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Page 2
SUPPLEMENTAL LUNAR TABLES.
IV. ELLIPTIC EQUATION of the Moon's Center. According to the Newtonian Theory.
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
15 361
115 381
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.
SIGN 6.
Letrbe equared mean Anomaly of ibe Moon be 72o. 12' 361 and present Eccentricity of Her Orbir, 105/70 Radius, or Sem. Tronjverje) to find ib.
Equation and also true Anomaly >
Ex, of the foregoing Rule.
Logo
By Difhop Hard's Hypothesis.
Loge.
As Rad.
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.
So S, M. An. 72° 12' 361"
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
True An. 66 51 52 St.-56 6.4343944 Constant Log. for Ecey, ,05
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.
EQUATION of the Mean to the present Elliptic EQUATION of the MOON'S CENTER.
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
9 30 15 28 17/26 21 24 18 22 14:20 015 4913 39 11 22 9 61 6.52 4 35 2 17 18
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.
ACCELERATION
EQUATION of the Node and Mean ANOMALY of the MOON.
of the MOON's
Argument. Mean Anomaly of the SUN.
Mean MOTION:
Or Equation of the O The lingle for the 8, and double of which Equation for Mean Anom.
D.
D's Mean Long.
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
5 37. 9 9
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
6
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
3
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.
7 31
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
5
16500
9 25 4 14 8 18 10 14
6
3 o 56
5 6 9
9
1700 o
26 4 23
10 15 9 23 5 54 045
4
9 1750 27 4 33
5 45
6
3 7 1800 o 9
9 28
8 36 4 42
10 17 8
6
9 14
5 36
9
18500 O15
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.
XII. EQUATION of the MOON'S EVECTION, or Second Equation of the MOON'S CENTER.
Arg. 12. Or 2. D à O cord. by D's Pl. at 10Eq. (not at 11th, of which this Eq. is zd. Part) - M. An. cord. or Arg. 11th. Sig. o. Sig. 1.
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.
6
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
6 32
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
O 52 21 I 15 50 I 1927
19 3 O 16 33
18 O 53 24
0 25 17
I 19 11 26 118 54 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
0
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
5
I 28
| 20 36
O 43 18
O 37 23
7 54 14
40 13
26 4 1 III
1 26
0 38 37 29
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.
Argument. Twice Dist. Moon from Sun Excentric Anom. Moon. Sig. o.
Sig. 2.
Sig. 3. Dif, Dif. Dif. Dif.
Dif.
0
o 36 59 18
4 5 6
14
4
O 36 59 I
5
38
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
5
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
7
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 1 13 43
I 7 3 O 42 27
O
6 27
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
o 38 5
I 18 6
4 43 I
1 0
I 18 39 0 36 59
I 30
I
0
O o
4 5
O
0 36 59
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.
By Bullialdus's Correction. Logs.
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!
S 15 o Equation, nearly.
147 Correction
5 14 52 Above,
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 Sem. Trans. i.
So Tangent M, Anom. 1200 or T, 60°. 119.2385606
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.
Half . : 59° 59' 3".. Tangent 10.2382834
By the Logarithmic Equations aforegoing, Const. Log. Orb. • 9.9580851
ist Term.
20 Term. 4.712363) Conft. Log.
5.138334) Const. Log.
57° 32' oll Tang IO.1963685
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"
39 60 d' 59!
O$ 27° 35' 1011
Jan. 1. / 1600NS
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' 18" o" 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
Euler's. + 28
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.
Halley +41 09.0010119753 47 -08.00123 50617
+,002247037037
+,00185185 &c.
exactly +1' 49" 17" 36iv exactly — 2' 13" 23" iziv 4'2" 401!48iv exactly 3' 20" exactly. Decimals, Decimals. Sign.
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,
Halley 118.9920392683
119.99 14778925 +,000 5613758
+,0004626558
14' 19' 45'" 15' 20" 23"
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
Our
59'8" 19" 45 iy
59' 819" 47iv
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
36545h 48m 54461h 1980: 36546h 14m os agih 1960 The same as a Revolution Rein à *. Dec.
Our Mean Solar Year.
Anomaliftical Year. of from O's An.
3654,256532906 Decimals. Decimals,
[6h 9m 245 26th 33 fo
Halley 365D9.2422996627 365D:,259398291 Sydereal Year, or Revolno 3654, 256391047
36545h 48m 549 411h270 36506h13m 3206h 43 Po from fixed Star,
[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.
The Mean PLACES and MOTIONS of MARS and JUPITER.
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"
+ 6513° 17' 19" 4 + 1' 10"
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
31' 26" 39" 24iv. 11" 31" 12iv 104 1412 piv 4' 59" 16" 56iv
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
v 12" 28" iziv
129' zei &c. Sign.
Sign. Minute I tooco1213128
t,coco019244
1" 18" збiv
12" 28iv.
Sign. Second +,00000020218
t.cooo00032076
1" 1 Siv &c.
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
Iyan. 1.2 1600 N.S. 6 15
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"
los 20 13' 20" los o 30' 0"
The PLANETS Mean Synodical REVOLUTIONS
18 18° 55' 26" 24" pos oo
5' 20" OS 00 I'12"
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
2' 0" 33" biv 12" gm 243 21156124
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
93 123 154 184 215 246 276 307 337
* 3 1095
800 292200 3
35 63 94 124 159
185 216 247 277 308 338
1461) ၂၀၁ 328725 4 5
36
64 95 125 156 186 217 248
309 339
2922
365250
37 65 96 126
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
317 347
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
107 137 168 198
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
113 143 174 204 235
266 296 327 357
80 29220
1st Year, as is evi23 24
55
83 114 144 175
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
27 27
86
117 147 208 239 270 300 331
96 35064
38 27 28 59 87 118 148, 179 209 240 271
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
Seasons fall back but one Day in 5200 Years.
5200 For, they fall back in 5200 Years by Julian Account = = 40 Days.
130
5200
They go forward in 5200 Years, by the Gregorian Account = X 3=39
400
Difference, they fall back in 5200 Years Gregorian Account 1 Day.
Or, because in 400 Gregorian Account, but i Day of the Season's falling back in the Julian Account is confidered,
and provided for, which happens in 390 Years, 10 Years, in every 400 Gregorian, are un provided for, in which the
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
Difference. The Years from Nicene Council to our Alteration of Stile . . 1427 1427
Now, = 11 Days, nearly, the Seasons fall back from the Time of the Nicene Council, to 1752, the Time
130
when the Stile was altered in England.
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 or common Year, is of different Length, according to the Custom among different
Civil Year. Nations. Some Nations reckon this Year by the Solar and some by the Lunar Motion.
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.
DOMINICAL-LETTERS for Gregorian or New Style, for ever. WEEK and MONTH-DAY. Shewing, by the
YEARS before CHRIST.
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
before 3300 340013500 3600
fince 3300 340013500 3600 Febr. 28. 29 12 13 14 15 16 17
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
F A B
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
of 4 Hundred Years will have for Years N. B. The Dominical Letter for any Sunday-Column is 7, 14, 21, 28, all the Sundays in
Lance Cbrif.
360/
Number of Years since Cbrift will be the that Month ; and to the Left the 19th Day is in the
18 Ys. Dom. L. fame, as the Dominical Letter for the Friday-Column, which therefore was on a Friday, re-
Hundreds 36001 Complement of thote Years to any Num- quired.
Ex. Before Christ
:
DCB ber of 4 Hundreds, before Chrift.
Hence Apr. 3ů, 33 Ch. 0. S. was on a Frill
Comp. firice Christi
Cbriff's Crucifixion.
So for ibe Reft.
Yrs. DL, And May 28th, 585 bef. Chř, on Mo-
N. B. Tho' there was no N. Style be-
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
II
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
6 24
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
4. 8
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
1327 26 1026
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
2 or the
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
5
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
Harwich, b
3 30 Oftend,
b 2 Spithead, Breft,
Hastings, Flushing,
b
b
4 0 Orfordness, 4 Shoreham, 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
Havre-de-Grace, b 5 30
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,
EXAMPLE, To find obe Time of High-Water at Rochester, on the 10th Day of the Moon's Age.
At London, on that Day, it is high Water
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,
,
Of Use in HISTORY and CHRONOLOGY.
From
D. GOLDEN Xmas Shrove Easter Rog. Ascen. Whit-Trin. Advent Easter Trinity
Ends.
Ends. L. NUMBERS. to Sh. Sund. Sunday Sunday Day. Sunday Sunday Sunday Term
Term
Sund.
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
31 May 5 9 191
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
5
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
6 11 Apr. 1 May 6
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
A Gereral TABLE of the Sun's Rising and Setting, for England and Ireland, New STYLE. To be used with Table, Page 153.
| 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.
Conditions 1.
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
expressing the same wbole Number,
Let ift Condition, = 2, then x 19a + 10. 19
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.
Therefore, . i . 50+4 = 120+11, a whole Number fought, d and a whole Numbers, required.
Subtract 4 from each Side .. sd = 12a+ 7, a wbile Number, divifible by 5.
Subtract icat 5, a wbole Number, divisible by so
Here a may be discovered 34. . . . 2a+ 2, a wbole Number, divisible by 5.
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
contrary. For determining the EPACT, and Fall of Easter, according to New Style, as settled by Pope Grow
gory. See Tab. p. 30. Also to find the Epact, 0. S. for the same Centuries. NoCols 3. 4. 5:
3 14. 5
6.
7.
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
retr. and den
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
13 25 2700 19
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
B. 800 & 8 19 29
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
15
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
* 5300 38
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
N. B. As o signifies the first Year current before Christ, fo 100, 200, 300, &c. lignify the 101, 201, 301 Years current before Cbrift;
being all Biffextile. So that i must be added to all years before Christ in the Table for the current Years. The Tabular Years being the
Years completed. The Years after Chrift are let down current (not completed) as they are used in Chronology.
For the MEMORY.
CONSTRUCTION. RULE I. Before Christ, take the Fourib from the Hundreds less one,
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
42+2=43, to be subtracted from the Old Style 2
for the New
} 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.
Example. To find tbe Week-day answering to May 28, 585 Years before Cbrifi, 0. S. D
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 Monday, Jan, o, or the gift of December, preceding Jan. 1. 23
+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.
Dates above compleat Centuries before Cbrift will have the same Days 1759 fince Cbrif,
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.
Years before Cbris reduced to Years since Cbris, 0, S.
RULE. Before Christ, take the Number of Years less by One,
From Hundreds by 7, and the Year since is known.
-~-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.
Rem. 816 Vears current fince Christ, having the same Domi- Example. II. Of the Golden Number 2189 fince Cbrift.
nical Letters, (viz. FE for 0. s.] and beginning with the same
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
From Hundreds by 4, the Year fince Cbrifi is done.
Sight, in two Pages, 148 and 149, foregoing, with the following
Example. 585 Yrs, current bef. Chr. Rults to those Pages,
For the COMMENCEMENT of the mot famous Æras (lince
$85 before Cbriff, -584
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.
Letters GF, Year begins on Monday, N, S, oz
584
Suo
2/
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-
Years of Gol.
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
B. 1760 13 FE BA
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
A D
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
A
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
1791 6 B E Feb. 20 Mar. 9 24 29 B. 1792 7 AG DC
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
A D
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,
To determine the right Ascension of any Star from the given rigbe Ascension of any orber Star.
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 is the Time marked by the same Clock, between the Passage of that and any other Star, through the Meridian, to their Difference of Right
Ascension.
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
Day at Noon. And by the Metbed of corresponding Altitudes, or otherwise, observe the Difference in R. A. between the chosen Star and the
Sun, at the same Instant of Noon. When the Sun has passed the following Solstice, and is returned nearly to the fame Parellel, observe, for
three or four Days together, its Meridian Altitudes, and its Difference in R. A. with the same Star, for determining, from these Observa-
tions, when the Sun comes into the same Parallel, as in the fir At Observatior, and the Difference of R. A. for the same Infiant.
This Metbud gives two Inftants when the Sun was at equal Distances from the fame Tropic; because, at equal Distances, on either Side a
Tropic, the Declinations are equal, as are likewise the corresponding Arcs of the Equator.
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.
in the Interval of ihese two Inftants.
Ihe Seljitial Colure therefore bisects that Are, the Complement of Half which will be the Sun's true R. A, at the first Observation,
The Sun's R, A, being thus determined, the R. A. of the Star is likewise determined by the observed Difference,
Merid. Alt. O Dif, R. A. bet. O &* at Noon,
Procyon, at Noon.
EXAMPLE. 1745, April 4.
46 58 41
97 52 10 East
Sept. 6. 47 29 32
53 39 29 West
7.
47 7 1 54 33 36 West 8.
46 44 24
55 27 43 West
Iriterpolating these Observations, it appears that if the Sun had been in the Meridian Sept. 7d għ som P. M. he would have had equal Ala
titude, with his Altitude on April 4th at Noon, preceeding ; viz.
460 581 41"
The Difference between his R. A. and that of the Star, had been
Therefore, from April 4, to September 2d 8h 50m Evening, the Sun had run through, in R. A.
152 45 49
Whence, on April 4d Noon, Sun's Distance in R. A. from the Tropic of 5 was
76 22 541 And had R. A.
37 51 The Star being to the East
97
52 10
The Star Procyon had R. A. required
Sum 111° 29' 15"}
USES of the RIGHT ASCENSION and DECLINATION of the STARS,
1. To find the Longitude and Latitude of those Stars.
2. Io sbew the order in diurnal Revolution, and the Intervals of Time they take in succeeding each other in their Pallage through the Meridian.
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,
for the Noon of the given Day, reduce this Difference to Time, by Tab. p. 28, which will be nearly the Interval of Time from Noon to Noon
of the Star’s Passage through the Meridian.
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
give the correct Instant of the Star's passing the Meridian.
EXAMPLE. Suppose the R. A. of Mars
, on a given Day at Noon be 1120 18', and the R. A. of tbe Sun 1830 42', the Difference 71° 24'
reduced to Time is 4 h 45mm 368. Now Mars being eaftward of the Sun, mull pass tbe Meridian about 45 45m 36s before Noon, that is, 7h 14m 248
in the Morning
The R. A. of Mars for that Time is
13
The R. A. of tbe Sun for that Time is
The Difference
71 16 58
Reduced to Time, is the Instant of the Palage of Mars through the Meridian
7h 14m 528 required.
This Computation is plainly the Reverse of the former, in finding the R. A. of the Stars by observing their Passages over the Meridian.
By the above Computation, the Times marked by a Clock may be proved.
For, observing at what Infiant any Star, whose R. A. is known, passes the Meridian, that Inflant being compared with the orber, found by
Computation, will shew whether the Clock agrees with true Time, or what it differs from it.
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
which is the same,
To find tbe Angle at the Pole, formed by the Meridian of a Place and the Circle of Declination paling through the Star.
MÉTHOD. Reduce ebe Interval of Time between Noon and tbe given Infiant, into Degrees, by 'Tab. p.
28, add obem to the Sun's R. A. at that
Inftant; and from the Sum subtra&t tbe Star's R. A.
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.
FROM Two of these THREE THINGS, the Poles Height, Sun or Star's DECLINATION, and Meridian ALTITUDE (fignified
by P, D, M. and their Complements by p, d, and m, respectively) being given to find a THIRD, by Addition and Subtraction, only.
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
II 38 7
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
6 65 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
12, 4 2 1
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
7 342 50 50
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
345 38 20 4 15 7 40
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
17 5 27
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
122 17
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
59 41 54 48
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
I 12 36
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.
N.S. North or South LATITUDE of the PLACE, correspondent to N. S. Declination of SUN or STAR. D) or 10 20 30
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
6 6 3 3
4
6 4
6
6 4 6 2
6
6 3 4
4 6
6
6
5
6 6 6 6 16
5
6 6
3
6 6 4
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
6
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
6 6 3 6
4 6
6 6 6
7 6
6 8 6
9 6 9 6 10
6 12 6 13
JO 6
6 4 4
5 6
7
6 8 6 9 6
9 6 16
6 12 6
13 6 14
11 6 3 6 4. 4
6 5
6 6 6 7 6 8 6 8 6
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 10 6 11 6 12 6 13
6 15
6 16 6 18 6 19 16 20 16
6 3 6
6
6 7
6 8 6
96 14
6 16
6 21 022 17 6
3 6 5 6 6 7 8
6 16
6 18 6 20 6 21 16 22 18
6
4 6
5
6 7 9 6 10 6 i
14
6 17 6 18
6 21
16
24
19
6
4 5
6 6 8 9
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
2264 6 6 5 6
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
15 6 17 19 20 6 22
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 16 6 18 6 20
6 25 6 30 6 32 6
34
6
37 39
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
5
6
6 10 6 12 6 15 6 17 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
6 2 6
2
6 2
6
2 6 3 6 1 6 61
6 I
6
1 6 I 6 1 6 1 16
I
1 2
6 2 6 6 I 6 1 6 6
1
6
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
6
5
2
6 6 I I 1 6
6 o 5 5 59 5 59 5 59
5 58
5 575 57 5 575 56 5 56 6
2
6 1 6
1 6 6 o 6 o 6 5 59 5 58
5 57 5 57 5 57
5 56 5 555 55
6 6 1 6 1 6
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
1 6 6 05 59
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 56
5 55 5 54 5 54 5 53 5 525 525 51 10
6 I 6
1
6
5 59 5 59 5 58 6
7 5 56 5 56 5 54 5 54 5 53 5 52
5 51 15 515 50
II 6 I
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
9 5 54 5 53 552 5 57 5 50 549
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
17 5 59 5 57 5 56 5 55
5 52 5 51 5 50 5 49 5 47 5 46 5 45 5 43 5 42 5 41 18
1
6 5 58 5 57 5 54 552 5 50 5 49
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
5 37 5 35 5 32 5 29 5 27 5 24 521
FOR
Page 25
For finding the Rising and Setting of the Sun and Stars.
SE MI DIURNAL DURATION ARCS.
North or South LATITUDE of the PLACE, correspondent to N. S. Declination
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
I 6
6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 7 6
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
6 33 34
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
33 6 34 6 366 37 6 38 39
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 3 7 5 7 8
7 10 17 13 15
7 15 46 48
53
57
7 7 3 7 5 7 7 10 7 13
7 15 17 18
7 21 16 6 49 51
6
53 6 55 6 57 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 10 7 13 7 15 7 18 7 21
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
24 7 16 7 19 7 21 7 25
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
7 57
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
5 15
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
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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.
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