degrees is equal to one hour. 
 
 By the rotation of the earth, the plane of 
 every meridian points at the sun, one hour af- 
 ter that meridian which is next to it eastward ; 
 and thus they successively point at the sun every 
 hour, so that the planes of the 24 meridian semi- 
 circles being extended, pass through thre sun in 
 a natural day. 
 
 To illustrate this, suppose the plane of the 
 strong brass meridian to coincide with the sun, 
 bring London to this meridian, and then move 
 the globe round, and you will find these 24 
 meridians successively pass under the strong 
 brass meridian, at one hour*s distance from 
 each other ; till in 24 hours the earth will re- 
 turn to the same situation, and the meridian of 
 218 
 
OF THE GLOBES. 33 
 
 London will again coincide with the strong brass 
 circle. 
 
 By passing the globe round, as in the fore- 
 going article, it will be evident to the pupil, 
 that if one of these meridians, 15 degrees east 
 of London, comes to the strong brass meridian, 
 or points at the sun one hour sooner than the 
 meridian of London, a meridian that is 30 de- 
 grees east comes two hours sooner, and so on ; 
 and consequently they will have noon, and 
 every other hour, so much sooner than at Lon- 
 don : while those, whose meridian is 15 degrees 
 westward from London, will have noon and 
 every other hour of the day, one hour later than 
 at London, and so on, in proportion to the 
 difference of longitude. These definitions being 
 well understood, the pupil will be prepared not 
 only to solve, but see the rationale of the follow- 
 ing problems. 
 
 PROBLEM I. 
 
 "To find the Longitude of any place on the Globe, 
 
 The reader will find no difficulty in solving 
 this problem, if he recollects the definition we 
 have given of the word longitude, namely, that 
 it is the distance of any place from the first 
 meridian measured on the equator. There- 
 fore, either set the moveable meridian to the 
 place, or bring the place under the strong brass 
 E 219 
 
34 DESCRIPTION AND USE 
 
 meridian, and that degree of the equator, which 
 is cut by either of the brazen meridians, is the 
 longitude in degrees and minutes, or the hour 
 and minute of its longitude, expressed in time. 
 
 As the given place may lie either east or west 
 of the first meridian, the longitude may be ex- 
 pressed accordingly. 
 
 It appears most natural to reckon the lon- 
 gitude always westward from the first meridian; 
 but it is customary to reckon one half round 
 the globe eastward, the other half westward 
 from the first meridian. To accomodate those 
 who may prefer either of these plans, there are 
 two sets of numbers on our globes : the num- 
 bers nearest the equator increase westward, from 
 the meridian of London quite round the globe 
 to 360°, over which another set of numbers is 
 engraved, which increase the contrary way j so 
 that the longitude may be reckoned upon the 
 equator, either east or west. 
 
 Example. Bring Boston, In New England, 
 to the graduated edge of either the strong brass, 
 or of the moveable meridian, and you will find 
 it*s longitude in degrees to be 70^, or 4 h, 
 42 min. In time ; Rome 1 2i degrees east, or 50 
 min. in time; Charles-Town, North-America, 
 is 79 deg. 50 min. west. 
 220 
 
OF THE GLOBES. 35 
 
 PROBLEM II. 
 
 To find the difference of longitude between any two 
 places. 
 
 If the pupil understands what is meant by the 
 difference of longitude, the rule for the solution 
 of this problem will naturally occur to his mind. 
 Now the difference of longitude between any 
 two places is the quantity of an angle (at the 
 pole) made by the meridians of those places 
 measured on the equator. To express this angle 
 upon the globe, bring the moveable meridian 
 to one of the places, and the other place under 
 the strong brass circle, and the required angle 
 is contained between these two meridians, the 
 measure or quantity of which is to be counted 
 on the equator. 
 
 Example, I find the longitude of Rome to 
 be 121 east, that of Constantinople to be 29 ; 
 the difference is 171 degrees. Again, I find 
 Jerusalem has 35 deg. 25 min. east longitude 
 from London ; and Pekin, in China, 1 1 6 deg. 
 52 min. east longitude ; the difference is 8 1 deg. 
 27 min. ; that is, Pekin is 81 deg. 27 min. east 
 longitude from Jerusalem ; or Jerusalem is 81 
 deg. 27 min. west longitude from Pekin. 
 
 If one place is east, and the other west of 
 the first meridian, either find the longitude of 
 both places westward, by that set of numbers 
 221 
 
3G DESCRIPTION AND USE 
 
 which increase westward from the meridian of 
 London to 360 deg. and the difference between 
 the number thus found is the answer to the 
 question : — or, add the east and west longitudes, 
 and the sum is the difference of longitude ; thus 
 the longitude of Rome is 12 deg. SO min. east, 
 of Charles-Town 79 deg. 50 min, west ; their 
 sum, 91 deg. 20 min. is the difference re- 
 quired. 
 
 It may be proper to observe here, that the 
 difference of time is the same with the difference 
 of longitude, consequently that some of the fol- 
 lowing problems are only particular cases of this 
 problem, or readier modes of computing this 
 difference. < 
 
 PROBLEM III. 
 
 To find all those places where it is noon, at any 
 given hour of the day, at any given place. 
 
 General rule. Bring the given place to the 
 brass meridian ; and set the index to the upper- 
 most XII ; then turn the globe, till the index 
 points to the given hour, and it will be noon to 
 all the places under the meridian. 
 
 As the diurnal motion of the earth is from 
 west to east, it is plain that all places which are 
 to the east of any meridian, must necessarily 
 pass by the sun before sf meridian which is to 
 the west can arrive at it. 
 222 
 
OF THE GLOBES. 37 
 
 N. B. As in nvf father*s globes, the XII, or 
 first meridian, passes through London, you have 
 only to bring the given hour to the east of 
 London, if in the morning, to the brass meri- 
 dian, and all those places which are under it 
 will have noon at the given hour ; but bring 
 the given hour westward of London, if it be in 
 the afternoon. 
 
 When it is 4 h. 50 min. in the afternoon at 
 Paris, it is noon at New Britain, New England, 
 St. Domingo, Terra Firma, Peru, Chili, and 
 Terra del Fuego. 
 
 When it is 7 h. 50 min. in the morning at 
 Ispahan, it is noon at the middle of Siberia, 
 Chinese Tartary, China, Borneo. 
 
 PROBLEM IV. 
 
 When it is noon at any place, to find what hour of 
 the day it is at any other place. 
 
 Rule. Bring the place at which it is noon, 
 to the strong brass meridian, and set the hour 
 index to the uppermost XII, and then turn the 
 globe about till the other place comes under 
 the strong brass meridian, and the hour index 
 will shew upon the equator the required hour. 
 If to the eastward of the place where it is 
 noon, the hour found will be in the afternoon ; 
 if to the westward, it will be in the forenoon. 
 
 223 
 
38 DESCRIPTION AND USE 
 
 Thus when it is noon at London, it is 50 min. 
 past XII, at Rome ; 32 min. past VII in the 
 evening at Canton, in China; 15 min. past VII 
 in the morning at Quebec, in Canada. 
 
 PROBLEM V. 
 
 The hour being given at any place, to tell what 
 hour it is in any other part of the world. 
 
 Rule. Bring the place where the time is re- 
 quired under the strong brass meridian, set the 
 hour index to the given time, then turn the 
 globe, till the other place is under the brass 
 meridian, and the horary index will point to 
 the hour required. 
 
 Thus suppose we are at London at IX o'clock 
 in the morning, what is the time at Canton, in 
 China? Answer, 31 min. past IV in the after- 
 noon. When it is IX in the evening at London, 
 it is about 15 min. past IV in the afternoon at 
 Quebec in Canada. 
 
 Thus also when it is III in the afternoon at 
 London, it is 18 min. past X in the forenoon at 
 Boston. When it is VI in the morning at the 
 Cape of Good Hope, it is 7 min. after mid- 
 night at Quebec. 
 
 224 
 
OF THE GLOBES. 39 
 
 OF LATITUDE. 
 
 I have already observed, that the equator 
 divides the globe into two hemispheres, the nor- 
 thern and the southern. 
 
 The latitude of a place is it's distance from 
 the equator tow^ards the north or south pole, 
 measured by degrees upon the meridian of the 
 place. 
 
 All places, therefore, that lie under the equa- 
 tor, are said to have no latitude. 
 
 All other places upon the earth are said to 
 be in north or south latitude, as they are situated 
 on the north or south side of the equator ; and 
 the latitude of any place will be greater or less, 
 according as it is farther from, or nearer to the 
 equator. 
 
 Lines, which keep always at the same distance 
 from each other, are called parallels. 
 
 If a circle, or circular line, be conceived keep- 
 ing at the same distance from the equator, it will 
 be a parallel to the equator. 
 
 Circles of this kind are commonly drawn 
 on the terrestrial globe, on both sides of the 
 equator. 
 
 A circle of this kind, at 10 degrees from the 
 equator, is called a parallel of 10 degrees. 
 
 When any such parallel passes through two 
 225 
 
40 DESCRIPTION AND USE 
 
 places on the globe's surface, those two places 
 have the same latitude. 
 
 Hence parallels to the equator are called pa- 
 rallels of latitude. 
 
 There are four principal lesser circles parallel 
 to the equator, which divide the globe into five 
 unequal parts, called zones. 
 
 The circle on the north side of the equator is 
 called the tropic of Cancer ; it just touches the 
 north part of the ecliptic, and shews the path 
 the sun appears to describe, the longest day in 
 summer. 
 
 That which is on the south side of the equa- 
 tor is called the tropic of Capricorn; it just 
 touches the south part of the echptic, and shews 
 the path the sun appears to describe, the short- 
 est day in winter. 
 
 The space between these two tropics, which 
 contains about 47 degrees, was called by the an- 
 cients the torrid zone. 
 
 The two polar circles are placed at the same 
 distance from the poles, that the two tropics are 
 from the equator. 
 
 One of these is called the northern, the other 
 the southern polar circle. 
 
 These include 231 degrees on each side of 
 their respective poles, and consequently contain 
 47 degrees, equal to the number of degrees in- 
 cluded between the tropics. 
 
 The space contained within the northern 
 226 
 
OF THE GLOBES. 41 
 
 i 
 
 polar circle, was by the ancients called the ?2ort/j 
 frigid zone ; and that within the southern polar 
 circle, the south frigid zone. 
 
 The spaces between either polar circle, and its 
 nearest tropic, which contain about 43 degrees 
 each, were called by the ancients the iivo temperate 
 zones. 
 
 PROBLEM VI. 
 
 To find the latitude of any place. 
 
 If the pupil comprehends the foregoing defi- 
 nition, he will find no difficulty in the solution 
 of this and some of the following problems. 
 
 Rule. Bring the place to the graduated side 
 of the strong brass meridian, and the degree 
 which is over it is the latitude. Thus London 
 will be found to have 51 deg. 30 min. north 
 latitude; Constantinople 41 deg. north latitude; 
 and the Cape of Good Hope 34 deg. south 
 latitude. 
 
 PROBLEM VII. 
 
 To find all those places which have the same lati- 
 tude ivith any given place. 
 
 Suppose the given place to be London ; turn 
 the globe round, and all those places which pass 
 under the same point of the strong brass meri- 
 dian, are in the same latitude. 
 F 227 
 
42 DESCRIPTION AND USB 
 
 I 
 
 PROBLEM VIII. 
 
 To find the difference of latitude between two 
 places. 
 
 Ride. If the places be in the same hemis- 
 phere, bring each of them to the meridian, and 
 subtract the latitude of one from the other. If 
 they are in different hemispheres, add the lati- 
 tude of one to that of the other. 
 
 Example. The latitude of London is 51 deg. 
 32 min. ; that of Constantinople 41 deg. ; their 
 difference is 10 deg. 32 min. The difference be- 
 tween London, 51 deg. 32 min. north, and the 
 Cape of Good Hope, 34 deg. south, is 84 deg. 
 32 min. 
 
 PROBLEM IX. 
 
 The latitude and longitude of any place being known ^ 
 to find that place upon the globe. 
 
 Rule. Seek for the given longitude in the 
 equator, and bring the moveable meridian to 
 that point ; then count from the equator on the 
 meridian, the degree of latitude either towards 
 the north or south pole, and bring the artificial 
 horizon to that degree, and the intersection of 
 it's edge with the meridian is the situation re- 
 quired. 
 
 By this problem any place not represented 
 qn the globe may be laid down thereon, and 
 228 
 
OF THE GLOBES. 43, 
 
 kt may be seen where a ship is when it*s latitude 
 and longitude are known. 
 
 Example. The latitude of Smyrna, in Asia, 
 is 38 d€g. 28 min. north ; it*s longitude 27 deg. 
 SO min. east of London ; therefore, bring 27 ^eg, 
 30 min. counted eastward on the equator, to the 
 moveable meridian, and slide the diameter of 
 the artificial horizon to 38 deg. 28 min. north 
 latitude, and it's center will be correctly placed 
 over Smyrna. 
 
 It may be proper in this place just to shew 
 the pupil, that the latitude of any place is always 
 equal to the elevation of the pole of the same place 
 above the horizon. The reason of this is, that 
 from the equator to the pole are 90 degrees, 
 from the zenith to the horizon are also 90 
 degrees ; the distance of the zenith to the pole 
 is common to both, and therefore if taken 
 away from both, must leave equal remains ; that 
 is, the distance from the equator to the zenith, 
 which is the latitude, is equal to the elevation of 
 the pole. 
 
 OF FINDING THE LONGITUDE. 
 
 As the finding the longitude of places forms 
 one of the most important problems in geogra- 
 phy and astronomy, some further account of it, 
 it is presumed, will prove entertaining and use- 
 ful to the reader. 
 
 229 
 
4>4: DESCRIPTION AND USE 
 
 " For what can be more interesting to a 
 person in a long voyage, than to be able to tell 
 upon what part of the globe he is, to know how 
 far he has travelled, what distance he has to go, 
 and how he must direct his course to arrive at 
 the place he designs to visit ? These important 
 particulars are all determined by knowing the 
 latitude and longitude of the place under con- 
 sideration. When the discovery of the com- 
 pass invited the voyager to quit his native shore, 
 and venture himself upon an unknown ocean, 
 that knowledge, which before he deemed of no 
 importance, now became a matter of absolute 
 necessity. Floating in a frail vessel, upon an 
 uncertain abyss, he has consigned himself to the 
 mercy of the winds and waves, and knows not 
 
 where he is.'** 
 
 The following instance will prove of what 
 
 use it is to know the longitude of places at sea. 
 
 The editor of Lord Anson's voyage, speaking 
 
 of the island of Julian Fernandez, adds, " The 
 
 uncertainty we were in of it's position, and our 
 
 standing in for the main on the iiSth of May, 
 
 in order to secure a sufficient easting, when we 
 
 were indeed extremely near it, cost us the lives 
 
 of between 70 and 80 of our men, by our 
 
 longer continuance at sea ; from which fatal 
 
 accident we might have been exempted, had 
 
 * Bcnnycaslle's Astronovny. 
 230 
 
OF THE GLOBES. 45 
 
 we been furnished with such an account of it*s 
 situation, as we could fully have depended on." 
 
 The latitude of a place the sailor can easily 
 discover ; but the longitude is a subject of the 
 utmost difficulty, for the discovery of which 
 many methods have been devised. It is indeed 
 of so great consequence, that the Parliament of 
 Great Britain proposed a reward of 10,000/. if 
 it extended only to 1 degree of a great circle, 
 or 60 geographical miles; 15,000/. if found to 
 40 such miles ; and 20,000/. to the person that 
 can find it within 30 minutes of a great circle, or 
 30 geographical miles. 
 
 As I cannot enter fully into this subject in 
 these essays, it will, I hope, be deemed sufficient, 
 if I give such an account as will enable the reader 
 to form a general idea of the solution of this im- 
 portant problem. 
 
 From what has been seen in the preceding 
 pages, it is evident that 15 degrees in longitude 
 answer to one hour in time, and consequently 
 that the longitude of any place would be known, 
 if we knew their difference in time ; or in other 
 words, how much sooner the sun, &c. arrives at 
 the meridian of one place, than that of another, 
 The hours and degrees being in this respect 
 commensurate, it is as proper to express the dis- 
 tance of any place in time as in degrees. 
 
 231 
 
4-6 DESCRIPTION AND USE 
 
 Now it is clear, that this difference in time 
 would be easily ascertained by the observation 
 of any instantaneous appearance in the heavens, 
 at two distant places ; for the difference in time 
 at which the same phenomenon is observed, will 
 be the distance of the two places from each other 
 in longitude. On this principle, most of the 
 methods in general use are founded. 
 
 Thus if a clock, or watch, was so contrived, 
 as to go uniformly in all seasons, and in all 
 places ; such a watch being regulated to Lon- 
 don time, would always shew the time of the 
 day at London ; then the time of the day under 
 any other meridian being found, the difference 
 between that time, and the corresponding Lon- 
 don time, would give the difference in longi- 
 tude. 
 
 For supposing any person possessed of one of 
 these time-pieces, to set out on a journey from 
 London, if his time piece be accurately adjust- 
 ed, wherever he is, he will always know the 
 hour at London exactly ; and when he has pro- 
 ceeded so far either eastward or westward, that 
 a difference is perceived betwixt the hour 
 shewn by his time-piece, and those of the 
 clocks and watches at the places to which he 
 goes, the distance of those places from London 
 in longitude will be known. But to whatever 
 degree of perfection such movements may be 
 09,0 
 
OF THE GLOBES. 47 
 
 made, yet as every mechanical instrument is 
 liable to be injured by various accidents, other 
 methods are obliged to be used, as the eclipses 
 of the sun and moon, or of Jupiter's satellites. 
 Thus supposing the moment of the beginning 
 of an eclipse was at ten o'clock at night at 
 London, and by accounts from two observers 
 in two other places, it appears that it began with 
 one of them at nine o'clock, and with the other 
 at midnight ; it is plain, that the place where it 
 began at nine is one hour, or 1 5 degrees east in 
 longitude from London ; the other place where 
 it began at midnight, is 30 degrees distant in 
 west longitude from London. Eclipses of the 
 sun and moon do not, however, happen often 
 enough to answer the purposes of navigation j 
 and the motion of a ship at sea prevents the ob- 
 servations of those of Jupiter's satellites. 
 
 If the place of any celestial body be com- 
 puted, for example, as in an almanack, for every 
 day or to parts of days, to any given meridian, 
 and the place of this celestial body can be found 
 by observation at sea, the difference of time 
 between the time of observation and the com- 
 puted time, will be the difference of longitude 
 in time. The moon is found to be the most 
 proper celestial object, and the observations of 
 her appulses to any fixed star is reckoned one 
 of the best methods for resolving this difficult 
 problem. 
 
 233 
 
48 DESCRIPTION AND USE 
 
 LENGTH OF THE DEGREES OF LONGITUDE. 
 
 Supposing the earth to be a perfect globe, 
 the length of a degree upon the meridian has 
 been estimated to be 69,1 miles ; but as the 
 earth is an oblate spheroid, the length of a degree 
 on the equator will be somewhat greater. 
 
 Whether the earth be considered as a sphe- 
 roid or a globe, all the meridians intersect one 
 another at the poles. Therefore, the number 
 of miles in a degree must always decrease as 
 you go north or south from the equator. This 
 is evident by inspection of a globe, where the 
 parallels of latitude are found to be smaller in 
 proportion as they are nearer the pole. Hence 
 it is that a degree of longitude is no where the 
 same, but upon the same parallel ; and that a 
 degree of longitude is equal to a degree of lati- 
 tude only upon the equator. 
 
 The following table shews how many geogra- 
 phical miles, and decimal parts of a mile, would 
 be contained in a degree of longitude, at each 
 degree of latitude from the equator to the poles, 
 if the earth was a perfect sphere, and the cir- 
 cumference of it's equinoctial line 360 degrees, 
 and each degree 60 geographical miles. 
 
 This table enables us to determine the velo- 
 city with which places upon the globe revolve 
 !2S4 
 
OF THE GLOBES. 49 
 
 eastward ; for the velocity is different, accord- 
 ing to the distance of the places from the equa- 
 tor, being swiftest as passing through a greater 
 space, and so by degrees slower towards the 
 pole, as passing through a less space in the same 
 time. Now as every part of the earth is moved 
 through the space of it's circumference, or 360 
 degrees, in 24 hours ; the space described in 
 one hour is found by deviding 360 by 24, which 
 gives in the quotient 1 5 degrees ; and so many 
 degrees does every place on the earth move in 
 an hour. The number of miles contained in so 
 many degrees in any latitude, is readily found 
 from the table. 
 
 Thus under the equator places revolve at the 
 rate of more than 1000 miles In an hour ; at 
 London, at the rate of about 640 miles in an 
 hour. 
 
 
 TABLE. 
 
 
 
 LAT. 
 
 
 LAT. 
 
 
 LAT. 
 
 Deg. Miles, 
 
 Deg, Miles. 
 
 Deg 
 
 •. Miles. 
 
 00 60,00 
 
 10 
 
 59,08 
 
 20 
 
 56,38 
 
 1 59,99 
 
 11 
 
 58,89 
 
 21 
 
 56,01 
 
 2 59,96 
 
 12 
 
 58,68 
 
 22 
 
 55,63 
 
 3 59,92 
 
 13 
 
 58,46 
 
 23 
 
 55,23 
 
 4 59,86 
 
 14 
 
 58,22 
 
 24 
 
 54,81 
 
 5 59,77 
 
 15 
 
 57,95 
 
 25 
 
 54,38 
 
 6 59,67 
 
 IQ 
 
 57,67 
 
 26 
 
 53,93 
 
 7 59,56 
 
 17 
 
 57,37 
 
 27 
 
 53,46 
 
 8 59,42 
 
 18 
 
 57,06 
 
 28 
 
 52,97 
 
 9 59,26 
 
 19 
 G 
 
 56,73 
 235 
 
 29 
 
 52,47 
 
50 DESCRIPTION AND USE 
 
 
 LAT. 
 
 LAT. 
 
 LAT. 
 
 Deg 
 
 . Miles. 
 
 Deg, 
 
 . Miles. 
 
 Deg, 
 
 Miles. 
 
 30 
 
 51,96 
 
 51 
 
 37,76 
 
 72 
 
 18,55 
 
 31 
 
 51,43 
 
 52 
 
 36,94 
 
 73 
 
 17,54 
 
 32 
 
 50,88 
 
 53 
 
 36,11 
 
 74 
 
 16,53 
 
 33 
 
 50,32 
 
 54 
 
 35,26 
 
 75 
 
 15,52 
 
 34 
 
 49,74 
 
 55 
 
 34,41 
 
 76 
 
 14,51 
 
 35 
 
 49,15 
 
 56 
 
 33,5^ 
 
 77 
 
 13,50 
 
 36 
 
 48,54 
 
 57 
 
 32,68 
 
 78 
 
 12,47 
 
 37 
 
 47,92 
 
 58 
 
 31,79 
 
 79 
 
 11,45 
 
 38 
 
 47,28 
 
 59 
 
 30,90 
 
 80 
 
 10,42 
 
 39 
 
 46,62 
 
 60 
 
 30,00 
 
 81 
 
 9,38 
 
 40 
 
 45,95 
 
 61 
 
 29,09 
 
 82 
 
 8,35 
 
 41 
 
 45,28 
 
 62 
 
 28,17 
 
 83 
 
 7,32 
 
 42 
 
 44,59 
 
 63 
 
 27,24 
 
 84 
 
 6,28 
 
 43 
 
 43,88 
 
 64 
 
 26.30 
 
 85 
 
 5,23 
 
 44 
 
 43,16 
 
 65 
 
 25,36 
 
 86 
 
 4,18 
 
 45 
 
 42,43 
 
 66 
 
 24,41 
 
 87 
 
 3,14 
 
 46 
 
 41,68 
 
 67 
 
 23,45 
 
 88 
 
 2,09 
 
 •47 
 
 40,92 
 
 68, 
 
 22,48 
 
 89 
 
 1,05 
 
 48 
 
 40,15 
 
 69 
 
 21,50 
 
 90 
 
 0,00 
 
 49 
 
 39,36 
 
 70 
 
 20,52 
 
 
 
 50 
 
 38,57 
 
 71 
 
 19,54 
 
 
 
 Another circumstance which arises from this 
 difference of meridians in time, must detain us 
 a Httle before we quit this subject. For from 
 this . difference it follows, that if a ship sails 
 round the world, always directing her course 
 eastward, she will at her return home find she 
 has gained one whole day of those that stayed at 
 home ; that is, if they reckon it May 1 , the ship's 
 company will reckon it May 2 j if westward, a 
 day less, or April 30. 
 
 236 
 
OF THE GLOBES. 51 
 
 This circumstance has been taken notice of 
 by navigators. " It was during our stay at 
 Mindanao, (says Capt. Dampier) that we were 
 first made sensible of the change of time in the 
 course of our voyage : for having travelled so 
 far westward, keeping the same course with the 
 sun, we consequently have gained something 
 insensibly in the length of the particular days, 
 but have lost in the tale the bulk or number of 
 the days or hours. . 
 
 " According to the different longitudes of 
 England and Mindanao, this isle being about 
 210 degrees west from the Lizard, the differ- 
 ence of time at our arrival at Mindanao ought 
 to have been about fourteen hours ; and so 
 much we should have anticipated our reckon- 
 ing, have gained it by bearing the sun com- 
 pany. 
 
 *' Now the natural day in every place must 
 be consonant to itself; but going about with, 
 or against the sun*s course, will of necessity 
 make a difference in the calculation of the civil 
 day, between any two places. Accordingly, at 
 Mindanao, and other places in the East Indies, 
 we found both natives and Europeans reckoning 
 a day before us. For the Europeans coming 
 eastward, by the Cape of Good Hope, in a 
 course contrary to the sun and us, wherever we 
 met, were a full day before us in their ac- 
 counts. 
 
 237 
 
52 DESCRIPTION AND USE 
 
 *' So among the Indian Mahometans, their 
 Friday was Thursday with us ; though it was 
 Friday also with those that came eastward from 
 Europe. 
 
 " Yet at the Ladrone islands we found the 
 Spaniards of Guam keeping the same compu- 
 tation with ourselves ; the reason of which I 
 take to be, that they settled that colony by a 
 course westward from Spain ; the Spaniards 
 going first to America and thence to the La- 
 drone islands." 
 
 It is clear, from what has been said in the 
 first part of this article, concerning both latitude 
 and longitude, that if a person travel ever so far 
 t^irectly towards east or west, his latitude would 
 be always the same, though his longitude would 
 be continually changing. 
 
 But if he went directly north or south, his 
 longitude would continue the same, but his 
 latitude would be perpetually varying. 
 
 If he went obliquely, he would change both 
 his latitude and longitude. 
 
 The longitude and latitude of places give 
 only their relative distances on the globe ; to 
 discover, therefore, their real distance, we have 
 recourse to the following problem. 
 23« 
 
OF THE GLOBES. 53 
 
 PROBLEM X. 
 
 Any place bein^ give?i, to find the distance of that 
 ■place from another, in a great circle of the 
 earth. 
 
 I shall divide this problem into three cases. 
 
 Case 1. If the places lie under the same me- 
 ridian. Bring them up to the meridian, and 
 mark the number of degrees intercepted be- 
 tween them. Multiply the number of degrees 
 thus found by fc>0, and they will give the num- 
 ber of geographical miles between the two 
 places. But if we would have the number of 
 English miles, the degrees before found must be 
 multiplied by 69|. 
 
 Case 2. If the places lie under the equator. 
 Find their difference of longitude in degrees, 
 and multiply, as in the preceding case, by 
 60 or 691. 
 
 Case 3. If the places lie neither under the 
 same meridian, nor under the equator. Then 
 lay the quadrant of altitude over the two places, 
 and mark the number of degrees intercepted 
 between them. These degrees multiplied as 
 above mentioned, will give the required dis- 
 t-ance. 
 
 239 
 
54 DESCRIPTION AND USJt 
 
 PROBLEM XI. ^ 
 
 To find the angle of position of places,. 
 
 The angle of position is that formed between 
 the meridian of one of the places, and a great 
 circle passing through the other place. 
 
 Rectify the globe to the latitude and zenith 
 of one of the places, bring that place to the 
 strong brass meridian, set the graduated edge 
 of the quadrant to the other place, and the 
 number of degrees contained between it and the 
 strong brass meridian, is the measure of the 
 angle sought. Thus, 
 
 The angle of position between the meridian 
 of Cape Clear, in Ireland, and St. Augustine, in 
 Florida, is about 82 degrees south westerly ; but 
 the angle of position between St. Augustine and 
 Cape Clear, is only about 46 degrees north 
 easterly. 
 
 Hence it is plain, that the line of position, or 
 azimuth, is not the same from either place to 
 the other, as the romb-line are. 
 
 PROBLEM y.n. 
 
 To find the bearing of one place from another. 
 
 The bearing of one sea-port from another 
 is determined by a kind of spiral, called a 
 romb-line, passing from one to the other, so as 
 240 
 
OF THE GLOBES. 55 
 
 to make equal angles with all the meridians it 
 passes by ; therefore, if both places are situated 
 on the same parallel of latitude, their bearing is 
 either east or west from each other ; if they are 
 upon the same meridian, they bear north and 
 south from one another; if they lie upon a romb- 
 line, their bearing is the same with it ; if they 
 do not, observe to which romb-line the two 
 places are nearest parallel, and that will shew 
 the bearing sought. 
 
 Example, Thus the bearing of the Lizard 
 point from the island of Bermudas is nearly 
 E. N. E. ; and that of Bermudas from the 
 Lizard is W. S. W. both nearly upon the same 
 romb-line, but in contrary directions. 
 
 OF THE TWILIGHT. 
 
 That light which we have from the sun be- 
 fore it rises, and after it sets, is called the twi- 
 light. 
 
 The morning twilight, or day break, com- 
 mences when the sun comes within eighteen de- 
 grees of the horizon, and continues till sun- 
 rising. The evening twilight begins at sun- 
 setting, and continues till it is eighteen degrees 
 below the horizon. 
 
 To illustrate the causes of the various length 
 of twilight in different places, a wire circle is 
 fixed eighteen degrees below the surface of the 
 241 
 
J6 DESCRIPTION AND USE 
 
 broad paper circle ; so that all those places 
 which are above the wire circle will have twi- 
 light, but it will be dark to all those places be- 
 low it. 
 
 I have already observed, that it is owing to 
 the atmosphere that we are favoured with the 
 light of the sun before he is above, and after he 
 is below, our horizon. Hence, though after 
 sun-setting we receive no direct light from the 
 sun, yet we enjoy his reflected light for some 
 time ; so that the darkness of the night does not 
 come on suddenlv, but by degrees. 
 
 In a right position of the sphere the twilights 
 are quickly over, because the sun rises and sets 
 nearly in a perpendicular ; but in an oblique 
 sphere they last longer, the sun rising and set- 
 ting obliquely. The greater the latitude of the 
 place, the longer is the duration of the twilight ; 
 so that all those who are in 49 degrees of lati- 
 tude have in the summer, near the solstice, their 
 atmosphere enlightened the whole night, the twi- 
 light lasting till sun-rising. 
 
 In a parallel sphere, the twilight lasts for 
 several months ; so that the inhabitants of this 
 position have either direct or reflex light of the 
 sun nearly all the year, as will plainly appear by 
 the globe. 
 
 242 
 
OF THE GLOBES. Sj 
 
 OF THE DIURNAL MOTION OF THE EARTH, 
 AND THE PROBLEMS DEPENDING ON THAT 
 MOTION. 
 
 As the daily motion of the earth about it*s 
 axis, and the phenomena dependent on it, are 
 some of the most essential points which a begin- 
 ner ought to have in view, we shall now endea- 
 vour to explain them by the globes ; and here I 
 think the advantage of globes mounted in my 
 father's manner, over those generally used, will 
 be very evident. 
 
 I have already observed, that in globes mount- 
 ed in our manner, the motion of the terrestrial 
 globe about it's axis represents the diurnal 
 motion of the earth, and that the horary index 
 will point out upon the equator the 24 hours of 
 one diurnal rotation, or any part of that time. 
 
 I shall now consider the broad paper circle as 
 the plane which distinguishes light from darkness ; 
 that is, the enlightened half of the earth's sur- 
 face, from that which is not enlightened. 
 
 For when the sun shines upon a globe, he 
 shines only upon one half of it ; that is, one half 
 of the globe's surface is enlightened by him, the 
 other not. 
 
 That the enlightened half may be that half 
 H 243 
 
58 DESCRIPTION AND USE 
 
 which is above the broad paper circle, we must 
 imagine the sun to be in our zenith. 
 
 Or let a sun be painted on the ceiling over 
 the terrestrial globe, the diameter of the picture 
 equal to the diameter of the globe. 
 
 Then all those places that are above the 
 broad paper circle will be in the sun's light ; that 
 is, it will be day in all those places. 
 
 And all places that are below this circle, will 
 be out of the sun's light ; that is, in all those 
 places it will be night. 
 
 When any place on the earth's surface comes 
 to the edge of the broad paper circle, passing 
 out of the shade into the light, the sun will ap- 
 pear rising at that place. 
 
 And when a place is at the edge of the broad 
 ^aper circle, going out of the light into the 
 shade, the sun will appear at that place to be 
 setting. 
 
 When we view the globe in this position, we 
 at once see the situation of all places in the illu- 
 tninated hemisphere, whose inhabitants enjoy the 
 light of the day. One edge of the broad paper 
 circle shews at what place the sun appears 
 rising at the same time ; and the opposite edge 
 shews at what places the sun is setting at the 
 Same time. 
 
 The horary index shews how long a place 
 is moving from one edge to the other ; that is, 
 how long the day or night is at that place. 
 244 
 
OF THE GLOBES. 59 
 
 and, consequently, when the globe is thus situ- 
 ated, you readily discover the time of the sun's 
 rising and setting on any given day, in any given 
 place. 
 
 TO RECTIFY THE TERRESTRIAL GLOBE. 
 
 To rectify the terrestrial globe, is to place it 
 in the same position in which our earth stands to 
 the sun, at all or at any given times. 
 
 That half of the earth's surface which is en- 
 lightened by the sun is not always the same ; it 
 differs according as the sun's declination differs. 
 
 To rectify, then, the terrestrial globe, is to 
 bring it into such a position, as that the enlight- 
 ened half of the earth's surface may be all above 
 the broad paper circle. 
 
 On the back side of the strong brass meridian, 
 and on each side of the north pole, the months 
 and days of the month are graduated in two 
 concentric spaces, agreeable to the declination of 
 the sun. 
 
 Bring the day of the month that is graduated 
 on the back side of the strong brass meridian, 
 to coincide with the broad paper circle, and the 
 globe is rectified. 
 
 Thus set the first of May to coincide with 
 the broad paper circle, and that half of the 
 earth's surface which is enlightened at any 
 245 
 
60 DESCRIPTION AND USE 
 
 time upon that day, will be all at once above 
 the said circle. 
 
 If the horary index be set to XII, when any 
 particular place is brought under the strong 
 brass meridian, it will shew the precise time of 
 sun-rising and sun-setting at that place, accord- 
 ing as that place is brought to the eastern or 
 western edge of the broad paper circle. 
 
 It will also shew how long any place is in 
 moving from the east to the west side of the 
 illuminated disk, and thence the length of the 
 day and night. 
 
 It will also point out the length of the twi- 
 light, by shewing the time in which the place is 
 passing from the twilight circle to the edge of 
 the broad paper circle on the western side j or 
 from the edge of this circle on the eastern side, 
 to the twilight wire, and thus determine the 
 length of the whole artificial day. 
 
 N. B. The twilight wire is placed at 18 de# 
 grees from the broad paper circle. 
 
 I shall now proceed to exemplify upon the 
 globes these particulars, at three different sea- 
 sons of the year, viz. the summer solstice, the 
 winter soktice, and the time or times of the 
 equinoxes* 
 
 246 
 
OF THE GLOBES Ol 
 
 PROBLEM XIII. 
 
 To place the globe ifi the same sit nation , luitb respect 
 to the Sim, as our earth is in at the time of the 
 
 SUMMER SOLSTICE. 
 
 Rectify the globe to the extremity of the di- 
 visions for the month of June, or 2ij\ degrees 
 north declination ; that is, bring these divisions 
 on the strong brass meridian to coincide with 
 the plane of the broad paper circle. 
 
 Then that part of the earth's surface, which 
 is within the northern polar circle, will be above 
 the broad paper circle, and will be in the light, 
 and the inhabitants thereof will have no night. 
 
 But all that space which is contained within 
 the southern polar circle, will continue in the 
 shade ; that is, it will there be continual 
 night. 
 
 In this position of the globe, the pupil will 
 observe how much the diurnal arches of the pa- 
 rallels of latitude decrease, as they are more and 
 more distant from the elevated pole. 
 
 If any place be brought under the strong 
 brass meridian, and the horary index is set to 
 that XII which is most elevated, and the place 
 be afterwards brought to the western side of 
 the broad paper circle, the hour index will 
 shew the time of sun-rising ; and when the 
 247 
 
62 
 
 DESCRIPTION AND USt 
 
 place is moved to the eastern edge, the index 
 points to the time of sun-setting. 
 
 The length of the day is obtained by the time 
 shewn by the horary index, while the globe 
 moves from the west to the east side of the broad 
 paper circle. 
 
 Thus it will be found, that at London the sun 
 rises about 15 minutes before IV in the morning, 
 and sets about 15 minutes after VIII at night. 
 
 At the following places it will be nearly at the 
 times expressed in the table. 
 
 
 
 
 Rising. 
 h. m. 
 
 O 
 
 Setting. 
 h. m. 
 
 Lcntjth 
 of day. 
 h. in- 
 
 light. 
 h. ni. 
 
 Cape Horn 
 
 8 44 
 
 3 16 
 
 6 32 
 
 2 35 
 
 Cape of Good Hope 
 
 7 9 
 
 i 51 
 
 9 42 
 
 1 43 
 
 Rio de Janeiro, in Brazil 
 
 6 42 
 
 5 19 
 
 10 38 
 
 1 23 
 
 Island of St. Thomas's near 
 
 
 
 
 
 the ecjuator. 
 Cape Lucas, California 
 
 6 
 5 12 
 
 6 
 
 6 48 
 
 12 
 13 36 
 
 1 20 
 
 1 35 
 
 We also see, that at the same time the sun is 
 rising at London, it is rising at the isles of Si- 
 cily and Madagascar. 
 
 And, that at the same time when the sun sets 
 at London it is setting at the island of Madeira, 
 and at Cape Horn. 
 
 And when the sun is setting at the island of 
 Borneo, in the East Indies, it is rising at Flo- 
 rida, in America. And many other similar 
 248 
 
OF THE GLOBES. 63 
 
 circumstances relative to other places, are seen 
 Hs it were by inspection. 
 
 PROBLEM XIV. 
 
 To explain the situation of the earthy ivith re- 
 spect to the sun, at the time of the winter 
 
 SOLSTICE. 
 
 Rectify the globe to the extremity of the di- 
 visions for the month of December, or to 231 
 degrees south declination. 
 
 When it will be apparent that the whole space 
 within the southern polar circle is in the sun's 
 light, and enjoys continual day; whilst that of 
 the northern polar circle is in the shade, and has 
 continual night. 
 
 If the globe be turned round, as before, the 
 horary index will shew, that at the several places 
 before-mentioned their days will be respectively 
 equal to what their nights were at the time of 
 the summer solstice. 
 
 It will appear farther, that it is now sun-set- 
 ting at the same time in those places in which it 
 was sun-rising at the same time at the summer 
 solstice ; and, on the contrary, sun-rising at the 
 time it then appeared to set. 
 249 
 
64 DESCRIPTION AND USE 
 
 PROBLEM. XV. 
 
 To plac^ the globe in the situation of the earthy at 
 the times of the equinox. 
 
 The sun has no decimation at the times of the 
 equinox, consequently there must be no eleva- 
 tion of the pole. 
 
 Bring the day of the month when the sun en- 
 ters the first point of Aries, or day of the month 
 when the sun enters the first point of Libra, to 
 the plane of the broad paper circle ; then the 
 two poles of the globe will be in that plane also, 
 and the globe will be in the position which is 
 called a right sphere. 
 
 For it is a right sphere when the two poles 
 are in the plane of the broad paper circle, be- 
 cause then all those circles which are parallel to 
 the equator will be at right angles to that plane. 
 
 If the globe b^ now turned from west to east, 
 it will plainly appear, that all places upon it's 
 surface are twelve hours above the broad paper 
 circle, and tv/elve hours below It ; that is, the 
 days are twelve hours long all over the earth, 
 and the nights are equal to the days, whence 
 these times are called the times of equinox. 
 
 Two of these occur in every year ; the first 
 250 
 
OF THE GLOBES. 65 
 
 is the autumnal, the second the vernal equi- 
 nox. 
 
 At these seasons the sun appears to rise at the 
 same time to all places that are on the same me- 
 ridian. The sun sets also at the same time in all 
 those places. 
 
 Thus if London and Mundford, on the gold 
 coast, be brought to the strong brass meridian, 
 the graduated side of which is in this case the 
 horary index, and they be afterwards carried to 
 the western edge of the broad paper circle, the 
 index will shew that the sun rises at VI at both 
 places ; when they are carried to the eastern 
 edge, the index points to VI for the time of sun- 
 setting. 
 
 N. B. If London be not the given place, the 
 hour index is to be set to the most elevated XII, 
 while the place is under the graduated edge of 
 the strong brass meridian. 
 
 The following circumstances, which usually 
 attend the four cardinal divisions of the year, 
 cannot be better introduced than at this place. 
 At the time of the equinoxes, when the sun 
 passes from one hemisphere into the other, 
 there is almost constantly some disturbance in 
 the weather ; the winds are then generally 
 higher : at the vernal equinox they are for the 
 most part easterly, cold, dry, and searching. 
 The solstitial point of the summer is often dis- 
 tinguished by violent rains, and that we call 
 I 251 
 
06 -' DESCRIPTION AND USE 
 
 a midsummer flood. The winter being less rainy' 
 than the summer, nothing particular happens 
 at the winter solstice, but that the frosts corii- 
 monly set in more severely, with some quantity 
 of snow upon the ground. 
 
 OF THE ARTIFICIAL OR TERRESTRIAL 
 HORIZON. 
 
 The brass circle, which may be slipped from 
 pole to pole on the moveable meridian, has 
 been already described. The circumference of 
 it is divided into eight parts, to which areaflix- 
 ed the initial letters of the mariner's compass. 
 
 When the center of it is set to any particular 
 place, the situation of any other place is seen, 
 with respect to that place ; that is, whether they 
 be east, west, north, or sc uth of it. 
 
 It will therefore represent the horizon of that 
 place. 
 
 We shall here use this artificial horizon, to 
 shew why the sun, although he be always in one 
 and the same place, appears to the inhabitants 
 of the earth at different altitudes, and in different 
 azimuths. 
 
 252 
 
OF THE GLOBES, fj" 
 
 PROBLEM XVr. 
 
 To exemplify the sun's altitude, as observed with 
 an artificial horizon. 
 
 The altitude of the sun is greater Or less, ac- 
 cording as the Hne which goes from us to the sun 
 is nearer to, or farther off from our horizon. 
 
 Let the moveable circle be applied to any place, 
 as London, then will the horizon of London be 
 thereby represented. 
 
 The sun is supposed, as before, to be in the 
 zenith, that is, directly over the terrestrial 
 globe. 
 
 If then from London a line go vertically up- 
 wards, the sun will be seen at London in that 
 line. 
 
 At sun-rising, when London is brought to the 
 west edge of the broad paper circle, the suppos- 
 ed line will be parallel to the artificial horizoUj 
 and the sun will then be seen in the horizon. 
 
 As the globe is gradually turned from the 
 west towards the east, the horizon will recede 
 from that line which goes from London verti- 
 cally upwards ; so that the line in which the 
 sun is seen gets further and further from the 
 horizon ; that is, the sun's altitude increases 
 gradually. 
 
 25S 
 
68 DESCRIPTION AND USE 
 
 When the horizon, and the hne "vhich goes 
 from London vertically upwards, are arrived at 
 the strong brass meridian, the sun is then at his 
 greatest or meridian altitude for that day, and 
 the line and horizon arc at the largest angle 
 they can make with each other. 
 
 After this, the motion of the globe being con- 
 tinued, the angle between the artificial horizon, 
 and the line which goes from London vertically 
 upwards, continually decreases, until London 
 arrives at the eastern edge of the broad paper 
 circle ; it'sjiorizon then becomes vertical again, 
 and parallel to the hne which goes vertically up- 
 wards. The sun will again appear in the hori- 
 zon, and will set. 
 
 PROBLEM XVII. 
 
 Of the suns meridian altitude^ at the three differ- 
 ent seasons. 
 
 Rectify the globe to the time of the winter 
 solstice, by problem xiv, and place the center of 
 the visible horizon on London. 
 
 When London is at the graduated edge of the 
 strong brass meridian, the line which goes verti- 
 cally upwards makes an angle of about 15 de- 
 grees ; this is the sun's meridian altitude at that 
 season, to the inhabitants of London. 
 
 If the globe be rectified to the times of 
 equinox, by problem xv, the horizon will be 
 254 
 
OF THE GLOBES. 69 
 
 farther separated from the line which goes verti- 
 cally upwards, and makes a greater angle there- 
 with, it being about 381 degrees ; this is the 
 sun's meridian altitude, at the time of equinox 
 at London. 
 
 Again, rectify to the summer solstice by 
 problem xiii, and you will find the artificial 
 horizon recede farther from the line which goes 
 from London vertically upwards, and the angle 
 it then makes is about 62 degrees, which shews 
 the sun's meridian altitude at the time of the 
 summer solstice. 
 
 Hence flows also the following arithmetical 
 problem. 
 
 PROBLEM XVIII. 
 
 To find the sun*s rncridian altitude universally. 
 
 Add the sun's declination to the elevation of 
 the equator, if the latitude of the place, and the 
 declination of the sun, are both on the same side. 
 
 If on contrary sides, subtract the declination 
 from the elevation of the equator, and you obtain 
 the sun's meridian altitude. 
 Thus the elevation of the equator at 
 
 London is ... 38" 28 
 
 The sun's declination on the 20th of 
 
 May - - - - 20 8 
 
 Their supi, the sun's meridian altitude 
 
 that day - - - - 58 2Q 
 255 
 
70 DESCRIPTION AND USE 
 
 Again, to the elevation of the equator 
 
 at London - - - Sti" 28 
 
 Add the sun's greatest declination at 
 
 the time of the summer solstice 23 29 
 
 The sum is the sun's greatest meridian 
 
 altitude at London - - 61 ^^7 
 
 PROBLEM xrx. 
 
 Of the sun*s azimuths, as co?npared with the artt- 
 » Jicial horizon. 
 
 The artificial horizon serves also to determine 
 the sun's azimuths. 
 
 An azimuth of the sun is denominated from 
 that point of the horizon, to which the sun, or 
 a line going to the sun, is nearest. 
 
 Thus if the sun, or a line going to the sun, 
 be nearest the south-east point of the horizon, 
 wliich point is 45 degrees distant from the me- 
 ridian, the sun's azimuth is an azimuth of 4J 
 degrees, and the sun will appear in the south- 
 east. 
 
 Imagine the sun, as we have done before, to 
 be placed directly over the globe. 
 
 In which case, a line going to the sun from 
 any place on the surface of the globe, will have 
 a vertical direction, and will go from that place 
 vertically upwards. 
 
 256 
 
 I 
 
OF THE GLOBt/il 71 
 
 If then we apply the artificial horizon to any 
 place, the point of this horizon to which a verti- 
 cal line is nearest, shews the sun's azimuth at 
 that time. 
 
 It is observable, that the point of the horizon 
 to which such a vertical line is nearest, will be 
 at all times that point which is most elevated. 
 
 To exemplify this, let the globe be in the 
 position of a right sphere, and let the artificial 
 horizon be applied to London. 
 
 When London is at the western edge of the 
 broad paper circle, which situation represents 
 the time when the sun appears to rise, the eastern 
 point of the artificial horizon being then most 
 elevated, shews that the sun at his rising is duo 
 east. 
 
 Turn the globe, till London comes to the 
 eastern edge of the broad paper circle, then the 
 western point of the artificial horizon will be 
 most elevated, shewing that the sun sets due 
 west. 
 
 Now place the globe in the position of an 
 oblique sphere ; and if London be brought to 
 the eastern or western side of the broad paper 
 circle, the vertical line will depart more or less 
 from the east and west points, in which case the 
 sun is said to have more or less amplitude. 
 
 If the departure be northward, it is called 
 257 
 
72 DESO^IIPTION AND USE 
 
 northern amplitude ; if southward, it is called 
 southern amplitude. 
 
 In whatever position the globe be placed,' 
 when London comes to the strong brass meri- 
 dian, the most elevated part of the artificial 
 horizon will be the south point of it. 
 
 Which shews that at noon the sun will always, 
 and in all seasons, appear in the south. 
 
 OF THE ANCIENT DIVISIONS OF THE EARTH 
 INTO ZONES AND CLIMATES. 
 
 Climates was a term used by the ancient as- 
 tronomers to express a division of the earth, 
 which, before the marking down the latitudes of 
 countries into degrees and minutes was in use, 
 served them for dividing the earth into certain 
 portions in the same direction, so as to speak of 
 any particular place with some degree of cer- 
 tainty, though not with due precision. 
 
 It was natural for the earliest observers to re- 
 mark, for one of the first things, the diversity 
 that there was in the sun's rising and setting : 
 it was by this they regulated what they called 
 climates ; which are a tract on the surface 
 of the earth, of various breadths, being regu- 
 lated by the different lengths of time be- 
 
 * The globe is not supposed in this case, or under this 
 view of things, ever to be elevated tibove the limits of the 
 sun's declination. 
 
 258 
 
OF THE GLOBES. 
 
 73 
 
 tv/een the rifmg and fetting of the fan in the 
 
 longefl day, in diir^reiit places. 
 
 From the equator to the latitude 65'- north 
 andfouth, a climate is conflituted by the ditter- 
 ence of half an hour in the length of the longett 
 day, and this is fufficient for underitandi ng the 
 ancients. Between the polar circle and the 
 pole, the length of the longeft day, in one pa- 
 rallel, exceeds the length of the longefl in the 
 next by a month ; but of thefe the ancients 
 knew no:hing. 
 
 Climates between the Eqjjator and 
 Polar Circles. 
 
 
 . 
 
 Latiludc. 
 
 Breadth. 
 
 
 V 
 
 
 Latitude. 
 
 Bre 
 
 adth 
 
 :i 
 
 
 
 
 
 
 
 
 
 
 
 
 
 F 
 
 3 
 
 
 
 
 
 
 h 
 
 a 
 
 
 
 
 
 I 
 
 
 12-1 
 
 D. 
 
 M. 
 
 D. 
 
 M. 
 
 
 
 •3 
 
 
 
 D. 
 
 M. 
 
 D 
 
 M. 
 
 8 
 
 25 
 
 8 
 
 25 
 
 i8i 
 
 59 
 
 58 
 
 I 
 
 29 
 
 2 
 
 13 
 
 16 
 
 25 
 
 8 
 
 00 
 
 
 M 
 
 '9 
 
 61 
 
 18 
 
 1 
 
 20 
 
 ^ 
 
 Ur 
 
 23 
 
 50 
 
 7 
 
 25 
 
 
 '5 
 
 i9i 
 
 62 
 
 25 
 
 I 
 
 07 
 
 5 
 
 '4 
 
 30 
 
 25 
 
 
 
 3*^ 
 
 
 16 
 17 
 
 20 
 
 (^3 
 
 22 
 
 
 
 57 
 
 14I 
 
 36 
 
 28 
 
 6 
 
 08 
 
 20-J 
 
 64 
 
 06 
 
 
 
 44 
 
 6 15 
 
 41 
 
 22 
 
 4 
 
 54 
 
 
 18 
 
 21 
 
 64 
 
 49 
 
 
 
 43 
 
 7 15I 
 
 4^ 
 
 29 
 
 4 
 
 07 
 
 
 '9 
 
 2li 
 
 ^^5 
 
 21 
 
 
 
 32 
 
 8 16 
 
 49 
 
 01 
 
 3 
 
 32 
 
 
 2C 
 
 2 i 
 
 22 
 
 65 
 
 47 
 
 
 
 22 
 
 91 16} 
 
 52 
 
 00 
 
 2 
 
 «:? 
 
 22i 
 
 66 
 
 06 
 
 
 
 J9 
 
 10 17 
 
 H 
 
 27 
 
 2 
 
 29 
 
 
 22 
 
 23 
 
 66 
 
 20 
 
 
 
 14 
 
 II I7r 
 
 5<5 
 
 37 
 
 2 
 
 10 
 
 
 2 ^ 
 
 23i 
 
 66 
 
 28 
 
 
 
 08 
 
 12 18 
 
 5« 
 
 29 
 
 I 
 
 52 
 
 
 24 
 
 24 
 
 66 
 
 3' 
 
 
 
 03 
 
 Therefore, to difcover in what climate a 
 place is, whofe latitude does not exceed 66j; 
 K 259 
 
74 DESCRIPTION AND USE 
 
 degrees, find the length of the longeft: day in that 
 place, and fubtra^lin^ i ?. hours from that length, 
 tne number ot half hours in the remainder will 
 fpecify the cli mate. 
 
 PrOBLLM XX. 
 
 To find the limits cf the climates. 
 
 Elevate the north pole to 23' 28', the fun's 
 declination on the longeft day ; and turn the 
 globe eafterly till the interfeftion of the meridian 
 with the equator that pafles through Libra comes 
 to the horizon, and the hour of VI will then be 
 under the meridian, which in this problem is 
 the hour index, becaufe the fun fets this day at 
 places on the equator as it does every day at VI 
 o'clock. Now turn the globe eafierly till the 
 time under the meridian is 15 min. paft VI. and 
 you find that 8' 34' of that graduated meridian 
 is cut by the horizon ; this is the beginning of 
 the fecond climate ; and the limits of all the cli- 
 mates may be determined, by bringing fuccef- 
 fively the time equal to half the length of the 
 longeft day under the meridian, and obferving 
 the degree of the graduated meridian cut by the 
 horizon. 
 
 Zones. 
 
 Zoner. is another divifion of the earth's fur_ 
 face uied by the ancients : that part which the 
 260 
 
OF THE GLOBES. 75 
 
 fun pafTes over in a year, comprehending 23^ 
 degrees on each fide the equator, was callrd by 
 the ancients the torrid zone. The two frigid 
 zones are contained between the polar circles. 
 Between the torrid and the two frigid zones are 
 contdiiied the two temperate ones, each being a- 
 bout 43 degrees broad. 
 
 The latitude of a place being the mark of it's 
 pofition with refpeft to the fun, may be confider- 
 cd as a general index to the temperature of the 
 climate : it is, however, liable to very great ex- 
 ceptions ; but to deny it abfolutely, would be to 
 deny that the fun is the fource of light and heat 
 below. 
 
 Nothing can be more hideous or mournful 
 than the piftures which travellers prefent us of 
 the polar regions. The feas, furrounding in- 
 hofpitable coafts, are covered with iflands of 
 ice, that have been increafing for many cen- 
 turies : fome of thefe iflands are immerfed fix 
 hundred feet under the furface of the fea, and 
 yet often rear up alfo their icy heads more than 
 one hundred feet above it's level, and are three 
 or four miles in circumference. The follow- 
 ing account will give fome idea of the fcenery 
 produced by ar6lic weather. At Smearing- 
 borough-Harbour, within fifteen degrees of the 
 pole, the country is full of mountains, pre- 
 cipices, and rocks ; thefe are covered with ice 
 and fnow. In the vallies are hills of ice, 
 261 
 
yG DESCRIPTION AND USE 
 
 \vhic?i feem daily to accumulate. 1 hefe hills 
 alTume many flrange and fantaftic appearances ; 
 foine looking like churches or ca(Ues, ruins, 
 Ihips in full fail, whales, monfters, and all 
 the various forms tliat fill the univerfe. There 
 are feven .of thefe ice-hills, which are the 
 highefl: in the country. When the air is clear, 
 and the light fliines full upon them, the prof- 
 pedi is inconceivably brilliant ; the fun is reflect- 
 ed from them as from glaf-. ; fometimes they 
 appear of a bright hue, like fapphire ;. fome- 
 times variegated with all the glories of the prif- 
 matic colours, exceeding, in the magnitude of 
 luftre, and beauty of colour, the richeft gems 
 in the world, difpofed in fliapes wonderful to 
 behold, dazzling the eye with the brilliancy of 
 it's fplendor. At Spltftergen, within ten de- 
 grees of the pole, the earth is locked up in Ice 
 till the middle of May ; in the beginning of 
 July the plants are in flower, and perfect their 
 feeds in a month's time: for though the fun is 
 much more oblique in the higher latitudes than 
 with us, his long continuance above the horizon 
 is attended with an accumulation of heat ex- 
 ceeding that of many placed under the torrid 
 zone ; and there is rcaibn to fuppofe, that the 
 rays of the fun, at any given altitude, produce 
 greater degrees of heat in the condenfed air of 
 the polar regions, than in the thinner air of this 
 climate. 
 
 262 
 
OF THE GLOBES. JJ 
 
 Yet, if we look for heat, and the remark- 
 able effeds of it, we mud go to the countries 
 near the equator, where we fliall find a fcenery 
 totally different from that of the frigid zone. 
 Here all things are upon a larger fcale than in 
 the temperate climates \ their days are burning 
 hot ; in foine parts their nights are piercing 
 cold ; their rains lulling and impetuous, like 
 torrents ; their dews exceffive \ their thunder 
 and lightning more frequent, terrible, and 
 dangerous ; the heat burns up the h"ghter foil, 
 and forms it into a fandy defert, while it quick- 
 ens all the moifter tracts with incredible vegeta- 
 tion. 
 
 The ancients fuppofed that the frigid zone 
 was uninhabitable from cold, and the torrid 
 from the intolerable heat of the fun ; we now, 
 however, know that both are inhabited. The 
 fentiments of the ancients, therefore, in this 
 refpeft, are a proof how inadequate the facul- 
 ties of the human mind are to difculTions of this 
 nature, when unaf^iifed by fads. 
 
 Of the ANcir.NT Distinction of Places, 
 BY THE Diversity of Shadows of up- 
 right Bodies at Noon. 
 
 When the fun at noon is in the zenith of 
 any place, the inhabitants of that place were 
 by the ancients called ajcii^ that is, without 
 2C3 
 
78 DESCRIPTION AND tJSE 
 
 fhadow ; for the fhadow of a man flanding up- 
 right, when the fun is directly over his head, 
 iij not extended beyond thut part of the earth 
 which is direclly under his body, and there- 
 fore will not be vifible. 
 
 As the ihadow of every opake body is ex- 
 tended from the fun, it follows, that when the 
 fun at noon is fouthward from the zenith of any 
 place, the fnadow of an inhabitant of that 
 place, and indeed of any other opake body, is 
 extended towards the north. 
 
 Bat when the fun is northward from the 
 zenith of any place, the fhadow falls towards 
 the fouth. 
 
 Thofe are called amphifcii, that have both 
 kinds of meridian fliadows. 
 
 Thofe, whofe meridian fliadows are always 
 projected one way, are termed heterofcii. 
 
 Problem xxi. 
 
 To illujlrate the di/iincfion of afcii, amphifcii, 
 heterofcii, and perifcii, by the globe. 
 
 Redify the globe to the fummer folftice, 
 and move the artificial horizon to the equator, 
 the north point will be the mod elevated at 
 noon. 
 
 Which fhews, that to thofe inhabitants 
 who live at the equator, the fun will at this 
 feafon appear to the north at noon, and their 
 264 
 
OF THE GLOBES. 
 
 79 
 
 fliadow will therefore be projeaed fouth- 
 wards. 
 
 But if you redify the globe to the winter 
 folitice, the fouth point being then the upper- 
 moft point at noon, the fame perfons wiil at 
 noon have the fun on the fouth fide of them, 
 and will projeft their fhadows northwards. 
 
 Thus they are amphifcii, projecting their 
 fhade both ways ; which is the cafe of all the 
 inhabitants within the tropics. 
 
 The artificial horizon remaining as before, 
 redify the globe to the times of the equinox, 
 and you will find that when this horizon is 
 under the (trong brafs meridian, a line going 
 vertically upwards will be perpendicular to it, 
 and confequently the fun will be diredly over 
 the heads of the inhabitants, and they will be 
 afcii, having no noon fliade ; their fhadow is in 
 the morning projeded diredly wefiward, in the 
 evening direftly eafhvard. 
 
 The fame thing will alfo happen to all the 
 inhabitants who live between the tropics of 
 Cancer and Capricorn ; fo that they are not 
 only afcii, but amphifcii alfo. 
 
 Thofe who live without the tropics are 
 heterofcii ; thofe in north latitude have the noon 
 fhade always direded to the north, while thofe 
 m fouth latitude have it always projeded to 
 the fouth. 
 
 The inhabitants of the polar circles are 
 265 
 
8o DESCRIPTION AND USE 
 
 called perifcii ; becaufe, as the fua goes round 
 them continually, their fliade goes round them 
 likewife. 
 
 Of ancient Distinctions from Situation. 
 
 Thefe terms being often mentioned by an- 
 cient geographical writers to exprefs the dif- 
 ferent fituation of parts of the globe, by the 
 relation which the feveral inhabitants bore to 
 one another, it will be neceffary to take lome 
 notice of them. 
 
 The antcoci are two nations which are in or 
 near the fame meridian ; the one in north, the 
 other in fouth latitude. 
 
 They have therefore the fame longitude, 
 but not the fame latitude ; oppofite feafons of 
 the yc^ar, but the fame hour of the day ; the 
 days of the one are equal ro the nights of the 
 other, and, vice ver/a^ when the days of the one 
 are at the longelt, they are (hortefl at the other. 
 
 When they look towards each other, the 
 fun feems to rife on the right hand of the one, 
 but on the left of the other. They have dif- 
 ferent poles elevated j and the (tars that never 
 fet to the one, are never feen by the other, 
 
 Perifje:i are alfo two oppofite nations, fitua- 
 ted on tlie fame parallel of latitude. 
 
 They have therefore the fame latitude, but 
 differ i8o degrees in longitude j the fame fea- 
 266 
 
OF THE GLOBES. 81 
 
 sons of the year, but opposite hours of the day ; 
 for when it is twelve at night to the one, it is 
 twelve at noon with the other. On the equi- 
 noctial days, the sun is rising to one, \vhen it is 
 setting to the other. 
 
 Antipodes are two nations diametrically, oppo- 
 site, which have opposite seasons and latitude, 
 opposite hours and longitude. 
 
 The sun and stars rise to the one, when they 
 set to the other, and that during the whole year, 
 for they have the same horizon. 
 
 The day of the one is the night of the other j 
 and when the day is longest with the one, the 
 other has it's shortest day. 
 
 They have the contrary seasons at the same 
 time ; different poles, but equally elevated ; and 
 those stars that are always above the horizon of 
 one, are always under the horizon of the other. 
 
 PROBLEM XXII. 
 
 To find the Antceci, the Perioeci, and the Antipodes 
 of any place. 
 
 Bring the given place to the strong brass me- 
 ridian, then in the opposite hemisphere, and un- 
 der the same degree of latitude with the given 
 place, you will find the antoeci. 
 
 The given place remaining under the me- 
 ridian, set the horary index to XII j then turn 
 L 267 
 
82 DESCRIPTION AND USE 
 
 the globe, till the other XII is under the index, 
 then will you find the pericEci under the same 
 degree of latitude with the given place. 
 
 Thus the inhabitants of the south part of 
 Chili are antoeci to the people of New England^ 
 whose Periceci are those Tartars who dwell on 
 the north borders of China, which Tartars 
 have the said inhabitants of Chili for their anti- 
 podes. 
 
 This will become evident, by placing the 
 globe in the position of a right sphere, and 
 bringing those nations to the edge of the broad 
 paper circle. 
 
 PROBLEM XXIII. 
 
 The day of the month being given, to find all those 
 places on the globe, over whose zenith the sun 
 will pass on that day. 
 
 Rectify the terrestrial globe, by bringing the 
 given day of the month on the back side of the 
 strong brass meridian, to coincide with the plane 
 of the broad paper circle ; observe the number 
 of degrees of the brass meridian, which corres- 
 ponds to the given day of the month. 
 
 This number of degrees, counted from the 
 
 equator on the strong brass meridian, towards 
 
 the elevated pole, is the point over which the 
 
 sun is vertical ; and all those places, which p«t5S 
 
 268 
 
OF THE GLOBES. 93 
 
 under this point, have the sun directly vertical 
 on the given day. 
 
 Example. Bring the 1 1 th of May to coincide 
 with the plane of the broad paper circle, and the 
 said plane will cut eighteen degrees for the eleva- 
 tion of the pole, which is equal to the sun*s de- 
 clination for that day, which being counted on 
 the strong brass meridian towards the elevated 
 pole, is the point over which the sun will be 
 vertical ; and all places that are under this de- 
 gree, will have the sun on their zenith on the 
 nth of May. 
 
 Hence, when the sun*s declination is equal to 
 the latitude of any place in the torrid zone, the 
 sun will be vertical to those inhabitants that day; 
 which furnishes us with another method of solv- 
 ing this problem. 
 
 OF PROBLEMS PECULIAR TO THE SUN. 
 PROBLEM XXIV. 
 
 To find the sun's place on the broad paper circle. 
 
 Consider whether the year in which you seek 
 the sun*s place is bissextile, or whether it is the 
 first, second, or third year after. 
 
 If it be the first year after bissextile, those 
 divisions to which the numbers for the days of 
 the months 2u*e affixed, are the divisions which 
 
 269 
 
84 DESCRIPTION AND USE 
 
 are to be taken for the respective days of each 
 month of that year at noon ; opposite to which, 
 in the circle of twelve signs, is the sun's place. 
 
 If it be the second year after bissextile, the 
 first quarter of a day backwards, or towards the 
 left hand, is the day of the month for that year, 
 against which, as before, is the sun's place. 
 
 If it be the third year after bissextile, then 
 three quarters of a day backwards is. the day of 
 the month for that year, opposite to which is 
 the sun's place. 
 
 If the year in which you seek the sun's place 
 be bissextile, then three quarters of a day back- 
 wards is the day of the month from the 1st of 
 January to the 'J8th of February inclusive. The 
 intercalary, or 29th day, is three-fourths of a day 
 to the left hand from the 1st of March, and the 
 1st of March itself one quarter of a day forward, 
 from the division marked I ; and so for every 
 day in the remaining part of the leap year j and 
 opposite to these divisions is the sun's place. 
 
 In this manner the intercalary day is very well 
 introduced every fourth year into the calendar, 
 and the sun's place very nearly obtained, accord- 
 ing to the Julian reckoning. 
 270 
 
OP THE GLOBES. 
 
 Thus, 
 
 
 
 
 A. D 
 
 Sun's 
 
 place. 
 
 Apr. 25. 
 
 1788 Bissextile 
 
 - - - 
 
 8 
 
 .5° So 
 
 1789 First year after 
 
 - 
 
 8 
 
 5 21 
 
 1790 Second 
 
 - 
 
 8 
 
 5 6 
 
 1791 Third - 
 
 . 
 
 8 
 
 4 55 
 
 Upon my father's globes there are twenty- 
 three parallels, drawn at the distance of one 
 degree from each other on both sides the equa- 
 tor, which, with two other parallels at 282 de- 
 grees distance, include the ecliptic circle. 
 
 The two outermost circles are called the tro- 
 pics ; that on the north side the equator is called 
 the tropic of Cancer, that which is on the south 
 side, the tropic of Capricorn. 
 
 Now as the ecliptic is inclined to the equator, in 
 an angle of 231 degrees, and is included between 
 the tropics, every parallel between these must 
 cross the ecliptic in two points, which two points 
 shew the sun's place when he is vertical to the 
 inhabitants of that parallel ; and the days of the 
 month upon the broad paper circle answering 
 to those points of the ecliptic, are the days on 
 which the sun passes directly over their heads at 
 noon, and which are sometimes called their two 
 midsummer days. 
 
 It is usual to call the sun's diurnal paths 
 parallels to the equator, which are therefore 
 aptly represented by the above-mentioned pa- 
 271 
 
S6 DESCRIPTION AND USE 
 
 rallel circle ; though his path is properly a 
 spiral line, which he is continually describing 
 all the year appearing to move daily about a 
 degree in the ecliptic. 
 
 PROBLEM XXV. 
 
 To find the sun^s declination, and thence the paraU 
 lei of latitude corresponding thereto. 
 
 Find the sun's place for the given day in 
 the broad paper circle, by the preceeding prob- 
 lem, and seek that place in the ecliptic line upon 
 the globe ; this will shew the parallel of the 
 sun's declination among the above-mentioned 
 dotted lines, which is also the corresponding 
 parallel of latitude ; therefore all those places, 
 through which this parallel passes, have the sun 
 in their zenith at noon on the given day. 
 
 Thus on the 23d of May the sun's declination 
 will be about 20 deg. 10 min. ; and upon the 
 23d of August it will be II deg. 13 min. What 
 has been said in the first part of this problem, 
 will lead the reader to the solution of the fol- 
 lowing. 
 
 272 
 
©F THE GLOBES. 87 
 
 PROBLEM XXVI. 
 
 To find the two days on which the sun is in fhe ze- 
 nith of any given place that is situated between 
 the two tropics. 
 
 That parallel of declination, which passes 
 through the given place, will cut the ecliptic line 
 upon the globe in two points, which denote the 
 sun*s place, against which, on the broad paper 
 circle, are the days and months required. Thus 
 the sun is vertical at Barbadoes April 24, and 
 August 18, 
 
 PROBLEM XXVII. 
 
 The day and hour at any place in the torrid zone 
 being given, to find where the sun is vertical at 
 that time. 
 
 Rectify the globe to the day of the month, 
 and you have the sun*s declination ; bring the 
 given placy to the meridian, and set the hour in- 
 dex to Xil; turn the globe till the index points 
 to the given hour on the equator ; then will the 
 place be under the degree of the declination 
 previously found. 
 
 Let the given place be London, and time 
 
 the nth day of May, at 4 min. past V in the 
 
 afternoon; bring the 11th of May to coincide 
 
 with the broad paper circle, and opposite to if 
 
 273 
 
88 DESCRIPTION AND USE 
 
 you will find 18 degrees of north declination 5 
 as London is the given place, you have only to 
 turn the globe till 4 min. past V vi^estward of it 
 is on the meridian, when you will find Port- 
 Royal, in Jamaica, under the 18th degree of the 
 meridian, which is the place where the sun if 
 vertical at that time. 
 
 PROBLEM XXVIII. 
 
 The time of the day at any one place being given^ 
 to find all those places where at the same instant 
 the sun is risings settings and on the ?neridian, 
 and where he is vertical ; likewise those places 
 where it is rnidnight, twilight, and dark night ; 
 as well as those places in which the twilight is 
 beginning and ending ; and also to find the su?i*s 
 altitude at any hour in the illuminated, and his 
 depression in the obscure, hemisphere. 
 
 Rectify the globe to the day of the month, on 
 the back side of the strong brass meridian, and 
 the sun's declination for that day ; bring the 
 given place to the strong brass meridian, and set 
 the horary index to XII upon the equator ; turn 
 the globe from west to east, until the horary in- 
 dex points to the given time. Then 
 
 All those places, which lie in the plane of 
 the western side of the broad paper circle, see 
 274 
 
OF THE GLOBES. 89 
 
 the sun rising, and at the same time those on 
 the eastern side of it see him setting. 
 
 It is noon to all the inhabitants of those places 
 under the upper half of the graduated side of 
 the strong brass meridian, whilst at the same 
 time those under the lower half have mid-night. 
 
 All those places which are between the upper 
 surface of the broad paper circle, and the wire 
 circle under it, are in the twilight, which begins 
 to all those places on the western side that are 
 immediately under the wire circle ; it ends at all 
 those which are in'the plane of the paper circle. 
 
 The contrary happens on the eastern sidej 
 the twilight is just beginning to those places in 
 which the sun is setting, and it's end is at the 
 place just under the wire circle. 
 
 And those places which are under the twi- 
 light wire circle have dark night, unless the 
 moon is favourable to them. 
 
 All places in the illuminated hemisphere have 
 the sun's latitude equal to their distance from 
 the edge of the enlightened disk, which is known 
 by fixing the quadrant of altitude to the zenith, 
 and laying it's graduated edge over any parti- 
 cular place. 
 
 The sun's depression is obtained in the same 
 manner, by fixing the center of the quadrant at 
 the nadir. 
 
 M 275 
 
90 DESCRIPTION AND USE 
 
 PROBLEM XXIX. 
 
 To find all those places within the polar circles on 
 ivhich the sun begins to shine, the time he shines 
 constantly, ivhen he 'begins to disappear, the 
 length of his absence, as icell as the first and 
 last day of his appearance to those inhabitants ; 
 the day of the month, or latitude of the place 
 being given. 
 
 Bring the given day of the month on the 
 back side of the strong brass meridian to the 
 plane of the broad paper circle ; the sun is just 
 then beginning to shine on all those places 
 which are in the parallel that just touches the 
 edge of the broad paper circle, and will for 
 several days seem to skim all around, and but 
 a little above their horizon, just as it appears to 
 us at it's setting ; but with this observable dif- 
 ference, that whereas our setting sun appears 
 in one part of the horizon only, by them it is 
 seen in every part thereof; from v^est to south, 
 thence east to north, and so to west again. 
 
 Or if the latitude be given, elevate the globe 
 to that latitude, and on the back of the strong 
 brass meridian, opposite to the latitude, you ob- 
 tain the day of the month ; then all the other 
 requisites are answered as above. 
 
 As the two concentric spaces, which con- 
 tain the days of the month on the back side of 
 276 
 
OF THE GLOBES. 91 
 
 the strong brass meridian, are graduated to shew 
 the opposite days of the year, at 1 SO degrees dis- 
 tance ; when the given day is brought to coin- 
 cide with the broad paper circle, it shews when 
 the sun begins to shine on that parallel, which is 
 the first day of it's appearance above the horizon 
 of that parallel. 
 
 And the plane of the broad paper circle cuts 
 the day of the month on the opposite concentric 
 space, when the sun begins to disappear to those 
 inhabitants. 
 
 The length of the longest day is obtained by 
 reckoning the number of days between the two 
 opposite days found as above, and their differ- 
 ence from 365 gives the length of the longest 
 night. 
 
 PROBLEM XXX. 
 
 To make use of the globe as ^ tellurian, cr that 
 kind of orrery ivhicb is chiefly intended to illus- 
 trate the phenomena that arise fj-om the annual 
 and diurnal motions of the earth. 
 
 Describe a circle with chalk upon the floor, 
 as large as the room will admit of, so that the 
 globe may be moved round upon it ; divide this 
 circle into twelve parts, and mark them with 
 the characters of the twelve signs, as they are 
 engraved upon the broad paper circle ; pla- 
 cing 55 at the north, V5 at the south, t in 
 277 
 
92 DESCRIPTION AND USE 
 
 the east, and =£= in the west : the mariner's com- 
 pass under the globe will direct the situation of 
 these points, if the variation of the magnetic 
 needle be attended to. 
 
 iVb/^, At London the variation is between 23 
 and 24 degrees from the north-westward. 
 
 Elevate the north pole of the globe, so that 
 66' degrees on the strong brass meridian may 
 coincide with the surface of the broad paper 
 circle, and this circle will then represent the 
 plane of the ecliptic, or a plane coinciding with 
 the earth's orbit. 
 
 Set a small table, or a stool, over the center 
 of the chalked circle, to represent the sun, and 
 place the terrestrial globe upon it's circum- 
 ference over the point marked \5 , with the north 
 pole facing the imaginary sun, and the north 
 end of the needle pointing to the variation ; 
 and the globe will be in the position of the 
 earth with respect to the sun at the time of the 
 summer solstice, about the 21st of June; and 
 the earth's axis, by this rectification of the globe, 
 is inclined to the plane of the large chalked 
 circle, as well as to the plane of the broad 
 paper circle, in an angle of Q^\ degrees; a 
 line, or string, passing from the center of 
 the imaginary sun to that of the globe, will 
 represent a central solar ray connecting the 
 centers of the earth and sun : this ray will fall 
 upon the first point of Cancer, and describe 
 - 278 
 
OF THE GLOBES. 93 
 
 that circle, shewing it to be the sun's place 
 upon the terrestrial ecliptic, which is the same 
 as if the sun's place, by extending the string, 
 was referred to the opposite side of the chalked 
 circle, here representing the earth's path in the 
 heavens. 
 
 If we conceive a plane to pass through the 
 center of the globe and the sun's center, it will 
 also pass through the points of Cancer and Ca- 
 pricorn, in the terrestrial and celestial ecliptic ; 
 the central solar ray, in this position of the earth, 
 is also in that plane : this can never happen but 
 at the times of the solstice. 
 
 If another plane be conceived to pass through 
 the center of the globe at right angles to the 
 center solar ray, it will divide the globe into two 
 hemispheres ; that next the center of the chalked 
 circle will represent the earth's illuminated disk, 
 the contrary side of the same plane will at the 
 same time shew the obscure hemisphere. 
 
 The reader may realize this second plane by 
 cutting away a semicircle from a sheet of card 
 paste board, with a radius of about 1 1 tenth of 
 an inch greater than that of the globe itself.* 
 
 If this plane be applied to 661 degrees upon 
 the strong brass meridian, it will be in the 
 pole of the ecliptic ; and in every situation of 
 
 * Or he may have a plane made of wood for this purpose 
 279 
 
94 DESCRIPTION AND USE 
 
 the globe round the circumference of the chalk- 
 ed circle, it will afford a lively and lasting idea 
 of the various phenomena arising from the par- 
 allelism of the earth's axis, and in particular the 
 daily change of the sun's declination, and the 
 parallels thereby described. 
 
 Let the globe be removed from vj to iji', 
 and the needle pointing to the variation as be- 
 fore, will preserve the parallelism of the earth's 
 axis ; then it will be plain that the string, or 
 central solar ray, will fall upon the first point of 
 Leo, six signs distant from, but opposite to the 
 sign ^, upon which the globe stands j the cen- 
 tral solar ray will now describe the 20th par- 
 allel of north declination, which will be about 
 the 23d of July. 
 
 If the globe be moved in this manner from 
 point to point round the circumference of the 
 chalked circle, and care be taken at every re- 
 moval that the north end of the magnetic needle, 
 when settled, points to the degree of variation, 
 the north pole of the globe will be observed to 
 recede from the line connecting the centers of 
 the earth and sun, until the globe is placed upon 
 the point Cancer ; after which, it will at every 
 removal tend more and more towards the said 
 line, till it comes to Capricorn again. 
 280 
 
OF THE GLOBES. Oj 
 
 PROBLEM. XXXI. 
 
 ICo rectify either globe to the latitude and horizon 
 of any place. 
 
 If the place be in north latitude, raise the 
 north pole ; if in south latitude, raise the south 
 pole, until the degree of the given latitude, 
 reckoned on the strong brass meridian under 
 the elevated pole, cuts the plane of the broad 
 paper circle ; then this circle will represent the 
 horizon of that place, while the place remains in 
 the zenith, but no longer. This rectification is 
 therefore unnatural, though it is the mode adopt- 
 ed in using the globes when mounted in the 
 old manner. 
 
 PROBLEM XXXIJ. 
 
 To rectify for the siin^s place ^ 
 
 After the former rectification, bring the 
 degrees of the sun's place in the ecliptic line 
 upon the globe to the strong brass meridian, 
 and set the horary index to that Xllth hour 
 upon the equator which is most elevated. 
 
 Or if the sun*s place is to be retained, to 
 answer various conclusions, bring the gra- 
 duated edge of the moveable meridian to fhe 
 degree of the sun's place in the ecliptic, and 
 slide the wire which crosses the center of the 
 281 
 
96 DESCRIPTION AND USE 
 
 artificial horizon thereto ; then bring it's center, 
 which is in the intersection of the aforesaid wire, 
 and graduated edge of the moveable meridian, 
 under the strong brass meridian as before, and 
 set the horary index to that XII on the equator 
 which is most elevated. 
 
 PROBLEM XXXIII. 
 
 To rectify for the zenith of any place. 
 
 After the first rectification, screw the nut of 
 the quadrant of altitude so many degrees from 
 the equator, reckoned on the strong brass meri- 
 dian towards the elevated pole, as that pole is 
 raised above the plane of the broad paper circle, 
 and that point will represent the zenith of the 
 place. 
 
 Note, The zenith and nadir are the poles of 
 the horizon, the former being a point directly 
 over our heads, and the latter, one directly 
 under our feet. 
 
 If, when the globe is in this state, we look on 
 the opposite side, the plane of the horizon will 
 cut the strong brass meridian at the comple- 
 njent of the latitude, which is also the elevation 
 of the equator above the horizon. 
 282 
 
OF THE GLOBES. 97 
 
 OF THE SOLUTION OF PROBLEMS, BY EXPOS- 
 ING THE GLOBES TO THE SUN*S RAYS. 
 
 In the year 1679, /. Moxon published a trea- 
 tise on what he called " The English Globe ; be- 
 ing (says he) a stabil and immobil one, perform- 
 ing what the ordinary globes do, and much 
 more ; invented and described by the Right 
 Hon. the Earle of Castlewainc.'* This glrbe was 
 designed to perform, by being merely exposed 
 to the sun*s rays, all those problems which in 
 the usual way are solved by the adventitious aid 
 of brazen meridians, hour indexevS, &c. 
 
 My father thought that this method might 
 be useful, to ground more deeply in the young 
 pupil's mind, those principles which the globes 
 are intended to explain ; and by giving him a 
 different view of the subject, improve and 
 strengthen his mind ; he therefore inserted on 
 his globes some lines, for the purpose of solv- 
 ing a few problems in Lord Castlemaine's man- 
 ner. 
 
 It appears to me, from a copy of Moxon's 
 publication, which is in my possession, that the 
 Earle of Castlemaine projected a new edition of 
 his works, as the copy contains a great number 
 of corrections, many alterations, and some ad- 
 ditions. It is not very improbable, that at some 
 N 283 
 
98 DESCRIPTION AND USE 
 
 future day I may re-publish this curious work, 
 and adapt a small globe for the solution of the 
 problems. 
 
 The meridians on our new terrestrial globes 
 being secondaries to the equator, are also hour 
 circles, and are marked as such with Roman 
 figures, under the equator, and at the polar cir- 
 cles. But there is a difference in the figures 
 placed to the same hour circle ; if it cuts the 
 Illd hour upon the polar circles, it will cut the 
 IX hour upon the equator, which is six hours 
 later, and so of all the rest. 
 
 Through the great Pacific sea, and the inter- 
 section of Libra, is drawn a broad meridian from 
 pole to pole ; it passes through the Xllth hour 
 upon the equator, and the Vlth hour upon each 
 of the polar circles ; this hour circle is graduated 
 into degrees and parts, and numbered from the 
 equator towards either pole. 
 
 There is another broad meridian passing 
 through the Pacific sea, at the IXth hour upon 
 the equator, and the Hid hour upon each polar 
 circle ; this contains only one quadrant, or 90 
 degrees ; the numbers annexed to it begin at the 
 northern polar circle, and end at the tropic of 
 Capricorn. 
 
 Here we must likewise observe, there are 23 
 
 concentric circles drawn upon the terrestrial 
 
 globe within the northern and southern polar 
 
 circles, which for the future we shall call polar 
 
 284 
 
OF THE GLOBES. 99 
 
 parallels ; they are placed at the distance of one 
 degree from each other, and represent the pa- 
 rallels of the sun's declination, but in a ditler- 
 ent manner from the 4? parallels between the 
 tropics. 
 
 The following problems require the globe to 
 be placed upon a plane that is level, or truly 
 horizontal, which is easily attained, if the floor, 
 pavement, gravel-walk in the gaiden, kc. should 
 not happen to be horizontal. 
 
 A flat seasoned board, or any box which is 
 about two feet broad, or two feet square, if the 
 top be perfectly flat, will ansver the purpose ; 
 the upper surface of either may be set truly 
 horizontal, by the help of a pocket spirit level, 
 or plumb rule, if you raise or depress this or 
 that side by a wedge or two, as the spirit level 
 shall direct ; if you have a meridian line drawn 
 on the place over which you substitute this ho- 
 rizpntal plane, it may be readily transferred from 
 thence to the surface just levelled ; this being 
 done, we are prepared for the solution of the 
 following problems. 
 
 It will be necessary to defme a term we are 
 obliged to make use of in the solution of these 
 problems, namely, \\\c shade of extubcrancy : by 
 this is meant that shade which is caused by the 
 sphericity of the globe, and answers to what 
 we have heretofore named the terminator, de- 
 fining the boundaries of the illuminated and 
 285 
 
100 DESCRIPTION AND USE 
 
 obscure parts of the globe ; this circle was, in 
 the solution of some of the foregoing problems, 
 represented by the broad paper circle, but is here 
 realized by the rays of the sun. 
 
 PROBLEM XXXIV. 
 
 To observe the sun's altitude (by the terrestrial 
 globe J ivhen he shines bright^ or when he can 
 but just be discerned through a cloud. 
 
 Elevate the north pole of the globe to 66| 
 degrees ; bring that meridian, or hour circle, 
 which passes through the IXth hour upon the 
 equator, under the graduated side of the strong 
 brass meridian ; the globe being now set upon 
 the horizontal plane, turn it about thereon, 
 frame and all, that the shadow of the strong 
 brass meridian may fall directly under itself; 
 or in other words, that the shade of it's gra- 
 duated face may fall exactly upon the aforesaid 
 hour circle ; at that instant the shade of extu- 
 berancy will touch the true degree of the sun*s 
 altitude upon that meridian, which passes 
 through the IXth hour upon the equator, reck- 
 oned from the polar circle, the most elevated 
 part of which will then be in the zenith of the 
 place where this operation is performed, and 
 is the same whether it should happen to be 
 either in north or south latitude. 
 
 Thus we may, in an easy and natural man- 
 286 
 
OF THE GLOBES. 101 
 
 ner, obtain the altitude of the sun, at any time 
 of the day, by the terrestrial globe ; for it is very 
 plain, when the sun rises, he brushes the zenith 
 and nadir of the globe by his rays ; and as he 
 always illuminates half of it, (or a few minutes 
 more, as his globe is considerably larger than 
 that of the earth) therefore when the sun is risen 
 a degree higher, he must necessarily illuminate 
 a degree beyond the zenith, and so on propor- 
 tionably from time to time. 
 
 But as the illuminated part is somewhat more 
 than half, deduct 13 minutes from the shade 
 of extuberancy, and you have the sun's altitude 
 with tolerable exactness. 
 
 If you have any doubt how far the shade of 
 extuberancy reaches, hold a pin, or your finger, 
 on the globe, between the sun and point in dis- 
 pute, and where the shade of either is lost, will 
 be the point sought. 
 
 When the sun docs not shine bright enough to cast a 
 shadow. 
 
 Turn the meridian of the globe towards the 
 sun, as before, or direct it so that it may lie in 
 the same plane with it, which may be done if 
 you have but the least glimpse of the sun 
 through a cloud ; hold a string in both hands, 
 it having first been put between the strong 
 brass meridian and the globe j stretch it at 
 287 
 
lO'J DESCRIPTION AND USE 
 
 right angles to the meridian, and apply your 
 face near to the globe, moving your eye lower 
 and lower, till you can but just see the sun ; then 
 bring the string held as before to this point 
 upon the globe, that it may just obscure the 
 sun from your sight, and the degree on the 
 aforesaid hour circle, which the string then lies 
 upon, will be the sun's altitude required, for his 
 rays would shew the same point if he shone out 
 bright. 
 
 Note. The moon's altitude may be observed 
 by either of these methods, and the altitude of 
 any star by the last of them. 
 
 PROBLEM XXXV. 
 
 To place the terrestrial globe in the sim's rays, that 
 it may represent the natural position of the earth, 
 either by a meridian line, or ivithout it. 
 
 If you have a meridian line, set the north 
 and south points of the broad paper circle di- 
 rectly over it, the north pole of the globe being 
 elevated to the latitude of the place, and stand- 
 ing upon a level plane, bring the place you are 
 in under the graduated side of the strong brass 
 meridian, then the poles and parallel circles 
 upon the globe will, without sensible error, 
 correspond with those in the heavens, and each 
 288 
 
OF THE GLOBES. 103 
 
 point, kingdom, and state, will be turned to- 
 wards the real one which it represents. 
 
 If you have no meridian line, then the day 
 of the month being known, find the sun's decli- 
 nation as before instructed, which will direct 
 you to the parallel of the day, amongst the 
 polar parallels, reckoned from either pole to- 
 wards the polar circle ; which you are to re- 
 member. 
 
 Set the globe upon your horizontal plane in 
 the sun-shine, and put it nearly north and south 
 by the mariner's compass, it being first elevated 
 to the latitude of the place, and the place itself 
 brought under the graduated side of the strong 
 brass meridian ; then move the frame and globe 
 together, till the shade of extuberancy, or term 
 of illumination, just touches the polar parallel 
 for the day, and the globe will be settled as 
 before ; and if accurately performed, the varia- 
 tion of the magnetic needle vi'ill be shewn by the 
 degree to which it points in the compass box. 
 
 And here observe, if the parallel for the day 
 should not happen to fall on any one of those 
 drawn upon the globe, you are to estimate a 
 proportionable part between them, and reckon 
 that the parallel of the day. If we had drawn 
 more, the globe would have been confused. 
 
 The reason of this operation is, that as the 
 264 
 
104 DESCRIPTION AND USE 
 
 sun illuminates half the globe, the shade of cx- 
 tuberancy will constantly be 90 degrees from the 
 point wherein the sun is vertical. 
 
 If the sun be in the equator, the shade and 
 illumination must terminate in the poles of the 
 ■world ; and when he is in any other diurnal 
 parallel, the terms of illumination must fall 
 short of, or go beyond either pole, as many de- 
 grees as the parallel which the sun describes that 
 day is distant from the equator ; therefore, when 
 the shade of extuberancy touches the polar par- 
 allel for the day, the artificial globe will be in 
 the same position, with respect to the sun, as the 
 earth really is, and will be illuminated in the 
 same manner. 
 
 PROBLEM XXXVI. 
 
 To find naturally the suit's declination, diurnal 
 parallel, and his place thereon. 
 
 '\he globe being set upon an horizontal 
 plane, and adjusted by a meridian line or other- 
 wise, observe upon which, or between which 
 polar parallel the term of illumination falls ; it*s 
 distance from the pole is the degree of the sun's 
 declination ; reckon this distance from the 
 equator among the larger parallels, and you 
 have the parallel which the sun describes that 
 day ; upon which if you move a card, cut in 
 the form of a double square, until it's shadow 
 290 
 
OF THE GLOBES. lOo" 
 
 falls under itself, you will obtain the very place 
 upon that parallel over which the sun is vertical 
 at any hour of that day, if you set the place you 
 are in under the graduated side of the strong 
 brass meridian. 
 
 Note, The moon's declination, diurnal paral- 
 lel, and place, may be found in the same manner. 
 Likewise, when the sun does not shine bright, 
 his declination, &c. may be found by an appli- 
 cation in the manner of problem xxxiv. 
 
 PROBLEM XXXVII. 
 
 To find the surCs azimuth naturally. 
 
 If a great circle, at right angles to the horizon, 
 passes through the zenith and nadir, and also 
 through the sun*s center, it's distance from the 
 meridian in the morning or evening of any day, 
 reckoned upon the degrees on the inner edge of 
 the broad papei^ circle, will give the azimuth 
 required. 
 
 Method 1. 
 
 Elevate either pole to the position of a pa- 
 rallel sphere, by bringing the north pole in 
 north latitude, and the south pole in south lati- 
 tude, into the zenith of the broad paper circle, 
 having first placed the globe upon your meri- 
 O 291 
 
1jG6 description and use 
 
 dian line, or by the other method before pre- 
 scribed ; hold up a plumb line, so that it may- 
 pass freely near the outward edge of the broad 
 paper circk, and move it so that the shadow of 
 the string may fall upon the elevated pole ; then 
 cast your eye immediately to it*s shadow on the 
 broad paper circle, and the degree it there falls 
 upon is the sun*s azimuth at that time, which 
 may be reckoned from either the south or north 
 points of the horizon. 
 
 Method II. 
 
 If you have only a glimpse, or faint sight of 
 the sun, the globe being adjusted as before, 
 stand on the shady side, and hold the plumb 
 Une on that side also, and move it till it cuts the 
 sun*s center, and the elevated pole at the same 
 time ; then cast your eye towards the broad 
 paper circle, and the degree it there cuts is the 
 sun*s azimuth, which must be reckoned from 
 the opposite cardinal point. 
 
 PROBLEM XXXVIII. 
 
 To shew that in some places of the earth's surface, 
 the sun will be twice in the same azimuth in 
 the morning, twice in the same azimuth in the 
 afternoon : or in other words. 
 
 When the declination of the sun exceeds 
 the latitude of any place, on either side of the 
 292 
 
OF THE GLOBES. 10? 
 
 equator, the sun will be on the same azimuth 
 twice in the morning, and twice in the after- 
 noon. 
 
 Thus, suppose the globe rectified to the 
 latitude of Antigua, which is about 17 deg. of 
 north latitude, and the sun to be in the begin- 
 ning of Cancer, or to have the greatest north 
 declination ; set the quadrant of altitude to the 
 21st degree north of the east in the horizon, 
 and turn the globe upon it*s axis, the sun*s 
 center will be on that azimuth at 6 h. 30 min. 
 and also at 10 h. 30 min. in the morning. At 
 S h. 30 min. the sun will be as it were station- 
 ary, with respect to it*s azimuth, for some 
 time ; as it will appear by placing the quadrant 
 of altitude to the 17th degree north of the east 
 in the horizon. If the quadrant be set to the 
 same degrees north of the west, the sun's center 
 will cross it twice as it approaches the horizon 
 in the afternoon. 
 
 This appearance will happen more or less to 
 all places situated in the torrid zone, whenever 
 the sun*s declitiation exceeds their latitude ; and 
 from hence we may infer, that the shadow of a 
 dial, whose gnomon is erected perpendicular to 
 an horizontal plane, must necessarily go back 
 several degrees on the same day. 
 
 But as this can only happen within the tor- 
 rid zone, and as Jerusalem lies about 8 degrees 
 
 293 
 
108 DESCRIPTION AND USE 
 
 to the north of the tropic of Cancer, the retro* 
 cession of the shadow on the dial of Ahaz, at 
 Jerusalem, was, in the strictest signification of 
 the word, miraculous. 
 
 PROBLEM XXXIX. 
 
 To observe the hour of the day in the most natural 
 manner, when the terrestrial globe is properly 
 placed in the sun-shine* 
 
 There are many ways to perform this opera- 
 tion with respect to the hour, three of which 
 are here inserted, being general to all the inha- 
 bitants of the earth ; a fourth is added, peculiar 
 to those of London, which will answer, without 
 sensible error, at any place not exceeding the 
 distance of 60 miles from this capital. 
 
 1j/, By a natural style. 
 
 Having rectified the globe as before directed, 
 and placed it upon an horizontal plane over 
 your meridian line, or by the other method, hold 
 a long pin upon the illuminated pole, in the 
 direction of the polar axis, and it's shadow will 
 shew the hour of the day amongst the polar 
 parallels. 
 
 The axis of the globe being the common 
 section of the hour circles, is in the plane of 
 each ; and as we suppose the globe to be pro- 
 perly adjusted, they will correspond with those 
 294 
 
OF THE GLOBES. 109 
 
 in the heavens ; therefore the shade of a pin, 
 which is the axis continued, must fall upon the 
 true hour circle. 
 
 2dly, By an artificial stile. 
 
 Tie a small string, with a noose, round the 
 elevated pole, stretch it's other end beyond the 
 globe, and move it so that the shadow of the 
 string may fall upon the depressed axis ; at that 
 instant it*s shadow upon the equator will give 
 the solar hour to a minute. 
 
 But remember, that either the autumnal or 
 vernal equinoctial colure must first be placed 
 under the graduated side of the strong brass 
 meridian, before you observe the hour, each of 
 these being marked upon the equator with the 
 hour XII. 
 
 The string in this last case being moved into 
 the plane of the sun, corresponds with the true 
 hour circle, and consequently gives the true hour. 
 
 Sdly, Without any stile at all. 
 
 Every thing being rectified as before, look 
 where the shade of extuberancy cuts the equa- 
 tor, the colure being under the graduated side 
 of the strong brass meridian, and you obtain the 
 hour in two places upon the equator, one of 
 them going before, and the other following the 
 sun. 
 
 295 
 
no DESCRIPTION AND USE 
 
 Note, If this shade be dubious, apply a pin, or 
 your finger, as before directed. 
 
 The reason is, that the shade of extuberancy 
 being a great circle, cuts the equator in half, 
 and the sun, in whatsoever parallel of decUna- 
 tion he may happen to be, is always in the pole 
 of the shade ; consequently the confines of light 
 and shade will shew the true hour of the day. 
 
 i^fhlyy Peculiar to the inhabitants of London, and 
 any place within the distance of sixty miles front 
 it. 
 
 The globe being every way adjusted as before, 
 and London brought under the graduated side 
 of the strong brass meridian, hold up a plumb- 
 line, so that it's shadow may fall upon the zenith 
 point, (which in this case is London itself) and 
 the shadow of the string will cut the parallel of 
 the day upon that point to which the sun is then 
 vertical, and that hour circle upon which this 
 intersection falls, is the hour of the day ; and as 
 the meridians are drawn within the tropics, at 
 twenty minutes distance from each other, the 
 point cut by the intersection of the string upon 
 the parallel of the day, being so near the equator, 
 may, by a glance of the observer's eye, be re- 
 feiTed thereto, and the true time obtained to a 
 minute. 
 
 The plumb-line thus moved is the azimuth ; 
 which, by cutting the parallel of the day, gives 
 296 
 
OF THE GLOBES. HI 
 
 the sun's place, and consequently the hour circle 
 which intersects it. 
 
 From this last operation results a corollary, 
 that gives a second way of rectifying the globe 
 to the sun's rays. 
 
 If the azimuth and shade of the illuminated 
 axis agree in the hour when the globe is recti- 
 fied, then making them thus to agree, must 
 rectify the globe. 
 
 COROLLARY. 
 
 Another method to rectify the globe to the sini's 
 rays. 
 
 Move the globe, till the shadow of the plumb- 
 line, which passes through the zenith cuts the 
 same hour on the parallel of the day, that the 
 shade of the pin, held in the direction of the 
 axis, falls upon, amongst the polar parallels, and 
 -the globe is rectified. 
 
 The reason is, that the shadow of the axis re- 
 presents an hour circle ; and by it's agreement 
 in the same hour, which the shadow of the azi- 
 muth string points out, by it's intersection on 
 the parallel of the day, it shews the sun to be in 
 the plane of the said parallel ; which can never 
 happen in the morning on the eastern side of 
 the globe, nor in the evening on the western side 
 of it, but when the globe is rectified. 
 297 
 
112 DESCRIPTION AND USB 
 
 This rectification of the globe is only placing 
 it in such a manner, that the principal great 
 circles and points may concur and fall in with 
 those of the heavens. 
 
 The many advantages arising from these prob- 
 lems, relating to the placing of the globe in the 
 sun*s rays, the tutor will easily discern, and 
 readily extend to his own, as well as to the 
 benefit of his pupil. 
 
 (iENERAL PRINCIPLES 
 
 DIALLING 
 
 ILLUSTRATED 
 
 BY THE TERRESTRIAL GLOBE. 
 
 THE art of dialling is of very ancient origin, 
 and was in former times cultivated by all 
 who had any pretensions to science ; and before 
 the invention of clocks and watches it was of the 
 highest importance, and is even now used to 
 correct and regulate them. 
 
 It teaches us, by means of the sun's rays, 
 to divide time into equal parts, and to repre- 
 298 
 
OF THE GLOBES. 113 
 
 sent on any given surface the different circles 
 into which, for convenience, we suppose the 
 heavens to be divided, but principally the hour 
 circles. 
 
 The hours are marked upon a plane, and 
 pointed out by the interposition of a body which 
 receiving the light of the sun, casts a shadow 
 upon the plane. This body is called the axis, 
 when it is parallel to the axis of the world. It 
 is called the stile, when it is so placed that only 
 the end of it coincides with the axis of the earth; 
 in this case, it is only this point which marks the 
 hours. 
 
 Among the various pleasing and profitable 
 amusements which arise from the use of globes, 
 that of dialling is not the least. By it the pupil 
 will gain satisfactory ideas of the principles on 
 which this branch of science is founded ; and it 
 will reward, with abundance of pleasure, those 
 that chuse to exercise themselves in the practice 
 of it. 
 
 If we imagine the hour circles of any place, 
 as London, to be drawn upon the globe of the 
 earth, and suppose this globe to be transparent, 
 and to revolve round a real axis, which is opake, 
 and casts a shadow ; it is evident, that when- 
 ever the plane of any hour semicircle points at 
 the sun, the shadow of the axis will fall upon 
 the opposite semicircle.* 
 
 * Long's Astronomy, vol i, page 82. 
 P 299 
 
114 DESCRIPTION AND USE 
 
 Let a P C p, fig. I, plate XIII, represent a 
 transparent globe ; a b c d e f g the hour semi- 
 circles ; it is clear, that if the semicircle Pap 
 points at the sun, the shadow of the axis will 
 fall upon the opposite semicircle. 
 
 If we imagine any plane to pass through the 
 center of this transparent globe, the shadow of 
 half the axis will always fall upon one side or 
 the other of this intersecting plane. 
 
 Thus let A B C D be the plane of the hori- 
 zon of London ; so long as the sun is above the 
 horizon, the shadow of the upper half of the 
 axis "will fall somewhere upon the upper side of 
 the plane A B C D ; when the sun is below the 
 horizon of London, then the shadow of the 
 lower half of the axis E falls upon the lower 
 side of the plane. 
 
 When the plane of any hour semicircle points- 
 at the sun, the shadow of the axis marks the 
 respective hour-line upon the intersecting plane. 
 The hour-line is therefore a line drawn from 
 the center of the intersecting plane, to that point 
 where this plane is cut by the semicircle oppo- 
 site to the hour semicircle. 
 
 Thus let A B C D, fig. i, plate XIII, the 
 horizon of London, be the intersecting plane j 
 when the meridian of London points at the 
 sun, as in the present figure, the shadow of the 
 half axis P E falls upon the line E B, which is 
 drawn from E, the center of the horizon, to 
 300 
 
OF THE GLOBES. 115 
 
 the point where the horizon is cut by the oppo- 
 site semicircle ; therefore, E B is the line for 
 the hour of twelve at noon. 
 
 By the same method the rest of the hour- 
 lines are found, by drawing for every hour a 
 line, from the center of the intersecting plane, 
 to that semicircle which is opposite to the hour 
 semicircle. 
 
 Thus fig. 2, plate XIII, shews the hour-lines 
 drawn upon the plane of the horizon of London, 
 with only so many hours as are necessary ; that 
 is, those hours, during which the sun is above 
 the horizon of London, on the longest day in 
 summer. 
 
 If, when the hour-lines are thus found, the 
 semicircles be taken away, as the scaffolding is 
 when the house is built, what remains, as in 
 fig. 2, will be an horizontal dial for London. 
 
 If, instead of twelve hour circles, as above 
 described, we take twice that number, we may 
 by the points, where the intersecting plane is 
 cut by them, find the lines for every half hour ; 
 if we take four times the number of hour cir. 
 cles, we may find the lines for every quarter of 
 an hour, and so on progressively. 
 
 We have hitherto considered the horizon of 
 London as the intersecting plane, by which is 
 seen the method of making an horizontal dial. 
 If we take any other plane for the intersecting 
 plane, and find the points where the hour semi- 
 circles pass through it, and draw the lines from 
 301 
 
116 DESCRIPTION AND USE 
 
 the center of the plane to those points, we shall 
 have the hour-lines for that plane. 
 
 Fig. 3, plate XIII, shews how the hour-lines 
 are found upon a south plane, perpendicular to 
 the horizon. Fig. 4, shews a south dial, with 
 it*s hour-lines, without the semicircle, by means 
 whereof they are found. 
 
 The gnomon of every sun-dial represents the 
 axis of the earth, and is therefore always placed 
 parallel to it ; whether it be a wire, as in the 
 figure before us, or the edge of a brass plate, as 
 in a common horizontal dial. 
 
 The whole earth, as to it's bulk, is but a 
 point, if compared to it's distance from the sun ; 
 therefore, if a small sphere of glass be placed on 
 any part of the earth's surface, so that it's axis 
 be parallel to the axis of the earth, and the 
 sphere have such lines upon it, and such planes 
 within it, as above described, it will shew the 
 hour of the day as truly as if it were placed at 
 the center of the earth, and the shell of the earth 
 were as transparent as glass. 
 
 A wire sphere, with a thin flat plate of brass 
 within it, is often made use of to explain the 
 principles of dialling. 
 
 From what has been said, it is clear that 
 dialling depends on finding where the shadow 
 of a strait wire, parallel to the axis of the 
 earth, will fall upon a given plane, every hour, 
 half hour, &c. the hour-lines being found as 
 802 
 
OF THE GLOBES. llY 
 
 above described, which we shall proceed to ex- 
 emplify by the globe. 
 
 Every dial-plane (that is, the plane surface 
 on which a dial is drawn) represents the plane 
 of a great circle, which circle is an horizon to 
 some country or other. 
 
 The center of the dial represents the center 
 of the earth ; and the gnomon which casts the 
 shade represents the axis, and ought to point 
 directly to the poles of the equator. 
 
 The plane upon which dials are delineated 
 may be either, 1. parallel to the horizon; 2. 
 perpendicular to the horizon ; or, 8. cutting it 
 at oblique angles. 
 
 PROBLEM. XL. 
 
 To construct an horizontal dial for any given lati- 
 tude, by 7ueans of the terrestrial globe. 
 
 Elevate the globe to the latitude of the 
 place, then bring the first meridian under the 
 graduated edge of the strong brazen one, which 
 will then be over the hour XII, or the equator. 
 As our globes have meridians drawn through 
 every fifteen degrees of the equator, these me- 
 ridians will represent the true circles of the 
 sphere, and will intersect the horizon of the 
 globe, in certain points on each side of the me- 
 ridian. The distance of these points from the 
 meridian must be carefully noted down upon a 
 303 
 
118 DESCRIPTION AND USE 
 
 piece of paper, as will be seen in the example. 
 The pupil need not, however, take out into his 
 table the distances further than from XII to VI, 
 which is just 90 degrees ; for the distances of 
 XI, X, IX, VIII, VII, VI, in the forenoon, are 
 the same from XII as the distances of I, II, 
 III, IV, V, VI, in the afternoon ; and these 
 hour-lines continued through the center will 
 give the opposite hour-lines on the other half of 
 the dial. 
 
 No more hour-lines need be drawn than 
 what answer to the sun's continuance above the 
 horizon, on the longest day of the year, in the 
 given latitude. 
 
 Example. Suppose the given place to be 
 London, whose latitude is 51 deg. 30 min. 
 north. 
 
 Elevate the north pole of the globe to 51-1 
 degrees above the horizon ; then will the axis 
 of the globe have the same elevation above the 
 broad paper circle, as the gnomon of the dial is 
 to have above the plane thereof. 
 
 Turn the globe, till the first meridian (which 
 on English globes passes through London) is 
 under the graduated side of the strong brazen 
 meridian ; then observe and note the points 
 where the hour-circles intersect the horizon ; and 
 as on our globes the inner graduated circle, on 
 the broad paper circle, begins from the two sixes, 
 or east and west, we shall begin from thence, 
 304 
 
OF THE GLOBES. 1 19 
 
 calling the hour - - - VI 0° O 
 
 we shall find the other hours intersecting the 
 horizon at the following degrees: V 18" 54 
 
 IV 
 
 36 
 
 24> 
 
 III 
 
 51 
 
 57 
 
 II 
 
 65 
 
 41 
 
 I 
 
 78 
 
 V 
 
 which are the respective distances of the above 
 hours from VI upon the plane of the horizon. 
 
 To transfer these, and the rest of the hours, 
 upon an horizontal plane, draw the parallel 
 right lines a c and b d, fig. 5, plate XIII, upon 
 that plane, as far from each other as is equal to 
 the intended thickness of the gnomon of the 
 dial, and the space included between them will 
 be the meridian, or twelve o*clock line upon the 
 dial ; cross this meridian at right angles by the 
 line g h, which will be the six o'clock line ; then 
 setting one foot of your compasses in the inter- 
 section a, describe the quadrant g e with any 
 convenient radius, or opening of the compasses; 
 after this, set one foot of the compasses in the 
 intersection b, as a center, and with the same 
 radius describe the quadrant f h ; then divide 
 each quadrant into 90 equal parts, or degrees, 
 as in the figure. 
 
 Because the hour-lines are less distant from 
 
 each other about noon, than in any other part 
 
 of the dial, it is best to have the centers of the 
 
 quadrants at some distance from the center of 
 
 S05 
 
120 DESCRIPTION AND USE 
 
 the dial-plane, in order to enlarge the hour-dis- 
 tances near XII ; thus the center of the plane 
 is at A, but the center of the quadrants is at a 
 and b. 
 
 Lay a rule over 78' 9', and the center b, 
 and draw there the hour-line of I. Through b, 
 and 65 41, gives the hour-line of II. Through 
 b, and 51 57, that of III. Through the same 
 center, and 36 24, we obtain the hour-line of 
 IV. And through it, and 1 8 54, that of V". 
 And because the sun rises about four in the 
 morning, continue the hour-lines of IV and V 
 in the afternoon, through the center b tq the 
 opposite side of the dial. 
 
 Now lay a rule successively to the center a 
 of the quadrant e g, and the like elevations or 
 degrees of that quadrant, 78 9, 65 41, 51 57, 
 36 24, 18 54, which will give the forenoon 
 hours of XI, X, IX, VIII, and VII ; and be- 
 cause the sun does not set before VIII in the 
 evening on the longest days, continue the hour- 
 lines of VII and VIII in the afternoon, and all 
 the hour lines will be finished on this dial. 
 
 Lastly, through 511 degrees on either quad- 
 rant, and from it's center, draw the right line 
 a g for the axis of the gnomon a g i, and from 
 g let fall the perpendicular g i upon the meri- 
 dian line a i, and there will be a triangle made^ 
 whose sides are a g, g i, and i a ; if a plate simi- 
 lar to this triangle be made as thick as the dis^ 
 f?0« 
 
OF THE GLOBES. 121 
 
 tance between the lines a c and b d, and be set 
 upright between them, touching at a and b, the 
 hne a g will, when it is truly set, be parallel to 
 the axis of the world, and will cast a shadow on 
 the hour of the day. 
 
 The trouble of dividing the two quadrants 
 may be saved, by using a line of chords, which 
 is always placed upon every scale belonging to 
 a case of instruments. 
 
 PROBLEM XLI. 
 
 To delineate a direct south dial for any given lati- 
 tude, by the globe. 
 
 Let us suppose a south dial for the latitude 
 of London. 
 
 Elevate the pole to the co-latitude of your 
 place, and proceed in all respects as above taught 
 for the horizontal dial, from VI in the morning 
 to VI in the afternoon, only the hours must be 
 reversed, as in fig. 3, plate XIII ; and the hypo- 
 thenuse a g of the gnomon a g f , must make an 
 angle with the dial plane to the co-latitude of the 
 place. 
 
 As the sun can shine no longer than from VI 
 in the morning to VI in the evening, there is no 
 occasion for having more than twelve hours upon 
 this dial. 
 
 In solving this problem, we have considered 
 our vertical south dial for the latitude of I^on- 
 Q 307 
 
122 DESCRIPTION AND USE 
 
 don, as an horizontal one for the complement of 
 that latitude, or 38 deg. 30 min. ; all direct 
 vertical dials may be thus reduced to horizontal 
 ones, in the same manner. The reason of this 
 will be evident, if the globe be elevated to the 
 latitude of London ; for by fixing the quadrant 
 of altitude to the zenith, and bringing it to in- 
 tersect the horizon in the east point, it will 
 point out the plane of the proposed dial. 
 
 This plane is at right angles to the meridian, 
 and perpendicular to the horizon ; and it is clear, 
 from the bare inspection of the globe thus ele- 
 vated, that it's axis forms an angle with this 
 plane, which is just the complement of that which 
 it forms with the horizon, and is therefore just 
 equal to the co-latitude of the place ; and that 
 therefore it is most simple to rectify the globe to 
 that co-latitude. 
 
 The north vertical dial is the same with the 
 south, only the stile must point upwards, and 
 that many of the hours from it's direction can 
 be of no use. 
 
 PROBLEM XLII. 
 
 To make an erecf dial, declining from the south 
 towards the east or west. 
 
 Elevate the pole to the latitude of the place, 
 and screw the quadrant of altitude to the zenith. 
 .'308 
 
OF THE GLOBES. 123 
 
 Then if your dial declines towards the east, 
 (which we shall suppose in the present instance) 
 count in the horizon the degrees of declination 
 from the east point towards the north, and bring 
 the lower end of the quadrant to coincide with 
 that degree of declination at which the reckon- 
 ing ends. 
 
 Then bring the first meridian under the gra- 
 duated edge of the strong brass meridian, which 
 strong meridian will be the horary index. 
 
 Now turn the globe westward, and observe 
 the degrees cut in the quadrant of altitude by the 
 first meridian, while the hours XI, X, IX, &c. 
 in the forenoon, pass successively under the 
 brazen one ; and the degrees thus cut on the 
 quadrant by the first meridian, are the respec- 
 tive distances of the forenoon hours, from XII, 
 on the plane of the quadrant. 
 
 For the afternoon hours, turn the quadrant of 
 altitude round the zenith, until it comes to the 
 degree in the horizon, opposite to that where it 
 was placed before, namely, as far from the west 
 towards the south, and turn the globe eastward ; 
 and as the hours I, II, III, &c. pass under the 
 strong brazen meridian, the first meridian will 
 cut on the quadrant of altitude the number of 
 degrees from the zenith, that each of the hours 
 is from XII on the dial. 
 
 When the first meridian goes off the quad- 
 309 
 
124 DESCRIPTION AND USE 
 
 rant at the horizon, in the forenoon, the hour 
 index will shew the time when the sun comes 
 upon this dial ; and when it goes off the quad- 
 rant in the afternoon, it points to the time when 
 the sun leaves the dial. 
 
 Having thus found all the hour distances 
 from XII, lay them down upon your dial plane, 
 either by dividing a semicircle into two quad- 
 rants, or by the Hne of chords. 
 
 In all declining dials, the line on which the 
 gnomon stands makes an angle with the twelve 
 o'clock line, and falls among the forenoon hour 
 lines, if the dial declines towards the east j and 
 among the afternoon hour lines, when the dial 
 declines towards the west ; that is, to the left 
 hand from the twelve o'clock line in the former 
 case, ami to the right hand from it in the latter. 
 
 Tc find the distance of this line from that of 
 twelve. 
 
 This may be considered, 1. If the dial de- 
 clines from the south towards the east, then 
 count the degrees of that declination in the ho- 
 rizon, from the east point towards the north, 
 and bring the lower end of the quadrant to 
 that degree of declination where the reckon- 
 ing ends ; then turn the globe, until the first 
 meridian cuts the horizon in the like number 
 310 
 
OF THE GLOBES. 125 
 
 of degrees, counted from the south point to- 
 wards the east, and the quadrant and first meri- 
 dian will cross one another at right angles, and 
 the number of degrees of the quadrant, which 
 are intercepted between the first meridian and 
 the zenith, is equal to the distance of this line 
 from the twelve o'clock line. 
 
 The numbers of the first meridian, which are 
 intercepted between the quadrant and the north 
 pole, is equal to the elevation of the stile above 
 the plane of the dial. 
 
 The second case is, when the dial declines 
 westward from the south. 
 
 Count the declination from the east point of 
 the horizon, towards the south, and bring the 
 quadrant of altitude to the degree in the horizon, 
 at which the reckoning ends, both for finding 
 the forenoon hours, and the distance of the sub- 
 stile, or gnomon line, from the meridian ; and for 
 the afternoon hours, bring the quadrant to the 
 opposite degrees in the horizon, namely, as far 
 from the west towards the north, and then pro- 
 ceed in all respects as before. 
 
 It is presumed, that the foregoing instances 
 will be sufficient to illustrate the general princi- 
 ples of dialling, and to give the pupil a general 
 idea of that pleasing science ; for accurate and 
 expeditious methods of constructing dials, we 
 must refer him to treatises written expressly or 
 that subject. 
 
 311 
 
126 DESCRIPTION AND USE 
 
 NAVIGATION 
 
 EXPLAINED BY THE GLOBE. 
 
 NAVIGATION is the art of guiding a ship 
 at sea, from one place to another, in the 
 safest and most convenient manner. In order 
 to attain this, four things are particularly ne- 
 cessary : 
 
 1. To know the situation and distance of 
 places. 
 
 2. To know at all times the points of the 
 compass. 
 
 J3. To know the line which the ship is to be 
 directed from one place to the other. 
 
 4. To know, in any part of the voyage, what 
 point of the globe the ship is upon. 
 
 The knowledge of the distance and situa- 
 tion of places, between which a voyage is to be 
 made, implies not only a general knowledge of 
 geography, but of several other particulars, as 
 the rocks, sands, streights, rivers, &c. near 
 which we are to sail ; the bending out, or run- 
 ning in of the shores, the knowledge of the 
 times that particular winds sets in, the seasons 
 when storms and hurricanes are to be expected, 
 312 
 
OF THE GLOBES. 127 
 
 but especially the tides ; these and many other 
 similar circumstances are to be learned from sea 
 charts, journals, &c. but chiefly by observation 
 and experience. 
 
 The second particular to be attained, is the 
 knowledge at all times of the points of the 
 compass, where the ship is. The ancients, to 
 whom the polarity ot the loadstone was un- 
 known, found in the day-time the east or west, 
 by the rising or setting of the sun ; and at night, 
 the north by the polar star. We have the 
 advantage of the mariner's compass, by which, 
 at any time in the wide ocean, and the darkest 
 night, we know where the north is, and conse- 
 quently the rest of the points of the compass. 
 
 Indeed, before the invention of the mariner's 
 compass, the voyages of the Europeans were 
 principally confined to coasting ; but this for- 
 tunate discovery has enabled the mariner to ex- 
 plore new seas, and discover new countries, 
 which, without this valuable acquisition, would 
 probably have remained for ever unknown. 
 
 The third thing required to be known, is 
 the line which a ship describes upon the globe 
 of the earth, in going from one place to ano- 
 ther. 
 
 The shortest way from one place to another, 
 is an arc of a great circle, drawn through the 
 two places. 
 
 31 S 
 
128 DESCRIPTION AND USE 
 
 The most convenient way for a ship, is that 
 by which we may sail from one place to another, 
 directing the ship all the while towards the same 
 point of the compass. 
 
 A ship is guided by steering or directing her 
 towards some points of the compass ; the line 
 wherein a ship is directed, is called the ship's 
 course, which is named from the point towards 
 which she sails. 
 
 Thus if a ship sails towards the north-east 
 point, her course is said to be N. E. 
 
 In long voyages, a ship's way may consist of 
 a great number of different courses, as from A 
 to B, from B to C, and from C to D, fig 9, 
 plate XIII ; when we speak of a ship's course, 
 we consider one of these at a time ; the seldomer 
 the course is changed, the more easily the ship 
 is directed. 
 
 If two places, A and Z, Jig. 7, plaie XIII. 
 He uhder the same meridian, the course from 
 the one side to the other is due north or south. 
 Thus let A Z be part of a meridian ; if A be 
 south of Z, the course from A to Z must be 
 north, and the course from Z to A south. This 
 is evident from the nature of a meridian, that 
 it marks upon the horizon the north and south 
 points, and that every point of any meridian is 
 north or south from every other point of it. 
 From hence we may deduce the following co- 
 314 
 
OF THE GLOBES. 129 
 
 rollary ; that if a ship sails due north or south, 
 she will continue on the same meridian. 
 
 If two places lie under the equator, the 
 course from one to the other is an arc of the 
 equator, and is due east or west. Thus let a z, 
 fig. 7, be a part of the equator ; if a be west 
 from z, the course from a to z is east, and the 
 course from z to a is west : for since the equa- 
 tor marks the east and west points upon the 
 horizon, every point of the equator lies east or 
 west of every other point of it, as may be seen 
 upon the globe, by placing it as for a right 
 sphere, and bringing a or z, or any of the in- 
 termediate points, to the zenith ; when it will 
 be evident, that if we are to go from one of 
 these points a, to the other z, or to any point 
 on the equator, we must continue our course 
 due east to arrive at a, or vice versa. From hence 
 we may deduce this consequence, that if a ship 
 under the equator sails due east or west, she will 
 continue under the equator. 
 
 In the two foregoing cases, the course being 
 an arc of a great circle, (the meridian or equator) 
 is the shortest and the most convenient way it 
 can sail. 
 
 If two places lie under the same parallel, the 
 course from one to the other is due east or 
 west ; this may be seen upon the globe, by the 
 following method : bring any point of a paral- 
 lel to the zenith, and stretch a thread over it, 
 R' 315 
 
130 DESCRIPTION AND USE 
 
 perpendicular to the meridian ; the thread will 
 then be a tangent to the parallel, and stand east 
 and west from the point of contact. Hence, 
 If a ship sails in any parallel, due east of west, 
 she will continue in the same parallel. In this 
 case, the most convenient course, though not 
 the shortest, from one to the other, is to sail due 
 east or west. 
 
 Jf two places lie neither under the equator, nor 
 on the same meridian^ nor in the same parallel^ the 
 most convenient, though not the shortest, course 
 from one to the other, is in a rhumb. 
 
 For if we should in this case attempt to go 
 the shortest way, in a great circle drawn through 
 the two places, we must be perpetually chang- 
 ing our course. Thus fig. 8, whatever is the 
 bearing of Z from A, the bearings of all the 
 intermediate points, as B, C, D, E, &c. will be 
 different from it, as well as different from each 
 other, as may be easily seen upon the globe, by 
 bringing the first point A to the zenith, and 
 observing the bearing of Z from each of them. 
 Thus suppose, when the globe is rectified to the 
 horizon of A, the bearing of Z from A be north- 
 east, and the angle of position of Z, with regard 
 to A, be 45 degrees ; if we bring B to the ze- 
 nith, we shall have a different horizon, and the 
 bearing and angle of position from Z to B will 
 be different from the former ; and so on of the 
 other points C, D, E, they will each of them 
 316 
 
OF THE GLOBES. ISl 
 
 have a different horizon, and Z will have a dif- 
 ferent bearing and angle of position. 
 
 From hence we may draw this corollary, that 
 when two places lie one from the other, towards 
 a point not cardinal, if we sail from one place 
 towards the point of the other's bearing, we 
 shall never arrive at the other place. Thus if Z 
 lies north-east from A, if we sail from A towards 
 the north-east, we shall never arrive at Z. 
 
 A rhumb upon the globe is a line drawn from 
 a given place A, so as to cut all the meridians 
 it passes through at equal angles ; the rhumbs 
 are denominated from the points of the compass, 
 in a different manner from the winds. Thus, 
 at sea, the north-east wind is that which blows 
 from the north-east point of the horizon, to- 
 wards the ship in which we are ; but we are said 
 to sail upon the N. E. rhumb, when we go to- 
 wards the north-east. 
 
 The rhumb A B C D Z, fig. 8, plate XIII. 
 passing through the meridians L M, N O, P Q, 
 makes the angles L A B, N B C, P C D, equal ; 
 from whence it follows, that the direction of a 
 rhumb is in every part of it towards the same 
 point of the compass ; thus from every point of 
 a north-east rhumb upon the globe, the direction 
 is towards the north-east, and that rhumb makes 
 an angle of 45 deg. with every meridian it \% 
 drawn through. 
 
 317 
 
J 32 DESCRIPTION AND USE 
 
 Another property of the rhumbs is, that equal 
 parts of the same rhumb are contained between 
 parallels of equal distance of latitude ; so that a 
 ship continuing in the same rhumb, will run the 
 same number of miles in sailing from the paral- 
 lel of 10 to the parallel of iiO, as she does in sail- 
 ing from the parallel of 30 to that of 50. 
 
 The fourth thing mentioned to be required 
 in navigation, was, to know at any time what 
 point of the globe a ship is upon. This depends 
 upon four things: 1. the longitude; 2. the 
 latitude ; 3. the course the ship has run j 4. the 
 distance, that is, the way she has made, or the 
 number of leagues or miles she has run in that 
 course, from the place of the last observation. 
 Now any two of these being known, the rest may 
 be easily found. 
 
 Having thus given some general idea of 
 navigation, we now proceed to the problems 
 by which the cases of sailing are solved on the 
 globe. 
 
 PROBLEM XLIII. 
 
 Given the difference of latitude, and difference of 
 longitude .i to find the course and distance sailed * 
 
 Example. Admit a ship sails from a port 
 
 * See Martin on the Globes. 
 318 
 
OF THE GLOBES. 133 
 
 A, in latitude 38 deg. to another port B, in 
 latitude 5 deg. and finds her difference of longi- 
 tude 43 deg. 
 
 Let the port A be brought to the meridian, 
 and elevate the globe to the given latitude of that 
 port 38 deg. and fixing the quadrant of altitude 
 precisely over it on the meridian, move the. quad- 
 rant to lie over the second port B, (found by the 
 given difference of latitude and longitude) then 
 will it cut in the horizon 50 deg. 45 min. for 
 the angle of the sbip's course to be steered from 
 the port A. Also, count the degrees in the 
 quadrant between the two ports, which you will 
 find 51 deg.; this number multiplied by 60, 
 (the nautical miles in a degree) will give 3060 
 for the distance run. 
 
 PROBLEM XLIV. 
 
 Given the differe^ue of latitude and course ^ to find 
 the difference of longitude and distance sailed* 
 
 Example, Admit a ship sails from a port A, 
 in 25 deg. north latitude, to another port B, in 
 30 deg. south latitude, upon a course of 43 deg. 
 
 Bri^ig the port A to the meridian, and rec- 
 tify the globe to the latitude thereof 25 deg. 
 where fix the quadrant of altitude, and place it 
 so as to make an angle with the meridian of 
 319 
 
134 DESCRIPTION AND USE 
 
 43 deg. in the horizon, and observe where the 
 edge of the quadrant intersects the parallel of 
 30 dcg. south latitude, for that is the place of 
 the port B. Then count the number of degrees 
 on the edge of the quadrant intersected between 
 the two ports, and there will be found 73 deg* 
 which, mulriplied by 60, gives 4380 miles for 
 the distance sailed. As the two ports are now 
 known, let each be brought to the meridian, and 
 observe the difference of longitude in the equa- 
 tor respectively, which will be found 50 degrees. 
 N. tB. Had this problem been solved by 
 loxodromics, or sailing on a rhumb, the differ- 
 ence of longitude would then have been 52 deg. 
 30 min. between the two ports. 
 
 PROBLEM XLV. 
 
 Given the difference of latitude and distance run, 
 to find the difference of longitude^ and angle of 
 the course. 
 
 Example. Admit a ship sails from a port 
 A, in latitude 50 deg. to another port B, in 
 latitude 17 deg. 30 min. and her distance run 
 be 2220 miles. Rectify the globe to the lati- 
 tude of the place A, then the distance run, re- 
 duced to degrees, will make 37 deg. which are 
 to be reckoned from the end of the quadrant 
 lying over the port A, under the meridian; 
 320 
 
OF THE GLOBES. 135 
 
 then is the quadrant to be moved, till the 37 
 deg. coincides with the parallel of 17 deg. 30 
 min. north latitude ; then will the angle of the 
 course appear in the arch of the horizon, inter- 
 cepted between the quadrant and the niericiicin, 
 which will be 32 deg. 40 min. ; and by makiT.g 
 a mark on the globe for the port B, and bring- 
 ing the same to the meridian, you will observe 
 what number of degrees pass under the meridian, 
 which will be 20, the difference of longitude 
 required. 
 
 PROBLEM XLVI. 
 
 Given the differe7ice of longitude and course^ to 
 find the difference of latitude and distance sail- 
 ed. 
 
 Example. Suppose a ship sails from A, in 
 the latitude 51 deg. on a course making an 
 angle with the meridian of 40 deg. till the dif- 
 ference of longitude be found just 20 deg. ; 
 then rectifying the globe to the latitude of the 
 port A, place the quadrant of altitude so as to 
 make an angle of 40 deg. with the meridian ; 
 then observe at what point it intersects the 
 meridian passing through the given longitude 
 of the port B, and there make a mark to repre- 
 sent the said port ; then the number of degrees 
 intercepted between that and the port A will 
 be 28, which will give 1 680 miles for the dis- 
 
 312 
 
1S6 DESCRIPTION AND USE 
 
 tance run. And the said mark for the port B, 
 being brought to the meridian, will have it*s 
 latitude there shewn to be 27 deg. 40 min. 
 
 PROBLEM XLVII. 
 
 Given the course and distance sailed, to find the 
 difference of longitude^ and difference of lati- 
 tude. 
 
 Example. Suppose a ship sails 1800 miles 
 from a port A, 51 deg. 15 min, south-west, on 
 an angle of 45 deg. to another port B. 
 
 Having rectified the globe to the port A, fix 
 the quadrant of altitude over it in the zenith, 
 and place it to the south-west point in the hori- 
 zon ; then upon the edge of the quadrant under 
 30 deg. (equal to 1 800 miles from the port A) 
 is the port B ; which bring to the meridian, and 
 you will there see the latitude ; and at the same 
 time, ic*s longitude on the equator, in the point 
 cut by the meridian. 
 
 In all these cases, the ship is supposed to be 
 kept upon the arch of a great circle, which is 
 not difficult to be done, very nearly, by means 
 of the globe, by frequently observing the lati- 
 tude, measuring the distance sailed, and (when 
 you can) finding the difference of longitude ; 
 for one of these being given, the place and 
 course of the ship is known at the same time ; 
 and therefore the preceding course may be al- 
 322 
 
OF THE GLOBfiS. 137 
 
 tered, and rectified without any trouble, through 
 the whole voyage, as often as such observations 
 can be obtained, or it is found necessary. Now 
 if any of these data are but of the quantity of 
 four or five degrees, it will sufiice for correcting 
 the ship's course by the globe, and carrying her 
 directly to the intended port, according to the 
 following problem. 
 
 PROBLEM XLVIII. 
 
 To steer a ship upon the arch of a great circle by 
 the given difference of latitude, or difference of 
 longitude, or distance sailed in a given time. 
 
 Admit a ship sails from a port A, to a very 
 distant port Z, whose latitude and longitude are 
 given, as well as it's geographical bearing from 
 A ; then. 
 
 First, having rectified the globe to the port A, 
 lay the quadrant of altitude over the port Z, and 
 draw thereby the arch of the great circle through 
 A and Z ; this will design the intended path or 
 tract of the ship. 
 
 Secondly, having kept the ship upon the 
 first given course for some time, suppose by an 
 observation you find the latitude of the present 
 place of the ship, this added to, or subducted 
 from the latitude of the port A, will give the 
 present latitude in the meridian ; to which 
 S 323 
 
1S8 DESCRIPTION AND USE 
 
 bring the path of the ship, and the part therein, 
 which Hes under the new latitude, is the true 
 place B of the ship in the great arch. To the 
 latitude of B rectify the globe, and lay the quad- 
 rant over Z, and it will shew in the horizon the 
 new course to be steered. 
 
 Thirdly, suppose the ship to be steered upon 
 this course, till her distance run be found 300 
 miles, or 5 deg. ; then, the globe being rectified 
 to the place B in the zenith, laying the quadrant 
 from thence over the great arch, make a mark 
 at the 5th degree from B, and that will be the 
 present place of the ship, which call C ; which 
 being brought to the meridian, it*s latitude and 
 longitude will be known. Then rectify the 
 globe to the place C, and laying the quadrant 
 from thence to Z, the new course to be steered 
 will appear in the horizon. 
 
 Fourthly, having steered some time upon 
 this new course, suppose, by some means or 
 other, you come to know the difference of longi- 
 tude of the present place of the ship, and of any 
 of the preceding places, C, B, A; as B, for 
 instance ; then bring B to the meridian, and 
 turn the globe about, till so many degrees of 
 the equator pass under the meridian as are 
 equal to the discovered distance of longitude ; 
 then the point of the great arch cut by the me- 
 ridian is the present place D of the ship, to 
 324 
 
OF THE GLOBES. 1S9 
 
 which the new course is to be found as be- 
 fore. 
 
 And thus, by repeating these observations at 
 proper intervals, you will find future places, 
 E, F, G, &c. in the great arch j and by rectify- 
 ing the course at each, your ship will be con- 
 ducted on the great circle, or the nearest way 
 from the port A to Z, by the tfse of the globe 
 only. 
 
 OF THE USE 
 
 or THE 
 
 TERRESTRIAL GLOBE, 
 
 WHEN MOUNTED 
 
 IN THE COMMON MANNER. 
 
 ALTHOUGH I have, in the first part of 
 this essay, laid before my readers the 
 reasons which induce me to prefer my father's 
 manner of mounting the globes, to the old or 
 Ptolemaic form, yet as many may be in posses- 
 sion of globes mounted in the old form, and 
 others may have been taught by those globes, I 
 thought it would render these essays more com- 
 325 
 
140 DESCRIPTION AND USE 
 
 plete, to give an account of so many of the lead- 
 ing problems, solved on the common globes, as 
 would enable them to apply the remainder of 
 those heretofore solved, to their own use. This 
 is the more expcdi«int, as, since the publication 
 of my father's treatise, there have been a few 
 attempts to do away some of the inconveniences 
 of the ancient form, particular that of the old 
 hour-circle, which is now generally placed under 
 the meridian. 
 
 I cannot, however, refrain from again observ- 
 ing to the pupil, that the solution of the prob- 
 lems on the old globes depends upon appear- 
 ances ; "that therefore, if he means to content 
 himself with the mere mechanical solution of 
 them, the Ptolemaic globes will answer his pur- 
 pose ; but if he wish-r-s to have clear ideas of the 
 rationale of those problems, he must use those 
 mounted in my father's manner. 
 
 The celestial globe is used the same way in 
 both mountings, excepting that in my father's 
 mounting it has some additional circles ; but the 
 difference is so trifling, that it is presumed the 
 pupil can find no di.'Bcuhy in applying the direc- 
 tions there given to the old form. 
 326 
 
OF THE GLOBES. L41, 
 
 PROBLEM I. 
 
 To find the latitude and longitude of any given place 
 on the globe. 
 
 Bring the place to the east side of the brass 
 meridian, then the degree marked on the meri- 
 dian over it shews it*s latitude, and the degree 
 of the equator under the meridian 'shews it's 
 longitude. 
 
 Hence, if the longitude and latitude of any 
 place be given, the place is easily found, by 
 bringing the given longitude to the meridian ; 
 for then the place will lie under the given de- 
 gree of latitude upon the meridian. 
 
 PROBLEM II. 
 
 To find the difference of longitude between any two 
 given places. 
 
 Bring each of the given places successively to 
 thei)razen meridian, and see where the meridian 
 cuts the equator each time ; the number of de- 
 grees contained between those two points, if it 
 be less than 180 deg. otherwise the remainder 
 to 360 deg. will be the difference of longitude 
 required. 
 
 327 
 
142 DESCRIPTION AND USE 
 
 PROBLEM III. 
 
 To rectify the globe for the latitude^ zenith, and 
 sun*s place. 
 
 Find the latitude of the place by prob. 1 , and 
 if the place be in the northern hemisphere, ele- 
 vate the north pole above the horizon, according 
 to the latitude of the place. If the place be in the 
 southern hemisphere, elevate the south pole 
 above the south point of the horizon, as many 
 degrees as are equal to the latitude. 
 
 Having elevated the globe according to it's 
 latitude, count the degrees thereof upon the 
 meridian from the equator towards the elevated 
 pole, and that point will be the zenith, or the 
 vertex of the place ; to this point of the meri- 
 dian fasten the quadrant of altitude, so that the 
 graduated edge thereof may be joined to the said 
 point. 
 
 Having brought the sun*s place in the eclip- 
 tic to the meridian, set the hour index to twelve 
 at nocn, and the globe will be rectified to the 
 sun's place. 
 
 328 
 
OF THE GLOBES. 143 
 
 PROBLEM IV. 
 
 The hour of the day at any place being given^ io 
 find all those on the globe^ 'where it is noon, mid- 
 nighty or any given hour at that titne. 
 
 On the globes when mounted in the common 
 manner, k is now customary to place the hour- 
 circle under the north pole ; it is divided into 
 twice twelve hours, and has two rows of figures, 
 one running from east to west, the other from 
 west to east ; this circle is moveable, and the 
 meridian answers the purpose of an index. 
 
 Bring the given place to the brazen meridian, 
 and the given hour of the day on the hour-circle, 
 this done, turn the globe about, till the meri- 
 dian points at the hour desired ; then, with all 
 those under the meridian, it is noon, midnight, 
 or any given hour at that time. 
 
 PROBLEM V. 
 
 The hour of the day at any place being given, ta 
 find the corresponding hour (or what o'clock it 
 is at that time) in any other place. 
 
 Bring the given place to the brazen meri- 
 dian, and set the hour-circle to the given 
 time ; then turn the globe about, until the 
 place where the hour is required comes to the 
 329 
 
144 DESCRIPTION AND USE 
 
 meridian, and the meridian will point out the 
 hour of the day at that place. 
 
 Thus, when is is noon at London, it is 
 
 H. M. 
 
 rRome - - - 52 p. M» 
 
 .1 Constantinople - - 2 7 p. m. 
 
 I Vera Cruz - - - 5 30 a. m. 
 
 LPekin in China - - 7 50 p. m. 
 
 PROBLEM VI. 
 
 The day of the month being given, to find all those 
 places on the globe where the sun will be vertical^ 
 or in the zenith, that day. 
 
 Having found the sun's place in the ecliptic 
 for the given day, bring the same to the brazen 
 meridian, observe what degree of the meridian 
 is over it, then turn the globe round it's axis, 
 and all places that pass under that degree of the 
 meridian, will have the sun vertical, or in the 
 zenith, that day ; /. e. directly over the head of 
 each place at it*s respective noon. 
 
 PROBLEM VII. 
 
 A place being given in the torrid zone, to find those 
 two days in the year on which the sun will be 
 vertical to that place. 
 
 Bring the given place to the brazen meri- 
 dian, and mark the degree of latitude that is 
 330 
 
OF THE GLOBES. 145 
 
 exactly over it on the meridian ; then turn the 
 globe about it's axis, and observe the two points 
 of the ecliptic which pass exactly under that de- 
 gree of latitude, and look on the horizon for 
 the two days of the year in which the sun is in 
 those points or degrees of the ecliptic, and they 
 are the days required ; for en them, and none 
 else, the sun's declination is equal to the latitude 
 of the given place. 
 
 PROBLEM. VIII. 
 
 To find the ant(£ci, pcriccci, and antipodes of any 
 given place ^ ' 
 
 Bring the given place to the brazen meri- 
 dian, and having found it's latitude, keep the 
 globe in that position, and count the same num- 
 ber of degrees of latitude on the meridian, from 
 the equator towards the contrary pole, and where 
 the reckoning ends, that will give the place of 
 the antoeci upon the globe. Those who live at 
 the equator have no antoeci. 
 
 The globe remaining in the same position, 
 bring the upper XII on the horary circle to the 
 meridian, then turn the globe about till the me- 
 ridian points to the lower XII ; the place which 
 then lies under the meridian, having the same 
 latitude with the given place, is the periceci re- 
 quired. Those who live at the poles, it any, 
 have no periceci. 
 
 T 331 
 
146 DESCRIPTION AND USE 
 
 As the globe now stands (with the index at 
 the lower XII), the antipodes of the given place 
 are under the same point of the brazen meri- 
 dian where it's antceci stood before. 
 
 PROBLEM. IX. 
 
 To find at what hour the sun rises and sets any 
 day in the year, and also upon what point of 
 the compass. 
 
 Rectify the globe for the latitude of the place 
 you are in ; bring the sun's place to the meri- 
 dian, and bring the XII to the meridian ; then 
 turn the sun*s place to the eastern edge of the 
 horizon, and the meridian will point out the hour 
 of rising ; if you bring it to the western edge 
 of the horizon, it will shew the setting. 
 
 Thus on the 16th day of March, the sun rose 
 a little past six, and set a little before six. 
 
 Note. In the summer the sun rises and sets 
 a little to the northward of the east and west 
 points, but in winter, a little to the southward 
 of them. If, therefore, when the sun's place is 
 brought to the eastern and western edges of the 
 horizon, you look on the inner circle, right 
 against the sun's place, you will see the point of 
 the compass upon which the sun rises and sets 
 that day. 
 
 332 
 
OF THE GLOBES. 147 
 
 PROBLEM. X. 
 
 To find the length of the day and night at any time 
 of the year. 
 
 " Only double the time of the sun's rising that 
 day, and it gives the length of the night ; dou- 
 ble the time of his setting, and it gives the length 
 of the day. 
 
 This problem shews how long the sun stays 
 with us any day, and how long he is absent from 
 us any night. 
 
 Thus on the 26th of May the sun rises about 
 four, and sets about eight ; therefore the day is 
 sixteen hours long, and the night eight. 
 
 PROBLEM XI. 
 
 To find the length of the longest or shortest day, at 
 any place upon the earth. 
 
 Rectify the globe for that place, bring the 
 beginning of Cancer to the meridian, bring XII 
 to the meridian, then bring the same degree of 
 Cancer to the east part of the horizon, and the 
 meridian will shew the time of the sun's rising. 
 
 If the same degree be brought to the 
 western side, the meridian will shew the set- 
 ting, which doubled, (as in the last problem) 
 ^'63 
 
148 DESCRIPTION AND USE 
 
 will give the length of the longest day and short- 
 est night. 
 
 If we bring the beginning of Capricorn to 
 the meridian, and proceed in all respects as be- 
 fore, we shall have the length of the longest 
 night and shortest day. 
 
 Thus in the Great Mogurs dominions, the 
 longest day is fourteen hours, and the shortest 
 night ten hours. The shortest day is ten hours, 
 and the longest night fourteen hours. 
 
 At Petersburgh, the seat of the Empress of 
 Russia, the longest day is about 192 hours, and 
 the shortest night 41 hours ; the shortest day 4j 
 hours, and longest night 19] hours. 
 
 Note, In all places near the equator, the sun 
 rises and sets at six the year round. From 
 thence to the polar circles, the days increase as 
 the latitude increases; so that at those circles 
 themselves, the long. X day is 24 hours, and the 
 longest night just the same. From the polar cir- 
 cles to the poles, the days continue to lengthen 
 into weeks and months; so that at the very pole, 
 the sun shines for six months together in sum- 
 mer, and is absent from it six months in winter, 
 
 JSlote, That when it is summer with the nor^ 
 thern inhabitants, it is winter with the southern, 
 and the contrary ; and every part of the world 
 partakes of an equal share of light and dark- 
 ness. 
 
 334 
 
OF THE GLOBES. 149 
 
 PROBLEM XII. 
 
 Tofnd all those inhabitants to zvhom the sun is this 
 ?fic?}ient rising or setting, in their meridian or 
 7nidnight. 
 
 Find the sun's place in the ecliptic, and raise 
 the pole as much above the horizon as the sun 
 (that day) declines from the equator ; then bring 
 the place where the sun is vertical at that hour 
 to the brass meridian ; so it will then be in the 
 zenith or center of the horizon. Now see what 
 countries lie on the western edge of the horizon, 
 for in them the sun is rising ; to those on the 
 eastern side he is setting ; to those under the 
 upper part of the meridian it is noon day ; and 
 to those under the lower part of it, it is midnight. 
 
 Thus on the 2oth of April, at six o'clock in 
 the evening, at Worcester, 
 
 The sun is rising at New Zealand ; and to 
 those who are sailing in the middle of the Great 
 South Sea. 
 
 The sun is setting at Sweden, Hungary, 
 Italy, Tunis, in the middle of Negroland and 
 Guinea. 
 
 In the meridian (or noon) at the middle of 
 Mexico, Bay of Honduras, middle of Florida, 
 Canada, &c. 
 
 235 
 
150 DESCRIPTION AND USE 
 
 Midnight at the middle of Tartary, Bengal, 
 India, and the seas near the Sunda isles. 
 
 PROBLEM XIII. 
 
 To find the beginning and end of twilight. 
 
 The twilight is that faint light which opens 
 the morning by little and little in the east, be- 
 fore the sun rises ; and gradually shuts in the 
 evening in the wtst, after the sun is set. It 
 arises from the sun's illuminating the upper 
 part of the atmosphere, and begins always when 
 he approaches within eighteen degrees of the 
 eastern part of the horizon, and ends when he 
 descends eighteen degrees below the western ; 
 when dark night commences, and continues till 
 day breaks again. 
 
 To find the beginning of twilight, rectify the 
 globe ; turn the degree of the ecliptic, which 
 is opposite to the sun*s place, till it is elevated 
 eighteen degrees in the quadrant of altitude 
 above the horizon on the west, so will the in- 
 dex point the hour twilight begins. 
 
 This short specimen of problems by the old 
 globes, it is presumed, will be sufficient to ena- 
 ble the pupil to solve any other. 
 3S6 
 
( 151 ) 
 
 PART IV 
 
 OF THE USE OF THE CELESTIAL GLOBE. 
 
 THE celestial globe is an artificial represen- 
 tation of the heavens, having the hscd 
 stars drawn upon it, in tht-ir natunU order iuid 
 situation; whilst it's rotation on it's axis repre- 
 sents the apparent diurnal motion of the sun, 
 moon, and stars. 
 
 It is not known how early the ancients had 
 any thing of this kind : w-e are not conain vhat 
 the sphere of Atlas or Musasus was; perhaps 
 Palamedes, who lived about the time of the 
 Trojan war, had something of this kind ; for of 
 him it is said. 
 
 To mark the signs that cloudless skies bestow, 
 To tell the seasons, when to suil and piow, 
 He first devised ; each planet's order found, 
 It's distance, period, in the blue profound. 
 337 
 
152 DESCRIPTION AND USE 
 
 From Pliny it would seem that Hipparchus 
 had a celestial globe with the stars delineated 
 upon it. 
 
 It is not to be supposed that the celestial 
 globe is so just a representation of the heavens 
 as the terrestrial globe is of the earth ; because 
 here the stars are drawn upon a convex surface, 
 whereas they naturally appear in a concave one. 
 But suppose the globe were made of glass, then 
 to an eye placed in the center, the stars which 
 are drawn upon it would appear in a concave 
 surface, just as they do in the heavens. 
 
 Or if the reader was to suppose that holes 
 were made in each star, and an eye placed in 
 the center of the globe, it would view, through 
 those holes, the same stars in the heavens that 
 they represent. 
 
 As the terrestrial globe, by turning on it's 
 axis, represents the real diunml motion of the 
 earth ; so the celestial globe, by turning on it's 
 axis, represents the apparent diurnal motion of 
 the heavens. 
 
 For the sake of perspicuity, and to avoid con- 
 tinual references, it will be necessary to repeat 
 here some articles which have been already men- 
 tioned. 
 
 The ecliptic Is that graduated circle which 
 crosses the equator In an angle of about 231 de- 
 338 
 
©F THE GLOBES. 153 
 
 grees, and the angle is called the obliquity of the 
 ecliptic. 
 
 ' This circle is divided into twelve equal parts, 
 consisting of 30 degrees each ; the beginnings of 
 ihem are marked with characters, representing 
 the twelve signs. 
 
 Aries t, Taurus «, Gemini n, Cancer s, 
 Leo SI, Virgo nj;. Libra ^, Scorpio n\_, Sagitta- 
 rius /, Capricornus vj, Aqliarius c^, Pisces, x. 
 Upon my father's globes, just under the eclip- 
 tic, the months, and days of each month, are 
 graduated, for the readier fixing the artificial 
 sun upon it's place in the ecliptic. 
 
 The two points where the ecliptic crosses the 
 equinoctial, (the circle that answers to the equa- 
 tor on the terrestrial globe) are called the equinoc- 
 tial points ; they are at the beginnings of Aries 
 and Libra, and are so called, because when the 
 sun is in either of them, the day and night is 
 every where equal. 
 
 The first points of Cancer and Capricorn are 
 called solstitial points ; because when the sun 
 arrives at either of them, he seems to stand in a 
 manner still for several days, in respect to his 
 distance from the equinoctial ; when he is in one 
 solstitial point, he makes to us the longest day ; 
 when in the other, the longest night. 
 
 The latitude and longitude of stars are deter- 
 mined from the ecliptic. 
 
 U 339 
 
154 DESCRIPTION AND USE 
 
 The longitude of the stars and planets is reck- 
 oned upon the ecliptic ; the numbers beginning 
 at the tirst points of Aries t, where the ecliptic 
 crosses the equator, and increasing according to 
 the order of the signs. 
 
 Thus suppose the sun to be in the 10th, de- 
 gree of Leo, we say, his longitude, or place, is 
 four signs, ten degrees ; because he has already 
 passed the four signs, Aries, Taurus, Geminij 
 Cancer, and is ten degrees in the fifth. 
 
 The latitude of the stars and planets is deter- 
 mined by their distance from the ech'ptic upon a 
 secondary or great circle passing through it's 
 poles, and crossing it at right angles. 
 
 Twenty-four of these circular lines, which 
 cross the ecliptic at right angles, being fifteen 
 degrees from each other, are drawn upon the 
 surface of our celestial globe ; which being pro- 
 duced both ways, those on one side meet in a 
 point on the northern polar circle, and those on 
 the other meet in a point on the southern polar 
 circle. 
 
 The points determined by the meeting of these 
 circles are called the poles of the ecliptic, one 
 north, the other south. 
 
 From these definitions it follows, that longi- 
 tude and latitude, on the celestial globe, bear 
 just the same relation to the ecliptic, as they do 
 on the terrestrial globe to the equator. 
 340 
 
OF THE GLOBES. 155 
 
 rhus as the longitude of places on the earth 
 is measured by degrees upon the equator, count- 
 ing from the first meridian ; so the longitude 
 of the heavenly bodies is measured by degrees 
 upon the ecliptic, counting from the first point 
 of Aries. 
 
 And as latitude on the earth is measured by 
 degrees upon the meridian, counting from the 
 equator ; so the latitude of the heavenly bodies 
 is measured by degrees upon a circle of longi- 
 tude, counting either north or south from the 
 ecliptic. 
 
 The sun, therefore, has no latitude, being al- 
 ways in t^ie ecliptic ; nor do we usually speak 
 of his longitude, but rather of his place in the 
 ecliptic, expressing it by such a degree and 
 minute of such a sign, as 5 degrees of Taurus, 
 instead of 35 degrees of longitude. 
 
 The distance of any heavenly body from the 
 equinoctial, measured upon the merrdian, is 
 called it's declination. 
 
 Therefore, the sun's declination, north or 
 south, at any time, is the same as the latitude of 
 any place to which he is then vertical, which is 
 never more than 23\ degrees. 
 
 Therefore all parallels of declination on the 
 celestial globe are the very same as parallels of 
 latitude on the terrestrial. 
 
 Stars may have north latitude and south decli- 
 nation, and vice versa. 
 
 341 
 
156 DESCRIPTION AND USE 
 
 That which is called longitude on the terres. 
 trial globe, is called right ascension on the celes- 
 tial ; namely, the sun or star's distance from that 
 meridian which passes through the first point of 
 Aries, counted on the equinoctial. 
 
 Astronomers also speak of oblique ascension 
 and descension, by which they mean the distance 
 of that point of the equinoctial from the first 
 point of Aries, which in an obUque sphere rises 
 or sets, at the same time that the sun or star 
 rises or sets. 
 
 Ascensional difference is the difference betwixt 
 right and oblique ascension. The sun's ascen- 
 sional difference turned into time, is ji^st so much 
 as he rises before or after six o'clock. 
 
 The celestial signs and constellations on the 
 surface of the celestial globe, are represented by 
 a variety of human and other figures, to which 
 the stars that are either in or near them, are re- 
 ferred. 
 
 The several systems of stars, which are applied 
 to those images, are called constellations. Twelve 
 of these are represented on the ecliptic circle, 
 and extend both northward and southward from 
 it. So many of those stars as fall within the 
 limits of 8 degrees on both sides of the ecliptic 
 circle, together with such parts of their images 
 as are contained within the aforesaid bounds, 
 constitute a kind of broad hoop, belt, or girdle, 
 which is called the %odiac. 
 342 
 
OF THE GLOBES. 157 
 
 The names and the respective characters of 
 the twelve signs of the ecliptic may be learned 
 by inspection on the surface of the broad paper 
 circle, and the constellations from the globe it- 
 self. 
 
 The zodiac is represented by eight circles 
 parallel to the ecliptic, on each side thereof; 
 these circles are one degree distant from each 
 other, so that the whole breadth of the zodiac is 
 16 degrees. 
 
 Amongst these parallels, the latitude of the 
 planets is reckoned ; and in their apparent motion 
 they never exceed the Hmits of the zodiac. 
 
 On each side of the zodiac, as was observed, 
 other constellations are distinguished ; those on 
 the north side are called northern, and those on 
 the south side of it, southern constellations. 
 
 OF THE PRECESSION OF THE EQUINOXES. 
 
 All the stars which compose these constella- 
 tions, arc supposed to increase their longitude 
 continually ; upon which supposition, the whole 
 starry firmament has a slow motion from west 
 to east ; insomuch that the first star in the con- 
 stellation of Aries, which appeared in the ver- 
 nal intersection of the equator and ecliptic in 
 the time of Meton the Athenian, upwards of 
 343 
 
158 DESCRIPTION AND USE 
 
 1900 years ago, is now removed about 30 de- 
 grees from it. 
 
 This change of the stars in longitude, which 
 has now become sufficiently apparent, is owing 
 to a small retrograde motion of the equinoctial 
 points, of about 50 seconds in a year, which is 
 occasioned by the attraction of the sun and 
 moon upon the protuberant matter about the 
 equator. The same causs also occasions a. small 
 deviation in the parallelism of the earth's axis, 
 by which it is continually directed towards dif- 
 ferent points in the heavens, and makes a com- 
 plete revolution round the ecliptic in about 
 25,920 years. The former of these motions is 
 called the precession of the eqiiinones^ the latter the 
 nutation of the earth'' s axis. In consequence of 
 this shifting of the equinoctial points, an altera- 
 tion has taken place in the signs of the ecliptic ; 
 those stars, which in the infancy of astronomy 
 were in Aries, being now got into Taurus, those 
 of Taurus into Gemini, &c. ; so that the stars 
 which rose and set at any particular seasons of 
 the year, in the times ol Hesiod, Eudoxus, and 
 Virgil, will not at present answer the descriptions 
 given of them by those writers. 
 .'344 
 
OF THE GLOBES. 159 
 
 PROBLEM I. 
 
 To represent the motion of the equinoctial points 
 backwards, or in antecedentia, upon ihe celestial 
 globe, elevate the north pole so that it's axis may 
 be perpendicular to the plane of the broad paper 
 circle, and the equator will then be in the same 
 plane ; let these represent the ecliptic, and thtn 
 the poles of the globe will also represent those 
 of the ecliptic ; the ecliptic line upon the globe 
 will at the same time represent the equator, in- * 
 clined in an angle of 23 1 degrees to the broad 
 paper circle, now called the ecliptic, and cutting 
 it in two points, which are called the equinoctial 
 intersections. 
 
 Now i[ you turn the globe slowly round upon 
 it's axis from east to west, while it is in this posi- 
 tion, these points of intersection will move round 
 the same way ; and the inclination of the circle, 
 which in shewing this motion reprOv*-ents the 
 equinoctial, will not be altered by such a revo- 
 lution of the intersecting or equinoctial points. 
 This motion is called the precession of the equi- 
 noxes, because it carries the equinoctial points 
 backwards amongst the fixed stars. 
 
 The polts of the world seem to describe a 
 circle from east to west, round the poles of the 
 ecliptic, arising from the precession of the 
 34-5 
 
160 DESCRIPTION AND USE 
 
 equinox. It is a very slow motion, for the equi- 
 noctial points take up 72 years to move one 
 degree, and therefore they ar^ 25,920 years in 
 describing 3G0 degrees, or completing a revo- 
 lution. 
 
 This motion of the poles is easily represented 
 by the above described position of the globe, in 
 which, if the reader remembers, the broad paper 
 circle represents the ecliptic, and the axis of the 
 globe being perpendicular thereto, represents 
 the axis of the ecliptic ; and the two points, 
 where the circular lines meet, will represent the 
 poles of the world, whence, as the globe is slowly 
 turned from east to west, these points will re- 
 volve the same way about the poles of the globe, 
 which are here supposed to represent the poles 
 of the ecliptic. The axis of the world may 
 revolve as above, although its situation, with 
 respect to the ecliptic, be not altered ; for the 
 points here supposed to represent the poles of 
 the world, will always keep the same distance 
 from the broad paper circle, which represents 
 the ecliptic in this situation of the globe.* 
 
 From the different degrees of brightness in 
 the stars, some appear to be greater than others, 
 or nearer to us ; on our celestial globe they are 
 distinguished into seven different magnitudes. 
 
 ■* Riithcrforlh's System of Nat. Philos. vol. ii. p. 730. 
 346 
 
( 161 ) 
 
 USE OF THE CELESTIAL GLOBE, 
 
 IN THE SOLUTION OF 
 
 PROBLEMS RELATIVE TO THE SUN. 
 
 EVERY thing that relates to the sim is of 
 such importance to man, that in all things 
 he claims a natural preheminence. The sun is 
 at once the most beautiful emblem of the Su- 
 preme Being, and, under his influence, the fos- 
 tering parent of worlds ; being present to them 
 by his rays, cheering them by his countenance, 
 cherishing them by his heat, adorning them at 
 each returning spring with the gayest and rich- 
 est attire, illuminating them with his light, and 
 feeding the lamp of life. 
 
 To the ancients he was known under a va- 
 riety of names, each characteristic of his dif- 
 ferent effects ; he was their Hercules, the great 
 deliverer, the restorer of light out of darkness, 
 the dispenser of good, continually labouring 
 for the happiness of a depraved race. He was 
 the Mithra of the Persians, a word derived 
 from love, or mercy, because the whole world 
 is cherished by him, and feels as it were the ef« 
 fects of his love. 
 
 X 347 
 
162 DESCRIPTION AND USE 
 
 In the sacred scriptures, the original source 
 of all emblematical writings, our Lord is called 
 our sun, and the sun of righteousness ; and as 
 there is but one sun in the heavens, so there is 
 but one true God, the maker and redeemer of 
 all things, the light of the understanding, and 
 the life of the soul. 
 
 As in scripture our God is spoken of as a 
 shield and buckler, so the sun is characterized 
 by this mark o, representing a shield or buck- 
 ler, the middle point, the umbo, or boss ; be- 
 cause it is love, or life, which alone can protect 
 from fear and death. 
 
 His celestial rays, like those of the sun, take 
 their circuit round the earth ; there is no cor- 
 ner of it so remote as to be without the reach 
 of their vivifying and penetrating power. As 
 the material light is always ready to run it's 
 heavenly race, and daily issues forth with re- 
 newed vigour, like an invincible champion, still 
 fresh to labour ; so likewise did our redeeming 
 God rejoice to run his glorious race, he ex- 
 celled in strength, and triumphed, and conti. 
 nues to triumph over all the powers of dark- 
 ness, and is ever manifesting himself as the de- 
 liverer, the protetor, the friend, and father, of 
 the human race.* 
 
 * Home on the Psalms, 
 348 
 
OF THE GLOBES. 163 
 
 PLOBLEM II. 
 
 To rectify the celestial globe. 
 
 To rectify the celestial globe .^ is to put it in that 
 position in which it may represent exactly the appa- 
 rent motion of the heavens. 
 
 In different places, the position will vary, and 
 that according to the different latitude of the 
 places. Therefore, to rectify for any place, find 
 first, by the terrestrial globe, the latitude of that 
 place. 
 
 The latitude of the place being found in de- 
 grees, elevate the pole of the celestial globe the 
 same number of degrees and minutes above the 
 plane of the horizon, for this is the name given 
 to the broad paper circle, in the use of the ce- 
 lestial globe. 
 
 Thus the latitude of London being 5\\ de- 
 grees, let the globe be moved till the plane of 
 the horizon cuts the meridian in that point. 
 
 The next rectification is for the sun's place, 
 which may be performed as directed in prob. 
 xxix J or look for the day of the month close 
 under the ecliptic line, against which is the sun*s 
 place, place the artificial sun over that point, 
 then bring the sun*s place to the graduated edge 
 of the strong brazen meridian, and set the hour 
 index to the most elevated twelve. 
 S49 
 
164 bESCRIPTION AND USE 
 
 Thus on the 24th of May the sun is in 3i 
 degrees of Gemini, and is situated near the 
 Bull's eye and the seven stars, which are not 
 then visible, on account of his superior light. 
 If the sun were on that day to suffer a total 
 eclipse, these stars would then be seen shining 
 with their accustomed brightness. 
 
 Lastly, set the meridian of the globe north 
 and south, by the compass. 
 
 And the globe will be rectified, or put into 
 a similar position, to the concave surface of the 
 heavens, for the given latitude. 
 
 PROBLEM III. 
 
 To find the right ascension and declination of the 
 sun for any day. 
 
 Bring the sun's place in the ecliptic for the 
 given day to the meridian, and the degree of 
 the meridian directly over it is the sun*s declina- 
 tion for that day at noon. The point of the 
 equinoctial cut by the meridian, when the sun's 
 place is under it, will be the right ascension. 
 
 Thus April 19, the sun's declination is ll" 
 14' north, his right ascension 27" 30'. On the 
 1st of December the sun's declination is 21° 54' 
 south, right ascension 247" 50'. 
 
 350 
 
OF THE GLOBES. 165 
 
 PROBLEM IV. 
 
 To find the sun*s oblique ascension and descension, 
 ji*s eastern and western afnplitude^ and time of 
 rising and settings on any given time, in any 
 given place. 
 
 1. Rectify the globe for the latitude, the ze- 
 nith, and the sun's place. 2. Bring the sun's 
 place to the eastern side of the horizon ; then 
 the 'number of degrees intercepted between a 
 degree of the equinoctial at the horizon and the 
 beginning of Aries, is the sun's oblique ascen- 
 sion. 3. The number of degrees on the hori- 
 zon intercepted between the east point and the 
 sun's place, is the eastern or rising amplitude. 
 4. The hour shewn by the index is the time 
 of sun-rising. 5. Carry the sun to the western 
 side of the horizon, and you in the same man- 
 ner obtain the oblique descension, western am- 
 plitude, and time of setting. Thus at London, 
 May 1, 
 The sun's oblique ascension 
 
 Eastern amplitude 
 
 Time of rising 
 
 Oblique descension 
 
 Western amplitude 
 
 Time of setting 
 S51 
 
 18° 
 
 48' 
 
 24 
 
 57 N 
 
 4h 
 
 40 m 
 
 257° 
 
 7' 
 
 26 
 
 9 
 
 7h 
 
 4m 
 
l66 DESCRIPTION AND USE 
 
 PROBLEM V. 
 
 To find the sun's meridian altitude. 
 
 Rectify the globe for the latitude, zenith, 
 and sun*s place ; and when the sun*s place is in 
 the meridian, the degrees between that point 
 and the horizon are it's meridian altitude. Thus, 
 on May 17, at London, the meridian altitude 
 of the sun is 5T 55. 
 
 PROBLEM VI. 
 
 To find the length of any day in the year, in any 
 latitude, not exceeding 66* degrees. 
 
 Elevate the celestial globe to the latitude, and 
 set the center of the artificial sun to his place 
 upon the ecliptic line on the globe for the given 
 day, and bring it*s center to the strong brass 
 meridian, placing the horary index to that XII 
 which is most elevated ; then turn the globe 
 till the artificial sun cuts the eastern edge of the 
 horizon, and the horary index will shew the 
 time of sun-rising ; turn it to the western side, 
 and you obtain the hour of sun-setting. 
 
 The length of the day and night will be ob- 
 tained by doubling the time of sun-rising and 
 setting, as before. 
 
 352 
 
OF THE GLOBES. 167 
 
 PROBLEM VII. 
 
 To find the length of the longest and shortest 
 days in any latitude that does not exceed Q6\ de- 
 grees. 
 
 Elevate the globe according to the latitude, 
 and place the center of the artificial sun for the 
 longest day upon the first point of Cancer, but 
 for the shortest day upon the first point of Ca- 
 pricorn ; then proceed as in the last problem. 
 
 But if the place hath south latitude, the sun 
 is in the first point of Capricorn on their longest 
 day, and in the first point of Cancer on their 
 shortest day. 
 
 PROBLEM VIII. 
 
 To find the latitude of a place^ in which it's long- 
 est day may be of any given length between 
 twelve and twenty four hours. 
 
 Set the artificial sun to the first point of Can- 
 cer, bring its center to the strong brass meri- 
 dian, and set the horary index to XII ; turn the 
 globe till it points to half the number of the 
 given hours and minutes ; then elevate or de- 
 press the pole till the artificial sun coincides 
 with the horizon, and that elevation of the pole 
 is the latitude required. 
 
 353 
 
168 DESCRIPTION AND USE 
 
 PROBLEM IX. 
 
 To find the time of the sun*s rising and settings 
 the length of the day and night, on any place 
 whose latitude lies between the polar circles ; and 
 also the length of the shortest day in any of those 
 latitudes, and in what cli?nate they are. 
 
 Rectify the globe to the latitude of the given 
 place, and bring the artificial sun to his place in 
 the ecliptic for the given day of the month ; 
 and then bring it's center under the strong brass 
 meridian, and set the horary index to that XII 
 which is most elevated. 
 
 Then bring the center of the artificial sun to 
 the eastern part of the broad paper circle, 
 which in this case represents the horizon, and 
 the horary index shews the time of the sun- 
 rising; turn the artificial sun to the western side, 
 and the horary index will shew the time of the 
 sun-setting. 
 
 Double the time of sun-rising is the length 
 of the night, and the double of that of sun-set- 
 ting is the length of the day. 
 
 Thus, on the 5th day of June, the sun rises 
 at 3 h. 40 min. and sets at 8 h. 20. min. ; 6y 
 doubhng each number it will appear, that the 
 length of this day is 1 6 h. 40. min. and that of 
 the night 7 h. 20 min. 
 
 S54 
 
OF THE GLOBES. 169 
 
 The longest day at all places in north latitude, 
 is when the sun is in the first point of Cancer. 
 And, 
 
 The longest day to those in south latitude, is 
 when the sun is in the first point of Capricorn. 
 
 Wherefore, the globe being rectified as above, 
 and the artificial sun placed to the first point of 
 Cancer, and brought to the eastern edge of the 
 broad paper circle, and the horary index being 
 set to that XII which is most elevated, on turn- 
 ing the globe from east to west, until the arti- 
 ficial sun coincides with the western edge, the 
 number of hours counted, which are passed over 
 by the horary index, is the length of the longest 
 day ; their complement to twenty-four hours 
 gives the length of the shortest night. 
 
 If twelve hours be subtracted from the length 
 of the longest day, and the remaining hours 
 doubled, you obtain the climate mentioned by 
 ancient historians ; and if you take half the 
 climate, and add thereto twelve hours, you 
 obtain the length of the longest day in that cli- 
 mate. This holds good for every climate be- 
 tween the polar circles. 
 
 A climate is a space upon the surface of 
 the earth, contained between two parallels of 
 latitude, so far distant from each other, that 
 y ^55 
 
i70 DESCRIPTION AND USE 
 
 the longest day in one, differs half an hour from 
 the longest day in the other parallel. 
 
 PROBLEM X. 
 
 The latitude of a place being given in one of the 
 polar circles, ("suppose the northern J to find 
 •what number of days (of 24 hours each) the 
 sun doth constantly shine upon the same, how 
 long he is absent, and also the first and last day 
 of his appearance. 
 
 Having rectified the globe according to the 
 latitude, turn it about until some point in the 
 first quadrant of the ecliptic (because the latitude 
 is north) intersects the meridian in the north 
 point of the horizon ; and right against that 
 point of the ecliptic, on the horizon, stands the 
 day of the month when the longest day begins. 
 
 And if the globe be turned about till some 
 point in the second quadrant of the ecliptic cuts 
 the meridian in the same point of the horizon, it 
 will shew the sun's place when the longest day 
 ends, whence the day of the month may be 
 found, as before ; then the number of natural 
 days contained between the times the longest 
 day begins and ends, ^s the length of the longest 
 day required. 
 
 Again, turn the globe about, until some 
 356 
 
OF THE GLOBES. 171 
 
 point in the third quadrant of the ecliptic cuts 
 the meridian in the south part of the horizon ; 
 that point of the ecliptic will give the time when 
 the longest night begins. 
 
 Lastly, turn the globe about, until some point 
 in the fourth quadrant of the ecliptic cuts the 
 meridian in the south point of the horizon ; and 
 that point of the ecliptic will be the place of the 
 sun when the longest night ends. 
 
 Or, the time when the longest day or night 
 begins being known, their end may be found by 
 counting the number of days from that time to 
 the succeeding solstice ; then counting the same 
 number of days from the solstitial day, will give 
 the time when it ends. 
 
 OF THE EQUATION OF TIME. 
 
 It is not possible, in a treatise of this kind, 
 to enter into a disquisition of the nature of 
 time. It is sufficient to observe, that if we 
 would with exactness estimate the quantity of 
 any portion of infinite duration, or convey an 
 idea of the same to others, we make use of 
 such known measures as have been originally 
 borrowed from the motions of the heavenly 
 bodies. It is true, none of these motions are 
 exactly equal and uniform, but are subject to 
 357 
 
172 DESCRIPTION AND USE 
 
 some small irregularities, which, though of no 
 consequence in the aflairs of civil life, must be 
 taken into the account in astronomical calcula- 
 tions. There are other irregularities of more 
 importance, one of which is in the inequality of 
 the natural day. 
 
 It is a consideration that cannot be reflected 
 upon without surprise, that wherever we look 
 for commensurabilities and equalities in nature, 
 we are always disappointed. The earth is spheri- 
 cal, but not perfectly so ; the summer is une- 
 qual, when compared with the winter ; the eclip- 
 tic disagrees with the equator, and never cuts it 
 twice in the same equinoctial point. The orbit 
 of the earth has an eccentricity more than double 
 in proportion to the spheroidity of it*s globe ; 
 no number of the revolutions of the moon coin- 
 cides with any number of the revolutions of the 
 earth in it*s orbit ; no two of the planets measure 
 one another : and thus it is wherever we turn 
 our thoughts, so different are the views of the 
 Creator from our narrow conception of things ; 
 where we look for commensuration, we find 
 variety and infinity. 
 
 Thus ancient astronomers looked upon the 
 
 motion of the sun to be sufficiently regular for 
 
 the mensuration of time ; but, by the accurate 
 
 observations of later astronomers, it is found 
 
 S5S 
 
OF THE GLOBES. 173 
 
 that neither the days, nor even the hours, as 
 measured by the sun's apparent motion, are of 
 an equal length, on two accounts. 
 
 1st, A natural or solar day of 24 hours, is 
 that space of time the sun takes up in passing 
 from any particular meridian to the same again y 
 but one revolution of the earth, with respect to a 
 fixed star, is performed in 23 hours, 56 minutes, 
 4 seconds ; therefore the unequal progression of 
 the earth through her elliptical orbir, (as she 
 takes almost eight days more to run through the 
 northern half of the ecliptic, than she does to 
 pass through the southern) is the reason that the 
 length of the day is not exactly equal to the 
 time in which the earth performs it's rotation 
 about it's axis. 
 
 2dly, From the obliquity of the ecliptic to the 
 equator, on which last we measure time ; and as 
 equal portions of one do not correspond to equal 
 portions of the other, the apparent motion of 
 the sun would not be uniform ; or, in other 
 words, those points of the equator which come 
 to the meridian, with the place of the sun on 
 different days, would not be at equal distances 
 from each other. 
 
 359 
 
374 DESCRIPTION AND USE 
 
 PROBLEM XI. 
 
 To illustrate^ hy the globe, so much of the equation 
 of time as is in consequence of the sun's apparent 
 motion in the ecliptic. 
 
 Bring every tenth degree of the ecliptic to the 
 graduated side of the strong brass meridian, and 
 you will find that each tenth degree on the equa- 
 tor will not come thither with it ; but in the 
 following order from t to ?x, every tenth de- 
 gree of the ecliptic comes sooner to the strong 
 brass meridian than their corresponding tenths 
 on the equator ; those in the second quadrant of 
 the ecliptic, from gs to ^, come later, from ^ 
 to vj sooner, and from V5 to Aries later, whilst 
 those at the beginning of each quadrant come to 
 the meridian at the same time ; therefore the sun 
 and clock would be equal at these four times, if 
 the sun was not longer in passing through one 
 half of the ecliptic than the other, and the two 
 inequalities joined together, compose that diffe- 
 rence which is called the equation of time. 
 
 These causes are independent of each other, 
 sometimes they agree, and at other times are 
 contrary to one another. 
 
 The inequality of the natural day is the cause 
 that clocks or watches are sometimes before, 
 sometimes behind the sun. 
 360 
 
OF THE GLOBES. 17 J 
 
 A good and well regulated clock goes uniformly 
 on throughout the year, so as to mark the equal 
 hours of a natural day, of a mean length ; a sun- 
 dial marks the hours of every day in such a 
 manner, that every hour is a 24th part of the 
 time between the noon of that day, and the noon 
 of the day immediately following. The time 
 measured by a clock is called equal or true 
 time, that measured by the sun-dial apparent 
 time. 
 
 THE USE OF THE CELESTIAL GLOBE, IN PROB- 
 LEMS RELATIVE TO THE FIXED STARS. 
 
 The use of the celestial globe is in no instance 
 more conspicuous, than in the problems con- 
 cerning the fixed stars. Among many other 
 advantages, it will, if joined with observations 
 on the stars themselves, render the practice and 
 theory of other probleins easy and clear to the 
 pupil, and vastly facilitate his progress in astro- 
 nomical knowledge. 
 
 The heavens are as much studded over with 
 stars in the day, as in the night j only they 
 are then rendered invisible to us by the bright- 
 ness of the solar rays. But when this glorious 
 luminary descends below the horizon, they be- 
 gin gradually to appear ; when the sun is about 
 twelve degrees below the horizon, stars of the 
 first magnitude become visible ; when he is 
 561 
 
176 DESCRIPTION AND USE 
 
 thirteen degrees, those of the second are seen j 
 when fourteen degrees, those of the third mag- 
 nitude appear ; when fifteen degrees, those of 
 the fourth present themselves to view ; when he 
 is descended about eighteen degrees, the stars 
 of the fifth and sixth magnitude, and those that 
 are still smaller, become conspicuous, and the 
 azure arch sparkles with all it's glory. , 
 
 PROBLEM XII. 
 
 To find the right ascension and declination of any 
 given star. 
 
 Bring the given star to the meridian, and the 
 degree under which it lies is it's declination j and 
 the point in which the meridian intersects the 
 equinoctial is it's right ascension. Thus the right 
 ascension of Sirius is 99", it's declination 1 6" 25' 
 south ; the right ascension of Arcturus is 211" 
 32'. it's declination 20" 20' north. 
 
 The declination is used to find the latitude of 
 places ; the right ascension is used to find the 
 time at which a star or planet comes to the me- 
 ridian ; to find at any given time how long it 
 will be before any celestial body comes to the 
 meridian ; to determine in what order those 
 bodies pass the meridian j and to make a cata- 
 logue of the fixed stars. 
 362 
 
OF THE GLOBES. 177 
 
 PROBLEM XIII. 
 
 To find the latitude and longitude of a given 
 star. 
 
 Bring the pole of the ecliptic to the meri- 
 dian, over which fix the quadrant of altitude, 
 and, holding the globe very steady, move the 
 quadrant to lie over the given star, and the de- 
 gree on the quadrant cut by the star, is it's la- 
 titude ; the degree of the ecliptic cut at the 
 same time by the quadrant, is the longitude of 
 the star. 
 
 Thus the latitude of Arcturus is 30" 30' ; 
 it's longitude 20" 20' of Libra : the latitude of 
 Capella is 22" 22' north j it's longitude 18 8' of 
 Gemini. 
 
 The latitude and longitude of stars is used 
 to fix precisely their place on the globe, to re- 
 fer planets and comets to the stars, and, lastly, 
 to determine whether they have any motion, 
 whether any stars vanish, or new ones appear, 
 
 PROBLEM XIV. 
 
 The right ascension and declination of a star being 
 giveuy to find it^s place on the globe* 
 
 Turn the globe till the meridian cuts the 
 equinoctial in the degree of right ascension. 
 Z SQ'i 
 
178 DESCRIPTION AND USE 
 
 Thus for example, suppose the right ascension 
 of Aldebaran to be 65" 30', and it*s declination 
 to be 16" north, then turn the globe about till 
 the meridian cuts the equinoctial in 65" 30', 
 and under the 16" of the meridian, on the nor- 
 thern part, you will observe the star Aldebaran, 
 or the bull's eye. 
 
 PROBLEM XV. 
 
 To find at what hour any known star passes the 
 7neridian, at any given day. 
 
 Find the sun's place for that day in the 
 ecliptic, and bring it to the strong brass meri- 
 dian, set the horary index to XII o'clock, then 
 turn the globe till the star comes to the meri- 
 dian, and the index will mark the time. Thus 
 on the 15th of August, Lyra comes to the me- 
 ridian at 45 min. past VIII in the evening. On 
 the 14th of September the brightest of the 
 Pleiades will be on the meridian at IV in the 
 morning. 
 
 This problem is useful for directing when 
 to look for any star on the meridian, in order to 
 find the latitude of a place, to adjust a clock, 
 &c. 
 
 364 
 
OF THE GLOBES. 179 
 
 PROBLEM XVI. 
 
 To find on what day a given star will co?fie to the 
 7neridiani at any given hour. 
 
 Bring the given star to the meridian, and 
 set the index to the proposed hour ; then turn 
 the globe till the index points to XII at noon, 
 and observe the degree of the ecliptic then at 
 the meridian ; this is the sun's place, the day 
 ansu^ering to which may be found on the calen- 
 dar of the broad paper circle. 
 
 By knovi'ing whether the hour be in the morn- 
 ing or afternoon, it will be easy to perceive 
 which way to turn the globe, that the proper 
 XII may be pointed to ; the globe must be turn- 
 ed towards the west, if the given hour be in the 
 morning, towards the east if it be afternoon. 
 
 Thus Arcturus will be on the meridian at III 
 in the morning on March the 5th, and Cor Le- 
 onis at VIII in the evening on April the 21st. 
 
 PROBLEM XVII. 
 
 To represent the face of the heavens on the globe for 
 a given hoiir on any day of the year, and learn 
 to distinguish the visible fixed stars. 
 
 Rectify the globe to the given latitude of 
 the place and day of the month, setting it due 
 
180 DESCRIPTION AND USE 
 
 north and south by the needle ; then turn the 
 globe on it's axis till the index points to the given 
 hour of the night ; then all the upper hemis- 
 phere of the globe will represent the visible face 
 of the heavens for that time, by which it will 
 be easily seen what constellations and stars of 
 note are then above our horizon, and what po- 
 sition they have with respect to the points of the 
 compass. In this case, supposing the eye was 
 placed in the center of the globe, and holes were 
 pierced through the centers of the stars on it*s 
 surface, the eye would perceive through those 
 holes the various corresponding stars in the fir- 
 mament ; and hence it would be easy to know 
 the various constellations at sight, and to be 
 able to call all the stars by their names. 
 
 Observe some star that you know, as one of 
 the pointers in the Great Bear, or Sirius ; find 
 the same on the globe, and take notice of the 
 position of the contiguous stars in the same or 
 an adjoining constellation j direct your sight to 
 the heavens, and you will see those stars in the 
 same situation. Thus you may proceed from one 
 constellation to another, till you are acquainted 
 with most of the principal stars. 
 
 " For example : the situation of the stars at 
 London on the 9th of February, at 2 min. past 
 IX in the evening, is as follows. 
 
 " Sirius, or the Dog-star, is on the meridian, 
 366 
 
OF THE GLOBES. 181 
 
 it's altitude 22°: Procyon, or the little Dog-star, 
 16" towards the east, it's altitude 43 1 : about 24" 
 above this last, and something more towards 
 the east, are the twins. Castor and Pollux : S.6 5" 
 E. and 35° in height, is the bright star Regulus, 
 or Cor Leonis : exactly in the east and 22" high, 
 is the star Deneb Alased in the Lion's tail : 30" 
 from the east towards the north Arcturus is 
 about 3 above the horizon : directly over Arc- 
 turus, and 31" above the horizon, is Cor Caroli: 
 in the north-east are the stars in the extremity 
 of the Great Bear's tail, Aleath the first star in 
 the tail, and Dubhe the northernmost pointer in 
 the same constellation ; the altitude of the first 
 of these is 30^, that of the second 41", and that 
 of the third 56". 
 
 " Reckoning westward, we see the beauti- 
 ful constellation Orion ; the middle star of the 
 three in his belt, is S. 20" W. it's altitude 35" : 
 nine degrees below the belt, and a little more 
 to the west, is Rigel the bright star in his heel : 
 above his belt in a strait line drawn from Rigel 
 between the middle and most northward in his 
 belt, and 9" above it, is the bright star in his 
 shoulder : S. 49" W. and 45^ above the horizon, 
 is Aldebaran the southern eye of the Bull : a 
 little to the west of Aldebaran, are the Hyadcs : 
 the same altitude, and about S. 70" W, are the 
 Pleiades : in the W. by S. point is Capella in 
 Auriga, it's altitude 73" : in the north-west, and 
 367 
 
18*2 DESCRIPTION AND USE 
 
 about 42" high, is the constellation Cassiopeia : 
 and almost in the north, near the horizon, is the 
 constellation Cygnus,*'* 
 
 PROBLEM XVIII. 
 
 To trace the circles of the sphere in the starry fir- 
 mament, 
 
 I shall solve this problem for the time of the 
 autumnal equinox ; because that intersection of 
 the equator and ecliptic will be directly under the 
 depressed part of the meridian about midnight ; 
 and then the opposite intersection will be ele- 
 vated above the horizon ; and also because our 
 first meridian upon the terrestrial globe passing 
 through London, and the first point of Aries, 
 when both globes are rectified to the latitude of 
 London, and to the sun's place, and the first 
 point of Aries is brought under the graduated 
 side of each of their meridians, we shall have 
 the corresponding face of the heavens and the 
 earth represented, as they are with respect to 
 each other at that time, and the principal circles 
 of each sphere will correspond with each other. 
 
 The horizon is then distinguished, if we be- 
 gin from the north, and count westward, by the 
 following constellations ; the hounds and waist 
 of Bootes, the northern crown, the head of 
 
 * Braniiby's Use of the Globes. 
 368 
 
OF THE GLOBES. 183 
 
 Hercules, the shoulders of Serpentarius, and 
 Sobleski's shield; it passes a little below the feet 
 of Antinous, and through those of Capricorn, 
 through the Sculptor's frame, Eridanus, the star 
 Rigel in Orion's foot, the head of Monoceros, 
 the Crab, the head of the Little Lion, and low- 
 er part of the Great bear. 
 
 The meridian is then represented by the equi- 
 noctial colure, which passes through the star 
 marked > in the tail of the Little Bear, under 
 the north pole, the pole star, one of the stars in 
 the back of Cassiopeia's chair marked /j, the 
 head of Andromeda, the bright, star in the wing 
 of Pegasus marked y, and the extremity of the 
 tail of the whale. 
 
 That part of the equator which is then above 
 the horizon, is distinguisiied on the western side 
 by the northern part of Sobieski's shield, the 
 shoulder of Antinous, the head and vessel of 
 Aquarius, the belly of the western fish in Pisces; 
 it passes through the head of the Whale, and a 
 bright star marked "^^ in the corner of his mouth, 
 and thence through the star marked j in the 
 belt of Orion, at that time near the eastern side 
 of the horizon. 
 
 That half of the ecliptic which is then above 
 the horizon, if we begin from the western side, 
 presents to our view Capricornus, Aquarius, 
 Pisces, Aries, Taurus, Gemini, and a part of 
 the constellation Cancer. 
 369 
 
184 BESCRIPTION AND USE 
 
 The solstitial colure, from the western side, 
 passes through Cerberus, and the hand of Her- 
 cules, thence by the western side of the constel- 
 lation Lyra, and through the Dragon's head 
 and body, through the pole point under the 
 polar star, to the east of Auriga, through the 
 star marked -^ in the foot of Castor, and through 
 the hand and elbow of Orion. 
 
 The northern polar circle, from that part of 
 the meridian under the elevated pole, advancing 
 towards the west, passes through the shoulder 
 of the Great Bear, thence a little to the north 
 of the star marked « in the Dragon's tail, the 
 great knot of the dragon, the middle of the 
 body of Cepheus, the northern part of Cassiopeia, 
 and base of her throne, through Cameloparda- 
 lus, and the head of the Great Bear. 
 
 The tropic of Cancer, from the western 
 edge of the horizon, passes under the arm of 
 Hercules, under the Vulture, through the Goose 
 and Fox, which is under the beak and wing of 
 the Swan, under the star called Sheat, marked /3 
 in Pegasus, under the head of Andromeda, and 
 through the star marked <!> in the fish of the con- 
 stellation Pisces, above the bright star in the 
 head of the Ram marked *, through the Pleiades, 
 between the horns of the Bull, and through a 
 group of stars at the foot of Castor, thence 
 above a star marked j, between Castor and Pol- 
 lux, and so through a part of the constellation 
 370 
 
OF THE GLOBES. 185 
 
 Cancer, where it disappears by passing under the 
 eastern part of the horizon. 
 
 The tropic of Capricorn, from the western 
 side of the horizon, passes through the belly, and 
 under the tail of Capricorn, thence under Aqua- 
 rius, through a star in Eridanus marked c, thence 
 under the belly of the Whale, through the base 
 of the chemical Furnace, whence it goes under 
 the Hare at the feet of Orion, being there depres- 
 sed under the horizon. 
 
 The southern polar circle is invisible to the 
 inhabitants of London, by being under our ho- 
 rizon. 
 
 Arctic and antarctic circles, br circles of perpetual 
 apparition and occultation. 
 
 The largest parallel of latitude on the terres- 
 trial globe, as well as the largest circle of decli- 
 nation on the celestial, that appears entire above 
 the horizon of any place in north latitude, was 
 called by the ancients the arctic circle, or circle 
 of perpetual apparition. 
 
 Between the arctic circle and the north pole 
 in the celestial sphere, are contained all those 
 stars which never set at that place, and seem to 
 us, by the rotative motion of the earth, to be 
 perpetually carried round above our horizon, 
 the circles parallel to the equator. 
 
 The largest parallel of latitude on the ter- 
 A a 371 
 
186 DESCRIPTION AND- USE 
 
 restrial, and the largest parallel of declination 
 on the celestial globe, which is entirely hid be- 
 low the horizon of any place, was by the an- 
 cients called the antarctic circle, or circle of 
 perpetual occultation. 
 
 This circle includes all the stars which never 
 rise in that place to an inhabitant of the nor- 
 thern hemisphere, but are perpetually below the 
 horizon. 
 
 All arctic circles touch their horizons in the 
 north point, and all antarctic circles touch their 
 horizons in the south point ; which point, in the 
 terrestrial and celestial spheres, is the intersec- 
 tion of the meridian and horizon. 
 
 If the elevation of the pole be 45 degrees, 
 the most elevated part either of the arctic or 
 antarctic circle will be in the zenith of the 
 place. 
 
 If the pole's elevation be less than 45 de- 
 grees, the zenith point of those places will fall 
 without it's arctic or antarctic circle j if greater, 
 it will fall within. 
 
 Therefore, the nearer any place is to the 
 equator, the less will it's arctic and antarctic 
 circles be ; and on the contrary, the farther any 
 place is from the equator, the greater they are. 
 So that. 
 
 At the poles, the equator may be consi- 
 dered as both an arctic and antarctic circle, 
 372 
 
OF THE GLOBES, 187 
 
 because it's plane is coincident with that of the 
 horizon. 
 
 But at the equator (that is, in a right sphere) 
 there is neither arctic nor antarctic circle. 
 
 They who live under the northern polar cir- 
 cle, have the tropic of Cancer for their arc- 
 tic, and that of Capricorn for their antarctic 
 circle. 
 
 And they who live on either tropic, have one 
 of the polar circles for their arctic, and the other 
 for their antarctic circle. 
 
 Hence, whether these circles fall within or 
 without the tropics, their distance from the ze- 
 nith of any place is ever equal to the difference 
 between the pole's elevation, and that of the 
 equator, above the horizon of that place. 
 
 From what has been said, it is plain there 
 may be as many arctic and "antarctic circles, as 
 there are individual points upon any one meri- 
 dian, between the north and south poles of the 
 earth. 
 
 Many authors liave mistaken these mutable 
 circles, and have given their names to the im- 
 mutable polar circles, which last are arctic and 
 antarctic circles, in one particular case only, as 
 has been shewn. 
 
 373 
 
188 DESCRIPTION AND USE 
 
 PROBLEM XIX. 
 
 To find the circle^ or parallel of perpetual appa- 
 rition^ or occulation of a fixed star, in a given 
 latitude. 
 
 By rectifying the globe to the latitude of the 
 place, and turning it round on it*s axis, it will 
 be immediately evident, that the circle of perpe- 
 tual apparition is that parallel of declination 
 which is equal to the complement of the given 
 latitude northward ; and for the perpetual oc- 
 cultation, it is the same parallel southward j that 
 is to say, in other words, all those stars, whose 
 declinations exceed the co-latitude, will always 
 be visible, or above the horizon ; and all those 
 in the opposite hemisphere, whose declination 
 exceeds the co-latitude, never rise above the 
 horizon. 
 
 For instance ; in the latitude of London 51 
 deg. 30 min. whose co-latitude is 3S 6.eg, 30 
 min. gives the parallels desired ; for all those 
 stars which are within the circle, towards the 
 north pole, never descend below our horizon ; 
 and all those stars which are within the same 
 circle, about the south pole, can never be seen 
 in the latitude of London, as they never ascend 
 above it's horizon. 
 
 374 
 
OF THE GLOBBS. 189 
 
 OF PROBLEMS RELATING TO THE AZIMUTH, S;C. 
 OF THE SUN AND STARS. 
 
 PROBLEM XX. 
 
 '6 
 
 The latitude of the place and the sun^s place bein 
 given, to find the sun*s amplitude. 
 
 That degree frofn east or west in the horizon, 
 •wherein any object rises or sets, is called the am- 
 plitude. 
 
 Rectify the globe, and bring the sun*s place 
 to the eastern side of the meridian, and the arch 
 of the horizon intercepted between that point 
 and the eastern point, will be the sun*s ampli- 
 tude at rising. 
 
 If the same point be brought to the western 
 side of the horizon, the arch of the horizon in- 
 tercepted between that point and the western 
 point, will be the sun*s amplitude at setting. 
 
 Thus on the 24th of May the sun rises at 
 four, with 36 degrees of eastern amplitude, that 
 is, 36 degrees from the east towards the north, 
 and sets at eight, with 36 degrees of western am- 
 plitude. 
 
 The amplitude of the sun at rising and set- 
 
 ting increases with the latitude of the place : 
 
 and in very high northern latitudes, the sun 
 
 scarce sets before^ he rises again. Homer had 
 
 375 
 
190 DESCRIPTION AND USIi 
 
 heard something of this, though it is not true of 
 the Lasstrygones, to whom he appUes it. 
 
 Six days and nights a doubtful course we steer; 
 The next, proud Lamos' lofty towers appear, 
 And Lacstygonia's gates arise distinct in air. 
 The shepherd quitthig here at night the plain, 
 Calls, to succeed his cares, the watchful swain. 
 But he that scorns the chains of sleep to wear, 
 And adds the herdsman's to the shepherd's care. 
 So near the pastures, and so short the way, 
 His double toils may claim a double pay, 
 And join the labours of the ngiht and day. 
 
 PROBLEM XXI. 
 
 } 
 
 •} 
 
 To find the sun^s altitude at any given time of the 
 day. 
 
 Set the center of the artificial sun to his 
 place in the ecliptic upon the globe, and rec- 
 tify it to the latitude and zenith ; bring the cen- 
 ter of the artificial sun under the strong brass 
 meridian, and set the hour index to that XII 
 which is most elevated ; turn the globe to the 
 given hour, and move the graduated edge of the 
 quadrant to the center of the artificial sun ; and 
 that degree on the quadrant, which is cut by the 
 sun's center, is the sun*s height at that time. 
 
 The artificial sun being brought under the 
 strong brass meridian, and the quadrant laid 
 376 
 
or THE GLOBES. 191 
 
 upon it's center, will she%u ifs jneridian, or great- 
 est altitude, for that day. 
 
 If the sun be in the equator, his greatest or 
 meridian altitude is equal to the elevation of 
 the equator, which is always equal to the co-la- 
 titude of the place. 
 
 Thus on the 24th of May, at nine o*clock, 
 the sun has 44 deg. altitude, and at six in the 
 afternoon 20 deg. 
 
 OF THE AZIMUTHAL OR VERTICAL CIRCLES. 
 
 The vertical point, that is, the uppermost 
 point of the celestial globe, represents a point 
 in the heavens;, directly over our heads, which 
 is called our zenith. 
 
 From this point circular lines may be con- 
 ceived crossing the horizon at right angles. 
 
 These are called az'unuthy or 'vertical circles. 
 That one which crosses the horizon at 10 deg. 
 distance from the meridian on either side, is 
 called an azimuth circle of 10 deg. ; that 
 which crosses at 20, is. called an azimuth of 
 20 deg. 
 
 The azimuth of 90 deg. is called the pritne 
 vertical : it crosses the horizon at the eastern 
 and western points. 
 
 Any azimuth circle may be represented by 
 the graduated e^ge. of the brass quadrant of 
 377 
 
192 DESCRIPTION AND USE 
 
 altitude, when the center upon which it turns 
 is screwed to that point of the strong brass me- 
 ridian which answers to the latitude of the 
 place, and the place is brought into the zenith. 
 
 If the said graduated edge should lie over 
 the sun's center or place, at any given time, 
 it will represent the sun's azimuth at that 
 time. 
 
 If the graduated edge be fixed at any point, 
 so as to represent any particular azimuth, and 
 the sun's place be brought there, the horary in- 
 dex will shew at what time of that day the sun 
 will be in that particular azimuth. 
 
 Here it may be observed, that the amplitude 
 and azimuth are much the same. 
 
 The amplitude shewing the bearing of any ob- 
 ject ijuhen it rises or iets, from the east and west 
 points of the horizon. 
 
 The azimuth the bearing of any object when 
 it is above the horizon, either from xh^ north or 
 south points thereof. These descriptions and 
 illustrations being understood, we may proceed 
 to 
 
 378 
 
OF THE GLOBES. 198 
 
 PROBLEM XXII. 
 
 To find at what time the sun is due east, the day 
 and the latitude being given. 
 
 Rectify the globe ; then if the latitude and 
 declination are of one kind, bring the quadrant 
 of altitude to the eastern point of the horizon, 
 and the sun's place to the edge of the quadrant, 
 and the index will shew the hour. 
 
 If the latitude and declination are of different 
 kinds, bring the quadrant to the western point 
 of the horizon, and the point in the ecliptic op- 
 posite to the sun's place to the edge of the quad- 
 rant, and then the index will shew the hour. 
 
 You will easily comprehend the reason of the 
 foregoing distinction, because when the sun is in 
 the equinoctial, it rises due east ; but when it is in 
 that part of the ecliptic which is towards the ele- 
 vated pole, it rises before it is in the eastern verti- 
 cal circle, and is therefore at that time above the 
 horizon: whereas when it is in the other part of 
 the ecliptic, it passes the eastern prime vertical 
 before it rises, that is behiv the horizon; whence 
 it is evident, that the opposite point of the ecliptic 
 must then be in the west, and above the horizon. 
 The sun is due east at Loudon at 7 h. C min. on 
 Bb 379 
 
194< DESCRIPTION AND USE 
 
 the 18th of May. The second of August, at 
 Cape Horn, the sun is due east at 5 h. 10 min. 
 
 PROBLEM XXIII. 
 
 To find the rising, setting, and culminating of a 
 star, it's continuance above the horizon, and it's 
 oblique ascension and descension, and also it's 
 eastern and western amplitude, for any given day 
 and place, 
 
 1. Rectify the globe to the latitude and ze- 
 nith, bring the sun's place for the day to the 
 meridian, and set the hour index to XII. 2. Bring 
 the star to the eastern side of the horizon, and 
 it*s eastern amplitude, oblique ascension, and 
 time of rising, will be found as taught of the 
 sun. 3. Carry the star to the western side of 
 the horizon ; and in the same manner it's west- 
 cm amplitude, oblique descension, and time of 
 setting, will be found. 4. The time of rising, 
 subtracted from that of setting, leaves the con- 
 tinuance of the star above the horizon. 5. This 
 remainder, subtracted from 24 hours, gives the 
 time of it's continuance below the horizon. 
 6. The hour to which the index points, when 
 the star comes to the meridian, is the time of it's 
 culminating or being on the meridian. 
 
 Let the given day be March 14, the place 
 380 
 
OF THE GLOBES. 193 
 
 London, the star Sirius j by working the prob- 
 lem, you will find 
 
 It rises at - - 2 h. 24 min. afternoon. 
 Culminates - - 6 57 
 Sets at - - 11 5a 
 
 Is above the horizon 9 6 
 
 It*s oblique ascension and descension are 1 20" 
 47', and 77" 15', it's amplitude 27% southward. 
 
 PROBLEM XXIV. 
 
 The latitude, the altitude of the sun by day, or of 
 a STAR by night, being given, to find the hour of 
 the day, and the sun*s or starts azimuth. 
 
 Rectify the globe for the latitude, the zenith, 
 and the sun's place, turn the globe and the quad- 
 rant of altitude, so that the sun's place, or the 
 given star, may cut the given degree of altitude, 
 the index will shew the hour, and the quadrant 
 will be the azimuth in the horizon. 
 
 Thus on the 2 1 st of August, at London, when 
 the sun's altitude is 36* in the forenoon, the hour 
 is IX, and the azimuth 58" from the south. 
 
 At Boston, December 8th, when Rigel had 15 
 of altitude, the hour was VIII, the azimuth S. E. 
 by,E. 7^ 
 
 381 
 
196 DESCRIPTION AND USE 
 
 PROBLEM XXV. 
 
 The latitude and hour of the day being given^ to 
 find the altitude and azimuth of the sun, or of 
 a star. 
 
 Rectify the globe for the latitude, the zenith, 
 and the sun's place, then the number of degrees 
 contained betwixt the sun's place and the vertex 
 is the sun's meridional zenith distance ; the 
 complement of which to 90 deg. is the sun's 
 meridian altitude. If you turn the globe 
 about until the index points to any other given 
 hour, then bringing the quadrant of altitude to 
 cut the sun's place, you will have the sun's alti- 
 tude at that hour ; and where the quadrant cuts 
 the horizon, is the sun's azimuth at the same 
 time. Thus May the 1st, at London, the sun's 
 meridian altitude will be 53| deg. ; and at 10 
 o'clock in the morning, the sun's altitude will be 
 46 deg. and his azimuth about 44 deg. from the 
 south part of the meridian. On the 2d of De- 
 cember, at Rome, at five in the morning, the 
 altitude of Capella is 41 deg. 58 min. its azi- 
 muth 60 deg. 50 min. from N. to W. 
 382 
 
\ 
 
 OF THE GLOBES. 197 
 
 PROBLEM XXVI. 
 
 The latitude of the place^ and the day of the month 
 being given, to find the depression of the sun below 
 the horizon, and the azimuth^ at any hour of the 
 night. 
 
 Having rectified the globe for the latitude, 
 the zenith, and the sun's place, take a point in 
 the ecliptic exactly opposite to the sun*s place, 
 and find the sun's altitude and azimuth, as by 
 the last problem, and these will be the depres- 
 sion and the altitude required. 
 
 Thus if the time given be the 1st of Novem- 
 ber, at 10 o'clock at night, the depression and 
 azimuth will be the same as was found in the 
 last problem. 
 
 PROBLEM XXVII. 
 
 The latitude, the sun^s place, and his azimuth being 
 given, to find his altitude, and the hour. 
 
 Rectify the globe for the latitude, the zenith, 
 and the sun's place ; then put the quadrant of 
 altitude to the sun's azimuth in the horizon, and 
 turn the globe till the sun's place meets the edge 
 of the quadrant ; then the said edge will shew 
 the altitude, and the index point to the hour. 
 
 Thus, May 21st, at London, when the sun 
 383 
 
198 * DESCRIPTION AND USE 
 
 is due east, his altitude will be about 24 deg. 
 and the hour about VII in the morning ; and 
 when his azimuth is 60 degrees south-westerly, 
 the altitude will be about 44} degrees, and the 
 hour 11 ~ in the afternoon. 
 
 Thus the latitude and the day being known, 
 and having besides either the altitude, the azi- 
 muth, or the hour, the other two may be easily 
 found, 
 
 PROBLEM XXVIII. 
 
 The latitude of the place, and the azimuth of the 
 sun or of a star being given, to find the hour of 
 the day or night. 
 
 Rectify the globe foir the latitude and sun's 
 place, and bring the quadrant of altitude to the 
 given azimuth in the horizon ; turn the globe 
 till the sun or star comes to the quadrant, and 
 the index will shew the time. November 5, at 
 Gibraltar, given the sun's azimuth 50 degrees 
 from the south towards the east, the time you 
 will find to be half past VIII in the morning. 
 Given the azimuth of Vega at London, 57 deg. 
 from the north towards the east, February the 
 8th, the time you will find twenty minutes past 
 II in the morning. 
 
 But as it may possibly happen that we may 
 see a star, and would be glad to know what star 
 it is, or whether it may not be a new star, or a 
 384 
 
OF THE GLOBES. 199 
 
 comet ; how that may be discovered, -will be seen 
 under the following 
 
 PROBLEM XXIX. 
 
 The latitude of the place^ the sun^s place, the hour 
 of the night, and the altitude a?id azimuth of 
 any star being given, to find the star. 
 
 Rectifying the globe for the latitude of the place, 
 and the sun's place ; fix the quadrant of altitude in 
 the zenith, and turn the globe till the hour index 
 points to the given hour, and set the quadrant of 
 altitude to the given azimuth ; then the star that 
 cuts the quadrant in the given altitude, will be 
 the star sought. 
 
 Though two stars, that have different right 
 ascensions, will not come to the meridian at the 
 same time, yet it is possible that m a certain lati- 
 tude they may come to the same vertical circle at 
 the same time j and that consideration gives the 
 following 
 
 PROBLEM XXX. 
 
 The latitude of the place, the sun^s place, and, tivo 
 stars, that have the same azimuth, being given, 
 to find the hour of the night. 
 
 Rectify the globe for the latitude, the ze- 
 nith, and the sun's place ; then turn the globe, 
 385 
 
200 DESCRIPTION AND USE 
 
 t 
 
 and also the quadrant about, till both the stars 
 coincide with it's edge ; the hour index will 
 shew the hour of the night, and the place where 
 the quadrant cuts the horizon will be the com- 
 mon azimuth of both stars. 
 
 On the 15th of March, at London, the star 
 Betelgeuje, in the shoulder of Orion, and Regel, 
 in the heel of Orion, were observed to have the 
 same azimuth ; on working the problem, you 
 will find the time to be 8 hours 47 minutes. 
 
 What hath been observed above, of two stars 
 that have the same azimuth, will hold good like- 
 wise of two stars that have the same altitude j 
 from whence we have the following 
 
 PROBLEM XXXI, 
 
 The latitude of the place ^ the sun's place, and two 
 stars, that have the same altitude, being given, 
 to find the hour of the night » 
 
 Rectify ^the globe for the latitude of the place, 
 the zenith, and the sun's place ; turn the globe, 
 so that the same degree on the quadrant shall 
 cut both the stars, then the hour index will shew 
 the hour of the night. 
 
 In the former propositions, the latitude of 
 the place is supposed to be given, or known ; 
 but as it is frequently necessary to find the lati- 
 tude of the place, especially at sea, how this 
 may be found, in a rude manner at least, hav- 
 386 
 
QF THE GLOBES. 201 
 
 ing the time given by a good clock, or watch, 
 will be seen in the following. 
 
 PROBLEM XXXII. 
 
 The suns's place, the hour of the flight, and l-icc 
 stars, that have the same azimuth, or altitude^ 
 being given, to find the latitude of the place. 
 
 Rectify the globe for the sun*s place, and 
 turn it till the index points to the given hour of 
 the night ; keep the globe from turning, and 
 move it up and down in the notches, till the two 
 given stars have the same azimuth, or altitude ; 
 then the brass meridian will shew the height of 
 the pole, and consequently the latitude of the 
 place. 
 
 PROBLEM XXXII. 
 
 Two stars being given, one on the 7neridian, and 
 the fther on the east and west part of the horizon, 
 to find the latitude of the place. 
 
 Bring the star observed on the meridian to the 
 meridian of the globe ; then keeping the globe 
 from turning round it's axis, slide the meridian 
 up or down in the notches, till the other star is 
 brought to the east or west part of the horizon, 
 and that elevation of the pole will be the lati- 
 tude of the place sought. 
 
 C c 387 
 
202 DESCRIPTION AND US£ 
 
 OBSERVATION. 
 
 From what hath been said, it appears, that 
 of these five things, 1. the latitude of the place; 
 2. the sun's place in the ecliptic ; 3. the hour of 
 the night; 4. the common azimuth of two known 
 fixed stars ; 5. the equal altitude of two known 
 fixed stars ; any three of them being given, the 
 remaining tivo will easily be found. 
 
 There are three sorts of risings and settings 
 of the fixed stars, taken notice of by ancient 
 authors, and commonly called poetial risi?igs and 
 settings, because mostly taken notice of by the 
 poets. 
 
 These are the cosmical, achronical, and helia- 
 cal.* 
 
 They are to be found in most authors that treat 
 on the doctrine of the sphere, and are now chief- 
 ly useful in comparing and understanding pas- 
 sages in the ancient writers; such are Hesiod, Vir- 
 gil, Columella, Ovid, Pliny, &c. How they are to 
 be found by calculation, may be seen in Petavi- 
 us's Uranologion, and Dr. Gregory's Astronomy. ^ 
 
 DKFINITION. 
 
 When a star rises or sets at sun-rising, it is said 
 to rise or set cosmically. 
 
 From whence we shall have the following 
 
 * Costard's History of Astronomj . 
 388 
 
OF THE GLOBES. 20^ 
 
 PROBLEM XXXIV, 
 
 The latitude of the place being given ^ to Jind, by 
 the globe, the time of the year when a given star 
 rises or sets costnically. 
 
 Let the given place be Rome, whose lati- 
 tude is 42 deg. 8 mill, north ; and let the given 
 star be the Lucida Pleiadum. Rectify the globe 
 for the latitude of the place ; bring the star to 
 the edge of the eastern horizon, and mark the 
 point of the ecliptic rising along with it ; that 
 will be found to be Taurus, 18 deg. opposite to 
 which, on the horizon, will be found May the 
 8th. The Lucida Pleiadum, therefore, rises cos- 
 mically May the 8th. 
 
 If the globe continues rectified as before, and 
 the Lucida Pleiadum be brought to the edge of 
 the western horizon, the point of the ecliptic, 
 which is the sun*s place, then rising on the 
 eastern side of the horizon, will be Scorpio, 29 
 deg. opposite to which, on the horizon, will be 
 found November the 2 1 st. The Lucida Pleia- 
 dum, therefore, sets cosmically November the 
 21st. 
 
 In the same manner, in the latitude of Lon- 
 don, Sirius will be found to rise cosmically Au- 
 gust the 10th, and to set cosmically November 
 the loth. 
 
 It is of the cosmical setting of the Pleiades, 
 389 
 
204^ ^DESCRIPTION AND USE 
 
 that Virgil is to be understood in this line, 
 
 and not of their setting in the east, as some have 
 imaginedj where stars rise, but never set, 
 
 DEFINITION. 
 
 When a star rises or sets at sun-setting, it is said 
 fo f-ise or set achronically. 
 
 Hence, likewisej we have the following 
 
 PROBLEM. XXXV. 
 
 The latitude of the place being given-, to find the 
 
 iwie of the year when a given star will rise or 
 
 set achronically. 
 
 Let the given place be Athens, whose lati- 
 tude is 37 deg. north, and let the given star be 
 Arcturus. 
 
 Rectify the globe for the latitude of the place, 
 ^id bringing Arcturus to the eastern side of the 
 horizon, mark the point of the ecliptic then set- 
 tirig on the w^estern side ; that will be found 
 ArieSj 12 deg. opposite to which^ on the horizon, 
 will be found April the 2d. Therefore Arctu- 
 rus rises at Athens achronically April the 2d. 
 
 It is of this rising of Arcturus that Hesiod 
 speaks in his Opera and Dies.f 
 
 Vv htn iVoin th6 soisiice sixty wint'ry dnyS 
 
 Their turns have finish'd, mark, with glitt'ring rays, 
 
 From ocean's sacred flood, jircturus rise. 
 
 Then first to gilcl ihe dusky evening skies. 
 
 * Georg, 1. 1. V. 221. t Lib. ii. ver. 285. 
 596 
 
OF THE GLOBES. 20J 
 
 11 the globe continues rectified to the latitude 
 of the place, as before, and Arcturus be brought 
 to the western side of the horizon, the point of 
 the ecliptic setting along with it will be Sagitta- 
 ry, 7 deg. opposite to which, on the horizon, 
 will be found November the l^Oth. At Athens, 
 therefore, Arcturus sets achronically November 
 the 29th. 
 
 In the same manner Aldebaran, or the Bull's 
 eye, will be found to rise achronically May the, 
 22d, and to set achronically Decem6er the 
 19th. 
 
 DEFINITION'. 
 
 Wheti a star first becomes 'disihle in a jnorning, 
 after it hath been so near the sun as to be hid 
 by the splendor of his rays, it is said to rise 
 
 HELIACALLY. 
 
 But for this there is required some certain 
 depression of the sun below the horizon, more 
 or less according to the magnitude of the staM» 
 A star of the first magnitude is commonly sup- 
 posed to require that the sun be depressed 12 
 deg. perpendicularly below the horizon. 
 
 This being premised, we have the follow-' 
 ing 
 
 B91 
 
1!06 DESCRIPTION AND US£ 
 
 PROBLEM XXXVI. 
 
 I be latitude of the place being give?i, to find the 
 time of the year when a given star ivill rise 
 heliacally. 
 
 Let the given place be Rome, whose latitude 
 is 42 dug. north, and let the given star be the 
 bright star in the Bull's horn. 
 
 Rectify the globe for the latitude of the 
 place, screw on the brass quadrant of altitude 
 in it*s zenith, and turn it to the western side of 
 the horizon. • Bring the star to the eastern side 
 
 O 
 
 of the horizon, and mark what degree of the 
 ecliptic is cut by 1 2 deg. marked on the quad- 
 rant of altitude ; that will be found to be Ca- 
 pricorn, 3 deg. the point opposite to which is 
 Cancer, 3 deg. and opposite to this will be found 
 on the horizon, June 25th. The bright star, 
 therefore, in the Bull's horn, in the latitude of 
 ^ome, rises heliacally June the 25th. 
 
 These kinds of risings and settings are not 
 only mentioned by the poets, but likewise by 
 the ancient physicians and historians. 
 
 Thus Hippocrates, in his book De .Tre, says 
 *' One ought to observe the heliacal risings and 
 settings of the stars, especially the Dog-star, and 
 Arcturiis ; likev/ise the cos?nical setting of the 
 Pidadesr 
 
 /\nd Polybius, speaking of the loss of the 
 392 
 
OF THE GLOBES. S^O? 
 
 Roman fleet, in the first Punic war, says, " It 
 was not so much owmg to fortune, as to the 
 obstinacy of the consuls, in not hearkening to 
 their pilots, who dissuaded them from putting^ 
 to sea, at that season of the year, which was 
 between the rising of Orioi and the Dog-star ; 
 it being always dangerous, and subject to 
 storms."*' 
 
 DEFINiriON'. 
 
 When a star is first immersed in the evening, or 
 bid by the sun's rays, it is said to set helia- 
 
 CALLY. 
 
 And this again is said to be, when a star of 
 the first magnitude comes within twelve degrees 
 of the sun, reckoned in the perpendicular. 
 
 Hence again we have the following 
 
 PROBLEM XXXVII. 
 
 The latitude of the place being given, to find the 
 time of the year when a given star sets helia- 
 cally. 
 
 Let the given place be Rome, in latitude 
 42 deg. north, and let the given star be the 
 bright star in the Bull's horn. Rectify the globe 
 for the latitude of the place, and bring the star 
 
 * Lib. i. p. 55. 
 393 
 
208 DESCRIPTION AND USE 
 
 (0 the edge of the western horizon ; turn the 
 quadrant of altitude, till 12 deg. cut the ecliptic 
 on the eastern side of tht meridian. This will be 
 found to be 7 deg. of Sagittary, the point oppo- 
 site to which, in the ecliptic, is 7 deg. of Ge- 
 mini ; and opposite to that, on the horizon, is 
 May the 28th, the time of the year when that 
 sets heliacally in the latitude of Rome. 
 
 OI^ THE COnRESPONDKXCE OF IHE CKLESTIAI. AN'D 
 TEUHESTKIAI. SPHEUES. 
 
 That the reader may thoroughly understand 
 what is meant by the correspondence between 
 the two spheres, let him imagine the celestial 
 globe to be delineated upon glass, or any othei 
 transparent matter, which shall invest or sur- 
 round the terrestrial globe, but in such a man- 
 ner, that either may be turned about upon the 
 poles of the globe, while the other remains 
 fixed ; and suppose the first point of Aries, on 
 the investing globe, to be placed on the first 
 point of Aries on the terrestrial globe, (which 
 point is in the meridian of London) then every 
 star in the celestial sphere will be directly over 
 those places to which it is a correspondent. 
 Each star will then have the degree of it's right 
 ascension directly upon the corresponding de- 
 gree of terrestrial longitude j their declination 
 394 
 
OF THE GLOBES. 209 
 
 will also be the same with the latitude of the 
 places to which they answer; or, in other words, 
 when the declination of a star is equal to the 
 latitude of a place, such star, within the space of 
 24 hours, will pass vertically over that place and 
 all others that have the same latitude. 
 
 If we conceive the celestial investing globe to 
 to be fixed, and the terrestrial globe to be gradu- 
 ally turned from west to east, it is clear, that as 
 the meridian of London passes -from one degree 
 to another under the investing sphere, every star 
 in the celestial sphere becomes correspondent to 
 another place upon the earth, and so on, until 
 the earth has completed one diurnal revolution ; 
 or till all the stars, by their apparent daily mo- 
 tion, have passed over every meridian of the 
 terrestrial globe. From this view of the subject, 
 an amazing variety, uniting in wonderful and 
 astonishing harmony, presents itself to the atten- 
 tive reader ; and future ages will find it difficult 
 to investigate the reasons that should induce the 
 present race of astronomers to neglect a subject 
 so highly interesting to science, even in a practi- 
 cal view, but which in theory would lead them 
 into more sublime speculations, than any that 
 ever yet presented themselves to their minds. 
 Dd 395 
 
210 DESCRIPTION AND L'SE 
 
 A GENERAL iJESCRIl'TIOK OF ThI-: PASSACfi OF TBt 
 STAK MARKED 7 IN TUK HEAD OF THE CONSTEL- 
 I^ATIOM PRACO, OVER THE PARALLEL OF LONDON. 
 
 The star 7, in the head of the constellation 
 Draco, having 51 deg. 32 min. north declina- 
 tion, equal to the latitude of London, is the cor- 
 respondent star- thereto. To find the places 
 which it passes over, bring London to the gradu- 
 ated side of the brass meridian, and you will find 
 that the degree of the meridian over London, and 
 the representative of the star, passes over from 
 London, the road to Bristol, crosses the Severn, 
 the Bristol channel, the counties of Cork and 
 Kerry in Ireland, the north part of the Atlantic 
 ocean, the streights of Belleisle, New Britain, the 
 north part of the province of Canada, New South 
 Wales, the southern part of Kamschatka, thence 
 over different Tartarian nations, several provinces 
 of Russia, over Poland, part of Germany, the 
 southern part of the United Provinces, when, 
 crossing the sea, it arrives again at the meridian 
 of London. 
 
 When the said star, or any other star, is on 
 the meridian of London, or any other meri- 
 dian, all other stars, according to their declina- 
 tion and right ascension, and difference of right 
 ascension, (which answers to terrestrial latitude, 
 (i96 - 
 
OF THE GLOBES. 211 
 
 longitude, and difference of longitude) will at the 
 same time be on such meridians, and vertical to 
 such places as correspond in latitude, longitude, 
 and difference of longitude, with the declination, 
 S:c. of the respective stars.* 
 
 Fronj the stars, therefore, thus considered, we 
 attain a copious field of geographical knowledge, 
 and may gain a clear idea of the proportionable 
 distances and real bearings, of remote empires, 
 kingdoms, and provinces, from our own zenith, at 
 the same instant of time ; which may be found in 
 the same manner as we found the place to which 
 the sun was vertical at any proposed time. 
 
 Many instances of this mode of attaining geo- 
 graphical knowledge, may be found in my 
 father's treatise on the globes. 
 
 oy THE USE OF THE -CELESTIAL GLOilE, I.V PKOBLETtfS 
 RELATIVE TO THE PLANETS, 
 
 The situation of the fixed stars being always 
 the same with respect to one another, they have 
 their proper places assigned to them on the 
 globe. 
 
 But to the planets no certain place can be as- 
 signed, their situation always varying. 
 
 ■'* Fairraan's Geography. 
 897 
 
212 DESCRIPTION AND USE 
 
 That space In the heavens, within the compass 
 of which the planets appear, is called the zodiac. 
 
 The latitude of the planets scarce ever ex- 
 ceeding 8 degrees, the zodiac is said to reach 
 about 8 degrees on each side the ecliptic. 
 
 Upon the celestial globe, on each side of the 
 ecliptic, are drawn eight parallel circles, at the 
 distance of one degree from each, other, includ- 
 ing a space of 16 degrees; these are crossed at 
 right angles, with segments of great circles at 
 every 5th degree of the ecliptic ; by these, the 
 place of a planet on the globe, on any given day, 
 may be ascertained with accuracy. 
 
 PROBLEM XXXVm. 
 
 To find the place of any planet upon the globe., and 
 
 ■ by that means to find it's place in the heavens : 
 
 also, to find at what hour any planet will rise or 
 
 set, or be on the tneridia?!, on any day in the 
 
 year. 
 
 Rectify the globe to the latitude and sun's 
 place, then place the planet's longitude and lati- 
 tude in an ephemeris, and set the graduated 
 edge of the .moveable meridian to the given 
 longitude in the ecliptic, and counting so ma- 
 ny degrees amongst the parallels in the zodiac, 
 either above or below the ecliptic, as her lati- 
 tude is north or south ; and set the center of the 
 398 
 
OF THE GLOBES- 213 
 
 artificial sun to that point, and the centre will 
 represent the place of the planet for that time. 
 
 Or fix the quadrant of altitude over the pole 
 of the ecliptic, and holding the globe fast, bring 
 the edge ot the quadrant to cut the given degree 
 of longitude on the ecliptic ; then seek the given 
 latitude on the quadrant, and the place under it 
 is the point sought. 
 
 While the globe moves about it's axis, this 
 point moving along with it will represent the 
 planet's motion in the heavens. If the planet 
 be brought to the eastern side of the horizon, the 
 horary index will shew the time of it*s rising. 
 If the artificial sun is above the horizon, the 
 planet will not be visible : when the planet is 
 under the strong brazen meridian, the hour 
 index shews the time it will be on that circle in 
 the heavens : when it is at the western edge, the 
 time of it's setting will be obtained. 
 
 PROBLEM XXXIX. 
 
 To find directly the -planets which arc above the 
 horizon at sufi-set, upon any given day and lati' 
 tude, ^ 
 
 Find the sun's place for the given day, 
 bring it to the meridian, set the hour index to 
 XII, and elevate the pole for the given lati- 
 tude : then bring the place of the sun to the 
 western semicircle of the horizon, and observe, 
 399 
 
214^ DtSCRIPTIGN AND USIL 
 
 what signs are in that part of the ecliptic abov.c; 
 the horizon, then cast your eye upon the ephe- 
 meris for. that month, and you will at once see 
 ■what planets possess any of those elevated signs ; 
 for such will be visible, and fit for observation 
 on the night of that day. 
 
 PROBLEM XL: 
 
 "To find the right ascension^ declination, amplitude, 
 azimuth, altitude, hour of the night, Isfc. of any 
 given planet, for a day of a nionth and latiiu(k 
 
 '^'aZ Mil '/ .:ji' 
 
 given. 
 
 Rectify the globe for the given latitude and 
 day of the month ; then find the planet's place, 
 as before directed, and then the right ascension, 
 declination, amplitude, azimuth, altitude, hour, 
 &c. are all found, as directed in the problems 
 for the sun ; there being no difference in the 
 process, no repetition can be necessary. 
 
 «F THE USE OF THE CELESTIAL GLOIJK, IN PKOBLEMS 
 RELATIVE TO THE MOON. 
 
 , From the sun and planets we now proceed 
 to those problems that concern the moon, the 
 brilliant sateUite of our earth, which every 
 ynonth enriches it with it's presence ; by the 
 mildness of it's light softening the darkness of 
 400 
 
QF THE GLOBES. 21.5 
 
 night ; by it*s influence affecting the tide ; and 
 by the variety of it's aspects, offering to ouv 
 view some very remarkable phenomena. 
 
 " Soon as the cv'ning; shades prevail, 
 The moon takes i;]5 the Avond'roiis talc ; 
 And ni;j;htlj' to the list'ning canh, 
 Repeats the story of her birth : 
 Whilst all tlic stars that rovmd her biMiu 
 And all the planets in Llicir turn, 
 ("onfirm the tidiiiijs as they roll, 
 And spread the tnith from pole lo polc.'^ 
 
 As the orbit of the moon is constantly vary- 
 ing in its position, and the place of the node 
 always changing, as her motion is even variable 
 in every part of her orbit, the solutions of the 
 problems which relate to her, are not altogether 
 so simple as those which concern the sun. 
 
 The moon increases her longitude in the eclip- 
 tic every day, about 13 degrees, 10 minutes, by 
 which means she crosses the meridian of any 
 place about 50 minutes later than she did the 
 preceding day. 
 
 Thus if on any day at noon her place (lon- 
 gitude) be in the 12th degree of Taurus, it will 
 be 13 deg. 10 min. more, or 25 deg. 10 min. in 
 Taurus on the succeeding noon. 
 
 It is new moon when the sun and moon 
 401 
 
t2IG DE6CRIl'*riON AND USE 
 
 have the same longitude, or are in or near the 
 same point of the ecHptic. 
 
 When they have opposite longitudes, or are 
 in opposite points of the ecliptic, it is full moon. 
 
 To ascertain the moon*s place with accuracy, 
 we must recur to an ephemeris; but as' even in 
 most ephemerides the moon's place is only shewn 
 at the beginning of each day, or XII o'clock at 
 noon, it becomes necessary to supply by a table 
 this deficiency, and assign thereby her place for 
 any intermediate time. 
 
 In the nautical ephemeris, published under 
 the authority of the Board of Longitude, we 
 have the moon's place for noon and midnight, 
 with rules for accurately obtaining any interme- 
 diate time ; but as this ephemeris may not always 
 be at hand, we shall insert, from Mr. Martin's 
 treatise on the globes, a table for finding the 
 hourly motion of the moon. In order, however, 
 to use this table, it will be necessary first to find 
 the quantity of the moon's diurnal motion in the 
 ecliptic, for any given day ; for the quantity of 
 the moon's diurnal motion varies from aibout 1 1 
 deg. 46 min. the least, to 15 deg. 16 min. when 
 greatest. 
 
 o 
 
 The following tables are calculated from 
 
 the least of 1 1 deg. 46 min. to the greatest of 
 
 15 deg. 16 min. every column increasing 10 
 
 minutes ; upon the top of the cobamn is the 
 
 402 
 
OF THE GLOBES. 217 
 
 quantity of the diurnal motion, and on the side 
 of the table are the 24 hours, by which means it 
 will be easy to find what part of the diurnal 
 motion of the moon answers to any given num- 
 ber of hours. 
 
 Thus suppose the diurnal motion to be 1 2° 32', 
 look on the top column for the number nearest 
 to it, which you will find to be 12° 36', in the 
 sixth column ; and under it, against 9 hours, 
 you will find 4 deg. 43 min. which is her motion 
 in the ecliptic in the space of 9 hours for that 
 day. The quantity of the diurnal motion for 
 any day is found by taking the difference be- 
 tween it and the preceding day. 
 
 Thus let the diurnal motion for the 11th of 
 May, 1787, be required. 
 
 SIGNS. DEG. MIN. 
 
 On the 1 1th of May her place was 11 2 35 
 On the 10th of May - - 10 19 47 
 
 The diurnal motion sought 12 48 
 
 Ee 403 
 
218 
 
 DESCRIPTION AND USE 
 
 TABLES 
 
 FOR VINDING THE HOURLY MOTION OF THE MOON, AN» 
 THEREBY HER TRUli". PLACE AT ANY TIME OF THE 
 
 DAY. 
 
 TABLE I. 
 
 r, 
 
 11 46 
 
 li 56 
 
 1» 6 
 
 13 16 
 
 13 96 
 
 12 36 
 
 12 46 
 
 12 56 
 
 13 6 
 
 13 16 
 
 13 26 
 
 
 d. m. 
 
 (J. m. 
 
 d. m. 
 
 d. rtu 
 
 d. m. 
 
 d. til. 
 
 d, m. 
 
 d. rtu 
 
 d. m. 
 
 d. m. 
 
 d. m. 
 
 1 
 
 2q 
 
 30 
 
 30 
 
 30 
 
 31 
 
 31 
 
 32 
 
 32 
 
 33 
 
 33 
 
 34 
 
 8 
 
 19 
 
 1 
 
 1 
 
 1 I 
 
 1 2 
 
 1 33 
 
 1 4 
 
 1 5 
 
 1 5 
 
 1 6 
 
 1 43 
 
 .1 
 
 1 28 
 
 1 20 
 
 1 31 
 
 1 <i2 
 
 : 33 
 
 1 35 
 
 1 36 
 
 1 37 
 
 1 38 
 
 1 39 
 
 1 41 
 
 4 
 
 1 58 
 
 1 59 
 
 2 1 
 
 2 3 
 
 3 4 
 
 2 6 
 
 3 8 
 
 2 9 
 
 2 11 
 
 2 13 
 
 2 14 
 
 S 
 
 2 27 
 
 2 29 
 
 3 31 
 
 2 34 
 
 2 35 
 
 2 37 
 
 2 40 
 
 2 42 
 
 2 44 
 
 2 46 
 
 2 48 
 
 6 
 
 8 37 
 
 2 59 
 
 3 1 
 
 3 4 
 
 3 6 
 
 3 9 
 
 3 11 
 
 3 14 
 
 3 16 
 
 3 19 
 
 3 21 
 
 7 
 
 3 26 
 
 3 29 
 
 3 32 
 
 3 35 
 
 3 38 
 
 3 40 
 
 3 43 
 
 3 46 
 
 3 49 
 
 3 52 
 
 3 55 
 
 8 
 9 
 
 3 55 
 
 3 59 
 
 4 2 
 
 4 6 
 4 36 
 
 4 9 
 
 4 12 
 
 4 15 
 
 4 13 
 
 4 22 
 
 4 25 
 4 58 
 
 4 20 
 
 4 25 
 
 4 28 
 
 4 32 
 
 4 40 
 
 4 43 
 
 4 47 
 
 4 51 
 
 4 55 
 
 5 2 
 
 10 
 
 4 54 
 
 4 58 
 
 5 3 
 
 5 7 
 
 5 11 
 
 5 1 
 
 5 19 
 
 5 23 
 
 5 27 
 
 5 32 
 
 5 56 
 
 n 
 
 5 24 
 
 5 28 
 
 5 33 
 
 5 37 
 
 5 42 
 
 5 4 
 
 5 51 
 
 5 56 
 
 6 
 
 6 3 
 
 6 9 
 
 13 
 13 
 
 5 53 
 
 -5 53 
 
 6 3 
 
 6 8 
 6 39 
 
 6 13 
 
 6 18 
 6 49 
 
 6 23 
 6 55 
 
 6 28 
 
 6 33 
 
 6 38 
 
 6 43 
 
 6 22 
 
 6 28 
 
 6 33 
 
 6 44 
 
 7 
 
 7 6 
 
 7 11 
 
 7 17 
 
 14 
 
 6 52 
 
 6 58 
 
 7 3 
 
 7 9 
 
 T 15 
 
 7 21 
 
 7 27 
 
 7 33 
 
 7 38 
 
 7 44 
 
 7 50 
 
 15 
 
 7 21 
 
 7 27 
 
 7 34 
 
 7 40 
 
 7 46 
 
 7 52 
 
 7 59 
 
 8 5 
 
 8 11 
 
 8 17 
 
 8 24 
 
 16 
 
 7 51 
 
 7 57 
 
 -8 4 
 
 8 U 
 
 8 17 
 
 8 24 
 
 8 31 
 
 8 37 
 
 8 44 
 
 8 51 
 
 8 57 
 
 17 
 
 8 iO 
 
 8 27 
 
 8 34 
 
 8 41 
 
 8 48 
 
 8 55 
 
 9 3 
 
 9 10 
 
 9 17 
 
 9 24 
 
 9 31 
 
 IS 
 
 8 49 
 
 8 57 
 
 9 4 
 
 9 12 
 
 9 19 
 
 9 27 
 
 9 34 
 
 9 42 
 
 9 49 
 
 9 57 
 
 10 4 
 
 19 
 
 19 
 
 9 26 
 
 9 35 
 
 9 43 
 
 9 51 
 
 9 58 
 
 10 6 
 
 10 14 
 
 10 22 
 
 10 30 
 
 10 38 
 
 20 
 
 9 48 
 
 9 56 
 
 10 5 
 
 10 13 
 
 10 21 
 
 10 30 
 
 10 38 
 
 10 47 
 
 10 55 
 
 11 3 
 
 11 12 
 
 21 
 
 10 17 
 
 10 26 
 
 10 36 
 
 10 44 
 
 10 53 
 
 11 1 
 
 n 10 
 
 11 19 
 
 11 27 
 
 11 36 
 
 11 43 
 
 22 
 
 10 47 
 
 10 56 
 
 11 6 
 
 11 15 
 
 11 21 
 
 11 33 
 
 11 42 
 
 11 51 
 
 12 
 
 12 10 
 
 12 19 
 
 23 
 
 n 17 
 
 11 26 
 
 11 36 
 
 11 46 
 
 11 55 
 
 12 4 
 
 12 14 
 
 12 24 
 
 12 33 
 
 12 43 
 
 12 52 
 
 24 
 
 U 46 
 
 11 56 
 
 12 6 
 
 12 16 
 
 12 26 
 
 12 36 
 
 12 46 
 
 12 56 
 
 13 6 
 
 13 16 
 
 13 26 
 
 404 
 
OF THE GLOBES. 
 
 219 
 
 TABLE II. 
 
 r, 
 
 IS SO 
 
 13 40 
 
 13 
 
 50 
 
 14 6 
 
 14 10 
 
 14 S6 
 
 14 36 
 
 14 46 
 
 14 56 
 
 15 6 
 
 15 16 
 
 PC 
 
 d. m. 
 
 rf. 7)1. 
 
 rf. 
 
 m. 
 
 (/. TO. 
 
 rf. m. 
 
 d. m. 
 
 rf. m. 
 
 rf. n>. 
 
 rf. ItXy 
 
 rf. ni. 
 
 rf. m. 
 
 1 
 
 31 
 
 34 
 
 
 
 35 
 
 36 
 
 36 
 
 36 
 
 36 
 
 37 
 
 37 
 
 38 
 
 38 
 
 2 
 
 1 8 
 
 1 9 
 
 1 
 
 16 
 
 1 10 
 
 1 11 
 
 1 12 
 
 1 13 
 
 1 14 
 
 I 15 
 
 1 15 
 
 1 15 
 
 3 
 
 1 42 
 
 1 42 
 
 1 
 
 46 
 
 1 46 
 
 1 47 
 
 1 48 
 
 1 49 
 
 1 51 
 
 1 51 
 
 1 53 
 
 1 54 
 
 4 
 
 2 16 
 
 2 8 
 2 52 
 
 2 
 
 19 
 
 2 21 
 
 2 22 
 
 2 24 
 
 2 26 
 
 2 28 
 
 2 20 
 
 2 31 
 
 2 33 
 
 S 
 
 2 50 
 
 2 
 
 54 
 
 2 56 
 
 2 58 
 
 3 
 
 3 3 
 
 3 5 
 
 a 7 
 
 3 9 
 
 3 11 
 
 fl 
 
 3 24 
 
 3 26 
 
 3 29 
 
 3 31 
 
 3 34 
 
 3 39 
 
 3 39 
 
 3 41 
 
 3 45 
 
 3 46 
 
 3 9 
 
 7 
 
 3 58 
 
 4 1 
 
 4 
 
 4 
 
 4 7 
 
 4 10 
 
 4 10 
 
 4 15 
 
 4 18 
 
 4 21 
 
 4 24 
 
 4 7 
 
 8 
 
 4 32 
 
 4 35 
 
 4 
 
 39 
 
 4 42 
 
 4 45 
 
 4 49 
 
 4 52 
 
 4 55 
 
 4 59 
 
 5 2 
 
 S 5 
 
 q 
 
 5 f) 
 
 5 10 
 
 5 
 
 13 
 
 5 17 
 
 4 21 
 
 5 25 
 
 5 28 
 
 J 32 
 
 5 36 
 
 5 40 
 
 5 43 
 
 10 
 
 5 40 
 
 5 42 
 
 5 
 
 48 
 
 5 52 
 
 5 57 
 
 6 1 
 
 6 5 
 
 6 9 
 
 6 13 
 
 6 17 
 
 6 22 
 
 11 
 
 6 14 
 
 6 19 
 
 6 
 
 23 
 
 6 28 
 
 6 32 
 
 6 37 
 
 6 41 
 
 6 46 
 
 6 51 
 
 6 55 
 
 7 
 
 12 
 
 6 48 
 
 6 5.1 
 
 b 
 
 50 
 
 7 3 
 
 7 8 
 
 7 13 
 
 7 28 
 7 54 
 
 7 23 
 
 7 28 
 
 7 33 
 
 7 28 
 
 1.1 
 
 7 22 
 
 7 27 
 
 7 
 
 S3 
 
 7 38 
 
 7 44 
 
 7 49 
 
 8 6 
 
 8 f 
 
 « 11 
 
 8 10 
 
 14 
 
 7 56 
 
 8 
 
 8 
 
 8 
 
 8 13 
 
 H 19| 8 25 
 
 8 31 
 
 8 37 
 
 8 43 
 
 8 48 
 
 8 54 
 
 15 
 
 8 30 
 
 8 36 
 
 8 
 
 42 
 
 8 49 
 
 8 S5 
 
 9 1 
 
 9 r 
 
 9 14 
 
 9 20 
 
 9 26 
 
 9 32 
 
 16 
 
 y 4 
 
 9 11 
 
 9 
 
 17 
 
 9 21 
 
 9 12 
 
 9 3- 
 
 9 44 
 
 9 51 
 
 9 57 
 
 10 4 
 
 10 11 
 
 17 
 
 9 38 
 
 9 45 
 
 9 
 
 52 
 
 9 59 
 
 10 20 
 
 10 J3 
 
 10 20 
 
 10 28 
 
 10 33 
 
 10 42 
 
 10 49 
 
 18 
 
 10 12 
 
 10 19 10 
 
 27 
 
 10 34 10 42 
 
 10 49 
 
 10 «7 
 
 11 4 
 
 11 12 
 
 11 19 
 
 11 87 
 
 19 10 4fi 
 
 10 54 11 
 
 5 
 
 11 10 11 18 
 
 11 26 
 
 11 34 
 
 11 41 
 
 11 49 
 
 11 57 
 
 12 5 
 
 20 
 
 >1 29 
 
 11 38 
 
 11 
 
 37 
 
 11 24 
 
 11 8 
 
 12 2 
 
 12 10 
 
 12 18 
 
 12 17 
 
 12 35 
 
 12 42 
 
 21 
 
 11 5S 
 
 12 3 
 
 12 
 
 11 
 
 12 20 
 
 12 9 
 
 12 38 
 
 12 40 
 
 12 55 
 
 13 4 
 
 13 13 
 
 13 21 
 
 22 
 
 12 2S 
 
 12 37 
 
 12 
 
 46 
 
 12 55 
 
 13 5 
 
 13 14 
 
 13 23 
 
 13 33 
 
 13 41 
 
 13 50 
 
 13 50 
 
 23 
 
 13 2 
 
 13 12 
 
 13 
 
 21 
 
 13 31 
 
 13 43 
 
 13 59 
 
 13 59 
 
 14 9 
 
 14 10 
 
 14 28 
 
 14 38 
 
 24 
 
 IS K 
 
 13 46 
 
 13 
 
 56 
 
 14 61 
 
 14 16 
 
 14 26 
 
 14 36 
 
 14 46 
 
 14 56 
 
 15 6 
 
 15 16 
 
 40.5 
 
220 DESCIRPTION AND USE 
 
 The moon's path may be represented on the 
 globe in a very pleasing manner, by tying a 
 silken line over the surface of the globe exactly 
 on the ecliptic ; then finding, by an ephemeris, 
 the place of the nodes for the given time, con- 
 fine the silk at these two points, and at 90 de- 
 grees distance from them elevate the line abcfut 
 5i deg. from the ecliptic, and depress it as 
 much on the other, and it will then represent the 
 lunar orbit for that day. 
 
 PROBLEM XLI. 
 
 To find the moorCs place in the ecliptic^ for any give?z 
 hour of the day* 
 
 First without an ephemeris, only knowing the 
 age of the moon, which may be obtained from 
 every common almanack. 
 
 Elevate the north pole of the celestial globe 
 to 90 degrees, and then the equator will be in 
 the plane of, and coincide with the broad paper 
 circle ; bring the first point of Aries, marked t 
 on the globe, to the day of the new moon on 
 the said broad paper circle, which answers to the 
 sun*s place for that day; and the day of the 
 moon's age will stand against the sign and degree 
 of the moon's mean place ; to which place apply 
 a small patch to represent the moon. 
 406 
 
 i 
 
OF THE GLOBES. 221 
 
 But if you are provided with an ephemeris,* 
 that will give the moon's latitude and place in 
 the ecHptic ; first note her place in the ecliptic 
 upon the globe, and then counting so many de- 
 grees amongst the parallels in the zodiac, either 
 above or below the ecliptic, as her latitude is 
 north or south upon the given day, and that will 
 be the point which represents the true place of 
 the moon for that time, to which apply the arti- 
 ficial sun, or a small patch. 
 
 Thus on the 1 1th of May, 1787, she was at 
 noon in 2 deg. 35 min. of Pisces, and her lati- 
 tude was 4 deg. 18 min.; but as her diurnal 
 motion for that day is 12 48 in nine hours, she 
 will have passed over 4 deg. 47 min. which 
 added to her place at noon, gives 7 h. 22 min. 
 for her place on the 11th of May, at nine at 
 night. 
 
 PROBLEM XLII. 
 
 To find the mocrCs declination for any given day or 
 hour. 
 
 The place in her orbit being found, by prob. 
 xli, bring it to the brazen meridian ; then the 
 arch of the meridian contained between it and 
 the equinoctial, will be the declination sought. 
 
 ^ The nautical almanack is the best English cpl'.emoris. 
 407 
 
222 DESCRIPTION AND US£ 
 
 PROBLEM XLllI. 
 
 To find the moon*s greatest and least meridian alti- 
 tudes in any given latitude, that of London for 
 example. 
 
 It is evident, this can happen only when the 
 •ascending node of the moon is in the vernal equi- 
 nox ; for then her greatest meridian ahitude will 
 be 5 dQg. greater than that of the sun, and there- 
 fore about 67 dcg. ; also her least meridian alti* 
 tud€ will be 5 deg. less than that of the sun, and 
 therefore only 10 deg. : there will therefore be 
 .57 deg. dift'erence in the meridian altitude of the 
 moon ; whereas that of the sun is but 47 deg. 
 
 N. B. When the same ascending node is ia 
 the autumnal equinox, then will her meridian 
 altitude differ by only 37 deg. ; but this pheno- 
 menon can separately happen but once in the 
 revolution of a node, or once in the space of 
 nineteen years : and it will be a pleasant enter- 
 tainment to place the silken line to cross the 
 ecliptic in the equinoctial points alternately ; for 
 then the reason will more evidently appear, why 
 you observe the moon sometimes within 23 deg. 
 of our zenith, and at other times not more than 
 10 deg. above the horizon, when she is full 
 south. 
 
 408 
 
©r THE GLOBES. 22S 
 
 PROBLEM XLIV* 
 
 To illustrate, by the globe, the phenomenon qj the 
 harvest moon. 
 
 About the time of the autumnal equinox, 
 when the moon is at or near the full, she is ob- 
 served to rise almost at the same time for several 
 nights together ; and this phenomenon is called 
 the harvest moon. 
 
 This circumstance, with which farmers were 
 better acquainted than astronomers, till within 
 these few years, they gratefully ascribed to the 
 goodness of God, not doubting that he had 
 ordered it on purpose to give them an immediate 
 supply of moon-light after sun-set, for their 
 greater convenience in reaping the fruits of the 
 earth. 
 
 In this instance of the harvest moon, as in 
 'many others discoverable by astronomy, the 
 wisdom and beneficence of the Deity is conspi- 
 cuous, v\ho really so ordered the cv^urse of the 
 moon, as to bi'-rtow more or less light on all parts 
 of the earth, as their several circumstances or 
 seasons render it more or less serviceable.* 
 
 About the equator, where there is no variety 
 of seasons, moon-light is not necessary for ga- 
 thering in the produce of the ground ; and 
 
 * Ferguson's Aitronoir.v. 
 409 
 
224- DESCRIPTION AND USE 
 
 there the moon rises about 50 minutes later 
 every day or night than on the former. At con- 
 siderable distances from the equator, where the 
 weather and seasons are more uncertain, the 
 autumnal full moons rise at sun-set from the 
 first to the third quarter. At the poles, where 
 the sun is for half a year absent, the winter full 
 moons shine constantly without setting, from the 
 first to the third quarter. 
 
 But this observation is still further confirmed, 
 when we consider that this appearance is only 
 peculiar with respect to the full moon, from 
 which only the farmer can derive any advantage; 
 for in every other month, as well as the three 
 autumnal ones, the moon, for several days to- 
 gether, will vary the time of it's rising very little; 
 but then in the autumnal months this happens 
 about the time when the moon is at the full ; in 
 the vernal months, about the time of new moon ; 
 in the winter months, about the time of the first 
 quarter ; and in the summer months, about the 
 time of the last quarter. 
 
 These phenomena depend upon the different 
 angles made by the horizon, and different parts 
 of the moon's -orbit, and that the moon can be 
 full but once or twice in a year, in those parts of 
 her orbit which rise with the least angles. 
 
 The moon's motion is so nearly in the 
 410 
 
OF THE GLOBES. 225 
 
 ecliptic, that we may consider heir at present as 
 moving in it. 
 
 The diiFereftt parts of the ecliptic, on account 
 of it's obliquity to the earth's axis, make very dif- 
 ferent angles with the horizon as they rise or set. 
 Those parts, or signs, which rise with the smalU 
 est angles, set with the greatest, and n^ke lersa. 
 In equal times, whenever this angle is least, a 
 greater portion of the ecliptic rises, than when 
 the angle is larger. 
 
 This may be seen by elevating the globe to 
 any considerable latitude, and then taming k 
 round it's axis in the horizon. 
 
 When the moon, therefore, is in those signs 
 which rise or set with the smallest angles, she 
 will rise or set with the least difference of time j 
 and with the greatest difference in those signs 
 which rise or set with the greatest angles. 
 
 Thus in the latitude of London, at the time 
 of the vernal equinox, when the sun is setting 
 in the western part of the horizon, the ecliptic 
 then makes an fengle of 62 deg. with the hori« 
 zon ; but when the sun is in the autumnal equi» 
 nox, and setting in the same western part of the 
 horizon, the ecliptic makes an angle but of 13 
 deg. with the horizon \ all which is evident by 
 a bare inspection of the globe only. 
 
 Again, according to the greater or less in- 
 clination of the ecliptic to the horizon, so a 
 greater or less degree of motion of the glob« 
 Ff 411 
 
226 DESCRIPTION AND USE ' 
 
 about it's axis will be necessary to cause the 
 same arch of the ecliptic to pass through the 
 horizon ; and consequently the time of it's pas- 
 sage will be greater or less, in the same propor- 
 tion ; but this will be best illustrated by an ex- 
 ample. 
 
 Therefore, suppose the sun in the vernal 
 equinox, rectify the globe for the latitude of 
 London, and the place of the sun ; then bring 
 the vernal equinox, or sun's place, to the west- 
 em edge of the horizon, and the hour index 
 will point precisely to VI ; at which time, we 
 will also suppose the moon to be in the au- 
 tumnal equinox, and consequently at full, and 
 rising exactly at the time of sun-set. 
 
 But on the following day, the sun, being 
 advanced scarcely one degree in the ecliptic, 
 will set again very nearly at the same time as 
 before ; but the moon will, at a mean rate, in 
 the space of one day, pass over 13 deg. in her 
 orbit ; and therefore, when the sun sets in the 
 evening after the equinox, the moon will be 
 below the horizon, and the globe must be 
 turned about till 1 3 deg. of Libra come up to 
 the edge of the horizon, and then the index 
 will point to 7 h. 16 min. the time of the moon's- 
 rising, which is an hour and quarter after sun- 
 set for dark night. The next day following 
 there will be 2i hours, and so on successively, 
 with an increar/^ of 1^ hour dark night each 
 •^12 
 
OF THE GLOBES. 227 
 
 evening respectively, at this season of the year ; 
 all owing to the very great angle which th^ 
 ecliptic makes with the horizon at the time of 
 the moon's rising. 
 
 On the other hand, suppose the sun in the 
 autumnal equinox, or beginning of Libra, and 
 the moon opposite to it in the vernal equinox, 
 then the globe (rectified as before) being turned 
 about till the sun's place comes to the western 
 edge of the horizon, the index will point to VI, 
 for the time of the setting, and the rising of 
 the full moon on that equinoctial day. On the 
 following day, the sun will set nearly at the 
 same time ; but the moon being advanced (in 
 the 24 hours) 13 deg. in the ecliptic, the globe 
 must be turned about till that arch of the eclip- 
 tic shall ascend the horizon, which motion of 
 the globe will be very little, as the ecliptic now 
 makes so small an angle with the horizon, as 
 is evident by the index, which now points to 
 VI h. 17. min. for the time of the moon's rising 
 on the second day, which is about a quarter of 
 an hour after sun-set. The third day, the moon 
 will rise within half an hour ; on the fourth, 
 within three quarters of an hour, and so on ; 
 so that it will be near a week before the nights 
 will be an hour without illumination j and in 
 greater latitudes this difference will be still great- 
 er, as you will easily find by varying the case, 
 in the practice of this celebrated problem, on 
 the globe, 
 
 413 
 
228 DESCRIPTION AND USE 
 
 This phenomenon varies in different years ; 
 the moon's orbit being inclined to the ecliptic 
 about five degrees, and the line of the nodes 
 continually moving retrograde, the inclination 
 of her orbit to the equator will be greater at 
 some seasons than it is at others, which prevents 
 her hastening to the northward, or descending 
 southward, in each revolution, with an equal 
 pace. 
 
 PROBLEM. XLV. 
 
 To Jind what azimuth the moon is upon at any 
 place when it is floods or high water ; and 
 thence the high, tide for any day of the moon's 
 fl^e at the same place. 
 
 Having observed the hour znd minute of 
 high water, about the time of new or full moon, 
 rectify the globe to the latitude and sun*s place ; 
 find the moon's place and latitude in an ephe- 
 meris, to which set the artificial moon,* and 
 screw the quadrant of altitude in the zenith ; 
 turn the globe till the horary index points to 
 the time of flood, and lay the quadrant over the 
 center of the artificial moon, and it will cut the 
 horizon in the point of the compass upon 
 
 * Or patch representing the moon. " 
 414 
 
O* THE GLOBES. 229 
 
 which the moon was, and the degrees on the 
 horizon contained between the strong brass me- 
 ridian and the quadrant, will be the moon*s azi- 
 muth from the south. 
 
 To find the time of high water at the same place. 
 
 Rectify the globe to the latitude and zenith, 
 find the moon's place by an ephemeris for the 
 given day of her age, or day of the month, and 
 set the artificial moon to that place in the zodi- 
 ac ; put the quadrant of altitude to the azimuth 
 before found, and turn the globe till the artifi- 
 cial moon is under it's graduated edge, and the 
 horary index will point to the time of the day 
 on which it will be high water. 
 
 The usk of the celestial globe iv the solution- 
 op PROBLEMS ASCERTAINING THE PLACES AND VISI- 
 BI/E MOTIONS OF ORBITS OR COMETS.* 
 
 There is another class or species of planets, 
 which are called comets. These move round 
 the sun in regular and stated periods of times, 
 in the same manner, and from the same cause, 
 as the rest of the planets do ; that is, by a cen- 
 tripetal force, every where decreasing as the 
 
 ♦Martin's Description and Use of the Globes. 
 415 
 
230 DESCRIPTION AND USE 
 
 squares of the distances increase, which is the 
 general law of the whole planetary system. But 
 this centripetal force in the comets being com- 
 pounded with the projectile force, in a very dif" 
 ferent ratio from that which is found in the 
 planets, causes their orbits to be much more el- 
 liptical than those of the planets, which are al- 
 most circular. 
 
 But whatever may be the form of a comet's 
 orbit in reality, their geocentric motions, or 
 the apparent paths which they describe in the 
 heavens among the fixed stars, will always be 
 circular, and therefore may be shewn upon the 
 surface of a celestial globe, as well as the mo- 
 tions and places of any of the rest of the 
 planets. 
 
 To give an instance of the cometary praxis 
 on the globe, we shall chuse that comet, for the 
 subject of these problems, which made it's ap- 
 pearance at Boston, in New England, in the 
 months of October and November, 1758, in it's 
 return to the sun ; after which, it approached 
 so near the sun, as to set heliacally^ or to be lost 
 in it's beams for some time spent in passing 
 the perihelion. Then afterwards emerging 
 from the solar rays, it appeared retrograde in 
 it's course from the sun towards the latter end 
 of March, and so continued the whole month 
 of April, and part of May, in the West Indies, 
 particularly in Jamaica, whose latitude ren- 
 416 
 
•F THE GLOBES, 231 
 
 dered it visibie in those parts, when it wns, for 
 the greatest part 'of the time, invisible to us, 
 by reason of it's southern course through the 
 heavens. 
 
 When two observations can be made of a 
 comet, it will be very easy to assign it*s course, 
 or mark it out upon the surface of the celestial 
 globe. These, with regard to the above-men- 
 tioned comet, we have, and they are sufficient 
 for our purpose in regard to the solution of 
 cometary problems. 
 
 By an observation made at Jamaica on the 
 31st of March, 1759, at five o'clock in the 
 morning, the comet's altitude was found to be 
 22 deg. 50 min. and it's azimuth 7 1 deg. south- 
 east. From hence we shall find its place on 
 the surface of the globe by the following pro- 
 blem. 
 
 PROBLEM XLVI. 
 
 To rectify the globe for the latitude of the place 
 of observation in Jamaica, latitude 17 deg* 
 SO ;«/■«. and given day of the months viz» 
 March 3 1 St. 
 
 « 
 
 Elevate the north pole to 17 deg. SO min, 
 above the horizon, then fix the quadrant of al- 
 titude to the same degree in the meridian, or 
 zenith point. Again, the sun's place for the 
 31st of March is in 10 deg. 34. min. t, which 
 417 
 
232 DESCRIPTION AND USE 
 
 bring to the meridian, and set the hour index 
 at XII, and the globe is then rectified for the 
 place and time of observation. 
 
 PROBLEM XLVII. 
 
 To determine the place of a comet on the surface of 
 the celestial globe from 7/'j given altitude^ azi' 
 muth, hour of the day^ and latitude of the place. 
 
 The globe being rectified to the given lati- 
 tude, and day of the month, turn it about to- 
 wards the east, till the hour index points to the 
 given time, viz. V o'clock in the morning j 
 then bring the quadrant of altitude to intersect 
 the horizon in 7 1 deg. the given azimuth in the 
 south-east quarter; then, under 22 deg. 50 min, 
 the given altitude, you will find the comet's 
 place, where you may put a small patch to re- 
 present it. 
 
 PROBLEM XLVIII. 
 
 To find the latitude, longitude, declifMiion, and 
 right ascension of the comets. 
 
 In the circles of latitude contained in the 
 zodiac, you will find the latitude of the comet 
 to be about 30 deg. 30 min. from the ecliptic ; 
 the same circle of latitude reduces it*s place to 
 the ecliptic in 26 deg. 30 min. of «^, which is 
 418 
 
OF THE GLOBES. 233 
 
 it's longitude sought. Then bring the cometary 
 parch to the brazen meridian, and it's declination 
 will be shewn to be 9 deg. 15 min. south. At 
 the same time, it's right aseension will be 227 
 deg. 30 min. 
 
 P ROBLEM XLIX. 
 
 To shew the time of the comet* s rising, southing, 
 setting, and amplitude, for the day of the obser- 
 servation at Jamaica, 
 
 Bring the place of the comet into the eastern 
 semicircle of the horizon, (the globe being recti- 
 fied as directed) the index will point to III hours 
 15 min. which is the time of it's rising in the 
 morning at Jamaica, the amplitude 10 deg. very 
 nearly to the south. The patch being brought 
 to the meridian, the index points to IX o'clock 
 10 min. for the time of culminating, or being 
 south to them. Lastly, bring the patch to touch 
 the western meridian, and the index will point 
 to III in the afternoon, for the time of the 
 comet's setting, with ten deg. of southern ampli- 
 tude, of course. 
 
 G g 419 
 
234 DESCRIPTION AND USE 
 
 PROBLEM L. 
 
 From the comet' s place being given, to find the time 
 of iCs rising in the horizon of London, on the 
 3 \ St day of March, 1759. 
 
 For this purpose, you need only rectify the 
 globe for the given latitude of London, and 
 bring the cometary patch to the eastern horizon, 
 and the index points to III hours 45 min. for 
 the time of It's rising at London, with about 14 
 deg. of south amplitude ; then turn the patch to 
 the western horizon, and the index points to II 
 hours 25 minutes, the time of it's setting. 
 
 N. B. From hence It appears, the comet rose 
 soon enough that morning to have been observed 
 at London, had the heavens been clear, and the 
 astronomers had been before-hand apprized of 
 such a phenomenon. 
 
 PROBLEM LI. 
 
 To determine another place of the same comet, from 
 an observation made at London on the 6th day 
 of May, at ten in the evening. 
 
 On the 6th day of May, 1759, at ten at 
 night, the place of the comet was observed, and 
 it's distance measured with a micrometer, from 
 420 
 
OF THE GLOBES, 235 
 
 two fixed stars marked /* and > in the constella- 
 tion called Hydra, and it's altitude was found 
 to be 16 deg. and it's azimuth 37 deg. south- 
 west ; from whence it's place on the surface of 
 the globe, is exactly determined, as in prob. 
 xlvii. and having stuck a patch thereon, you 
 will have the two places of the comet on the 
 surface of the globe, for the two distant days and 
 places of observation, as required. 
 
 PROBLEM LII. 
 
 From two given places of a comet, to assign it^s ap- 
 parent path among the fixed stars in the heavens. 
 
 The two places of the comet being deter- 
 mined by the observations on the 31st of 
 March, 1758, and the 6th of May following, 
 and denoted by two patches respectively, you 
 mnst move the globe up and down, in the 
 notches of the horizon, till such time as you 
 bring both the patches to coincide with the 
 horizon ; then will the arch of the horizon be- 
 tween the two patches shew, upon the celestial 
 globe, the apparent place of the comet in the 
 interval between the two observations, and by 
 drawing a line with a black lead pencil along 
 by the frame of the horizon, it's path on the 
 surface of the globe will be delineated, as re- 
 quired. And here it may be observed, that 
 421 
 
236 DESCRIPTION AND USE 
 
 it*s apparent path lay through the following 
 southern constellations, viz. the tail of Capri- 
 corn, the tail of Piscis Australis, by the head of 
 Indus, the neck and body of Pavo, through the 
 neck of Apus, below Triangulum Australe, 
 above Musca, by the lowermost of the Crosiers, 
 across the hind legs arid through the tail of 
 Centaurus, from thence between the two stars 
 in the back of the Hydra before-mentioned ; af- 
 ter this, it passed on to Sextans Uraniae, and 
 then to the ecliptic near Cor Leonis, soon after 
 which it totally disappeared. 
 
 PROBLEM LIII. 
 
 To estimate the apparent velocity of a comet, tws 
 places thereof being given by observation. 
 
 Let one place be ascertained near the be- 
 ginning of it*s appearance, and the other to- 
 wards the end thereof ; then bring these two 
 places to the horizon, and count the number 
 of dtgrees intersected between them, which be- 
 ing the space apparently described in a given 
 time, will be the velocity required. Thus, in 
 the case of the above-mentioned comet, you will 
 find that it described more than 150 deg. in the 
 space of 36 days, which is more than 4 deg. 
 per day. 
 
 422 
 
OF THE GLOBES. 237 
 
 PROBLEM LIV. 
 
 To represent the general phenomena of the comet, 
 for any given latitude. 
 
 Bring the visible path of the comet to coin- 
 cide with the horizon, by which it was drawn, 
 and then observe what degree of the meridian is 
 in the north point of the horizon, which, in the 
 case of the foregoing comet, will be the 23 deg. 
 This will shew the greatest latitude in which the 
 whole path can be visible in any latitude less 
 than this, as that of Jamaica; where, for instance, 
 the most southern part of the path will be ele- 
 vated more than 5 deg. above the horizon, and 
 the comet visible through the whole time of it's 
 apparition. But rectifying the globe for the 
 latitude of London, the path of the said comet 
 will be for the most part invisible, or below 
 the horizon ; and therefore it could not have 
 been seen in our latitude, but at times very near 
 the beginning and end of it's appearance ; be- 
 cause, by bringing the comet's path on one part 
 to the south point of the horizon, it will imme- 
 diately appear in w^hat part the comet ceases to 
 be visible ; and then the bringing the other part 
 of the path to the point, it will appear in what 
 part it will again become visible. 
 423 
 
238 
 
 DESCRIPTION AND USE, &C. 
 
 After this manner may the problems relating 
 to any other comets be performed; and thus 
 the paths of the several comets, which have 
 hitherto been observed, may be severally deli- 
 neated on the celestial globe, and their various 
 phenomena in different latitudes be thereby 
 shewn. 
 
 424 
 
ESSAY III, 
 
 CONTAINING 
 
 A DESCRIPTION 
 
 OF THE MOST IMPROVED 
 
 Planetarium, Lunarium, & Tellurian. 
 
 I 
 
 Now proceed, in purfuance of my original 
 plan, to defcribe one of the inftruments 
 contrived to facilitate the fludy of geography 
 and aftronomy. It will realize to the eye of 
 the pupil many phenomena, and imprefs them 
 flrongly on his memory. The inflrument here 
 defcribed may be confidere^ as on e of the beft 
 hitherto contrived for explaining the celeftial 
 motions. The defcription of this will, with 
 very few alterations, apply to mod other in- 
 flruments defigned for the fame purpofe. The 
 explanation of the inftrument will alfo enable 
 me to render fome articles plainer, and to treat 
 others more fully ; while thofe who have not 
 thoroughly comprehended what has been al- 
 li 425 
 
10 DESCRIPTION AND USE 
 
 ready faid, may gain more perfed ideas of the 
 fubjeft. 
 
 It feems highly probable, that the ancients 
 were not unacquainted with planetary ma- 
 chines, and that the fame powers of genius 
 which led them to contemplate and reafon 
 upon the motion of the heavenly bodies, in- 
 duced them to realize their ideas, and form in- 
 ftruments for explaining them ; and we may 
 fairly prefume, that thefe were carried to no 
 fmall degree of perfection, when we confider 
 that of one, Archimedes was the maker, and 
 Cicero the encomiaft. 
 
 The inflrument now to be defcribed was 
 invented by the celebrated Huygens, though 
 lince his time it has been afcribed to almofl: as 
 many inventors as makers ; each deviation in 
 form, the mounting it in this mode or the other, 
 the addition of a zodiac, or fome fuch flight 
 changes, have been deemed by many of fuffi- 
 cient importance to give them a claim to the 
 title of inventors : — be it fo. Let the friend 
 of fcience encourage every humble effort to 
 improve it ; and let him bellow a name which, 
 though it may in fome meafure gratify vanit3'', 
 yet incites to labour, rather than by contempt 
 check the ardour, or difcourage the talents 
 which, when called forth, may be of the great- 
 eft fervice to fociety. 
 
 426 
 
OF PLANETARIUMS, &C. 11 
 
 Description of the Planetarium, 
 
 Fig. I , plate XI, reprefents the planetari- 
 um. The box contains the wheel- work by 
 which the planets are made to move round a 
 brafs ball, reprefenting the fun : this motion is 
 communicated to them by turning a handle. 
 
 A planetarium may be confidered, in fome 
 fort, as a diametrical fedion of our univerfe, in 
 which the upper and lower hemifpheres are 
 fupprefled. The upper plate is to anfwer for 
 the ecliptic ; on this therefore are placed, in 
 two oppofite circles, correfponding to each 
 other, the figns of the ecliptic, and the days of 
 the month, by means whereof the planets may 
 be eafily fet to their mean places in the ecliptic 
 for any day in the year. Through the center 
 of the plate there paffes a ftrong ftem, on which 
 the brafs ball O is placed, which reprefents 
 the fun ; round the ftem are the different fock- 
 ets, which carry the arms, by which the balls 
 reprefenting the planets are fupported. The 
 planets are ivory balls, having the hemifphere 
 which is next the fun white, the other black, 
 to exhibit their refpeftive phafes to each other. 
 The planets may be eafily put on or taken oflF 
 their fockets, as occafion requires. About the 
 primary planets are placed the fecondary plan- 
 427 
 
12 DESCRIPTION AND USE 
 
 ets, or moons, v^hich are in this inflrument 
 only moveable by hand ; but when the inflru- 
 mentis fitted upon a large fcale, and in a more 
 expenfive form, even thefe are put in motion 
 by the wheel-work. 
 
 The planets are difpofed in the following 
 order : in the center is the brafs ball O to re- 
 prefent the fun, then Mercury ^, Venus 9 , the 
 Earth ©, Mars S, Jupiter jj., and Saturn b ; 
 then the Georgium Sidus ^. 
 
 "When the pupil has been gratified by put- 
 ting the inflrument in motion, and making his 
 own obfervations on thofe motions, it will be 
 proper to acquaint him with the names of the 
 different planets, and of their divifion into pri- 
 mary and fecondary, to (hew him how they 
 were firfl: diftinguifhed from the fixed ftars, 
 and how the length of their periodic revolution 
 was difcovered. Here it will be proper to 
 obferve, that the annual motion of the earth, or 
 the time it takes to perform it's period round 
 the fun, is made the bafis to which the others 
 are compared ; and this is one of the reafons 
 why the months, and days of our months, are 
 engraved on the circle. Having obferved this, 
 'the planets may be put in motion, and they 
 will be found to revolve round the reprefenta- 
 tive of the fun in their proportionable times, 
 each planet always completing it's revolution 
 
 428 
 
OF PLANETARIUMS, &C. I3 
 
 in the fame fpace of time, in periods regulated 
 and proportioned to their diftance from the 
 fun : the curve which they defcribe in their 
 revolution, is what is termed their orbit. 
 
 General Explanation of the Solar Sys- 
 tem BY THE Planetarium. 
 
 In the center of the fyflem is the fun, placed 
 in the heavens by that Almighty Power who faid 
 " Let there be light, and there was light," to 
 be the fountain of light and heat to all the 
 planets revolving round him. 
 
 -" His rapid rays, 
 
 " Themfelves unmcafur'd, mcafure all our days : 
 *' A thoufand worlds confcfs his quick'ning heat, 
 ** And all he cheers are fruitful, fair, and fweet." 
 
 The fituation of this glorious body, in the 
 fyflem, is pointed out in this machine by the 
 brafs ball in the center. 
 
 Mercury is the neareft planet to the fun 
 and moves round him in about 88 days. To 
 obferve this by the planetarium, obferve the 
 parts of the ecliptic where Mercury and Venus 
 are fituated, or fet them to any two given 
 places therein, and then turn the handle ; and 
 when Mercury is returned to the place from 
 whence he fet out, the earth will have gone 
 over 88 days of the ecliptic. In the fame 
 
 429 
 
14 DESCRIPTION AND USE 
 
 manner you will find the periods of the other 
 planets correfponding to their refpedive pe- 
 riods in the heavens. 
 
 As Mercury moves round him in rather 
 lefs than three months, that confequently is 
 the length of his year ; the year in each planet 
 being the fpace of time which it occupies in 
 going round the fun. Mercury is feldom feen, 
 on account of his being fo near to the fun as to 
 be generally concealed by his rays ; and the 
 time of his rotation on his axis, or the length 
 of his days and nights, has not yet been difcov- 
 ered. 
 
 Venus, the next planet to Mercury, diftin- 
 guifhed in the heavens by her fuperior luftre 
 and brightnefs, completes her annual or yearly 
 revolution round the fun in about 225 days ; 
 and her diurnal or daily rotation upon her own 
 axis in about 23I- hours. When this planet 
 appears to the weft of the fun, fhe rifes before 
 him in the morning, and is called the morning 
 flar ; and when fhe appears to the eaft of the 
 fun, fhe fliines in the evening after he fets, and 
 is then called the evening flar ; being in each 
 fituation, alternately, for about 7-^ months. 
 
 The next planet above Venus is the Earth, 
 whofe annual revolution is performed in ^6^ 
 days, 5 hours, and 49 minutes, or rather more 
 than 12 months, (the brazen ecliptic is how- 
 ever only divided into 365 days) and it's diur- 
 
 430 
 
OF PLANETARIUMS, &C, l^ 
 
 nal rotation in about 24 hours. Every fourth 
 year, one day is added at the end of February, 
 to recover the time which the earth fpends in 
 her annual courfe above the 365 days, which 
 compofe a common year. This fourth year 
 therefore confifts of 366 days, and is called bif- 
 fextile, and alfo leap-year. 
 
 Next above the earth's orbit is that of Mars^ 
 who completes his revolution round the fun 
 in fomewhat lefs than two of our years, and his 
 rotation upon his axis in rather more than 24-j. 
 hours. 
 
 Jupiter, the largeft of all the planets, holds 
 the next place to Mars in diflance from the 
 fun. He performs his annual revolution in ra- 
 ther lefs than 12 years, and his diurnal rotation 
 in about 10 hours. Jupiter, as well as Venus, 
 is fometimes called a morning, and fometimes 
 an evening ftar. 
 
 Next to the orbit of Jupiter is that of 5^- 
 turn, who completes his annual revolution 
 round the fun in about 29!- years. The time 
 of his diurnal rotation is unknown. 
 
 Saturn was generally confidered as the re- 
 moteft planet of our fyftem, till, on the 13th of 
 March, 1781, Dr. Herfchel difcovered another, 
 ftill further diftant from the fun, round which 
 it revolves, in an orbit nearly circular, in about 
 82 years. To this planet Dr. Herfchel has 
 given the name of the Georgium Sidus. 
 
 431 
 
l6 DESCRIPTION AND USE 
 
 Befides thefe feven primary planets, there 
 
 are fourteen others, c-aWtdi fecondnry planets, or 
 
 fatelUtes, which move round their primaries 
 
 in the fame manner as thefe move round the 
 
 fun. 
 
 The firft of thefe is the vioon, reprefented 
 by the fmall ball annexed to the earth. While 
 it accompanies the earth in it's annual pro- 
 grefs through it's orbit, it is continually revolv- 
 ing round it ; as you will fee in that part of the 
 inftruinent that is particularly defigned to illuf- 
 trate the phenomena of the moon. 
 
 Jupiter has four fatellites, Saturn feveral, 
 and the Georgium Sidus two ; they are all invi- 
 fible to the naked eye, and are only to be feen 
 by the afliltance of telefcopes. Saturn, befides 
 his feven fatellites, has a bright Ihining ring, 
 which encompafles him : it is at fuch a dif- 
 tance from his body, that the fixed flars may 
 frequently be feen between the inner edge of 
 the ring and the planet itfelf. Dr. Herfchel 
 has lately difcovered that this ring is divided 
 into two parts, an inner and an outer ring, 
 which are feparated from each other by a fpace 
 of one ihoufand miles. 
 
 432 
 
OF PLANETARIUMS, &C. I7 
 
 To explain, by the planetarium, why the fun, be- 
 ing a fixed body, appears to pafs through all 
 the figns of the zodiac in twelve months, or 
 one year. It will fljcw that this phenomenon 
 is occaftoned by the annual motion of the 
 earth. 
 
 As the general phenomena of the planetary 
 fyftem will be beft underftooJ by an indu>5lion 
 of particulars, I (hould advife the tutor to re- 
 move all the planets but thofe whofe motion he 
 is going to explain ; for inftance, let him now 
 leave only the earth and fun ; place the earth 
 over Libra, and it is plain that the fun will 
 then be transferred by the eye of the fpedator 
 to Aries, in which fign it will appear at the 
 latter end of March : move the earth on in it's 
 orbit to Capricornus, and the fun will appear 
 at Cancer in June, feeming to have moved 
 from T to Id, though it has not ftirred, the 
 real motion of the earth having caufcd the fpec- 
 tator to transfer the fun to all the intermediate 
 points in the heavens, and thus given it an ap. 
 parent morion. Continue to move the earth 
 till it arrives at Aries, and the fun will be feen 
 in Libra in the month of September : movincT 
 the earth on to Cancer, the vifual ray of the 
 fpedlator refers the fun to Capricorn, as it ap- 
 pears in the month of December. Ladly, con- 
 tinue moving the earth, and it will arrive at 
 Kk 433 
 
l8 DESCRIPTION AND USE 
 
 Aries, where we fet out. Thus we have fliewn 
 that it is the motion of the earth which caufes 
 the fun to appear in all the different figns of 
 the zodiac. Cuftom, indeed, has taught us lo 
 fay the fun is in Aries, when it is between us 
 and Aries, and fo of any other fign ; whereas it 
 would have been more proper to fay, that the 
 earth is in Libra. 
 
 To Jheiv why at different times of the year ive fee 
 the heavens decorated with an entire different 
 colled ion of ftars. 
 
 This phenomenon is occafioned by the 
 earth's progreffive or annual motion ; while the 
 earth is traverling his courfe under the vafl 
 concave of fixed ftars, we are gradually carried 
 under the different conflellations. From hence 
 it is evident, that at night when the earth is 
 turned from the fun, we fhall in fuccefTion have 
 the opportunity of viewing from time to time 
 all the ftars in the zodiac, and confequently a 
 different conftellation will prefent itfelf every 
 month. 
 
 Thus, the Pleiades are not vifible in the 
 fummer ; but in the winter the earth is got be- 
 tween the fun and them. Thefe flars are ob- 
 fervable at night, becaufe they are not inter- 
 cepted from our fight by the fun's rays ; and in 
 this manner they appear during the whole 
 
 434 
 
OF PLANE TARIUMS, &C. I9 
 
 winter, only they feem to get more weflerly 
 every night, as the earth moves gradually by 
 them to the eail. To make this ftill more clear, 
 place the earth in the planetarium between the 
 fun and any of the figns, that fide towards the 
 fun will be day, and that towards the fign night : 
 it follows, that at night we are turned tow rds 
 the ftars, which in that fign (fuppofe, as before, 
 the Pleiades in Taurus) will then be confpicuous 
 to us ; but as the fpring approaches, the earth 
 withdraws itfelf from between the fun and the 
 Pleiades, till at length the earth, by it's pro- 
 greflive motion, gets the fun between it and the 
 flars, which then lie hid behind the folar rays : 
 after the fame manner, while the earth per- 
 forms her annual trad:, the fun, which always 
 feems to move the contrary way, darkens, by 
 his fplendor, the other conftellations fucceflively; 
 but the ftars oppofite to thofe hid by the fun, 
 are at night prefented to our view. 
 
 General Phenomena of the Planets. 
 
 Let the tutor now place the earth, Mars, 
 and Venus, on the planetarium ; and as each 
 planet moves with a different degree of velo- 
 city, they are continually changing their rela- 
 tive pofitions. Thus on turning the handle of 
 the machine, he will find, ift, that the earth 
 moves twice as faft as Mars, making two revo- 
 lutions while he makes one ; and Venus, on the 
 
 435 
 
20 DESCRIPTION AND USE 
 
 Other hand, moves much fader than the earth. 
 Secondly, that in each revolution of the earth 
 thefe planets continually change their relative 
 pofitions, correfponding fometimes viih the 
 fame point of the ecliptic, but much oftener 
 with different points. 
 
 To explain the conjunction^ oppofttion, elcngali^n, 
 and other phenomena of the inferior planets. 
 
 I may now proceed to make fome obferva- 
 tions on the motions of Venus, as obfeived in 
 the planetarium. If confidered as viewed from 
 the fun, we fhall find that Venus would appear 
 at one time nearer to the earth than at another ; 
 that fometimes flie would appear in the fame 
 part of the heavens, and at others in oppofite 
 parts thereof. 
 
 As the planets, when feen from the fun, 
 change their pofition with refpeft to the earth, 
 fo do thev alfo, when feen from the earth, 
 change their pofition with refpect to the fun, 
 being fometimes nearer to, at others farther 
 from, and at times in conjundion with him. 
 
 But the conjundtions of Venus or Mercury, 
 feen from the earth, not only happen when they 
 are feen together from the fun, but alfo when 
 they appear to be in oppofition to the folar 
 fpedator. To illuftrate this, bring the earth 
 and Venus to the firfl; point of Capricorn j then 
 436 
 
OF PLANET A RIUMS, &C, 21 
 
 by applying a firing from the fun over Venus 
 and the earth, you will find them to be in con- 
 iundion, or on the fame point of the ecliptic. 
 
 Whereas if you turn the handle till the fun 
 is between Venus and the earth, a fpedator in 
 the fun will fee Venus and the earth in oppofi- 
 tion ; but an inhabitant of the earth will fee 
 Venus not in oppofition to the fun, but in con- 
 junclion with him. 
 
 In the firli conjunction Venus is between 
 the fun and earth ; this is called the inferior 
 conjundion. In the fecond, the fun is fituated 
 between x.\ie earth and Venus j this is called the 
 fuperior conjundion. 
 
 After either of thefe conjundions, Venus 
 will be feen to recede daily from the fun, but 
 never departing beyond certain bounds, never 
 appearing oppofite to the fun ; but when (he is 
 feen at the greateft di (lance from hi in, a line 
 joining her centre with the centre of the earth, 
 will be a tangent to the orbit of Venus. 
 
 To illuftrate this, take off the fun from it's 
 fupport, and the ball of Venus from it's fup- 
 porting (lem ; place the wire, fig. 2, plate XI, 
 fo that the part P may be on the flem that fup- 
 ports the earth, and a fimilar focket, fig. 3, on 
 the pin which fupports the ball of Venus ; the 
 wire F is to lie in a notch at the top of the 
 focket, which has been put upon the fupporting 
 rtem of Venus ; then will the wire reprefent a 
 vifual ray going from an inhabitant of the earth 
 
 437 
 
22 DESCRIPTION AND USE 
 
 to Venus. By turning the handle, you will 
 now find that the planet never departs further 
 than certain limits from the fun, which are 
 called it's greateft elongations, when the wire 
 becomes a tangent to the orbit ; after which, it 
 approaches the fun, till it arrives at either the 
 inferior or fuperior conjunction. 
 
 It will alfo be evident from the inflrument, 
 that Venus, from her fuperior conjundion, 
 when fhe is furthefl: from the earth, to the time 
 of her inferior conjunction, when fhe is nearefl:, 
 fets later than the fun, is feen after fun-fet, and 
 is, as it were, the forerunner of night and dark- 
 nefs. But from the inferior conjunction, till 
 fhe comes to the fuperior one, ihe is always 
 feen well ward of the fun, and mufl: confequently 
 fet before him in the evening, and rife before 
 him in the morning, foretelling that light and 
 day are at hand. 
 
 Bring. Venus and the earth to the begin- 
 ning of Aries, when they will be in conjunc- 
 tion ; and turn the handle for nearly 225 days, 
 and as Venus moves fafter than the earth, fhe 
 will be come to Aries, and have finiflied her 
 courfe, but will not have overtaken the earth, 
 who has moved on in the mean time ; and Ve- 
 nus mufl go on for fome time, in order to over- 
 take her. Therefore, if Venus fhould be this 
 day in conjunction with the fun, in the infe'rior 
 part of her orbit, fhe will not come again to 
 438 
 
OF PLANETARIUMS, &C. 23 
 
 the fame conjundlon till after i year, 7 months, 
 and 12 days. 
 
 It is alfo plain, by infpe6lion of the plane- 
 tarium, that though Venus does always keep 
 nearly at the fame diftance from the fun, yet 
 {he is continually changing her diftance from 
 the earth ; her diftance is greateft when {he is 
 in her fuperior, and leaft when {he is in her 
 inferior conjunQion. 
 
 To explain the phafes, the retrograde, dired, and 
 Jiationary fituations of the planets. 
 
 As Venus is an opake globe, and only {hines 
 by the light {he receives from the fun, that face 
 which is turned towards the fun will always be 
 bright, while the oppofite one will be in dark- 
 nefs ; confequently, if the fituation of the earth 
 be fuch, that the dark fide of Venus be turned 
 towards us, {he will then be invlfible, except 
 file appear like a fpot on the diik of the fun. 
 If her whole illuminated face is turned towards 
 the earth, as it is in her fuperior conjundlon, 
 {he appears of a circular form ; and according 
 to the dift'erent pofitions of the earth and Ve- 
 nus, {he will have different forms, and appear 
 with dilFerent phafes, undergoing the fame 
 changes of form as the moon. Thefe different 
 phafes are feen very plain in this inftrument, as 
 the fide of the planet, which is oppofite to the 
 fun, is blackened ; fo that in any pofition, a line 
 drawn from the earth to the planet, will repre- 
 fent that part of her dilk which is vifible to us. 
 
 439 
 
24 DESCRIPTION AND USE 
 
 The Irregularilies in the apparent motions 
 of the planets, is a fubjeft that this inftrument 
 will fully elucidate ; and the pupil will fiDd that 
 they are only apparent, taking their rile from 
 the fituaiion and motion of the obferver. To 
 illuftrate this, let us fuppofe the above-men- 
 tioned wire, when conneded with Venus and 
 the earth, to be the vifual ray of an obferver on 
 the earth, it will then point out how the mo- 
 tions of Venus appear in the heavens, and the 
 path (he appears to us to defcribe among the 
 fixed ftars. 
 
 Let Venus be placed near her fuperior con- 
 jun£tion, and the inflrument in motion, the 
 wire will mark out the apparent motion of Ve- 
 nus in the ecliptic. Thus Venus will appear 
 to move eaftward in the ecliptic, till the wire 
 becomes a tangent to the orbit of of Venus, in 
 which fituation fhe will appear to us to be (la- 
 tionary, or not to advance at all among the 
 fixed ftars ; a circumftance which is exceeding 
 vifible and clear upon the planetarium. 
 
 Continue turning, till Venus be in her fu- 
 perior conjun£tion, and you will find by the 
 wire, or vifuai ray, that fiie now appears to 
 move backward in the ecliptic, or from eafl to 
 weft, till ftie is arrived to that part where the 
 vifual ray again becomes a tangent to her orbit. 
 In which pofition, Venus will again appear fta- 
 
 440 
 
OF PLANETARIUMS, &C. 
 
 25 
 
 tionary for fome time ; after which (he will 
 commence anew her direct motion. 
 
 Hence, when Venus is in the fuperior part 
 of her orbit, (he is always feen to move direftly, 
 according to the order of the ilgns ; but when 
 fhe is in the inferior part, flie appears to naove 
 in a contrary direction. 
 
 What has been faid concerning the motions 
 of Venus, is applicable to thofe of Mercury j 
 but the conjundions of Mercury with the fun 
 as well as the times of his being dired, fla- 
 lionary, or retrograde, are more frequent than 
 thofe of Venus. 
 
 Of the fuperior planets, as fee?i from the earth. 
 
 If the tutor wiflies to extend his obferva- 
 tions on the inftrument to Mars, he will find 
 by the vifual ray, that Mars, when in conjunc- 
 tion, and when in oppofition, will appear in 
 the fame point of the ecliptic, whether it is 
 feen from the fun or the earth ; and in this 
 fituation only is it's real and apparent place the 
 fame, becaufe then only the ray proceeds as if 
 it came from the center of the univerfe. 
 
 He will obferve, that the dired motion of 
 the fuperior planets is fwifter the nearer it is to 
 the conjunclion, and flower when it is nearer 
 to quadrature with the fun ; but that the retro- 
 grade motion of a fuperior planet is fwifter 
 LI 441 
 
26 DESCRIPTION AND USE 
 
 the nearer it is to oppofition, and flower the 
 nearer it is to quadrature ; but at the time of 
 change from direct to retrograde, it's motion 
 becomes infenfible. 
 
 To prove by the planetarium the truth of the 
 Copernican, and abfurd'ity of the Ptolemaic 
 Jyjlem. 
 
 Of al! the prejudices which philofophy con- 
 tradicts, there is none fo general as that the 
 earth keeps it's place unmoved. This opinion 
 feems to be univerfal, till it is 'correded by 
 inftrudtion, or by philofophical fpeculation. 
 Thofe who have any tinfture of education, are 
 not now in danger of being held by it ; but yet 
 they find at firft; a reluctance to believe that 
 there are antipodes, that the earth is fpherical, 
 and turns round it's axis every day, and round 
 the fun every year. They can recollect the 
 time when reafon ftruggled with prejudice 
 upon thefe points, and prevailed at length, but 
 not without fome efforts.* 
 
 The planetarium gives occular demonftration 
 of the motion of the earth about the fun, by 
 {hewing that it is thus only that the celeflial 
 phenomena can be explained, and making the 
 abfurdity of the Ptolemaic fyftem evident to 
 the fenfes of young people. For this purpofe, 
 
 * Reld's EfTays on the Intelleftual Powers of Man. 
 442 
 
OF PLANETARIUMS, &C, 27 
 
 take off the brafs ball which reprefents the 
 fun, and put on the fmall ivory ball, which 
 accompanies the inftrument in it's place, to 
 reprefent the earth, and place a fmall brafs ball 
 for the fun, on that arm which carries the 
 earth. 
 
 The inflrument in this (late will give an 
 idea of the Ptolemiac fyflem, with the earth 
 immoveable in the center, and the heavenly 
 bodies revolving about in the following order : 
 Mercury, Venus, the fun. Mars, Jupiter, and 
 Saturn. Now, in this difpofition of the plan- 
 ets, feveral circumflances are to be obferved, 
 that are contrary to the real appearances of the 
 celeflial motions, and which therefore prove 
 the falfity of this fyftem. 
 
 It will appear from the inftrument, that on 
 this hypothefis Mercury and Venus could ne- 
 ver be feen to go behind the fun, from the 
 earth, becaufe the orbits of both of them are 
 contained between the fun and the earth ; but 
 thefe planets are feen to go as often behind the 
 fun as before it ; we may, therefore, from 
 hence conclude, that this fyllem is erroneous. 
 
 It is alfo apparent in the planetarium, that 
 on this fcheme thefe planets might be feen in 
 conjunction with, or in oppofition to the fun, 
 or at any diftance from it. But this is con- 
 trary to experience, for they are never feen in 
 oppofition to the fun, or on the meridian of 
 
 443 
 
28 DESCRIPTION AND USE 
 
 London, for inflance, at midnight, nor ever 
 recede foin it beyond certain limits. 
 
 Again, on the Ptolemiac fyflem all the 
 planets would be at an equal diitance from the 
 earth, in all parts of their orbits, and would 
 therefore neceffarily appear always of the fame 
 magnitude, and moving with equal and uni- 
 form velocities in one direction ; circumftances 
 which are known to be repugnant to obferva- 
 tion and experience. 
 
 To rcB'ifj the planetarium, or place the planets 
 in their true fituations, as feen from the 
 fun. 
 
 The fituations of the planets in the heavens 
 are accurately calculated by aftronomers, and 
 publiflied in almanacks appropriated to the 
 purpofe, as the Nautical Almanack, White's 
 Ephemeris, &c. An ephemeris is a diary or 
 daily regifter of the motions and places of the 
 heavenly bodies, fliewing the fituation of each 
 planet at ii o'clock each day. Thefe fituations 
 it exhibits both as feen from the fun, and from 
 the earth ; but as the former, or the heliocen- 
 tric, is the only one of any ufe for this purpofe, 
 we fhall here infert, and explain, fo much of 
 that part of Mr. White's ephemeris, as will 
 enable the pupil to rectify his planetarium. 
 
 444 
 
OF PLANETARIUMS, &C, 
 
 29 
 
 n 
 
 Day 
 
 Lengih 
 
 Helioc. Hclioc. 
 
 Helioc. 
 
 Helio<:. 
 
 heiiuc 
 
 H.;ocl 
 long. 
 
 w 
 
 increas 
 
 of day. 
 
 long. long. 
 
 long. 
 
 long. 
 
 long. 
 
 
 
 
 h y- 
 
 % 
 
 e 
 
 ? 
 
 •J 
 
 I 
 7 
 
 7 4 
 7 24 
 
 14 4^ 
 
 15 8 
 
 27X35, 2.1X1 4 
 
 27 47I 2 42 
 
 27axi6 
 29 57 
 
 'I in, 14 
 17 2 
 
 8,35 
 .8 7 
 
 I .1^ 
 
 26n53 
 
 '3 
 
 7 44 
 
 C5 2S 
 
 27 59 3 
 
 ^8 11; 3 3- 
 28 23 ^ 5 
 
 2.^39 
 
 2t 52 
 
 7 37 
 
 3 51 4 
 
 198 
 
 '5 44 
 
 5 2028 36 
 
 7<> 7 
 
 4-i>:i5 
 
 (25l8 IV 
 
 .6 c 
 
 8 3' 4^22 
 
 16 36' Oji- c 
 
 In the foregoing table, for May, 1790, you 
 have the hehocentric places calculated to every 
 fix days of the month, which is fufficiently ac- 
 curate for general purpofes. Thus, on the 
 19th, you have Saturn in 28 1 1' of Pifces, Ju- 
 piter 3" 37' of Virgo, Mars in 5 20' of Libra, 
 the Earth 28' 36' of Virgo. Venus 7" 7' of Ca- 
 pricorn, and Mercury 4" 1 5' of Virgo ; to which 
 places, on the ecliptic of the planetarium, 
 the feveral planets are to be fet, and they will 
 then exhibit their real fituations, both with re- 
 fpeft to the fun and the earth, for that day. 
 
 To vje the injirument as a tellurian, plate XII, 
 A- '• 
 The fun, the earth, and the moon, are bodies 
 which, from our connexion with them, are fo 
 interefting to us, that it is neceffary to enter 
 into a minute detail of their refpedive pheno- 
 mena. To render this inflrument a tellurian, 
 all the planets are firft to be taken off, the piece 
 of wheel-work A B is to be placed on in their 
 (lead, in fuch a manner, that the wheel c may 
 fall into the teeth that are cut upon the edge of 
 445 
 
30 DESCRIPTION AND USE 
 
 the ecliptic. The milled nut D is then to be 
 fcrewed on, to keep the wheel-work firmly in 
 it's place. It is bed to place this wheel-work 
 in fuch a manner, that the index E may point 
 to the 2 1 fl of June, and then to move the globe, 
 fo that the north pole may be turned towards 
 the fun. 
 
 The inftrument will then fhew, in an ac- 
 curate and clear manner, all the phenomena 
 arifing from the annual and diurnal motion of 
 the earth ; as the globe is of three inches dia- 
 meter, all the continents, feas, kingdoms, &c. 
 may be diflinftly feen ; the equator, the eclip- 
 tic, tropics, and other circles, are very vifible, 
 fo that the problems relative to peculiar places 
 may be farisfaftorily folved. The axis of the 
 earth is inclined to the ecliptic in an angle of 
 66^ degrees, and preferves it's parallelifm during 
 the whole of it's revolution. About the globe 
 there is a circle, to reprefent the terminator, or 
 boundary between light and darknefs, dividing 
 the enlightened from the dark hemifphere. At 
 N O is an hour circle, to determine the time of 
 fun-rifmg orfetting. 
 
 The brafs index G reprefents a central folar 
 ray ; it ferves to fliew when it is noon, or when 
 the fun is upon the meridian at any given place ; 
 it alfo ihews what fign and degree of the eclip- 
 tic on the globe the fun defcribes on any day, 
 snd the parallel it defcribes. 
 446 
 
OF PLANETARIUMS, &C. 3I 
 
 The plane of the terminator H I pafTes 
 through the center of the earth, and is perpen- 
 dicular to the central folar ray. The index E 
 points out the fun's place in the ecliptic ot the 
 inftrument for any given day in the year. 
 
 To explain the changes of feafom by ihc 
 tellurian* 
 
 Before I Ihew how the feafons are ex- 
 plained by the inftrument, it is neceffary to 
 alTume two propofitions : i. That a globular 
 luminous body, fending out parallel rays of 
 light, will only enlighten one half of another 
 globe, and that of courfe will be the hemi- 
 fphere turned towards the luminous body. 
 2. That the earth moves round the fun in fuch 
 a manner, that in all parts of it's orbit it's 
 axis is parallel to itfelf, and has a certain in- 
 clination to the plane of the orbit. Thefe be- 
 ing underftood, the firft thing to be done is to 
 reftify the tellurian ; or, in other words, to put 
 the globe into a pofition fimilar to that of the 
 earth, for any given day. Thus to reftify the 
 tellurian for the 21ft of June, turn the handle 
 till the annual index comes to the given day ; 
 then move the globe by the arm K L, fo that 
 the north pole may be turned towards the fun ; 
 and adjuft the terminator, fo that it may jufh 
 touch the edge of the arftic circle. The globe 
 is then in the fituation of the earth for the 
 
 447 
 
32 DESCRIPTION AND USE 
 
 longeft day in our northern hemifphere, the 
 annua! index pointing to the firft point of 
 Cancer and the sift of June ; bring the meri- 
 dian of London to coincide with the central 
 fo!ar ray, and move the hour circle N O, till 
 the index L points to XII ; we then liavc the 
 fituation of London with refpecl to the longtll 
 day. 
 
 Now, on gently turning the handle of the 
 machine, the point reprefenting London will, 
 by the rotation of the earth, be carried away 
 towards the eaft, while the fun feems to move 
 weftward ; and when London has arrived at the 
 eaftern part of the terminator, the index will 
 point on the hour circle the time of fun-fetting 
 for that day ; continue to turn on, and London 
 will move in the fhaded part of the earth, on the 
 other fide of the terminator, when the index is 
 again at XII, it is midnight at London ; by 
 moving on, London will emerge from the weit- 
 ern fide of the terminator, and the index will 
 point out the time of fun-rifing, the fun at that 
 inftant appearing to rife above the horizon in 
 the eaft, to an inhabitant of London. 
 
 It will be evident by the inflrument, w^hile 
 in this pofltion, that the central folar ray, during 
 the whole revolution of the earth on it's axis, 
 only points to the tropic of Cancer, and that 
 the fun is vertical to no other part of the earth, 
 but thofe who are under this tropic. 
 448 
 
OF PLANETARIUMS, ^C, 33 
 
 By obferving how the terminator cuts the 
 feveral parallels of the globe, we fhall find that 
 all thofe between the northern and fouthern 
 polar circles ("except the equator) are divided 
 unequally into diurnal and nofturnal arches, the 
 former being greatefl: on the north fide of the 
 equator, and the latter on the fouth fide of it. 
 
 In this pofition the northern polar circle is 
 wholly on that fide of the terminator which is 
 nearefl: the fun, and therefore altogether in the 
 enlightened hemifphere, and the inhabitants 
 thereof enjoy a continual day. In the fame 
 manner, the inhabitants of the fouthern polar 
 circle continue in the dark at this time, not- 
 withftanding the diurnal revolution of the 
 earth ; it is the annual motion only which can. 
 relieve them from this fituation of perpetual 
 darknefs, and bring to them the bleflings of 
 day, and the enjoyments of fummer ; while in 
 this ftate the inhabitants in north latitude are 
 neareft to the central folar ray, and confe- 
 quently to the fun's perpendicular beams, and 
 of courfe a greater number of his rays will fall 
 upon any given place, than at any other time; 
 the fun's rays do now alfo pafs through a lefs 
 quantity of the atmofphere, which, together, 
 with the length of the day, and the fliortnefs of 
 the night, are the reafons of the increafe of 
 heat in fummer, together with all it's other 
 delightful effeds. 
 
 M m 449 
 
34 DESCRIPTION AND USE 
 
 While the earth continues to turn round on 
 it's own axis once a day, it is continually ad- 
 vancing from weft to eaft, according to the 
 order of the figns, as is feen by the progrcfs of 
 the annual index E, which points fuccefTively 
 to all the figns and degrees of the ecliptic ; the 
 fun in the mean time feems to defcribe the 
 ecliptic alfo, going from weft to eaft, at the 
 diftance of fix figns from the earth ; that is, 
 when the earth really fets out from the firft 
 point of Capricorn, the fun feems to fet out 
 from the firft point of Cancer, as is plain from 
 the index. 
 
 But as during the annual revolution of the 
 earth, the axis always remains parallel to itfelf, 
 the fituation of this axis, with refped to the 
 fun, muft be continually changing. 
 
 As the earth moves on in the ecliptic, the 
 northern polar circle gets gradually under the 
 terminator, fo that when the earth is arrived 
 at the firft point of Aries, and the annual index 
 is at the firft point of Libra on the 22d of Sep- 
 tember, this circle is divided into two equal 
 parts by the terminator, as is alfo every other 
 parallel circle, and confequently the diurnal 
 and nocturnal arches are equal ; this is called 
 the time of equinox, the days and nights ^re 
 then equal all over the earth, being each of 
 them 12 hours long, as will be feen by the ho- 
 rary index L. The central folar ray G having 
 
 450 
 
OF PLANETARIUMS, &C. ^^ 
 
 fucceflively pointed to all the parallels that 
 may be fuppofed to be between the equator 
 and the tropic of Cancer, is at this period per- 
 pendicular to the inhabitants that live at the 
 equator. 
 
 By continuing to turn the handle, the earth 
 advances in the ecliptic, and the terminator 
 fhews how the days are continually decreafing, 
 and the diurnal arches fhortening, till by de- 
 grees the whole fpace contained by the northern 
 polar circle is on that fide of the terminator 
 which is oppofite to the fun, which happens 
 when the earth is got to the firft point of Can- 
 cer, and the annual index is at the lirft point of 
 Capricorn, on the 2i(tof December. In this 
 (late of the globe, the northern polar circle, 
 and all the country within that fpace, have no 
 day at all ; whilft the inhabitants that live 
 within the fouthern polar circle, being on that 
 ifide of the terminator which is next the fun, 
 enjoy perpetual day. By this and the former 
 fituation of the earth, the pupil will obferve 
 that there are nations to whom a great portion, 
 of the year is darknefs, who are condemned to 
 pafs weeks and months without the benign in- 
 fluence of the folar rays. The central folar 
 ray is now perpendicular to the tropic of Ca- 
 pricorn ; the length of the days is inverfely what 
 it was when the fun entered Cancer, the days 
 being now at their fliortefl:, and the nights 
 
 451 
 
36 DESCRIPTION AND USE 
 
 longefl in the northern hemifphere ; the length 
 of each is pointed out by the horary index. 
 
 The earth being again carried on till it 
 enters Libra, and the fun Aries, we fliall again 
 have all the phenomena of the equinoctial fea- 
 fons. The terminator will divide all the pa- 
 rallels into two equal parts ; the poles will again 
 be in the plane of the terminator, and confe- 
 quently, as the globe revolves, every place from 
 pole to pole will defcribe an equal arch in the 
 enlightened and obfcure hemifpheres, entering 
 into and going out of each exactly at fix o'clock, 
 as (hewn by the hour index. 
 
 As the earth advances, more of the northern 
 polar circle comes into the illuminated hemi- 
 fphere and confequently the days increafe with 
 us, while thofe on the other fide of the equa- 
 tor decreafe, till the earth arrives at the firfl 
 point of Capricorn, the place from which we 
 firfl began to make our obfervations. 
 
 To explain the phenomena that take place in a 
 . parallel) direct ^ and right fphere. 
 
 Takeoff the globe and it's terminator, and 
 put on in it's place the globe which accom- 
 panies the inftrument and which is furnilhed 
 with a meridian, horizon, and quadrant of alti- 
 tude; the edge of the horizon, is graduated 
 from the eafl: and weft, to the north and fouth 
 452 
 
OF PLANETARIUMS, &C. S7 
 
 points, and within thefe divifions are the points 
 of the compafs to the under fide of this hori- 
 zon ; but at 1 8 de_erees from it another circle 
 is affixed, to reprefent the twilight circle ; the 
 meridian is graduated like the meridian of a 
 globe ; the quadrant of altitude is divided into 
 degrees, beginning at the zenith, and finifliing 
 at the horizon. 
 
 1 his globe, if the horizon be differently fet 
 with refped to the folar ray, will exhibit the 
 various phenomena arifing from the fituation 
 of the horizon with refped to the fun, either in 
 a right, a parallel, or an oblique fphere ; or 
 having fet the horizon to any place, you will 
 fee by the central folar ray how long the fun is 
 above or below the horizon of that place, and 
 at what point of the compafs he rifes, his me- 
 ridian altitude, and many other curious parti- 
 culars, of which we fliall give a few examples. 
 
 Set the horizon to coincide with the equa- 
 tor, and place the earth in the firfl: point of 
 Libra ; then will the globe be in the pofition of 
 a parallel fphere, and of the inhabitants of the 
 poles at that feafon of the year, which inha- 
 bitants are reprefcnted by the pin at the upper 
 part of the quadrant of altitude ; the handle 
 being turned round gently, the earth will re- 
 volve upon it's axis, and the folar ray will coin- 
 cide with the horizon, without deviating in the 
 leafl: to the north or fouth ; fliewing, that on 
 
 453 
 
38 DESCRIPTION AND USE 
 
 the 2 1 ft of March the fun does not appear to 
 rife or fet to the terreftrial poles, but paffes 
 round through all the points of the compafs, 
 the plane of the horizon bifeding the fun*s 
 di(k. 
 
 Now place the horizon fo that it may coin- 
 cide with the poles, and the pin reprefenting 
 an inhabitant be over the equator, the globe in 
 this pofition is faid to be in that of a right 
 fphere ; the equator, and all the parallels of la- 
 titude, are at right angles, or perpendicular to 
 the horizon ; by turning the handle till the 
 earth has completed a year, or one revolution 
 about the fun, we fhall perceive all the folar 
 phenomena as they happen to an inhabitant of 
 the equator ; which are, i. That the fun rifes 
 at fix, and fets at fix, throughout the year, fo 
 that the days and nights there are perpetually 
 equal. 2. That on the 21ft of March, and 22d 
 of September, the fun is in the zenith, or exact- 
 ly over the heads of the inhabitants. 3. That 
 one half of the year, between March and Sep- 
 tember, the fun is every day full north, and the 
 other half, between September and March, is 
 full fouth of the equator, his meridian altitude 
 being never lefs than 66^ degrees. 
 
 If the pin reprefenting an inhabitant be 
 ROW removed out of the equator, and fet upon 
 any place between it and the poles, the horizon 
 will not then pafs through either of the poles, 
 
 454 
 
OF PLANETARIUMS, &C» 39 
 
 nor coincide with the equator, but cut it 
 obliquely, one half being above, the other half 
 below the horizon j the globe in this ftate is 
 faid to be in that of an oblique fphere, of which 
 there are as many varieties as there are places 
 between the equator and either pole. But one 
 example will be fufficient ; for whatever appear- 
 ance happens td one place, the fame, as to kind, 
 happens to every other place, differing only in 
 degree, as the latitudes differ. Bring the pin, 
 therefore, over London, then will the horizon 
 reprefent the horizon of London, and in one 
 revolution of the earth round the fun, we fhall 
 have all the folar appearances through the four 
 feafons clearly exhibited, as they really are in 
 nature ; that is, the earth (landing at the firfl 
 degree of Libra, and the fun then entering into 
 Aries, the meridian turned to the folar ray, and 
 the hour index fet to XII, you will then have 
 the globe (landing in the fame pofition to- 
 wards the fun, as our earth does at noon on the 
 2 1 ft of March. If the handle be turned round, 
 when the folar ray comes to the weftern edge 
 of the horizon, the hour index will point to VI, 
 which (liews the time of fun-fetting ; London 
 then paiTes into, and continues in darknefs, till 
 the hour index having paffed over XII hours, 
 comes again to VI, at which time the folar ray 
 gains the eaftern edge of the horizon, thereby 
 defining the time of fun-rifmg ; fix hours aftcr- 
 
 455 
 
40 DESCRIPTION AND USE 
 
 wards the meridian again comes to the folar ray, 
 and the hour index points to XII, thereby evi- 
 dently demonftrating the equality of" the day 
 and night, when the fun is in the equino(f^iaI. 
 You may then alfo obferve, that the fun riles 
 due eaft, and fets due well. 
 
 Continuing to move the handle, you will 
 find that the folar ray declines from the equator 
 towards the north, and every day at noon rifes 
 higher upon the graduations of the meridian 
 than it did before, continually approaching to 
 London, the days at the fame time growing 
 longer and longer, and the fun rifmg and fet- 
 ting more and more towards the north, till the 
 2 1 ft of June, when the earth gets in the firfl 
 degree of Capricorn, and the fun appears in the 
 tropic of Cancer, rifmg about 40 minutes pad 
 III in the morning, and fetting about 20 min. 
 paft VIII in the evening ; and after continuing 
 about feven hours in the nether hemifphere, 
 appears rifing in the north-eaft, as before. 
 From the 2 id of June to the 22d of September, 
 the fun recedes tothe fouth, and the days grad- 
 ually decreafe to the autumnal equinox, when 
 they again become equal. 
 
 During the three fucceeding months, the 
 fun continues to decline towards the fouth pole, 
 till the 2 1 ft of December, when the fun enters 
 the tropic of Capricorn, rifing to the fouth-eaft 
 point of the compafs about 20 minutes paft 
 
 45^ 
 
OF PLANETARIUMS, &C. 41 
 
 VIII in the morning, and fetting about 40 min- 
 utes part III in the evening, at the fouth-weft 
 point upon the horizon ; after which, the fun 
 continues in the dark hemifphere for 17 hours, 
 and then appears again in the fouth-eall as be- 
 fore. From this chill foKtice the fun returns 
 towards the north, and the days continually 
 increafe in length till the vernal equinox, when 
 all things are reftored in the fame order as at 
 the beginning. 
 
 Thus all the varieties of the feafons, the 
 time of fun-rifing and fetting, and at what 
 point of the compafs, as alfo the me idian alti- 
 tude and declination every day of the year, 
 and duration of twilight, and to what place the 
 fun is at any time vertical, are fully exemplified 
 by this globe and it*s apparatus. 
 
 Before we quit the phenomena particularly 
 arifing from the motion and pofition of the 
 earth, let the globe, with the meridian and 
 horizon, be removed, and the ivory ball which 
 fits upon a pin be placed thereon, to reprefent 
 the earth. 
 
 As the axis of this globe fta nds perpendicular 
 to the plane to the ecliptic, you will find that 
 the folar ray continually points to the equator 
 of this little ball, and will never deviate to the 
 north or fouth j though by turning the handle, 
 the ball is made to complete a revolution round 
 the fun. This fhews that the earth in this po- 
 Nn 457 
 
42 DESCRIPTION AND USE 
 
 fition would have the days and nights equal in 
 every part of the globe, all the year long ; there 
 "would have been no difference in the climates 
 of the earth ; no diftin^lions of feafons ; an eter- 
 nal funimer, or never-ceafing winter, would 
 have been our portion ; an unvaiied famcnefs, 
 that would have limited inquiry, and fatiaied 
 curiofity ; and that the variety of the feafons is 
 owing to it's axis being inclined to the plane of 
 it's orbit. 
 
 An explanation of the caufes of the vicif- 
 fitudes of the feafons, fo naturally introduces 
 the following refledions of Mr. Cowper, in his 
 Winter's Walk, that I hope they will not be 
 deemed impertinent, either by the tutor or 
 his pupil. 
 
 What prodigies can power divine perform 
 More grand than it produces year by year, 
 And all in fight of inattentive man? 
 Familiar withth' effcft we fliglit the canfe, 
 And, in the conftancy of nature's courfe, 
 The regular return of genial months, 
 And renovation of a faded world, 
 See nought to wonder at. Should God again, 
 As once in Gibcon, interrupt the race 
 Of the undeviating and punctual fun, 
 How would the world admire! but fpeaks it kTs 
 An agency divine, to make him know 
 His moment went to fink, and when to rife, 
 Age after age, than to arreft his courfe ? 
 All we behold is miracle ; but feen 
 So duly, all is miracle in vaiu. 
 458 
 
Of planetariums, &c, 43 
 
 Where now the vital energy that moved, 
 
 While fummcr was, the pure and fubtle lymph 
 
 Through th* impreceptibe meand'ring veins 
 
 Of leaf and flowi;r ? It fleeps, and tli' icy touch 
 
 Of unprolific winter has imprefs'd 
 
 A cold ftagnation on th' intelline tide ; 
 
 But let the months go round, a few fliort months, 
 
 And all fliall be rcftor'd. Tiiefe naked ftioots, 
 
 Barren as lances, among which the wind 
 
 Makes wintry mufic, fighing as it goes. 
 
 Shall put their graceful foliage on again ; 
 
 And more afpiring, and with ampler fpread, 
 
 Shall boaft new charms, and more than they have loft. 
 
 And all this uniform, uncoulour'd fcene 
 
 Shall be difmantled of it's fleecy load, 
 
 And flufli into variety again, 
 
 From dearth to plenty, and from death to life, 
 
 Is nature's progrefs when (he ledlures man 
 
 In heavenly truth ; evincing, as flie makes 
 
 The grand tranfition, that there lives and works 
 
 A foul in all things, and that foul is God. 
 
 The beauties of the wildernefs are his. 
 
 That makes fo gay the folitary place. 
 
 Where no eyes fees them. And the fairer form!«. 
 
 That cultivation glories in, are his. 
 
 He fets the bright procellion on it's way. 
 
 And marfhals all the order of the year. 
 
 He feeds the fccret fire 
 By which the mighty procefs is maintain'd : 
 Who fleeps not, is not weary ; in whofe fight 
 Slow circling ages are as tranfient days ; 
 W^hofe work is without labour ; whofe defigns 
 No flaw deforms, no difficulty thwarts ; 
 And whofe beneficence no change exhaufts. 
 
 459 
 
44 DESCRIPTION AND USE 
 
 Of the Lunarium, Fig. 2, Plate XII. 
 
 Having thus illuflrated the phenomena, 
 which arife particularly from the inclination 
 of the earth's axis to the plane of the ecliptic, 
 from it's rotation round it's axis, and revo- 
 lution round the fun ; I now proceed to ex- 
 plain, by this inftrument, the phenomena of the 
 moon. But in order to this, it will be necef- 
 fary to fpeak firft of the inftrument, which is 
 put in motion, like the preceding one, by the 
 teeth on the fixed wheel ; it is alfo to be 
 placed upon the fame focket as the tellurian, 
 and confined down by the fame milled nut. 
 
 The floping ring P Q^reprefents the plane 
 of the moon's orbit, or path, round the earth ; 
 fo that the moon in her revolution round the 
 earth does not move parallel to the plane of the 
 ecliptic, but on this inclined plane ; the two 
 points of this plane, that are conne£led by the 
 brafs wire, are the nodes, one of which is 
 marked a, for the afcending node, the other 
 ?5 for the defcending node. The moon is 
 therefore fometimes on the north, and fome- 
 times on the fouth fide of the ecliptic, which 
 deviations from the ecliptic are called her 
 north or fouth latitude ; her greateft deviation, 
 which is when fhe is at her higheft and lowefl 
 points, called her limits, is 5 deg. i8min. ; this 
 460 
 
 ^ 
 
OF PLANETARIUMS, ^C. 45 
 
 with all the other intermediate degrees of lati- 
 tude, are engraved on this ring, beginning at 
 the nodes, and numbered both ways from them. 
 At each fide of the nodes, and at about 18 de- 
 grees diflant from them, we find this mark ©» 
 and at about 12 degrees this D, to indicate 
 that when the full moon is got as far from the 
 nodes as the mark ]>, there can be no eclipfe of 
 the moon, nor any eclipfe of the fun; when 
 the new moon has paffed the mark o, thefe 
 points are generally termed the limits of 
 eclipfes. The nodes of the moon do not re- 
 main fixed at the fame point of the ecliptic, 
 but have a motion contrary to the order of the 
 figns. 
 
 T V is a fmall circle parallel to the ecliptic ; 
 it is divided into 12 figns, and each fign into 
 30 degrees; this circle is moveable in it*s 
 focket, and is to be fet by hand, fo that the 
 fame fign may be oppofite to the fun, that is 
 marked out by the annual index. Thefe figns 
 always keep parallel to themfelves, as they go 
 round the fun ; but the inclined plane with it*s 
 nodes go backwards, fo that each node recedes 
 through all the above figns in about i 9 years. 
 R S is a circle, on which are divided the days 
 of the moon's age ; X Y is an ellipfis, to repre- 
 fent the moon's elliptical orbit, the direct mo- 
 tion of the apogee, or the line of the apfides, 
 with the fituation of the elliptical orbit of the 
 461 
 
46 DESCRIPTION AND USE 
 
 moon, and place of the apogee in the ecliptic 
 at all times. 
 
 To rcdify the lunarlum. 
 
 Set the annual index on the larf, 
 
 to the firfl: of Capricorn ; then turii . 
 
 with the moon's fignr upon ir, until \\\q be- 
 ginning of Capricorn pcijits direftly at the fun ; 
 turn the handle till the annual index comes t.-> 
 the firll: of January; then find the place of the 
 north node in an ephemeris, to which place 
 among the moon's fignp, fet thi nr-rfh node of 
 her inclined orbit, by turning it ti;lit is in it's 
 proper place in the circle of figr.s ; let the 
 moon to the day of her age. 
 
 General Phenomena of the Moon. 
 
 Having reftified the lunarlum for ufe, on 
 putting it into motion it will be evident, 
 
 1. Ihat the moon, by the mechanifra of the 
 inftrument, always moves in an orbit inclined 
 to that of the ecliptic, and confequently in an 
 crbit analogous to that in which the moon 
 moves in the heavens. 
 
 2. That file moves from weft to eaft. 
 
 3. That the white or illuminated face of the 
 moon is always turned towards the fun. 
 
 4. That the nodes have a revolution con- 
 
 462 
 
OF PLANETARIUMS, &C. 47 
 
 trary to the order of the figns, that is, from 
 Aries to I'^ifces ; that this revolution is perform- 
 ed in about nineteen years, as in nature. 
 
 5. That the moon's rotation upon her axis 
 is effeded and completed in about 27J- days, 
 whereas it is 29^ days from one conjunction 
 with the fun to the next. 
 
 6. That every part of the moon is turned 10 
 the fun, in the fpace of her monthly or periodic 
 revolution. 
 
 To be more particular. On turning the 
 handle, you will obferve another motion of the 
 earth, which has not yet been fpoken of, 
 namely, it's monthly motion about the com- 
 mon center of gravity between the earth and 
 moon, which center of gravity is rcprefcnted 
 by the pin Z. From hence we learn, that it is 
 not the center of the earth Vv^hich defciibes what 
 is called the annual orbit, but the center of gra- 
 vity between the earth and moon, and that the 
 earth has an irregular, vermicular, or fpiral mo- 
 tion about this center, fo that it is every month 
 at one time nearer to, at another further from 
 the fun. It is evident from the inftrument, 
 that the moon does not refrard the center of 
 
 o 
 
 the earth, but the center of gravity, as the 
 center ot her proper motion ; that the center 
 of the earth is furtheft from the fun at nev/ 
 moon, and neareft at the full moon ; that in 
 the quadratures the monthly parallax of the 
 463 
 
48 DESCRIPTION AND USE 
 
 earth is fo fenfible, as to require a particular 
 equation in aftronomical tables. Thefe parti- 
 culars were firft applied to the orrery, by the 
 late ingenious Mr. Benjamin Martin. 
 
 To explain the phafes of the moon. 
 
 The moon alTumes different phafes to us, 
 I. on account of her globular figure; 2. on ac- 
 count of the motion in her orbit, between the 
 earth and the fun, for whenever the moon is 
 between the earth and the fun, we call it new 
 moon, the enlightened part being then turned 
 from us ; but when the earth is between the 
 fun and the moon, we then call it full moon, 
 the whole of the enlightened part being then 
 turned towards us. 
 
 The phafes of the moon are clearly exhi- 
 bited in this inftrument ; for we here fee that 
 half which is oppofite to the fun is always dark, 
 while that which is next to the fun is white, to 
 reprefent the illuminated part. Thus, when it 
 is new moon, you will fee the whole white part 
 next the fun, and the dark part turned towards 
 the earth, (hewing thereby it's difappearance, 
 or the time of it's conjunction and change : on 
 turning the handle, a fmall portion of the white 
 part will begin to be feen from the earth, which 
 portion will increafe towards the end of the 
 7th day, when you will perceive that half of 
 the light, arid half of the dark fide, is turned 
 464 
 
OF PLANETARIUMS, &c, 49 
 
 towards the earth, thus illuftrating the appear- 
 ance of the moon at the firfl quarter. From 
 hence the h'ght fule will continually fliew it- 
 felf more and more in the gibbous form, till at 
 the end of fourteen days the whole white fide 
 will be turned towards the earth, and the dark 
 fide from it, the earth now (landing in a line 
 between the fun and moon ; and thus the in- 
 ftrument explains the oppofition, or full moon. 
 On turning the handle again, fome of the 
 fhaded part will begin to turn towards the 
 earth, and the white fide to turn away from it, 
 decreafing in a gibbous form till the laft quar- 
 ter, when the moon will appear again as a cref- 
 cent, which (he preferves till (he has attained 
 another conjunftion. 
 
 In this lunarium the moon has always the 
 fame face or (ide to the earth, as is evident from 
 the fpots delineated on the furface of the ivory 
 ball, revolving about it's axis in the courfe of 
 one revolution round the earth ; in confequence 
 of which the light and dark parts of the moon 
 appear permanent to us, and the phafes are 
 (hewn as they appear in the heavens. 
 
 The tutor will be enabled by this inftru- 
 ment to explain fome other circumftances to 
 his pupil ; namely, that as the earth turnsround 
 it's axis once in 24 hours, it muft in that time 
 exhibit every part of it's furface to the inhabi- 
 
 Oo 465 
 
50 DESCRIPTION AND USE 
 
 tants of the moon, and therefore it's luminous 
 andvOpake parts will be feen by them in con- 
 ftant rotation. As that half of the earth which 
 is oppofed to the fun is always dark, the earth 
 will exhibit the fame phafes to the lunarians 
 that we do to them, only in a contrary order, 
 that when the moon is new to us, we fhall be 
 full to them, and vice verfa. But as one hemi- 
 fphere only of the moon is ever turned to- 
 wards us, it is only thofe that are in this 
 hemifphere who can fee us ; our earth will ap- 
 pear to them always in one place, or fixed in 
 the fame part of the heavens : the lunarians in 
 the oppofite hemifphere never fee our earth, nor 
 do we ever view that part of the moon which 
 they inhabit. The moon's apparent diurnal 
 motion in the heavens is produced by the daily 
 revolution of our earth. 
 
 If we confider the moon with refpect to 
 the fun, the inftrument fhews plainly that one 
 half of her globe is always enlightened by the 
 fun ; that every part of the lunar ball is turned 
 to the fun, in the fpace of her monthly or pe- 
 riodic revolution ; and that therefore the length 
 of the day and night in the moon is always the 
 fame, and equal to 14^- of our day. When the 
 fun fets to the lunarians in that hemifphere 
 next the earth, the terreftrial moon rifes to 
 them, and they can therefore never have any 
 
 466 
 
OF PLANETARIUMS, &C. 5I 
 
 dark night ; while thofe on the other henii- 
 fphere can have no h'ght by night, but what the 
 ftars afford. 
 
 Of the periodical and fynodical month. 
 
 The difference between the periodical 
 month, in which the moon exaclly dcfcribes 
 the echptic, and the fynodical, or time be- 
 tween any two new moons, is here rendered 
 very evident. To (hew this difference, obferve 
 at any new moon her place in the ecliptic, 
 then turn the handle, and when the moon has 
 got to the fame point in the ecliptic, you will 
 fee that the dial fliews 2y\ days, and the moon 
 has finifhed her periodic revolution. But the 
 earth at the fame time having advanced in it's 
 annual path about 27 degrees of the ecliptic, 
 the moon will not have got round in a dired 
 line with the fun, but will require 28 days and 
 4 hours more, to bring it into conjundion with 
 the fun aorain. 
 
 o 
 
 Of edipfes of the fun and moon. 
 
 There is nothing in aftronomy more worthy 
 of our contemplation, nor any thing more 
 fublime in natural knowledge, than rightly to 
 comprehend thofe fudden obfcurations of the 
 heavenly bodies that are termed eclipfes, and 
 467 
 
52 DESCRIPTION AND USE 
 
 the accuracy with which they are now fore- 
 told. " One of the chief advantages derived 
 by the prefent generation, from the improve- 
 ment and difFufion of philofophy, is deHvery 
 from unnecefTary terror, and exemption from 
 falfe alarms. 1 he unufual appearances, whe- 
 ther regular or accidental, which once fpread 
 confternation over ages of ignorance, are now 
 the recreations of inquifitive fecurity. The 
 fun is no more lamented when it is eclipfed, than 
 when it fets ; and meteors play their corrufca- 
 tions without prognoflic or predidion." 
 
 I have already obferved, that the fun is 
 the only real luminary in the folar fyftem, and 
 that none of the other planets emit any light 
 but what they have received from the fun; 
 that the hemifphere which is turned towards 
 the fun is illuminated by his rays, while the 
 other fide is involved in darknefs, and projeds 
 a fhadow, which arifes from the luminous 
 body. 
 
 When the fliadow of the earth falls upon 
 the moon, it caufes an eclipfe of the moon ; 
 when the fliadow of the moon falls upon the 
 earth, it caufes an echpfe of the fun. 
 
 An eclipfe of the moon, therefore, never 
 happens but when the earth's opake body in- 
 terpofes between the fun and the moon, that is, 
 at the full moon ; and an eclipfe of the fun 
 never happens but when the jnoon comes in a 
 468 
 
OF PLANETARIUMS, &C, 50 
 
 line between the earth and the fun, that is, at 
 the new moon. 
 
 From what we have already feen by the in- 
 ftrument, it appears that the moon is once 
 every month in conjundion, and once in op- 
 pofition ; from hence it would appear, that 
 there ought to be two eclipfes, one of the fun, 
 the other of the moon, every month ; but this 
 is not the cafe, and for two reafons, firfl:, be- 
 caufe the orbit of the moon is inclined in an 
 angle of about 5 degrees to the plane of the 
 ecliptic ; and fecondly, becaufe the nodes of 
 this orbit have a progrefTive motion, which 
 caufes them to change their place every luna- 
 tion. Hence it often happens, that at the 
 times of oppofition or conjunclion, the moon 
 has fo much latitude, or, what is the fame 
 thing, is fo much below or above the plane of 
 the ecliptic, that the light of the fun will in 
 the firfl: cafe reach the moon, without any ob- 
 flacle, and in the other the earth ; but as the 
 nodes are not fixed, but run fucceffively through 
 all the figns of the ecliptic, the moon is often, 
 both at the times of conjunction and oppo- 
 fition, in or very near the plane of the eclip- 
 tic ; in thefe cafes an eclipfe happens, either of 
 the fun or moon, according to her fituation. 
 The whole of this is rendered clear by the lu- 
 narium, where the wire projeding from the 
 earth fhews when the moon is above, below, 
 
 469 
 
54 DESCRIPTION AND USE 
 
 or even with the earth, at the times of conjunc- 
 tion and oppofition, and thus when there will 
 be, or not, any eclipfes. 
 
 The diftance of the moon from the earth 
 varies fenfibly with refped to the fun ; it does 
 not move in a circular, but in an elUptic orbit 
 round us, the earth being at one of the foci of 
 this curve.* The longer axis oF the lunar or- 
 bit is not always directed to the fame point of 
 the heavens, but has a movement of it's own, 
 which is not to be confounded with that of the 
 nodes ; for the motion of the laft is contrary to 
 the order of figns, but that of the line of apfides 
 is in the fame direction, and returns to the 
 fame point in the heavens in about nine years. 
 This motion is illuftrated in the lunariura by 
 means of the brafs ellipfis X Y, which is car- 
 ried round the earth in little lefs than nine 
 years : thus (hewing the fituation of the ellip- 
 tical orbit of the moon, and the place of the 
 apogee in the ecliptic. 
 
 Thofe who wifti to extend the application 
 of the inftrument further, may have an appa- 
 ratus applied to it for explaining the Jovian 
 and Saturnian fyftems, illuftrating the motion 
 
 * That point of her orbit wherein fhe is neareft the earth 
 i<; called her psn^ee ; the oppofite point, in which fhe is fartheft 
 off", is called her apogee. Thcfe two points are called her 
 npfidesj the apogee is the higher, the perigee the lower 
 apfis. 
 
 470 
 
OF PLANETARIUMS, &C. ^j 
 
 of their fatellites, and of the ring of Saturn. 
 But as this application would extend the price 
 of the inftrunient beyond the reach of mofl: 
 purchafers, I have thought it would be unne- 
 ceffary to defcribe them ; the more fo, as the 
 phenomena they are intended to explain are 
 accurately and clearly defcribed in feveral intro- 
 dudory works of aftronomy. 
 
 Having furveyed and endeavoured to illuf- 
 trate the general phenomena of the heavens, let 
 us turn the mental eye towards our Lord, who 
 hath made all things in heaven and earth, and 
 whofe tender care is over all. 
 
 " Innumerable worlds flood forth at thy 
 command, and by thy word they are filled 
 with glorious works. 
 
 " Who can comprehend the boundlefs uni- 
 verfe ? or number the ftars of heaven ? 
 
 " Amidfl: them thou hafl: provided a dwelling 
 for man, that he might praife thy name. 
 
 " The fun fhineth, and is very glorious, and 
 we rejoice in the light thereof. 
 
 " We admire it's brightnefs, and perceive 
 it's greatnefs ; and^our earth vaniflies in com- 
 parifon with it. 
 
 " Many worlds are nouriftied by it, and it's 
 glory is great. By it's influence the earth is 
 cloathed with plenty, and the habitation of man 
 rendered exceeding beautiful. 
 
^6 DESCRIPTION AND USE, £i?C. 
 
 " Yet what is this amidft thy works ? is it 
 not as a point, and as nothing in the firmament 
 of heaven ? 
 
 " What then is man, that thou art mindful 
 of him, or the fon of nian, that thou vifiteft 
 him ? 
 
 " Thy power is circumfcribed by no bounds, 
 both great and fmall are aUke unto thee. 
 
 " From the fun in the firmament of heaven, 
 to the fand on the fea-fhore, all is the operation 
 of thy hand. 
 
 " From the cherubim and feraphim which 
 fland before thee, to the worm in the bowels of 
 the earth, all living creatures receive of thee 
 what is good and expedient for them."* 
 
 Praife then the Lord, O my foul, praife his 
 name for ever and ever. 
 
 * See " Hymns to the Supreme Being, in imitation of the 
 Eaftern Songs." London, 1780. 
 
 472 
 
( 57 } 
 
 ESSAY IV. 
 
 AN 
 
 INTRODUCTION 
 
 l^ractical 9iftxonomv^ 
 
 THERE is no part of mathematical fclence 
 more truly calculated to intereft and fur- 
 prize mankind, than the meafurement of the 
 relative pofitions and distances of inaccejjlble 
 objeds. 
 
 To determine the dijiance of a fliip feen on 
 a remote fpot of the unvaried face of the ocean, 
 to afcertain the height of the clouds and me- 
 teors which float in the invifible fluid above 
 our heads, or to fliew with certainty the di- 
 mcnfions of the fun, and other bodies, in the 
 heavens, are among the numerous problems 
 which to the vulgar appear far beycnd the reach 
 of human art, but which are nevcrthelefs truly 
 refolved by the incontrovertible principles of the 
 mathematics, 
 
 P P 473 
 
^8 INTRODUCTION TO 
 
 Thefe principles, fimple in themfelves, and 
 eafy to be underftood, are applied to the con- 
 ftruclion of a variety of inflruments ; and the 
 following pages contain an account of their ufe 
 in the quadrant and the equatorial. 
 
 The pofition of any objed, with regard to a 
 fpeftator, can be confidered in no more than 
 two ways ; namely, as to it^s diftance^ or the 
 length of a line fuppofed to be drawn from the 
 eye to the objeft ; and as to it* s diredioii^ or the 
 fituation of that line with refpeft to any other 
 lines of direction ; or,- in other words, whether 
 it lies to the right or left, above or below thofe 
 lines. The firft of thefe two modes bears re- 
 lation to a line abfolutely confidered, and the 
 fecond to an ajigle. It is evident that the dif- 
 tance can be diredly come at by no other 
 means than by meafuring it, or fucceffively ap- 
 plying fome known meafure along the line in 
 queftion ; and therefore, that in many cafes the 
 diftance cannot be diredlly found ; but the pofi- 
 tion of the line, or the angle it forms, with 
 fome other aflumed line, may be readily afcer- 
 tained, provided this lad line do likewife ter- 
 minate in the eye of the fpe6lator. Now the 
 •whole artifice of meafuring inaccellible dif- 
 tances confifts in finding their lengths, from 
 the confideration of angles, obferved about 
 fome other line, whofe length can be fub- 
 
 474 
 
PRACTICAL ASTRONOMY. 59 
 
 mitted to actual menfuration. How this is 
 done, I fhall proceed to flievv. 
 
 Every one knows the form of a common 
 pair of compafl'es. If the legs of this inftru- 
 ment were mathematical lines, they would 
 form an angle greater or lefs, in proportion to 
 the fpace the points would have pafl'ed through 
 in their opening. Suppofe an arc of a circle 
 to be placed in fuch a manner, as to be pafled 
 over by thefe points, then the angles will be in 
 proportion to the parts of the arc palled over ; 
 and if the whole circle be divided into any 
 number of equal parts, as for example 360, the 
 number of thefe comprehended between the 
 points of the compafl'es, will denote the mag- 
 nitude of the angle. This is fufficiently clear; 
 but there is another circumdance which begin- 
 ners r.re not often fufficiently aware of, and 
 which therefore requires to be well attended 
 to : it is, that the angle will be neither en- 
 larged nor diminifned by any change in the 
 length of the legs, provided their pofltion re- 
 mains unaltereo ; becaufe it is the inclination 
 of the legs, (and not their length,) or the fpace 
 between them, which conftitutes the angle. 
 So that if a pair of compaflcs, with very long 
 legs, were opened to the fame angle as another 
 fmaller pair, the intervals between their ref- 
 peOive points would be very different, but 
 the number of degrees on the circles, fuppofcd 
 475 
 
6o INTRODUCTION TO 
 
 to be applied to each, would be equal, becaufe 
 the degrees themfelves on the fmaller circle 
 would be exactly proportioned to the (hortnefs 
 of the legs. This property renders the ad- 
 meafurement of angles vc-y eafy, becaufe the 
 diameter of the meafuring circle may be varied 
 at pleafure, as convenience requires. 
 
 In practice, however, the magnitude of in- 
 flruments is limited on each fide. If they are 
 made very large, they are difficult to manage ; 
 and their weight, bearing a high proportion to 
 their ftrength, renders them liable to change 
 their figure, by bending, when their pofition 
 is altered : but, on the contrary. If they are very 
 fmall, the errors of conflrudlion and graduation 
 amount to more confiderable parts of the divi- 
 fions on the limb of the inftrument. 
 
 General Principles of Calculation. 
 
 Before we proceed any further, I fliall 
 nightly notice the general principles of the 
 calculations we are going to ufe. 
 
 Plane trigonopietry is the art of meafuring 
 and computing the fides of plane triangles, or 
 of fuch whofc fides are right lines. 
 
 In mod cafes of pradtice, it is required to 
 find lines or angles whofe adlual admeafure- 
 ment is difficult or impradlicable. Thefe ma- 
 thematicians teach us to difcover by the rela- 
 476 
 
PRACTICAL ASTRONOMY. 6l 
 
 tion they bear to other given lines or angles, and 
 proper methods of calculation. 
 
 Finding the comparifon of one right line 
 with another right line, more eafy than the 
 comparifon of a right line with a curve ; they 
 meafure the quantities of the angles not by the 
 arc itfelf, which is defcribed on the angular 
 point, but by certain lines defcribed about that 
 point. 
 
 If any three parts of a triangle are known, 
 the remaining unknown parts may be found 
 either by conjiru^ion or by calculation. 
 
 If two angles of a triangle are known in de- 
 grees and minutes, the third is found by fubtrac- 
 ting their fum from i So degrees; but if the 
 triangle be right-angled, either angle in de- 
 grees, taken from 90 degrees, gives the other 
 angle. 
 
 Before the required fide of a triangle can be 
 found by calculation, it's oppofite angle muft be 
 given or found. 
 
 The required part of a triangle mufl: be the 
 lafl: of four proportionals, written in order one 
 under the other, whereof the three firft: terms 
 are given or known. 
 
 Againft the three firft terms of the propor- 
 tion, are to be written the correfponding num- 
 bers taken from tables which have been con- 
 ftrufted to facilitate calculation. 
 
 477 
 
62 INTRODUCTION TO 
 
 Thefe tables are called logarithms ; and arc " 
 fo contrived, that multiplicaiioti is performed by 
 addition, arid divifion by fubtradiom 
 
 If the value, then, of the firfl: term of your 
 proportion be taken from the fum of the lecond 
 and third, you obtain the value of the fourth, 
 or quantity required ; becaufe the addition and 
 fubtradion of logarithms correfponds with 
 the multiplication and divifion of natural num- 
 bers. 
 
 To avoid even the fubtraction of the firil 
 term, when radius is not one of the propor- 
 tionals, fome chufe to add the aritbmetical com- 
 flemeni. 
 
 To find the arithmetical complement of a lo- 
 garithm, begin at the left hand, and write down 
 what each figure wants of 9, and what the laH: 
 figure wants of 10. The number thus found is 
 to be added to the fecond and third values ; the 
 fum, rejecting the borrowed index, is the tab- 
 ular number cxpreffing the quantity requir- 
 ed : thus the arithmetical complement of 
 2.6963564 is 7.3036436. 
 
 To find the logarithm of a given number. 
 Here you mud remember that the integral part 
 of a logarithm is called it's index, becaufe it 
 denotes the number of figures in the natural 
 number anfwering to the logarithm. The 
 decimal part of every logarithm belongs equally 
 
 478 
 
PRACTICAL ASTRONOMY. 
 
 63 
 
 to a whole number, a mixed number, or a de- 
 cimal number ; that is, they are exprefled by 
 the fame figures, in the fame order, but the 
 index varies according to the value of the ex- 
 prelTion. The index of a logarithm is always 
 an unit lefs than the number of figures in the 
 integer number, of which it is the logarithm. 
 
 Hence the following general rule for find- 
 ing the index of a logarithm. To the left of 
 the logarithm, write that figure or figures 
 which expreifes the diflance from unity, of the 
 highefl place digit in the given number, reck- 
 oning the units place o, the next place i, the 
 next to that 2, the next to that 3, &c. 
 
 By attending to the following example, it 
 will be eafy for you to find the logarithm of a 
 given number, and the number correfponding 
 to a given logarithm. 
 
 Thus let the number be 7854. One column 
 gives the decimal part ; the next the logarithm 
 completed with the indexes. 
 
 Number. 
 
 7854 
 
 785.4 
 
 78.54 
 
 7.854 
 
 0.7854 
 
 C. 07854 
 
 Decim. Part. 
 
 0.895091 
 0.895091 
 0.895091 
 0.895091 
 0.895091 
 0.895091 
 
 Complete Log. 
 
 3.895091 
 2.895091 
 1. 895091 
 0.895091 
 1.895091 
 2.895091 
 
 479 
 
64 INTRODUCTION TO 
 
 Tables of logarithms are alfo conftrucled for 
 fines, tangents, &c. of an arc : thefe are to be 
 taken out from the tables, according to their 
 refpcdlive value. 
 
 Spherical trigonometry is the fcience of calcu- 
 lating' the triangles formed on the furface of a 
 globe, by three arches oi great circles : the fmal- 
 ler circles of a fphere are not noticed in the cal- 
 culations of a fpherical trigonometry. This 
 fcience is too intricate to be any way explained 
 in this eifay ; we mufl therefore content our- 
 felves with only giving the proportions necelTary 
 to anfwer our purpofe. 
 
 Of the Quadrant, and it's Uses. 
 
 Every circle being fuppofed to be divided 
 into 360 equal part?:, or degrees, it is evident 
 that go degrees, or one-fourth part cf a circle, 
 will be fufficient to meafure all angles formed 
 between a line perpendicular to the hoiizon, 
 and other lines which are not directed to points 
 below the level. Fig. i, pi. XIV, is a drawing 
 of a very fim.ple and ufeful inflrument of this 
 kind. A B C is a quadrant mounted upon an 
 axis and pedeftal : by means of the axis, it may 
 be immediately placed in any vertical pofition, 
 and the pedeftal being moveable in the axis of 
 the circle E F, ferves to place it in the direc- 
 tion of any azimuth, or towards any point of 
 480 
 
PRACTICAL ASTRONOMY. 65 
 
 the compafs. The limb A B is divided into 
 degrees and halves, numbered from A; and 
 upon the radius B C are fixed two fights, of 
 which B is perforated with a fmall hole, and 
 is provided with a dark glafs, to defend the 
 eye from the fun's light ; and the other fight 
 C has a larger hole, furniflied with crofs wires, 
 and alfo a fmaller, which is of ufe to take the 
 fun's altitude by the projection of the bright 
 image of that luminary upon the oppofite fight. 
 From the center C hangs a plumb-line C P. 
 The horizontal circle F E is divided into four 
 quadrants of 90 degrees ; and an arm E, con- 
 neded with the pedeital, moves along the limb, 
 and confequently (hews the pofition of the plane 
 of the quadrant, as will hereafter be more 
 minutely explained. Laftly, the fcrews G, H, I, 
 render it very eafy to fet the whole inftrument 
 fteadily and accurately in ic's proper pofition, 
 notwithftanding any irregularity in the table or 
 ftand it may be placed upon. 
 
 The rationale of this inftrument is very 
 clear and obvious. It is ufed to meafure the 
 angular diftance of any body, or appearance, 
 either from the zenith or point immediately- 
 above our heads, or from the horizon or level. 
 The plumb-hne C P, if continued upwards 
 from C, would be direded to the zenith Z ; 
 and the line C L, fuppofed to be drawn from 
 
65 INTRODUCTION TO 
 
 the center of the quadrant to an objefl L, will 
 form an angle L C Z, which is the zenith dif- 
 tance, and is equal to the angle B C P, formed 
 between the oppofite parts of the fame lines. 
 We fee, therefore, that the degrees on the arc, 
 comprehended on the limb of the quadrant, 
 between the plumb-line and the extremities next 
 the eye, meafure the angle of zenith diftance. 
 
 Again, the line C K (forming a right angle 
 with the perpendicular C Z) is level, or hori- 
 zontal ; the angle L C K mufl therefore be the 
 altitude or elevation of L above the horizon; 
 and this laft angle mud be equal to the angle 
 meafured between the plumb-line and the end 
 A farthefl: from the eye ; becaufe both thefe are 
 equal to the quantity which would be left, after 
 taking the zenith diftance from a right angle, 
 or the whole quadrant. 
 
 The determination of the altitude or zenith 
 diflance of an obje<3: is not fufficient to afcer- 
 tain it's place, becaufe the obje£i: may be 
 placed in any direftion with refpecl to azi- 
 muth, or the points of the compafs, without 
 increafe or diminution of it's altitude. Hence 
 it is that an horizontal graduated circle is a 
 neceffary addition to a quadrant which is not 
 intended to be always ufed in the fame plane. 
 The bearing or pofition of an objeft relative to 
 the cardinal points, together with the altitude. 
 
 482 
 
PRACTICAL ASTRONOMY. 6'] 
 
 is fufficient to afcertain the place of any object or 
 phenomenon. 
 
 After this fliort account of the general 
 principles of the quadrant, I fhall proceed to 
 fhew fome of the leading problems refolved by 
 it. 
 
 Problem i. 
 
 To adjujh the quadrant for ohfcr'Oaiton, 
 
 The quadrant is adjufted for obfervation, when 
 it's plane continues perpendicular to the horizon 
 in all pofitions in the line of fight. 
 
 To efFed this, bring the index to 90'' on 
 the horizontal circle, and turn one or both of 
 the fcrews which are fixed oppofite 60", till 
 the plumb-line lightly touches the plane of 
 the quadrant ; then turn the index to o", and 
 make the fame adjuftment by means of the 
 fcrew at o", and the quadrant is ready for obfer- 
 vation. 
 
 Or otherwife ; fet the index at o", and ob- 
 ferve the degree marked by the plumb-line on 
 the limb ; then turn the index to the other o", 
 which is diametrically oppofite, and obfervc 
 the degree marked by the plumb-line : if it 
 be thefam^eas before, there will be no occafion 
 to alter the fcrews at 60"; but if otherwife, one 
 or both of thofe fcrews mud be turned, till the 
 plumb-line intcrfeds the middle degree, or 
 
 483 
 
68 INTRODUCTION TO 
 
 part, between the two. After this operation, 
 the degree marked by the plumb-Hne mufl: be 
 obferve'd, as before, by fetfing the index at both 
 the 90", and the adjuftment of the plumb-line 
 to the middle diftance mull be made by the fcrew 
 at o", taking care not to touch the other 
 fcrews. 
 
 The latter method of adjuftment, being more 
 accurate in pra6lice, may be ufed after the for- 
 mer. 
 
 The larger or more expenfive inflruments 
 have apparatus for fetting the axis of motion at 
 right angles to the planes of the horizontal circle 
 and quadrant, the line of fight or collimation pa- 
 rallel to the radius paffing through 90", &c. &c. 
 In fmall inftruments, thefe adjuftments are made 
 by the workman. 
 
 Introductory Problems. 
 
 Problem ii. 
 
 To find the dijiance of an obje6f on the earth, by 
 obfervations made from two fiations on the fame 
 level. 
 
 Observations. 
 
 Chufe two ftations, between which the 
 ground is level, and place a vifible mark on 
 each. The diftance between them ought not 
 to be lefs than the feventh or eighth part of the 
 
 4^4 
 
PRACTICAL ASTRONOMY. Gi) 
 
 eftimated diftance of the objefts, and neither 
 (lation ought to be confiderably nearer the ob- 
 jeft than the other. Meafure the diftance be- 
 tween the ftations, by means of meafuring 
 poles, a chain, or a piece of ftretched cord. 
 From one ftation dired the quadrant to the 
 obje6t, by looking through the hole in one 
 fight, and moving the upright axis about, till 
 the oLjccl is feen through the hole in the other, 
 exactly at the interfedion of the crofs wires. 
 Obferve the degrees and parts fliewn by the in- 
 dex on the horizontal circle, then dire«fl the 
 quadrant in the fame manner to the mark of 
 the other ftation, and obferve the degrees and 
 parts ftiewn by the index. The number of de- 
 grees and parts intercepted between this and 
 the former pofition of the index, is the angle at 
 the firft ftation. The fame operations repeated 
 at the fecond ftation, will give the angle at that 
 ftation. 
 
 Thus let F, fig. I , plate XV, be the objefl. A, 
 B, the two ftations 880 feet diftant from each 
 other ; the angle obferved at A found to be 
 83" 45', that obferved at B 85" 15. 
 
 Solution. Take the fum of the two ob- 
 ferved angles from 180', and the remainder 
 will be the angle under which the two ftation- 
 marks would be feen from the objcin:. Let 
 F be the obje£t, A and B the two ftations, the 
 angle at A found by obfervation to be 83^ 45', 
 
 485 
 
yO INTRODUCTION TO 
 
 that at B 85" 15', the fum of thefe two angles is 
 
 169% which, taken from 180% gives 11'' for 
 
 the value of angle. F. 
 
 Then as the fine of angle 
 
 F, at the objeft - 11° 00' 9.2805988 
 
 Is to the fine of angle A at 
 
 one ftation A - 83° 45' 9.99741 10 
 
 So is the diftance A B be- 
 tween the ftations 880 2.9444827 
 
 To the diftance of the ob- 
 
 je6l B F from the other 
 
 llation - 4584.5 feet 3.6612949 
 
 Solution of the problem by protraElion, From 
 a fcale of equal parts, lay down a right line to 
 reprefent the meafured bafe. By means of the 
 protractor, or by the line of chords, draw a line 
 from each extremity of the bafe, forming an- 
 gles equal to thofe adlually obferved ; continue 
 thefe lines till they interfed. 
 
 The interval between the point of inter- 
 fe£lion at one extremity of the bafe being 
 taken between the compafTes, and applied to 
 the line of equal parts, will fhew the diftance 
 between the objed and the ftation reprefented 
 by that extremity. 
 
 This problem may, in cafes of fmall dif- 
 , tance, be conveniently applied to a bafe line 
 meafured within a room, and the obfervation 
 taken out at the windows. 
 486 
 
PRACTICAL ASTRONOMY. 7I 
 
 Problem hi. 
 
 To find the height of a fpire, a mountain y or any 
 other elevation. 
 
 Cafe I. When the diftance D E, fig. 2, 
 plate XV, of the point F immediately beneath 
 the objeft can be meafured.* 
 
 Obferve the angle of altitude C D E with 
 the quadrant, by viewing the fummit through 
 the fights, and noting the degrees and parts 
 indicated by the interfedion of the plumb- 
 line ; meafure alfo the horizontal diftance ; let 
 the angle CDE be 47" 30', the line D E 100 
 feet. 
 
 Then as radius - - 10.0000000 
 
 To the tangent of^ CDE 47 30' iO'0379475 
 So is the meafured diflance DE 100 2.0000000 
 
 To the height required, 109.5 ' ^•'^379475 
 Or by conftrudion. Draw a right line equal 
 to the meafured bafe, taken from a fcale of 
 equal parts. 
 
 Ercdt a perpendicular from one extremity, 
 and from the other draw a line inclined towards 
 the perpendicular, and forming an angle with 
 the bafe, equal to the obferved angle. 
 
 The interval between the interfedion of 
 this lad line, and the perpendicular, and the 
 lower extremity of the perpendicular itfelf, 
 
 * As the point cannot conveniently be taken from the 
 ground, you muft add the height of the eye at the obferva- 
 tion, to the height found. 
 
 487 
 
72 
 
 INTRODUCTION TO 
 
 being tziken in the compaffes, and applied to 
 the line of equal parts, will (hew the height re- 
 quired. 
 
 Cafe 1. When the diflance of the point A 
 immediately beneath the fummit cannot be mea- 
 fured. 
 
 Find the diilance by prob. ii, and the height 
 by cafe i, of this problem. 
 
 Or other wife meafure a bafe line D C, 
 fig. 3, plate XV, diredlly towards the objeft, 
 and take the altitude from each end of the 
 bafe. 
 
 Let D C, the bafe, be loo feet, the angle ob- 
 ferved at C 32', the angle at D 58"; fubtraft 
 the lefler altitude from the greater, and the dif- 
 ference is the angle B 26". 
 Then as the fine of this differ- 
 ence 26^ - - 9.6418420 
 Is to the fine of the lefler alti- 
 tude 32" - - ,9.7242097 
 So is tne bafe line 100 - 2,0000000 
 
 To the direft diilance between 
 
 the fummit and nearer end ol 
 
 the bafe line - - 2.0823677 
 
 And, 
 
 As radius or angle A 50" - 10. 
 
 Is to the fine of the greater alti- 
 tude 58' - - 9.9284205 
 So is the diftance lail found 2.0823677 
 
 To the height required, 102.51 feet 2.0107822 
 488 
 
PRACTICAL ASTRONOMY. 73 
 
 Or by conftruftion. Set off the bafe line, 
 and from it's extremities draw lines inclined to 
 the bafe in the refpeclive angles obferved, but 
 in fuch a manner, as that the lefs angle may be 
 formed by the bafe itfelf, and the greateft by 
 the prolongation of the bafe. 
 
 Thefe lines will interfed. 
 
 From the point of interfedlion let fall a 
 perpendicular on the prolongation of the bafe, 
 and it will give the height required. 
 
 The firlt method of folving this cafe is in 
 general the bed in pradtice. It is for the mod 
 part much more eafy to find a bafe fufficiently 
 long and level between two ftations, nearly 
 equi-diftant from the eminence, as the firil re- 
 quires, than in a diredion towards it, becaufe 
 the ground ufually rifes irregularly towards 
 mountains. And in the latter cafe alfo, if the 
 difference between the two altitudes be not 
 very confiderable, the refult will be rendered 
 erroneous by a very fmall inaccuracy of ob- 
 fervation. 
 
 Problem iv. 
 
 To plot a field by a bafe line meafured ivithin 
 thefield. 
 
 Set up marks in the corner of a field, and 
 meafure a line in the field in fuch a diredlion 
 R r 489 
 
74 INTRODUCTION TO 
 
 as that it may be fet as far as poflible from 
 pointing towards any of the angles. 
 
 Direfl the fights from one end of the bafe 
 to each of the angles fucctflively, and alfo to 
 the other extremity of the bafe, carefully noting 
 the degrees and parts of the horizontal circle 
 marked out by the index. Repeat the like 
 operations at the other end of the bafe line. 
 
 Conftni5lion. Draw a faint line upon paper, 
 upon which fet off from a fcale of equal parts 
 the meafured bafe. From it*s extremities draw 
 lines, forming the refpeftive angles obferved. 
 The interfedions of thofe lines will fhew the 
 corners, or angles, of the field, and mufl be 
 joined by right lines. 
 
 This problem being nothing more than a 
 determination of the pofition of the angular 
 points with refpe6l to the bafe line, by prob. ii, 
 will be more accurate in practice, the more 
 nearly the conditions there exprefl'ed are ad- 
 hered to. If a bafe line cannot be had in view 
 of all the angles, and in a convenient pofition, 
 two or more bafe lines may be meafured, and 
 conneded together by the obfervation of the 
 requifite angles ; or the three fides of a triangle 
 may be meafured in the field, according to the 
 difcretion of the ingenious learner, and the 
 bearings of the corners of the field taken from 
 fuch extremities of any of thefe meafured Hnes 
 as are befi adapted to the purpofe. 
 
 400 
 
PRACTICAL ASTRONOMY. 75 
 
 As this method is far from being laborious, 
 the ftudent will do well to meafure the field 
 twice, but from a different bafe each time. 
 
 It may be proper to obferve, for the ufe of 
 fuch as are unacquainted with furveying of 
 land, that the Tnglilh acre is 4840 fquare 
 yards, and that land is molt conveniently mea- 
 fured by the Gunter's chain, of 22 yards in 
 length, divided into 100 links; becaufe the 
 fquare chain, or 22 multiplied by 22, equal to 
 484, is exadly the tenth part of an acre. 
 If the plot of a field meafured in chains and 
 links be therefore made upon paper, and di- 
 vided into a number of triangles, by drawing 
 right lines within it, the bafc and perpendi- 
 cular of each triangle may be fneafured from 
 the fcale of equal parts, and half their produd 
 will be the area of the triangle in fquare 
 chains ; the fum of all the areas of the triangles 
 will be the area of the field ; which divided by 
 10, will Ihew the number of acres ; the remain- 
 ing decimal fradion multiplied by 4, gives the 
 roods ; and the decimal part of this laft product 
 multiplied by 40, gives the perches. 
 
 In the following example is a more ready 
 method of obtaining the contents. 
 
 Example. Let A B C D E F, fi,^. 4, pi. XV, 
 be the field, in which I alTumed two flations, 
 P, Qj at the diftance of 10 chains from each 
 other. 
 
 491 
 
y6 INTRODUCTION TO 
 
 From P, I obferved the following angles : 
 Q^PA to be 21" 20'; ABP49" 10'; BPC 
 Sf 12'; CPD 29-40'; DPE 64' 25'; EPF 
 79" 16'. 
 
 From the flatlon Q^, I obferved the follow- 
 ing angles: P Q^D 10' 40'; D (^C 18' 30'; 
 CQ^B 42' 00'; BQ^A 6y' 05'. A Q^F is 
 equal to A Q^O added to E Q^O ; that is, 137'^; 
 FQ^E 62-52'. 
 
 Solution. ConflruiSl the figure as directed, 
 and divide it into two trapeziums, D C B A, 
 and D E F A ; then apply the perpendiculars 
 Q^C, H B, L D, I F, and the diagonals B D, 
 A E, and the fide AD, to a fcale of equal 
 parts, and you will obtain the area near the 
 truth.* But it may be obtained accurately by 
 
 Trigonometry. 
 
 1. In the triangle A Q^B you will find Q^A 
 10.428, Q^B 15.198, and the angle A Q^B 
 
 67" 5'- 
 
 2. In the triangle B P Q^ you find Q^ 3 
 
 15.198, BP 15.259, the angle BPQ^38" 20'. 
 
 3. In the triangle QJ* C we have P C 
 12.404, PB 15.259, angle BPC ^j" 12'. 
 
 4. In the trianii^le Q^PD we find PD 8.941, 
 PC 12.404, CPB 29-40'. 
 
 5. In the triangle Q^P F we have P E 
 10.950, PD 8.941, angle DPE 64' 25'. 
 
 * The angles are in fome inftanccs in this example af- 
 fumed too ohlique to be afcertalned with accuracy in pradlice, 
 but anfwcr fully the purpofe of illuftration. 
 
 192 
 
PRACTICAL ASTRONOMY. 77 
 
 6. In the triangle P QJF we obtain P F equal 
 16.820, QJF 14.471, anglePF 0^36" i8\ 
 
 7. In the triangle EPF, P E is 10.950, 
 PF 16.820, angle EPF 79" i6'. 
 
 8. In the triangle AQ^F, QJF is 14.471, 
 AQ^io.428, angle AQV 137". 
 
 Now writers on menfuration have fliewa, 
 that if you add the logarithms of the two fides 
 of a triangle and the included angle together, 
 the fum, rejecting radius, will be the loga- 
 rithm of double the area of that triangle. By 
 this method we find, 
 
 1. the double area of a AQJB to be 145.984 
 
 2. - - - 
 
 3. - - - 
 
 4. - - - 
 
 5. - - - 
 
 6. - - - 
 
 7. - - - 
 
 8. - - - 
 
 BPQ^ 
 
 143.844 
 
 BPC 
 
 159-143 
 
 CPD — 
 
 54.895 
 
 DPE — 
 
 88.304 
 
 PFQ^ 
 
 144-105 
 
 EPF 
 
 180.964 
 
 AQJ — 
 
 102.916 
 
 Divide by 2 J 10 
 
 20.155 
 
 510.077 
 
 The young fludent In trigonometry will find 
 the folution of this problem no contemptible 
 exercife ; he may likewife. If he has a fufEcient 
 degree of patience aud Induftry, find every Hne 
 drawn In the figure. 
 
 493 
 
^8 INTRODUCTION TO 
 
 Problem v. 
 
 To plot a JielJj by meafuring the fides and 
 angles. 
 
 Set up marks at each of the angles, and at 
 every one of thefe marks direft the quadrant to 
 ihe two adjacent marks on each fide. The 
 number of degrees and parts between the two 
 pofitions of the index on the horizontal circle, 
 will (hew the angle at the ftation where the 
 obfervation is made. Meafure the diftance to 
 the next ftation, and obferve the angle there in 
 the fame manner. And thus proceed complete- 
 ly round the field. 
 
 Conjlruclion. From the fcale of equal parts 
 draw a line equal to the firft meafured fide, and 
 from it's extremities draw two lines, forming 
 angles equal to thofe a6lually obferved. 
 
 Make thefe lad lines equal to the fides they 
 reprefent, and from their extremities draw two 
 other lines at angles refpedively found by ob- 
 fervation. 
 
 Proceed thus till the whole field is plotted. 
 When all the angles of a field are thus mea- 
 fured, their fum, if the operation has been truly 
 made, will be equal to twice as many right an- 
 gles, dedu£ling four, as there are angles in all, 
 provided they be all inward angles. Btit if any 
 
 494 
 
PRACTICAL ASTRONOMY, jg 
 
 of them be outward angles, their refpeftive fup- 
 plements to 360' mud be taken in making up 
 the fum inftead of the angles themfelves. When 
 the fum proves either greater or lefs than jufl 
 the figure, it will not anfwer on paper ; and as 
 obfervations made with fmall inftruments can- 
 not be expected to be free from perceptible 
 errors, it will be expedient to correal the an- 
 gles by adding or fubtrading fuch defedl or 
 excefs, to or from all the angles, in proportion 
 to their magnitude, or more readily in equal 
 proportions among them. 
 
 This way of meafuring is much ufed in Ame- 
 rica, by the meafuring wheel and mariner's 
 compafs, and is applicable to extenfive woody 
 or mountainous trads of land, where great ac- 
 curacy is not required. It may alfo be ufed in 
 conjundlion with other methods, for delineating 
 a fea-coaft, &c. 
 
 The following example will fhew how you 
 may obtain the contents of the field. 
 
 Example. In furveying the field A B C D E, 
 fig. 5, plate XV, I obferved at A the angle 
 F A E to be 5 r 1 3', at B the angle C B G was 
 69" 30', at C the angle A C B was 39" 7', and 
 the angle A^C D 78 35' ; at D the angle E D H 
 was 88" 40' and at E the angle C E A 54" 20' ; 
 the fide A B meafured 1940 links, BC 1555, 
 CD 2125, DE 2741, and EA 1624. We 
 have now to find the area of the field. 
 
 495 
 
8o INTRODUCTION TO ^ 
 
 Subtra£t the angle CBC 69" 30' from 
 180", and you have the angle CAB no 30' ; 
 to which if you add the angle A C B 39° 7', and 
 fubtrad this fum from 180, you obtain the 
 angle CAB 30" 23'. We find by trigonometry 
 A C to be 288 links. The fum of the angles 
 EAF and CAB, taken from 180", gives the 
 angle EAC 98" 24'. Laftly, fubtrad the 
 angle HDE from 180, and you get the angle 
 ED C 91'' 20'. 
 
 Then, by the preceding problem, in the tri- 
 angle A B C we obtain from the two fides A B, 
 B C, and the included angle ABC, the double 
 area _ . . 28256 8 
 
 In the triangle EAC, from the fides 
 
 A C, AE, and angle E A C - 4625146 
 In the triangle E D C from the fides 
 
 D E, D C, and angle E D C - 5823047 
 
 2)13273851 
 
 Area 66.36925 
 An/wer, 66 acres, i rood, 19 perches. 
 If the angles had been meafured with a 
 mariner's compafs, they mufi; have been arran- 
 ged in a traverfe table fimilar to p.ane failing 
 in navigation, and the content found by the 
 method (hewn in my Graphical EJfcys. 
 496 
 
PRACTICAL ASTRONOMY. 8l 
 
 Problem vi. 
 
 To find the altitude and height of fire-balls^ and 
 other meteors, in the atmofphere. 
 
 Though the extreme velocity and tran- 
 fient nature of fiery meteors in the atmofphere, 
 in a great meafure prevents the making of fuch 
 obfervations as might tend to afcertain their 
 diftance, yet they form a fubjedl of inquiry fo 
 curious and interefting, as renders fuch as can 
 be made of great value. An obferver, who 
 preceives an appearance of this kind, ought 
 carefully to note the buildings, trees, ftars, &c. 
 near which it partes ; and, as foon afterwards as 
 convenient, take their altitude and bearings. 
 If two fuch obfervations be taken by perfons at 
 different places, fufficiently diftant from each 
 other, the dillance on the earth may be confi- 
 dered as the bafe, and from this and the two 
 obferved angles the height of the meteor may 
 be found by problem ii. 
 
 By obfervations of this kind it has been 
 found, that the larger fire-balls are elevated 
 about 60 miles above the earth's furface, and 
 that fome of them are near five miles in dia- 
 meter. 
 
 Sf 497 
 
82 INTRODUCTION TO 
 
 Problem vii. 
 
 To find the height of a cloudy by obfervation of 
 a jiojh of lightning. 
 
 If the altitude of that part of a cloud, from 
 which a flafli of lightning has iflued, be imme- 
 diately taken with the quadrant, and the num- 
 ber of feconds of time elapfed between the 
 inftant of the flafli, and the firfl arrival of the 
 thunder, be reckoned, thefe data will be fuffi- 
 cient to determine the height of the thunder- 
 cloud. For found is admitted to pafs through 
 ii42feetin a fecond ; but light has fuch an 
 extreme velocity, that it pafTes through thirty- 
 five thoufand miles in a fecond, and may there- 
 fore be reckoned inflantaneous in all obferva- 
 tions upon the earth. Hence it follows, that 
 the number of feconds obferved, multiplied by 
 1 142, will give the didance of the cloud in feet; 
 and 
 
 As radius 
 
 Is to the fine of the obferved angle j 
 
 So is the diftance of the cloud 
 
 To it's height. 
 
 Example. Suppofe the angle of elevation 
 CAB, from whichaflafhof lightning ifTued, was 
 53 8', and that between the flafli and the report 
 of the thunder 5 feconds were counted ; then 
 
 ' 498 
 
PRACTICAL ASTRONOMY. 83 
 
 1 142 feet multipled by 5 gives 5710 feet for the 
 diftance of the cloud. Fig. 6, plate XV. 
 And as radius or fine of 90" 10.0000000 
 
 Is to the fine of the obferved an- 
 gle 53' 8' - - 9.9031084 
 So is the diftance of the cloud ^y 1 o 3.7566361 
 
 To it's height 4568 feet - 3.6597445 
 
 Or by conftruftion. From a point in any 
 right line, draw another right line, forming the 
 obferved angle. Set off on this left line, from 
 the angular point, the diftance of the cloud, 
 taken from a fcale of equal parts. From the 
 extreme of the laft-mentioned line let fall a 
 perpendicular on the other line ; and this per- 
 pendicular will be the height required. 
 
 If the flafli of lightning ftrike dire£lly 
 down, the height of the cloud will alfo be the 
 length of the flafti. But this is not often the 
 cafcc 
 
 Problem viii. 
 
 To determine the height of a cloud by obfervations 
 on it^s altitude and velocity. 
 
 When the fty abounds with detached clouds, 
 moving with confidtrable velocity, it is eafy to 
 determine the degree of fwiftnefs, by obferv- 
 ing the progrefs of their fliadows which pafs 
 
 499 
 
84 INTRODUCTION 'to 
 
 along the ground. For this purpofe nothing 
 more is neceflary, than to note the inftants of 
 time when one of thefe (hadows pafles over two 
 objects, fuch as hedges, trees, &c. lying in it's 
 direction ; and to meafure \he interval pafled 
 over during the intermediate time. When 
 this velocity is thus found, place the plane of 
 the quadrant in the diredion of the wind, and 
 fetting the fights to a confiderable altitude, to 
 be written down, take notice of fome remark- 
 able edge of a cloud, which palTi. s acrofs the 
 wire in the aperture of the fartheft fight, giv- 
 ing notice at the fame inftant to an afiiftant to 
 note the time. Then move the quadrant on it's 
 axis twenty or thirty degrees, and give the like 
 notice to the alTiitant when the fame part of 
 the cloud pafles the wire ; write down this laft 
 altitude. The perpendicular height of the 
 cloud will be found by the following propor- 
 tions. 
 
 As the number of feconds obferved when the 
 
 fliadow of the former cloud was feen on the 
 
 ground 
 Is to the number or feconds elapfed between the 
 
 two obfervations with the quadrant ; 
 So is the diftance meafured on the ground 
 To the diftance pafled through by the cloud 
 
 (whofe altitude was taken) during the time 
 - of obfervation. 
 
 500 
 
PRACTICAL ASTRONOMY. 85 
 
 Then, 
 As the fine of the dliference between the two 
 
 ahitudes 
 Is to the fine of the lefs altitude ; 
 So is the diftance paffed over by the cloud, 
 To it's diftance from the obferver, when the 
 
 greater altitude was taken. 
 
 And laftly, 
 As radius 
 
 Is to the fine of the greater altitude ; 
 So is the diftance laft found 
 To the perpendicular height of the cloud. 
 
 Example. Ihe fliadow of a cloud was ob- 
 ferved to pafs over 1230 yards in 50 feconds ; 
 it's altitude at that inflant was 41 degrees; 
 three minutes after, it's altitude was 1 1 degrees 
 37 minutes : to find it's height. 
 
 Now the fpaces defcribed by bodies moving 
 with equal velocity, are as the times of defcrip- 
 tion ; therefore, by the fird part of the rule, as 
 50 fee, to 180 fee. fo is 1230 yds. to 4428 yds. 
 the diftance paffed over by the fliadow during 
 the obfervation. 
 
 But the progreflive motion of the fliadow 
 from B to C, fig. 7, plate XV , during the elapfed 
 time between the obfervations, is the fame as if 
 the obferver had moved in the fame time from v 
 B towards A ; or the effed would be exaAly the 
 fame if an obferver at A took the lefs altitude, 
 while another at B took the greater altitude at 
 
 5o» 
 
86 INTRODUCTION TO 
 
 the fame inftant. Hence the fecond part of 
 the rule is evident ; for AD E is the comple- 
 ment of the lefs angle, and B D E that of the 
 greater. The difference of thefe complements 
 is equal to the angle A D B ; but the difference 
 of the complements muft be equal to the differ- 
 ence of the altitudes j therefore, by the fecond 
 part of the rule. 
 As the fine A D B of the difference 
 
 between the two altitudes 29" 38' 9.6907721 
 Is to the fine of the lefs altitude 
 
 DAB 11^37' - - 9-3039794 
 
 So is the diftance A B paffed over 
 
 by the cloud 4428 yards - 3.6462076 
 
 12.9501870 
 
 9.6907721 
 
 To it*s diftance at the time of the 
 
 greater altitude B D 1817.2 yds. 3.2594042 
 
 Laftly, by the lafl: part of the rule, fee like- 
 wife the rule to problem viii. 
 
 As radius fine of 90 - - 10. 
 
 Is to fine of greater altitude 41 9.8169429 
 
 So is the diftance B D 1817.2 - 3.2594049 
 
 To the perpendicular height D E 
 
 1192.2 yards - - 3-07^347^ 
 
 502 
 
PRACTICAL ASTRONOMY. Sj 
 
 Principles and Problems preparatory to 
 THE Application of the Instruments 
 TO Practical Astronomy. 
 
 By praftical aflronomy is underflood the 
 knowledge of obferving the celeftial bodies, 
 with refpecl to their pofition, and time of the 
 year ; and of deducing from thefe obfervations 
 certain conclufions, ufeful in calculating the 
 time when any propofed pofition of thofe bodies 
 fhall happen. 
 
 Of Terrestrial Latitude. 
 
 The latitude of any place is equal to the 
 elevation of the pole of the equator above that 
 place. 
 
 The diflance between the zenith and the 
 horizon, and that between the pole, is equal, 
 for each of them are 90 degrees. If, therefore 
 we take away the diflance of the zenith from the 
 pole, which is common to both, the remainder, 
 that is, the elevation of the pole, or latitude of 
 the place, is equal to the diflance from the ze- 
 nith to the equator. 
 
 The diflance from the zenith to the pole, is 
 equal to the complement of the latitude to 90 
 degrees. 
 
 5°: 
 
88 INTRODUCTION TO 
 
 The inclination of the equator to the hori- 
 zon, is alfo equal to the complement of the lat- 
 itude to 90 degrees'* 
 
 All thofe ftars that are not further from the 
 pole than the latitude, are called circunipolar 
 ftars. 
 
 If the greatefl: and leafl: altitudes of a circum- 
 polir ftar be determined by obfervation, half the 
 fum gives you the latitude of the place. 
 
 The complement of the meridian altitude 
 of a flar is it's ■zenith dijlance ; and this is called 
 
 * In fi;^. 5, plate III, P reprefcnts the pole, E C) the 
 equator, H O the hoiizon, P H the elevation of the pole, 
 Z the zeniih. H Z O, or the vifible part of the heavens, con- 
 tains twice 90, or 180 degrees; it being 90 degrees from Z 
 to H, and 90 decrees from Z to O : but it Is alfo 90 from 
 the pole P, to E the equator If you take away PE, there re- 
 main 90 degrees for the other two arcs. In other words, the 
 elevation of the pole and the elevation of the equator are 
 together equal to 90 degrees ; /. e. in technical terms, the ele- 
 vation of the pole is the complement of the elevation of the 
 equator to 90 d^^grees. Hence one being known and fub- 
 tradled from 90, gives the other. 
 
 Hence alfo it is clear, that the elevation of the equator is 
 equal to the diftance of the pole from the zenith, btth being 
 equal to the diftanee of the pole from 90 degrees. 
 
 Hence alfo the diftance of the equator from the zenith is 
 equal to the elevation of the pole, or latitude of the place ; 
 for H Z is equal to 90, and P E is equal to 90 : take away 
 P Z, common to both, and the remainders, P H, Z E, mull 
 be equal. 
 
 5°4 
 
PRACTICAL ASTRONOMY. 89 
 
 north or fouth, according as the ftar is north 
 or fouth at the time of obfervation. 
 
 The latitude of a place is equal to a ftar*s 
 meridian zenith diftance added to the declina- 
 tion, if the ftar pafles between the zenith and 
 the equator. In all other cafes, the latitude is 
 the difference between the meridian zenith dif- 
 tance and the declination of the ftar. 
 
 The greateft declination of the fun, is equal 
 to the inclination of the ecliptic to the equator. 
 
 The inclination of the equator to the eclip- 
 tic, is equal to half the difference between the 
 fun's meridian altitudes on the longed and (hort- 
 eft days. 
 
 the latitude of the place, and the zenith dijlance 
 of a flar, being given, to find the declination 
 of the flar, 
 
 1. When the latitude of the place and zenith 
 diflance are of different kinds, that is, one north, 
 and the other fouth, their difference is the de- 
 clination ; and it is of the fame name with the 
 latitude, when that is the greater of the two ; 
 otherwife it is of the contrary kind. 
 
 2. When the latitude and zenith diftance 
 are of the fame kind, that is, both north, or 
 both fouth, their /m/« is the declination, and it 
 is of the fame kind with the latitude. 
 
 Tt 505 
 
go INTRODUCTION TO 
 
 Of Celestial Longitude, Latitude, Sec. 
 
 It has been already obferved, that in order 
 to meafure and eftimate the motion of the fun 
 and flars, it was necelTary to fix on fome point 
 in the heavens to which their motions might 
 be referred. The vernal eqitinodial point is 
 that point from which aftronomers reckon what 
 is called longitude in the celeftial fphere. The 
 ecliptic is divided into twelve figns, of 30 de- 
 grees each, with whofe names and charaders 
 you are acquainted. Aftronomers begin at the 
 firft point of Aries, and reckon from weft to 
 eaft. 
 
 Celejiial longitude is therefore the number 
 of degrees on the ecliptic contained between 
 the firft point of Aries and any celeftial objed, 
 or between the firft point of Aries and a circle 
 pafling through the objed perpendicular to 
 the ecliptic. Thus if t c, fig. 8, plate XV, 
 reprefents the ecliptic, and t the firft point 
 of Aries, and any ftar be at S on the ecliptic, 
 or at s on a circle p s S, perpendicular to the 
 ecliptic then will the arch r S be the longi- 
 tude of the ftars S, s. 
 
 The latitude of a celejiial objed: is it's dif- 
 
 tance from the ecliptic, reckoned on a circle 
 
 perpendicular thereto. Thus a ftar at s, fig. 8, 
 
 plate XV, will have for latitude the arc S s j 
 
 506 
 
PRACTICAL ASTRONOMY. 9I 
 
 but placed atS on the ecliptic, will have no lati- 
 tude. 
 
 As the diurnal motion is in the direction 
 of the equator, aflronomers, to facilitate both 
 obfervation and calculation, found it neceffary 
 to determine (he fituation of celefb'al bodies 
 with refpea to this circle, which is effefted by 
 determining their right afcenfion and decli- 
 nation. Right ajcenftomxidi declination are, with 
 refped to the equator^ what longitude and lati- 
 tude are with refpeft to the ecliptic. Thus if 
 T (^ reprefent the equator, and r the firft 
 point of Aries, then will r E be the right 
 afcenfion of a ftar fituated at E on the equator, 
 or at e in a circle e E perpendicular thereto : 
 the ftar at E will have no declination, but that 
 at e is meafured by the arch e E. 
 
 General Observations. 
 
 To fix your attention, with. greater cer- 
 tainty, to the objects of refearch, it may be 
 proper to obferve, that as praSiical ajironomy 
 confifts in determining the pofition of celeftial 
 objedts for a given inftant, it may be reduced to 
 three things. 
 
 1. The knowledge of the obliquity of the eclip- 
 tic. 
 
 2. The meafure ef time. 
 
 5^7 
 
g2 INTRODUCTION TO 
 
 3. 77je right afcenfions and declinations of the 
 Jiarsy l5fc. 
 
 Of the Obliqitity of the Ecliptic. 
 
 The obliquity of the ecliptic is a very 
 important element of aftronomy, becaufe it 
 enters into the calculation of all fpheric tri- 
 angles where the ecliptic and equator are con- 
 cerned. 
 
 The obliquity of the ecliptic being equal to 
 the fun's greatefl declination, /. e. when in the 
 tropics, the obliquity may be afcerlained by ob- 
 ferving the meridian height of the fun's center 
 on one of the folftitial days ; and this quan- 
 tity taken from the height of the equator, at 
 the place of obfervanon, gives the declination of 
 the tropic. Or, more accurately, obferve the 
 fun's meridian altitude in each tropic : this will 
 give their diftance, half of which is the diftance 
 of each tropic from the equator, that is, the 
 obliquity of the ecliptic. From good obferva- 
 tions, made in 1772, this obliquity was found to 
 be 23 £8'. 
 
 Of the Measure of Time. 
 
 All aflronomical obfervations depend on, 
 or have a reference to time. To meafure this 
 
 508 
 
PRACTICAL ASTRONOMY. 93 
 
 with accuracy, is one of the primary objeds of 
 an aftronomer. 
 
 As the diurnal revolution of the earth is found 
 to be uniform, they have taken this for the mea- 
 fure of time, comparing it with the fun. Af- 
 tronomers confider noon as the beginning of the 
 diurnal revolution ; or, in other words, din ajiro- 
 nomical day commences at the inftant the center 
 of the fun is the plane of our meridian, and fin- 
 ifhes when it has returned thereto, after one en- 
 tire revolution. 
 
 The ajironomical day begins therefore twelve 
 hours lat^r than the civil day of the fame deno- 
 mination, and is counted up to twenty-four hours, 
 or the fucceeding noon, when the next day be- 
 gins. Thus the day of the month, and the hour 
 of the day, are the fame in this method as in the 
 civil account at noon, and from noon till mid- 
 night : but from midnight till noon, they differ ; 
 for in the civil account a frefli day begins at mid- 
 night and the hours alfo begin again, but in the 
 aftronomical method the day is ftill continued 
 beyond the midnight. Hence five o'clock in the 
 morning of April the loth, is called by aftrono- 
 mers April 9, 17 hours. 
 
 As the earth revolves uniformly on it*s 
 axis, if it had no real annual motion, and con- 
 fequently the fun no apparent annual motion, 
 or if this motion was uniform, the days would 
 
 509 
 
P4 INTRODUCTION TO 
 
 be all neceflarily of one length, and that would 
 be about 23 hours ^6 minutes, for in that time 
 a diurnal revolution of the earth is completed, 
 as appears by an eafy obfervation ; for any fixed 
 ftar that is on the meridian at a given hour of the 
 night, will, after 23 hours ^6 minutes, be on the 
 meridian again the night following. This inter- 
 val of time is called a fiderial day. 
 
 But accurate obfervations have fhewn, that 
 the folar days are not equal to each other, and 
 that the time which elapfes between the fun's 
 being on the meridian of any place, and it's re- 
 turn thereto again, is confiderably longer fome- 
 times than at others. 
 
 Hence aflronomers have been obliged to dif- 
 tinguifh two forts of time j one they call apparent^ 
 the other mean time. 
 
 Apparent time (called by foreign writers true 
 time) is that determined immediately from the 
 fun, by obferving when his center tranfits the 
 meridian, which is at the inflant of apparent 
 noon, when a new aftronomical day commen- 
 ces. 
 
 Mean time is that which would be obferved 
 every day, if the apparent diurnal motion of the 
 fun was regular ; or that fhewn by good clocks 
 or watches, which go uniformly. The mean day 
 of 24 hours, pointed out by thefe, muft neceflari- 
 ly be always of the fame length. 
 
 The inequality in the length of the natural 
 510 
 
PRACTICAL ASTRONOMY. Q^ 
 
 tural days is termed the equation of time. Now 
 as agronomical tables can only be calculated 
 to mean or uniform time, the proper refults 
 from an obfervation cannot be obtained, till the 
 obferved or apparent time is reduced to mean 
 time ; for which purpofe proper tables are cal- 
 culated, called tables of the equation of time. 
 
 Thefe are inferted on ihe fecond page of 
 every month in the Nautical Almanac, for the 
 noon of each day at Greenwich. It is marked 
 fubtraSlivey when the fun comes to the meri- 
 dian fooner, and additive, when it comes to the 
 meridian later than the time of mean noon ; 
 that is, the quantity given by the table is to be 
 fubtraded from apparent, in order to obtain 
 mean time, in the firft cafe, and added to it in 
 the fecond. 
 
 Of Corresponding or Equal Altitudes. 
 
 At equal diftances from the meridian, a 
 flar has equal altitudes. If, therefore, equal 
 altitudes of an heavenly body be taken on dif- 
 ferent fides of the meridian, the middle point 
 of time between the obfervations will give the 
 time when the body is upon the meridian, if it 
 has not changed it's declination. By this 
 means the tijne when any body comes to the 
 meridian may be afcertained j and when ap- 
 
g6 INTRODUCTION TO 
 
 plied to the fun, or a fixed ftar, the rate at which 
 a clock (adjufled to the mean folar or fiderial 
 time) gains or lofes may be determined with ac- 
 curacy. 
 
 The method of afcertaining time by equal 
 altitudes is univerfally ufed by pratlical aftro- 
 nomers, becaufe it depends neither on an ac- 
 curate knowledge of the jatitude, nor on that 
 of the declination ; for thsfe elements are only 
 neceffary in taking out the equation of declina- 
 tion, and any probable error therein will not 
 fenfibly efFe:t chat equation ; neither does it 
 depend on the exact quantity of the altitude, 
 provided only it be the fame in both obfervations. 
 
 Of the Right Ascension and Declination 
 OF THE Stars, 
 
 The decUnntion of ftars, he. is eafily found 
 by obferving their meridian altitudes ; and their 
 right afcenfion is alfo eafily attained by know- 
 ing how to meafure time. 
 
 For as all ftars in the fame circle of decli- 
 nation have the fame right afcenfion, it fol- 
 lows, I ft, That all ftars pafTing at the fame 
 time through the fame meridian, have then 
 the fame right afcenfion. idly. The right 
 afcenfion of ftars palling the meridian at 
 
 512 
 
PRACTICAL ASTRONOMY. 97 
 
 different times, differ in proportion to the inter- 
 vals of the times of heir piilfage. 
 
 Examp'e. The (tars make a revolution in 
 23 ^6' ^' mean time. If, therefore, by a clock 
 regulated to mean time, and an inftrument fixed 
 in the plane of the meridian, or by correfpond- 
 ing altitudes, or otherwife, a ftar be obferved 
 to pafs I lie meridian one hour after the other ; 
 fay a<? 23 ' 56' 4'''', the time of one revolution, is 
 to 360 of the equator paffcd over the meridian 
 in the fame time, i^:) is one hour, the difference 
 between the tranfits of the ilars, to 15" 2' 28^'', 
 difference between their right afcenfions ; then 
 the right afcenfion of one being known, the 
 other is alfo known. 
 
 Whence it follows, that to determine the 
 right afcenfion of any (far, or even of all the 
 ftars, it is fufficient to know the right afcenfion 
 of one fiar only, and to have a clock which 
 (hews an equal interval of time for the diurnal 
 revolution of the feveral different fixed flars. 
 
 Problem ix. 
 
 To reduce degrees of the equator into time, and 
 time into degrees of the equator. 
 
 I. To reduce degrees into time, multiply 
 by 4; obferving that minutes, when multiplied 
 by 4, produce feconds, and degrees produce 
 minutes. 
 
 Uu 513 
 
^8 INTRODUCTION TO 
 
 Reduce 23" 56' into time 
 
 4 
 
 I 33' 44'' 
 
 Reduce 69" 20' 45^'' into time. 
 4 
 
 4'' 37' 23'' oo'"''^'=- 
 
 2. To reduce time into degrees, multiply by 
 10 in a fimilar manner, and increafe the produce 
 one-half, or divide the time by 4. 
 
 Reduce i*" 33' 44" into degrees. 
 
 i' 33' 44" 
 10 
 
 15 37 20 
 Half 7 48 40 
 
 Degrees 23 26 o 
 
 5H 
 
PRACTICAL ASTRONOMY. 99 
 
 Reduce 4'' '^'j' 23'''' to degrees. 
 10 
 
 46 1350 
 Half 23 6 ss 
 
 Degrees 69 20 45 
 Of Reductioi^ from one Meridian to 
 
 ANOTHER. 
 
 As all the heavenly bodies rife, cuhiiinate, 
 and fet, fooner to thofe who are towards the eaft, 
 and later to thofe who are towards theweft, and as 
 all tables and calculations in England for aftron- 
 omy and navigation are adapted to the meri- 
 dian of Greenwich, it is necelfary for thofe who 
 may be under any other meridian, to be able to 
 find the time at Greenwich correfponding to 
 that pointed out by their own clocks and 
 watches. 
 
 Without this redudlion no calculations can 
 be made from fuch tables, or from the various 
 articles contained in the Nautical Almanac, re- 
 lating to the longitude, right afcenfion and de- 
 clination of the fun, the equation of time, 
 moon's motion, hz. fo as to adju!l them to any 
 other meridian than that for which they were 
 made. 
 
lOO INTRODUCTION TO 
 
 To find the time at Greenwich correfponding ivith 
 any given time under another meridian. 
 
 1. Find the difference of longitude between 
 the two meridians, or how much the given place 
 or meridian is to the eafl or well of Greenwich, 
 and reduce this difference to time, by the fore- 
 going rule. 
 
 2. If the given place be eaft of Greenwich, 
 fubtradl the difference of meridians from your 
 time ; if it be weft, add the difference to your 
 time. The refult will give the time it then is at 
 Greenwich. 
 
 N. B. The time being given at Greenwich, 
 the correfponding time under any other meridi- 
 an is found by reverfing this rule. 
 
 Example. What is the time at Greenwich, 
 when it is 8 '' 17' 19'''' at Jerufalem, ^5" 30' eaft 
 of Greenwich, or in time 1'^ 21' 20^''? Jnfivcr^ 
 
 5" 55' 59" 
 
 Required the time at Greenwich, when it is 
 23'' 32' i7''''at Boflon, on the 12th of June; Bof- 
 ton being 4' 42' 29'''' weft. Jnf. 28'' 14' 46'''', 
 or 4'' 1 4 46^^ P. M. on the 1 3th of June. 
 
 What is the time at Jerufalem, when it is 
 21 49' iy^\ on the 9th of September, at Green- 
 wich ? Anfwer^ 24'' lo' 37^'', or o^ 10' o^Y °^ 
 the I oth of September. 
 
 Again, required the time at Boflon, when 
 
PRACTICAL ASTRONOMY. lOl 
 
 it is 3'' 37' o" on the ift of May at Greenwich ? 
 Anfwer, 22 54' 31^'' of the lall day of the pre- 
 ceding monih, or 10 54' 31'''' of civil time, on 
 the morning of the ill of May. 
 
 N. B. To know the time at Paris, Genoa, 
 kz. when it is any given time where you are, 
 take the difference between your meridian and 
 that of Paris, <?cc. and then proceed as in the 
 foregoing rule. 
 
 To find any of the motions of the fun or phmets, 
 the equation of time^ right afcenfton^ declina- 
 tion, fefni'diarneter, and parallax of the moon; 
 alfo the moon^s diftance from the fiars^ for 
 any pven time, under any other meridian. 
 
 Rule. I ft, Find by the preceding problem 
 the time at Greenwich which correfponds to the 
 time under the given meridian. 2dly, Take 
 the daily, the half-daily, &:c. (according to the 
 interval for which you are to calculate) vaiia- 
 tion from the Nautical Ephemeris, and by even 
 proportions find the time that correfponds to 
 the interval between this time, and that given 
 in the Ephemeris. 3dly, Add or fubtradl this 
 variation according as the motion is increafmg 
 or decreafinsc. 
 
 Example. What is the fun^s declination at 
 Greenwich, March 27, 1790, at 9'. The rea- 
 
 5»7 
 
102 INTRODUCTION TO 
 
 fon why Greenwich is mentioned, and not any 
 other place, is, becaufe the time, at whatever 
 place you may want the declination, is fuppofed 
 to be already reduced to that of Greenwich, as 
 the firfl ftep to be attended to in all fuch pro- 
 blems. 
 
 March 28. Declination at noon 3" 10' 47^'' N. 
 March 27. Ditto ditto 2 47 23 
 
 Variation of declination in 24 
 
 hours - - o 23 24 
 
 Variation in 9 hours, per table o 8 46 
 Which, added to declination, 2 47 23 
 
 Gives the required declination 2 56 9 
 
 Example. Required the fun's declination, 
 1790, Auguft 24, 2" ^y' at Greenwich? 
 Auguft: 24. Declination at noon 10 58 59 
 25. Ditto ditto 10 38 16 
 
 Variation in 24 hours - o 20 43 
 
 Variarion in 2 hours 57 min. o 2 36 
 
 Which fubtraded from - 10 58 59 
 
 Gives the decHnation required 10 56 23 
 
 518 
 
PRACTICAL ASTRONOMY. I03 
 
 Problem x. 
 
 I'd find at what time, by a clock keeping mean time, 
 any fixed fiar will be on the meridian on any 
 given day. 
 
 The right afcenfion of the ftars being reck- 
 oned on the equator, they pafs the meridian 
 fucceflively in times proportional to their refpec- 
 tive diftances therefrom. The diflance of a 
 ftar from the meridian, is therefore nothing 
 more than it's difference, in right afcenfion, 
 from the fun reduced to time ; from whence it 
 is plain, that to find the time when any ftar 
 comes to the meridian, you muft fubtrad: the 
 right afcenfion of the fun at noon from that of 
 the ftar ; the difference is the time required. 
 
 This fimple calculation would be fufScient 
 in general for finding the time when a ftar tran- 
 fits the meridian, if it always preferred the 
 fame difference in right afcenfion from the fun : 
 but the fun, by it's diurnal acceleration, ap- 
 proaches the ftar infenfibly ; and will confe- 
 qently pafs the meridian fooner, by a quantity 
 proportional to this acceleration, and it's dif- 
 tance from the fun. It is therefore necelfary 
 to fubtrad from the quantity firft found, ano- 
 ther fmall quantity, that may be afcertained. 
 Hence the following rule. 
 
 S^9 
 
104 INTRODUCTION TO 
 
 Rule. 
 
 Take the difference between the fun's and 
 planet's motion, in right afcenfion, in 24 hours, 
 if the planet is progreflive, or their fum if retro- 
 grade ; then fay, 
 
 As 24 hours, diminifhed by this fum, or differ- 
 ence, when the planet's motion is greater than 
 the fun's, or increafed by it, when the fun's 
 motion is the greater, 
 : Is to 24 hours, 
 
 : : So is the difference between the fun*s * and 
 planet's right afcenfion at noon, to the time 
 required. 
 
 For ajiar. 
 
 Take the increafe of the fun's right afcen- 
 fion in 24 hours, and add it to 24 hours j then 
 fay, 
 
 As this fum 
 : Is to 24 hours, 
 : : So is the difference between the fun's * an4 
 
 ftar's right afcenfion 
 : To the time required. 
 
 * In the latter part of both thefe rule?, the fun's right 
 afcenfion is to be taken 'rom the planet's or ftar's right 
 afcenfion ; and if their right afcenfions fhould be lefs than the 
 fun's, they mufl be Increafed by 24 hours, before you fub- 
 trad. 
 
 520 
 
PRACTICAL ASTRONOMY. lOJ 
 
 Examples. 
 
 On July I ft, 1767, the fun's right afcenfion, 
 when on the meridian of Greenwich, was 6" 
 40' 25^^; and on July 2d, it was 6 44' '})3>'^ ' 
 alfo the moon's right afcenfion was 159' 2' ; 
 and on July 2d, it was 169 39'. Required the 
 time of the moon's palfage over the meri- 
 dian ? 
 
 Sun's G's R. A. July i, 6'' 40' if 
 — ~ -^ 2, 6 44 33 
 
 Daily increafe 048 
 
 Moon's 3's R. A. 159" 2' - 10'' 36' 8^' 
 — — 169 39 - II 18 36 
 
 Daily increafe o 42 28 
 
 Moon's motion in 24 hours 42' 28^ 
 Sun's - - 4 8 
 
 Difference 38 20 
 
 Sun's R. A. at noon 6' 40' 25''' 
 Moon's R. A. at noon 10 36 8 
 
 Difference 3 ^^ 43 
 X X 521 
 
108 INTRODUCTION TO 
 
 As24''38'2o'''=23''2i'4o^-24::3" 55' 4f 
 60 60 
 
 1401 22,5 
 60 60 
 
 84100 14143 
 24 
 
 5^57^ 
 28286 
 
 84100 j 336400 \^4' 2 9 
 
 3032 
 60 
 
 84100 
 
 \ 18 1920 / 
 y 168200 I ^ 
 
 13720 
 60 
 
 - \823200/ 
 
 66300 
 
 >^«/wfr 4'' 2' 9''', the time required. 
 
 522 
 
PRACTICAL ASTRONOMY. IO5 
 
 At what time will the ftar Ar6lurus come 
 to the meridian of Greenwich on the firft of 
 September, 1787 ? 
 
 Sun's R. A. iSept. lo" 41' 59''' Star's R.A. i/^'G'q' 
 2 10 45 37 - 10 41 59 
 
 Increafein 24'' o 3 38 DifF. 3 24 i 
 
 As 24" 2/ 2>^' : 24'' : : 3" 24' 1" : 3' ^3' Z^' 
 the time required. 
 
 Problem xi. 
 
 To find the altitude of the fun, or any other 
 celejlial body. 
 
 This confifls in the fimple application of the 
 quadrant to a celeftial body, in the fame man- 
 ner as I have already fhewn with refpeft to ter- 
 reftriai objeds. 
 
 The quadrant being adjufled as it (hould be,' 
 in all cafes previous to it's ufe, the celeftial 
 body mull be viewed through the fights, and 
 the plumb-line will flievv it's altitude on the 
 graduated limb of the inftrument. 
 
 If the obfervation be made on the fun, the 
 dark glafs mufl: be ufed to defend the eye, or 
 the luminous fpot formed by the fmall hole 
 
 523 
 
106 INTRODUCTION TO 
 
 mufl: be made to fall on the center of the crofs 
 immediately beneath the eye-hole. 
 
 The fun having no vifible point to mark 
 out it's center, you mufl take the altitude either 
 of the upper or lower limb. If the lower limb 
 be obferved, you muft add the fun's femi- 
 diameter thereto, in order to find the altitude 
 of the fun's center. If the altitude of the up- 
 per limb be obferved, the femi-diameter muit 
 be fubtrafted. The mean femi-diameter of the 
 fun is 16 minutes, which for common ob- 
 fervation may be taken as a conftant quantity, 
 for the greatefl deviations from this quantity 
 fcarcely exceed a quarter of a minute. When 
 greater accuracy is aimed at, the femi-diameter 
 may be taken from the Nautical Almanac. 
 The obferved altitude of the fun's lower limb 
 being 18" 41', add thereto i6min. for the fun's 
 femi-diameter, and you obtain 18' ^f, the cen- 
 tral altitude. 
 
 The apparent altitudes of all the heavenly 
 bodies are increafed by refradion, except when 
 they are fituated in the zenith. An obferved 
 angle of a ftar, or any otl e- objeft in the heav- 
 ens, mufl: be diminifhed a fniisU quantity, to 
 be taken from the table of refraclions. 
 
 Where greater exaftnefs is required, a fmall 
 quantity is to be added for the error occafioned 
 by parallax, or the difference between the alti- 
 tude of an objecl as feen from the center and 
 524 
 
PRACTICAL ASTRONOMY. Ill 
 
 the furface of the earth. That from the center 
 is the true altitude, and the greateft, except at 
 the zenith, where parallax vanilhes ; confequent- 
 ly the apparent altitude ot the fun is to be aug- 
 mented by a fmall quantity taken from the tuble 
 of the fun's parallax. 
 
 Jane 6, 1788, the apparent altitude of the 
 fun's lower limb was. obferved to be 62 19': re- 
 quired the true altitude of the fun's center, asfeen 
 from the center of the earth. 
 
 Obferved altitude - - 62" lo' 
 
 Semi-diameter - - ig 
 
 Subtract for refraction 
 
 Add for parallax 
 
 6^ ZS 
 
 2>^ 
 
 62 34 30 
 4 
 
 True central altitude - 62 44 26 
 
 If it is a fixed ftar that has been obferved, 
 there is no correction for femi-diameter or pa- 
 rallax ; you have only to fubtrad for refradion, 
 in order to obtain the true altitude. 
 
 Thus let the obferved altitude of 
 
 Ardurus be - - ^S" 40' 
 
 Subtraa for refradion - 110 
 
 True altitude - - 3^ 38 50 
 
 5^S 
 
112 INTRODUCTION TO 
 
 Problem xii. 
 
 To find the latitude of the place of obfervation. 
 
 When the fun, or a flar, is nearly on the me- 
 ridian, or a few minutes before twelve at noon, 
 take it's altitude, and repeat this cbfervation, 
 at jfhort intervals of time, till it is found neither 
 to incrcafe nor diminifli. This laft, or greateft 
 altitude, is the meridian altitude. When the 
 fun is the cbjeft, you mud obtain the true cen- 
 tral altitude, by correding for femi-diameter 
 and refraction, as fhewn in the preceding pro- 
 blem. 
 
 Having obtained the meridian altitude, the 
 firfl object for confideration is, whether the lati- 
 tude be north or fouth, and whether the declina- 
 tion of the object be north or fouth. If the 
 latitude and declination be both north, or both 
 fouth, they are faid to be of the fame name ; but 
 if one be north, and the other fourh, they are 
 faid to be of different denominations. This 
 being determined, to find the latitude, 
 
 I. Take the given altitude from 90", to find 
 the zenith diltance. 2dly, If the zenith diflance 
 and declination be of one name, fubtrad; one 
 from the other, and the difference is the latitude} 
 but if they have contrary names, their fum gives 
 the latitude. 
 
 526 
 
PRACTICAL ASTRONOMY. 
 
 109 
 
 The latitude is always of the fame namt 
 with the declination, unlefs when the decli- 
 nation has been fubtraded from the zenith 
 diflance. 
 
 Example. 
 
 Aug. 17, 1776, Cambridge. The 
 apparent altitude of the fun*s 
 lower limb 
 
 Sun's femi-diameter 
 
 Apparent altitude of the fun's 
 centre - , _ 
 
 Subtrad for refradion 
 
 54 2 8 
 41 
 
 54 I 17 
 
 Real altitude of the fun's centre 
 
 This fum, taken from 90% gives 
 
 the zenith diflance of the fun's 
 
 ^^"^^f - - IS S^ 43 
 
 Add for the fun's declination 16 ,3 .^ 
 
 The fum is the latitude of Cam- ^ ' 
 
 ^"'^g* - - 52 12 40 
 
 N. B. The fun's declination, as found in 
 the tables, is to be reduced by the rules given 
 t P* S^l^ to the meridian of obfervation. 
 
 Nov. 6, 1792. Long. 158" W. the meridian 
 altitude of the fun's lower limb was obferved 
 to be %r Z7' N. required the latitude ? 
 
 t Refer to the pages at bottom. 
 5^7 
 
101 INTRODUCTION TO 
 
 Obferved altitude - ^j" 'ij 
 
 Sun*sfemi-diameter - 16 
 
 -Altitude of the fun's center - 87 ^7, 
 This, from 90, give the zenith 
 
 diftance - - 27 
 
 Declination reduced - 16 25 S. 
 
 Latitude required - - i^ 32 iS. 
 
 Dec. I, 1793. The obferved meridian al- 
 titude of Sirius was 59' 50' S. required the la- 
 titude ? 
 
 Obferved altitude - 59'^ 50' S. 
 
 Zenith diftance - - 30 ic N. 
 
 Declination of Sirius - 16 ly S. 
 
 Latitude required - . - 13 43 N. 
 
 Problem xiii. 
 
 To find the i'wie by equal or correfpondhig 
 altitudes. 
 
 This problem is of extenfive ufe, for the 
 bafis of all afironomical obfervation is the deter- 
 mination of the exad time of any appearance 
 in the heavens ; which cannot be attained, un- 
 lefs you are affured of the going of your watch 
 or clock. I have before fhewn you, that a 
 528 
 
PRACTICAL ASTORNOMY. II3 
 
 mean folar day is always confiJered as of the 
 fame determinate length; bat the length of aa 
 apparent day is variable, being fometimes 
 longer, fometimes fhorter, than a mean day. 
 I'he inftant, therefore, of apparent noon will 
 lometimes follow, at others precede, that of 
 mean noon. The interval between apparent 
 and mean time, is called the equation of 
 time. 
 
 To find, then, the time of apparent noon, 
 obferve the fun's altitude in the morning, and 
 alio the time by a clock or watch. Leave the 
 quadrant in the fame fituation, taking care 
 that it's pofition be not altered by any accident ; 
 and in the afternoon direct it to the fun, by mov- 
 ing the index of the horizontal circle only, and 
 obferve the time when the fun's altitude corref- 
 ponds with that to which the quadrant was fet in 
 the morning. Add the times ol obfervation to- 
 gether ; the middle inftant between thefe times 
 of obfervation is that of apparent noon : this 
 being corrected, by adding or fubtrading the e- 
 quation of time, g ves the time of true noon. If 
 it be precifely Xll, the clock is right ; but if it 
 differ, the clock is fafter or flower, by the quan- 
 tity of the difference greater or lels than Xll, 
 
 Yy 529 
 
114 INTRODUCTION TO 
 
 f Thus fuppofe the time in the 
 
 morning to be - - 21° 35' 8* 
 
 ' That in the afternoon - 2 55 43 
 
 ^ . 24 30 51 
 
 The time of moon by watch 12 15 51 
 
 Equation of time - - '3 29 
 
 Mean noon by watch - 12 2 22 
 
 The watch is therefore 2 min. 22 fee. too 
 faft. 
 
 To be more particular and accurate. In 
 our latitude, the ahitudes fhould be taken when 
 the fun is at leafl two hours diftant from the 
 meridian. The bed time is when the fun is 
 on or near the prime vertical, or eaft and weft 
 point of the compafs ; becaufe his motion per- 
 pendicular to the horizon is greateft at that 
 
 time. 
 
 About this time, in theforenoon, take feveral 
 
 altitudes of the fun, writing down the degrees 
 
 and minutes fhewn on the arch, and alfo the 
 
 exa6t time fhewn by the clock at each obferva- 
 
 tion : the obfcrvations to be written one below 
 
 the other, in the order, they were made ; the 
 
 time of each obfervation being previoufly increaf- 
 
 ed by 12 hours. 
 
 530 
 
""rfmt^ 
 
 PRACTICAL AS 
 
 In the afternoon fet the in 
 degree and minute as the laft obf;., 
 exadly the time Ihewn by the clock * 
 fun is come down to the fame altitu 
 write down the time oppofite to the faTn^QW 
 ing altitude; proceed in the fame manner m*i 
 note the time of all the altitudes correfponding 
 to thofe taken in the morning, writing down 
 each of them oppofite to that morning one 
 with which it correfponds. 
 
 Half the fum of any pair of correfponding 
 altitudes, will be the time of noon by the watch 
 uncorreded. Find the mean of all the times of 
 noon thus deduced from each correfponding 
 pair of obfervations ; which corred for the 
 change in the fun's declination, and you obtain 
 the exad time (hewn by the clock at folar noon. 
 This, correded by the equation of time, gives 
 the time of mean noon ; and the watch will be 
 too fad or too flow, according as the time of 
 noon thus found is more or lefs than 12 hours. 
 
 Example i. Equal altitudes taken, June 1782. 
 
 Morning. Afternoon. 
 
 20' ss' 46' 3" 8' 44' 
 
 20 57 41 36 48 
 
 20 59 27 34 58 
 
 53^ 
 
 M 
 
 ^ 
 
EDUCTION TO 
 
 2u pair 20I1 57"^ 41' 3d pair 20'' SO^^^J 
 3 6 48 3 4 58 
 
 / 
 
 4 30 24 4 29 24 4 25 
 
 2 15 12 2 144. 12 2 I2i 
 
 - me feconds differ, add them together, and 
 divide the Sum by 3 (the number of pairs) 
 which gives you a mean 1 5 
 
 12i 
 
 3)42 
 
 Therefore the mean of the ob- 
 
 ferved time is - - 12'' 2' 14.*^ 
 
 Equation for 6 hours difference 
 
 in declination - - { 
 
 12 2148 
 
 Time per watch of apparent 
 
 noon 
 Equation of time - i 55 i 
 
 Time per watch of mean noon 12 0197 
 
 The watch is 1 9 fee. 7 thirds too fafl for 
 mean time. 
 
vy^^^'. 
 
 PRACTICAL AS 
 
 M 
 
 Example 2. January^ 
 
 Morning. Afti 
 
 21" 35' 8 25 
 
 21 36 8 2 54 42 
 
 21 38 9 2 52 41 C 
 
 2 1 39 12-f 2 51 38 " • 
 
 iftpr.2t''35 '»' 2d2i ''36'''8= 3d2i'' 39 9" 411121'^ ^Q^^a 5* 
 2 55 43 2 54 '2 2 5. 41 2 2 5r 38 
 
 24. 30 50 2 
 12 15 25 I 
 
 24 30 505 
 12 15 25 2 
 
 Sum 24 30 51 24 30 50 
 i funi 12 15 255 12 15 25 
 
 The dlfF^^rence here is only among the 
 thirds, which added together are 8^'", divided 
 by 4 we have 2. Therefore 
 The mean of the obferved time is 12'' 15' 25'''' 2'''" 
 Equation for declination - 20 2 
 
 Time of apparent noon by watch 12 15 50 
 Equation of time - o 13 29 8 
 
 Time by watch of mean moon 
 Watch too fad for mean time 
 
 12 
 
 I 35 2 
 J 35 2 
 
 Problem xiv. 
 
 To find the error of a clock or watch, by correfpon- 
 ding or equal altitudes of ajipicdflar. 
 
 Rule I. 
 
 Add half the elapfed time between the 
 obfervations, to the time when the firit altitude 
 533 
 
DUCTION TO 
 
 I" 
 
 1 you have the time of the ftar's 
 ^'^^ meridian per wateh. 
 
 "^ Rule. 2. 
 
 ^ ^trad the fun's right afcenfion from 
 \ie Itar s, increafed by 24 hours, if neceffary. 
 Take the increafe of the fun's right afcenfion in 
 24 hours, and add it to 24 hours j then fay. 
 As this fum 
 : Is to 24 hours, 
 : : So is the difference between the fun and 
 
 flar's right afcenfion 
 : To the true time of the (lar's tranfit. 
 If the watch be regulated to folar time, the 
 difference between the true time of the ftar's 
 tranfit and the time ihewn by the watch, will be 
 the error. 
 
 If your meridian be different from that of 
 Greenwich, fay. 
 As 24 hours 
 : Are to the daily difference of the fun's right 
 
 afcenfion ; 
 : So is the longitude, in time, 
 : To a proportional part, which muff be 
 added to the true time of the ftar's tranfit, 
 if the longitude be eaft, but fubtradted if 
 weft. 
 
 If the watch be regulated to mean 
 folar time, that is, if it divides the time 
 equally, apply the equation of time as directed 
 in page II. of the Nautical Almanac, to the 
 
 534 
 
M 
 
 PRACTICAL A.V 
 
 true apparent time of the flai 
 you fubtrad. 
 
 Examples. 
 
 On the fixth of November, 1787, at 11'' lo'V 
 P.M. and at 16^^' i5^''folar time, the ftar 
 Aldebaran had equal altitudes at Greenwich. - ^^ 
 Was the watch too faft or too flow ? ^ 
 
 16'' 4' if 
 II 10 9 
 
 2) 454 6 
 
 % 
 
 A 
 
 Half elapfed time; - 2 27 3 
 
 Time i ft altitude 
 
 1 1 10 9 
 
 Star's tranfit per watch 13 ^y 13 
 
 Star's R. A. 4'' 23' ^o'' 
 24 
 
 28 23 50 
 
 Sun's R. A 14 46 15 
 
 ^^ff- 13 37 35 
 
 Sun's R. A. Nov. 6 14'' 46' 15^ 
 — — 7 14 50 15 
 Increafe in 24 hours 040 
 
 535 
 
/■ 
 
 DUCTION TO 
 
 ^'^j"'37'35''-i3'35'»9^truetime. 
 f'J-ir watch 13 37 12 
 
 Vatch too faft o i 53 
 
 ^^. July 13, 1792, in longitude 23" 26' E. the 
 following equal altitudes of Altair were ob- 
 ferved. Required the errors of the watch ? 
 
 Time per watch. A'titndc. Time per watch. 
 
 8^ ly' d' - 27 23' - 14 i^ sf 
 o 19 16 - 27 40 - o 33 42 
 o 20 12 - 27 55 - o 32 44 
 
 O SI 54 - 28 12 - O 31 5 
 
 o 23 16 - 28 30 - o 29 41 
 S 25 55 - 28 52 - 14 27 r 
 
 Sum 50 7 33 - - 87 io 10 
 
 Mean 8 21 15 5 - - 14 3^ 4* 
 
 Mean time of ifl: obfervation 8'' 21' if 5'" 
 Meantime of 2d obfervation 14 31 41 6 
 
 2) 6 10 26 I DifT. 
 
 Half elapfed time 3 S ^1} 
 
 Star's R. A. 19'' 40' 40^ 
 Sun's R. A. 8 13 41 
 
 Difference 11 26 59 
 
r'Tfr^^f^'/T' . 
 
 PRACTICAL 
 
 Sun's R. A. at noon, 
 Ditto - 241 
 
 Increafe it 24 hours 
 
 Trui 
 
 24'3'58''' : 24 :: 1 1'' 26' 5/ ; i,"2^ 
 24" : 3' 58''' :: i" 33' 44>ro part, o o 
 
 True time of flar's tranfit cor- i^ 
 
 reded for longitude - 11 25 2 r 
 
 Time per watch - 1 1 26 28 
 
 Watch too fad for apparent time o i 7 
 
 Secondly, Suppofe the watch had been regu- 
 lated to mean folar time. Then, 
 
 True apparent time of (lar's tran- 
 fit, as above - 11'' 2 c' 21'*' 
 Equation of time - o 6 -2 
 
 True mean folar time - 1 1 3 1 24 
 
 Time per watch - - 11 26 28 
 
 Watch too flow for mean folar time 
 
 o 4 56 
 
 M 
 
 Zz 
 
 537 
 
JCTION TO 
 
 J 
 
 'ROBLEM XV. 
 
 , .Man line, or to find the cardinal 
 ■,jof the cojiipafs, by equal altitudes of the 
 , cr a Jiar. 
 
 if'-'^qnal altitudes of the fun be taken, as 
 ided in problem xiii, and the place of the 
 ex on the horizon circle be carefully noted 
 each time of obfervation, the middle de- 
 ee or part between each, will be the place 
 where the index will (land, when the fights 
 of the quadrant are directed to the fouth, or 
 north, according as the fun is to the fouthward 
 or northward of the place of obfervation at 
 noon. Set the index to this middle point, and 
 direct the fights of the quadrant to fome re- 
 mote and fixed object on the earth. This ob- 
 ject will be a fouth meridian mark, and will 
 ferve to fet the quadrant at any future time. 
 Then take up the iufhrument, and after fetting 
 the index to o, place it again on the table, or 
 fupport, and move the vi'hole inflrument, not 
 by any of it's parts, but entirely about upon the 
 table, till the fights are truly directed to the me- 
 ridian mark. Adjuit the horizontal circle by 
 prob. i, and the index will then ferve to fliew 
 the true bearing of any obje6t j becaufe the 
 diameter joining the two zeros, or go's, anfwers 
 to the meridian line. 
 
M 
 
 PRACTICAL^ 
 
 If the table, or fupp 
 will be proper to make ♦^ 
 tions, to receive the poi? 
 which means the horizo: 
 llantly, at any time, fet in i 
 with refpecl to the cardinal 
 rizon. ,^, / Uf 
 
 It often happens that there is not ah\ ^^l» 
 (low in a houfe, from which the fun can bo 
 morning and evening. In this cafe, the m 
 dian may be determined by obfervations oi 
 equal altitude of the pole-ftar, or any other near j/ 
 the pole. 
 
 Problem xvi. 
 
 To find the time by the fun's tranjit over the jue- 
 vidian. 
 
 Adjufl the quadrant to the cardinal points 
 bythelaft problem, a fliort time before noon. 
 Set the index to o, and elevate the quadrant, fo 
 that the (liadow of the fight with the crofs wire 
 may fall upon the other. As the inftant of 
 apparent noon approaches, the bright fpot 
 formed by the fun's light through the lower 
 hole in the former fight, will be feen approach- 
 ing the mark on the latter. If the obferver 
 chufes to look at the fun, he mull now put up 
 the dark glafs, and apply to the obfervations. 
 The inftants when the firit limb, or edge of the 
 
 539 
 
f 
 
 ION TO 
 
 .le perpendicular wire, 
 
 limb appears to leave 
 
 clock or watch. The 
 
 ^parent noon. Or if he 
 
 ■>y the bright fpot only, the 
 
 Sot is feen upon the nnark is 
 
 ^'enw^*. i ; and this, corre£led by the 
 
 '»n of time, will (hew how much the clock 
 
 or flow. 
 
 y 
 
 Jk Problem xvii. 
 
 To find the time by an obfervation of the JurCs al- 
 titude and azimuth. 
 
 Adjufl: the inftrument to the cardinal points, 
 and obferve the fun's altitude. Take notice 
 likewife of the angle of azimuth from the meri- 
 dian, as ftiewn by the index. 
 
 Then, 
 As the fine complement of the fun's decli- 
 nation 
 Is to the fine complement of the altitude ; 
 So is the fine of the azimuth 
 To the fine of the fun's horary angle. 
 
 Which lalt being reduced into time, by al- 
 lowing fifteen degreees to one hour, and in pro- 
 portion for the other parts, gives the apparent 
 time, if afternoon ; but if before noon, it muft 
 be deducted from 12 hours, to give the time. 
 
 540 
 
M 
 
 PRACTICAL 
 
 This apparent time i. 
 
 
 
 equatioa of time. ^ 
 
 
 
 Example. Suppofe, 
 
 
 
 June, the fun*s altitude 
 
 
 ^ 
 
 ^6 25', and his azimuth 1 , 
 
 
 
 tion being 23' 29'. 
 
 
 ^?^ 
 
 /is the cofme oi the fun's « 
 
 • 
 
 ■%. 
 
 tion 23' 29' 
 
 
 
 Is to the cofine of the altitude 
 
 
 4625' 
 
 9.?: 
 
 
 So is the fine of the azimuth 
 1 12" 59', or 67" i' 
 
 9.96 
 
 A21 
 
 9-96245^70 . p / 
 
 To the fine of the horary angle 
 
 43" 47' » 3" - 9-S40I039 
 
 As i5"to 1'', fo is 43" 47' 13'''' to 2'' 55' ^'\ 
 the apparent or true time part noon, to 9*' 4' 52'''' 
 before noon ; but neither of thefe times will 
 agree with a watch which meafures time 
 equally. 
 
 The equation of time for noon at Green- 
 wich is i' i$>g^\ the daily difference 13''''; 
 therefore, as 24" is to ii^\ fo is 2'' 55' 8^'' to 
 1.5''''; confequently 1.5^'' added to i' 15.9", or 
 i' 17.4^'', is the equation of time to be added 
 
 541 
 
riON TO 
 
 fi 2'' 5s' S'' added to 
 the time pafl noon per 
 
 y to remark, that when- 
 
 c equation of time to that 
 
 I from calculation, you 
 
 , iS the Nautical Ephemeris 
 
 1 IX ..xd time is not very near noon, 
 
 make a proportion as above ; but if 
 
 ply the equation of time to the time per 
 
 you muft fubtradt where the ephemeris 
 
 J you to add, and vice verfa. 
 
 I d 
 
 542 
 
nrrj Hf^f^fifV 
 
 M 
 
 PRACTICE 
 
 A - 
 
 OF 
 
 EQUATO 
 
 OR ' 
 
 A21 
 
 Q^JPt^mJn*^^' 
 
 UJVIFERSAL SUJV-D "'** 
 
 AND IT'S USES 
 
 THE plumb-line, or direftion in whicL" 
 vity a6ls, being the only line we can at (^J^A-2 
 times have immediate rccourfe to, for determin- - r -^ 
 ing the pofitionof objeds, is the chief particular] 
 to which the circles in the inftrument laft de-1 
 fcribed are adapted; and accordingly their planes 
 are placed the one parallel, and the other perpen- 
 dicular to that line. But as there are few places 
 on the earth, whofe vertical or horizontal circled 
 Gorrefpond with thofe in which the celeflial mo- 
 tions are performed, it was found neceffary, at a 
 very early period, to conftrud inftruments a- 
 dapted not only to the meafurement of altitudes 
 and azimuths, but alfo to follow the heavenly 
 bodies in their refpedive pajb.s,.» and determine 
 their right afcenfions and decnv^^^rns, more im- 
 
 543 . 
 
)N TO 
 
 by the quadrant and 
 
 aatorialis the moft ap- 
 
 'nt for this purpofe. 
 
 following parts ; 
 
 ,-ie E F, plate XIV, fig. 2, 
 
 ^^ the former inftrument, 
 
 nts, of 90' each. But inftead 
 
 Die index, there is a fixed nonius 
 
 ind the circle itfelf may be turned on 
 
 - center of the horizonal circle is fixed 
 
 / upright pillar, which fupports the cen- 
 
 a verticle femicircle A B, divided into 
 
 uadrants of 90" each. This is called the 
 
 rcle of altitude, and fupplies the place of 
 
 /quadrant in the former inftrument ; but it is 
 
 more extenfively ufeful, becaufe one quadrant 
 
 ferves to meafure altitudes, and the other depref- 
 
 fions. It has no plumb line, but a nonius plate 
 
 at K. 
 
 At right angles to the plane of this femicircle, 
 the equatorial circle M N is firmly fixed. It re- 
 prefents the equator, and is divided into twice 
 twelve hours, every hour being divided into 
 twelve parts, of five minutes each. 
 
 Upon the equatorial circle moves another 
 circle, with a chamfered edge, carrying a no- 
 nius, by which the divifions on the equatorial 
 
 544 
 
M 
 
 PRACTIC 
 
 may be read off to fm^ 
 
 angles to this moveable 
 
 circle of declination D, 
 
 rants of 90 each. / 
 
 The piece which carri> 
 
 fixed to an index moveable r^ 
 
 declination, and carrying a n6i Mt 
 
 fight O, to which the eye is to be ^ /^r 
 
 two fmall holes, and a dark glafs f 
 either occafionally ; and the fight 
 
 pieces fcrewed on, the lower having, 
 
 to admit the folar ray, and the up'^ 0^2 
 
 two crofs wires. == 
 
 Laftly, there are two fpirit Iev?*^<3. geo^3»^-^<>«~-i 
 the horizontal circle at right angles ^ 
 other. '•C-'. QR.4^ m 
 
 The following are among the many problems " ' 'J 
 which may be folved with peculiar facility, by 
 means of this ufeful inftrument. 
 
 Problem xviii. 
 To adjuji the equatorial for obfervation. 
 
 Set the inftrument on a firm fupport. Firft 
 to adjuft the levels, and the horizontal or azi- 
 muth circle. Turn the horizontal circle, till 
 the beginning O of the divifions coincides' with 
 the middle ftroke of the nonius, or near h. 
 In this fituation, one of the levels will be found 
 A a 545 
 
/ 
 
 m 
 
 TO 
 
 J joining the two foot- 
 l the nonius, orelfepa- 
 'e. By means of the two 
 caufe the bubble in the 
 imary in the middle of the 
 iorizontal circle half round, 
 .T-ti?Sr O to the nonius ; and if 
 .omains in the middle, as before, the 
 ! adjufted ; if it does not, correcl the 
 he level, by turning one or both of 
 which pafs through it's ends, (by 
 y.'urn-fcrew,) till the bubble has moved 
 ance it ought to come to reach the 
 t^caufe it to move the other half, by 
 , foot fcrews already mentioned. Re- 
 i horizontal circle to it's firfl: pofition, and 
 n tne adjuftments have been vi^ell made, the bub- 
 ble will remain in the middle; if otherwife, the 
 procefs of altering the level and the foot-fcrews, 
 with the reverting, mud be repeated till it bears 
 this proof of it's accuracy. Then turn the hori- 
 zontal circle till 90" ftands oppofite to the no- 
 nius ; and by the the foot-fcrew, immedially op- 
 pofite the other 90", (without touching the 
 others,) caufe the bubble of the fame level to (land 
 in the middle of the glafs. Lailly, by it's own 
 proper fcrews fet the other level (not yet attend- 
 ed to) fo that it's bubble may occupy the middle 
 of it's glafs. 
 
 654 
 
M 
 
 P R A C T I C . 
 
 Secondly, to adju 
 the nonius on the d( 
 the nonius on the horax 
 nonius on the femici , ^ 
 Look through the fights' . : 
 the horizon, where there is 
 
 objedts. Level the hori2rohve ,^ 
 
 thenobferve what object appear?^ '•>'■! 
 
 of the crofs wires. Reverie tW *^^ 
 
 altitude, lb that the other 90' m., 
 nonius ; taking care at the fame" 
 other three noniufes continue ,^ <iB42 
 
 of their refpeclive graduatic , ^21 
 
 the remote objeft continues ':^^i and geo^i^v...., 
 center of the crofs wires, the \\, ~^ 
 
 truly adjufted; but if not, unfcrcwl-^.. . GA4^ 
 fcrews which carry the frame of the crofs wire^ ^ V 
 and move the frame till the interfedion appears 
 to lie on a new objecl:, half way between the 
 objea firft oblerved, and that to which the wires 
 are applied in the lall polition. Return the 
 femicircle of altitude to it's original pofition : 
 if the interfedion of the wires be then found 
 to be on the objed to which they were lall di- 
 redled, the line of fight is truly adjufted ; but 
 if not, the frame muft be again altered as be- 
 fore : and the lame general operation mud be 
 repeated, till the crofs wires in both pofitions ap- 
 ply to the fame objed. 
 
 547 
 
JN TO ^ 
 
 of the center of in- 
 
 that one of the wires 
 
 eof the declinaricn femi- 
 
 •: right angles to that 
 
 „ are fixed at right angles 
 
 ^djuftment of one of them 
 
 . "' For this purpofe, obferve 
 
 '^ on one of the wires ; if it be 
 
 /e, move the index of the femi- 
 
 v^ation ; or if the other, move the 
 
 femicircle on the axis of the 
 
 \'In either cafe the objeft will 
 
 wire during it's motion, if the 
 
 , if not, alter that pofition, ta- 
 
 to difplace the center from it*s 
 
 JUUfllv^i't. 
 
 To adjuft the piece which carries the hole 
 for forming the folar fpot, direft the fights to 
 the fun, fo that the center of the luminous cir- 
 cle, formed by the aperture which carries the 
 crofs wires, may fall precifely on the upper fight- 
 hole. T hen move the frame, with the fmall 
 perforation, till the folar fpot falls exadly on 
 the lower fight-hole. 
 
 Thirdly, to find the correction to be applied 
 to obfervations by the femicircle of altitude. 
 Set the nonius on the declination femicircle 
 to O, and the nonius on the horary circle to 
 XII ; direct the fights to any fixed and diftant 
 
 548 
 
 oj 
 
PRACTIC 
 
 M 
 
 objedlj by moving 
 
 femicircle of altitu^^^^^ 
 
 the degree and niir 
 
 fion ; Teverfe the dec^, / 
 
 rtOing the nonius on i.;. 
 
 oppofite XII; diuft i. 
 
 fame objed, by means of the 
 
 and ftmicircle of ahitude, a;^ 
 
 altitude, cr depTtfT.rn, be xW 
 
 ferved in the other pcfitit n, l. 
 
 be required ; but if otherwil^ 
 
 ence of the two angles is (he 
 
 added to all obfervations or y, 
 
 with that quadrant, or half >.,*l_andgeo^^*-'^<'»~-i 
 
 which fliew the leaft angle; or *• 
 
 from all obfervations or redificationfr-rt(fiU. U]3 r^ 
 
 t he other quadrant, or half. *"^y 
 
 When the levels and crofs wires are once 
 truly fet, they will preferve their adjufment 
 a long time, if not deranged by violence ; and 
 the corredion to be applied to the Itmicircle cf 
 altitude is a conftant quantity. 
 
 Problem xix. 
 
 --MM 
 A21 
 
 '/^ 
 
 To meafure angles, eiiher cf cziniuih, aliiiudi^ 
 or depr(JJion. 
 
 Set the middle mark of the nonius on the 
 
 declination at O, ar.d fix it by means of the 
 
 milled fcrew behind. Set the horary circle at 
 
 549 
 
TO 
 
 e inflruinent (pre- 
 
 - obfervation. Then 
 
 iceflively to any two 
 
 ninutes contained be- 
 
 .of the nonius, on the 
 
 Circle, will fhew the ho- 
 
 .n<^iame manner as has been de- 
 
 ii, of the quadrant. And 
 
 .ghts be direfted to any object, 
 
 -iorizontal circle and femicircle 
 
 degree and minute marked by 
 
 lait-mentioned femicircle will 
 
 dtude, if on the quadrant or 
 
 .ye, or of depreffion, if on the 
 
 At, 
 
 Cemarfs. It is proper in this place to de- 
 icribe the nature and ufe of the admirable con- 
 trivance commonly called a iionius. It de- 
 pends on the fimple circumflance, that if any 
 line be divided into equal parts, the length of 
 each part will be greater, the fewer the divi- 
 fions ; and contrariwife, it will be lefs in pro- 
 portion as thofe divifions are more numerous. 
 Thus it may be obferved, that the diftance be- 
 tween the two extreme ftrokes on the nonius, 
 in the equatorial before us, is exactly equal to 
 eleven degrees on the limb, but that it is di- 
 vided into tweb^e equal parts. Each of thefe 
 laft pares v/ill therefore be fhorter than the de- 
 gree in the proportion of 1 1 to 12 j that is to 
 
 550 
 
iVl 
 
 PRACTC 
 
 QM 
 
 c 
 
 fay, It will be one-i 
 
 fliorter. Confeque^j^^^.i 
 
 fet precifely oppofite 
 
 pofitions of the nonL^. / 
 
 tered five minutes of 
 
 the two adjacent ftroke& \ 
 
 nonius, can be brought to 
 
 neareft flroke of a degree ; ix. . 
 
 fecond flrokes on the nonius 
 
 change of ten minutes, the thirc^ 
 
 fo forth to thirty, when the mi 
 
 nonius will be feen to be eq^ /_ " 
 
 two of the flrokes on the lin,i^ " 
 
 the lines on the oppofite fide cMand geo^ro«*v»4-~T 
 
 coincide in fucceflion with the* / 
 
 limb. .~-^- pB4^ 
 
 It is clear from this, that whenever the mid-'^ "^l '^ 
 die flroke of the nonius does not fland precifely 
 oppofite to any degree, the odd minutes, or 
 diftance between it and the degree immediately 
 preceding, may be known by the number of 
 the flroke on the nonius, which coincidcj 
 with any of the flrokes on the limb. It mufl 
 be obferved, however, that as the degrees in 
 feveral quadrants are reckoned in oppofite di- 
 reftions, fo likewife the nonius has two fets of 
 numbers : for the ufe of which, it need only be 
 remembered, that they always begin from the 
 middle, and go to 30 minutes, and thence from 
 
CO 
 
 he fame dlreftion id 
 
 .nuft always be reck- 
 
 <on to the degrees on 
 
 .**J-EM XX- 
 
 "7ce of an object on the earthy by 
 ns 7nade at two Jiations, 
 
 done by meafuring a bafe line 
 
 tal angles, and proceeding as 
 
 o. ii. But as the equatorial 
 
 .s ot deprelTion as well as ele- 
 
 ,jii, ii\e ftations may not only be on the 
 
 Xame level, but may be vertically the one above 
 
 the other. For example, if the altitude of any 
 
 objeft be taken from a lower window of any 
 
 building, and it's depreflion from a window 
 
 immediately above, and the ciftance of the two 
 
 ftations of the inftrument be accurately mea- 
 
 fured. 
 
 * In this inftrument they muft be read in the oppolite di- 
 reAion ; but when the nonius plate has it's divilions fewer 
 than the number of parts on the limb to which it is equal, 
 they coincide fucceflively in the fame diredlion as that of the 
 motion of the index. 
 
P R A C T I C A (^ 
 
 Then, 
 As the fine of the ^ 
 
 and depremon, (v 
 
 be altitude, or bo 
 Is to the fine of the an/* 
 So is the didance betwet* 
 To the diftance of the oL 
 
 ftation. 
 
 vt. 
 
 QM2 
 A21 
 
 Exa?iiple I. From 
 torn of a houfe, the ai^ > 
 fig. 9, plate XV, ot an obj ^ 
 be 40' ; eighteen feet above 
 
 fition, the angle BDE was ""%! and geo^ro-v,^»^■ 
 37' 3°'* ^ ®^ 
 
 Tnen, _=_ QB4^ 
 
 As fine of the difference of th. 
 
 et 
 
 two angles 2 ' 30' 
 
 Is to fine angle B D C, equal anp-/' 
 BDE, plus 90 i27.3c>/ 
 
 So is DC 18 feet 
 
 ASI 
 
 ^>, 
 
 8.6396796 
 
 To B C, the required diftance, 
 327.38 feet 
 
 2.5150596 
 
 Example 2. From C, fig. 10, plate XV, a 
 window near the bottom of a houfe, the angle 
 B C A of elevation of B was found to be 15° 
 Bb 553 
 
N TO 
 
 •ngle of depreffion 
 
 les 25" 9.6259483 
 
 9-9933515 
 
 1-2552725 
 
 1 1.2486240 
 9.6259483 
 
 1.6226757 
 
 ,OBLEM XXI. 
 
 ^re heights and dijiances. 
 
 jircle of altitude anfwers every 
 quadrant, in the inftrument be- 
 nd the horizontal circle is corn- 
 will be eafy for the intelligent 
 rm the problems iii, iv, vii, viii, 
 •quatorial, from the inflrudions 
 each refpedtively. 
 
 Problem xxii. 
 To plot a piece of land. 
 
 The problems v, and vi, with all others 
 which are folved by the menfuraiion of hori- 
 zontal angles, may likewife be performed with 
 facility by the equatorial. 
 
 554 
 
PRACTU 
 
 Problems xxir^^"*'^ 
 
 Under this title itSJ.^ 
 problems xi, xii, xiii, x'' 
 
 for finding the latitude ,; 
 
 tudes, the pofition o. 
 the time by the fun's tr 
 or by it's altitude and 
 
 ed with equal eafe. anj. "^^ 
 
 horizontal circle and feu.. QB42 
 
 indrument before us, as by '^art A21 
 
 of under thofe problems. rel 
 
 I (hall now proceed to ^iree ~ ^~7^ 
 
 to which the equatorial is ^or / r^Cl A O 
 
 ted. nil— ^ Qp"^^ 
 
 Problem xxvii: 
 
 To find the latitude of the place by » 'ib 
 
 known fixed Jiar. .. ,,-^., jiT'^^. 
 
 The indrument being adjufled according 
 to the dire£lions already given, fet the femi- 
 circle of altitude to 90, and when the fun is 
 coming near the meridian, elevate the fights 
 till the center of the fun is exactly in the 
 center of the crofs wires ; then follow the fun, 
 
 555 
 
JN TO 
 
 il and declination 
 
 's at his greateft; 
 
 fclination will then 
 
 ^, from which fub- 
 
 ^.*%e north, or add i t if it 
 
 ^Jr, lif north, and the fum, 
 
 e equator, that is, the 
 
 .'; from which fubtract 
 
 ^'>ned by refraction, and 
 
 Tom 90' gives your la- 
 
 \ 
 
 ^ed meridian 
 ti's lower limb 
 le fun 
 
 < center 
 h 
 
 uator, or co-lati- 
 rraftion 
 
 Co-/ c"- ,orrected 
 
 Which fuorracled from 90'' gives 
 the latitude 
 
 44" 51' 23 
 16 
 
 45 7 23 
 6 57 37 
 
 38 9 46 
 
 5 54 
 
 38 3 52 
 51 56 8 
 
 The latitude may be obtained in the fame 
 manner by a fixed ftar, whofe declination is 
 known. 
 
 556 
 
PRACTl 
 
 Pi 
 
 1<^«»J'X,.»1 
 
 To find the meridiar\ I 
 
 ONE OBSERVAl 
 
 declination an'^\ 
 known. 
 
 al €Lnd geofl:ro-»^ *'•'-■» 
 
 8. 
 
 B0^3 
 
 
 This problem u. 
 muth and altitude — 
 
 quickly ; and this is. (iB42 
 
 cafe more eminently, th6 fart A31 
 
 is from the meridian. Therei 
 
 At the diitance of three 
 either before or after noor 
 zontal circle ; fet the femi 
 that it's nonius may fland' 
 lay the plane of the lad-— 
 in the meridian, by eflin" / 
 directed towards the depreflei. 
 nonius of the declination fen. _ j 
 
 clination, whether north or ic Ji- 
 
 reft the line of fight towards th' , by 
 
 moving the declination femiciie i.is 
 
 ot the equatorial circle, and part' lioving 
 
 the horizontal circle on it*s own There 
 
 is but one pofition of thefe which will admit of 
 the folar fpot falling diredly on the mark on 
 the oppofite fight. When this pofition is ob- 
 
 SS7 
 
 /^^ 
 
N TO 
 
 torial, or horary 
 , and the circle 
 'ane of the meridian. 
 
 LIX. 
 
 ititude, the furCs 
 ..n, are known* 
 
 found by equal alti- 
 
 ar, which is the befl 
 
 .y a meridian mark, 
 
 I, to fet the fcrews in, place 
 
 accordingly, and adjuft it by 
 
 ■ the femicircle of altitude to 
 
 ^he place, and the index of 
 
 the declination of the fun. 
 
 ircle, till the fights are ac- 
 
 the fun. The nonius will 
 
 8 horary circle. 
 
 - \ is more accurate than the 
 
 y -^^-c J. may be applied at all times 
 
 wh i vifible. 
 
<iB42 
 A21 
 
 ■iomlcal and geo^» 
 38ay8. 
 
 80p"« 
 
 E 
 
 / 
 
 
 / 
 
 
"X, 
 
 TM 
 
 qB42 
 A21 
 
 -lomical and geo^r*-'^ *'«'*■• 
 
 
 38aya. 
 
 IE 
 
 
 B' 
 
 / 
 
it 
 
 I 
 
iVl 
 
 \ 
 
 Adams. 
 
 A21 
 
 Astronomi cal and. geo^ro-^^^-- 
 ^'■^•-^ essays. ~" 
 
 QB4^ 
 
 H 
 

 
 I 
 
 
 
 'Vc^ 
 
 
 '^; ^z":^ 
 
 .• ?^ 
 
 ' .*J 
 
 
 
 ^^-^^•^ 
 
 5^:' 
 
 
 I