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SUPPLEMENTAL LUNAR TABLES. ARGUMENT. The Moon's Equated Anomaly, or ) 3. Equa. D. - Ap. 2. Equated. fr. D 45000 50000 60000 D. Eq 65000 D.Eq.. for Eg. ). Dif. for D. Eq. D. Dif. for D. Eq. D. Dif. for D. Eq. D. Dif. For D. Eg. ). Dif. for D. eq 10 A. 5000 A. 5000 5000 SOCO 15000
27 31 15 34/3 8 307 36 72 38 527 7.14 563 05917 41 7 10 17 445 7.22 7 48;
12 422 11 3716 38 412 4 5916 2 29 50 10 47 491 9 281 37 596 508 551 40 4 6 11 491 31 96 531 8 151 32 3.1 15 328 431 22 20 6 15 16 16 38 % 241 336
2 28 85 351
12 42 32 1953 ! 37 19 17 3 20 541 7 개 15 23 18 44 3 14 56 58119 3013 40 2416 619 56 30 73 4 51118 31 2 56 12 32 7 1.2 37 41 113 18.5613 33 52 19 22.29 | 3 16 1993 53 3 7 12 17 5712 50 44 18 93 8 5316 18 35/3 45 49 5 33 7 32 27 49 17 353 2 466 12 17 17 17 2212 45 11 17 473 20 33 5 35 16 47 16 482 39 36 412 22 48 17 12 3 13 46 17 36 26/12 6 512 17 441 16 122 33 56 50 6 16 473 23 437 2716 57 25 10 16 181 5 7 10 612 12 37 16. 15 42 55 15 372 28 14 15 47 2 44 16.03 6 22 16 11 3 16 12 72 727 15 1 222 28!546 13,112 37 396 25 15 23/2 53 2 8 19 45 23 15 13 812 5 49 17. 3 Hol 14 25/2 16 39 14 35 2 3?. 1416 291 14 452.45 59 10 | 91 56 59 15 15 13 4812 10 47 15 521 13 5812 24 456 33 14 14 491 2 53 11 18 14 3! 21 S 55 110 51 41 91 13 11 2 4 52 13 2012 18 121 13 3012 31 42 13 41 45 23 13 5220 17 13 57 17 51 n. 46 21 91 12 341 58 55 12 522 24 29 13 2 2 37 31 *3 121191C 17 17 8 121 40 59 11 561 52 55% 12 132 17 12 2 29 35 12 34118111! 15 24 3 41 17 3 11 1711 46 52 131 35 35 11 261 58 181 1 3412 9 52 16 7 23 3 814130 10 391 40 47 51 34 10 5512 II 6 2 13 33 41 1 13 16 3 6 15 29 17 25 7151 24 391 II 34 40 81 44 48 10 101 55 - 4 5 27 6 16 15 30 8 8 7 29 9 9. 221 28 31 119 9 9 361 47 35 9 441 57 19 17. 31 9 52 14|| 8 6171 13 37 8 9 4 149 8 9 13113!| 9 8 17 33 5 35 34 8 41 16 8 7 9 8 16 8 40 54 23 55 7 31|12 8 16 191 9 52 7 29 17 21 16 7 351 24 56 1 32 38 7 42 56 7 4911 7 37 8 19 2010 56 52 6 491 10 25 6 541 I 17 19 7 24 19 7 16 18 16 2110 514 17 39 6 410 57 18 6 9 3 27 6 131 940 6 19 15 59 6 251 9 15 39 17 40 28 5 41|220 45 35 0 56 27 5 331 o 5 37 I 7 37 5 411 8 8 5 40 7 42 24 412310 39 55 4 480 49 27 4 silo 54 18 4 551 0 59 13 8 4 591 7 5 40 25 41 4124° 34 15 -4 ! 310 38 18 4 710 42 25 4 ulo 46 36 4 120 50 48 15 41 17. 3 2||2510 28 34) 18 26 7 45 3 2310 31 57 3 25 0 35 22 3 2910 38 511 3 331 5ll 21 26 15 421 7 3 2 420 25 34 2 45 0 28 19 10 33 55 18 29 Z 17 41 15 43 21|27|0 17 9 II 40 21 15 2 710 25 27 17 5 91 3 15 431 I 2210 12 48 11 26 I 220 14 10 I 240 15 341 o 16 58 [ 241 2 15 43 175 8 24 17 47 oll290 5 43 0410 O 420 7 47 8 29 O 42 5 43 17. 47 5 0 421 18 za ol|390 O Olo olo OO + + 15000 5000 Eq. ). Dif. b. E, Eq.). Dif. D. E, Eq. ). Dir. D.Eq. Eq. ). Dif. Eq. D. Dif. 5000 Eq. D. Dif. 5000D D.Eq. 65000 co 60000 45000 50000 55000 A. Logo Loge. Cont. Log. for Orb. 9.9565343 To Cof. M. An, or Sine 17° 47' 24". 9.4850526 M. Anomaly. 360 67 81 T. 9.86303;3 So Ecci. += = ,0625. 8.7958800 True Anom. 33 29 13 T. 9,8194681 ,0190957 8.2809326 Doubled is the True Anomaly 60 + 1. Sem. Trans, Equated M. Anom. 72 12 36 > requireda 1.0190957 9.99 17850 co. Whence the Equation 5 22 10 Το 0.1 Eccy, doubled 9.0000000 By Bullialdus's Correction of Ward. 9.9787203 As Sem. Conj. v1.05X,95 cool 0.0005435 To S. 5° 21' 40" 8.9705053 To Sem. Trans. 3 So T. M. Anom. 720 121 3611 10.4936676 Eq. reg.-5 20 44 6.9115159 cubed. To T. corrected M. An. 72 13 S 10.4942111 M. An. 72 12 36 0.4771215 conft. The Half 360 6' 55" ,501 9.0630994 9.9565342 required True Anom. 33° 354 4914 9.8 3y6338 By Dr. Halley's Correction of Bitkop Ward. - 14" From Dr. Halley. M. An. 36° 6' 1819 Eccy. Equation 29 58 Correction Error. Cor, M. A. 36 7 3 Tan. 9.8631328 N. B. The į Dif. between M. and corrected M, An, is the Eco I True An. 33 25 56 Tan. 9.8196071 Correction of M. or cquated A2. by Bullialdus, Loubd. tr. A. 66 51 52 as before. SUPPLEMENTAL Page 3
SUPPLEMENTAL LUNAR TABLES. SIGN 5 Arg. O à D's Apogee, Argument. Equated ANOMALY of the Moon; Or, D 3. equated Ap.) 2. equated. 1. equated. oo 20 4 6° | 8° | 10° 14° 18° 20° 22° 24° 26° 28° 300 + + + + + + + + + + + + 6 16 012 01146 2 43 21 40 38 37 48134 5331 55 28 5525 48 22 41 19 31116 1913 9546 35 3 17 28||45 53 43 1340 31 37 41 34 46 31 50 28 50 25 4322 36 19 27 16 1613 4 9 49 6 32 3 17 41 26||45 37 42 58 40 1637 27 34 3331 3728 3925 33 22 28 19 21 16 10 12 59 9 46 6 30 3 15 6 24|45 12142 34 39 54\37 6/34 14 31 2028 23 25 19 22 1619 916 112 511 9 401 6 27 3 14 81 2244 32 41 5639 18 36 33 33 44 30 52 27 57 24 57 21 5718 5215 5712 40 9 31 6 21 3 1 20 43 42141 8138 3335 53 33 630 17 27 26 24 27 21 31118 31 15 2912 26 9 21 6 131 3 7 IZ 1842 41 40 12 37 40135 2 32 20 29 35 26 4923 55 21 2118 5115 9 9 8 6 5 3 3 14 16141 39139 4|36 37 34 3)31 25 28 46 26 4 23 15 20 2017 35 14 42 11 498 525 54 57 161 14140 7 37 45 35 23 32 57 30 23 27 49 25 11 22 26 19 44117 14 1217 24 8 34 5 42 2 51 12 38 39|36 24134 7131.43|29 15 26 4624 16 21 38119 2116 24113 4211 o 8 16 5 31 2 46 1036 54 34 45 32 34 30 18 27 57 25 35 23 11 20 40 18 1015 38 13 410 30 7 541 5 15 2 38 030 50128 45 20 32 24 17 22 0 19 38 17 16 14 5112 25 9 59 7 311 4 59 2 29 24 7131 10 29 12 27 1025 322 56 20 47 18 32 16 1814 211 44 9 26 7 5 4 42 2 21 261 4/30 54/29 527 15 25 2023 22 21 24 19 24 17 18 15 13 13 610 571 8 47 6 4 22 2 1 2 28 2 28 36 26 50 25 1523 2021 3919 49 17 57 16 114 512 8110 488 8 6 714 4 2 026 1024 37123 5121 2S119 47118 616 25 14 3912 5311 6 9 16 7 271 5 303 43 SI 7 211 28 23 38 22 15 20 54 19 2317 5216 21:14 49113.13 3910 31 3 21 I 41 4 26 21 10 19 47 18 33 17 1415 5314 3213 1011 4610 22 8 557 26 5 58 4 29 2 59 61 24||18 13117 916 614 59 13 4712 3612 2010 12 8 551 7 44 6 27 5 10 3 5312 351 1 18 8 22115 2214 2813 3512 37" 38110 39 9 39 8 30 7 34 6 311 5 26 4.22 3 17 2 11 6 20|12 25 11 4-10 5910 11 9 24 8 361 7401 6 57 6 8 5 17 4 24 3 32' 2 391 1 46 0 54 18 9 25 8 52 8 1917 4317 8 6 331 5 55 5 15 4 391 4 0 3 10 2 41 2 04.1 16 6 21 5 581 5 371 5 13 4 491 4 25) 4 0.3 33 3 2 421 2 15) 1 49 1 201 0 54 28 16 14 3 14) 3 31 253) 2 40 2 28 2 16 2 4 1 491 1 36 1.2315 9 O S60 41 o 280 15 18 4 6 o 41 0 51 51 4 o 31 O 4 3 + + I +7 $ + 3 9.2 55 2.412 301 2 20 81 1 561 1 461 1 321 1 18 ! 51.0 53 42 0 281 0 13 8 6 it 5 541 5 2915 44 43 4 19 3 55 3 32 3 5 2 39 2 14 1 481 1 23 0 56 27 851 8 151 742 7 71 6305 53 5 18 4 39 3 59 3 21 2 41 2 3 O41 11 4811 Olio 16 9 30 8 411 7 51 7 2) 6 IT 5 20 4 271 3 33 2 42 I 491 0 54 28 315 37 14 42 13 4412 48 11 49 10 48) 9 46 8 45 7 42 6 39 5 32 4 26 3 21 2 14 7 0 4 0118 3917 32 16 2315 1714_012 530 39 10 25 9 11 7 521.6.371 5 171 4 2 401 1 19 8 2 10 28 21 55 20 18 18 58 17 42 16-1914'55136 29 12 410 381 9 13 7.40 6 71 4 371 3. 5 I 32 26 4 24 2622 58 21 28/20 i 18 2826 52 15 1513 39 12 110.25 8 40 6 50 5 13 32911 44 6 241|27 8/25 30123 52 22 15/20 34 18 45 16 5815 10 13 2111 32 9. 37 7 41 5 47 3 53 1 57 8) 22||29 4227 57 26 8|24. 2122 2820 32 18 36 16 38|14 37 12 37 10 30 8 24 4 151 2 7 26 34 25|32 2330 28 28 14 23 47 21 33 19 1616 50 14 3612 11 9 45 7 21 4 55 -14) 16 36 31 34 22 32 8 29 5527 3625 14 22 51 20 2517 5745 28 12 55|10 211 7 48 5 13 2 36 16 1438 22 36 733 47 31 28 29 2 21 2918 53.16 1613 3410 52 811 18 337 42 35 1532 49 30 16 27 40125 422 2419 41 16.57 14 91 20 8 33 5 42 2 51 19:42 29/39 3130 32 34 031 21 28 40125 28 23 13 20 24 17 33114 39111 448 51 5 54 842 4040 11 37 36 35 0 32 17 29 32 26 45 23 55 21 1113 615 712 69 516 41.3 1 24 61143 37/41 4138 25 35 4632 59 30 10 27 19 24 25 25 2018 2615 2312 19 9 19 6 133 7 26 41|44 18 41 41 39 036 18 33 29 30 37 27 4324 47 21 45 18 42 15 36 12 39 9.271 6 19 3 9 28 2144 4042 3 39 21 36 38 33 47/30 5327 58 25 421 5718 5315 4612 38 9 32 6 23 3 11 3 3 0144 50 42 12 39 2936 45 33 5330 59 28 4125 522 2/18 57115 5912 41 934 6 23 3 11 19 9 260 220 120 10° 8° 6° Oà D's Ap. 4° 1. equated SIGN 6. N. B. Whether you solve the Central Equation by this Method, or former one of Eccentricilies, you mujt go back for the other Equations, according to the Newtonia n Tbeory, and its Improvements, SUPPLEMENTAL Page 4
SUPPLEMENTAL LUNAR LUNAR EQUATIONS. According to the Construction of Mr. MAYE R. EQUATION of the Node and Mean ANOMALY of the MOON. Argument. Mean Anomaly of the SUN. D. M. o Sig. i Sig. 2 Sig. 4 Sig. 5 Sig. M. Y+sb.& + Dif. An. D. + D. D. + D. + D. + D. An. lin. Ch. B. 8001 9 48 5 1 10 18 6 9 4 5 17 30 5 29 9 Ch.700 1 4 19 TO 18 8 59 s 8 5 15 9 600 o 59 41 5 10 8 5 19 10 58 10 18 28 4 58 15 9 500 o 54 3 3 5 28 9 3 315 10 18 4 48 9 6 27 10 400 o 49 15 O 43 841 26 4 35 9 5 6 300 0 44 40 5 5 46 9 14 4 28 25 4 21 9 5 6 6 200 0 40 19 4 4 8 55 9 19 8 IO 16 7 10 100 0 36 11 7 3 9 23 4 8 3 55 6 23 4 oo 32 16 8 9 27 8 16 10 4 6 10 S. 100 o 28 $5 9 9 31 8 1o 8 328 4 Ch.200 0 25 7 7 8 935 3 8 3 14 4 7 300 o 21 53 6 36 8 9 39 7 56 3 3 27 8 19 3 400 o 18 52 6 5 44 8 7 48 2 47 8 18 3 17 4 6 13 7 52 6 7 41 3 6 8 12 34 17 10 7 600 0 13 31 14 7 9 50 8 4 7 34 2 56 15 8 700 O 11 IO 15 9 53 2 45 15 7 8 8 3 16 800 o 9-3 7 16 10 9 59 2 35 7 14 8 3 900 o 7 9 17 7 23 8 7 10 10 13 8 3 1000 18 O 3 5. 9 53 7 2 12 1 27 7 3 8 1100 4 I 19 7 38 3 9 50 13 7 4 8 1 200 2 48 3 25 7 45 5 51 IO 7 3 9 1300 o I 47 3 35 7 943 8 9 4 1400 o I o 3 44 9 8 10 9 39 4 9 150010 o 27 23 8 3 54 5 IO II 9 35 © 20 8 1боо о 24 4 4 10 13 9 31 6 7 9 25 4 14 8 18 10 14 6 5 6 9 9 26 4 23 10 15 9 23 5 54 045 4 9 1750 27 4 33 5 45 3 7 1800 o 9 9 28 8 36 4 42 10 17 8 6 9 14 5 36 9 29 4 52 8 42 9 9 5 27 o 12 9 to 1900 o 30 5 8 47 9 4 S 17. D. ID. D. D. OM. D. 1950 o OM.) 2000l o 1 이 An. 11 Sig. 10 Sig. 8 Sig. An. 6 Sig. REMARKS on Mr. MAYER's LUNAR TABLES: To which our own LUNAR Tables are reducible in the Mean Places and Motions: Sce Examples farther on. HE did not prefume (he says) to send his Tables of the Lunar Motions into the World, without being thoroughly convinced of their very near, and scarce to be hoped-for nearer Agreement with the Heavens. That briefly to tell us, he says, of more than two bundred Observations of the Moon made not only in this but in the preceding Age, scarce ren were found, from which his Tables differ one Minute and a half; a great many of them come nearer than a single Minute, a:d not one of them all discovered an Error in his Tables of two Minutes. Which as no Tables heretofore published perform the like, the best of them often erring four or five Minutes, he was the ' more unwilling his Tables should lie any longer concealed; especially, as the most celebrated Astronomers of almost every Age have ardently wished for a perfect Tbeory of the Moon (to wbich bis Tables are said nearly to approach) on Account of its fingular Ufe in Navigation. Nos, indeed, (he fays) do they seem worthy of Publication for the sake of this particular Service, in compleating the Theory only, but also on Account of that easy and expeditious Method, by which that particular Service from them may be had, in computing the Longitude and Latitude. For, if you look into other Tables, you will find, on Comparison, these larger Equations fo few in Number, and the Rest of them fol imall, that there is no Need- of having Recourse to the troublesome Method of interpoluring, nor of making the Computation of the Arguments to Seconds. He has contructed thefe Tables, he says, with Respect to the Inequalities of Motions, from that famous Tbrory of the GREAT NEWTON, which that eminent Mathematician Eulerus first elegantly reduced to general analyrical Equations. And, in the resolving of these Equations, after some fruitless Essays by other Methods, he has hit (as he says) upon a particular Method, pretty clogant and concle, which is would be too tedious for him to explain at large in his Preface. For which Reason he has concluded only to give fuch Hints as may conduce to lay open the Origin and Causes of the Inequalities exhibited in the Equation Tables, fo far as it can be done without making Vie of Calculations. Page 5
SUPPLEMENTAE LUNAR EQUATIONS. According to the Construction of Mr. M A YER. Sig. 2. Sig 3. Sig. 4. levection. Dif. Dif. Dif. Dif. Dif.
0 39 50 1 20 42 O 40 52 42 24 041 2 4 ( 20 43 942 39 38 44 29 23 41 1 20 42 28 2 47 O 42 14 45 16 23 40 O 43 25 Il 25 | 20 39 8 13 3 0.37 7 4 10 27 17 23 39 I 20 35 044 35 [ 7 27 26 4 4 O 35 50 5 33 9 23 37 47 511 17. 1 20 30 O 45 44 ( 1241 47 5 34 33 25 8 IS 23 36 7 6 0 46 52 ( 13 17 1 20 23 5 52 33 15 24 18 7 8 23 34 50 0 47 59 I20 I 13 51 5 7 031 57 9 42 23 51 23 7 33 19 I 20 8 4 11 O II Q 30 38 5 I 14 24 O 49 6 5 53 o 12 27 21 I 14 56 I 19 54 o29 19 9 O 50 12 31 13 54 1 o 13 49 o 27 59 15 27 51 17 19 41 4 29 55 o 26 38 19 3 O 16 33 18 O 53 24 0 25 17 57 o 59 30 23 55 17 13 o 17 54 21 25 19 18 16. I 1 O 55 27 I 17 15 o 58 38 o 1915 14 35 24 o 20 36 I 17 30 0 56 28 I 18 15 15 15 57 39 O 22 0 56 39 23 o 19 43 16 I 18 o 21 56 I 17 53 14 O 57 28 21 1 o 23 16 17 0 58 26 il 18 22 1 17 30 57 6 18 0 24 35 I 17 54 36 20 4 19 O I 18 o 25 54 19 59 o 53 32 15 37 55 o 19 5 17 16 0 27 13 1 16 13 19 o 14 13 6 18 54 O 15 29 O 28 31 25 1 19 31 15 44 O 12 48 6 9 I. 18 53 30 50 15 25 8 o 29 49 3 I 19 43 52 O I 2 17 31 10 49 8 251 1 6 1 14 43 7 23 3 53 9 58 8 0 31 19 57 17 II 25 8 6 1 20 8 4 4 33 24 0 32 23 114 10 16 49 O 9 9 8 7 25 1 13 3 I 20 I 5 3 o 33 39 25 5 8 10 15 48 6 1 20 23 O O 45 41 5 43 4 6 15 47 0 36 9 37 25 8 1 20 31 1 12 23 7 4 18 27 o 44 30 3 26 46 14 38 I 28 | 20 36 O 43 18 7 54 14 40 13 26 4 1 III 1 26 5 5 13 43 26 2 41 13 1 20 42 I 10 24 40 52 0 39 50 30 Dif. Dif. + + + Dif. + Dif. Dif + + Dif. evecevection. Sig. 11 Sig 10. Sig. 9. Sig. 7 S. Sig. 8. Of Mr. MAYER's LUNAR EQUATIONS ad MOTIONS. He, not being furnished with such accurate Observations, could not promie that the Latitude found by his Tables will come nearer than one Minute: but, in Eclipses, the Error, he afferts, will not amount to 20". And how plain and caly the Method of computing the Latitude is by Tables thus contrived, (like our own for Facility) and how different from all Methods heretofore laid down, is too evident to require making Mention. In settling the mean Motion of the Moon he has endeavoured to arrive at some Degree of Certainty, as well as Agreement with the Observations if ancient Times. He has examined the earliest. Observations of the Lunar Eclipses made by the Babylonians, as well as Hipparchus, and Proleing; though they are so gross and incorrect, that he in vain attempted to bring them tolerably near their Times, by the Tables; but this will not appear ftrange to any one, who considers, that the Ancients, in oblerving the 'Times of these Pbænomena, did not much regard a Quarter * Half an Hour. Besides which there is great Reason to suspect, that Ptolemy, from whom we have the Accounts of these Eclipses, has too boldly altered the Times of fome, and adapted them to the Numbers of his own Hypotheses. Instances of which are produced by Iļmael Baldus, in the Afiros, Plilol. B. III. C. 7. For this Reaion no Body will impute it as a Fault in Mr. Mayer, if his Tables should be found in the Calculation of one or two of those E lipses, not to come within half an Hour. But, notwithstanding this Difference, arising either from Jehe Negligence of the Ancients, or the Unfaithfulness of PTOLEMY, these Observations have concurrently shewn, that the Moon's Motion pof old was sensibly focuer than it is discovered to be in our Age. Halley, and some other Altronomers, have taken Notice of this Acceleration la the Moon's Motion; but the Quantity thereof has scarcely been well ascertained by any one. In order there ore to determine it the more faccurately, Mr. Mayer has, with great Pains and Affiduity, examined the Observations made between those of Prolemy and our 'Time; viz. those ho: Alba:egnius and other Arabian Astronomers. Among which he found two Observations of folar Eclipses , that because of some singular Circumstankes attending them, tbe Sun's Alitude taken at tbeir Beginning and End, ought, in his Judgment, to be accounted more valuable than Gold and Silwer. He does not remember that any of these Gentiemen who compiled Tables of the Moon's Motion, having made any Use of theie observations; though probably more Advantage might be reaped from those alone than from all the Observations of Poclemy. For wnich Reason, and as they are particularly useful to demonstrate the Acceleration of the Moon's Motion, he thought them worthy of a Place, co copied them, as follows, from the Prolegomena of Tycho's Historia Cæleftis, where they have hitherto lain hid among others of leis AC « In tbe Year of Mahomet's Flighe 367, on Thursday tb2 2816 of tbe latter Montb Rabia, was observed at Grand Cairo, the Metropolis of ** Egypt, ibe Beginning of an Eclipse of the Sun, wbicb, a: rbar Time, was 15° 43'. bigb, rbe Quantity of the Obscurarion 8 Digits; ariel « End obe Sun's Altitude was 33o. 1. Tbe fame Year, on Sunday the 2915 of ibe Morib Sywal obe Sun was eclipsed į į Digits; ar thé Begina SUPPLEMCATAL Page 6
IV. EQUATION of the MOON, or EVECTION. Sig. 2. Sig. 3. Dif, Dif. Dif. Dif. Dif.
0 o 36 59 18 4 5 6 14 4 O 36 59 I 5 39 I lo 38 5 4 43 I 13 59 16 3 26 0 35 53 I 8 29 1 7 37 2 41 2 O 39 12 18 | 13 57 I 6 5 28 34 45 35 I 41 4 ୨) 3 3 52 5 13 53 55 0 40 18 1 2 4 33 36 27 I 17 10 5. 44 4 4 5 9 O41 23 31 18 13 49 I I 20 26 4 10 32 44 O 42 27 I 7 3 | 13 43 O O 31 16 3 33 8 10 45 6 7 44 O 43 30 7 36 I 13.35 0 59 51 30 6 17 1 2 I 30 II 7 9 9 1 O 44 32 6 1 8 I 13 26 O 28 O 59 5 55 1 2 23 17 12 30 IO 47 8 O 10 18 O 45 34 I 16 13 0 58 18 © 27 43 22 1 28 17 O I I 2 II O II 35 0 46 34 9 1 o 26 9 4 13 16 5 O 57 30 21 31 28 o 1 O 13 13 49 O 12 51 10 O 47 34 I 9 32 I 0 56 41 20 1 1 17 59 25 51 14 13 O 14 IT 0 48 33 8 I O O 55 50 9 57 24 5 O 19 25 16 52 14 1 2 O 15 23 O 49 31 10 22 I 12 22 o 54 55 18 0 22 51 1 24 51 13 141 O O 50 27 I 10 46 I I2 021 37 5 O 54 7 17 15 57 21 17 53 13 0 17 54 14 o 51 24 III II 48 0 20 24 16 O 53 14 1 15 55 21 20 55 15 15 o 199 o 5? 19 Il 28 I 28 O 52 19 O 19 9 15 1 15 55 O 20 2) 55 1 16 0 20 24 0 53 14 II II 7 o 51 24 o 17 54 1 13 53 17 21 o 21 37 o 54 7 17 57 I 12 I 10 46 5 o 50 27 o 16 39 14 O 51 17 24 1 18 16 22 51 0 54 58 I 12 22 IO 22 O 49 31 O 15 23 52 16 I 0 24 5 19 12 38 I 9 57 0 48 33 8 1 51 14 59 17 20 o 56 41 I 25 18 9 32 O 47 34 0 12 51 10 1 13 49 2316 21 o 57 30 31 I 5 0 46 34 9 4 Oil 35 9 1 48 o 12 II 28 17 22 o 27 43 O 58 18 I 45 34 0 10 13 12 O 47 IO 1 30 0 59 5 8 17 23 6 113 26 O O 44 32 I 9 I 11 o 9 30 I 2 24 O 30 6 O 0 59 51 13 35 7 36 O 43 30 7 44 I 10 8 45 1 33 3 17 25 O 36 I 7 3 O 42 27 O 5 6 1 10 32 I 18 26 0 32 26 1 I 20 I 13 49 041 23 5 9 4 II 44 4 1 5 171 27 0 33 36 I 2 4 I 13 53 I 5 55 O 40 18 3 52 3 1 4 1 9 41 35 28 18 O 34 45 I 13 57 I 2 O 39 12 8 2 1 41 O 37 I I 16 29 O 35 53 3 26 I I 18 6 4 43 I 1 0 I 18 39 0 36 59 I 30 I 0 O o 4 5 O 4 5 Dif. + Dif. + Dif. Dif. Dif. + Arg. Dif. Arg. pro. Sig. II. Sig. 10. Sig. 9. Sig. 7. pro: MAYER's Argument to the above EvectioN-EQUATION is twice the Moon from Sun - Mean Anom. Moon. The above Maximum 1°14' on MAYER's Maximum of Evection or XII. Equation
Difference, EULER's Maximum too little Hence, MAYER's Evection-Equation divided by 12,02, and the Quotient taken from that Equation, will give the above Equation of EULER, correspondent. For the above Equation use MAYER's XII. Equation, if you negle&t the following V. Equation of EULER. But, if you retain the Vth, with the above Evection of EULER, they will, conjuncily used, come near MAYER's Evection or XII. EQUATION; and compensate for some Errors, or Inequalities, of the Lunar Orbit. N. B. The Eveflion-Equation according to STREET's intricate Method of computing it (from the Chord Evection, and Argument of half the Synodical Anomaly) is supplied by the easier Computation of the Evection-Equation above. Which Equation is applied to the central Equation for the mean Eccentricity, and is therefore equal to about halt of STREET's Evection, applied to the central (or correspondent eccentric) Equation, for the least Eccentricity of the Lunar Orbit. Page 7
Different METHODS of folving the KEPLERIAN PROBLEM. 1. Term. 2. Term. As Sem. Conj. = V1,048219 X 0.951781..0.000 5554 Co. 4.71148 Consta Log, 1.71252 Conft. Log. To Sem. Trans. = 1, 0.0000000 7.64925 twice Log. Eccentricity. 8.82463 Log. Eccy, So Tang. 75° Mean Anom. 10.5719475 2.36073 Conft. Log, for at Term 0.53715 Con Lo, for 2d Ter. To Tang. 75o 13" 45" 2 at Upper Focus 10.5725029 9.99335 Log. S. 2. An=280oor 80° | 9.80806 Log. S. An=1400, 1 37 30 33 • Tang. 9.8851243 2.35408 Log. 2261 = 3' 36"- 0.34521 Const. Log. Orba 9.9580851 2+ tripled 1.03563 Log. 21' fere + 34° 52' 3011 i. Tang. 9.8432094 3' 34" - Correction, agreeing with Halley's TaDoubled 69 45 o The true Anom. nearly. {bles, pro expediendo calculo, &c. 75 o M. Anomaly. Halley. M. Anom. 700 ol ool! 147 Correction į Lat Upper Focus 69 58 13 Tangent 10.4382336 + 8" Error. Log. for Eq. ) Cent. 9.9419120 Here it is obfervable that Bullialdus's is a near Correction, 67° 22' 37'.25"" Tangent 10.3801456 EXAMPLE II. Doubled 134 45 14 50 True Anom, D required. 140 00 00 09 Mean Anom. ). Required the trae Anom, from the Mean 120°, in the same Orbit ? Ift Term. 20 Term. -5 14 45 10 Correct Equation D's Center, 4.71148 const. Log. 1171252 conft. Log. · M. Eq. ) Center. 7.36643 tw.Log. Ecy. 8.68322 Log. Eccy. By p. 68. Argt, 49 20o = 140° Anom. 4° 16' 34" For greatest Eccentricity +58 17 Gr. Dif. Eq. 2.07791 co. L. for 1. T. 0.39574 const. Lo. for 2d Ter. (above. 9.93753 Lo.S.. An= 9.93755 Log. S. An. = 120°. 5 14' 51 Eq. D Center [240° nearly as above, 2.01544 L.103.1, 62-J 0.33329 By Bullialdus's Correction. 9,95 + trip.o.99937 Log. 9,95+ Logo. As Sem. Conje = 1.066777 X ,933223 0.0009705 co. -1'33' 4011=93,67- Correction. To Sem. Transverse=1, M.A. 1200 o oo So Tangent M. Anom.' 140° or T. 400 9.9238135 119 58 26 20 the correct 2 at the Upper Focus, from Aphel, To Tang. 40° 3' 47" or 139° 56' 13'' Logs. 9.9247840 169 58 67 Tan. 10.4381375 half 59 59 13 10 • Tangent 10.2383328 Const. Log. for Orb. 9.9419120 Contt, Log, Orb. 9.9586851 670 22' 30' Tan. 10.3800995 57 32 10 13. Tangent 10.1964179 o The true Anomaly, nearly. doubl. 115 4 20 26 The true Anom, 140 0 M, Anom, o oo oo M. Anom. 5 15 o Equation, nearly. 4° 55' 40" The corre& Equation, agreeing with Dr. Halley's 5 14 45 Equation fr. above correct. Tables. By Bullialdus's Correction, +15" Error, by Bullialdxs. Log. As Sem, Conjugate of the Orbit 0.0005554, CO. EX A M P L E IV. To find the Angle at ibe Upper Focus at 110° M. Anomaly in the Or bit of Mars, wbose. Eccentricity, according to Dr. Halley, is To Tang, 1190 581 674 or 600 '1' 54.". 10.2391160 0,09263936 ? And likewise to determine the true Anomaly, and the 2 at the Upper Focus, nearly. Equation of the Orbir. By the Logarithmic Equations aforegoing, Const. Log. Orb. • 9.9580851 ist Term. 20 Term. 4.712363) Conft. Log. 5.138334) Const. Log. 7.933591| 2 Log. Eccy, 6.900387) 3 Log. Eccy. 4 o True Anom, nearly. 9.9981391 co. Log. d. 9.998139) co. Log. d. o M. Anom. 2.644093 Sum. For the Orbita. 2.036860 Sum. 4 56 o Equation nearly +9.808067 Log. S, 2 A=220°. 9.911957 3 Log. S. A, 4 55 40 Correct Equation from above, 2.452160 Log.283",24 1.955817 Log. 904,334 +2011 Error, by Bullialdus. 4'43",24 ist Term. +i 30, 33 20 Term. EX AMPLE III. 3 12, 91 Correction. Required the Correction of 140°. Mean Anomaly of tbe Moon's Orbit ; 110°.o. oo, oo M, Anom. the centrician being greateft , or 0,0667777 Also to find the true Equation and Anomaly ? 109 56 47, 09 at the Upper Focus. Page 8
PRINCIPLES of the PLANETS PLACES and MOTIONS. The SUN's Mean RADICAL PLACES and MOTIONS, in REVOLUTIONS SIGNS and DECIMALS. RADICAL YEARS. Sun's mean Place from the Sun's mean Anomaly, Sun's Apogee, First * Aries, Old and New Style. Equinox. from Equinox. from Equinox. from Equinox. Jan. 1. s 1600 70. S. 98 20° 12' 31" 69 140.11' 32" O$ 27° 35' 1011 9 8 6 4 3 6 o 57 27 35 9 Jan. 1. $ 1700 7 0, S. 58 3 14 34 7 43 29 Jan. o. 1700 N. S. 6 7_32 24 28 7 43 27 59 19 Newton's by o' 3" by o 3! by Our Places Halley's to 5 10 5 N. B. The Eqs, foregoreduce to Morris's to 10 ISO + 2 ing being connected with Muyer's 8 those of Motion below, and Euler's . -23 23 +2 both joined with our preBradley's wanting. fent Places will give those Equation of Places. N. B. Mayer's Paris by others, Places are but 23" lers than those correspe Places at Greenwicb. TIME forward. Mean Motion O. Mean Motion O An. Mean Motion Apog. Mean Motion 1*g. 100 Julian Years. IOOT OS 45' 32" our 99' 11% 29° 3' 2!! 1° 42' 3017 1° 24' 1011 Our Motions in 100 Ju- Newton's by 1217 cull by 1' 30" han Years, reduce, from Halley's +1 23 1 22 4011 O 50 1600 and 1700, to Mayer's . + 14.40 to 10 17 8 + 1 40 Equation of Motion. Pradley's wanting. Divide each Quantity above by 100, for the Equation of Motion our Places tor 1 Year, which multiplied by the Years trom 1600 os 1700 will be the whole Equation of Motion, and connected with Equation of Place above will be the Equation of our present Places to others. Decimals. Decimals. Sign. Sign. +47 09.00101185185&c. 47-09.00126592592 I+,0022777777 +,00187037037 Our exactly +1' 49" 16" 48iv exactly — 2' 16" 43" 12iv + 4'6" exactly. +3' 22" exactly. Sign. Sign. +,002247037037 +,00185185 &c. Sign. 1 Com. Year, Our +11.9920392374 +118.9914778627 +,000561374756 +,0004672725 113 99° 45' 40" 14""'&c. 113.29°44' 39' 36'"&c. I'O" 37'' 421v &c. so' 27" 53 or 365 Days Sign. Sign, 119.99 14778925 +,000 5613758 +,0004626558 ti'o 37 +49' 57" 56" Common Years 31 30 40 46 +2 15 3: - 42 59 17 46 + 53 [Halley. I + 1 40 1 40 35 After Biffextile Our. + 2 2 31 23 Our Sign. Sign. Sign. Sign. +,0328549021 +,032853364 +,000001538 +,0000012802 g'" 58iv 8" 17iv 44V Sign, + Hous +,0013689542 +,00 136389 O's Apogee this Anom. Therefore when it is Leapd and 2' 27' 50!!!, &c. 2! 27" 50111 &c. his Longitude. There-Year, a Day, and Day'sMoSim. Sign. fore, O Longitude - his tion must be fubtrafied for Minute +,0000228 15904 +,000022814 Ap. = his Anomaly. the Months of Jan, and Fed. 2" 27" 5oiv. 21 27") soiv Being the New and shorter Sign. Sign. N.B. Tlie Rad. Pis, for the Computation : the Lp.-Yr. Second +.00000038026 +,00000038024 Beginns. of Leap-Yrs are not taking Place till 29th Halley of February 2" 27iv 50V, &c. 21" 27iv qov &c. advanced a Day's Mot. + Decimals Decimals. Jul. Yrs. Dec. jul. Yrs Dec. REVOLUTION. 365Ds.242 3006021 365D3:259727107 21073,1707317 25663,366336 Anomaliftical Year. of from O's An. 3654,256532906 Decimals. Decimals, [6h 9m 245 26th 33 fo [619m 129 110 &c Our Sydercal Year greater Day, Years Solar, ano- Our ,030797591 +,038908428 than our Solar by 204 299+,026131624 malistical, or Syde-) 44m 205541h4260 56m 18 41th 17 fo 2611 1401 1460 &c. 3.6 25$ 46th 2010 real, retard or advac Day. Day. Dr. Halley's Sydereal greater Day, Jot 4 Julian Years, l Hall, -,0308013493 1,037593164 than his Solar by 20m 179 +,025564188 according to y or t, as 44m 215147h Ijto 54m 89 2th 57f0 zoth &c. 36m 488 44th &c. to Month-days. Seasons go back, in Yrs. And advance in 4 Yrs. *s advance, in 4 Yrs. + 5h 48m 54 Verral Equinox. Our Anomaliftical Y' great- Dr. Halley's Anomaliftical Com, Years 37 49 Mar, gi 2h 16 in 44,1700 er than our Solar by 250 greater than his Solar Year 3. + 17 26 44 Mar, 8 15 54 30, 0, S. 5' 391h &c. by 24" 378 1g/h 1670 &c. After Biffextils Seaíons go forward each Y', 0: 19, N. S. Halley (1756 PRINCIPLES Page 9
ELEMENTS of the PLANETS PLACES and MOTIONS, according to our late JMPROVEMENTS. In REYOLUTIONS, SIGNS and DECIMALS. Mean Places RADICAL YEARS, from Equinox. M, Pl. Aph. M. Pls. Node. Mean Places 24 from Equinox. M. Pls. Aph. 24. 11. Pls. Node 24. Pan, 1. § 1600? 0.S. 38 25° 26' 49" 49 280 36' 40" 15 16° 21' 22" 145 100 20" 24" 9° 34' 24" 35 50 34' 10" fas. 1. .71600 N.S 36 33 16 14 9 30 31 6 9 5 34 9 127. 1. S 1700 20, S. 5$ 270 9' 9 5$ 033 20 18 17° 24' 42" 98 16° 48' 35" 6 S 90 33' 48" 38 Yan. 5 23 15 5 0 33 18 17 24 41 15 53 43 6 3 iTME forward. M. Mot, of irom E:*. M. Mot Aph. M. Mot. Node . Mean Motion 21. M. Mot. A,. 4.M Mot. Nowe 21. 1oo Julian Years. 531 25 1° 42' 20" 1° 56' 40" 3' 20" 1.85 55 60 287 u on los 10 23' 20" 27 13 15° 40' 5" 36"os 4' 40" Los 2' 32" ||0 451027'31" 38"'24141cs 4 43"Os Decknads Deg. Degs. Decimals. Dess. Degs. +258.52227407407 +0,07777777 &c. 12,0422222 &c. +49.04862629629 +,08 +,0555555 &c. Decimals. Decimals. 365 Days. +65.37620125438 + i' 10" It 38" +138.01146379045 + 1' 12" It +IS 00 200 599 +1 12" to Com. Years. +-10 22 34 19 28 + 2 + 16 +2 41 16 10 + 2 24 3. +7 3 51 29 12 + 3 30 +3 1 54 15 + 3 36 + 2 After Biffextile. Sign. Secs. Secs, Sign. Secs. Secs, Day +,01746904454 +,00277113367 +,197 11"147"1/1234 Sign. Secs. Secs. Sign. Secs. Secs. Hour +,00072787685 +.0001154639 1,00820833 &c. 1,00570833. &c., 1' 18" 16" &c. 280114840 115"'13 129' zei &c. Sign. Sign. Minute I tooco1213128 t,coco019244 12" 28iv. Sign. Second +,00000020218 t.cooo00032076 sziv 28v &c. The Mear PLACES and MOTIONS O: SATURN. RADICAL YEARS. Mean Places h M.Pis Node h.M.Pls. Node h. The PLANETS Mean Periodical REVOLUTIONS, yan. I. S 1600 20.5. 6s 160 10' 32" 85 280 31' 56" 35 180 51' 46". Decimals Ds h 28 31 543 18 51 45 8 87.968454378 87 23 14 34 27 yan. I. S 1700 70.S. 11s 9° 16' 32" 185 28° 33' 10" 39 21° 우 224.695493091 224 16 41 30 36 8 Jan. o. 1700 N.SI 3 S 28 33 18 686.929383687 686 22 18 18 45 3 5 5 Mean Motion h. 34;30.357686018 TIME forward. 4330 8 35 4 4 M. Mot. Ap. h. M. Mot. Node ḥ h 10750.551876380 10750 13 14 4 100 Julian Years. 13 43 23° 6' 0" The PLANETS Mean Synodical REVOLUTIONS with each other. 4 Julian Years. Decimals. Degs. Ds Decimals. Ds h +15.6308 1+,088888 &c. 5,02 39.6300348836 39 15 7 15 Decimals. 31.1035889370 31 2 29 10 5 365 Days. 109.4974209445 It i' 10" + 18" 29.5305908501 29 12 44 3 3 28 10 52 42 35 os 12° 13' 21" 27" + ' 20" 28.4532706809 + 18" 4 Com. Years. 27 11 52 53 8 24 26 27.4950595246 42 54 + 2 40 + 36 27.3911968963 27 923 1924 3. 6 40 4 21 54 After Biffextile. 144.5662497937 114 13 35 23 59 O 115.8775019497 3 30 10 Sign, Secs. S.cs. | 100.8882436086 100 21 19 4 14 Day ,00111162217 +,219 +,049 21 89.7925323996 89 JO I 12 38 hl 88.6942117894 88 16 39 39 54 Sign. 0 583.92 14751501 583 22 6 55 27 Hour +,0000465092 +,009125 +,002041666 우 3 333.9217217235 7 16 45 5" 1" 22iv 32"11 5782 2236.9926725095 236 23 49 26 54 Sign. h| 229.492o68 3698 229 11 48 34 43 Minute +,0000007751 | 779.9370265795 779 22 29 19 5 5" iiv 22v 27 398.8861976230 398 21 16 7 28 Sign. 5 378 087553478 6 4 37 Second +,0000000129 24 816.4425616661 816 10 37 17 19 | 733.8182627679 733 19 39 17 5+ To determine tbe Place of a Planet at any Time by its periodical Revolution, and \be Place of that Planet given for some one Time Before or After? 24 RULE. Divide the Time, in Days and Decimals, after or before the radical ņ17251.1412534284 17251 323 24 17 Time of the Place given, by the Time of the Planet's periodical Revolution, in Pays and Decimals, and the Quotient will be the Number of Revolutions perform d in that Interval, which turned into Signs, Degrees, Minules, &c. (neglecting whole Revolutions) and added or subtracted to or from the mean radical Place, according as the Time of the Place Tought is after or before the Time of the Place given, and you will have the mean Place required : Which Operation may be readily performed by a Table of Logarithms to many Płaces. See Examples for finding the Mear Places from ibose given, further on. ELEMENTS Page 10
A TABLE Thewing, at Sight, the NUMBER OF DAYS, from the itt of January to A TABLE for reducing Julian any Month-Day of the Year following in a common or Leap Year. Years to Days, and the contrary. Feb. Mar. Apr. May June July Aug. Sept. Oct. Nov. Dec. Year, Year, Julian Days. MDS M. Do No Ds No Ds No Do No Do NDS No Ds NOI) NO Ds No DS No DS No Ds No Ds Years. Years. 1 60 91 120 152 182 213 244 274 305 335 * 1 365 600 219150 61 92 I 22 214 245 275 306 336 * 2 730 700 255675 3 34 62 * 3 1095 800 292200 3 35 63 94 124 159 185 216 247 277 308 338 1461) ၂၀၁ 328725 4 5 36 309 339 2922 365250 157 187 218 249 279 310 340 4383 7;0,00 7 38 66 97 127 158 219 250 280 311 341 584+1 3000 1095750 8 67 98 159 189 220 251 281 312 342 730$ 4000 1461CCO 9 9 40 129 160 221 252 232 313 343 24 8766 scco 1826250 10 TO 9 41 100 69 130 161 191 283 3'4 344 10227 6000 2191500 11 JO II 42 70 IOI 131 162 192 223 254 315 345 32 11688 N.B. There being 12 11 12 43 71 132 193 224 255 285 316 346 36 13149 1461 Days in every 13 12 13 44 72 103 133 164 194 225 256 286 40 14610 13 14 4.Yulian Years, when 45 73 104 134 195 226 257 287 44 1607 1 either the ift, zd, or 14 15 46 74 105 135 166 196 227 258 288 319 349 17532) 3d (marked with *) 15 10 47 106 136 167 197 228 289 320 350 52 18993 is Billextile, or Leap 17 16 48 76 260 290 321 351 56 20454 Year, one Day must 18 17 18 49 77 108 138 169 199 230 291 322 352 60 25915 be added to the Days 19 18 19 50 78 109 139 170 200 231 262 292 323 353 64 23376 in the Right-Hand 20 19 20 51 79 110 140 171 201 263 293 324 354 68 24837 Column, for the true 21 20 21 52 80 III 141 172 202 233 294 Number of Days, in 325 355 72 26298 23 21 22 53 81 II2 142 173 203 234 295 76 Succeffion from the 27759 23 23 54 82 266 296 327 357 80 29220 1st Year, as is evi23 24 55 205 267 297 84 30681 dent by the 3 first 25 56 24 84 IIS 145 176 206 268 237 298 Numbers fet down, 329 359 88 32142 36 of 365 Days, in each 26 25 116 57 146 177 269 299 330 92 86 96 35064 301 332 36525 29 28 29 60 88 119 149 180 210 241 302 333 363 730,0 30 29 30 89 120 181 211 273 303 334 364 300 109575 31 30 90 121 151 182 212 243 274 304 335 146100 91 192 244 305 500 1826251 CONSTR. After the ift 3 Yrs, 1461 EXAMPLE I. Days are added for each 4 Yrs, from the ift 4 Yrs, continually, as far as ico To find tbe Number of Days from January 1, to October 31, following, in a common and alfo Leap-Year? Days. Yrs; then 36525 Days for 100 Yrs are continually added to the Days for the last hundred Years. Againft 31 in Month-Day Columns { in the common Year Aritbmetically, EXAMPLE II. Multiply the No. of Julian Yrs by 365 Ds, and to the Product add the Quo tiene of those Yrs divided by 4, and the To find obe Number of Day, from sbe if of January, so tbe 23d of February, in a common or Leap-Year! Sum will be the Ds in those Yrs, when the 4th from the ift is a Leap-Year. Againf 23 in the firft Month-Day Column (serving for January and February in common and Leap But if the jít, 2d, or 3d is a Leap-YF, Years) you find under February 34 Days, for both Years, required.. then a Day must be added to the said Sum for the exact No. of Days required, N. B. The above Table is firft made according to the common Year, or Firft Column, serving equally Ex. To find the Number of Days in 18 for January and February in common and Leap Years. And therefore a Day's Place advanced in Second rears, tbe famous Eclipsc-Period? Column, serves for Leap-Year, after February (of 29 Days) by adding a Day to that Month. Hence, the Reason for our adding a Day's Motion to the Epacbas, or Places, for the Beginning of Leap 18 Years Years, to make them correspond with Places for January if, at Noon. For thus contrived, you see the Day's Motion ordered to be added, in orber Astronomical Tables, for all months after February, in Leap-Year, 2920 is alseady done in our Epocbas for the Beginning of that Year, whilst there is only a Day and Day's Motion 365 to be taken our less for ebé two Montbs of January and February, for each Leap-Year. Product 6570 +4=18:44 In like Manner the Day's Difference between Old and New Stile do not take place till February the 2915 Sum 6574 Days required, of the Julian Century when 3d or 4th Ýr, fr. ist is a Leap-Y!. but 6575 Days, when ist or 2d Y:. from it is Leap-Y". 223 Lunations =6585Ds 7h 4320. Yrs. Beg. 18Y11076437200}: 1 LP-Y!! 18 For 16 Yrs = 584 Days 2 Yrs 730,+i -6574, and 6575 6585 . . 6685 Page 11
The SYDEREAL and SOLAR DAY.
THE Rotation of the Earth, on its own Axis to the Left, or Easterly, being uniform, (causing an apparent uniform Revolution of the fixed Stars, about the Earth, to the Right, or Westerly) is the equal Measure of Time. For, the Diameter of the Earth's Orbit being but a Point in Proportion to the immense Distance of the fixed Stars, their Position cannot be altered to us by any other Motion of the Earth than that of its Rotation on its own Axis, except a small apparent Change caused by the progreslive Motion of Light, and of the Earth in its Orbit. And therefore the real Rotation Easterly of the same Point, or Meridian of the Earth, to the same fixed Point in the Heavens, for the apparent Revolution, Westerly, of the same fixed Star, to the fame Spot, or Meridian, of the Earth) through an entire Revolution, is alyays the equal Measure of what is called the Sydereal Day. But, the Earth having an accelerated or retarded Motion, through its Orbit, to the Left, round the Sun, and a Rotation the same way, or to the Left, on its Axis, causes an apparent Motion of the Sun to the Right. The Interval of these two Motions (real or as parent) at the Sun's next Return to the same Meridian, is what the Astronomers call the Afronomical, or mean Solar Day, which they make to begin and end at Noon. For if they reckoned it to begin and end from and to any other Time of the Day, (as from and to Morning or Evening) the Inequalities of the solar Daws would be much greater, on Account of the Increase ard Decrease of art ficial Days. And the Sun being the bigger Light, and the Stars revolving in Succellion through the Year, the solar Day, for that Reason, is found more convenient than the sydereal, for the common Measure of Time. If the Sun had no other apparent Motion than that of its diurnal Revolution round the Earth, it would, every Day, appear to describe the fame Parallel , through the Heavens, (from Rising to Setting) and be accompanied with the fame fixed Stars at its Return to the same Meridian. But by the Earth's Progresfion in its Orbit, as before described, the Sun, every Day, appears to be removed as much to the Left, or Eastward, of the Sun's Place on the former Day, as the Earth has really moved the fame Way, in the oppofite Part of the Orbit or Ecliptic. And therefore, apparently , the Sun returns to the same Meridian each Day, about 59'8" (the Earth's mean diurnal Motion in right Ascension) later than on the former Day, or Return of the same fixed Star to the fame Meridian. For the Stars appear to advance, each Day, about 59'8", (or 76 Part of a Revolution) of the Sun.' Hence i mean astronomical or solar Day is measured by the Sum of 1 Revolution of the Earth on its Axis, and Part of another Revolution, = 3650 + 59' 8", OR An ASTRONOMICAL or SOLAR D'AY, AT ALL TIMES, is accurately , measured by the Sum of 360° of the Equatory, and an Are of the Equator correspondent to the Are of the elliptic Orbit, described by the Earth (or Sun apparently) in that Day, i. e. 360° + Diff. R. Å, in that Day. For, when the Earth has described a Revolution of 360° to the fixed Stars, on its own Axis, it must still revolve to the Left, that Day, as much as its annual Departure in R. A. the same way in its Orbit, to bring the Meridian of the Earth under the Sun; then apparently removed to the Left, or Eastward, as much as the Earth has advanced in the contrary Part of her elliptic Orbit. The like is also evident by the apparent Metier of the Sun and Stars exhibited on the cæleftial Globes. Therefore, if a. fixed Star comes to the Meridian with the Sun, at Noon, the fame fixed-Star, after one Monitor iz of a Year, will come to the fame Meridian exactly ti of 24 Hours, or 2 Hours, sooner, and so, in Proportion, for any Number of Months after. In 6 Months, or Half a Year, it will come to the Meridian at Midnight, 12 Hours preceding the Suņ; and in 365 Days, being almost a folar Year, it will come to the Meridian about one Day sooner, or nearly. return to it again with the Sun; in which last Intervai, the same fixed Star will: have returnú to the Meridian about. 366 Times, or made nearly that Number of Revolutions to 365 Returns to the Meridian, or Revolutions, of the Sun. 365 Days Hence, = 23h 56m 3' 56th 360 56", &c. = Time of i Revolution of the Earth or fixed Stars : 366 Revs, being nearly the Quantity of the Sydereal Day, in mean folar Time, but not correctly. See Fergusen's Afrmony (P. 95, 96) erroneously making 366 Sydereal Revolutions, exactly, in 365 folar Days. KB The above Computation does not consider the Earth's Motion (or : un’s apparently) through the whole Orbit, or Ecliptic in right Ascension ; but only provides for 365 Days of a Revolution. Therefore the compleat Year must be divided by itself +1, the Revolution gained in that Time, for the correcter Length of the sydereal Day. 365.2423006021 Days. Hence, 366.2423006021 Revs, ,9972695617 Day 23" 56m 4' 5th 26fo, &c. correcter Time of the SYDEREAL DAY. Page 12
DIVISION of TIME. March the 20th, 3h 54 30°, Morning ; and fell about 44" 21°, later in 1752, that Year for which the Oli Stile was corrected to correspond with the new one, or foreign Account of Time, and likewise adapted to the Error of the Equinex, falling on the 21st, instead of on the 20th of March, as it fell at the Nicene Council, and falls at this Time , though the Alteration of our Stile to correspond with the foreign Account was the principal View. Pope Gregory XIII. first settled the New St le 1582, who called 5th Oftober the 15th for that Year, thereby striking 10 Days out of the Calendar. For, dividing 1257 Years since the Nicene Council, by 130 Years, in which the Seasons fall back a Day, the Quotient will be above 93 Days, the Seasons were then fallen back. From hence, 1257 Solar Years, fince the Nicene Council appear to have been compleated, besides 91 Days, in 1257 Years of the Julian Reckoning; for which Reason 10 Days loft in the solar Account of Time, were first struck out of the Julian Calendar, lince made to correspond with solar Time. And to prevent (as much as possible) the falling Back of the Seasons in the Month Days for Alteration of Style. the future, and to keep a Conformity between the Gregorian and Solar Account of Time, (the one in whole Days, and the other in Days and Parts, to the Year) Pope Gregory farther ordered, that every Fourth Hundred Year, from 1600, should confitt of 366 Days, as usual; but that every Three Hundred Years or Centuries, in Succession from even Hundreds, mould consist of 365 Days only (fimilar to three fucceffive Years after each B://extile) and not contain 366 Days each, as formerly. Thus he provided for 3 Days, that the Seasons fall back in every 400 (instead of 390) Years. See p. 30, 31. In this New AcCOUNT of Time, called the GREGORIAN or New Stile, from Pope Gregory it's Author, the 5200 For, they fall back in 5200 Years by Julian Account = = 40 Days. 130 5200 400 130 Seasons fall Back ; and therefore = 13, Times 400 Years = 5200 Years Gregorian, as before, in which the Seasons fall back i Day. Anno Chr. The Old Stile was corrected in England to the New, for 1752 The Year of the Nicene Council 325 Now, = 11 Days, nearly, the Seasons fall back from the Time of the Nicene Council, to 1752, the Time 130 Which u Days loft in the solar Account of Time, were fupplied in the Gregorian Account, in our Calendar, by ca' ing the 3d of September 1752, the 14th of that Month. This Alteration of Style reduced the Seafons (with regard to the Month Days) as they stood at the Council of Nice: For 1427 solar Years and 11 Days over are nearly compleated in that Time instead of 1427 Years only, reckoned by the Julian Account. Hence it appears, that reducing the same Number of Days into different Years of any kind, does not give a different Value to those Years in either Account of the same Time ; which is contrary to common Opinion that those Days are loft. For, whether we reckon the same Number of Shillings, in Guineas, at Twenty Shillings and Six Pence, or at 21 Shillings each Guinea, the different Number of Guineas by either Account, in the same Number of Shilling Pieces, will have but the same Value, similar to the same Number of Days in a different Number of Solar, Juhan, and Gregorian Years. Of YEARS. The Civil Year, in moft Parts of Europe, contains 365 Days for three Years fuccefively, olar, Lunar. called common Years, and every 4th Year contains 366 Days, called Leap-Year, or Bifextile. These Civil Years are called also Julian Years, from Julius Cæsar, who added a Day every 4th Year to make ( 25 he expected) the Civil and Solar Account of Time keep Pace together; and keep the Seasons, by that Means, nearly to the same Days of the Month. The civil or common lunar Year is likewise Complete, or Vacant. The Complete consists of 354 Complete. Facant. Days, at the End of which the Year begins again. The Vacant, or Embolimic Year, is that wherein a Month is added to make the Lunar correspond with the solar Account of Time. By this Method, the Jerus kept their Account of Time, according to the Lunar Motion. But, by adding no more than a Month of 30 Days, called Ve-Adar, every third Year, in their Account, it fell Short of the folar Reckoning, in that Time, by about 3 Days. The Page 13
There are (befides the Appearances spoke of ) cloudy Siars in the Heavens, so called from their appearing of a dim and misty Cloudy Stars. Light to the naked Eye ; but appear through a Telescope, to be broad illuminated Parts of the Sky, containing one, or more Stars. Five of these cloudy Stars are mentioned by Ptolemy. 1. One, at the Extremity of the Right-hand of Perseus. 2. One, in the midit of the Crab. 3. One, unformed, near the Sting of the Scorpion. 4. The Eye of Sagittary. 5. Ore, in the Head of Orion. In the first of these more Stars appear, through the Telescope, than in any of the rest; though 21 have been reckoned in Orion's Head; and above 40 in the Crab. Two are visible in the Eye of Sagitrary, without a Telescope ; but several more appear by the Use of that Instrument. Flimfecit observed a cloudy Star in the Bow of Sagittary, containing many small Stars. Cassini and Flamifeed observed one between the Great and Lille Dog, appearing full of Stars, only vifible by the Telescope. The two cubilish Spols near the South Pole, called the Magellanic Clouds. Magellanic Clouds, by Sailors, resembling the Milky Way, to the naked Eye, appear through Telescopes to be a Mixture of small Clouds and Stars. But, the most remarkable of all the cloudy Stars is in the middle of Orion's Sword, where Seven Stars (three of which are close together) seem to hine through a Cloud, very lucid near the middle ; but faint and imperfect about the Skirts : looking like a Gap in the Sky, thrcugh which appears Part of a brigbler Region. Though most of the cloudy Spaces are but a few Minutes of a Degree in Breadth, yet, as they are anions, the Fixed Stars, they must be every one larger Spaces than our Solar Syjiem occupies; as in which there seems to be a perpctual uninterrupted Day, among innumerable Worlds. Of New PERIODICAL STARS. Several Stars are described by antient Aftronomers not now to be found; and others are now visible to the naked Eye rot recorded in antient Catalogues. Hipparcbus observed a new Star about 150 Years before Ciris, who las not mentioned in what Part of the Change of Stars. Heavens it was seen ; though it occafioned his making a Catalogue of the Stars the most antient of any that we now have. The first new Star that we have any certain Account of was discovered by Cornelius Gemma, on the Sib of November, 1572, in Cufficpea's Cbarr. It furpassed Sirius in Magnitude and Brightness, and was seen for 16 Months in Succession. It appeared, at first, bigger than Jupiter to some Eyes, by which Means it was seen at Mid-Day; afterwards it dec yed gradually in its Lustre and Magnitude, till March 1573; when it became invisible. On the 13th of August, 1596, David Fabricius observed the Stella Mira, or wonderful Star, in the Neck of the Periodical Stars. Wbale, fince disappearing and appearing, pericdically, seven Times fix Years, continuing in its greatest Lufire, for 15 Days together, which is never quite extinguished. In the Year 1600, William Jansenius discovered a changeable Star in the Neck of the Savan, which, in Time, became so small, as made it thought to have disappeared till the Years 1657, 1658, and 1659, when it recovered irs former Luftre ard M.fognitude; but loon decayed in both, and is now of the smallejl Size. In tée Tear 1604, Kepler, and several of his Friends, saw a new Star near the Heel of the Right Foot of Serpentarius, fo bright and sparkling, that it exceeded any Thing of the Kind they before had seen, who observed that it was every Moment changing into Lime of the Colours of the Rainbow, except when it was near the Horizon, and generally appeared white. It exceeded jupiter in Magnitude, which it was near during the Month of Oktober, but distinguished from Jupiter by his steadier Light. This Star disappeared buruien Ufeber 160s and Fitruary following, and has not fince appeared. in the Year 1670, July the 15th, Hewelius discovered a necu Star, which, in 0sicher following was so decayed as to be hardly perceptible. In April following, it regained its former Lustre; but wholly disappeared in Auguft. In March 1672 it appeared again very li.ali, diappearing ever fince. In ibe Year 1686, a new Star was discovered by Kircb, disappearing and returning periodically in 404 Days. In ibe Tear. 1672, Caffini observed a Star in the Neck of the Bull, which he judged was not vitible in Tycko's Time, nor yet whes Bayer made his Catalogue. Of Changes in the HEAVENS. Many Stars, besides those before-mentioned, have been observed to change their Magnitudes and Appearances ; but as Periodical Stars Done of them were ever observed to have Tails, 'tis concluded they could none of them be Comer; having no Parallax accounted for. in their greatest Lustre and Magnitudes. It appears probable, that theie periodical Stars, having vaft Clusters of dark Spois, make flow Rotations on their own Axes; by which Means they disappear when the Side covered with Spots is turned towards us. And those Stars, breaking out of a sudden, with such resplendent Brightness, are probabiy Suns of other Syßems, whole Fuel being much exhausted, acquire their Blaze and Splendor, continuing for some Time by the Acceffion of the Comets of that System, lodging on their Surface. For, ibis (according to Sir Isaac Newton) appears to be the greates Use and End of tbe Cemetary Part of a System. And M. Maupertuis, in his Dissertation of the Figures of the Celestial Bodies (p.61 to 63).is of Opinion, that some Stars, by their prodigious swift Rotation on their Axes, assume not only the Figures of flatted Globes next their Axes, but, by the great centrifugal Force, ari fing from such swift Rotations, may become of the Figure of Mill-stones, or even be reduced to jilat circular Planes, so thin, as to be quite invisible when their Edges are turned towards us: As Saturn's Ring is invisible in such Positions. That, when very excentric Planets, or Comits, go round any flat Star in Orbits much inclined to its Equator, the Attraction of the Planets or Comets, in their Peribelion, must alter the Iscliration of the Star; on which Account, it will appear more or less large and luminous, as its Broadfide is more or less turned towards And thus he thinks we may account for the apparent Changes of ibe Mognitud, and Lure of tbofe Stars; as likewise for their appearing and diluppearing at certain Intervals. Some of the Stars, particularly Areturus, have been observed in chan e their Places, in the Heavens, above a Minuse of a Degree, in Refect of the Situation of other Stars. But whether this is owing to any real Motion of the Stars then felves is the Business of many Ages 10 de If our Solar System changes its Place, with Regard to abble Space, it mut, in Time, occafion an apparent Change in the Distances of the Stars from one another. And, in such a Cafe, the Places of the neareft Stars to us being more affected than those at a greater Distance, their relative Pctions will seem to alter, though the Stars themielves were really im novcable. On the other hand, if our Suytron remains at Rest, and any of the Siers of other Synums, have real Motion, in respect of intimice Space, their Positions will be charged thereby, and apparent Places, more or less, according as those Stars are nearer or further from us; and the swifter or power those Motions are, and iheir Directions more or less suited to our Perception. And the same will happen froin rial and differeni Motions in the Systems themelves. The obliquity of the Ecliptic to the equivalis, at preient, about one skird i'art of a Degree less than Piclemy deterIclipe de Obliquity mined it. For most of the Aftroncmcis aiter hire found this Obliquity to decreale gradualy down to Tycko's Time. It changes. it be objected that we cannot depend on the Obiervations of the autient Astronomers, on Account of the Incorrefiness of their Instruments, it may be urzed, that Tyrio anu Flamjleed were both able Observators, and yet Flamfleed makes the Estiptic Oblicuity about 2! Min. of a Degree leíó than Tychodid, atvut 100 Years before ; which Difference can hardly arise from the different Cor. Page 14
2/30158186 B 3/31/59/3710
CHRONOLOGICAL TABLES. YEARS fince CHRIST. Sunday Letter, of either Style, the Day of CENTURIES. CENTURIES the Week to any. Day of the Month, in D2 that Year, for ever. SUNDAY-LETTERS, 200 300 400 200 300 400 MONTHS. 500 600 700 800 500, 600 700 800 ABICIDE IF G 900 1000 11001 200 900 1000 11001200 3 41 5 6 7 1300 1400 1500 1600 1300 1400 1500 1600 JANUARY 31 8 9 10 11 12 13 14 1700 1300 190012000 1700 1800 1900/2000 OCTOBER 31 15 16 17 18 19 20 21 YEAR S 2100 2200 2300|2400 YEARS 2100 220012300|2400 22 23 24 25 26 27 28 above 2500 2600 2700 2800 above 12500 2600 2700 2800 293031 1 3 4 Centaries 2900 3000 310013200 Centuries 2900 3000 2100 3200 516 7 8 910 II 18 CHÁIST. 3700 3800 3900 4000 | CHRIST. 3700 3800 3900 4000 MARCH 3119120121|22 23 24 25 G E BA С E G BA November 30126 27 28 29 30 31 1129157185 A F D С 1129157105B F IG 31 41 5 6 7 8. G E D 230 58 36 A IC E F APRIL 30 9 10 11 12 13 14.15 A F E B D E JULY 31 16 17 18 19 20 21 22 4326038 EDC BAGGF 413260881F E AGCB DC 23 24 25 26 27 28 29 D B А 5133|61|29 D 30 3! 3 4 5 613462.90 G E C B 6 34|02 900 E G A 6 7 8 9 10 11 12 7 3563911A F D IC 713516391 B D F G AUGUST 31 13 14 15 16 17|18 19 8 306422 CB AGFEED 8 1366492 AGCB EDFE 22 23 24 25 26 9137 65193 D B F 9370323F A С D 27128129 30 31 10386694E с A IG 10138.66 19+ DE G B С 31 41 5 6 7 8 9 11 3967195 F D B A ໂ 13927195 D F A B SEPTEMBER 30110 112 13 14 15 16 12/4068 90 AGFE DCCB 124068 96C BED GFAG DECEMBER 3117 18 19 20 21 22 23 1341 69971B G 1341091971 A e F 24 25 26 27 28 29 30 14:42 70198 C A F E 41427098 G B D E 31 3 15437199 D B G F 15 4379199 F A с D 7 8 9 1614472 FE DCBA AG 164472 EDGFBA CB MAY 31 14 15 16 17 18 19 20 17145 73 G E B 1714573 IC E G A 21 22 23 24 25 26 27 18.40 741 1 F D C 18145741 B D F F 28 29 30 31 3 19 47 75 B G E D 194775 A ICE F 4 5 6 7 8 20 48176 DCBA G F F E GF BA DCED JUNE 30 11 12 13 14 15 16 17 21'4977 E ІС G 21/4977 JE G B с 18 19 20 21 22 23 24 22 50.781 F D B В A 2215078 D F A B 251261271281291301 23511791 IG E с |В 2315"79 C E G A 24'52 80 BAGFED DC BA DCFEG F USE. Under the Sunday-Letter, for the Year, anak againit the Month, is the Sunday-Column, of all the C A F ТЕ G B D E Sundays in that Month, for that YEAR. Next to 26 54 82 D B G Է` 26 154 82 F А IC D which, on the Right, is the Monday-Column, next 2755 83 E A 27155 83 E G B ic Tuesday-Column, 8c. Whence all the Week-Days of that Month are immediately known. 2856184 GFED ICBB A 28156841 IDCFE JAG IBA Example 1. To find on what Week ibe 121b of June USE. The Dominical letter Itands un- USE. The Dominical Letter stands un-bappened 455 Years since Cbrifi, N. S. der the Column of Centuries, or whole der the Column of Centuries, and against The Dominical Letter was (by the foregoiag Table) Hundreds, and against the Year (on the the Year (on the Left) above Centuries, C. - Now, under C, against June 6, 13, 20, 27, is Left) above Centuries, before Christ, for since Cbrift, for the Letter required. the Sunday-Column; next to which (on the Left) is the the Letter required. Conftru&tion. In every 4 Hundred Gre- Il Saturday-Column, wherein is found 12, which thereConstruction. There being a Revolution | gorian Years there are 20871 Weeks just, fore was on a Saturday, required. of the Gregorian Dom. Letter every 400 or 3 Days less than in the fame No. of Example 2. Required the Week-day of September Grą. Years, any No. of Years before Cbrift | Jul. Years; hence à Revolution of the 19, 1777 Years before Christ, according 10 N. 3,7 will have the fame Greg. Domi Lefter as Dominical Letter every 4 Hundred Grego- The Duminical Letter is found DC the Complement of those years to any No. rian Years is evident. Hence, under E, against September (10 the Left) the Number of Years since Cbrift will be the that Month ; and to the Left the 19th Day is in the : Hence Apr. 3ů, 33 Ch. 0. S. was on a Frill Cbriff's Crucifixion. Yrs. DL, And May 28th, 585 bef. Chř, on Mo- Hundreds 4000) after a Battle between the Medes and Ly fore Pope Gregory ordained it, in 1982, Ex. Since Cbrift .-2333 iday, Peace А Wednesday, according to Ferguson's (by calling the 5 08. O S. the 15 N.) Author mistakes the ift of Chr. f. yet the Years may be thus computed in Comp. before Chrift 166 A the Year before) Christ: 'W'. Conformity to our present Style. So for the Rijt. chronological Æras, N. B. By increafing the Columns of Hundreds by Fours, the Dom. Letter may be found for any No. of though never so great. Page 15
A TABLE of the Sun's Place throughout the Year; by which the Moon's Place may be found, and her Rising and Setting nearly, for London, or any Part of the known World. According to New Style. Dayel Jan. Feb. March. April. May June July Aug. Sept. O&t.
org h OXor ०४ OD OD ON OIO om of 6 6 r 911 II 9 1180 13° *+99 3 90 12 A 48 go O 13 3 A 43 o 12 I 2 IO 3 jo 026 12 1 36 2 4 2.0 17 3.14 U JI 1 14 3 713 15 3 9 4 52 ४ 16 12 14 II 4 4 14 I 23 I 6 6 1113 8 12 15 5 13 15 5 552 10 1 416 15 3 17 14 14 14 013 14 219 4 48 6 26 8 II 1118 3.1417 13 14 15 3 2 17 7 5 36 7 7 19 18 8 3 18 18 19 1616 16 16 3 7 55 $ 8 17 .1 17 5 17 16 17 9 3 28 19 7 12 9 50 1922 5 18 19 1318 28 12 95? 3 21 22 1620 19 23 19 19 JO 11 19 119 4 25 8 48 1320 2 2 2 20 19 22 IZ 8 5 23 I 2 12 4 22 21 21 + 23 IM8 23 13 5 21 13 25 23 5 26 22 5 25 21 6 14 14 4 118 2 6 15 26 27 23 15 25 25 23 24 3 5 26 16 1328 5 26 1327 15 24 25 23 24 7 121118 3 43 2 2 28 17 7 13 1 36 4 20 13 28 28 26 29 30 27 27 25 7 26 2 24 4 52 1828 27 1526 26 4 26 29 1227 19 8 10 19 29 ml 3 12 1528 1227 1 28 28 27 20 S 30 20 23 7015 1530 29 4 28 1228 28 3 29 29 9 6 6 20 1 7 4 305229 4 9 CD 1 29 30 971 22 9 10 5 36 7 7 IS + 1 17 2 11 39 30 30 23 3 5 IO 23 2 6 24 1 2 911 3 3 omi 24 JO 15 24 4 7 12 50 2 2 2 17 2 8 4 3 0 5 4 IO 28 5 7 25 9 25 053 26 6 128 6 17 3 9 3 3 3 4 8 48 10 59 2 9 6 17 7 4 9 7 4 4 12 27 5 27 9 36 4 I28 1 17 128 9 3 8 6 6 5 7 28 10 24 1 17 6 6 14 6 Il 8 14 6 7 9 9 II 12 9 7 2 29 5 1 6 10 8 7 14 7 7 3 7 8 9 30 3 o 6 9 11 8 il 8 10 I find the Mcon's Place and R,2013, USE. The Sun's Place is expressed in Signs and Degrees under each Month. On the left Hand July 16, 1760? The Golden No being of the Degrees of the Sun's Place stand the Golden Numbers, respectively answering to the Days of 13, tlands against 13th goly at New the Montb, whereon the New Moons happen; when the Moon's Place is the same with the Sun's. Moon, when the Sun and Moon's Place From whence, the Days of her Age must be reckoned forward to the Month Day, whereon the will be 39 210 Moon's Place is required: Adding the signs and Degrees gone forward, by the Moor, according to the For 3 Days of the Moon add 9 Number of Days of her Age, in the annexed Table. Wben the Sign and Degree of the Moon's Place Sum are found, observe against what Day of the Montb the fame Sun's Place flands in the Table, and the 5 Moon's balf Time above the Horizon, will be the same as that balf Day: known by the nearest Or noo, to which answers Aug. 23, Month-Day in Table p. 156, of Sun's Setting, which must be deducted from the Time of the Moon's wben the HalfDay, (equal the hali conSouthing for her Rising, or added thereto for her Setting, at London, or in England. tinuance of Moon above the Horizon) is In other Parts of the World, use the Semi-Duration Art, according to the Place's Latitude, and h 3m which taken from 2h 24m D's Moon's Place or Decla, considered without Latitude.. See Tab. of Semi-Duration Arcs farther on. Southing, leaves 7h 21m Mo: ning her Rifing. And so for other Car:s. HIGH WATER, at the following Places, in Hours and Minutes, before or after the Time of High Water at London. Note, a stands for after, and b for before. Amsterdam, a oh30' Fowey, 3 10 3 30 Oftend, b 2 Spithead, Breft, Hastings, Flushing, b b 4 Bidlington Piet, a 2 Gouries Gut, bo 5 St. Helens, Plymouth, 3 10 Ticmouth llavena o 30 Bridgewater, Gravesend, a 4 40 bi 20 Portland, @ 5 50 Tinmouth, € 3 40 Buoy of Nore, 6 i 30 Gunfleet, 64 0 Loo, a 3 10 Portímouth, b 2 Torbay, B 3 40 Calais, b bi 20 3 Hartlepool, 2 O 30 Lime, a 3 50 Rochester, Topinam, Dartmouth, Leigh, bo 5 bi 20 4 3 30 Humber, Rammekins, Texel, 2 4 40 Dover, Hull, « 3 30 Mountbay, Redsand, b2 Weyanguth, a 4 25 Dieppe, b Harborough • 3 30. Maze, Scilly, Yarimouth Pier, b 4 40 a I 45 Exmouth, Shoe Bacon b 2 a 3 50 Harflew, a 5 50 Needles, gh 53 subtract i Page 16
CHRONOLOGICAL T A BL E S.
A TABLE, thewing, at Sight, the Moveable FEASTS, and Terms, for ever, by the DOMINICAL LETTER, ,
From Ends. Ends. L. NUMBERS. to Sh. Sund. Sunday Sunday Day. Sunday Sunday Sunday Term Term begins. begins. 2.5.13.10 ow on Feo. 5 Mar.26 Apr. 30 May 4 May 14 May 21 Dec. 3 Apr. 12 May 8 May 26 Jun. 14 7.10.15.13 7 12 Apr. 2 May 7 28) 3 19 15 Jun. 2 A 1.4.9.12 8 19 91 14 18 3 26 9 23 3.6.11.14.179 20 3 May 3 16 July 5 8.19 23 28 Jun. 1 18 3 10 Jun. 5 23 2.5 13.16 6 i Feb. 6 Mar.27 May 1 May 5 May 15 May 22 No. 27 Apr. 13 May 9 May 27 Jun. 15 4.7.10 15.187 13 Apr. 3 8 29 27 16 Jun. 3 B 1.9.12.17 8 1 15 19 29 Jun. 5 27 27 23 29 3.6.11.14 9 27 17 20 Jun. 5 27 May 4 30 171 July 6 I Mar. 6. 24 2 Jun. 2 19 27 u Jun. 6 24 2.5.10.4.16 6 2 Feb. 7 Mar.28 May 2 May 6 May 16 May 23 28 Apr. 14 May 10 May 28 Jun. 16 4.7.15.18 7 14 Apr. 4 9 131 23 30 28 17 Jun. 4 23 с 1.6.9.12.17 8 21 161 30 Jun. 6 28 28 24 3.11.14.19 9 23 18 23 27 Jun. 6 13 28 May 5 31 18 July 7 8 2 Mar. 71 25 30 Jun. 3 13 28 12 Jun. 7 14 16 3 Feb. 7 Mar.22 Apr. 26 Apr. 30 May 10 May 17 29 Apr. 8 May 4 May 22 Jun. 10 á 2.5.10.13 6 3 8 29 May 3 May 7 17 24 29 15 29 17 D 4.7.12.15.187 3 15 Apr. 5 10 14 31 24 1.6.9.17 8 17 31 Jun. 29 29 25 12 July 1 3.8.11.14.199 3 Mar. 1 191 28 Jun. 7 14 29 May 6 Jun. i 19 8 5 Feb. 2 Mar.23 Apr. 27 1 May 11 May 18 30 Apr. 9 May 5 May 23 Jun. II 2.10.13.18 6 9 30 May 4 8 18 25 30 16 30 18 E 7 4 16 Apr. 6 II 15 25 Jun, 1 30 23 25 6.9 14.17 8 4 23 13 181 22 Jun. 8 30 26 13 July 2 3.8.11.19 9 Mar. 2 20 25 29 8 15 30 May 7 Jun. 2 9 5.16 5 5 Feb. 3.Mar.24 Apr. 28 2 May 12 May 19 Dec. 1 Apr. 10 May 6 May 24 Jun. 12 2.7.10.13.186 5 26 17 13 31 19 F 1.4.12.15 7 5 16 - 17 Apr. 7 20 Jun. 2 24 20 Jun. 7 26 } 8 3.6.9.14.17 5 241 14 19 23 Jun. 2 9 1 May 1 27 14 July 3 9 5 Mar. 31 26 30 9 16 6 Feb. 4 Mar. 25 Apr.29 3 May 13 May 20 2 Apr. 11 May 7 May 23 Jun. 13 2.7.10.18 6 SO 27 18 14 Jun. 1 G 1.4.9.12.15 7 6 181 8 131 17 27 Jun. 3 25 8 27 3.6.14.17 8 6 25 15. 24 Jun. 3 2 May 2 28 15 July 4 8.11.19 6 Mar. 41 9 27 31 171 Jun. 41 | January February. March. April. May. june. July. August, September October November, December, Days riles.fsets. riles.llets. rifes. sets. frises.rets. rises.fiets. riles.sets. rises.ffets. rises.rets. frites.liets. rises.liets. rises. Jsets. rites. fets. hmhmhmhmhmhmhmhmhmhmhmhmhmhmhmhmhmh mh mhmhmhmhmh 3 8 3 3 57 7 234 376 295 325 2716 344 327 29 3 508 103 468 1414 227 375 176 426 1615 437 15'4 447 5914 6 8 13 577 184 436 235 385 216 404 2717 34/3 47 3 133 488 12 4 277 32 5 236 366 225 3717 204 398 23 38 975814 27 13 4 486 175 445 166 454 227 393 468 143 518 94 317 285 295 306 2815 3117 254 348 413 56 5514 57 84 536 1115.505 106 514 3717 443 458 153 548 64 367 235 356 24 6 17 314 288 63 54 15 l3 5114 917 24 596 55 565 416 574 13 7 483 443 163 578 34 42 7 175 4116 1816 3915 2017 364 243 73 53 18 7 484 12 6 565 55 596 24 587 34 87 533 438 17 018 47,6 126 455 1417 414 1988 3 52 21 13 444 166 505 10 5 536 84 537 84 47 5713 438 1714 117 564 537 526 76 515 87 454 153 8 13 52 24 17 394 2116 4515 1615 476 1414 487 134 03 13 433 174 87 534 587 15 586 76 5515 217 494 118 13 52 27 344 266 395 215 436 204 427 193 578 413 448 16 4 127 4815 416 5516 415 5517 24 5717 524 88 73 53 30 17 3014 301 Ś 3516 261+ 3717 2113 5418 713 4518 1514 1717 436 96 506 105 49 7 714 5267_5614 418 513 55 N. B. The Time of ibe San's Setting, in the above Table, being doubled, will shew tbe Lengtb of tbat Day, in the Year. Page 17
QUESTIONS in CHRONOLOGY answered. 3. 3. xtr-u *+92 +3-9 x+y Put x = Year fought. Then will be the 3 Conditions of the Question, 19 15 19 28 15 Subftitute this Value of x in 2d Condision. Then, 19a +-17 17 a whole Number.
5326+99 Substitute, the foregoing Value x, in the 3d Condition. Then a wbole Number, 15 7btoo Viz. 356 +6+ a wbole Number AFFIRMATIVE THEOREM. 15 Whence, x=79800+ 1701. And when c= 0, then 1701 is the Date of the But , a wbole Number, Year, 0. S. required, 15 86 + 6 Ist Dif. a wbole Number. 15
Here, b=150+ 9. 2d Dif. =l, a wbole Number, 15 N. B. Tbe above Numbers can bappen but once in a Julian Period of 7980 Julian Years, as appears by the Tbeorem : Notwithstanding wbich, as many conditional Numbers of the same Properties may be found by the Tbeorem as you please. The GENERAL PROPOSITION (Page 161) OTHERWISE Answered. LET tbe Quotient of tbe same whole Number when divided by anotber wbole Number be called a, wben divided by a second whole Number be called b, by a bird c, by a fouribd, by a fifth e, by a fixibf, &c. FORMER EXAMPLE. To find a whole Number, which being divided by 2, 3, 4, 5 and 6; 1, 2, 3, 4, and 5 shall, respectively, remain; but being divided by 7, Nothing shall remain. Conditions 3. 4. 5: 6. Here, zatı = 36+2, = 4+3 = 50+4 = 6c+5 = 7f, which are the 6 Conditions of the Question, expressing the same wbole Number. N. B. The cbief Thing bere to be considered to find the Value of the different Quetients a, b, c, d, &c. of the same whole Number, when divided by different wbole Numbers, so as Norbing, shall remain, according to the several Expregions, and Conditions, as above. Axiom. Any wbole Number taken from ebe same, or a different wbile Number, a wbole Number, or Nothing, shall remain. 2. Conditions. In the if and 2d Conditions. 20+1 = 35+2, a wbole No. fought ; a and b conditional whole Nos, required. Subtract 1 from each Side, 2a = 36-4-1, a conditional wbole Number, divisible by 2. Subtract 2b. a whole Number, divisible by 2. Wbence, 364-255, the ift and 2d Conditions. Here b=1, leafl. bti, a whole Number, divisible by 2. NOW, 6 being the least Multiple, divifible by 2, 3, the Divifors respecting the 2 first Conditions, 3: 1. 2. Cordicions, Therefore,'. 4+3 = 6a+5, a wbole Number fought, cand a whole Numbers, required, Subtract 3 from each Side . . . 46 = 6a+2, a wbole Number, divisible by 4. Subtract 40 a whole Number, divisible by 4.
2a + 2, a whole Number, divisible by 4. Whence, 6a+5=11, The 1. 2. 3. Conditions. . . . Here a=1, leaft atı, a whole Number, divisible by * 2 NOW, 12 being the least Multiple, divisible by 2, 3, 4, the Divifors respecting the 3 firft Conditions, 1. 2. 3. Conditions. Subtract icat 5, a wbole Number, divisible by so sa a whole Number, divisible by s. 30% 2, a wbsle Number, divisible by s. Whence, 12atue 59, The 1. 2. 3. 4. Conditions, . . Here a-z4, leall ar 4, a wbile Number, divisible by . NOW, Page 18
A TABLE for finding the NUMBER OF DAYS advanced and retreated by the EPACTS and LUNATIONS, in the Month Days, (from 6000 Years before to 6000 Years after Christ) from Old to New Style, from 1800, and the gory. See Tab. p. 30. Also to find the Epact, 0. S. for the same Centuries. NoCols 3. 4. 5: 3 14. 5 6. 3. 4. 5. 6. 7. Sum, DA, Sum, ) A. Sum, A. Days Days and Days Days Days Days and Days Dill. Days) and retr. Centuries Diff. Adv. Epas Centuries Adv. Epas Days Diff. Adv. Epas retr. of Centuries from before and Adv. Gol. before and from and Adv. Gol- from and retr. Gol- Old Epas fince Epas > Epas fince den Old retr, from of D Old CHRIST, retr. from den N.S. N.S. || CHRIST. Cycle Cyc. N.S. Nos. N.S. to CHRIST, ino of Diretr. Nos. N.S. in of Old Nos. Jin 0. New N.S. New Cyc.r.o. New Old Cyc.) to [Style Style New from toN. Style from New Style Style 1800 Style X X 180c Style Soo Style + + + + + + -1 B.voco 47 23 6 29 B.2000 6 16 B.2000 13 6 24 5900 46 24 23 1900 116 II 27 14 I 2 19 5800 45 24 17 1800 15 4 15 13 16 13 5700 44 *1 23 13 1700 814 JO 4 16 2200 14 44 23 21 7 8 10 4 17 B.2400 16 3 13 7 4 5500 43 23 12 1500 11413 3 2500 17 14. 12 28 5400 42 17 27 1400 1312 2600 18 15 17 5300 41 19 3 1300 201 9 4 15 3 18 41 19 8 17 B.J200 WIB 18 B.2800 9 4 15 8 13 5100 40 13 12 IIO 4. 16 2900 20 4 16 13 7 5000 39 18 18 6 IOCO Vo9 ti 9 3000 21 5 16 18 4900 38 17 4 9002 14 4 3100 5 17 4 27 B.4800 38 20 18 27 5 17 9 4700 37 17 14 700 7 5 25 3300 23 17 14 17 4600 36 20 19 15 * 3400 24 18 19 II 4 500 35 16 5 JI 500 12 5 7 15 13 3500 25 6 19 5 6 B.4400 35 19 16 6 B. 40055 6 B.3600 25 7 18 4300 34 19 15 15 * 3004 6 4 3700 26 7 19 15 26 4200 33 18 26 200 3 28 3800 27 7 4100 32 o 18 14 · 6 20 32 5 3 16 23 3900 28 8 B.4000 32 18 14 15 B. 3 8 B.4000 28 8 3900 31 17 14 16 100 4 4100 29 8 21 16 3800 30 17 13 5 200 Fo 27 4200 30 8 22 * 3700 29 17 7 -29 300 5 16 4300 *1 9 25 B. 3600 29 16 13 25 5 17 31 9 3500 28 16 19 500 3 12 4500 32 9 23 17 14 3400 27 16 II 14 4600 33 10 23 10 3300 26 16 10 8 700 4 3 7 17 4700 34 JO 24 8 4 15 II 13 4 B, Sco 4 6 27 B.4800 34 10 24 13 29 3100 25 15 IO 18 28 900 4900 35 1 24 18 24 3000 24 15 23 I000 13 15 5000 36 25 4 19 2900 23 14 9 9 18 JIOO 7 18 IO 5100 37 II 26 9 13 B. 2800 23 14 14 B. 1200 13 8 B 4 6 5200 37 25 14 9 2700 22 14 19 8 9 26 19 3 2600 21 13 1400 14 25 39 I2 27 28 2500 13 10 27 1 500 to 19 19 5500 40 13 27 23 B.2400 20 13 7 15 B. 1600 IO 5 15 B.5600 40 o 13 27 15 18 2300 19 18 1700 o 10 5700 41 o 13 28 I 13 2200 18 6 6 12 1800 12 * II 15 5800 42 14 28 2 JOO 17 이 12 5 1900 13 12 29 5900 43 20 2 6000 43 o 14 For the MEMORY. Then add two: and the Difference of Style will be known. Year Ex. 55100 before Christ. RULE II. From the Hundreds fince Christ, take their Fourth, and more two, And obe Days will remain betwixe Old Style and New.
54 13 reje Ds Year } 2+1=311 28 Days to be added to the old Style, for the New. N. B. The D's Age and Epacts retr. (-) the same No. of Days that the Lunations adv. (+) from 0. to N. S. and the contrary, explaining 5. Col. being the Dif. or Sum of ad and 4. Columns, according to Signs. TO Page 19
The ANTIENT Paseball To find the Letter in ibe Roman Calendar, correspondent to any Montb-Day in tbe Year, before or fince Christ, arith. TABLE for finding metically? EASTER, O. S. RULÉ. Divide the Number of Days, counting from the Beginning of the Year, or January o, to the given Month-day (see Tab. p. 129.) by 7, and what * remains will be the Number of the Letter, required. Glen Dom, Month No. Letter. Day. Example. Required the Letter answerable to the 15th of November, in any common or Bisextile Years? Com. Yr. Bil. Yr. 16 7)319(45 7)320145 D 39 40 E 23 Letter D, required, Letter E, required, 13 24 for a common Year. for a Biffextile Year. 25 A B C D E F G. А 26 3. 4. 5. 6. 7. B 27 28 RULES FOR FINDING THE WEEK-DAYS. 18 29 7 30 To find the Week-Day, arithmetically, answerable to a given Month-day, in any Year before Cbrisl, O. S. ? 31 RULE. To the Years, less 1, before Chrift, add their Fourth,.(being the Number of their Biffextiles) and 3, G IS Apr. 1 and also the Complement of the Number of the Month-day, from Jan. o. (from Tab. p. 129.) to next Sevens, or (universally) to 371, divide the last Sum by 7, and deduct the Remainder from 7, and what laft *remains wilí 4 A be the Week-day, required. Sun. Mon. Tu. Wed. Th. Fr. Sat. B 3 с 3. 4. 6. 5. Yrs. Ds. E 585 From Jan. , to May 28, Bifr. 149– 9 F G 371 17 A 9 584 Comp. 222 B 146 (add Or "7) 149(2 14 S 13 Otherwise Rem. 2 Week-days, 28th May 14 584 7)*955(136 is forward of Jan. o. 15 146 25 A 16 3 45 B 17 18 7)733(14 -3- D 19 7 E 7 Wednesday, 0. S. requiredo +2 Week-days 28th of May is forward, B 24 25 Wednesday, as before. N. B. The Dominical Letter, before Christ, advances, (in Reckoning back, as the Dom. Let, Tab. fhews, p. 148, Ex. To find aber Easter for Years before Cbrift.) and consequently obe Week-day, on Jan. o, each Year goes back or retreats, bappened 1593, wben the Hence the Reason of adding the Comp. of the Month-days to Sevens from January. G. No, was 17, and Dominical Letter G? To find the Week-day for any Monib-day and Year before Cbrifl, N. S. arithmetically? RULE. To the Years, lefs 1, before Chrift, add their Fourth and 3, (but 2 from Feb. 25 to the End of Cen. Against 17, G. No, in turies, not Lp. Yrs. N. S.) and also the Complement of the No. of the Month-day fince Jan. 0, (fr. Tab. p. 129.) the ift Column, stands A, to next Sevens, or (universally.) to 371, and likewife the Complement of the Day's Difference between 0. and N. s. and against G, the Domi- to next Sevens, then divide the Sum by 7, taking the Remainder fram 7, and the last Remainder will thew the nical Let. following, stands Week-day, N. S. required. April 15, for the Time of Let obe Week-day for tbe 28th of May, N. S. be required ? Eafter, required. 585 De. From Jan, o, to May 28, Biff. 149 N. B. The Day of the Ds. 6 Dif, bet, O. and N. S. 371 Month against the Golden 584 Number, April 9, is the .. 146 Comp. 222 Day of Eafter Full Moon, 3 Comp preceding Easter - Sunday. If the Dominical Letter ftands against the Golden Number, or the Easter Orberwise. 7)956(1 Moon be on a Sunday, 4 Wednesday, 0. S. then Easter is on the Sun. +6 Dif. Ds, fr. O, to N. S. dey following, for the 7 Dominical Letter must fol- 7)10(1 low the Golden Number, Tuesday, N. S. required. Rem. . . . Tuesday, N. S. as before. (Ålding the Days Difference of Styles to the Week-Day of O. S. dividing So for the Reft. by 7, taking the Remainder for the Week-Day, N. S.) Page 20
In Table, p. 168, the Day's Difference of Style between O. S. Since Cbrif the Years current from 4 Hundreds take, Leap-year, and those Centuries, not Leap-years, N. S. before Chrift, Adding i to what's Left, Years before Christ will make. take place only for those compleat Centuries, and only from February 25, to the End of those Centuries, not Leap-years, N. S. respective 1759 Years current fince Cbrif. ly; and the Rest of the Numbers likewise take place in the same 3200 8 Hundreds by 4. Manner, for the same compleat Centuries, And therefore, any Yrs. 3441 Difference in the ad Column between Old and New Style, and like- Dominical Letter G, +I wise the same Numbers in the 4th and 5th Columns, as at the pre- Year begins on ceding compleat Centuries, and so in Succession, Monday, N. S. 1442 Yrs current bef. Cbrift, Tbał, to find the Difference of Days between Old and New Style, Dominical Letter G, Year begins on a Retreat of Lunations in Old Style, and Advance and Retreat of Lu Monday, N. S. nations and Moon's Age, from Old to New Style, [in Col. 2, 4, & 5, from Tab. p. 168.) for Years above compleat Centuries before In the same Manner, the Tears fince Cbrift, are found corresponCbrift. dent to the Tears before Cbrift, having ibe fame Golden Number, Cycle You must take out the Numbers for 100 Years preceding, as you of the Sun, or Indiction; by subduering i from current Tears before do for Years above compleat Centuries fince Cbrifl, which will iben Christ, and taking the Remainder from any Number of Hundreds by 19, exactly agree with the foregoing PRACTICAL RULE, for finding the 28, and 15, and the Years since Cbrift will, respectively, remain. And, Difference of Styles for Tears above compleat Hundreds before Chrif. on the contrary, taking the current Tears since Chrift, from any Number of Hundreds by 19, 28, and 15, adding 1, to each Remainder, and the TO reduce YEARS BEFORE, to YEARS SINCE, CHRIST, and Years current before Christ will result, kaving the fame Golden Number, ebe contrary; Having the SAME DOMINICAL LETTER, or LETTERS, || Cycle of the Sun, ard Indiction, respectively. and consequently, beginning with the same DAY OF THE WEEK, OLD and NEW STYLE. Yrs. Example I. Of the Golden Number 1612 before Chrif. -~-16 Example. 585 Years current before Cbrift. 02 584 goo .. 1 Hundred by 19. 2/02 Years current since Cbriß 289 584 And 1612 before, and 289 Years since Christ, have the same Golden 1400 2 Hundreds by 7. Number, viz. 5. 3800. 2 Hundreds by 19. Weck-day, (viz. Tuesday] as 585 Tears current before Chris, 0, S. 1611 Years fince Cbrift reduced to Years before Christ, O.S. ti RULE, Years current fince Cbrift take from Hundreds by Seven, Yrs. Add i to what's Left; Years before Cbrift are given. 2189 fince Chrift, 1612 before Christ. Examples 1759 Years current fince Chriß. Az 1959 Golden Number 5. . . By Tab. p. 150. • . Golden Number 5. 2800 . . 4 Hundreds by 7. 34 The Examples for tbe Solar Cycle and Indiction are similar to ibe fore1041 going. to 342 As the antient Egyptian, Arabic, Grecian, Persian, Jewish, and 1042 Years current before Chrif, having the same later Accounts of Time, are reduced, (for astronomical and chronoDominical Letter (viz. C, 0. S.) and beginning with the same logical Purposes ) to correspond with the Julian Form of the Week-day, (viz. Friday] as 1759 Years since Chrift, o.s.2oT | Year, or Account of time, long before any such Year had Existence, so, in Conformity to the late Correction of the Julian Account of N.B. The RULES ABOVE serve for N. S. by using Hundreds by 4, Time, we have reduced the Yulian to the Gregorian Style, as far instead of Hundreds by 7. Viz. for N. S. backward and forward as remoteit Antiquity, and Futurity, for the Before Chrif take the Number of Years less by 1, Improvement of Chronology and Astronomy. This is performed at Sight, in two Pages, 148 and 149, foregoing, with the following For the COMMENCEMENT of the mot famous Æras (lince Creation) and the REDUCTION of CHRONOLOGY, sie furiber sn. Dom. Letters GF, 16со . i 4 Hundreds by 4. Year begins on Mono day, N. S. 2016 Years since Cbrift, Dom. 584 Page 21
PER P E T U AL TI M E - TABLES: Or General RULES for CHRONOLOGISTS, HISTORIANS, &c.
MOVE ABLE FEASTS from 1759 to 1800, N. S.
Jun. 7 May 22 14 Jun. 3 May 19 Jun. 7 May 30
II 22 3 14 25 6 17 28 9 20
Dom. Dom. Septua- Ah- Easter Letter. Letter. gesima Wedner. Sunday, Sunday. Rogat. Christ. N'. N. S. O. S. Sunday G Feb. 11 с 1759 Feb. 28 May 20 3 1761 D G Jan. 18 4 Mar.22 Apr. 26 1762 с F 24 Apr. 11 May 16 16 1763 B E Jan. 30 16 3 8 B. 1764 17 AG DC Feb. 19 Mar. 7 27 1765 18 F B 3 7 12 19 E А Jan. 20 I 2 Mar.30 4 1767 D G Feb. 15 Mar. 4. Apr. 19 24 B. 1768 CB FE Jan. 31 Feb. 17 3 8 1769 3 22 8 Mar.20 Apr 30 1770 G Feb. 11 4 с 28 Apr. 15 May 20 1771 F B 13 5 ED AG Feb. 16 Mar. 4 24 C F 7 Feb. 24 1773 7 16 8 1774 B E 16 3 8 Feb. 12 1775 9 D Mar. 1 16 B. 1776 GF CB 4 Feb. 21 7 12 E A 1777 Jan. 20 I 2 4 D G Mar. 4 Apr. 19 24 1779 13 с Jan. 31 Feb. 12 4 9 B. 1780 14 BA ED 23 9 Mar.26 Apr. 30 1781 G 15 28 с Apr. 15 May 20 1782 16 F B Jan. 27 13 Mar.31 5 1783 17 E A Feb. 16 Mar. 5 Mar. 5 Apr. 20 25 B. 1784 18 DC GF 8 Feb. 25 11 16 1785 B E 9 Mar.27 1786 А D Feb. 12 Mar. 1 Apr. 16 1787 G с 4 Feb. 21 8 13 B. 1788 3 FE BA Jan, 20 6 Mar.23 Apr. 27 1789 4 D G Feb. 8 25 Apr. 12 (May 17 1790 с F Jan. 31 17 4 9 5 Feb.22 8 13 1793 8 f B Jan. 27 13 Mar.31 5 1794 9 E А Feb. 16 Mar. 5 Apr. 20 D 1795 Feb. 18 5 IO B. 1796 CB FE Jan. 24 10 Mar. 1 1797 Apr. 16 21 13 G с Feb. 4 Feb,21 8 13 F 14 B 1799 6 Mar.24 Apr. 28 Jan. 20 1800 15 E AG 26 Apr. 13 May 18
Jun. 4 May 26 18 Jun. 7 May 23 14 Jun. 5 May 19
28 13 4 24 9 29 20 5 25 17 Page 22
RIGHT ASCENSION and DECLINATION of STARS, AY, as the Time marked by a Clock, going uniformly, whether regulated or not, during the Interval of a Star's lution, is to 360°, To determine the Rigbe Afcenfion of any particular Star? RULE. When the Sun is near the Equinox, where its Change in Declination is swiftes, observe its Meridian Height or Declination fome This Metbud gives two Inftants when the Sun was at equal Distances from the fame Tropic; because, at equal Distances, on either Side a The Difference of R. A. answering to these two Inftants, will give (the Star being fixed) the Arc of the Equator, or Sun's Motion in R. A. Ihe Seljitial Colure therefore bisects that Are, the Complement of Half which will be the Sun's true R. A, at the first Observation, Merid. Alt. O Dif, R. A. bet. O &* at Noon, Procyon, at Noon. 46 58 41 97 52 10 East 53 39 29 West 47 7 1 54 33 36 West 8. 46 44 24 55 27 43 West 460 581 41" 152 45 49 76 22 541 And had R. A. 37 51 The Star being to the East 97 52 10 Sum 111° 29' 15"} 3. To compute at wbat Time each Star palies the Meridian. Thus, Take the Difference between the Star's R. A. and the R. A. of the Sun, The above Computation gives the Time of the Passage but nearly; because neither the Sun or Star are supposed to have any Motion in R. A. But, to find the correct Time, compute the Sun and Star's R. A. for the Time already found, and their Difference, reduced to Time, will , on a given Day at Noon be 1120 18', and the R. A. of tbe Sun 1830 42', the Difference 71° 24' 13 71 16 58 7h 14m 528 required. For, observing at what Infiant any Star, whose R. A. is known, passes the Meridian, that Inflant being compared with the orber, found by 4. Another Use of the R. A. and Declination of Stars is, To find the Distance of any Star from the Meridian of a Place at a given Time. Or To find tbe Angle at the Pole, formed by the Meridian of a Place and the Circle of Declination paling through the Star. 28, add obem to the Sun's R. A. at that N. B. When the said Sum is less than the Star's R. A, add to it 360°
RULES for SUN and S T A R S. Page 23
A Solar E P H E MERIS, commencing 1756, and serving by Means of EQUATION8 to the End of the present CENTURY. J A NU A RY. F E BRU A RY. Placet. Dir. 's Dec. S. Dit. O's R. Alc. Dif, Pla Dif. lo's Dec. S. Dit. O's R. Alc. Dif. Days Days 22 58 22 282 39 12 66 13 10 41 315 39 11 4 34 9 12 39 17 2 22 52 48 60 49 16 36 6 17 29 283 45 21 62 66 14 II 30 3 60 316 40 0 17 45 3 22 46 46 16 18 21 284 51 24 6 28 3317 40 37160 25 18 60 46 4 3 14 41 38 22 40 18 28; 57 19 16 4 6 56 60 44 318 41 15 42 43 22 33 22 2.87 3 9 5 17 13 48 319 41 15160 1 6 16 43 58 22 26 288 8 53 6 61 65 36 15 23 23 18 22 18 12 17 45 7 51 289 14 29 59 49 7 815 19 15 13 15 4 32 18 46 17 321 41 5 6 65 29 19 9 57 61 290 19 58 8 20 15 54 842 9 322 40 41 19 21 40 9 59 24 22 61 I 15 21 16 34 291 25 18 9 5 9 323 40 5 IO 9 20 48 35 19 35 21 52 9 292 30 27 10 22 17 12 6 14 61 30 8 9 32 19 49 59 2 11 21 49 43 61 21 42 37 II 293 35 30 23 17 49 13 46 41 325 38 20 .9 58 2 12 22 50 51 35 21 32 39 294 40 22 12 24 18 24 13 26 39 10 326 37 7 20 16 23 13 33 23 51 58 21 22 16 295 45 4 25 18 57 13 61 6 13 23 6 327 35 44 32 24 53 4 58 26 21 II 30 296 49 37 26 14 12 45 54 61 19 29 328 34 10 11 12 5 15 2.+ 54 9 21 O 18 61 297 54 15 36 15 12 25 13 27 19 59 5 4 16 26 55 14 20 48 |298 58 13 16 61 28 20 28 330 30 32 I 4 17 20 36 44 61 300 2 14 57 55 17 29 20 55 63 51 II 43 17 12 22 331 28 29 18 28 57 21 301 6 5 20 24 22 18 * 21 20 57 44 II 22 61 12 46 63 40 19 29 58 24 20 11 36 302 9 45 57 34 I 21 43 II 19 61 63 28 '13 57 37 333 23.45 m 59 26 19 58 29 303 13 13 61 5 JO 39 13 32 63 15 57 13 21 19 44 57 61 21 3 22 25 63 4. 10 17 15 13 52 60 18 335 13 21 22 3 1 27 19 31 5 305 19 32 22 60 59 4 22 43 14 15 60 17 22 4 2 26 4 55 306 22 24 19 60 23 5 23 58 14 35 337 12 21 24 156 46 3 24 19 2 IS 307 25 5 24 6 23 15 60 13 9 II 3 9 22 21 7 56 37 25 6 4 22 18 47 16 25 62 16 15 13 22 28 5 44 56 28 26 7 519 13 32 3 309 29 51 26 8 23 40 340 2 12 15 37 27 6 15 8 18 16 26 56 21 27 8 9 23 50 60 5 3 39 60 8 22 33 18 O 28 9 7 10 28 34 311 33 47 10 3 58 56 13 7 4 25 14.1 54 46 16 16 29 8 5 5 17 44 12 16 1312 35 27 61 28 Kin Leap-lier, take out for a Day Juoner, for fan, and tebe 33 30 II 8 58 17 27 39 313 36 55 60 52 | 16 53 only. Xrs. Lo. Logo 31 9 50 17 10 46 314 38 9 Years after 2.5" 48 55 7r.fpeétively 92423 For 2 Lp-Yr, take II 37 50 for all S Months. 27269 1385, Jooner. . . * T T MARCH. Days 1 APRIL 4 18 6 12 10 40 N II II 45 22 46 4 49 19 55 57 59 2 6 23 54 32 343 46 47 13 9 42 6 17 60 5 12 21 23 13 55 49 O 54 35 3 13 24 11 32 7 160 344 42 36 3 14 8 42 13 o 52 122 23 5 55 44 54 35 6 4 14 24 11 9 5 58 9 13 55 31 59 59 23 13 55 36 55 54 40 5 15 24 10 346 33 56 5 45 49 5 35 14 50 II 59 36 123 19 55 31 22 38 52 54 43 6 6 5 22 30 347 29 27 6 6 43 32 15 44 54 59 54 23 17 155 23 122 30 51 54 46 7 17 24 o 348 24 50 4 59 13 18 7 4 18 7 6 59 52 23 25 8 22 24 49 8 8 54 51 19 3 7 7 28 26 17 34 31 59 50 23 29 55 14 47 54 54 9 19 23 42 4 12 19 350 15 22 20 9 54 7 50 43 45 22 9 54 52 1ο 20 23 30 350 10 30 10 o 39 19 24 21 23 33 55 I 21 59 55 I II 21 23 16 3 25 15 352 5 31 21 59 21 20 19 22 59 45 123 37 21 52 12 J 3 353 12 22 58 2 59 43 54 54 23 38 39 121 43 13 2 38 23 22 44 23 56 41 13 22 353 55 22 23 39 9 39 21 34 14 24 22 25 2 14 21 14 354 50 10 24 55 18 9 40 o 23 4 55 23 42 21 24 15 25 22 3 T50 39 15 25 53 54 10 I 24 24 23 42 54 43 33 21 14 16 356 39 41 16 10 22 38 24 55 43 59 34 23 43 54 41 21 4 55 32 17 27 21 13 1 3 14 17 357 34 22 27 50 59 10 43 42 25 51 15 23 41 18 154 37 55 35 30 358 28 59 0 39 33 18 II 4 35 23 42 54 34 58 28 120 44 55 47 19 015 51 19 359 23 33 29 47 57 11 25 19 27 42 38 23 43 54 33 55 52 20 or 19 44 6 o 18 25 8 46 22 20 I 45 49 -3 41 54 30 58 20 20 21 55 57 21 1 19 10 O 31 33 21 I 44 45 I2 6 10 29 34 27 23 39 58 22 8 59 24 20 2 22 34 o 55 12 7 4 22 2 43 7 12 26 18 30 30 29 123 37 158 20 56 11 19 55 23 3 1 32 23 3 41 27 12 46 13 40 123 36 24 I 42 25 24 13 4 39 45 32 22 58 23 34 54 27 25 5 59 4 50 27 25 5 38 59 15 33_19 25 23 32 54 27 158 14 19 18 31 26 6 15 49 2 29 31 5 54 54 26 6 36 15 13 44 44 34 15 56 159 14 194 7 15 3 27 55 41 54 27 2 52 59 6 39 21 27 14. 3. 48 35 12 37 II 18 49 46 47 28 28 8 32 39 14 22 37 18 36 924 599 35 56 54 29 13 24 3 3943 29 9 30 48 158 14 41 12 18 23 597 2 57 10 12 31 30 4 1ο 2 59 30 10 28 56 58 14 59 35 3 31 4 26 II 54 30 10 17 14 N. B. The Dits, for a Day preceding any Month-day of Leap-year being Xd by ,2423 ; 14846; ,7269, will give the Quantity to be subtracted from or added to the Leap-year Quantity, for That to the fame Month-day, 1, 2, 3 Yrs. after Leap-year, respectively: Or 6158, 3145; 1385, being respectively added to the Lo. 1.ogs. of Diffs, for a Day preceding the Month-day of Leap-year will give the Lo. Log. of a Quantity to be fubd. fr. or added to the Leap-year Quantity for the Quant. for the fame Month-day 1, 2, 3 Years after Leap-year, respectively. See Examples farther on, and Equations for 4 Years forward of the Quantitiis, or Places, for any given Year. A Page 24
For finding the Time of RISING and SETTING of the Sun and STARS. SEMI DIURNAL OR DURATION ARC S. 60 70 80 9° TI 13° 14° 159 1бо 17° Dec. N.S. H. M. H. M. H. M. H. M.JH, M.H. M. H. M.H. M. H. M.H. MH. M. H. M.H. M. H. M. H. M. H.M.H.M. I 6 2 6 2 6 2 6 2 6 2 6 3 6 3 6 3 3 6 3 6 3 6 3 6 3 6 3 63 3 6 2 6 2 6 3 6 3 6 3 6 3 3 3 6 4 4 4 4 6 6 4 3 6 2 6 3 4 6 4 6 6 4 6 2 6 6 3 4 4 6 6 6 6 6 6 6 16 3 5 5 56 7 6 8 16 8 6 3 6 6 3 6 5 6 6 6 6 6 6 6 7 8 6 8 6 9 9 7 6 3 6 3 6 4 6 4. 6 6 6 6 6 7 6 7 6 8 8 6 9 6 9 6 10 6 11 8 6 3 6 36 4 6 4 6 6 6 7 6 7 6 8 6 8 6 9 6 10 6 u 6 11 4 6 6 6 6 7 6 6 8 6 9 6 9 6 10 6 12 6 13 6 4 4 5 6 7 9 6 16 6 12 6 13 6 14 6 5 9 6 10 6 13 6 13 6 14 6 15 6 16 12 6 3 6 4 6 6 6 6 6 6 7 6 8 6 9 6 jo 6 ií 6 13 6 15 6 16 13 3 6 6 6 7 6 8 6 9 6 10 6 II 6 12 6 13 6 15 6 15 6 18 14 6 3 6 6 6 6 7 6 8 6 9 6 10 6 11 6 12 6 14 6 15 6 18 16 19 15 6 3 6 46 6 6 8 6 9 6 15 6 16 6 18 6 19 16 20 16 6 3 6 6 6 7 6 8 6 96 14 6 21 022 17 6 3 6 5 6 6 7 8 6 16 6 18 6 20 6 21 16 22 18 6 5 6 7 9 6 10 6 i 14 6 17 6 18 6 21 16 24 6 15 6 16 6 18 6 19 ó 22 6 23 16 25 6 27 20 6 66 9 6 11 15 6 176 19 6 22 6 6 26 6 28 21 6 4 6 7 6 8 6 13 6 15 6 16 6 18 6 19 6 23 6 24 6 26 16 28 7 6 8 6 10 17 6 19 6 20 6 24 6 27 236 46 6 6 7 6 9 14 6 16 18 6 21 6 32 24 6 6 6 6 8 6 9 6 28 6 30 6 32 6 34 25 6 6 6 8 6 10 6 14 15 19 6 27 29 6 31 33 6 35 26 6 4 6 6 6 8 6 14 6 16 6 18 6 24 6 26 6 28 6 30 6 32 10 39 27 6 6 6 6 8 6 II 6 13 6 17 623 6 29 32 34 16 36 22 6 7 6 9 6 13 6 17 6 22 6 24 6 26 6 28 6 31 33 35 36 38 40 29 6 7 6 9 6 14 6 25 6 30 6 32 6 34 6 6 42 30 6 5 7 6 9 6 14 6 16 6 26 6 28 31 6 33 6 38 16 41 6 45 31 6 19 6 22 6 27 6 29 32 0 34 6 37 40 42 545 32 6 S 6 7 6 12 615 6 18 6 20 6 23 625 6 28 6 6 73 61 6 3 44 5 S.N. 1 6 2 6 2 2 6 2 6 3 6 1 6 61 6 I 1 2 6 2 6 6 I 6 1 6 6 1 6 I 1 6 6 o 6 o 16 0 16 o 3 6 2 6 6 1 6 1 6 1 6 1 6 4 6 0 6 6 0 6 o 65 59 5 59 5 595 59 4 6 2 6 5 59 6 1 6 16 o 4 6 6 5 59 5 59 5 59 5 59 5 58 5 58 2 6 o 5 5 59 5 59 5 59 5 58 5 575 57 5 575 56 5 56 6 2 5 57 5 57 5 57 5 56 5 555 55 6 5 59 6 6 5 58 5 57 5 57 5 56 5 56 5 55 5 55 15 545 54 8 6 I 6 5 59 6 6 5 57 5 57 5 56 5 55 5 55 5 54 5 545 53 5 52 9 6 I 6I 6 6 5 59 6 7 5 57 5 55 5 54 5 54 5 53 5 525 525 51 10 6 I 6 1 5 51 15 515 50 6 1 6 O 5 59 5 58 5 57 6 8 5 55 5 54 5 54 5 53 5 52 5 51 5 50 15 495 49 12 I I 6 o 5 59 5 57 6 8 5 55 5 54 5 54 5 53 5 52 5 51 5 50 5 49 15 48 5 47 13 I 5 59 5 58 5 57 5 57 9 5 55 5 54 5 53 5 52 5 SI 5 50 5 49 5 47 46 14 6 I5 59 5 576 5 47 15 6 I 5 59 5 57 5 56 6 10 5 54 5 52 5 51 5 50 5 49 5.48 5 47 16 6 5 59 5 56 5 55 5 53 5 52 5 51 5 49 5 48 5 47 545 5 43 5 42 5 52 5 51 5 50 5 49 5 47 5 46 5 45 5 43 5 42 5 41 18 1 5 45 5 44 5 42 5 41 15 40 19 6 3 5 59 5 58 5 57 5 55 5 54 5 51 5 50 5 47 5 45 5 44 5 43 5 41 5 40 5 38 20 6 I 5 59 5 565 55 5 53 5 51 | 5 49 545 543 5 41 5 40 5 385 37 26 6 5 59 5 58 5 56 5 55 5 53 6 13 5 50 5 47 545 5 44 5 42 5 40 5 39 5 37 5 35 22 6 5 59 5 57 5 56 5 54 5 53 6 14 5 49 5 44 S 43 5 41 5 39 5 38 15 36 5 34 23 I 5 59 5 57 5 55 5 54 5 52 6 14 5 47 5 45 5 43 5 42 5 40 5 38 5 36 15 345 33 24 6 5 59 5 57 5 55 5 53 5 52 6 15 5 44 5 42 541 5 39 5 37 5 35 5 335 31 25 6 5 59 5 57 555533_5516 15 5 47 5 45 5 43 5 42 5 40 5 38 i 5 36 5 345 325 30 26 6 5 58 5 ;6 5 55 5 53 $51 6 10 5 47 5 45 S43 5 41 5 39 5 37 5 37 5 32 .30 5 28 27 5 58 5 54 1 5 52 5 50 6 17 5 44 S 42 540 5 38 5 365 33 31 15 29 15 26 28 58 5 56 5 54 5 52 5 go 6 17 5 45 5 43 541 5 39 5 37 5 34 5 32 5 30 5 27 525 29 5 58 5 56 5 54 5 51 5 4.9 6 18 5 45 5 42 5 40 56 5 33 5 31 26 30 6 5 24 58 5 55 5 53 5 51 5 49 6 19 5 44 5 39 5 37 555 5 32 1 5 9 5 27 i 24 31 6 5 55 5 53 5 50 548 019 S43 5 41 5 38 5 34 15 23 520 6 5 57 5 55 5 52 5 50 5 47 6 20 5 43 5 40 FOR Page 25
For finding the Rising and Setting of the Sun and Stars. SE MI DIURNAL DURATION ARCS. of Son or STAR. 37° 380 390 400 43° 449 450 47° 49°
V.S. H. M. H. M. H. M. H. M. H. M. H. M.H. M. H. MH. M.H. M.H, M. H. M.H. M. H. M. H. M.H.M. H.M 7 6 7 6 7 6 0 8 6 8 6 S 2 6 8 6 8 6 9 6 6 96 10 6 to 6 II 3 6 12 6 12 6 13 6 13 6 14 6 15 6 15 6 16 6 17 6 18 6 18 4 6 14 6 14 6.15 6 16 6 16 6 17 6 17 6 18 6 18 6 19 6 21 o 22 5 6 17 6 18 6 18 6 19 6 20 6 20 6 21 6 22 6 23 6 24 6 25 6 26 6 6 19 6 23 6 24 6 25 6 25 6 26 6 27 6 28 6 30 6 31 6 32 7 6 24 6 24 6 25 6 26 16 26 6 27 6 28 6 29 6 30 6 31 32 34 6 36 6 37 8 6 27 6 28 6 29 6 30 6 31 6 32 38 6 37 6 386 39 6 28 41 9 6 29 6 43 6 30 31 6 32 6 6 33 35 6 36 6 37 6 40 6 44 45 6 47 10 6 32 6 6 41 6 42 44 6 45 6 48 6 52 54 11 6 34 6 39 6 42 6 43 6 45 50 51 53 6 55 12 57 6 37 6 42 45 49 6 50 6 52 6 56 6 58 o 7 7 2 13 6 40 6 6 7 43 46 6 48 49 6 51 6 53 6 55 6 47 7 1 7 3 7 5 17 7 7 IO 14 6 43 44 6 46 51 53 6 55 6 57 6 59 7 I 7 10 17 13 15 7 15 46 48 53 57 7 15 17 18 7 21 16 6 49 51 6 59 7 1 7 3 7 5 7 7 7 10 7 12 7 15 7 18 17 7 21 7 24 17 27 6 52 6 6 54 56 o 7 2 7 5 7 7 7 9 7 12 7 14 7 17 7 20 7 23 7 26 7 29 17 33 18 6 55 6 57 7 7 2 6 7 9 7 14 7 16 7 197 28 7 31 17 35 7 38 19 6 59 I 7 3 7 5 7 8 7 24 7 27 7 30 7 34 7 37 7 41 7 45 20 7 2 7 4 7 7 7 9 7 12 7 14 7 17 7 20 7 23 7 29 7 32 7 35 7 39 743 7 47 17 51 21 7 S 7 8 7 13 7 15 7 18 7 21 7 24 7 27 7 30 7 34 7 37 7 41 7 45 7 49 7 53 7 57 22 79 7 13 7 17 7 19 7 25 7 29 7 32 7 35 7 39 7 43 7 50 7 55 17 59 8 4 23 7 12 7 15 7 18 7 21 7 24 7 27 7 30 7 33 7 37 7 40 7. 44 7 48 7 52 7 56 8 186 7 28 7 31 7 34 7 38 7 42 7 45 7 49 7 54 7 58 8 3 12 8 18 25 7 19 7 22 7 25 7 29 7 32 7 35 7 39 7 43 7 47 7 51 7 55 7 59 8 4 8 9 14 19 8 25 26 7 23 7 29 7 33 736 7 40 7 44 7 48 7 52 7 56 8 I 8 8 15 8 21 8 27 8 27 7 27 7 34 7 30 33 7 37 7 417 45 7 49 7 53 8 8.6 2 8 12 8 17 8 28 8 28 8 34 7 39 7 34 7 38 7 42 7.45 7 49 7 54 8 7 58 41 3 8 7 8 12 8 18 8 23 29 8 35 8 42 29 7 35 746 7 So 7 42 7 54 8 49 8 4 8 13 8 19 8 30 37 8 43 8 50 18 58 30 8 7 39 7 43 7 47 7 51 7.95 8 5 8 9 8 14 8 20 8 44 8 52 8 59 9 8 8 747 7 51 . 8 31 7 43 8 8 26 8 32 8 38 8 45 52 9 32 747 7 51 8 o 9 9 19 18 1 8 8 10 5 8 16 21 8 278 39 8 8 53 9 T 9 9 9 19 19 28 S.N. 1 6 o 60 6 o 6 o 5 59 5 59 5 59 5 59 5 59 5 59 5 59 5 59 5 59 5 59 5 595 595 58 5 57 5 57 5 575, 56 5 56 5 56 5. 56 5 55 5 55 5 55 5 55 5 55 554 5 545 545 53 3 5 54 5 54 5 545 53 5 53 5 53 5 525 52 5 52 5 51 5 51 5 51 5 so 5 50 5495 495 49 4 5 51 5 51 5 51 5 50 5 50 5 49 5 49 5 48 5. 47 5 47 5 46 5 45 5 455 445 44 5 5 49 5 485 48 5 47 5 45 5 45 5 44 5 44 5 43 5 42 5 42 541 5 40 15 395 39 6 5 45 5 445 44 5 43 5 43 5 42 5 41 5 40 5. 40 5 39 5 37 5 36 5 355 355 34 5 43 5 4.2 541 541 5 40 5 39 5 38 5 37 5 37 5 365 35 5 34 5 33 5 32 5 315 30 5 29 8 5 40 5 39 5 385 3.7 5 37 5.3.6 5 355 34 5 33 5 32 5 31 5 30 27 9 5 37 5.36 5 355 34 533 5 32 5 315 30 5 29 5 27 5 25 5 24 5 23 5 215 20 10 5 34 5 33 5 325 31 5 30 5 18 5 29 26 S 525 524 5 22 21 5 20 5 185 IS 513 II 5 31 5 30 5 29 5 28 5 27 5 25 5 24 5 23 5 18 5 17 515 5 13 5 12 5 IO IZ 5 28 5 27 5 23 22 5 5 205 19 5 17 5 14 59 5 715 13 5 25 5 24 5 23 5 21 5 20 18 5 175 15 5 13 5 10 8 5 6 5 4 5 25 o 14 5 19 5 18 5 15 5 13 II5 9 5 7 5 5 5. 3 5 I 4 59 4 57 15 5 19 5 18 544 52 5 16 5 14 5 13 5 915 7 5 5 5 3 5 I 4 59 4 57 4 54 4 52 494 46 16 5 15 5 13 15 11 5 9 5. 7 5 5 5 3 5 3 4 59 4 57 4 54 4 52 4 49 4 46 4 17 5 13 II 5 10 5 8 4 41 I 4 59 4 57 4 55 4 52 4 50 4 47 4 44 4 41 18 6 5 10 5 5 4 5 2 4 59 4 574 55 4 53 4 50 4 47 4 45 4 42 4 39 4 36 4 33 4 29 19 5 7 5 5 S 3 50 4 58 4 56 4 534 51 4 48 4 43 4 40 4 37 4 34 4 304 274 23 20 5 4 5 2 4 594 57 4 54 4 52 4 49 4 47 4 44 4 38 4 35 4 32 4 254 21 4 45 4 42 4 39 4 33 4 30 4 23 4 19 4 15 4 22 4 57 4 554 524 49 4 47 4 44 4 414 38 4 35 4 32 4 28 25 4 21 4 17 4 134 94 23 4 544 51 4 494 46 4 43 4 40 4 37 4 33 4 30 4 27 4 23 19 15 4 74 33589 24 4 504 484 45 4 42 4 39 4 35 4 324 29 4 25 4 22 4 18 4 10 4 5 4 1 25 4 47 3 56 4 444 41 4 384 34 4 31 351 4 20 4 17 4 13 4 4 3 59 354 3 49 344 26 4 43 4 40 4 36 4 34 4 30 4 27 4 23 4 19 4 15 4 II 4 7 4 3 3 53 27 4 364 334 29 4 26 4 22 4 6 4 I 3 57 3 52 28 4 364 324 29 4 25 4 17 3 50 3 45 3 40 3 34 3 28 29 4 284 254 21 4 32 4 17 4 13 4 4 3 59 3 54 3 49 3 44 3 33 3 26 30 4 28 4 24 4 20 4 16 4 12 4 4 3 3 99 3 54 3 12 3 43 3 37 3 31 3 25 3 18 3 11 31 3 4 4 24 4 20 4 15 4 12 4 7 4 8 3 581 3 53 3 42 3 37 3 31 3 24 3 17 32 4_19 4 15 4 7 4 3 57 3 52 3 47 3 42 3 36 2 54 330 323 3 17 3 9 3 2 44 Page 26
For finding the VARIATION of the COMPASS. AMPLITUDE of RISING and SETTING, from East and WEST. N.S. North or South LATITUDE of the Place, correspondent to N. S. Declination of Sun or Star. Declin. Sun or 33° 340 350 37° 380 39° 420 43° 440 45° Star. N. S. 1 1 0 10 1 36 I 47 I 50 I 52 I 54 I 57 2 2 44 2 46 2 49 2 52 2 54 2 57 3 0 3.4 3 7 3 14 3 22 3 3 49 3 52 3 55 3 59 4 2 4 6 4 10 4 14 4 18 4 22 4 31 4 36 4 41 4 47 4 w 4 59 5 3 5. 7 5 16 5 20 5 25 5 30 5 35 5 40 5 52 5 6 12 6 14 6 29 6 34 6 40 6 46 6 59 7 6 7 13 7 29 7 37 7 25 7 30 7 36 7 42 7 49 7 56 8 3 8 10 8 18 8 26 8 36 8 49 8 56 93 9 II 9 19 9 37 9 56 10 6 10 16 10 28 9 40 9 47 9 54 то 2 10 10 IO 18 II 6 10 58 11 6 I2 3 12 26 13 5 13 20 10 12 1 12 9 12 18 12 28 12 48 12 58 13 9 13 21 13 34 13 47 14 o 14 15 14 30 14 46 II 13 21 13 31 13 41 13 51 14 2 14 14 14 27 14 40 14 53 15 23 15 38 15 55 12 14 22 14 32 14 43 14 54 15 5 15 30 15 44 15 58 16 13 16 28 17 2 17 20 17 40 13 15 33 15 44 15 55 16 20 17 I 17 17 17 33 17 50 18 8 18 26 18 46 19 7 17 8 17 21 17 34 17 48 18 36 18 53 19 II 19 31 19 51 20 12 17 55 18 7 19 4 1920 19 37 19 55 20 14 21 38 16 19 6 19 19 19 33 19 48 20 4 20 20 22 41 23 5 23 31 17 5 20 17 20 46 21 2 21 36 123 18 23 42 24 6 24 33 25 1 18 21 28 22 O 22 16 22 53 23 12 123 32 23 54 24 17 24 41 25 6 25 32 26 1 19 22 56 26 59 27 29 28 23_5224 924 27 24 46 25 6 25 26 | 26 36 27 I 27 57 28 27 28 59 29 32 21 125 4125 22 25 41 26 I 26 22 27 7 27 31 27 57 28 24 53 29 23 29 55 30 29 31 4 22 E 26 16 26 35 27 38 28 1 28 26 28 52 129 19 29 47 30 50 31 24 31 59 32 37 23 27 29 27 49 28 jo 29 19 129 45 30 41 31 43 32 17 32 53 33 31 24 329 25 29 48 30 38 31 5 31 34 32 4 32 36 33 46 34 24 35 3 35 46 25 29 55 30 17 30 40 31 4 31 3031 57 31 25 32 56 33 28 34 I 34 37 35 IS 35 55 36 37 37 22 26 31 31 31 31 55 32 21 32 48 33 16 33 40 34 52 35 27 36 37 28 38 12 39 27 32 22 32 46 33 11 33 38 34 6 34 36 35 8 35 41 136 17 37 34 38 16 39 1 40 39 23 33 36 34 1 34 56 35 57 37 537 42 138 22 39 4 40 35 42 19 29 34 50 35 16 35 44 36 14 36 45 37 53 39 9 39 51 40 35 41 22 42 11 43 5 44 2 30 1 36 5 136 32 37 2 37 33/38 638 42 57 43 49 44 45 31 37 20 37 49 38 20 38 52 40 3 40 41 41 22 42 5 42 51 43 40 44 33 45 28 46 28 47 32 32 38 36 139 6 41 26 46 11 47 10 49 21 N.S. IO 0 51 o 51 O 51 o 51 o 51 og1 O 51 0 52 o 52 0 52 o 52 o 53 2 2 z 2 2 2 2 3 2 4 2 5 6 2 7 2 8 2 JO 2 II 2 13 2 14 2 16 2 18 3 31 3 34 3 37 3 40 343 4 21 4 23 4 25 4 30 4 33 4 36 4 39 4 43 4 46 5 7 5 31 5 34 5 37 5 40 5 44 5 52 6 O 6 5 6 41 6 45 6 49 6 53 6 57 7 2 7 7 18 7 24 7 30 7 30 743 7 50 5 8 II 8 16 8 22 8 28 835 8 42 8 57 9 5 9 14 9 23 9 1 9 7 9 12 9 18 9 24 9 31 9 38 9 45 9 53 10 1 10 10 13 IO 28 10 38 10 48 IO 12 10 24 10 38 II I II JO 11 2050 12 2 10 U 22 11 36 12 o I 2 9 12 18 12 28 12 39 13 I 13 13 13 40 11 12 48 12 56 13 5 13 14 13 24 13 35 13 46 13 58 14 10 14 23 14 36 14 51 15 12 13 4213 51 14 O 14 9 14 19 14 29 14 41 14 52 15 4 15 17 15 30 15 45 16 16 16 13 14 53 15 2 15 33 15 44 16 9 16 51 17 7 17 41 17 59 14 16 4 16 14 16 24 16 35 17 o 17 13 17 27 17 41 17 56 18 12 15 17 14 17 25 17 37 17 49 18 2 18 29 19 o 19 16 19 34 19 52 2012 16 2 18 25 18 37 19 2 19 30 19 46 20 55 21 36 21 58 22 22 17 0 19 36 19 49 20 20 31 22 39 23 1 23 25 123 50 18 20 47 21 I 21 46 22 2 22 20 22 38 22 57 23 18 23 41 24 3 24 27 24 52 125 19 19 22 13 22 28 23 1 23 37 23 57 24 17 24 39 25 3 25 27 25 53 26 20 20 23 10 23 25 23 41 23 58 24 35 24 55 25 16 25 38 26 26.26 27 19 27 48 28 19 21 24 38 24 55 25 13 25 32 25 52 (26 58 27 23 27 49 29 17 29 30 22 25 34 125 51 26 9 26 23 26 48 127 9 27 31 27 55 128 20 29 43 30 14 47 23 26 46 27 4 27 23 27 43 4 28 26 28 50 29 15 129 41 30 9 30 38 31 9 31 42 32 17 32 54 24 27 58 28 37 | 28 58 29 44 30 9 30 35 31 3 31 33 31 4 32 37 33 49 25:29 10 29 30 29 52 30 14 30 38 31 3 31 29 31 56 32 57 33 30 34 5 34 42 36 3 26 30 23 30 44 31 7 31 30 31 55 132 21 32 49 33 18 33 49 34 57 35 33 30 13 36 54 27 31 36 31 58 32 22 32 47 33 13 33 40 34 9 34 40 35 13 35 47 37 337 44 38 28 39 15 32 50 33 13 33 37 34 3 34 31 135 0 35 31 36 3 36 37 37 14 37 53 38 34 39 17 40 4 40 53 29 34 3 34 28 34 54 35 21 35 50 36 20 36 52 38 3 38 41 40 5 40 52 41 41 42 33 30 35 18 35 43 36 10 36 39 37 8 137 41 41 38 42 27 43 19 44 15 31 36 32 36 59 37 27 37 57 38 29.392 39 38 40 56 41 39 42 24 43 13 44 4 45 o 45 59 32 37_47_138 15 138 45 39_49_140_25 41 2 41 42 142 27 143 9 43 57 44 48 45 43 47 45 |
What should be added to each of 3/15 38 and 134 so that the number become proportionate to each other?
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