RECORD: Maskelyne, Nevil. 1802. Tables requisite to be used with the Nautical ephemeris. 3d ed. London.

REVISION HISTORY: Transcribed (single key) by AEL Data 8.2013. RN1

NOTE: This work formed part of the Beagle library. The Beagle Library project has been generously supported by a Singapore Ministry of Education Academic Research Fund Tier 1 grant and Charles Darwin University and the Charles Darwin University Foundation, Northern Territory, Australia.


[page i]

TABLES

REQUISITE TO BE USED WITH THE

NAUTICAL EPHEMERIS,

FOR FINDING THE

LATITUDE AND LONGITUDE AT SEA.

PUBLISHED BY ORDER OF THE

Gt. Bzit. COMMISSIONERS OF LONGITUDE.

THE THIRD EDITION,

CORRECTED AND IMPROVED.

London:

PRINTED BY T. BENSLEY,

AND

SOLD BY JAMES PAYNE AND JOHN MACKINLAY, IN THE STRAND, BOOKSELLERS TO THE SAID COMMISSIONERS.

1802.

[Price Five Shillings, stitched in blue Paper.]

[page ii]

[page iii]

PREFACE.

THE first Edition of the Requisite Tables was drawn up by myself, and published at the same, time with the first Nautical Almanac, that of 1767, by order of the Commissioners of Longitude.

A second Edition, with considerable additions and improvements, was published in 1781. In this Mr. Lyons and Mr. Dunthorne's methods of calculating the effects of refraction and parallax upon the moon's distance from the sun or a star were put into new forms by myself, and rendered much easier than before; all Mr. Lyons tables being suppressed, except the last; and new rules given for calculating the effect of the star's refraction, or of the difference of the sun's refraction and parallax, upon a plan similar to that which he had given for finding the effect of the moon's parallax; and the rest of the calculation altered to shew the effect of the difference of the moon's parallax and refraction, instead of that of the parallax only. A new rule was substituted for Mr. Dunthorne's, but adapted wholly to logarithms, and requiring no distinction of cases. To facilitate the use of this method, Mr. Dunthorne's tables had been altered and extended, as shewn in the explanation. Two other methods of correcting the apparent distance were also given, taken from the Nautical

a 2

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Almanac of 1772, one invented by myself, and the other by the late Mr. George Witchell, F. R. S. Master of the Royal Academy at Portsmouth.

Several other useful tables were also introduced, particularly extensive logarithmic solar tables for finding the latitude from two observed altitudes of the sun, and the time between, taken from the Nautical Almanacs of 1771 and 1781; and a table of latitudes and longitudes of places, that had been settled from astronomical observations and good geographical surveys.

The new tables were constructed, and the explanation and use of them drawn up by the late Mr. William Wales, F. R. S. and Master of the Royal Mathematical School, in Christ's Hospital; a person well qualified for this work by his knowledge in the practice as well as theory both of Astronomy and Navigation.

A third edition being now wanted, care has been taken to correct the errata that had been discovered in the second edition, and to introduce several new improvements, mentioned in the explanation and use of the tables; a part of the work which has been entirely new written by Mr. Wales.

At the end of Table VI. a direction is added how to use it near the equinox; the errata in Table XV. are corrected, which was chiefly requisite to make the last figure true to the nearest unit, over or under. In Table XVII. the line of the 60th minute is added, which had been left out before. The table of latitudes and longitudes of places, which before stood Table XX. but now put more conveniently the last of all, Table XXIX. has been greatly improved in accuracy, as well as extended in size, by the collections and calculations of Mr. Wales; who consulted the Philosophical Transactions, and all the foreign memoirs for this purpose. Another geographical table (Table XXX.) has been added, taken from the Grand Trigonometrical Survey, published in the Philosophical Transactions.

[page] v

Moreover, three tables of Mr. Brinkley's contrivance, relative to an improvement made by him upon the method of finding the latitude from two observations, with the time between, have been taken from the Nautical Almanacs of 1795, &c. with some corrections and improvements, and stand here Tables XXIII, XXIV, XXV; whose use is explained in Problem V. to correct the latitude found by Problem IV. after one computation. The rules, relating to the use of these three Tables, have been improved and rendered more precise, and extended in their use, by myself, under Problem V.

The three Tables relating to my method of correcting the apparent distance, which were taken from the Nautical Almanac of 1772, and put in the appendix of the second edition, are here inserted in a regular order, among the other Tables, and stand Tables XXVI, XXVII, XXVIII. Mr. Witchell's method has been improved and put in a better form by Mr. Wales, in page 42, and the two following pages of the precepts.

Greenwich,
July 9, 1802.

NEVIL MASKELYNE,

ASTRONOMER ROYAL.

[page vi]

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TABLE I.
The Refractions of the Heavenly Bodies in Altitude.
App. Alt. Refr. App. Alt. Refr. Ap. Alt. Refr.
D. M. M. S. D. M. M. S. D. M. S.
0.0 33.0 6.30 7.51 30 1.38
0.5 32.10 6.40 7.40 31 1.35
0.10 31.22 6.50 7.30 32 1.31
0.15 30.35 7.0 7.20 33 1.28
0.20 29.50 7.10 7.11 34 1.24
0.25 29.6 7.20 7.2 35 1.21
0.30 28.22 7.30 6.53 36 1.18
0.35 27.41 7.40 6.45 37 1.16
0.40 27.0 7.50 6.37 38 1.13
0.45 26.20 8.0 6.29 39 1.10
0.50 25.42 8.10 6.22 40 1.8
0.55 25.5 8.20 6.15 41 1.5
1.0 24.29 8.30 6.8 42 1.3
1.5 23.54 8.40 6.1 43 1.1
1.10 23.20 8.50 5.55 44 0.59
1.15 22.47 9.0 5.48 45 0.57
1.20 22.15 9.10 5.42 46 0.55
1.25 21.44 9.20 5.36 47 0.53
1.30 21.15 9.30 5.31 48 0.51
1.35 20.46 9.40 5.25 49 0.49
1.40 20.18 9.50 5.20 50 0.48
1.45 19.51 10.0 5.15 51 0.46
1.50 19.25 10.15 5.7 52 0.44
1.55 19.0 10.30 5.0 53 0.43
2.0 18.35 10.45 4.53 54 0.41
2.5 18.11 11.0 4.47 55 0.40
2.10 17.48 11.15 4.40 56 0.38
2.15 17.26 11.30 4.34 57 0.37
2.20 17.4 11.45 4.29 58 0.35
2.25 16.44 12.0 4.23 59 0.34
2.30 16.24 12.20 4.16 60 0.33
2.35 16.4 12.40 4.9 61 0.32
2.40 15.45 13.0 4.3 62 0.30
2.45 15.27 13.20 3.57 63 0.29
2.50 15.9 13.40 3.51 64 0.28
2.55 14.52 14.0 3.45 65 0.26
3.0 14.36 14.20 3.40 66 0.25
3.5 14.20 14.40 3.35 67 0.24
3.10 14.4 15.0 3.30 68 0.23
3.15 13.49 15.30 3.24 69 0.22
3.20 13.34 16.0 3.17 70 0.21
3.25 13.20 16.30 3.10 71 0.19
3.30 13.6 17.0 3.4 72 0.18
3.40 12.40 17.30 2.59 73 0.17
3.50 12.15 18.0 2.54 74 0.16
4.0 11.51 18.30 2.49 75 0.15
4.10 11.29 19.0 2.44 76 0.14
4.20 11.8 19.30 2.39 77 0.13
4.30 10.48 20.0 2.35 78 0.12
4.40 10.29 20.30 2.31 79 0.11
4.50 10.11 21.0 2.27 80 0.10
5.0 9.54 21.30 2.24 81 0.9
5.10 9.38 22.0 2.20 82 0.8
5.20 9.23 23.0 2.14 83 0.7
5.30 9.8 24.0 2.7 84 0.6
5.40 8.54 25.0 2.2 85 0.5
5.50 8.41 26.0 1.56 86 0.4
6.0 8.28 27.0 1.51 87 0.3
6.10 8.15 28.0 1.47 88 0.2
6.20 8.3 29.0 1.42 89 0.1
TABLE II.
Depression or Dip of the Horizon of the Sea.
Height of the Eye. Dip of the Horizon
Feet. M. S.
1 0.57
2 1.21
3 1.39
4 1.55
5 2.8
6 2.20
7 2.31
8 2.42
9 2.52
10 3.1
11 3.10
12 3.18
13 3.26
14 3.34
15 3.42
16 3.49
17 3.56
18 4.3
19 4.10
20 4.16
21 4.22
22 4.28
23 4.34
24 4.40
26 4.52
28 5.3
30 5.14
35 5.39
40 6.2
45 6.24
50 6.44
60 7.23
70 7.59
80 8.32
90 9.3
100 9.33
TABLE III.
The Sun's Parallax in Altitude.
Sun's Alt. Sun's Parallax.
D. S.
0 9
10 9
20 8
30 8
40 7
50 6
55 5
60 4
65 4
70 3
75 2
80 2
85 1
90 0
TABLE IV.
Augmentation of the Moon's Semi-diameter.
Moon's Alt. Augmentation.
D. S.
0 0
5 1
10 3
15 4
20 6
25 7
30 8
35 9
40 10
45 11
50 12
55 13
60 14
70 15
80 &c. 16
TABLE V. Dip of the Sea at different Distances from the Observer.
Dist. of the Land in Sea Miles. Height of the Eye above the Sea in Feet.
5 10 25 20 25 30 35 40
Dip. Dip. Dip. Dip. Dip. Dip. Dip. Dip.
M. M. M. M. M. M. M. M.
¼ 11 22 34 45 56 68 79 90
½ 6 11 17 22 28 34 39 45
¾ 4 8 12 15 19 23 27 30
1 4 6 9 12 15 17 20 23
3 5 7 9 12 14 16 19
3 4 6 8 10 12 14 15
2 2 3 5 6 8 10 11 12
2 3 5 6 7 8 9 10
3 2 3 4 5 6 7 8 8
2 3 4 5 6 6 7 7
4 2 3 4 4 5 6 7 7
5 2 3 4 4 5 5 6 6
6 2 3 4 4 5 5 6 6

A

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TABLE VI. For reducing the SUN'S DECLINATION, as given in the Nautical Almanac for Noon at GREENWICH, to any other Time under that Meridian; or to Noon under any other Meridian.
Add aft.N. Sub.aft.N. H M H M H M H M H M H M H M H M Sub. aft. N. Add aft. N.
Sub.bef.N. Add bef.N. 0.20 0.40 1.0 1.20 1.40 2.0 2.20 2.40 Add bef. N. Sub. bef. N.
Add. in W. Sub. in W. Sub. in W. Add in W.
Sub.in E. Add in E. 5Deg. 10D. 15D. 20D. 25D. 30D. 35D. 40D. Add in E. Sub. in E.
Days. Days. M S M S M S M S M S M S M S M S Days. Days.
Decem. 21 Decem. 21 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 21 June. 21 June.
20 22 0.0 0.1 0.1 0.1 0.2 0.2 0.2 0.3 22 20
19 23 0.0 0.1 0.2 0.2 0.3 0.4 0.5 0.6 23 19
18 24 0.1 0.2 0.3 0.4 0.6 0.7 0.8 0.9 24 18
17 25 0.1 0.3 0.4 0.6 0.7 0.9 0.11 0.12 25 17
16 26 0.2 0.4 0.5 0.7 0.9 0.11 0.13 0.15 26 16
15 27 0.2 0.5 0.6 0.8 0.11 0.13 0.15 0.18 27 15
14 28 0.3 0.6 0.7 0.10 0.12 0.15 0.18 0.21 28 14
13 29 0.3 0.7 0.9 0.12 0.15 0.18 0.21 0.24 29 13
12 30 0.3 0.7 0.10 0.13 0.17 0.20 0.23 0.27 30 June. 12
11 Decem. 31 0.4 0.8 0.11 0.15 0.19 0.22 0.26 0.30 1 July. 11
10 January 1 0.4 0.8 0.12 0.16 0.20 0.24 0.28 0.32 2 10
9 2 0.4 0.8 0.13 0.17 0.21 0.26 0.30 0.35 3 9
8 3 0.5 0.9 0.14 0.19 0.24 0.29 0.33 0.38 4 8
7 4 0.5 0.10 0.15 0.21 0.26 0.31 0.36 0.41 5 7
6 5 0.5 0.11 0.16 0.22 0.28 0.33 0.38 0.44 6 6
5 6 0.6 0.12 0.17 0.24 0.30 0.35 0.41 0.47 7 5
4 7 0.6 0.12 0.18 0.25 0.31 0.37 0.43 0.49 8 4
3 8 0.6 0.13 0.19 0.26 0.33 0.39 0.45 0.52 9 3
2 9 0.7 0.14 0.20 0.27 0.34 0.41 0.48 0.55 10 2
Decem. 1 10 0.7 0.14 0.21 0.29 0.36 0.43 0.50 0.57 11 1 June.
Novem. 30 11 0.7 0.15 0.22 0.30 0.37 0.45 0.52 1.0 12 31 May.
29 12 0.8 0.16 0.23 0.31 0.39 0.47 0.55 1.3 13 30
28 13 0.8 0.16 0.24 0.33 0.41 0.49 0.57 1.6 14 29
27 14 0.8 0.17 0.25 0.34 0.42 0.51 0.59 1.8 15 28
26 15 0.9 0.18 0.26 0.35 0.44 0.53 1.2 1.11 16 27
25 16 0.9 0.18 0.27 0.37 0.46 0.55 1.4 1.13 17 26
24 17 0.9 0.19 0.28 0.38 0.47 0.57 1.6 1.16 18 25
23 18 0.10 0.20 0.29 0.39 0.49 0.58 1.9 1.19 19 24
22 19 0.10 0.20 0.30 0.40 0.50 1.0 1.10 1.20 20 23
21 20 0.10 0.21 0.31 0.41 0.51 1.2 1.12 1.22 21 22
20 21 0.11 0.22 0.32 0.43 0.53 1.4 1.14 1.25 22 21
19 22 0.11 0.22 0.33 0.44 0.55 1.6 1.17 1.28 23 20
18 23 0.11 0.23 0.34 0.45 0.56 1.7 1.19 1.30 24 19
17 24 0.12 0.23 0.34 0.46 0.57 1.9 1.21 1.32 25 18
16 25 0.12 0.24 0.35 0.47 0.59 1.11 1.23 1.35 26 17
15 26 0.12 0.24 0.36 0.48 1.0 1.12 1.24 1.36 27 16
14 27 0.12 0.25 0.37 0.49 1.2 1.14 1.26 1.39 28 15
13 28 0.13 0.26 0.38 0.51 1.4 1.16 1.28 1.41 29 14
11 January 30 0.13 0.26 0.39 0.53 1.6 1.19 1.32 1.45 31 July. 12
9 February 1 0.13 0.27 0.41 0.55 1.9 1.22 1.36 1.50 2 August 10
7 3 0.14 0.28 0.42 0.57 1.11 1.25 1.39 1.53 4 8
5 5 0.14 0.29 0.43 0.58 1.13 1.27 1.42 1.56 6 6
3 7 0.15 0.30 0.45 1.0 1.15 1.30 1.44 1.59 8 4
Novem. 1 9 0.15 0.31 0.46 1.2 1.17 1.32 1.47 2.3 10 2 May.
October 30 11 0.16 0.32 0.47 1.3 1.19 1.35 1.50 2.6 12 30 April.
28 13 0.16 0.32 0.48 1.5 1.21 1.37 1.53 2.9 14 28
26 15 0.16 0.33 0.49 1.6 1.22 1.39 1.56 2.12 16 26
24 17 0.17 0.34 0.50 1.7 1.24 1.41 1.58 2.15 18 24
21 20 0.17 0.34 0.52 1.9 1.27 1.44 2.1 2.19 21 21
18 23 0.17 0.35 0.53 1.11 1.29 1.46 2.4 2.22 24 18
15 Feb. 26 0.18 0.36 0.54 1.13 1.31 1.49 2.7 2.25 27 15
12 March 1 0.18 0.37 0.55 1.14 1.32 1.51 2.9 2.28 30 August 12
9 4 0.19 0.38 0.56 1.15 1.34 1.53 2.12 2.30 2 Septem. 9
6 7 0.19 0.38 0.57 1.16 1.35 1.54 2.13 2.32 5 6
October 3 10 0.19 0.38 0.57 1.17 1.36 1.55 2.14 2.34 8 3 April.
Septem. 30 13 0.19 0.39 0.58 1.17 1.37 1.56 2.15 2.35 11 31 March.
27 16 0.19 0.39 0.58 1.18 1.38 1.57 2.16 2.36 14 28
24 19 0.20 0.39 0.58 1.18 1.38 1.57 2.16 2.36 17 25
After the Equinox. Until the Equinox. 0.20 0.40 0.59 1.19 1.39 1.58 2.17 2.36 20 and till Equinox. 22 After Equinox.
0.20 0.40 0.59 1.19 1.39 1.58 2.17 2.36

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TABLE VI. For reducing the SUN'S DECLINATION, as given in the Nautical Almanac for Noon at GREENWICH, to any other Time under that Meridian; or to Noon under any other Meridian.
Add aft. N. Sub. aft. N. H M H M H M H M H M H M H M Sub. aft. N. Add aft. N.
Sub. bef. N. Add bef. N. 3.0 3.20 3.40 4.0 4.20 4.40 5.0 Add bef. N. Sub. bef. N.
Add. in W. Sub. in W. Sub. in W. Add. in W.
Sub. in E. Add in E. 45D. 50D. 55D. 60D. 65D. 70D. 75D. Add in E. Sub. in E.
Days. Days. M S M S M S M S M S M S M S Days. Days.
Decem. 21 Decem. 21 0.0 0.0 0.0 0.0 0.0 0.0 0.0 21 June. 21 June.
20 22 0.3 0.3 0.4 0.4 0.4 0.5 0.5 22 20
19 23 0.6 0.7 0.8 0.9 0.9 0.10 0.11 23 19
18 24 0.10 0.11 0.12 0.13 0.14 0.15 0.16 24 18
17 25 0.13 0.15 0.16 0.18 0.19 0.20 0.22 25 17
16 26 0.16 0.18 0.20 0.22 0.24 0.26 0.27 26 16
15 27 0.20 0.22 0.24 0.26 0.29 0.31 0.33 27 15
14 28 0.23 0.25 0.28 0.31 0.34 0.36 0.38 28 14
13 29 0.26 0.29 0.32 0.35 0.38 0.41 0.44 29 13
12 30 0.30 0.33 0.36 0.40 0.43 0.46 0.50 30 June. 12
11 Decemb 31 0.33 0.37 0.40 0.44 0.48 0.51 0.55 1 July. 11
10 January 1 0.36 0.40 0.44 0.48 0.53 0.57 1.1 2 10
9 2 0.39 0.44 0.48 0.53 0.57 1.2 1.6 3 9
8 3 0.43 0.48 0.53 0.57 1.2 1.7 1.11 4 8
7 4 0.46 0.51 0.56 1.1 1.7 1.12 1.17 5 7
6 5 0.49 0.55 1.0 1.6 1.11 1.17 1.22 6 6
5 6 0.52 0.58 1.4 1.10 1.16 1.22 1.27 7 5
4 7 0.55 1.1 1.7 1.14 1.20 1.26 1.32 8 4
3 8 0.58 1.5 1.11 1.18 1.24 1.31 1.37 9 3
2 9 1.1 1.8 1.15 1.22 1.29 1.36 1.43 10 2
Decem. 1 10 1.4 1.12 1.19 1.26 1.33 1.41 1.48 11 1 June.
Novemb. 30 11 1.7 1.15 1.23 1.30 1.37 1.45 1.52 12 31 May.
29 12 1.10 1.18 1.26 1.34 1.42 1.50 1.57 13 30
28 13 1.13 1.22 1.30 1.38 1.46 1.54 2.2 14 29
27 14 1.16 1.25 1.34 1.42 1.50 1.58 2.7 15 28
26 15 1.19 1.28 1.37 1.46 1.55 2.3 2.12 16 27
25 16 1.22 1.31 1.40 1.49 1.59 2.8 2.17 17 26
24 17 1.25 1.35 1.44 1.53 2.3 2.12 2.21 18 25
23 18 1.28 1.38 1.47 1.57 2.7 2.16 2.26 19 24
22 19 1.30 1.41 1.51 2.1 2.11 2.21 2.31 20 23
21 20 1.33 1.44 1.54 2.4 2.15 2.25 2.35 21 22
20 21 1.36 1.47 1.57 2.8 2.19 2.29 2.40 22 21
19 22 1.39 1.50 2.0 2.11 2.22 2.33 2.44 23 20
18 23 1.41 1.53 2.4 2.15 2.26 2.37 2.48 24 19
17 24 1.43 1.55 2.7 2.18 2.30 2.41 2.52 25 18
16 25 1.46 1.58 2.10 2.21 2.33 2.45 2.56 26 17
15 26 1.48 2.1 2.13 2.25 2.37 2.49 3.1 27 16
14 27 1.51 2.4 2.16 2.28 2.40 2.52 3.5 28 15
13 28 1.54 2.7 2.19 2.31 2.44 2.56 3.9 29 14
11 January 30 1.58 2.11 2.24 2.37 2.51 3.4 3.17 31 July. 12
9 February 1 2.3 2.17 2.30 2.43 2.57 3.11 3.24 2 August. 10
7 3 2.7 2.21 2.35 2.49 3.3 3.17 3.32 4 8
5 5 2.11 2.25 2.40 2.54 3.9 3.23 3.38 6 6
3 7 2.14 2.29 2.44 2.59 3.14 3.29 3.44 8 4
Novemb. 1 9 2.18 2.33 2.49 3.4 3.19 3.35 3.50 10 2 May.
October 30 11 2.22 2.38 2.53 3.9 3.25 3.41 3.56 12 30 April.
28 13 2.25 2.41 2.58 3.14 3.30 3.46 4.3 14 28
26 15 2.29 2.45 3.2 3.18 3.35 3.51 4.8 16 26
24 17 2.32 2.49 3.5 3.22 3.39 3.56 4.13 18 24
21 20 2.36 2.53 3.11 3.28 3.45 4.3 4.20 21 21
18 23 2.40 2.58 3.15 3.33 3.51 4.8 4.26 24 18
15 February 26 2.43 3.1 3.20 3.38 3.56 4.14 4.32 27 15
12 March 1 2.46 3.5 3.23 3.42 4.1 4.19 4.38 30 August. 12
9 4 2.49 3.8 3.26 3.45 4.4 4.23 4.41 2 Septem. 9
6 7 2.51 3.10 3.29 3.48 4.7 4.26 4.45 5 6
October 3 10 2.53 3.13 3.32 3.51 4.10 4.29 4.49 8 3 April.
Septem. 30 13 2.55 3.14 3.33 3.53 4.13 4.32 4.51 11 31 March.
27 16 2.56 3.15 3.34 3.54 4.14 4.33 4.52 14 28
24 19 2.56 3.15 3.35 3.55 4.15 4.33 4.52 17 25
After the Equinox. Until the Equinox. 2.56 3.15 3.35 3.55 4.15 4.34 4.53 20 And till Equinox. 22 After Equinox.
2.56 3.15 3.35 3.55 4.15 4.34 4.53

A 2

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TABLE VI. For reducing the SUN'S DECLINATION, as given in the Nautical Almanac for Noon at GREENWICH, to any other Time under that Meridian; or to Noon under any other Meridian.
Add aft. N. Sub. aft. N. H M H M H M H M H M H M H M Sub. aft. N. Add aft. N.
Sub. bef. N. Add bef. N. 5.20 5.40 6.0 6.20 6.40 7.0 7.20 Add bef. N. Sub. bef. N.
Add. in W. Sub. in W. D D D D D D D Sub. in W. Add. in W.
Sub. in E. Add in E. 80 85 90 95 100 105 110 Add in E. Sub. in E.
Days. Days. M S M S M S M S M S M S M S Days. Days.
Decem. 21 Decem. 21 0.0 0.0 0.0 0.0 0.0 0.0 0.0 21 June. 21 June.
20 22 0.5 0.6 0.6 0.7 0.8 0.8 0.8 22 20
19 23 0.11 0.12 0.13 0.14 0.15 0.15 0.16 23 19
18 24 0.17 0.19 0.20 0.21 0.22 0.23 0.24 24 18
17 25 0.23 0.25 0.26 0.28 0.29 0.31 0.32 25 17
16 26 0.29 0.31 0.33 0.35 0.37 0.38 0.40 26 16
15 27 0.35 0.38 0.40 0.42 0.44 0.46 0.49 27 15
14 28 0.41 0.43 0.46 0.49 0.51 0.54 0.57 28 14
13 29 0.47 0.50 0.53 0.56 0.59 1.2 1.5 29 13
12 30 0.53 0.56 0.59 1.3 1.6 1.9 1.12 30 June. 12
11 Decemb. 31 0.59 1.2 1.6 1.10 1.13 1.17 1.21 1 July. 11
10 January 1 1.5 1.9 1.13 1.17 1.21 1.25 1.29 2 10
9 2 1.11 1.15 1.19 1.24 1.28 1.32 1.37 3 9
8 3 1.16 1.21 1.26 1.31 1.35 1.40 1.45 4 8
7 4 1.22 1.27 1.32 1.37 1.42 1.47 1.53 5 7
6 5 1.27 1.33 1.38 1.44 1.49 1.54 2.0 6 6
5 6 1.33 1.39 1.45 1.51 1.57 2.2 2.8 7 5
4 7 1.39 1.45 1.51 1.57 2.3 2.9 2.16 8 4
3 8 1.44 1.50 2.57 2.4 2.10 2.16 2.23 9 13
2 9 1.50 1.56 2.3 2.10 2.17 2.23 2.30 10 2
Decemb. 1 10 1.55 2.2 2.9 2.16 2.23 2.30 2.38 11 1 June.
Novem. 30 11 2.0 2.7 2.15 2.22 2.30 2.37 2.45 12 31 May.
29 12 2.5 2.13 2.21 2.29 2.37 2.44 2.52 13 30
28 13 2.10 2.19 2.27 2.35 2.43 2.51 3.0 14 29
27 14 2.16 2.25 2.33 2.42 2.50 2.58 3.7 15 28
26 15 2.21 2.30 2.38 2.47 2.56 3.5 3.13 16 27
25 16 2.26 2.35 2.44 2.53 3.2 3.11 3.21 17 26
24 17 2.31 2.40 2.50 2.59 3.9 3.18 3.28 18 25
23 18 2.36 2.46 2.55 3.5 3.15 3.24 3.34 19 24
22 19 2.41 2.51 3.1 3.11 3.21 3.31 3.41 20 23
21 20 2.46 2.56 3.6 3.17 3.27 3.37 3.48 21 22
20 21 2.50 3.2 3.12 3.23 3.33 3.44 3.55 22 21
19 22 2.55 3.6 3.17 3.28 3.39 3.50 4.1 23 20
18 23 3.0 3.11 3.22 3.33 3.45 3.56 4.7 24 19
17 24 3.4 3.16 3.27 3.39 3.50 4.1 4.13 25 18
16 25 3.8 3.20 3.32 3.44 3.56 4.7 4.19 26 17
15 26 3.13 3.25 3.37 3.49 4.1 4.13 4.26 27 16
14 27 3.17 3.29 3.42 3.54 4.6 4.19 4.31 28 15
13 28 3.22 3.34 3.47 4.0 4.12 4.25 4.38 29 14
11 January 30 3.30 3.43 3.56 4.9 4.22 4.36 4.49 31 July. 12
9 February 1 3.38 3.51 4.5 4.18 4.32 4.46 4.59 2 August. 10
7 3 3.46 4.0 4.14 4.28 4.42 4.56 5.10 4 8
5 5 3.52 4.6 4.21 4.36 4.50 5.5 5.19 6 6
3 7 3.59 4.14 4.29 4.44 4.59 5.14 5.29 8 4
Novemb. 1 9 4.5 4.21 4.36 4.52 5.7 5.23 5.38 10 2 May.
October 30 11 4.12 4.28 4.44 5.0 5.16 5.31 5.47 12 30 April.
28 13 4.19 4.35 4.51 5.7 5.23 5.40 5.56 14 28
26 15 4.24 4.41 4.57 5.14 5.30 5.47 6.4 16 26
24 17 4.30 4.47 5.3 5.21 5.38 5.55 6.12 18 24
21 20 4.37 4.55 5.12 5.29 5.47 6.4 6.21 21 21
18 23 4.44 5.2 5.19 5.37 5.55 6.13 6.31 24 18
15 February 26 4.50 5.8 5.26 5.44 6.2 6.20 6.38 27 15
12 March 1 4.56 5.15 5.33 5.52 6.10 6.29 6.47 30 August. 12
9 4 5.0 5.19 5.38 5.57 6.16 6.34 6.53 2 Septem. 9
6 7 5.4 5.23 5.42 6.1 6.20 6.39 6.58 5 6
October 3 10 5.8 5.27 5.46 6.5 6.25 6.44 7.3 8 3 April.
Septemb. 30 13 5.11 5.30 5.49 6.8 6.28 6.47 7.6 11 31 March.
27 16 5.12 5.31 5.51 6.11 6.31 6.50 7.9 14 28
24 19 5.12 5.32 5.52 6.12 6.32 6.51 7.11 17 25
After the Equinox. Until the Equinox. 5.13 5.33 5.53 6.13 6.33 6.52 7.11 20 And till Equinox. 22 After Equinox.
5.13 5.33 5.53 6.13 6.33 6.52 7.11

[page] 5

TABLE VI. For reducing the SUN'S DECLINATION, as given in the Nautical Almanac for Noon at GREENWICH, to any other Time under that Meridian; or to Noon under any other Meridian.
Add aft. N. Sub. aft. N. H M H M H M H M H M H M H M Sub. aft. N. Add aft. N.
Sub. bef. N. Add bef. N. 7.40 8.0 8.20 8.40 9.0 9.20 9.40 Add bef. N. Sub. bef. N.
Add. in W. Sub. in W. D D D D D D D Sub. in W. Add. in W.
Sub. in E. Add in E. 115 120 125 130 135 140 145 Add in E. Sub. in E.
Days. Days. M S M S M S M S M S M S M S Days. Days.
Decem. 21 Decem. 21 0.0 0.0 0.0 0.0 0.0 0.0 0.0 21 June. 21 June.
20 22 0.9 0.9 0.9 0.10 0.10 0.10 0.10 22 20
19 23 0.17 0.18 0.18 0.19 0.19 0.20 0.21 23 19
18 24 0.25 0.26 0.27 0.28 0.29 0.30 0.31 24 18
17 25 0.34 0.35 0.36 0.38 0.39 0.41 0.42 25 17
16 26 0.42 0.44 0.46 0.48 0.49 0.51 0.53 26 16
15 27 0.51 0.53 0.55 0.57 0.59 1.1 1.3 27 15
14 28 0.59 1.2 1.5 1.7 1.9 1.12 1.14 28 14
13 29 1.8 1.11 1.14 1.17 1.19 1.22 1.25 29 13
12 30 1.16 1.19 1.23 1.26 1.29 1.32 1.35 30 June. 12
11 Decemb. 31 1.24 1.28 1.32 1.35 1.39 1.43 1.46 1 July. 11
10 January 1 1.33 1.37 1.41 1.45 1.49 1.53 1.57 2 10
9 2 1.42 1.46 1.51 1.55 1.59 2.3 2.7 3 9
8 3 1.49 1.54 1.59 2.4 2.9 2.13 2.18 4 8
7 4 1.58 2.3 2.8 2.13 2.19 2.23 2.28 5 7
6 5 2.5 2.11 2.16 2.22 2.28 2.33 2.39 6 6
5 6 2.14 2.20 2.26 2.32 2.38 2.43 2.49 7 5
4 7 2.22 2.28 2.34 2.41 2.47 2.53 2.59 8 4
3 8 2.29 2.36 2.43 2.49 2.56 3.3 3.9 9 3
2 9 2.37 2.44 2.51 2.58 3.5 3.12 3.19 10 2
Decemb. 1 10 2.45 2.52 2.59 3.6 3.14 3.21 3.28 11 1 June.
Novemb. 30 11 2.52 3.0 3.7 3.15 3.23 3.30 3.38 12 31 May.
29 12 3.0 3.8 3.16 3.24 3.32 3.39 3.47 13 30
28 13 3.8 3.16 3.24 3.32 3.40 3.49 3.57 14 29
27 14 3.15 3.24 3.32 3.41 3.49 3.58 4.6 15 28
26 15 3.22 3.31 3.40 3.49 3.58 4.7 4.16 16 27
25 16 3.30 3.39 3.48 3.57 4.7 4.16 4.25 17 26
24 17 3.37 3.46 3.56 4.6 4.16 4.24 4.34 18 25
23 18 3.44 3.54 4.4 4.14 4.24 4.33 4.43 19 24
22 19 3.51 4.1 4.11 4.21 4.31 4.41 4.51 20 23
21 20 3.58 4.8 4.19 4.29 4.39 4.50 5.0 21 22
20 21 4.5 4.16 4.27 4.37 4.48 4.59 5.9 22 21
19 22 4.12 4.23 4.34 4.45 4.56 5.7 5.18 23 20
18 23 4.19 4.30 4.41 4.53 5.4 5.15 5.26 24 19
17 24 4.25 4.36 4.48 5.0 5.12 5.23 5.34 25 18
16 25 4.31 4.43 4.55 5.7 5.19 5.30 5.42 26 17
15 26 4.38 4.50 5. 5.14 5.26 5.38 5.50 27 16
14 27 4.43 4.56 5.8 5.21 5.33 5.46 5.58 28 15
13 28 4.50 5.3 5.16 5.28 5.40 5.54 6.6 29 14
11 January 30 5.2 5.15 5.28 5.41 5.54 6.8 6.21 31 July. 12
9 February 1 5.13 5.27 5.40 5.54 6.8 6.22 6.35 2 August. 10
7 3 5.24 5.38 5.52 6.6 6.20 6.35 6.49 4 8
5 5 5.34 5.49 6.4 6.18 6.33 6.47 7.2 6 6
3 7 5.44 5.59 6.14 6.29 6.44 6.59 7.14 8 4
Novemb. 1 9 5.53 6.9 6.24 6.40 6.55 7.11 7.26 10 2 May.
October 30 11 6.3 6.18 6.34 6.50 7.6 7.21 7.37 12 30 April.
28 13 6.12 6.28 6.44 7.0 7.16 7.32 7.48 14 28
26 15 6.20 6.36 6.53 7.10 7.26 7.42 7.58 16 26
24 17 6.29 6.45 7.2 7.19 7.36 7.52 8.9 18 24
21 20 6.39 6.56 7.13 7.31 7.48 8.5 8.22 21 21
18 23 6.48 7.6 7.24 7.42 8.0 8.17 8.34 24 18
15 February 26 6.57 7.15 7.34 7.52 8.10 8.28 8.46 27 15
12 March 1 7.6 7.24 7.42 8.1 8.20 8.38 8.57 30 August. 12
9 4 7.12 7.31 7.50 8.9 8.28 8.46 9.6 2 Septem. 9
6 7 7.17 7.36 7.55 8.14 8.33 8.53 9.12 5 6
October 3 10 7.23 7.42 8.1 8.20 8.39 8.59 9.18 8 3 April.
Septemb. 30 13 7.26 7.45 8.4 8.24 8.43 9.3 9.22 11 31 March.
27 16 7.29 7.48 8.7 8.27 8.47 9.6 9.25 14 28
24 19 7.30 7.50 8.10 8.29 8.49 9.8 9.27 17 25
After the Equinox. Until the Equinox. 7.31 7.50 8.10 8.30 8.50 9.9 9.28 20 And till Equinox. 22 After Equinox.
7.31 7.50 8.10 8.30 8.50 9.9 9.28

[page] 6

TABLE VI. For reducing the SUN'S DECLINATION, as given in the Nautical Almanac for Noon at GREENWICH, to any other Time under that Meridian; or to Noon under any other Meridian.
Add aft.N. Sub.aft.N. H M H M H M H M H M H M H M Sub.aft.N. Add aft. N.
Sub. bef. N. Add bef. N. 10.0 10.20 10.40 11.0 11.20 11.40 12.0 Add bef.N. Sub. bef. N.
Add. in W. Sub. in W. D D D D D D D Sub. in W. Add. in W.
Sub. in E. Add in E. 150 155 160 165 170 175 180 Add in E. Sub. in E.
Days. Days. M S M S M S M S M S M S M S Days. Days.
Decem. 21 Decem. 21 0.0 0.0 0.0 0.0 0.0 0.0 0.0 21 June. 21 June.
20 22 0.11 0.11 0.12 0.12 0.12 0.13 0.13 22 20
19 23 0.22 0.23 0.24 0.24 0.25 0.26 0.26 23 19
18 24 0.33 0.34 0.35 0.36 0.37 0.38 0.39 24 18
17 25 0.44 0.46 0.47 0.48 0.50 0.51 0.53 25 17
16 26 0.55 0.57 0.58 1.0 1.2 1.4 1.6 26 16
15 27 1.6 1.8 1.11 1.13 1.15 1.17 1.19 27 15
14 28 1.17 1.20 1.23 1.25 1.27 1.30 1.32 28 14
13 29 1.28 1.31 1.34 1.37 1.40 1.43 1.46 29 13
12 30 1.39 1.42 1.45 1.49 1.52 1.55 1.59 30 12
11 Decem. 31 1.50 1.54 1.57 2.1 2.5 2.8 2.12 1 July. 11
10 January 1 2.1 2.5 2.9 2.13 2.17 2.21 2.25 2 10
9 2 2.12 2.16 2.20 2.25 2.30 2.34 2.38 3 9
8 3 2.23 2.27 2.32 2.37 2.42 2.47 2.51 4 8
7 4 2.34 2.39 2.44 2.49 2.54 2.59 3.4 5 7
6 5 2.44 2.50 2.55 3.0 3.6 3.12 3.17 6 6
5 6 2.55 3.1 3.6 3.12 3.18 3.24 3.30 7 5
4 7 3.5 3.11 3.17 3.23 3.29 3.36 3.42 8 4
3 8 3.15 3.21 3.28 3.34 3.41 3.48 3.54 9 3
2 9 3.25 3.32 3.38 3.45 3.52 3.59 4.6 10 2
Decem. 1 10 3.35 3.42 3.49 3.56 4.4 4.11 4.18 11 1 June.
Novem. 30 11 3.45 3.52 3.59 4.7 4.15 4.22 4.30 12 31 May.
29 12 3.55 4.3 4.10 4.18 4.26 4.34 4.42 13 30
28 13 4.5 4.13 4.21 4.29 4.38 4.46 4.54 14 29
27 14 4.15 4.23 4.31 4.40 4.49 4.57 5.5 15 28
26 15 4.24 4.33 4.41 4.50 4.59 5.8 5.17 16 27
25 16 4.34 4.43 4.52 5.1 5.10 5.19 5.28 17 26
24 17 4.43 4.53 5.2 5.11 5.21 5.30 5.40 18 25
23 18 4.52 5.2 5.12 5.22 5.32 5.41 5.51 19 24
22 19 5.1 5.12 5.22 5.32 5.42 5.52 6.2 20 23
21 20 5.10 5.21 5.31 5.42 5.53 6.3 6.13 21 22
20 21 5.20 5.31 5.41 5.52 6.3 6.14 6.24 22 21
19 22 5.29 5.40 5.51 6.2 6.13 6.24 6.34 23 20
18 23 5.37 5.49 6.0 6.11 6.23 6.34 6.44 24 19
17 24 5.45 5.57 6.9 6.20 6.32 6.43 6.54 25 18
16 25 5.54 6.6 6.17 6.29 6.41 6.53 7.4 26 17
15 26 6.2 6.14 6.26 6.38 6.51 7.3 7.14 27 16
14 27 6.10 6.22 6.34 6.47 7.0 7.12 7.24 28 15
13 28 6.19 6.31 6.43 6.56 7.9 7.22 7.34 29 14
11 January 30 6.34 6.47 7.0 7.13 7.26 7.40 7.53 31 July. 12
9 February 1 6.49 7.3 7.16 7.30 7.43 7.57 8.11 2 August. 10
7 3 7.3 7.17 7.31 7.45 7.59 8.13 8.28 4 8
5 5 7.16 7.31 7.45 8.0 8.14 8.28 8.43 6 6
3 7 7.29 7.44 7.59 8.14 8.28 8.43 8.58 8 4
Novem. 1 9 7.41 7.56 8.12 8.27 8.42 8.58 9.13 10 2May
October 30 11 7.53 8.8 8.24 8.40 8.56 9.12 9.28 12 30 April.
28 13 8.4 8.20 8.36 8.53 9.9 9.25 9.42 14 28
26 15 8.15 8.32 8.48 9.5 9.21 9.38 9.54 16 26
24 17 8.26 8.43 9.0 9.17 9.34 9.50 10.7 18 24
21 20 8.40 8.57 9.14 9.32 9.49 10.6 10.24 21 21
18 23 8.52 9.10 9.28 9.46 10.3 10.21 10.39 24 18
15 Feb. 26 9.4 9.22 9.40 9.58 10.16 10.34 10.53 27 15
12 March 1 9.15 9.33 9.51 10.10 10.29 10.47 11.6 30 August. 12
9 4 9.24 9.43 10.1 10.20 10.39 10.58 11.16 2 Sept. 9
6 7 9.30 9.50 10.9 10.28 10.47 11.6 11.24 5 6
October 3 10 9.37 9.56 10.16 10.35 10.54 11.13 11.32 8 3 April.
Septem. 30 13 9.41 10.0 10.21 10.40 10.59 11.18 11.38 11 31 March.
27 16 9.45 10.4 10.24 10.44 11.3 11.22 11.42 14 28
24 19 9.47 10.6 10.26 10.46 11.5 11.24 11.44 17 25
After the Equinox. Until the Equinox. 9.48 10.7 10.27 10.47 11.6 11.25 11.45 20 And till Equinox. 22 After Equinox.
9.48 10.7 10.27 10.47 11.6 11.25 11.45

[page] 7

TABLE VII. The Right Ascensions and Declinations of the principal FIXED STARS of the First and Second Magnitudes, adapted to the Beginning of the Year 1796, with their annual Variations.
Names and Situations of the Stars. Character. Magnitude. Right Ascension in Time. An. var. in Right Ascen Declination. Ann. var. in Declination.
H M S S + D M S S
Extremity of the wing of Pegasus, Algenib γ 2 0.2·45 3,06 14.2·55 N + 20,04
In the head of the Phoœnix α 2 0.16·10 2,98 43.24·30 S −20,00
Bright star in the tail of the Whale β 2 0.33·20 3,00 19.6·32 S −19,84
In the girdle of Andromeda β 2 0.58·21 3,30 34.32·6 N +19,41
The Spring of the River Erida, Achernar α 1 1.30·6 2,24 58.16·37 S −18,52
In the following horn of the Ram α 2 1.55·42 3,34 22.29·29 N +17,46
In the neck of the Whale ο 2 2.9·3 3,01 3.54·36 S −16,56
In the jaw of the Whale α 2 2.51·38 3,11 3.17·2 N +14,69
In the head of Medusa, Algol β 2 2.54·58 3,85 40.9·29 N +14,49
The bright star in Perseus α 2 3.9·50 4,20 49.7·21 N +13,56
The southern eye of the Bull, Aldebaran α 1 4.24·14 3,42 16.5·14 N +8,14
In the left shoulder of Auriga, Capella α 1 5.1·39 4,41 45.46·30 N +5,06
The bright foot or Orion, Rigel β 1 5.4·44 2,87 8.26·54 S −4,78
Northern horn of the Bull β 2 5.13·24 3,78 28.25·14 N +4,06
The western shoulder of Orion γ 2 5.14·12 3,21 6.9·7 N +3,99
Preceding star in the belt of Orion δ 2 5.21·33 3,06 0.27·46 S −3,35
Bright star in the Dove α 2 5.32·17 2,17 34.11·27 S −2,42
The eastern shoulder of Orion α 1 5.44·8 3,24 7.21·22 N +1,39
In the poop of the Ship Argo, Canopus α 1 6.19·26 1,33 52.35·22 S +1,70
In the mouth of the greater Dog, Sirius α 1 6.36·9 2,65 16.26·47 S +4,35
In the back of the greater Dog δ 2 7.0·6 2,44 26.4·49 S +5,20
In the tail of the greater Dog η 2 7.16·2 2,37 28.54·50 S +6,53
In the head of the northern Twin, Castor α 1 7.21·33 3,86 32.19·9 N −6,98
The lesser Dog, Proeyon α 1 7.28·37 3,14 5.44·40 N −7,55
In the head of the southern Twin, Pollux β 1 7.32·48 3,69 28.30·19 N −7,89
In the row-lock of the Ship Argo ζ 2 7.56·25 2,11 39.26·5 S +9,75
In the poop of the Ship Argo γ 2 8.3·16 1,85 46.44·24 S +10,26
In the middle of the Ship Argo δ 2 8.39·5 1,66 53.57·48 S +12,83
In the oars of the Ship Argo β 1 9.10·50 0,74 68.52·46 S +14,84
The heart of the female Hydra α 2 9.17·33 2,94 7.46·52 S +15,22
The Lion's heart, Regulus α 1 9.57·29 3,20 12.57·30 N −17,25
Southerm.star in the squ. of the great Bear β 2 10.49·26 3,71 57.28·20 N −19,10
Northerm.star in the squ. of the great Bear α 1 10.51·1 3,82 62.50·59 N −19,14
The Lion's tail β 2 11.38·38 3,06 15.42·47 N −19,96
In the foot of the Cross α 1 12.15·24 3,23 61.58·9 S +20,00
In the top of the Cross γ 2 12.19·56 3,24 55.58·2 S +19,97
In the following arm of the Cross β 2 12.35·55 3,41 58.34·18 S +19,80
The Virgin's Spike α 1 13.14·28 3,14 10.5·29 S +19,00
Last star in the tail of the great Bear η 2 13.39·31 2,36 50.20·12 N −18,19
The western foot of the Centaur β 2 13.49·35 4,10 59.22·43 S +17,80
In the Tail of the Dragon α 2 13.58·53 1,63 65.21·16 N −17,41
The bright star in Bootes, Arcturus α 1 14.6·21 2,79 20.15·1 N −19,09
Eastern foot of the Centaur α 1 14.26·13 4,44 59.59·34 S +16,11
The southern scale of Libra α 2 14.39·37 3,29 15.10·58 S +15,39
The northern scale of Libra β 2 15.6·4 3,22 8.37·11 S +13,80
Bright star in the Crown α 2 15.26·3 2,54 27.24·39 N −12,48
In the neck of the Serpent α 2 15.34·13 2,94 7.4·37 N −11,92
The Scorpion's heart, Antares α 1 16.16·55 3,65 25.57·49 S +8,72
In the head of Hercules α 2 17.5·21 2,73 14.38·1 N −4,73
In the head of Ophiuchus α 2 17.25·28 2,77 12.43·19 N −3,02
In the head of the Dragon γ 2 17.51·53 1,39 51.31·9 N −0,71
The bright star in the Harp, Lyra α 1 18.30·2 2,03 38.35·59 N +2,61
Bright star in the Eagle, Atair α 1 19.40·50 3,16 8.20·14 N +8,54
The Eye of the Peacock α 2 20.9·24 4,84 57.22·20 S −10,72
The tail of the Swan α 2 20.34·29 2,03 44.33·29 N +12,52
The western wing of the Crane α 2 21.55·18 3,84 47.56·16 S −17,15
In the mouth of the south. Fish, Fomalhaut α 1 22.46·20 3,33 30.41·54 S −19,02
In the shoulder of Pegasus β 2 22.53·54 2,87 26.58·39 N + 19,22
In the wing of Pegasus, Markab α 2 22.54·36 2,96 14.6·39 N + 19,23
The head of Andromeda α 2 23.57·52 3,06 27.57·51 N + 20,04

[page] 8

TABLE VIII. For reducing the apparent Altitude of the MOON to the true.
Moon's horizontal Parallax. Apparent Altitude of the Moon's Center.
10° 11°
Corr. Corr. Corr. Corr. Corr. Corr. Corr. Corr. Corr.
M S M S M S M S M S M S M S M S M S M S
53 0 38.20 41.1 42.54 44.15 45.16 46.0 46.32 46.57 47.15
10 38.30 41.11 43.4 44.25 45.26 46.10 46.42 47.7 47.25
20 38.40 41.21 43.14 44.35 45.36 46.20 46.52 47.17 47.35
30 38.50 41.31 43.24 44.45 45.46 46.30 47.2 47.26 47.45
40 39.0 41.41 43.34 44.54 45.55 46.39 47.12 47.36 47.54
50 39.10 41.51 43.43 45.4 46.5 46.49 47.22 47.46 48.4
54 0 39.20 42.1 43.53 45.14 46.15 46.59 47.32 47.56 48.14
10 39.30 42.11 44.3 45.24 46.25 47.9 47.42 48.6 48.24
20 39.40 42.21 44.13 45.34 46.35 47.19 47.51 48.16 48.34
30 39.50 42.31 44.23 45.44 46.45 47.29 48.1 48.26 48.43
40 40.0 42.41 44.33 45.54 46.55 47.38 48.11 48.35 48.53
50 40.10 42.51 44.43 46.4 47.5 47.48 48.21 48.45 49.3
55 0 40.20 43.1 44.53 46.14 47.15 47.58 48.31 48.55 49.13
10 40.30 43.11 45.3 46.24 47.25 48.8 48.41 49.5 49.23
20 40.40 43.21 45.13 46.34 47.35 48.18 48.50 49.15 49.32
30 40.50 43.31 45.23 46.44 47.45 48.28 49.0 49.25 49.42
40 41.0 43.41 45.33 46.54 47.54 48.38 49.10 49.34 49.52
50 41.10 43.51 45.43 47.4 48.4 48.48 49.20 49.44 50.2
56 0 41.20 44.1 45.53 47.14 48.14 48.58 49.30 49.54 50.12
10 41.30 44.11 46.3 47.24 48.24 49.7 49.40 50.4 50.21
20 41.40 44.21 46.13 47.34 48.34 49.17 49.50 50.14 50.31
30 41.50 44.31 46.23 47.44 48.44 49.27 49.59 50.24 50.41
40 42.0 44.41 46.33 47.54 48.54 49.37 50.9 50.34 50.51
50 42.10 44.51 46.43 48.3 49.4 49.47 50.19 50.43 51.1
57 0 42.20 45.1 46.53 48.13 49.14 49.57 50.29 50.53 51.11
10 42.30 45.11 47.3 48.23 49.24 50.7 50.39 51.3 51.20
20 42.40 45.21 47.13 48.33 49.34 50.17 50.49 51.13 51.30
30 42.50 45.31 47.23 48.43 49.44 50.27 50.59 51.23 51.40
40 43.0 45.41 47.33 48.53 49.54 50.37 51.9 51.33 51.50
50 43.10 45.51 47.42 49.3 50.4 50.47 51.19 51.42 52.0
58 0 43.20 46.0 47.52 49.13 50.14 50.57 51.29 51.52 52.9
10 43.30 46.10 48.2 49.23 50.24 51.6 51.38 52.2 52.19
20 43.40 46.20 48.12 49.33 50.34 51.16 51.48 52.12 52.29
30 43.50 46.30 48.22 49.43 50.43 51.26 51.58 52.22 52.39
40 44.0 46.40 48.32 49.53 50.53 51.36 52.8 52.32 52.49
50 44.10 46.50 48.42 50.3 51.3 51.46 52.18 52.41 52.59
59 0 44.20 47.0 48.52 50.13 51.13 51.56 52.28 52.51 53.8
10 44.30 47.10 49.2 50.23 51.23 52.6 52.38 53.1 53.18
20 44.40 47.20 49.12 50.33 51.33 52.16 52.48 53.11 53.28
30 44.50 47.30 49.22 50.43 51.43 52.26 52.58 53.21 53.38
40 45.0 47.40 49.32 50.53 51.53 52.36 53.7 53.31 53.48
50 45.9 47.50 49.42 51.2 52.3 52.46 53.17 53.41 53.58
60 0 45.19 48.0 49.52 51.12 52.13 52.56 53.27 53.50 54.7
10 45.29 48.10 50.2 51.22 52.23 53.5 53.37 54.0 54.17
20 45.39 48.20 50.12 51.32 52.33 53.15 53.47 54.10 54.27
30 45.49 48.30 50.22 51.42 52.43 53.25 53.57 54.20 54.37
40 45.59 48.40 50.32 51.52 52.52 53.35 54.7 54.30 54.47
50 46.9 48.50 50.42 52.2 53.2 53.45 54.16 54.40 54.57
61 0 46.19 49.0 50.52 52.12 53.12 53.55 54.26 54.50 55.6
10 46.29 49.10 51.2 52.22 53.22 54.4 54.36 54.59 55.16
20 46.39 49.20 51.12 52.32 53.32 54.14 54.46 55.9 55.26
30 46.49 49.30 51.22 52.42 53.42 54.24 54.56 55.19 55.36
40 46.59 49.40 51.32 52.52 53.52 54.34 55.6 55.29 55.46
50 47.9 49.50 51.42 53.2 54.2 54.44 55.16 55.39 55.56
62 0 47.19 50.0 51.52 53.12 54.12 54.54 55.26 55.49 56.5

[page] 9

TABLE VIII. For reducing the apparent Altitude of the MOON to the true.
Moon's horizontal Parallax. Apparent Altitude of the Moon's Center.
12° 13° 14° 15° 16° 17° 18° 19° 20°
Corr. Corr. Corr. Corr. Corr. Corr. Corr. Corr. Corr.
M S M S M S M S M S M S M S M S M S M S
53 0 47.27 47.35 47.40 47.42 47.40 47.36 47.31 47.23 47.13
10 47.37 47.45 47.50 47.52 47.50 47.46 47.41 47.33 47.22
20 47.47 47.55 47.59 48.1 47.59 47.55 47.50 47.42 47.32
30 47.56 48.4 48.9 48.11 48.9 48.5 48.0 47.52 47.41
40 48.6 48.14 48.19 48.21 48.19 48.15 48.9 48.1 47.50
50 48.16 48.24 48.28 48.30 48.28 48.24 48.19 48.10 48.0
54 0 48.26 48.34 48.38 48.40 48.38 48.34 48.28 48.20 48.9
10 48.36 48.43 48.48 48.50 48.47 48.43 48.38 48.29 48.19
20 48.45 48.53 48.58 48.59 48.57 48.53 48.47 48.39 48.28
30 48.55 49.3 49.7 49.9 49.6 49.2 48.57 48.48 48.38
40 49.5 49.13 49.17 49.19 49.16 49.12 49.6 48.58 48.47
50 49.15 49.22 49.27 49.28 49.26 49.21 49.16 49.7 48.57
55 0 49.25 49.32 49.36 49.38 49.35 49.31 49.25 49.16 49.6
10 49.34 49.42 49.46 49.48 49.45 49.41 49.35 49.25 49.16
20 49.44 49.52 49.56 49.57 49.54 49.50 49.44 49.35 49.25
30 49.54 50.1 50.5 50.7 50.4 50.0 49.54 49.44 49.34
40 50.4 50.11 50.15 50.16 50.14 50.10 50.3 49.53 49.44
50 50.14 50.21 50.25 50.26 50.23 50.19 50.13 50.3 49.53
56 0 50.23 50.31 50.35 50.36 50.33 50.29 50.22 50.13 50.2
10 50.33 50.41 50.44 50.45 50.42 50.38 50.32 50.22 50.12
20 50.43 50.50 50.54 50.55 50.52 50.48 50.41 50.32 50.21
30 50.53 51.0 51.4 51.5 51.2 50.57 50.51 50.41 50.31
40 51.2 51.10 51.13 51.14 51.11 51.7 51.0 50.51 50.40
50 51.12 51.20 51.23 51.24 51.21 51.16 51.10 51.0 50.50
57 0 51.22 51.29 51.33 51.34 51.31 51.26 51.19 51.10 50.59
10 51.32 51.39 51.42 51.43 51.40 51.35 51.29 51.19 51.8
20 51.42 51.49 51.52 51.53 51.50 51.45 51.38 51.29 51.18
30 51.51 51.59 52.2 52.2 51.59 51.54 51.48 51.38 51.27
40 52.1 52.8 52.11 52.12 52.9 52.4 51.57 51.47 51.37
50 52.11 52.18 52.21 52.22 52.19 52.14 52.7 51.57 51.46
58 0 52.21 52.28 52.31 52.31 52.28 52.23 52.16 52.6 51.55
10 52.30 52.38 52.41 52.41 52.38 52.33 52.26 52.16 52.5
20 52.40 52.47 52.50 52.51 52.48 52.43 52.35 52.25 52.14
30 52.50 52.57 53.0 53.0 52.57 52.52 52.45 52.35 52.23
40 53.0 53.7 53.10 53.10 53.7 53.2 52.54 52.44 52.33
50 53.10 53.17 53.19 53.20 53.17 53.11 53.4 52.54 52.42
59 0 53.19 53.26 53.29 53.29 53.26 53.21 53.13 53.3 52.51
10 53.29 53.36 53.39 53.39 53.36 53.30 53.23 53.13 53.1
20 53.39 53.46 53.49 53.49 53.46 53.40 53.32 53.22 53.10
30 53.49 53.56 53.58 53.58 53.55 53.50 53.42 53.32 53.20
40 53.58 54.5 54.8 54.8 54.5 53.59 53.51 53.41 53.29
50 54.8 54.15 54.18 54.18 54.14 54.9 54.1 53.51 53.39
60 0 54.18 54.25 54.28 54.27 54.24 54.18 54.10 54.0 53.48
10 54.28 54.35 54.37 54.37 54.34 54.28 54.20 54.9 53.57
20 54.38 54.44 54.47 54.47 54.43 54.38 54.29 54.19 54.7
30 54.47 54.54 54.57 54.56 54.53 54.47 54.39 54.28 54.16
40 54.57 55.4 55.6 55.6 55.2 54.57 54.48 54.38 54.25
50 55.7 55.14 55.16 55.16 55.12 55.6 54.58 54.47 54.35
61 0 55.17 55.23 55.26 55.25 55.21 55.16 55.7 54.57 54.44
10 55.27 55.33 55.35 55.35 55.31 55.25 55.17 55.6 54.53
20 55.36 55.43 55.45 55.45 55.41 55.35 55.26 55.15 55.3
30 55.46 55.53 55.55 55.54 55.50 55.45 55.36 55.25 55.12
40 55.56 56.2 56.4 56.4 56.0 55.54 55.45 55.34 55.21
50 56.6 56.12 56.14 56.14 56.9 56.4 55.55 55.44 55.31
62 0 56.16 56.22 56.24 56.23 56.19 56.13 56.4 55.53 55.40

B

[page] 10

TABLE VIII. For reducing the apparent Altitude of the MOON to the true.
Moon's horizontal Parallax. Apparent Altitude of the Moon's Center.
21° 22° 23° 24° 25° 26° 27° 28° 29°
Corr. Corr. Corr. Corr. Corr. Corr. Corr. Corr. Corr.
M S M S M S M S M S M S M S M S M S M S
53 0 47.2 46.48 46.33 46.18 46.0 45.42 45.22 45.1 44.39
10 47.11 46.57 46.42 46.27 46.9 45.51 45.31 45.10 44.48
20 47.21 47.7 46.52 46.36 46.18 46.0 45.40 45.19 44.56
30 47.30 47.16 47.1 46.45 46.27 46.9 45.49 45.27 45.5
40 47.39 47.25 47.10 46.54 46.36 46.18 45.58 45.36 45.13
50 47.49 47.34 47.19 47.3 46.45 46.27 46.7 45.45 45.22
54 0 47.58 47.44 47.29 47.12 46.55 46.36 46.16 45.54 45.31
10 48.7 47.53 47.38 47.22 47.4 46.45 46.24 46.3 45.39
20 48.17 48.2 47.47 47.31 47.13 46.54 46.33 46.12 45.48
30 48.26 48.12 47.57 47.40 47.22 47.3 46.42 46.21 45.57
40 48.35 48.21 48.6 47.49 47.31 47.12 46.51 46.29 46.6
50 48.45 48.30 48.15 47.58 47.40 47.21 47.0 46.38 46.15
55 0 48.54 48.39 48.24 48.7 47.49 47.30 47.9 46.47 46.24
10 49.4 48.49 48.33 48.16 47.58 47.39 47.18 46.56 46.32
20 49.13 48.58 48.42 48.25 48.7 47.48 47.27 47.5 46.41
30 49.22 49.7 48.52 48.35 48.17 47.57 47.36 47.13 46.50
40 49.32 49.17 49.1 48.44 48.26 48.6 47.45 47.22 46.58
50 49.41 49.26 49.10 48.53 48.35 48.15 47.54 47.31 47.7
56 0 49.50 49.35 49.19 49.2 48.44 48.24 48.3 47.40 47.16
10 49.59 49.44 49.28 49.11 48.53 48.33 48.12 47.49 47.25
20 50.9 49.54 49.38 49.20 49.2 48.42 48.20 47.58 47.34
30 50.18 50.3 49.47 49.29 49.11 48.51 48.29 48.7 47.42
40 50.27 50.12 49.56 49.39 49.20 49.0 48.38 48.15 47.51
50 50.37 50.22 50.5 49.48 49.29 49.9 48.47 48.24 48.0
57 0 50.46 50.31 50.14 49.57 49.38 49.18 48.56 48.33 48.9
10 50.55 50.40 50.23 50.6 49.47 49.27 49.5 48.42 48.17
20 51.5 50.49 50.33 50.15 49.56 49.36 49.14 48.51 48.26
30 51.14 50.59 50.42 50.24 50.5 49.45 49.23 49.0 48.35
40 51.23 51.8 50.51 50.34 50.14 49.54 49.31 49.8 48.44
50 51.33 51.17 51.1 50.43 50.23 50.3 49.40 49.17 48.52
58 0 51.42 51.26 51.10 50.52 50.32 50.12 49.49 49.26 49.1
10 51.51 51.36 51.19 51.1 50.41 50.21 49.58 49.35 49.9
20 52.1 51.45 51.28 51.10 50.50 50.30 50.7 49.44 49.18
30 52.10 51.54 51.37 51.19 50.59 50.39 50.16 49.53 49.27
40 52.19 52.4 51.47 51.29 51.9 50.47 50.25 50.1 49.36
50 52.29 52.13 51.56 51.38 51.18 50.56 50.34 50.10 49.45
59 0 52.38 52.22 52.5 51.47 51.27 51.5 50.43 50.19 49.54
10 52.47 52.31 52.14 51.56 51.36 51.14 50.51 50.28 50.2
20 52.57 52.41 52.23 52.5 51.45 51.23 51.0 50.37 50.11
30 53.6 52.50 52.32 52.14 51.54 51.32 51.9 50.46 50.20
40 53.15 52.59 52.42 52.23 52.3 51.41 51.18 50.54 50.29
50 53.25 53.9 52.51 52.32 52.12 51.50 51.27 51.3 50.37
60 0 53.34 53.18 53.0 52.41 52.21 51.59 51.36 51.12 50.46
10 53.43 53.27 53.9 52.51 52.30 52.8 51.45 51.21 50.55
20 53.53 53.36 53.18 53.0 52.39 52.17 51.54 51.30 51.4
30 54.2 53.45 53.27 53.9 52.48 52.26 52.3 51.39 51.12
40 54.11 53.55 53.37 53.18 52.57 52.35 52.12 51.47 51.21
50 54.21 54.4 53.46 53.27 53.6 52.44 52.21 51.56 51.30
61 0 54.30 54.13 53.55 53.36 53.15 52.53 52.30 52.5 51.39
10 54.39 54.22 54.4 53.45 53.25 53.2 52.38 52.14 51.47
20 54.49 54.32 54.14 53.55 53.34 53.11 52.47 52.23 51.56
30 54.58 54.41 54.23 54.4 53.43 53.20 52.56 52.32 52.5
40 55.7 54.50 54.32 54.13 53.52 53.29 53.5 52.40 52.14
50 55.17 55.0 54.42 54.22 54.1 53.38 53.14 52.49 52.22
62 0 55.26 55.9 54.51 54.31 54.10 53.47 53.23 52.58 52.31

[page] 11

TABLE VIII. For reducing the apparent Altitude of the MOON to the true.
Moon's horizontal Parallax. Apparent Altitude of the Moon's Center.
30° 31° 32° 33° 34° 35° 36° 37° 38°
Corr. Corr. Corr. Corr. Corr. Corr. Corr. Corr. Corr.
M S M S M S M S M S M S M S M S M S M S
53 0 44.15 43.51 43.26 42.59 42.32 42.3 41.34 41.4 40.33
10 44.24 44.0 43.34 43.7 42.40 42.11 41.42 41.12 40.41
20 44.33 44.8 43.43 43.16 42.48 42.19 41.50 41.20 40.49
30 44.41 44.17 43.51 43.24 42.57 42.28 41.59 41.28 40.56
40 44.50 44.26 44.0 43.33 43.5 42.36 42.7 41.36 41.4
50 44.59 44.34 44.8 43.41 43.13 42.44 42.15 41.44 41.12
54 0 45.7 44.43 44.16 43.50 43.22 42.53 42.23 41.52 41.20
10 45.16 44.51 44.25 43.58 43.30 43.1 42.32 42.0 41.28
20 45.25 45.0 44.33 44.7 43.38 43.9 42.40 42.8 41.36
30 45.33 45.8 44.42 44.15 43.47 43.18 42.48 42.16 41.43
40 45.42 45.17 44.50 44.23 43.55 43.26 42.56 42.24 41.51
50 45.51 45.25 44.59 44.32 44.3 43.34 43.4 42.32 41.59
55 0 45.59 45.34 45.7 44.40 44.11 43.42 43.12 42.40 42.7
10 46.8 45.43 45.16 44.48 44.20 43.50 43.20 42.48 42.15
20 46.17 45.51 45.24 44.57 44.28 43.58 43.28 42.56 42.23
30 46.25 46.0 45.33 45.5 44.36 44.6 43.36 43.4 42.31
40 46.34 46.8 45.41 45.13 44.45 44.15 43.44 43.12 42.39
50 46.43 46.17 45.49 45.22 44.53 44.23 43.52 43.20 42.47
56 0 46.51 46.25 45.58 45.30 45.1 44.31 44.0 43.28 42.55
10 47.0 46.34 46.6 45.39 45.9 44.39 44.8 43.36 43.2
20 47.9 46.42 46.15 45.57 45.17 44.47 44.16 43.44 43.10
30 47.17 46.51 46.23 45.55 45.26 44.55 44.24 43.52 43.18
40 47.26 47.0 46.32 46.4 45.34 45.4 44.32 44.0 43.26
50 47.35 47.8 46.40 46.12 45.42 45.12 44.40 44.8 43.34
57 0 47.43 47.17 46.49 46.24 45.51 45.20 44.48 44.16 43.42
10 47.52 47.25 46.57 46.29 46.0 45.28 44.57 44.24 43.50
20 48.1 47.34 47.6 46.38 46.8 45.36 45.5 44.32 43.58
30 48.9 47.43 47.14 46.46 46.16 45.45 45.13 44.40 44.5
40 48.18 47.51 47.23 46.54 46.25 45.53 45.21 44.47 44.13
50 48.27 48.0 47.31 47.3 46.33 46.1 45.29 44.55 44.21
58 0 48.35 48.8 47.40 47.11 46.41 46.9 45.37 45.3 44.29
10 48.44 48.17 47.48 47.19 46.49 46.17 45.45 45.11 44.37
20 48.53 48.26 47.57 47.28 46.57 46.25 45.53 45.19 44.45
30 49.1 48.34 48.5 47.36 47.6 46.33 46.1 45.27 44.53
40 49.10 48.43 48.14 47.44 47.14 46.42 46.9 45.35 45.1
50 49.19 48.52 48.22 47.53 47.22 46.50 46.17 45.43 45.8
59 0 49.27 49.0 48.31 48.1 47.30 46.58 46.25 45.51 45.16
10 49.36 49.9 48.39 48.10 47.39 47.6 46.33 45.59 45.24
20 49.45 49.17 48.48 48.18 47.47 47.14 46.41 46.7 45.32
30 49.53 49.26 48.56 48.27 47.55 47.23 46.50 46.15 45.40
40 50.2 49.34 49.5 48.35 48.4 47.31 46.58 46.23 45.48
50 50.11 49.42 49.13 48.43 48.12 47.39 47.6 46.31 45.56
60 0 50.19 49.51 49.22 48.52 48.20 47.47 47.14 46.39 46.4
10 50.28 49.59 49.30 49.0 48.29 47.55 47.22 46.47 46.11
20 50.37 50.8 49.39 49.8 48.37 48.4 47.30 46.55 46.19
30 50.45 50.17 49.47 49.17 48.45 48.12 47.38 47.3 46.27
40 50.54 50.26 49.56 49.25 48.54 48.20 47.46 47.11 46.35
50 51.3 50.34 50.4 49.34 49.2 48.28 47.54 47.19 46.43
61 0 51.11 50.43 50.13 49.42 49.10 48.37 48.2 47.27 46.51
10 51.20 50.51 50.21 49.50 49.18 48.45 48.10 47.35 46.59
20 51.29 51.0 50.30 49.59 49.27 48.53 48.18 47.43 47.7
30 51.37 51.8 50.38 50.7 49.35 49.1 48.27 47.51 47.15
40 51.46 51.17 50.47 50.15 49.43 49.9 48.35 47.59 47.23
50 51.55 51.25 50.55 50.24 49.52 49.18 48.43 48.7 47.31
62 0 52.3 51.34 51.4 50.32 50.0 49.26 48.51 48.15 47.39

B 2

[page] 12

TABLE VIII. For reducing the apparent Altitude of the MOON to the true.
Moon's horizontal Parallax. Apparent Altitude of the Moon's Center.
39° 40° 41° 42° 43° 44° 45° 46° 47°
Corr. Corr. Corr. Corr. Corr. Corr. Corr. Corr. Corr.
M S M S M S M S M S M S M S M S M S M S
53 0 40.1 39.28 38.54 38.20 37.44 37.8 36.32 35.54 35.16
10 40.8 39.36 39.2 38.27 37.51 37.15 36.39 36.1 35.22
20 40.16 39.43 39.9 38.34 37.59 37.23 36.46 36.8 35.29
30 40.24 39.51 39.17 38.42 38.6 37.30 36.53 36.15 35.36
40 40.32 39.59 39.25 38.49 38.13 37.37 37.0 36.22 35.43
50 40.39 40.6 39.32 38.57 38.21 37.44 37.7 36.29 35.50
54 0 40.47 40.14 39.40 39.4 38.28 37.52 37.14 36.35 35.56
10 40.55 40.22 39.47 39.12 38.35 37.59 37.21 36.42 36.3
20 41.3 40.29 39.55 39.19 38.43 38.6 37.28 36.49 36.10
30 41.10 40.37 40.2 39.27 38.50 38.13 37.35 36.56 36.17
40 41.18 40.45 40.10 39.34 38.57 38.20 37.42 37.3 36.24
50 41.26 40.52 40.17 39.42 39.5 38.28 37.49 37.10 36.31
55 0 41.34 41.0 40.25 39.49 39.12 38.35 37.56 37.17 36.37
10 41.42 41.8 40.32 39.57 39.19 38.42 38.4 37.24 36.44
20 41.49 41.15 40.40 40.4 39.27 38.49 38.11 37.31 36.51
30 41.57 41.23 40.47 40.12 39.34 38.56 38.18 37.38 36.58
40 42.5 41.31 40.55 40.19 39.41 39.4 38.25 37.45 37.5
50 42.13 41.38 41.2 40.27 39.49 39.11 38.32 37.52 37.12
56 0 42.21 41.46 41.10 40.34 39.56 39.18 38.39 37.59 37.18
10 42.28 41.54 41.18 40.41 40.3 39.25 38.46 38.6 37.25
20 42.36 42.1 41.25 40.49 40.11 39.32 38.53 38.13 37.32
30 42.44 42.9 41.33 40.56 40.18 39.40 39.0 38.20 37.39
40 42.52 42.17 41.41 41.3 40.25 39.47 39.7 38.27 37.46
50 43.0 42.24 41.49 41.11 40.33 39.54 39.14 38.34 37.53
57 0 43.7 42.32 41.56 41.18 40.40 40.1 39.21 38.41 37.59
10 43.15 42.40 42.4 41.26 40.47 40.8 39.29 38.47 38.6
20 43.23 42.47 42.11 41.33 40.55 40.15 39.36 38.54 38.13
30 43.31 42.55 42.19 41.40 41.2 40.23 39.43 39.1 38.20
40 43.38 43.3 42.26 41.48 41.9 40.30 39.50 39.8 38.27
50 43.46 43.10 42.34 41.55 41.17 40.37 39.57 39.15 38.34
58 0 43.54 43.18 42.41 42.3 41.24 40.44 40.4 39.22 38.40
10 44.2 43.26 42.49 42.10 41.31 40.51 40.11 39.29 38.47
20 44.9 43.33 42.56 42.17 41.39 40.59 40.18 39.36 38.54
30 44.17 43.41 43.4 42.25 41.46 41.6 40.25 39.43 39.1
40 44.25 43.49 43.11 42.32 41.53 41.13 40.32 39.50 39.8
50 44.33 43.56 43.19 42.40 42.1 41.20 40.39 39.57 39.15
59 0 44.41 44.4 43.26 42.47 42.8 41.27 40.46 40.4 39.21
10 44.48 44.12 43.34 42.54 42.15 41.35 40.54 40.11 39.28
20 44.56 44.19 43.41 43.2 42.23 41.42 41.1 40.18 39.35
30 45.4 44.27 43.49 43.9 42.30 41.49 41.8 40.25 39.42
40 45.12 44.35 43.56 43.17 42.37 41.56 41.15 40.32 39.49
50 45.20 44.42 44.4 43.24 42.44 42.3 41.22 40.39 39.56
60 0 45.27 44.50 44.11 43.32 42.52 42.11 41.29 40.46 40.2
10 45.35 44.58 44.19 43.39 42.59 42.18 41.36 40.52 40.9
20 45.43 45.5 44.27 43.47 43.6 42.25 41.43 40.59 40.16
30 45.51 45.13 44.34 43.54 43.14 42.32 41.50 41.6 40.23
40 45.59 45.21 44.42 44.2 43.21 42.39 41.57 41.13 40.30
50 46.6 45.28 44.49 44.9 43.28 42.47 41.4 41.20 40.37
61 0 46.14 45.36 44.57 44.17 43.36 42.54 42.11 41.27 40.43
10 46.22 45.44 45.4 44.24 43.43 43.1 42.18 41.34 40.50
20 46.30 45.51 45.12 44.31 43.50 43.8 42.25 41.41 40.57
30 46.38 45.59 45.19 44.39 43.58 43.15 42.32 41.48 41.4
40 46.45 46.7 45.27 44.46 44.5 43.23 42.39 41.55 41.11
50 46.53 46.14 45.34 44.54 44.12 43.30 42.46 42.2 41.18
62 0 47.1 46.22 45.42 45.1 44.19 43.37 42.53 42.9 41.24

[page] 13

TABLE VIII. For reducing the apparent Altitude of the MOON to the true.
Moon's horizontal Parallax. Apparent Altitude of the Moon's Center.
48° 49° 50° 51° 52° 53° 54° 55° 56°
Corr. Corr. Corr. Corr. Corr. Corr. Corr. Corr. Corr.
M S M S M S M S M S M S M S M S M S M S
53 0 34.37 33.57 33.16 32.35 31.54 31.11 30.28 29.44 29.0
10 34.43 34.4 33.22 32.41 32.0 31.17 30.34 29.50 29.6
20 34.50 34.10 33.29 32.47 32.6 31.23 30.40 29.56 29.11
30 34.56 34.17 33.35 32.54 32.12 31.29 30.46 30.1 29.17
40 35.3 34.23 33.42 33.0 32.18 31.35 30.52 30.7 29.22
50 35.10 34.30 33.48 33.6 32.24 31.41 30.58 30.13 29.28
54 0 35.17 34.36 33.55 33.13 32.30 31.47 31.3 30.19 29.33
10 35.23 34.43 34.1 33.19 32.37 31.53 31.9 30.24 29.39
20 35.30 34.49 34.8 33.25 32.43 31.59 31.15 30.30 29.45
30 35.37 34.56 34.14 33.32 32.49 32.5 31.21 30.36 29.50
40 35.43 35.2 34.21 33.38 32.55 32.11 31.27 30.42 29.56
50 35.50 35.9 34.27 33.44 33.1 32.17 31.33 30.47 30.1
55 0 35.57 35.16 34.34 33.51 33.7 32.23 31.39 30.53 30.7
10 36.3 35.22 34.40 33.57 33.14 32.29 31.44 30.59 30.12
20 36.10 35.29 34.47 34.3 33.20 32.35 31.50 31.4 30.18
30 36.17 35.35 34.53 34.10 33.26 32.41 31.56 31.10 30.24
40 36.23 35.42 34.59 34.16 33.32 32.47 32.2 31.16 30.29
50 36.30 35.48 35.6 34.22 33.38 32.53 32.8 31.22 30.35
56 0 36.37 35.55 35.12 34.29 33.44 32.59 32.14 31.28 30.41
10 36.43 36.1 35.19 34.35 33.51 33.6 32.20 31.33 30.46
20 36.50 36.8 35.25 34.41 33.57 33.12 32.26 31.39 30.52
30 36.57 36.14 35.31 34.48 34.3 33.18 32.31 31.45 30.57
40 37.3 36.21 35.38 34.54 34.9 33.24 32.37 31.50 31.3
50 37.10 36.28 35.44 35.0 34.15 33.30 32.43 31.56 31.8
57 0 37.17 36.34 35.51 35.6 34.21 33.36 32.49 32.2 31.14
10 37.23 36.41 35.57 35.12 34.28 33.42 32.55 32.8 31.19
20 37.30 36.47 36.3 35.19 34.34 33.48 33.1 32.13 31.25
30 37.37 36.54 36.10 35.25 34.40 33.54 33.7 32.19 31.31
40 37.43 37.1 36.16 35.31 34.46 34.0 33.13 32.25 31.36
50 37.50 37.7 36.22 35.37 34.52 34.6 33.18 32.30 31.42
58 0 37.57 37.14 36.29 35.44 34.58 34.12 33.24 32.36 31.48
10 38.3 37.20 36.35 35.50 35.5 34.18 33.30 32.42 31.53
20 38.10 37.27 36.42 35.56 35.11 34.24 33.36 32.48 31.59
30 38.17 37.33 36.48 36.3 35.17 34.30 33.42 32.53 32.4
40 38.23 37.40 36.55 36.9 35.23 34.36 33.48 32.59 32.10
50 38.30 37.46 37.1 36.15 35.29 34.42 33.54 33.5 32.15
59 0 38.37 37.53 37.8 36.22 35.35 34.48 34.0 33.11 32.21
10 38.43 37.59 37.14 36.28 35.42 34.54 34.5 33.16 32.27
20 38.50 38.6 37.21 36.34 35.48 35.0 34.11 33.22 32.32
30 38.57 38.13 37.27 36.41 35.54 35.6 34.17 33.28 32.38
40 39.4 38.19 37.33 36.47 36.0 35.12 34.23 33.33 32.43
50 39.11 38.26 37.40 36.53 36.6 35.18 34.29 33.39 32.49
60 0 39.18 38.32 37.46 37.0 36.12 35.24 34.35 33.45 32.55
10 39.24 38.39 37.53 37.6 36.19 35.30 34.40 33.51 33.0
20 39.31 38.45 37.59 37.12 36.25 35.36 34.46 33.57 33.6
30 39.38 38.52 38.6 37.18 36.31 35.42 34.52 34.2 33.11
40 39.44 38.59 38.12 37.25 36.37 35.48 34.58 34.8 33.17
50 39.51 39.5 38.19 37.31 36.43 35.54 35.4 34.14 33.22
61 0 39.58 39.12 38.25 37.37 36.49 36.0 35.10 34.20 33.28
10 40.4 39.18 38.32 37.44 36.56 36.6 35.15 34.25 33.34
20 40.11 39.25 38.38 37.50 37.2 36.12 35.21 34.31 33.39
30 40.18 39.31 38.44 37.56 37.8 36.18 35.27 34.37 33.45
40 40.24 39.38 38.50 38.3 37.14 36.24 35.33 34.42 33.50
50 40.31 39.44 38.57 38.9 37.20 36.30 35.39 34.48 33.56
62 0 40.38 39.51 39.3 38.15 37.26 36.36 35.45 34.54 34.2

[page] 14

TABLE VIII. For reducing the apparent Altitude of the MOON to the true.
Moon's horizontal Parallax. Apparent Altitude of the Moon's Center.
57° 58° 59° 60° 61° 62° 63° 64° 65°
Corr. Corr. Corr. Corr. Corr. Corr. Corr. Corr. Corr.
M S M S M S M S M S M S M S M S M S M S
53 0 28.15 27.30 26.44 25.57 25.10 24.22 23.35 22.46 21.57
10 28.20 27.35 26.49 26.2 25.15 24.27 23.39 22.50 22.1
20 28.26 27.40 26.54 26.7 25.20 24.32 23.44 22.55 22.5
30 28.31 27.46 26.59 26.12 25.25 24.36 23.48 22.59 22.10
40 28.37 27.51 27.4 26.17 25.30 24.41 23.53 23.3 22.14
50 28.42 27.56 27.9 26.22 25.35 24.46 23.57 23.8 22.18
54 0 28.48 28.1 27.14 26.27 25.39 24.51 24.2 23.12 22.23
10 28.53 28.7 27.20 26.32 25.44 24.55 24.6 23.17 22.27
20 28.59 28.12 27.25 26.37 25.49 25.0 24.11 23.21 22.31
30 29.4 28.17 27.30 26.42 25.54 25.5 24.15 23.26 22.36
40 29.9 28.23 27.35 26.47 25.59 25.9 24.20 23.30 22.40
50 29.15 28.28 27.40 26.52 26.3 25.14 24.24 23.34 22.44
55 0 19.20 28.33 27.45 26.57 26.8 25.19 24.29 23.39 22.48
10 29.26 28.38 27.50 27.2 26.13 25.23 24.33 23.43 22.52
20 29.31 28.44 27.56 27.7 26.18 25.28 24.38 23.47 22.57
30 29.36 28.49 28.1 27.12 26.23 25.32 24.42 23.52 23.1
40 29.42 28.54 28.6 27.17 26.28 25.37 24.47 23.56 23.5
50 29.47 29.0 28.11 27.22 26.33 25.42 24.51 24.0 23.9
56 0 29.53 29.5 28.16 27.27 26.37 25.47 24.56 24.5 23.13
10 29.58 29.10 28.22 27.32 26.42 25.54 25.0 24.9 23.18
20 30.4 29.16 28.27 27.37 26.47 25.56 25.5 24.13 23.22
30 30.9 29.21 28.32 27.42 26.52 26.1 25.9 24.18 23.20
40 30.15 29.26 28.37 27.47 26.57 26.5 25.14 24.22 23.31
50 30.20 29.31 28.42 27.52 27.2 26.10 25.19 24.26 23.35
57 0 30.26 29.37 28.47 27.57 27.6 26.15 25.23 24.31 23.39
10 30.31 29.42 28.53 28.2 27.11 26.19 25.28 24.35 23.43
20 30.37 29.47 28.58 28.7 27.16 26.24 25.32 24.40 23.47
30 30.42 29.53 29.3 28.12 27.21 26.29 25.37 24.44 23.52
40 30.47 29.58 29.8 28.17 27.26 26.33 25.42 24.49 23.56
50 30.53 30.3 29.13 28.22 27.31 26.38 25.46 24.53 24.0
58 0 30.58 30.9 29.18 28.27 27.35 26.43 25.51 24.58 24.4
10 31.4 30.14 29.24 28.32 27.40 26.47 25.55 25.2 24.8
20 31.9 30.19 29.29 28.37 27.45 26.52 26.0 25.6 24.13
30 31.15 30.24 29.34 28.42 27.50 26.57 26.4 25.11 24.17
40 31.20 30.30 29.39 28.47 27.55 27.1 26.9 25.15 24.21
50 31.26 30.35 29.44 28.52 28.0 27.6 26.13 25.19 24.25
59 0 31.31 30.40 29.49 28.57 28.4 27.11 26.18 25.24 24.30
10 31.37 30.45 29.55 29.2 28.9 27.15 26.22 25.28 24.34
20 31.42 30.51 30.0 29.7 28.14 27.20 26.27 25.32 24.38
30 31.48 30.56 30.5 29.12 28.19 27.25 26.31 25.37 24.42
40 31.53 31.1 30.10 29.17 28.24 27.30 26.36 25.41 24.47
50 31.58 31.6 30.15 29.22 28.29 27.35 26.40 25.45 24.51
60 0 32.4 31.12 30.20 29.27 28.34 27.40 26.45 25.50 24.55
10 32.9 31.17 30.26 29.32 28.39 27.44 26.49 25.54 24.59
20 32.15 31.22 30.31 29.37 28.44 27.49 26.54 25.59 25.3
30 32.20 31.28 30.36 29.42 28.49 27.54 26.58 26.3 25.8
40 32.26 31.33 30.41 29.47 28.54 27.58 27.3 26.8 25.12
50 32.31 31.38 30.46 29.52 28.59 28.3 27.8 26.12 25.16
61 0 32.36 31.44 30.51 29.57 29.3 28.8 27.12 2.17 25.20
10 32.42 31.49 30.57 30.2 29.8 28.12 27.17 26.21 25.24
20 32.47 31.54 31.2 30.7 29.13 28.17 27.21 26.26 25.29
30 32.53 32.0 31.7 30.12 29.18 28.22 27.26 26.30 25.33
40 32.58 32.5 31.12 30.17 29.23 28.26 27.31 26.34 25.37
50 33.4 32.10 31.17 30.22 29.28 28.31 27.35 26.39 25.41
62 0 33.9 22.16 31.22 30.27 29.32 28.36 27.40 26.43 25.46

[page] 15

TABLE VIII. For reducing the apparent Altitude of the MOON to the true.
Moon's horizontal Parallax. Apparent Altitude of the Moon's Center.
66° 67° 68° 69° 70° 71° 72° 73° 74°
Corr. Corr. Corr. Corr. Corr. Corr. Corr. Corr. Corr.
M S M S M S M S M S M S M S M S M S M S
53 0 21.8 20.18 19.28 18.38 17.47 16.56 16.4 15.12 14.20
10 21.12 20.22 19.32 18.41 17.50 16.59 16.7 15.15 14.23
20 21.16 20.26 19.35 18.45 17.54 17.3 16.10 15.18 14.26
30 21.20 20.30 19.39 18.48 17.57 17.6 16.13 15.21 14.28
40 21.24 20.34 19.43 18.52 18.0 17.9 16.16 15.24 14.31
50 21.28 20.38 19.47 18.55 18.4 17.12 16.20 15.27 14.34
54 0 21.32 20.42 19.51 18.59 18.7 17.15 16.23 15.30 14.37
10 21.36 20.46 19.54 19.3 18.11 17.19 16.26 15.33 14.40
20 21.40 20.50 19.58 19.6 18.14 17.22 16.29 15.36 14.42
30 21.45 20.53 20.2 19.10 18.18 17.25 16.32 15.38 14.45
40 21.49 20.57 20.6 19.14 18.21 17.28 16.35 15.41 14.48
50 21.53 21.1 20.10 19.17 18.24 17.32 16.38 15.44 14.51
55 0 21.57 21.5 20.13 19.21 18.28 17.35 16.41 15.47 14.53
10 22.1 21.9 20.17 19.24 18.31 17.38 16.44 15.50 14.56
20 22.5 21.13 20.21 19.28 18.34 17.41 16.47 15.53 14.59
30 22.9 21.17 20.24 19.31 18.38 17.44 16.51 15.56 15.1
40 22.13 21.21 20.28 19.35 18.42 17.48 16.54 15.59 15.4
50 22.17 21.25 20.32 19.39 18.45 17.51 16.57 16.2 15.7
56 0 22.21 21.29 20.36 19.42 18.49 17.54 17.0 16.5 15.10
10 22.25 21.33 20.39 19.46 18.52 17.58 17.3 16.8 15.13
20 22.29 21.37 20.43 19.49 18.55 18.1 17.6 16.11 15.15
30 22.34 21.40 20.47 19.53 18.59 18.4 17.9 16.14 15.18
40 22.38 21.44 20.50 19.57 19.2 18.7 17.12 16.17 15.21
50 22.42 21.48 20.54 20.0 19.5 18.11 17.15 16.20 15.24
57 0 22.46 21.52 20.58 20.4 19.9 18.14 17.18 16.23 15.26
10 22.50 21.56 21.2 20.7 19.12 18.17 17.21 16.26 15.29
20 22.54 22.0 21.6 20.11 19.16 18.21 17.25 16.29 15.32
30 22.58 22.4 21.9 20.15 19.19 18.24 17.28 16.32 15.35
40 23.2 22.8 21.13 20.18 19.23 18.27 17.31 16.34 15.37
50 23.6 22.12 21.17 20.22 19.26 18.30 17.34 16.37 15.40
58 0 23.10 22.16 21.21 20.25 19.30 18.33 17.37 16.40 15.43
10 23.14 22.20 21.24 20.29 19.33 18.37 17.40 16.43 15.46
20 23.18 22.24 21.28 20.32 19.36 18.40 17.43 16.46 15.49
30 23.22 22.27 21.32 20.36 19.40 18.43 17.46 16.49 15.51
40 23.26 22.31 21.35 20.40 19.43 18.46 17.49 16.52 15.54
50 23.30 22.35 21.39 20.43 19.47 18.50 17.52 16.55 15.57
59 0 23.34 22.39 21.43 20.47 19.50 18.53 17.55 16.58 16.0
10 23.39 22.43 21.47 20.50 19.54 18.56 17.59 17.1 16.2
20 23.43 22.47 21.50 20.54 19.57 18.59 18.2 17.3 16.5
30 23.47 22.51 21.54 20.57 20.1 19.3 18.5 17.6 16.8
40 23.51 22.55 21.58 21.1 20.4 19.6 18.8 17.9 16.11
50 23.55 22.58 22.2 21.4 20.7 19.9 18.11 17.12 16.13
60 0 23.59 23.2 22.6 21.8 20.11 19.12 18.14 17.15 16.16
10 24.3 23.6 22.9 21.12 20.14 19.15 18.17 17.18 16.19
20 24.7 23.10 22.13 21.15 20.18 19.19 18.20 17.21 16.22
30 24.11 23.14 22.17 21.19 20.21 19.22 18.24 17.24 16.24
40 24.15 23.18 22.21 21.22 20.24 19.25 18.27 17.27 16.27
50 24.19 23.22 22.24 21.26 20.28 19.29 18.30 17.30 16.30
61 0 24.23 23.26 22.28 21.30 20.31 19.32 18.33 17.33 16.33
10 24.27 23.30 22.32 21.33 20.35 19.35 18.36 17.36 16.35
20 24.31 23.33 22.36 21.37 20.39 19.39 18.39 17.39 16.38
30 24.35 23.37 22.39 21.40 20.42 19.42 18.42 17.41 16.41
40 24.39 23.41 22.43 21.44 20.46 19.45 18.45 17.44 16.44
50 24.44 23.45 22.47 21.47 20.49 19.48 18.48 17.47 16.46
62 0 24.48 23.49 22.51 21.51 20.52 19.52 18.51 17.50 16.49

[page] 16

TABLE VIII. For reducing the apparent Altitude of the MOON to the true.
Moon's horizontal Parallax. Apparent Altitude of the Moon's Center.
75° 76° 77° 78° 79° 80° 81° 82° 83°
Corr. Corr. Corr. Corr. Corr. Corr. Corr. Corr. Corr.
M S M S M S M S M S M S M S M S M S M S
53 0 13.28 12.35 11.42 10.49 9.55 9.2 8.8 7.15 6.21
10 13.30 12.37 11.44 10.51 9.57 9.3 8.9 7.16 6.22
20 13.33 12.40 11.46 10.53 9.59 9.5 8.11 7.18 6.23
30 13.35 12.42 11.49 10.55 10.1 9.7 8.13 7.19 6.25
40 13.38 12.45 11.51 10.57 10.3 9.9 8.14 7.20 6.26
50 13.40 12.47 11.53 10.59 10.5 9.11 8.16 7.22 6.27
54 0 13.43 12.50 11.56 11.2 10.7 9.13 8.18 7.23 6.28
10 13.45 12.52 11.58 11.4 10.9 9.14 8.19 7.25 6.29
20 13.48 12.54 12.0 11.6 10.11 9.16 8.21 7.26 6.30
30 13.51 12.57 12.2 11.8 10.13 9.18 8.22 7.28 6.32
40 13.54 22.59 12.5 11.10 10.15 9.20 8.24 7.29 6.33
50 13.56 13.2 12.7 11.2 10.17 9.21 8.25 7.30 6.34
55 0 13.59 13.4 12.9 11.14 10.19 9.23 8.27 7.31 6.35
10 14.1 13.7 12.12 11.16 10.20 9.25 8.29 7.33 6.36
20 14.4 13.9 12.14 11.18 10.22 9.26 8.30 7.34 6.38
30 14.6 13.11 12.16 11.21 10.24 9.28 8.31 7.36 6.39
40 14.9 13.14 12.19 11.23 10.26 9.30 8.33 7.37 6.40
50 14.11 13.16 12.21 11.25 10.28 9.32 8.35 7.39 6.41
56 0 14.14 13.19 12.23 11.27 10.30 9.33 8.37 7.40 6.42
10 14.17 13.21 12.25 11.29 10.32 9.35 8.38 7.41 6.44
20 14.19 13.23 12.28 11.31 10.34 9.37 8.39 7.42 6.45
30 14.22 13.26 12.30 11.33 10.36 9.38 8.41 7.44 6.46
40 14.24 13.28 12.32 11.35 10.38 9.40 8.42 7.45 6.47
50 14.27 13.31 12.34 11.37 10.40 9.42 8.44 7.47 6.48
57 0 14.30 13.33 12.36 11.39 10.42 9.44 8.46 7.48 6.50
10 14.32 13.36 12.39 11.41 10.43 9.46 8.47 7.49 6.52
20 14.35 13.38 12.41 11.43 10.45 9.47 8.48 7.51 6.53
30 14.38 13.41 12.43 11.45 10.47 9.49 8.50 7.52 6.54
40 14.40 13.43 12.45 11.47 10.49 9.51 8.51 7.53 6.55
50 14.43 13.46 12.48 11.49 10.51 9.53 8.53 7.55 6.56
58 0 14.46 13.48 12.50 11.51 10.53 9.54 8.55 7.56 6.57
10 14.48 13.50 12.52 11.54 10.55 9.56 8.56 7.57 6.59
20 14.51 13.53 12.54 11.56 10.57 9.58 8.57 7.59 7.0
30 14.53 13.55 12.57 11.58 10.58 9.59 8.59 8.0 7.1
40 14.56 13.57 12.59 12.0 11.0 10.1 9.1 8.2 7.2
50 14.58 13.59 13.1 12.2 11.2 10.3 9.3 8.3 7.3
59 0 15.1 14.2 13.3 12.4 11.4 10.5 9.5 8.5 7.4
10 15.4 14.5 13.5 12.6 11.6 10.6 9.6 8.6 7.6
20 15.6 14.7 13.8 12.8 11.8 10.8 9.8 8.7 7.7
30 15.9 14.10 13.10 12.10 11.10 10.10 9.9 8.9 7.8
40 15.12 14.12 13.12 12.12 11.12 10.11 9.11 8.10 7.9
50 15.14 14.15 13.14 12.14 11.14 10.13 9.12 8.12 7.10
60 0 15.17 14.17 13.17 12.16 11.16 10.15 9.14 8.13 7.12
10 15.19 14.19 13.19 12.19 11.18 10.17 9.16 8.14 7.13
20 15.22 14.22 13.21 12.21 11.20 10.18 9.17 8.16 7.14
30 15.25 14.24 13.23 12.23 11.21 10.20 9.19 8.17 7.15
40 15.27 14.27 13.20 12.25 11.23 10.22 9.21 8.18 7.16
50 15.30 14.29 13.28 12.27 11.25 10.24 9.22 8.20 7.17
61 0 15.32 14.31 13.30 12.29 11.27 10.25 9.24 8.21 7.19
10 15.33 14.34 13.32 12.31 11.29 10.27 9.25 8.22 7.20
20 15.36 14.36 13.35 12.33 11.31 10.29 9.27 8.24 7.21
30 15.38 14.39 13.37 12.35 11.33 10.31 9.28 8.25 7.22
40 15.41 14.41 13.39 12.37 11.35 10.32 9.30 8.27 7.23
50 15.44 14.44 13.41 12.39 11.37 10.34 9.31 8.28 7.25
62 0 15.48 14.46 13.44 12.41 11.39 10.36 9.33 8.30 7.26

[page] 17

TABLE VIII. For reducing the apparent Altitude of the MOON to the true.
Moon's horizontal Parallax. Apparent Altitude of the Moon's Center.
84° 85° 86° 87° 88° 89°
Corr. Corr. Corr. Corr. Corr. Corr.
M S M S M S M S M S M S M S
53 0 5.26 4.32 3.38 2.43 1.49 0.54
10 5.27 4.33 3.39 2.43 1.49 0.54
20 5.28 4.34 3.39 2.44 1.49 0.54
30 5.29 4.35 3.40 2.45 1.50 0.55
40 5.30 4.36 3.41 2.45 1.50 0.55
50 5.31 4.37 3.42 2.46 1.51 0.55
54 0 5.33 4.37 3.42 2.47 1.51 0.56
10 5.34 4.38 3.43 2.47 1.51 0.56
20 5.35 4.39 3.44 2.48 1.52 0.56
30 5.36 4.40 3.44 2.48 1.52 0.56
40 5.37 4.41 3.45 2.49 1.52 0.56
50 5.38 4.42 3.46 2.49 1.53 0.57
55 0 5.39 4.43 3.46 2.50 1.53 0.57
10 5.40 4.44 3.47 2.50 1.54 0.57
20 5.41 4.45 3.48 2.51 1.54 0.57
30 5.42 4.46 3.48 2.51 1.54 0.57
40 5.43 4.46 3.49 2.52 1.55 0.57
50 5.44 4.47 3.50 2.52 1.55 0.58
56 0 5.45 4.48 3.50 2.53 1.55 0.58
10 5.46 4.49 3.51 2.53 1.56 0.58
20 5.47 4.50 3.52 2.54 1.56 0.58
30 5.48 4.51 3.52 2.54 1.56 0.58
40 5.49 4.52 3.53 2.55 1.57 0.58
50 5.50 4.52 3.54 2.55 1.57 0.59
57 0 5.51 4.53 3.55 2.56 1.57 0.59
10 5.53 4.54 3.55 2.56 1.58 0.59
20 5.54 4.55 3.56 2.57 1.58 0.59
30 5.55 4.56 3.57 2.57 1.58 0.59
40 5.56 4.57 3.57 2.58 1.59 0.59
50 5.57 4.58 3.58 2.58 1.59 0.59
58 0 5.58 4.58 3.59 2.59 1.59 1.0
10 5.59 4.59 3.59 2.59 2.0 1.0
20 6.0 5.0 4.0 3.0 2.0 1.0
30 6.1 5.1 4.1 3.1 2.1 1.0
40 6.2 5.2 4.1 3.1 2.1 1.0
50 6.3 5.3 4.2 3.2 2.1 1.0
59 0 6.4 5.4 4.3 3.2 2.2 1.1
10 6.5 5.5 4.3 3.3 2.2 1.1
20 6.6 5.5 4.4 3.3 2.2 1.1
30 6.7 5.6 4.5 3.4 2.3 1.1
40 6.8 5.7 4.5 3.4 2.3 1.1
50 6.9 5.8 4.6 3.5 2.3 1.1
60 0 6.10 5.9 4.7 3.5 2.4 1.2
10 6.12 5.10 4.7 3.6 2.4 1.2
20 6.13 5.10 4.8 3.6 2.5 1.2
30 6.14 5.11 4.9 3.7 2.5 1.2
40 6.15 5.12 4.9 3.7 2.5 1.2
50 6.16 5.13 4.10 3.8 2.6 1.3
61 0 6.17 5.14 4.11 3.9 2.6 1.3
10 6.18 5.15 4.11 3.9 2.6 1.3
20 6.19 5.15 4.12 3.10 2.7 1.3
30 6.20 5.16 4.13 3.10 2.7 1.3
40 6.21 5.17 4.13 3.11 2.7 1.3
50 6.22 5.18 4.14 3.11 2.8 1.4
62 0 6.23 5.19 4.15 3.12 2.8 1.4

C

[page] 18

TABLE IX. Logarithms for readily computing the true Distance of the MOON from the SUN or a Fixed Star.
Horizontal Parallax of the Moon. Apparent Altitude of the Moon's Center.
M S Logarithm. Logarithm. Logarithm. Logarithm. Logarithm. Logarithm.
53 0 9.99983·9 9.99972·7 9.99961·2 9.99949·6 9.99938·0 9.99926·4
10 9.99983·8 9.99972·5 9.99961·0 9.99949·4 9.99937·7 9.99926·1
20 9.99983·6 9.99972·3 9.99960·8 9.99949·1 9.99937·4 9.99925·7
30 9.99983·5 9.99972·1 9.99960·6 9.99948·9 9.99937·1 9.99925·4
40 9.99983·3 9.99972·0 9.99960·4 9.99948·6 9.99936·9 9.99925·1
50 9.99983·2 9.99971·8 9.99960·2 9.99948·4 9.99936·6 9.99924·7
54 0 9.99983·1 9.99971·6 9.99959·9 9.99948·1 9.99936·3 9.99924·4
10 9.99982·9 9.99971·4 9.99959·7 9.99947·9 9.99936·0 9.99924·1
20 9.99982·8 9.99971·3 9.99959·5 9.99947·6 9.99935·7 9.99923·8
30 9.99982·7 9.99971·1 9.99959·3 9.99947·4 9.99935·4 9.99923·4
40 9.99982·6 9.99970·9 9.99959·1 9.99947·1 9.99935·1 9.99923·1
50 9.99982·4 9.99970·7 9.99958·9 9.99946·9 9.99935·8 9.99922·8
55 0 9.99982·3 9.99970·6 9.99958·7 9.99946·6 9.99934·5 9.99922·5
10 9.99982·1 9.99970·4 9.99958·4 9.99946·4 9.99934·2 9.99922·2
20 9.99982·0 9.99970·2 9.99958·2 9.99946·1 9.99933·9 9.99921·9
30 9.99981·9 9.99970·0 9.99958·0 9.99945·9 9.99933·7 9.99921·6
40 9.99981·7 9.99969·9 9.99957·8 9.99945·6 9.99933·4 9.99921·2
50 9.99981·6 9.99969·7 9.99957·6 9.99945·4 9.99933·1 9.99920·9
56 0 9.99981·5 9.99969·5 9.99957·4 9.99945·1 9.99932·8 9.99920·6
10 9.99981·3 9.99969·3 9.99957·1 9.99944·9 9.99932·5 9.99920·3
20 9.99981·2 9.99969·2 9.99956·9 9.99944·7 9.99932·2 9.99919·9
30 9.99981·1 9.99969·0 9.99956·7 9.99944·4 9.99932·0 9.99919·6
40 9.99980·9 9.99968·8 9.99956·5 9.99944·2 9.99931·7 9.99919·3
50 9.99980·8 9.99968·6 9.99956·3 9.99943·9 9.99931·4 9.99919·0
57 0 9.99980·7 9.99968·5 9.99956·1 9.99943·7 9.99931·1 9.99918·6
10 9.99980·5 9.99968·3 9.99955·9 9.99943·4 9.99930·8 9.99918·3
20 9.99980·4 9.99968·1 9.99955·7 9.99943·2 9.99930·5 9.99918·0
30 9.99980·3 9.99968·0 9.99955·5 9.99942·9 9.99930·3 9.99917·6
40 9.99980·1 9.99967·8 9.99955·3 9.99942·7 9.99930·0 9.99917·3
50 9.99980·0 9.99967·6 9.99955·1 9.99942·4 9.99929·7 9.99917·0
58 0 9.99979·9 9.99967·5 9.99954·9 9.99942·2 9.99929·4 9.99916·7
10 9.99979·7 9.99967·3 9.99954·6 9.99941·9 9.99929·1 9.99916·3
20 9.99979·6 9.99967·1 9.99954·4 9.99941·7 9.99928·8 9.99916·0
30 9.99979·4 9.99966·9 9.99954·2 9.99941·4 9.99928·6 9.99915·7
40 9.99979·3 9.99966·8 9.99954·0 9.99941·2 9.99928·3 9.99915·4
50 9.99979·1 9.99966·6 9.99953·8 9.99940·9 9.99928·0 9.99915·1
59 0 9.99979·0 9.99966·4 9.99953·6 9.99940·7 9.99927·7 9.99914·7
10 9.99978·9 9.99966·2 9.99953·3 9.99940·4 9.99927·4 9.99914·4
20 9.99978·7 9.99966·1 9.99953·1 9.99940·2 9.99927·1 9.99914·1
30 9.99978·6 9.99965·9 9.99952·9 9.99939·9 9.99926·8 9.99913·7
40 9.99978·5 9.99965·7 9.99952·7 9.99939·7 9.99926·5 9.99913·4
50 9.99978·3 9.99965·5 9.99952·5 9.99939·4 9.99926·2 9.99913·1
60 0 9.99978·2 9.99965·3 9.99952·3 9.99939·2 9.99925·9 9.99912·8
10 9.99978·1 9.99965·2 9.99952·0 9.99938·9 9.99925·7 9.99912·4
20 9.99977·9 9.99965·0 9.99951·8 9.99938·7 9.99925·4 9.99912·1
30 9.99977·8 9.99964·8 9.99951·6 9.99938·4 9.99925·1 9.99911·8
40 9.99977·7 9.99964·6 9.99951·4 9.99938·2 9.99924·8 9.99911·5
50 9.99977·5 9.99964·5 9.99951·2 9.99937·9 9.99924·5 9.99911·1
61 0 9.99977·4 9.99964·3 9.99951·0 9.99937·6 9.99924·2 9.99910·8
10 9.99977·2 9.99964·1 9.99950·7 9.99937·4 9.99923·9 9.99910·5
20 9.99977·1 9.99963·9 9.99950·5 9.99937·1 9.99923·6 9.99910·2
30 9.99976·9 9.99963·8 9.99950·3 9.99936·9 9.99923·3 9.99909·8
40 9.99976·8 9.99963·6 9.99950·1 9.99936·6 9.99923·0 9.99909·5
50 9.99976·6 9.99963·4 9.99949·9 9.99936·4 9.99922·7 9.99909·2
62 0 9.99976·5 9.99963·2 9.99949·7 9.99936·1 9.99922·4 9.99908·9

[page] 19

TABLE IX. Logarithms for readily computing the true Distance of the MOON from the SUN or a Fixed Star.
Horizontal Parallax of the Moon. Apparent Altitude of the Moon's Center.
10° 11° 12° 13° 14°
M S Logarithm. Logarithm. Logarithm. Logarithm. Logarithm. Logarithm.
53 0 9.99914·8 9.99903·2 9.99891·7 9.99880·3 9.99868·8 9.99857·4
10 9.99914·4 9.99902·8 9.99891·3 9.99879·8 9.99868·3 9.99856·9
20 9.99914·0 9.99902·4 9.99890·8 9.99879·4 9.99867·8 9.99856·3
30 9.99913·7 9.99902·1 9.99890·4 9.99878·9 9.99867·3 9.99855·8
40 9.99913·3 9.99901·7 9.99890·0 9.99878·4 9.99866·8 9.99855·3
50 9.99912·9 9.99901·3 9.99889·5 9.99877·9 9.99866·3 9.99854·7
54 0 9.99912·6 9.99900·9 9.99889·1 9.99877·4 9.99865·8 9.99854·2
10 9.99912·2 9.99900·5 9.99888·6 9.99877·0 9.99865·3 9.99853·7
20 9.99911·9 9.99900·1 9.99888·2 9.99876·5 9.99864·8 9.99853·1
30 9.99911·5 9.99899·7 9.99887·8 9.99876·0 9.99864·3 9.99852·6
40 9.99911·2 9.99899·3 9.99887·3 9.99875·6 9.99863·8 9.99852·1
50 9.99910·8 9.99898·9 9.99886·9 9.99875·1 9.99863·3 9.99851·5
55 0 9.99910·5 9.99898·5 9.99886·5 9.99874·6 9.99862·8 9.99851·0
10 9.99910·1 9.99898·1 9.99886·0 9.99874·2 9.99862·3 9.99850·4
20 9.99909·8 9.99897·7 9.99885·6 9.99873·7 9.99861·8 9.99849·8
30 9.99909·4 9.99897·3 9.99885·2 9.99873·2 9.99861·3 9.99849·3
40 9.99909·1 9.99896·9 9.99884·7 9.99872·7 9.99860·7 9.99848·8
50 9.99908·7 9.99896·5 9.99884·3 9.99872·2 9.99860·2 9.99848·2
56 0 9.99908·3 9.99896·1 9.99883·9 9.99871·8 9.99859·7 9.99847·7
10 9.99907·9 9.99895·7 9.99883·4 9.99871·3 9.99859·2 9.99847·1
20 9.99907·6 9.99895·3 9.99883·0 9.99870·8 9.99858·7 9.99846·6
30 9.99907·2 9.99894·9 9.99882·6 9.99870·4 9.99858·2 9.99846·0
40 9.99906·9 9.99894·5 9.99882·1 9.99869·9 9.99857·7 9.99845·5
50 9.99906·5 9.99894·1 9.99881·7 9.99869·4 9.99857·2 9.99844·9
57 0 9.99906·2 9.99893·7 9.99881·3 9.99869·0 9.99856·7 9.99844·4
10 9.99905·8 9.99893·4 9.99880·8 9.99868·5 9.99856·2 9.99843·9
20 9.99905·5 9.99893·0 9.99880·4 9.99868·0 9.99855·7 9.99843·3
30 9.99905·1 9.99892·6 9.99880·0 9.99867·6 9.99855·2 9.99842·8
40 9.99904·8 9.99892·2 9.99879·5 9.99867·1 9.99854·6 9.99842·3
50 9.99904·4 9.99891·8 9.99879·1 9.99866·6 9.99854·1 9.99841·8
58 0 9.99904·0 9.99891·4 9.99878·7 9.99866·2 9.99853·6 9.99841·2
10 9.99903·7 9.99891·0 9.99878·2 9.99865·7 9.99853·1 9.99840·7
20 9.99903·3 9.99890·6 9.99877·8 9.99865·2 9.99852·6 9.99840·1
30 9.99902·9 9.99890·2 9.99877·4 9.99864·8 9.99852·1 9.99839·6
40 9.99902·6 9.99889·8 9.99876·9 9.99864·3 9.99851·6 9.99839·1
50 9.99902·2 9.99889·4 9.99876·5 9.99863·8 9.99851·1 9.99838·5
59 0 9.99901·8 9.99889·0 9.99876·1 9.99863·4 9.99850·6 9.99838·0
10 9.99901·4 9.99888·6 9.99875·6 9.99862·9 9.99850·1 9.99837·4
20 9.99901·1 9.99888·2 9.99875·2 9.99862·4 9.99849·6 9.99836·9
30 9.99900·7 9.99887·8 9.99874·8 9.99861·9 9.99849·1 9.99836·3
40 9.99900·4 9.99887·4 9.99874·3 9.99861·5 9.99848·6 9.99835·8
50 9.99900·0 9.99887·0 9.99873·9 9.99861·0 9.99848·1 9.99835·2
60 0 9.99899·7 9.99886·6 9.99873·5 9.99860·5 9.99847·6 9.99834·7
10 9.99899·3 9.99886·2 9.99873·0 9.99860·0 9.99847·1 9.99834·1
20 9.99899·0 9.99885·8 9.99872·6 9.99859·6 9.99846·6 9.99833·6
30 9.99898·6 9.99885·4 9.99872·2 9.99859·1 9.99846·1 9.99833·0
40 9.99898·2 9.99885·0 9.99871·7 9.99858·6 9.99845·5 9.99832·5
50 9.99897·9 9.99884·6 9.99871·3 9.99858·1 9.99845·0 9.99831·9
61 0 9.99897·5 9.99884·2 9.99870·9 9.99857·7 9.99844·5 9.99831·4
10 9.99897·1 9.99883·8 9.99870·4 9.99857·2 9.99844·0 9.99830·8
20 9.99896·8 9.99883·4 9.99870·0 9.99856·7 9.99843·5 9.99830·3
30 9.99896·4 9.99883·0 9.99869·5 9.99856·2 9.99843·0 9.99829·7
40 9.99896·0 9.99882·6 9.99869·1 9.99855·8 9.99842·5 9.99829·2
50 9.99895·7 9.99882·2 9.99868·7 9.99855·3 9.99842·0 9.99828·6
62 0 9.99895·3 9.99881·8 9.99868·3 9.99854·8 9.99841·5 9.99828·1

C 2

[page] 20

TABLE IX. Logarithms for readily computing the true Distance of the MOON from the SUN or a Fixed Star.
Horizontal Parallax of the Moon. Apparent Altitude of the Moon's Center.
15° 16° 17° 18° 19° 20°
M S Logarithm. Logarithm. Logarithm. Logarithm. Logarithm. Logarithm.
53 0 9.99846·0 9.99834·8 9.99823·6 9.99812·4 9.99801·3 9.99790·2
10 9.99845·4 9.99834·2 9.99823·0 9.99811·7 9.99800·6 9.99789·5
20 9.99844·9 9.99833·6 9.99822·3 9.99811·0 9.99799·8 9.99788·7
30 9.99844·3 9.99832·9 9.99821·7 9.99810·4 9.99799·1 9.99788·0
40 9.99843·7 9.99832·3 9.99821·0 9.99809·7 9.99798·4 9.99787·2
50 9.99843·2 9.99831·7 9.99820·3 9.99809·0 9.99797·7 9.99786·5
54 0 9.99842·6 9.99831·1 9.99819·7 9.99808·3 9.99797·0 9.99785·7
10 9.99842·0 9.99830·5 9.99819·0 9.99807·6 9.99796·3 9.99785·0
20 9.99841·4 9.99829·9 9.99818·4 9.99806·9 9.99795·5 9.99784·2
30 9.99840·9 9.99829·3 9.99817·7 9.99806·3 9.99794·8 9.99783·5
40 9.99840·3 9.99828·7 9.99817·1 9.99805·6 9.99794·1 9.99782·7
50 9.99839·7 9.99828·1 9.99816·4 9.99804·9 9.99793·4 9.99782·0
55 0 9.99839·1 9.99827·5 9.99815·8 9.99804·2 9.99792·7 9.99781·2
10 9.99838·6 9.99826·9 9.99815·1 9.99803·5 9.99792·0 9.99780·5
20 9.99838·0 9.99826·2 9.99814·5 9.99802·8 9.99791·3 9.99779·7
30 9.99837·4 9.99825·6 9.99813·8 9.99802·2 9.99790·5 9.99779·0
40 9.99836·8 9.99825·0 9.99813·2 9.99801·5 9.99789·8 9.99778·2
50 9.99836·3 9.99824·4 9.99812·5 9.99800·8 9.99789·1 9.99777·5
56 0 9.99835·7 9.99823·8 9.99811·9 9.99800·1 9.99788·4 9.99776·7
10 9.99835·1 9.99823·2 9.99811·2 9.99799·4 9.99787·7 9.99776·0
20 9.99834·5 9.99822·5 9.99810·6 9.99798·7 9.99786·9 9.99775·2
30 9.99833·9 9.99822·9 9.99809·9 9.99798·1 9.99786·2 9.99774·5
40 9.99833·4 9.99821·3 9.99809·3 9.99797·4 9.99785·5 9.99773·7
50 9.99832·8 9.99820·7 9.99808·6 9.99796·7 9.99784·8 9.99773·0
57 0 9.99832·2 9.99820·1 9.99808·0 9.99796·0 9.99784·1 9.99772·2
10 9.99831·6 9.99819·5 9.99807·3 9.99795·3 9.99783·4 9.99771·5
20 9.99831·1 9.99818·9 9.99806·7 9.99794·6 9.99782·6 9.99770·7
30 9.99830·5 9.99818·3 9.99806·0 9.99794·0 9.99781·9 9.99770·0
40 9.99829·9 9.99817·7 9.99805·4 9.99793·3 9.99781·2 9.99769·2
50 9.99829·4 9.99817·1 9.99804·7 9.99792·6 9.99780·5 9.99768·5
58 0 9.99828·8 9.99816·5 9.99804·1 9.99791·9 9.99779·8 9.99767·7
10 9.99828·2 9.99815·9 9.99803·4 9.99791·2 9.99779·0 9.99767·0
20 9.99827·6 9.99815·2 9.99802·8 9.99790·5 9.99778·3 9.99766·2
30 9.99827·1 9.99814·6 9.99802·1 9.99789·9 9.99777·6 9.99765·5
40 9.99826·5 9.99814·0 9.99801·5 9.99789·2 9.99776·9 9.99764·7
50 9.99825·9 9.99812·4 9.99800·8 9.99788·5 9.99776·2 9.99764·0
59 0 9.99825·3 9.99812·8 9.99800·2 9.99787·8 9.99775·4 9.99763·2
10 9.99824·7 9.99812·2 9.99799·5 9.99787·1 9.99774·7 9.99762·5
20 9.99824·1 9.99811·5 9.99798·9 9.99786·4 9.99774·0 9.99761·7
30 9.99823·5 9.99810·9 9.99798·2 9.99785·8 9.99773·3 9.99761·0
40 9.99823·0 9.99810·3 9.99797·6 9.99785·1 9.99772·5 9.99760·2
50 9.99822·4 9.99809·7 9.99796·9 9.99784·4 9.99771·8 9.99759·4
60 0 9.99821·8 9.99809·1 9.99796·3 9.99783·7 9.99771·1 9.99758·6
10 9.99821·2 9.99808·5 9.99795·6 9.99783·0 9.99770·4 9.99757·9
20 9.99820·6 9.99807·8 9.99795·0 9.99782·3 9.99769·6 9.99757·1
30 9.99820·1 9.99807·2 9.99794·3 9.99781·7 9.99768·9 9.99756·4
40 9.99819·5 9.99806·6 9.99793·7 9.99781·0 9.99768·2 9.99755·6
50 9.99818·9 9.99806·0 9.99793·0 9.99780·3 9.99767·5 9.99754·9
61 0 9.99818·3 9.99805·4 9.99792·4 9.99779·6 9.99766·7 9.99754·1
10 9.99817·7 9.99804·8 9.99791·7 9.99778·9 9.99766·0 9.99753·4
20 9.99817·1 9.99804·1 9.99791·1 9.99778·2 9.99765·3 9.99752·6
30 9.99816·5 9.99803·5 9.99790·4 9.99777·5 9.99764·6 9.99751·9
40 9.99816·0 9.99802·9 9.99789·8 9.99776·8 9.99763·8 9.99751·1
50 9.99815·4 9.99802·3 9.99789·1 9.99776·1 9.99763·1 9.99750·4
62 0 9.99814·8 9.99801·7 9.99788·5 9.99775·4 9.99762·4 9.99749·6

[page] 21

TABLE IX. Logarithms for readily computing the true Distance of the MOON from the SUN or a Fixed Star.
Horizontal Parallax of the Moon. Apparent Altitude of the Moon's Center.
21° 22° 23° 24° 25° 26°
M S Logarithm. Logarithm. Logarithm. Logarithm. Logarithm. Logarithm.
53 0 9.99779·2 9.99768·4 9.99757·7 9.99746·8 9.99736·3 9.99725·7
10 9.99778·4 9.99767·5 9.99756·8 9.99745·9 9.99735·4 9.99724·7
20 9.99777·6 9.99766·7 9.99756·0 9.99745·0 9.99734·4 9.99723·8
30 9.99776·9 9.99765·9 9.99755·1 9.99744·2 9.99733·5 9.99722·8
40 9.99776·1 9.99765·1 9.99754·2 9.99743·3 9.99732·6 9.99721·8
50 9.99775·3 9.99764·3 9.99753·4 9.99742·4 9.99731·7 9.99720·9
54 0 9.99774·5 9.99763·5 9.99752·5 9.99741·5 9.99730·7 9.99719·9
10 9.99773·7 9.99762·6 9.99751·7 9.99740·6 9.99729·8 9.99719·0
20 9.99773·0 9.99761·8 9.99750·8 9.99739·7 9.99728·9 9.99718·0
30 9.99772·2 9.99761·0 9.99750·0 9.99738·8 9.99728·0 9.99717·1
40 9.99771·4 9.99760·2 9.99749·1 9.99738·0 9.99727·0 9.99716·1
50 9.99770·6 9.99759·4 9.99748·3 9.99737·1 9.99726·1 9.99715·2
55 0 9.99769·8 9.99758·6 9.99747·4 9.99736·2 9.99725·2 9.99714·2
10 9.99769·0 9.99757·7 9.99746·5 9.99735·3 9.99724·3 9.99713·2
20 9.99768·3 9.99756·9 9.99745·7 9.99734·4 9.99723·3 9.99712·3
30 9.99767·5 9.99756·1 9.99744·8 9.99733·5 9.99722·4 9.99711·3
40 9.99766·7 9.99755·3 9.99743·9 9.99732·6 9.99721·5 9.99710·3
50 9.99765·9 9.99754·5 9.99743·1 9.99731·8 9.99720·6 9.99709·4
56 0 9.99765·1 9.99753·7 9.99742·2 9.99730·9 9.99719·6 9.99708·4
10 9.99764·4 9.99752·8 9.99741·3 9.99730·0 9.99718·7 9.99707·5
20 9.99763·6 9.99752·0 9.99740·5 9.99729·1 9.99717·8 9.99706·5
30 9.99762·8 9.99751·2 9.99739·6 9.99728·2 9.99716·9 9.99705·6
40 9.99762·0 9.99750·4 9.99738·8 9.99727·3 9.99716·0 9.99704·6
50 9.99761·2 9.99749·5 9.99738·0 9.99726·4 9.99715·0 9.99703·7
57 0 9.99760·4 9.99748·7 9.99737·1 9.99725·5 9.99714·1 9.99702·7
10 9.99759·6 9.99747·9 9.99736·2 9.99724·6 9.99713·2 9.99701·8
20 9.99758·8 9.99747·0 9.99735·4 9.99723·7 9.99712·3 9.99700·8
30 9.99758·0 9.99746·2 9.99734·5 9.99722·8 9.99711·3 9.99699·9
40 9.99757·2 9.99745·4 9.99733·6 9.99722·0 9.99710·4 9.99698·9
50 9.99756·4 9.99744·6 9.99732·8 9.99721·1 9.99709·5 9.99698·0
58 0 9.99755·6 9.99743·8 9.99731·9 9.99720·2 9.99708·6 9.99697·0
10 9.99754·9 9.99742·9 9.99731·0 9.99719·3 9.99707·6 9.99696·1
20 9.99754·1 9.99742·1 9.99730·2 9.99718·4 9.99706·7 9.99695·1
30 9.99753·3 9.99741·3 9.99729·3 9.99717·5 9.99705·8 9.99694·2
40 9.99752·5 9.99740·5 9.99728·5 9.99716·6 9.99704·9 9.99693·2
50 9.99751·7 9.99739·6 9.99727·6 9.99715·7 9.99704·0 9.99692·3
59 0 9.99750·9 9.99738·8 9.99726·8 9.99714·8 9.99703·0 9.99691·3
10 9.99750·1 9.99738·0 9.99725·9 9.99713·9 9.99702·1 9.99690·4
20 9.99749·3 9.99737·1 9.99725·1 9.99713·0 9.99701·2 9.99689·4
30 9.99748·6 9.99736·3 9.99724·2 9.99712·2 9.99700·3 9.99688·4
40 9.99747·8 9.99735·5 9.99723·4 9.99711·3 9.99699·3 9.99687·5
50 9.99747·0 9.99734·7 9.99722·5 9.99710·4 9.99698·4 9.99686·5
60 0 9.99746·2 9.99733·9 9.99721·7 9.99709·5 9.99697·5 9.99685·5
10 9.99745·4 9.99733·0 9.99720·8 9.99708·6 9.99696·6 9.99684·6
20 9.99744·6 9.99732·2 9.99719·9 9.99707·7 9.99695·6 9.99683·6
30 9.99743·8 9.99731·4 9.99719·1 9.99706·8 9.99684·7 9.99682·7
40 9.99743·0 9.99730·6 9.99718·2 9.99706·0 9.99693·8 9.99681·7
50 9.99742·2 9.99729·7 9.99717·4 9.99705·1 9.99692·9 9.99680·8
61 0 9.99741·4 9.99729·0 9.99716·5 9.99704·2 9.99691·2 9.99679·8
10 9.99740·7 9.99728·1 9.99715·7 9.99703·3 9.99691·0 9.99678·8
20 9.99739·9 9.99727·3 9.99714·8 9.99702·4 9.99690·1 9.99677·9
30 9.99739·1 9.99726·5 9.99714·0 9.99701·5 9.99689·1 9.99676·9
40 9.99738·3 9.99725·7 9.99713·1 9.99700·6 9.99688·2 9.99675·9
50 9.99737·5 9.99724·8 9.99712·3 9.99699·7 9.99687·3 9.99675·0
62 0 9.99736·7 9.99724·0 9.99711·4 9.99698·8 9.99686·3 9.99674·0

[page] 22

TABLE IX. Logarithms for readily computing the true Distance of the MOON from the SUN or a Fixed Star.
Horizontal Parallax of the Moon. Apparent Altitude of the Moon's Center.
27° 28° 29° 30° 31° 32°
M S Logarithm. Logarithm. Logarithm. Logarithm. Logarithm. Logarithm.
53 0 9.99715·2 9.99704·8 9.99674·5 9.99684·4 9.99674·3 9.99664·3
10 9.99714·2 9.99703·8 9.99693·5 9.99683·3 9.99673·2 9.99663·2
20 9.99713·2 9.99702·8 9.99692·4 9.99682·2 9.99672·1 9.99662·0
30 9.99712·2 9.99701·7 9.99691·4 9.99681·2 9.99671·0 9.99660·9
40 9.99711·2 9.99700·7 9.99690·3 9.99680·1 9.99669·9 9.99659·8
50 9.99910·2 9.99699·7 9.99689·3 9.99679·0 9.99668·8 9.99658·6
54 0 9.99709·2 9.99698·7 9.99688·2 9.99677·9 9.99667·6 9.99657·5
10 9.99708·3 9.99697·7 9.99687·2 9.99676·8 9.99666·5 9.99656·3
20 9.99707·3 9.99696·6 9.99686·1 9.99675·7 9.99665·4 9.99655·2
30 9.99706·3 9.99695·6 9.99685·1 9.99674·6 9.99664·3 9.99654·0
40 9.99705·3 9.99694·6 9.99684·0 9.99673·5 9.99663·2 9.99652·9
50 9.99704·3 9.99693·6 9.99683·0 9.99672·4 9.99662·0 9.99651·7
55 0 9.99703·3 9.99692·6 9.99681·9 9.99671·3 9.99660·9 9.99650·6
10 9.99702·3 9.99691·5 9.99680·9 9.99670·3 9.99659·8 9.99649·5
20 9.99701·4 9.99690·5 9.99679·8 9.99669·2 9.99658·7 9.99648·3
30 9.99700·4 9.99689·5 9.99678·8 9.99668·1 9.99657·6 9.99647·2
40 9.99699·4 9.99688·5 9.99677·7 9.99667·0 9.99656·4 9.99646·0
50 9.99698·4 9.99687·5 9.99676·7 9.99665·9 9.99655·3 9.99644·9
56 0 9.99697·4 9.99686·4 9.99675·6 9.99664·8 9.99654·2 9.99643·7
10 9.99696·4 9.99685·4 9.99674·6 9.99663·8 9.99653·1 9.99642·6
20 9.99695·4 9.99684·4 9.99673·5 9.99662·7 9.99652·0 9.99641·5
30 9.99694·5 9.99683·4 9.99672·5 9.99661·6 9.99650·8 9.99640·3
40 9.99693·5 9.99682·4 9.99671·4 9.99660·5 9.99649·7 9.99639·1
50 9.99692·5 9.99681·3 9.99670·4 9.99659·4 9.99648·6 9.99638·0
57 0 9.99691·5 9.99680·3 9.99669·3 9.99658·3 9.99647·5 9.99636·8
10 9.99690·5 9.99679·3 9.99668·3 9.99657·3 9.99646·4 9.99635·7
20 9.99689·5 9.99678·3 9.99667·2 9.99656·2 9.99645·2 9.99634·5
30 9.99688·5 9.99677·2 9.99666·2 9.99655·1 9.99644·1 9.99633·4
40 9.99687·6 9.99676·2 9.99665·1 9.99654·0 9.99643·0 9.99632·2
50 9.99686·6 9.99675·2 9.99664·1 9.99652·9 9.99641·9 9.99631·1
58 0 9.99685·6 9.99674·2 9.99663·0 9.99651·8 9.99640·8 9.99629·9
10 9.99684·6 9.99673·1 9.99662·0 9.99650·8 9.99639·6 9.99628·8
20 9.99683·6 9.99672·1 9.99660·9 9.99649·7 9.99638·5 9.99627·6
30 9.99682·6 9.99671·1 9.99659·8 9.99648·6 9.99637·4 9.99226·5
40 9.99681·6 9.99670·1 9.99658·8 9.99647·5 9.99636·3 9.99625·3
50 9.99680·6 9.99669·0 9.99657·7 9.99646·4 9.99635·2 9.99624·2
59 0 9.99679·6 9.99668·0 9.99656·6 9.99645·3 9.99634·0 9.99623·0
10 9.99678·6 9.99667·0 9.99655·6 9.99644·2 9.99632·9 9.99621·9
20 9.99677·6 9.99666·0 9.99654·5 9.99643·1 9.99631·8 9.99620·7
30 9.99676·6 9.99664·9 9.99653·5 9.99642·0 9.99630·7 9.99619·6
40 9.99675·6 9.99663·9 9.99652·4 9.99640·9 9.99629·6 9.99618·4
50 9.99674·6 9.99662·9 9.99651·4 9.99639·8 9.99628·4 9.99617·3
60 0 9.99673·7 9.99661·9 9.99650·3 9.99638·7 9.99627·3 9.99616·1
10 9.99672·7 9.99660·8 9.99649·3 9.99637·7 9.99626·2 9.99615·0
20 9.99671·7 9.99659·8 9.99648·2 9.99636·6 9.99625·1 9.99613·8
30 9.99970·7 9.99658·8 9.99647·1 9.99635·5 9.99624·0 9.99612·6
40 9.99669·7 9.99657·8 9.99646·1 9.99634·4 9.99622·8 9.99611·5
50 9.99668·7 9.99656·7 9.99645·0 9.99633·3 9.99621·7 9.99610·3
61 0 9.99667·7 9.99655·7 9.99643·9 9.99632·2 9.99620·6 9.99609·1
10 9.99666·7 9.99654·7 9.99642·9 9.99631·2 9.99619·5 9.99608·0
20 9.99665·7 9.99653·7 9.99641·8 9.99630·1 9.99618·4 9.99606·8
30 9.99664·7 9.99652·6 9.99640·8 9.99629·0 9.99617·3 9.99605·7
40 9.99663·7 9.99651·6 9.99639·7 9.99627·9 9.99616·1 9.99604·5
50 9.99662·7 9.99650·6 9.99638·6 9.99626·8 9.99615·0 9.99603·4
62 0 9.99661·7 9.99649·6 9.99637·6 9.99625·7 9.99613·9 9.99602·2

[page] 23

TABLE IX. Logarithms for readily computing the true Distance of the MOON from the SUN or a Fixed Star.
Horizontal Parallax of the Moon. Apparent Altitude of the Moon's Center.
33° 34° 35° 36° 37° 38°
M S Logarithm. Logarithm. Logarithm. Logarithm. Logarithm. Logarithm.
53 0 9.99654·5 9.99644·7 9.99635·1 9.99625·6 9.99616·2 9.99606·9
10 9.99653·3 9.99643·5 9.99633·9 9.99624·3 9.99614·9 9.99605·6
20 9.99652·1 9.99642·3 9.99632·6 9.99623·1 9.99613·6 9.99604·2
30 9.99651·0 9.99641·1 9.99631·4 9.99621·8 9.99612·3 9.99602·9
40 9.99649·8 9.99639·9 9.99630·2 9.99620·5 9.99611·0 9.99601·6
50 9.99648·6 9.99638·6 9.99628·9 9.99619·3 9.99609·7 9.99600·3
54 0 9.99647·4 9.99637·4 9.99627·7 9.99618·0 9.99608·4 9.99598·9
10 9.99646·2 9.99636·2 9.99626·4 9.99616·7 9.99607·1 9.99597·6
20 9.99645·0 9.99635·0 9.99625·2 9.99615·4 9.99605·8 9.99596·3
30 9.99643·8 9.99633·8 9.99623·9 9.99614·2 9.99604·5 9.99595·0
40 9.99642·7 9.99632·6 9.99622·7 9.99612·9 9.99603·2 9.99593·6
50 9.99641·5 9.99631·4 9.99621·4 9.99611·6 9.99601·9 9.99592·3
55 0 9.99640·3 9.99630·2 9.99620·2 9.99310·3 9.99600·6 9.99591·0
10 9.99639·1 9.99628·9 9.99619·0 9.99609·1 9.99599·3 9.99589·6
20 9.99637·9 9.99627·7 9.99617·7 9.99607·8 9.99598·0 9.99588·3
30 9.99636·8 9.99626·5 9.99616·5 9.99606·5 9.99596·7 9.99587·0
40 9.99635·6 9.99625·3 9.99615·3 9.99605·2 9.99595·4 9.99585·6
50 9.99634·4 9.99624·1 9.99614·0 9.99604·0 9.99594·1 9.99584·3
56 0 9.99633·2 9.99622·9 9.99612·8 9.99602·7 9.99592·8 9.99583·0
10 9.99632·1 9.99621·7 9.99611·5 9.99601·4 9.99591·5 9.99581·6
20 9.99630·9 9.99620·5 9.99610·3 9.99600·2 9.99590·2 9.99580·3
30 9.99629·7 9.99619·3 9.99609·0 9.99598·9 9.99588·9 9.99579·0
40 9.99628·5 9.99518·1 9.99607·8 9.99597·6 9.99587·6 9.99577·6
50 9.99627·3 9.99616·9 9.99606·5 9.99596·3 9.99586·3 9.99576·3
57 0 9.99626·2 9.99615·7 9.99605·3 9.99595·1 9.99585·0 9.99575·0
10 9.99625·0 9.99614·4 9.99604·1 9.99593·8 9.99583·7 9.99573·6
20 9.99623·8 9.99613·2 9.99602·8 9.99592·6 9.99582·4 9.99572·3
30 9.99622·6 9.99612·0 9.99601·6 9.99591·3 9.99581·1 9.99571·0
40 9.99621·4 9.99610·8 9.99600·3 9.99590·0 9.99579·8 9.99569·6
50 9.99620·3 9.99609·6 9.99599·1 9.99588·7 9.99578·5 9.99568·3
58 0 9.99619·1 9.99608·4 9.99597·9 9.99587·5 9.99577·2 9.99567·0
10 9.99617·9 9.99607·2 9.99596·6 9.99586·2 9.99575·9 9.99565·6
20 9.99616·7 9.99606·0 9.99595·4 9.99584·9 9.99574·6 9.99564·3
30 9.99615·5 9.99604·7 9.99594·1 9.99583·6 9.99573·3 9.99563·0
40 9.99614·4 9.99603·5 9.99592·9 9.99582·4 9.99572·0 9.99561·6
50 9.99613·2 9.99602·3 9.99591·6 9.99581·1 9.99570·7 9.99560·3
59 0 9.99612·0 9.99601·1 9.99590·4 9.99579·8 9.99569·4 9.99559·0
10 9.99610·8 9.99599·9 9.99589·2 9.99578·5 9.99568·0 9.99557·6
20 9.99609·6 9.99598·7 9.99587·9 9.99577·3 9.99566·7 9.99556·3
30 9.99608·5 9.99597·5 9.99586·7 9.99576·0 9.99565·4 9.99555·0
40 9.99607·3 9.99596·3 9.99585·5 9.99574·7 9.99564·1 9.99553·6
50 9.99606·1 9.99595·1 9.99584·2 9.99573·5 9.99562·8 9.99552·3
60 0 9.99604·9 9.99593·9 9.99583·0 9.99572·2 9.99561·5 9.99551·0
10 9.99603·7 9.99592·6 9.99581·7 9.99570·9 9.99560·2 9.99549·6
20 9.99602·5 9.99591·4 9.99580·5 9.99569·6 9.99558·9 9.99548·3
30 9.99601·4 9.99590·2 9.99579·2 9.99568·4 9.99557·6 9.99547·0
40 9.99600·2 9.99589·0 9.99578·0 9.99567·1 9.99556·3 9.99545·6
50 9.99599·0 9.99587·8 9.99576·7 9.99565·8 9.99555·0 9.99544·3
61 0 9.99597·8 9.99586·6 9.99575·5 9.99564·5 9.99553·7 9.99543·0
10 9.99596·6 9.99585·3 9.99574·2 9.99563·3 9.99552·4 9.99541·6
20 9.99595·4 9.99584·1 9.99573·0 9.99562·0 9.99551·1 9.99540·3
30 9.99594·3 9.99582·9 9.99571·7 9.99560·7 9.99549·8 9.99539·0
40 9.99593·1 9.99581·7 9.99570·5 9.99559·4 9.99548·5 9.99537·6
50 9.99591·9 9.99580·5 9.99569·2 9.99558·2 9.99547·2 9.99536·3
62 0 9.99590·7 9.99579·3 9.99568·0 9.99556·9 9.99545·9 9.99535·0

[page] 24

TABLE IX. Logarithms for readily computing the true Distance of the MOON from the SUN or a Fixed Star.
Horizontal Parallax of the Moon. Apparent Altitude of the Moon's Center.
39° 40° 41° 42° 43° 44°
M S Logarithm. Logarithm. Logarithm. Logarithm. Logarithm. Logarithm.
53 0 9.99597·7 9.99588·7 9.99579·8 9.99571·1 9.99562·5 9.99554·0
10 9.99596·4 9.99587·3 9.99578·4 9.99569·7 9.99561·0 9.99552·5
20 9.99595·0 9.99585·9 9.99577·0 9.99568·2 9.99559·5 9.99551·0
30 9.99593·7 9.99584·6 9.99575·6 9.99566·8 9.99558·1 9.99549·5
40 9.99592·3 9.99583·2 9.99574·1 9.99565·3 9.99556·6 9.99548·0
50 9.99591·0 9.99581·8 9.99572·7 9.99563·9 9.99555·1 9.99546·5
54 0 9.99589·6 9.99580·4 9.99571·3 9.99562·4 9.99553·6 9.99545·0
10 9.99588·3 9.99579·0 9.99569·9 9.99561·0 9.99552·2 9.99543·5
20 9.99586·9 9.99577·6 9.99568·5 9.99559·6 9.99550·7 9.99542·0
30 9.99585·6 9.99576·2 9.99567·1 9.99558·1 9.99549·2 9.99540·5
40 9.99584·2 9.99574·8 9.99565·7 9.99556·7 9.99547·8 9.99539·0
50 9.99582·9 9.99573·5 9.99564·3 9.99555·2 9.99546·3 9.99537·5
55 0 9.99581·5 9.99572·1 9.99562·8 9.99553·8 9.99544·8 9.99536·0
10 9.99580·1 9.99570·7 9.99561·4 9.99552·3 9.99543·4 9.99534·5
20 9.99578·8 9.99569·3 9.99560·0 9.99550·9 9.99541·9 9.99533·1
30 9.99577·4 9.99567·9 9.99558·6 9.99549·4 9.99540·4 9.99531·6
40 9.99576·1 9.99566·5 9.99557·2 9.99548·0 9.99539·0 9.99530·1
50 9.99574·7 9.99565·2 9.99555·8 9.99546·5 9.99537·5 9.99528·6
56 0 9.99573·3 9.99563·8 9.99554·4 9.99545·1 9.99536·0 9.99527·1
10 9.99572·0 9.99562·4 9.99552·9 9.99543·7 9.99534·6 9.99525·6
20 9.99570·6 9.99561·0 9.99551·5 9.99542·2 9.99533·1 9.99524·1
30 9.99569·3 9.99559·6 9.99550·1 9.99540·8 9.99531·6 9.99522·6
40 9.99567·9 9.99558·2 9.99548·7 9.99539·4 9.99530·2 9.99521·1
50 9.99566·6 9.99556·8 9.99547·3 9.99537·9 9.99528·7 9.99519·5
57 0 9.99565·2 9.99555·4 9.99545·9 9.99536·5 9.99527·2 9.99518·1
10 9.99563·8 9.99554·1 9.99544·4 9.99535·0 9.99525·8 9.99516·6
20 9.99562·5 9.99552·7 9.99543·0 9.99533·6 9.99524·3 9.99515·1
30 9.99561·1 9.99551·3 9.99541·6 9.99532·1 9.99522·8 9.99513·6
40 9.99559·7 9.99549·9 9.99540·2 9.99530·7 9.99521·4 9.99512·1
50 9.99558·4 9.99548·5 9.99538·8 9.99529·2 9.99519·9 9.99510·6
58 0 9.99557·0 9.99547·1 9.99537·4 9.99527·8 9.99518·4 9.99509·1
10 9.99555·6 9.99545·7 9.99535·9 9.99526·3 9.99516·9 9.99507·6
20 9.99554·3 9.99544·3 9.99534·5 9.99524·9 9.99515·5 9.99506·1
30 9.99552·9 9.99542·9 9.99533·1 9.99523·4 9.99514·0 9.99504·6
40 9.99551·6 9.99541·6 9.99531·7 9.99522·0 9.99512·5 9.99503·1
50 9.99550·2 9.99540·2 9.99530·3 9.99520 5 9.99511·0 9.99501·6
59 0 9.99548·8 9.99538·8 9.99528·9 9.99519·1 9.99509·5 9.99500·1
10 9.99547·5 9.99537·4 9.99527·4 9.99517·7 9.99508·1 9.99498·6
20 9.99546·1 9.99536·0 9.99526·0 9.99516·3 9.99506·6 9.99497·1
30 9.99544·7 9.99534·6 9.99524·6 9.99514·8 9.99505·1 9.99495·6
40 9.99543·4 9.99533·2 9.99523·2 9.99513·4 9.99503·7 9.99494·1
50 9.99542·0 9.99531·8 9.99521·8 9.99511·9 9.99502·2 9.99492·6
60 0 9.99540·7 9.99530·4 9.99520·4 9.99510·5 9.99500·7 9.99491·1
10 9.99539·3 9.99529·1 9.99518·9 9.99509·0 9.99499·3 9.99489·6
20 9.99537·9 9.99527·7 9.99517·5 9.99507·6 9.99497·8 9.99488·1
30 9.99536·6 9.99526·3 9.99516·1 9.99506·1 9.99496·3 9.99486·6
40 9.99535·2 9.99524·9 9.99514·7 9.99504·7 9.99494·9 9.99485·1
50 9.99533·8 9.99523·5 9.99513·3 9.99503·2 9.99493·4 9.99483·6
61 0 9.99532·5 9.99522·1 9.99511·9 9.99501·8 9.99491·9 9.99482·1
10 9.99531·1 9.99520·7 9.99510·4 9.99500·3 9.99490·4 9.99480·6
20 9.99529·7 9.99519·3 9.99509·0 9.99498·9 9.99489·0 9.99479·1
30 9.99528·4 9.99518·0 9.99507·6 9.99497·4 9.99487·5 9.99477·6
40 9.99527·0 9.99516·6 9.99506·2 9.99496·0 9.99486·0 9.99476·1
50 9.99525·6 9.99515·2 9.99504·8 9.99494·5 9.99484·5 9.99474·6
62 0 9.99524·3 9.99513·8 9.99503·3 9.99493·1 9.99483·0 9.99473·1

[page] 25

TABLE IX. Logarithms for readily computing the true Distance of the MOON from the SUN or a Fixed Star.
Horizontal Parallax of the Moon. Apparent Altitude of the Moon's Center.
45° 46° 47° 48° 49° 50°
M S Logarithm. Logarithm. Logarithm. Logarithm. Logarithm. Logarithm.
53 0 9.99545·6 9.99537·4 9.99529·4 9.99521·5 9.99513·7 9.99506·1
10 9.99544·1 9.99535·9 9.99527·9 9.99519·9 9.99512·1 9.99504·5
20 9.99542·6 9.99534·4 9.99526·3 9.99518·3 9.99510·5 9.99502·8
30 9.99541·0 9.99532·8 9.99524·7 9.99516·7 9.99508·9 9.99501·2
40 9.99539·5 9.99531·3 9.99523·1 9.99515·1 9.99507·2 9.99499·5
50 9.99538·0 9.99529·8 9.99521·6 9.99513·5 9.99505·6 9.99497·9
54 0 9.99536·5 9.99528·2 9.99520·0 9.99511·9 9.99504·0 9.99496·2
10 9.99535·0 9.99526·7 9.99518·4 9.99510·3 9.99502·4 9.99494·6
20 9.99533·4 9.99525·1 9.99516·8 9.99508·7 9.99500·8 9.99493·0
30 9.99531·9 9.99523·6 9.99515·3 9.99507·1 9.99499·1 9.99491·3
40 9.99530·4 9.99522·0 9.99513·7 9.99505·5 9.99497·5 9.99489·7
50 9.99528·9 9.99520·5 9.99512·1 9.99503·9 9.99495·9 9.99488·0
55 0 9.99527·4 9.99518·9 9.99510·5 9.99502·3 9.99494·3 9.99486·4
10 9.99525·8 9.99517·4 9.99508·9 9.99500·7 9.99492·6 9.99484·7
20 9.99524·3 9.99515·8 9.99507·4 9.99499·1 9.99491·0 9.99483·1
30 9.99522·8 9.99514·3 9.99505·8 9.99497·5 9.99489·4 9.99481·4
40 9.99521·3 9.99512·7 9.99504·2 9.99495·9 9.99487·8 9.99479·8
50 9.99519·7 9.99511·2 9.99502·6 9.99494·3 9.99486·1 9.99478·1
56 0 9.99518·2 9.99509·6 9.99501·1 9.99492·7 9.99484·5 9.99476·5
10 9.99516·7 9.99508·0 9.99499·5 9.99491·1 9.99482·9 9.99474·8
20 9.99515·2 9.99506·5 9.99497·9 9.99489·5 9.99481·3 9.99473·2
30 9.99513·6 9.99504·9 9.99496·4 9.99487·9 9.99479·6 9.99471·5
40 9.99512·1 9.99503·4 9.99494·8 9.99486·3 9.99478·0 9.99469·9
50 9.99510·6 9.99501·8 9.99493·2 9.99484·7 9.99476·4 9.99468·2
57 0 9.99509·1 9.99500·3 9.99491·6 9.99483·1 9.99474·8 9.99466·6
10 9.99507·6 9.99498·7 9.99490·1 9.99481·5 9.99473·1 9.99464·9
20 9.99506·0 9.99497·2 9.99488·5 9.99479·9 9.99471·5 9.99463·3
30 9.99504·5 9.99495·6 9.99486·9 9.99478·3 9.99469·9 9.99461·6
40 9.99503·0 9.99494·1 9.99485·3 9.99476·7 9.99468·3 9.99460·0
50 9.99501·5 9.99492·5 9.99483·7 9.99475·1 9.99466·6 9.99458·3
58 0 9.99500·0 9.99491·0 9.99482·2 9.99473·5 9.99465·0 9.99456·7
10 9.99498·4 9.99489·4 9.99480·6 9.99471·9 9.99463·4 9.99455·0
20 9.99496·9 9.99487·9 9.99479·0 9.99470·3 9.99461·8 9.99453·4
30 9.99495·4 9.99486·3 9.99477·5 9.99468·7 9.99400·1 9.99451·7
40 9.99493·9 9.99484·8 9.99475·9 9.99467·1 9.99458·5 9.99450·1
50 9.99492·3 9.99483·2 9.99474·3 9.99465·5 9.99456·9 9.99448·4
59 0 9.99490·8 9.99481·7 9.99472·7 9.99463·9 9.99455·3 9.99446·8
10 9.99489·3 9.99470·1 9.99471·2 9.99462·3 9.99453·6 9.99445·1
20 9.99487·8 9.99478·6 9.99469·6 9.99460·7 9.99452·0 9.99443·5
30 9.99486·2 9.99477·0 9.99468·0 9.99459·1 9.99450·4 9.99441·8
40 9.99484·7 9.99475·5 9.99466·5 9.99457·5 9.99448·8 9.99440·2
50 9.99483·2 9.99473·9 9.99464·9 9.99455·9 9.99447·2 9.99438·5
60 0 9.99481·7 9.99472·4 9.99493·3 9.99454·3 9.99445·5 9.99436·9
10 9.99480·1 9.99470·8 9.99461·7 9.99452·7 9.99443·9 9.99435·2
20 9.99478·6 9.99469·3 9.99460·1 9.99451·1 9.99442·3 9.99433·6
30 9.99477·1 9.99467·7 9.99458·6 9.99449·5 9.99440·7 9.99431·9
40 9.99475·6 9.99466·2 9.99457·0 9.99447·9 9.99439·0 9.99430·3
50 9.99474·0 9.99464·6 9.99455·4 9.99446·3 9.99437·4 9.99428·6
61 0 9.99472·5 9.99463·1 9.99453·8 9.99444·7 9.99435·8 9.99427·0
10 9.99471·0 9.99461·5 9.99452·3 9.99443·1 9.99434·2 9.99425·3
20 9.99469·5 9.99460·0 9.99450·7 9.99441·5 9.99432·5 9.99423·7
30 9.99467·9 9.99458·4 9.99449·1 9.99439·9 9.99430·9 9.99422·0
40 9.99466·4 9.99456·9 9.99447·6 9.99438·3 9.99429·3 9.99420·4
50 9.99464·9 9.99455·3 9.99446·0 9.99436·7 9.99427·7 9.99418·7
62 0 9.99463·4 9.99453·8 9.99444·4 9.99435·1 9.99426·0 9.99417·1

D

[page] 26

TABLE IX. Logarithms for readily computing the true Distance of the MOON from the SUN or a Fixed Star.
Horizontal Parallax of the Moon. Apparent Altitude of the Moon's Center.
51° 52° 53° 54° 55° 56°
M S Logarithm. Logarithm. Logarithm. Logarithm. Logarithm. Logarithm.
53 0 9.99498·6 9.99491·3 9.99484·2 9.99477·3 9.99470·5 9.99463·9
10 9.99496·9 9.99489·6 9.99482·5 9.99475·6 9.99468·7 9.99462·1
20 9.99495·2 9.99487·9 9.99480·8 9.99473·8 9.99467·0 9.99460·3
30 9.99493·6 9.99486·2 9.99479·1 9.99472·1 9.99465·2 9.99458·6
40 9.99491·9 9.99484·6 9.99477·4 9.99470·3 9.99463·5 9.99456·8
50 9.99490·2 9.99482·9 9.99475·7 9.99468·6 9.99461·7 9.99455·0
54 0 9.99488·6 9.99481·2 9.99473·9 9.99466·8 9.99459·9 9.99453·2
10 9.99486·9 9.99479·5 9.99472·2 9.99465·1 9.99458·2 9.99451·4
20 9.99485·2 9.99477·8 9.99470·5 9.99463·4 9.99456·4 9.99449·6
30 9.99483·6 9.99476·1 9.99468·8 9.99461·6 9.99454·7 9.99447·9
40 9.99481·7 9.99474·4 9.99467·1 9.99459·9 9.99452·9 9.99446·1
50 9.99480·2 9.99472·7 9.99465·4 9.99458·2 9.99451·2 9.99444·3
55 0 9.99478·6 9.99471·0 9.99463·7 9.99456·4 9.99449·4 9.99442·5
10 9.99476·9 9.99469·3 9.99461·9 9.99454·7 9.99447·6 9.99440·8
20 9.99475·2 9.99467·6 9.99460·2 9.99453·0 9.99445·9 9.99439·0
30 9.99473·6 9.99466·0 9.99458·5 9.99451·2 9.99444·1 9.99437·2
40 9.99471·9 9.99464·3 9.99456·8 9.99449·5 9.99442·3 9.99435·4
50 9.99470·2 9.99462·6 9.99455·1 9.99447·8 9.99440·6 9.99433·7
56 0 9.99468·6 9.99460·9 9.99453·4 9.99446·0 9.99438·8 9.99431·9
10 9.99466·9 9.99459·2 9.99451·6 9.99444·3 9.99437·1 9.99430·1
20 9.99465·2 9.99457·5 9.99449·9 9.99442·5 9.99435·3 9.99428·3
30 9.99463·6 9.99455·8 9.99448·2 9.99440·8 9.99433·6 9.99426·5
40 9.99461·9 9.99454·1 9.99446·5 9.99439·1 9.99431·8 9.99424·7
50 9.99460·2 9.99452·4 9.99444·8 9.99437·3 9.99430·1 9.99423·0
57 0 9.99458·6 9.99450·7 9.99443·1 9.99435·6 9.99428·3 9.99421·2
10 9.99456·9 9.99449·0 9.99441·4 9.99433·9 9.99426·5 9.99419·4
20 9.99455·2 9.99447·3 9.99439·6 9.99432·1 9.99424·8 9.99417·6
30 9.99453·6 9.99445·7 9.99437·9 9.99430·4 9.99423·0 9.99415·8
40 9.99451·9 9.99444·0 9.99436·2 9.99428·7 9.99421·3 9.99414·0
50 9.99450·2 9.99442·3 9.99434·5 9.99426·9 9.99419·5 9.99412·3
58 0 9.99448·6 9.99440·6 9.99432·8 9.99425·2 9.99417·7 9.99410·5
10 9.99446·9 9.99438·9 9.99431·1 9.99423·4 9.99416·0 9.99408·7
20 9.99445·2 9.99437·2 9.99429·4 9.99421·7 9.99414·2 9.99406·9
30 9.99443·6 9.99435·5 9.99427·6 9.99420·0 9.99412·5 9.99405·1
40 9.99441·9 9.99433·8 9.99425·9 9.99418·2 9.99410·7 9.99403·3
50 9.99440·2 9.99432·1 9.99424·2 9.99416·5 9.99409·0 9.99401·6
59 0 9.99438·5 9.99430·4 9.99422·5 9.99414·7 9.99407·2 9.99399·8
10 9.99436·9 9.99428·7 9.99420·8 9.99413·0 9.99405·4 9.99398·0
20 9.99435·2 9.99427·0 9.99419·1 9.99411·2 9.99403·7 9.99396·2
30 9.99433·5 9.99425·3 9.99417·4 9.99409·5 9.99401·9 9.99394·4
40 9.99431·9 9.99423·6 9.99415·6 9.99407·8 9.99400·2 9.99392·7
50 9.99430·2 9.99421·9 9.99413·9 9.99406·0 9.99398·4 9.99390·9
60 0 9.99428·5 9.99420·2 9.99412·2 9.99404·3 9.99396·6 9.99389·1
10 9.99426·9 9.99418·5 9.99410·5 9.99402·6 9.99394·9 9.99387·3
20 9.99425·2 9.99416·8 9.99408·8 9.99400·8 9.99393·1 9.99385·5
30 9.99423·5 9.99415·2 9.99407·1 9.99399·1 9.99391·3 9.99383·7
40 9.99421·9 9.99413·5 9.99405·4 9.99397·4 9.99389·6 9.99382·0
50 9.99420·2 9.99411·8 9.99403·6 9.99395·6 9.99387·8 9.99380·2
61 0 9.99418·5 9.99410·1 9.99401·9 9.99393·9 9.99386·0 9.99378·4
10 9.99416·8 9.99408·4 9.99400·2 9.99392·1 9.99384·3 9.99376·6
20 9.99415·2 9.99406·7 9.99398·5 9.99390·4 9.99382·5 9.99374·8
30 9.99413·5 9.99405·0 9.99396·8 9.99388·6 9.99380·8 9.99373·1
40 9.99411·8 9.99403·3 9.99395·1 9.99386·9 9.99379·0 9.99371·3
50 9.99410·1 9.99401·6 9.99393·4 9.99385·1 9.99377·3 9.99369·5
62 0 9.99408·4 9.99399·9 9.99391·6 9.99383·4 9.99375·5 9.99367·7

[page] 27

TABLE IX. Logarithms for readily computing the true Distance of the MOON from the SUN or a Fixed Star.
Horizontal Parallax of the Moon. Apparent Altitude of the Moon's Center.
57° 58° 59° 60° 61° 62°
M S Logarithm. Logarithm. Logarithm. Logarithm. Logarithm. Logarithm.
53 0 9.99457·4 9.99451·2 9.99445·1 9.99439·2 9.99433·5 9.99427·9
10 9.99455·6 9.99449·4 9.99443·2 9.99437·4 9.99431·6 9.99426·0
20 9.99453·8 9.99447·6 9.99441·4 9.99435·5 9.99429·7 9.99424·1
30 9.99452·0 9.99445·8 9.99439·6 9.99433·7 9.99427·9 9.99422·2
40 9.99450·2 9.99443·9 9.99437·7 9.99431·8 9.99426·0 9.99420·3
50 9.99448·4 9.99442·1 9.99435·9 9.99430·0 9.99424·1 9.99418·4
54 0 9.99446·6 9.99440·3 9.99434·1 9.99428·1 9.99422·2 9.99416·5
10 9.99444·8 9.99438·5 9.99432·2 9.99426·3 9.99420·4 9.99414·6
20 9.99443·0 9.99436·6 9.99430·4 9.99424·4 9.99418·5 9.99412·7
30 9.99441·2 9.99434·8 9.99428·5 9.99422·5 9.99416·6 9.99410·9
40 9.99439·4 9.99433·0 9.99426·7 9.99420·7 9.99414·7 9.99409·0
50 9.99437·6 9.9941·2 9.99424·9 9.99418·8 9.99412·9 9.99407·1
55 0 9.99435·8 9.99429·4 9.99423·0 9.99416·9 9.99411·0 9.99405·2
10 9.99434·0 9.99427·5 9.99421·2 9.99415·1 9.99409·1 9.99403·3
20 9.99432·2 9.99425·7 9.99419·4 9.99413·2 9.99407·2 9.99401·4
30 9.99430·4 9.99423·9 9.99417·5 9.99411·4 9.99405·4 9.99399·5
40 9.99428·6 9.99422·1 9.99415·7 9.99409·5 9.99403·5 9.99397·6
50 9.99426·8 9.99420·3 9.99413·9 9.99407·7 9.99401·6 9.99395·7
56 0 9.99425·0 9.99418·4 9.99412·0 9.99405·8 9.99399·7 9.99393·8
10 9.99423·2 9.99416·6 9.99410·2 9.99403·9 9.99397·8 9.99391·9
20 9.99421·4 9.99414·8 9.99408·3 9.99402·1 9.99395·9 9.99390·0
30 9.99419·6 9.99413·0 9.99406·5 9.99400·2 9.99394·0 9.99388·2
40 9.99417·8 9.99411·2 9.99404·6 9.99398·4 9.99392·2 9.99386·3
50 9.99416·0 9.99409·3 9.99400·8 9.99396·5 9.99390·3 9.99384·4
57 0 9.99414·2 9.99407·5 9.99400·9 9.99394·6 9.99388·5 9.99382·5
10 9.99412·4 9.99405·7 9.99399·1 9.99392·8 9.99386·6 9.99380·6
20 9.99410·6 9.99403·9 9.99397·3 9.99390·9 9.99384·7 9.99378·7
30 9.99408·8 9.99402·1 9.99395·4 9.99389·1 9.99382·8 9.99376·8
40 9.99407·0 9.99400·2 9.99393·6 9.99387·2 9.99381·0 9.99374·9
50 9.99405·2 9.99398·4 9.99391·8 9.99385·4 9.99379·1 9.99373·0
58 0 9.99403·4 9.99396·6 9.99389·9 9.99383·5 9.99377·2 9.99371·1
10 9.99401·6 9.99394·8 9.99388·1 9.99381·6 9.99375·3 9.99369·2
20 9.99399·8 9.99393·0 9.99386·3 9.99379·8 9.99373·5 9.99367·3
30 9.99398·0 9.99391·1 9.99384·4 9.99377·9 9.99371·6 9.99365·4
40 9.99396·2 9.99389·3 9.99382·6 9.99376·0 9.99369·7 9.99363·5
50 9.99394·4 9.99387·5 9.99380·8 9.99374·2 9.99367·8 9.99361·6
59 0 9.99392·6 9.99385·7 9.99378·9 9.99372·3 9.99366·0 9.99359·7
10 9.99390·8 9.99383·9 9.99377·1 9.99370·5 9.99364·1 9.99357·9
20 9.99389·0 9.99382·0 9.99375·3 9.99368·6 9.99362·2 9.99356·0
30 9.99387·2 9.99380·2 9.99373·4 9.99366·8 9.99360·3 9.99354·1
40 9.99385·4 9.99378·4 9.99371·6 9.99364·9 9.99358·4 9.99352·2
50 9.99383·6 9.99376·6 9.99369·7 9.99363·0 9.99356·6 9.99350·3
60 0 9.99381·8 9.99374·8 9.99367·9 9.99361·2 9.99354·7 9.99348·4
10 9.99380·0 9.99372·9 9.99366·0 9.99359·3 9.99352·8 9.99346·5
20 9.99378·2 9.99371·1 9.99364·2 9.99357·4 9.99350·9 9.99344·6
30 9.99376·4 9.99369·3 9.99362·3 9.99355·6 9.99349·0 9.99342·7
40 9.99374·6 9.99367·5 9.99360·5 9.99353·7 9.99347·1 9.99340·8
50 9.99372·8 9.99365·7 9.99358·7 9.99351·8 9.99345·3 9.99338·9
61 0 9.99371·0 9.99363·8 9.99356·8 9.99350·0 9.99343·4 9.99337·0
10 9.99369·2 9.99362·0 9.99355·0 9.99348·1 9.99341·5 9.99335·1
20 9.99367·4 9.99360·2 9.99353·2 9.99346·2 9.99339·6 9.99333·2
30 9.99365·6 9.99358·4 9.99351·3 9.99344·4 9.99337·8 9.99331·3
40 9.99363·8 9.99356·6 9.99349·5 9.99342·5 9.99335·9 9.99329·4
50 9.99362·0 9.99354·8 9.99347·7 9.99340·6 9.99334·0 9.99327·5
62 0 9.99360·2 9.99352·9 9.99345·8 9.99338·8 9.99332·1 9.99325·6

D 2

[page] 28

TABLE IX. Logarithms for readily computing the true Distance of the MOON from the SUN or a Fixed Star.
Horizontal Parallax of the Moon. Apparent Altitude of the Moon's Center.
63° 64° 65° 66° 67° 68°
M S Logarithm. Logarithm. Logarithm. Logarithm. Logarithm. Logarithm.
53 0 9.99422·4 9.99417·2 9.99412·1 9.99407·3 9.99402·7 9.99398·2
10 9.99410·5 9.99415·3 9.99410·2 9.99405·3 9.99400·7 9.99396·2
20 9.99418·6 9.99413·4 9.99408·3 9.99403·4 9.99398·7 9.99394·2
30 9.99416·7 9.99411·4 9.99406·3 9.99401·4 9.99396·8 9.99392·2
40 9.99414·8 9.99409·5 9.99404·4 9.99399·5 9.99394·8 9.99390·2
50 9.99412·9 9.99407·6 9.99402·5 9.99397·5 9.99392·8 9.99388·2
54 0 9.99411·0 9.99405·7 9.99400·5 9.99395·6 9.99390·8 9.99386·2
10 9.99409·1 9.99403·8 9.99398·6 9.99393·6 9.99388·9 9.99384·3
20 9.99407·2 9.99401·8 9.99396·6 9.99391·7 9.99386·9 9.99382·3
30 9.99405·3 9.99399·9 9.99394·7 9.99389·7 9.99384·9 9.99380·3
40 9.99403·4 9.99398·0 9.99392·7 9.99387·7 9.99383·0 9.99378·3
50 9.99401·5 9.99396·1 9.99390·8 9.99385·8 9.99381·0 9.99376·3
55 0 9.99399·6 9.99394·1 9.99388·8 9.99383·8 9.99379·0 9.99374·3
10 9.99397·7 9.99392·2 9.99386·9 9.99381·9 9.99377·0 9.99372·4
20 9.99395·7 9.99390·3 9.99385·0 9.99379·9 9.99375·1 9.99370·4
30 9.99393·8 9.99388·4 9.99383·0 9.99378·0 9.99373·1 9.99368·4
40 9.99391·9 9.99386·4 9.99381·1 9.99376·0 9.99371·1 9.99366·4
50 9.99390·0 9.99384·5 9.99379·1 9.99374·0 9.99369·2 9.99364·4
56 0 9.99388·1 9.99382·6 9.99377·2 9.99372·1 9.99367·2 9.99362·4
10 9.99386·2 9.99380·7 9.99375·3 9.99370·1 9.99365·2 9.99360·5
20 9.99384·3 9.99378·7 9.99373·3 9.99368·2 9.99363·2 9.99358·5
30 9.99382·4 9.99376·8 9.99371·4 9.99366·2 9.99361·3 9.99356·5
40 9.99380·5 9.99374·9 9.99369·5 9.99364·2 9.99359·3 9.99354·5
50 9.99378·6 9.99373·0 9.99367·5 9.99362·3 9.99357·3 9.99352·5
57 0 9.99376·6 9.99371·0 9.99365·6 9.99360·3 9.99355·3 9.99350·5
10 9.99374·7 9.99369·1 9.99363·6 9.99358·4 9.99353·4 9.99348·6
20 9.99372·8 9.99367·2 9.99361·7 9.99356·4 9.99351·4 9.99346·6
30 9.99370·9 9.99365·2 9.99359·8 9.99354·5 9.99349·4 9.99344·6
40 9.99369·0 9.99363·3 9.99357·8 9.99352·5 9.99347·4 9.99342·6
50 9.99367·1 9.99361·4 9.99355·9 9.99350·5 9.99345·5 9.99340·6
58 0 9.99365·2 9.99359·4 9.99353·9 9.99348·6 9.99343·5 9.99338·6
10 9.99363·2 9.99357·5 9.99352·0 9.99346·6 9.99341·5 9.99336·6
20 9.99361·3 9.99355·6 9.99350·0 9.99344·7 9.99339·6 9.99334·6
30 9.99359·4 9.99353·7 9.99348·1 9.99342·7 9.99337·6 9.99332·7
40 9.99357·5 9.99351·7 9.99346·1 9.99340·7 9.99335·6 9.99330·7
50 9.99335·6 9.99349·8 9.99344·2 9.99338·8 9.99333·6 9.99328·7
59 0 9.99353·7 9.99347·9 9.99342·2 9.99336·8 9.99331·7 9.99326·7
10 9.99351·8 9.99345·9 9.99340·3 9.99334·9 9.99329·7 9.99324·7
20 9.99349·8 9.99344·0 9.99338·4 9.99332·9 9.99327·7 9.99322·7
30 9.99347·9 9.99342·1 9.99336·4 9.99331·0 9.99325·8 9.99320·7
40 9.99346·0 9.99340·2 9.99334·5 9.99329·0 9.99323·8 9.99318·7
50 9.99344·1 9.99338·2 9.99332·5 9.99327·0 9.99321·8 9.99316·7
60 0 9.99342·2 9.99336·3 9.99330·6 9.99325·1 9.99319·8 9.99314·7
10 9.99340·3 9.99334·4 9.99328·6 9.99323·1 9.99317·9 9.99312·8
20 9.99338·4 9.99332·4 9.99326·7 9.99321·2 9.99315·9 9.99310·8
30 9.99336·5 9.99330·5 9.99324·8 9.99319·2 9.99313·9 9.99308·8
40 9.99334·6 9.99328·6 9.99322·8 9.99317·2 9.99311·9 9.99306·8
50 9.99332·7 9.99326·7 9.99320·9 9.99315·3 9.99310·0 9.99304·8
61 0 9.99330·8 9.99324·7 9.99318·9 9.99313·3 9.99308·0 9.99302·8
10 9.99328·9 9.99322·8 9.99317·0 9.99311·4 9.99306·0 9.99300·8
20 9.99327·0 9.99320·9 9.99315·0 9.99309·4 9.99304·0 9.99298·8
30 9.99325·0 9.99318·9 9.99313·1 9.99307·5 9.99302·1 9.99296·8
40 9.99323·1 9.99317·0 9.99311·1 9.99305·5 9.99300·1 9.99294·8
50 9.99321·2 9.99315·1 9.99309·2 9.99303·5 9.99298·1 9.99292·8
62 0 9.99319·3 9.99313·1 9.99307·2 9.99301·6 9.99296·1 9.99290·8

[page] 29

TABLE IX. Logarithms for readily computing the true Distance of the MOON from the SUN or a Fixed Star.
Horizontal Parallax of the Moon. Apparent Altitude of the Moon's Center.
69° 70° 71° 72° 73° 74°
M S Logarithm. Logarithm. Logarithm. Logarithm. Logarithm. Logarithm.
53 0 9.99393·9 9.99389·8 9.99385·8 9.99382·2 9.99378·8 9.99375·3
10 9.99391·9 9.99387·8 9.99383·8 9.99380·2 9.99376·7 9.99373·2
20 9.99389·9 9.99385·8 9.99381·7 9.99378·1 9.99374·6 9.99371·2
30 9.99387·9 9.99383·8 9.99379·7 9.99376·1 9.99372·6 9.99369·1
40 9.99385·9 9.99381·8 9.99377·7 9.99374·0 9.99370·5 9.99367·1
50 9.99383·9 9.99379·8 9.99375·7 9.99372·0 9.99368·4 9.99365·0
54 0 9.99381·8 9.99377·7 9.99373·7 9.99369·9 9.99366·4 9.99363·0
10 9.99379·8 9.99375·7 9.99371·6 9.99367·9 9.99364·3 9.99360·9
20 9.99377·8 9.99373·7 9.99369·6 9.99365·8 9.99362·3 9.99358·8
30 9.99375·8 9.99371·7 9.99367·6 9.99363·8 9.99360·2 9.99356·8
40 9.99373·8 9.99369·7 9.99365·6 9.99361·7 9.99358·2 9.99354·7
50 9.99371·8 9.99367·7 9.99363·6 9.99359·7 9.99356·1 9.99352·6
55 0 9.99369·8 9.99365·6 9.99361·5 9.99357·6 9.99354·1 9.99350·6
10 9.99367·8 9.99363·6 9.99359·5 9.99355·6 9.99352·0 9.99348·5
20 9.99365·8 9.99361·6 9.99357·5 9.99353·6 9.99350·0 9.99346·4
30 9.99363·8 9.99359·6 9.99355·5 9.99351·5 9.99347·9 9.99344·4
40 9.99361·8 9.99357·6 9.99353·5 9.99349·5 9.99345·9 9.99342·3
50 9.99359·8 9.99355·6 9.99351·4 9.99347·5 9.99343·8 9.99340·2
56 0 9.99357·8 9.99353·5 9.99349·4 9.99345·5 9.99341·8 9.99338·2
10 9.99355·8 9.99351·5 9.99347·4 9.99343·4 9.99339·7 9.99336·1
20 9.99353·8 9.99349·5 9.99345·4 9.99341·4 9.99337·7 9.99334·0
30 9.99351·8 9.99347·5 9.99343·4 9.99339·4 9.99335·6 9.99332·0
40 9.99349·8 9.99345·5 9.99341·3 9.99337·3 9.99333·0 9.99329·9
50 9.99347·8 9.99343·5 9.99339·3 9.99335·3 9.99331·5 9.99327·8
57 0 9.99345·8 9.99341·5 9.99337·3 9.99333·3 9.99329·5 9.99325·8
10 9.99343·8 9.99339·4 9.99335·3 9.99331·2 9.99327·4 9.99323·7
20 9.99341·8 9.99337·4 9.99333·2 9.99329·2 9.99325·4 9.99321·7
30 9.99339·8 9.99335·4 9.99331·2 9.99327·2 9.99323·3 9.99319·6
40 9.99337·8 9.99333·4 9.99329·2 9.99325·1 9.99321·3 9.99317·6
50 9.99335·8 9.99331·4 9.99327·2 9.99323·1 9.99319·2 9.99315·5
58 0 9.99333·8 9.99329·4 9.99325·1 9.99321·1 9.99317·2 9.99313·5
10 9.99331·8 9.99327·3 9.99323·1 9.99319·0 9.99315·1 9.99311·4
20 9.99329·8 9.99325·3 9.99321·1 9.99317·0 9.99313·1 9.99309·4
30 9.99327·8 9.99323·3 9.99319·1 9.99314·9 9.99311·0 9.99307·3
40 9.99325·8 9.99321·3 9.99317·0 9.99312·9 9.99309·0 9.99305·3
50 9.99323·8 9.99319·3 9.99315·0 9.99310·8 9.99306·9 9.99303·2
59 0 9.99321·8 9.99317·3 9.99313·0 9.99308·8 9.99304·9 9.99301·2
10 9.99319·8 9.99315·2 9.99311·0 9.99306·8 9.99302·8 9.99299·1
20 9.99317·8 9.99313·2 9.99308·9 9.99304·7 9.99300·8 9.99297·0
30 9.99315·8 9.99311·2 9.99306·9 9.99302·7 9.99298·7 9.99295·0
40 9.99313·8 9.99309·2 9.99304·9 9.99300·7 9.99296·7 9.99292·9
50 9.99311·8 9.99307·2 9.99302·9 9.99298·6 9.99294·6 9.99290·8
60 0 9.99309·8 9.99305·2 9.99300·8 9.99296·6 9.99292·6 9.99288·8
10 9.99307·8 9.99303·1 9.99298·8 9.99294·6 9.99290·5 9.99286·7
20 9.99305·8 9.99301·1 9.99296·8 9.99292·5 9.99288·5 9.99284·7
30 9.99303·8 9.99299·1 9.99294·8 9.99290·5 9.99286·4 9.99282·6
40 9.99301·8 9.99297·1 9.99292·7 9.99288·5 9.99284·4 9.99280·6
50 9.99299·8 9.99295·1 9.99290·7 9.99280·4 9.99282·3 9.99278·5
61 0 9.99297·8 9.99283·1 9.99288·7 9.99284·4 9.99280·3 9.99276·5
10 9.99295·8 9.99291·0 9.99286·7 9.99282·4 9.99278·2 9.99274·4
20 9.99293·8 9.99289·0 9.99284·6 9.99280·3 9.99276·2 9.99272·3
30 9.99291·8 9.99287·0 9.99282·6 9.99278·3 9.99274·1 9.99270·3
40 9.99289·8 9.99285·0 9.99280·6 9.99276·2 9.99272·1 9.99268·2
50 9.99287·8 9.99283·0 9.99278·6 9.99274·2 9.99270·0 9.99266·1
62 0 9.99285·8 9.99281·0 9.99276·5 9.99272·1 9.99268·0 9.99264·1

[page] 30

TABLE IX. Logarithms for readily computing the true Distance of the MOON from the SUN or a Fixed Star.
Horizontal Parallax of the Moon. Apparent Altitude of the Moon's Center.
75° 76° 77° 78° 79° 80°
M S Logarithm. Logarithm. Logarithm. Logarithm. Logarithm. Logarithm.
53 0 9.99372·1 9.99369·1 9.99366·4 9.99364·0 9.99361·7 9.99359·5
10 9.99370·0 9.99367·0 9.99364·3 9.99361·9 9.99359·6 9.99357·4
20 9.99367·9 9.99364·9 9.99362·3 9.99359·8 9.99357·5 9.99355·3
30 9.99365·9 9.99362·9 9.99360·2 9.99357·7 9.99355·4 9.99353·2
40 9.99363·8 9.99360·8 9.99358·1 9.99355·6 9.99353·3 9.99351·1
50 9.99361·7 9.99358·7 9.99356·0 9.99353·5 9.99351·2 9.99349·0
54 0 9.99359·7 9.99356·7 9.99354·0 9.99351·4 9.99349·1 9.99346·9
10 9.99357·6 9.99354·6 9.99351·9 9.99349·3 9.99347·0 9.99344·8
20 9.99355·5 9.99352·5 9.99349·8 9.99347·2 9.99344·9 9.99342·7
30 9.99353·5 9.99350·5 9.99347·7 9.99345·1 9.99342·8 9.99340·6
40 9.99351·4 9.99348·4 9.99345·6 9.99343·0 9.99340·7 9.99338·5
50 9.99349·3 9.99346·3 9.99343·6 9.99340·9 9.99338·6 9.99336·4
55 0 9.99347·3 9.99344·3 9.99341·5 9.99338·8 9.99336·5 9.99334·3
10 9.99345·2 9.99342·2 9.99339·4 9.99336·8 9.99334·4 9.99332·2
20 9.99343·1 9.99340·1 9.99337·3 9.99334·7 9.99332·3 9.99330·1
30 9.99341·1 9.99338·0 9.99335·2 9.99332·6 9.99330·2 9.99328·0
40 9.99339·0 9.99336·0 9.99333·1 9.99330·5 9.99328·1 9.99325·9
50 9.99336·9 9.99333·9 9.99331·0 9.99328·4 9.99326·0 9.99323·8
56 0 9.99334·9 9.99331·8 9.99328·9 9.99326·3 9.99323·9 9.99321·7
10 9.99332·8 9.99329·7 9.99326·9 9.99324·2 9.99321·8 9.99319·6
20 9.99330·7 9.99327·6 9.99324·8 9.99322·1 9.99319·7 9.99317·5
30 9.99328·7 9.99325·5 9.99322·7 9.99320·0 9.99317·6 9.99315·4
40 9.99326·6 9.99323·4 9.99320·6 9.99317·9 9.99315·5 9.99313·3
50 9.99324·5 9.99321·4 9.99318·5 9.99315·8 9.99313·4 9.99311·1
57 0 9.99322·5 9.99319·3 9.99316·4 9.99313·7 9.99311·3 9.99309·0
10 9.99320·4 9.99317·2 9.99314·4 9.99311·7 9.99309·2 9.99306·9
20 9.99318·3 9.99315·1 9.99312·3 9.99309·6 9.99307·1 9.99304·8
30 9.99316·3 9.99313·1 9.99310·2 9.99307·5 9.99305·0 9.99302·7
40 9.99314·2 9.99311·0 9.99308·1 9.99305·4 9.99302·9 9.99300·6
50 9.99312·1 9.99308·9 9.99306·0 9.99303·3 9.99300·8 9.99298·5
58 0 9.99310·1 9.99306·8 9.99303·9 9.99301·2 9.99298·7 9.99296·4
10 9.99308·0 9.99304·7 9.99301·8 9.99299·1 9.99296·6 9.99294·3
20 9.99305·9 9.99302·7 9.99299·7 9.99297·0 9.99294·5 9.99292·2
30 9.99303·9 9.99300·6 9.99297·7 9.99294·9 9.99292·4 9.99290·1
40 9.99301·8 9.99298·5 9.99295·6 9.99292·8 9.99290·2 9.99288·0
50 9.99299·7 9.99296·4 9.99293·5 9.99290·7 9.99288·1 9.99285·8
59 0 9.99297·7 9.99294·4 9.99291·4 9.99288·6 9.99286·0 9.99283·7
10 9.99295·6 9.99272·3 9.99289·3 9.99286·5 9.99283·9 9.99281·6
20 9.99293·5 9.99290·2 9.99287·2 9.99284·4 9.99281·8 9.99279·5
30 9.99291·5 9.99288·1 9.99285·1 9.99282·3 9.99279·7 9.99277·4
40 9.99289·4 9.99286·0 9.99283·0 9.99280·2 9.99277·6 9.99275·2
50 9.99287·3 9.99284·0 9.99280·9 9.99278·1 9.99275·5 9.99273·1
60 0 9.99285·3 9.99281·9 9.99278·8 9.99276·0 9.99273·4 9.99271·0
10 9.99283·2 9.99279·8 9.99276·8 9.99273·9 9.99271·3 9.99268·9
20 9.99281·1 9.99277·7 9.99274·7 9.99271·8 9.99269·2 9.99266·8
30 9.99279·1 9.99275·6 9.99272·6 9.99269·7 9.99267·1 9.99264·7
40 9.99277·0 9.99273·6 9.99270·5 9.99267·6 9.99265·0 9.99262·6
50 9.99274·9 9.99271·5 9.99268·4 9.99265·5 9.99262·9 9.99260·5
61 0 9.99272·9 9.99269·4 9.99266·3 9.99263·4 9.99260·8 9.99258·4
10 9.99270·8 9.99267·3 9.99264·2 9.99261·4 9.99258·7 9.99256·3
20 9.99268·7 9.99265·3 9.99262·1 9.99259·3 9.99256·6 9.99254·2
30 9.99266·6 9.99263·2 9.99260·0 9.99257·2 9.99254·5 9.99252·0
40 9.99264·5 9.99261·1 9.99258·0 9.99255·1 9.99252·4 9.99249·9
50 9.99262·5 9.99259·0 9.99255·9 9.99253·0 9.99250·3 9.99247·8
62 0 9.99260·4 9.99257·0 9.99253·8 9.99250·9 9.99248·2 9.99245·7

[page] 31

TABLE IX. Logarithms for readily computing the true Distance of the MOON from the SUN or a Fixed Star.
Horizontal Parallax of the Moon. Apparent Altitude of the Moon's Center.
81° 82° 83° 84° 85° 86°
M S Logarithm. Logarithm. Logarithm. Logarithm. Logarithm. Logarithm.
53 0 9.99357·7 9.99356·0 9.99354·5 9.99353·2 9.99352·1 9.99351·2
10 9.99355·6 9.99353·9 9.99352·3 9.99351·1 9.99350·0 9.99349·1
20 9.99353·5 9.99351·8 9.99350·2 9.99348·9 9.99347·8 9.99346·9
30 9.99351·3 9.99349·6 9.99348·1 9.99346·8 9.99345·7 9.99344·8
40 9.99349·2 9.99347·5 9.99346·0 9.99344·7 9.99343·6 9.99342·7
50 9.99347·1 9.99345·4 9.99343·9 9.99342·6 9.99341·5 9.99340·5
54 0 9.99345·0 9.99343·3 9.99341·8 9.99340·5 9.99339·3 9.99338·4
10 9.99342·9 9.99341·2 9.99339·7 9.99338·3 9.99337·2 9.99336·2
20 9.99340·8 9.99339·0 9.99337·5 9.99336·2 9.99335·1 9.99334·1
30 9.99338·7 9.99336·9 9.99335·4 9.99334·1 9.99332·9 9.99331·9
40 9.99336·5 9.99334·8 9.99333·3 9.99332·0 9.99330·8 9.99329·8
50 9.99334·4 9.99332·7 9.99331·2 9.99329·8 9.99328·7 9.99327·7
55 0 9.99332·3 9.99330·6 9.99329·0 9.99327·7 9.99326·5 9.99325·5
10 9.99330·2 9.99328·4 9.99326·9 9.99325·6 9.99324·4 9.99323·4
20 9.99328·1 9.99326·3 9.99324·7 9.99323·4 9.99322·3 9.99321·3
30 9.99326·0 9.99324·2 9.99322·6 9.99321·3 9.99320·1 9.99319·1
40 9.99323·8 9.99322·1 9.99320·5 9.99319·2 9.99318·0 9.99317·0
50 9.99321·7 9.99320·0 9.99318·4 9.99317·1 9.99315·9 9.99314·9
56 0 9.99319·6 9.99317·8 9.99316·2 9.99314·9 9.99313·7 9.99312·7
10 9.99317·5 9.99315·7 9.99314·1 9.99312·8 9.99311·6 9.99310·6
20 9.99315·4 9.99313·6 9.99312·0 9.99310·6 9.99309·5 9.99308·5
30 9.99313·3 9.99311·5 9.99309·8 9.99308·5 9.99307·3 9.99306·3
40 9.99311·1 9.99309·4 9.99307·7 9.99306·4 9.99305·2 9.99304·2
50 9.99309·0 9.99307·2 9.99305·6 9.99304·2 9.99303·1 9.99302·1
57 0 9.99306·9 9.99305·1 9.99303·5 9.99302·1 9.99300·9 9.99299·9
10 9.99304·8 9.99303·0 9.99301·3 9.99299·9 9.99298·8 9.99297·8
20 9.99302·7 9.99300·9 9.99299·2 9.99297·8 9.99296·7 9.99295·7
30 9.99300·6 9.99298·8 9.99297·1 9.99295·7 9.99294·6 9.99293·5
40 9.99298·5 9.99296·6 9.99295·0 9.99293·6 9.99292·4 9.99291·4
50 9.99296·4 9.99294·5 9.99292·8 9.99291·4 9.99290·3 9.99289·3
58 0 9.99294·3 9.99292·4 9.99290·7 9.99289·3 9.99288·1 9.99287·1
10 9.99292·1 9.99290·3 9.99288·6 9.99287·1 9.99286·0 9.99285·0
20 9.99290·0 9.99288·1 9.99286·5 9.99285·0 9.99283·9 9.99282·9
30 9.99287·9 9.99286·0 9.99284·3 9.99282·9 9.99281·7 9.99280·7
40 9.99285·8 9.99283·9 9.99282·2 9.99280·7 9.99279·6 9.99278·6
50 9.99283·7 9.99281·8 9.99280·1 9.99278·6 9.99277·5 9.99276·5
59 0 9.99281·6 9.99279·7 9.99278·0 9.99276·5 9.99275·3 9.99274·3
10 9.99279·5 9.99277·5 9.99275·8 9.99274·4 9.99273·2 9.99272·2
20 9.99277·3 9.99275·4 9.99273·7 9.99272·2 9.99271·1 9.99270·1
30 9.99275·2 9.99273·3 9.99271·6 9.99270·1 9.99269·0 9.99267·9
40 9.99273·1 9.99271·2 9.99269·5 9.99268·0 9.99266·8 9.99265·8
50 9.99271·0 9.99269·1 9.99267·3 9.99265·9 9.99264·7 9.99263·7
60 0 9.99268·9 9.99266·9 9.99265·2 9.99263·8 9.99262·5 9.99261·5
10 9.99266·8 9.99264·8 9.99263·1 9.99261·6 9.99260·4 9.99259·4
20 9.99264·7 9.99262·7 9.99261·0 9.99259·5 9.99258·3 9.99257·3
30 9.99262·6 9.99260·6 9.99258·8 9.99257·4 9.99256·1 9.99255·1
40 9.99259·4 9.99258·5 9.99256·7 9.99255·2 9.99254·0 9.99253·0
50 9.99258·3 9.99256·3 9.99254·6 9.99253·1 9.99251·9 9.99250·8
61 0 9.99256·2 9.99254·2 9.99252·5 9.99251·0 9.99249·7 9.99248·7
10 9.99254·1 9.99252·1 9.99250·3 9.99248·8 9.99247·6 9.99246·5
20 9.99252·0 9.99250·0 9.99248·2 9.99246·7 9.99245·5 9.99244·4
30 9.99249·9 9.99247·9 9.99246·1 9.99244·6 9.99243·3 9.99242·3
40 9.99247·8 9.99245·7 9.99244·0 9.99242·4 9.99241·2 9.99240·1
50 9.99245·6 9.99243·6 9.99241·8 9.99240·3 9.99239·1 9.99238·0
62 0 9.99243·5 9.99241·5 9.99239·7 9.99238·2 9.99236·9 9.99235·8

[page] 32

TABLE IX. Logarithms for readily computing the true Distance of the MOON from the SUN or a Fixed Star.
Horizontal Parallax of the Moon. Apparent Altitude of the Moon's Center.
87° 88° 89° 90°
M S Logarithm. Logarithm. Logarithm. Logarithm.
53 0 9.99350·5 9.99349·9 9.99349·7 9.99349·5
10 9.99348·3 9.99347·7 9.99347·5 9.99347·4
20 9.99346·2 9.99345·6 9.99345·4 9.99345·2
30 9.99344·1 9.99343·5 9.99343·2 9.99434·1
40 9.99341·9 9.99341·3 9.99341·1 9.99340·9
50 9.99339·8 9.99339·2 9.99338·9 9.99338·8
54 0 9.99337·7 9.99337·1 9.99336·8 9.99336·6
10 9.99335·5 9.99334·9 9.99334·6 9.99334·5
20 9.99333·4 9.99332·8 9.99332·5 9.99332·3
30 9.99331·3 9.99330·6 9.99330·3 9.99330·1
40 9.99329·1 9.99328·5 9.99328·2 9.99328·0
50 9.99327·0 9.99326·4 9.99326·1 9.99325·8
55 0 9.99324·8 9.99324·2 9.99323·9 9.99323·7
10 9.99322·7 9.99322·1 9.99321·8 9.99321·5
20 9.99320·5 9.99319·9 9.99319·7 9.99319·4
30 9.99318·4 9.99317·8 9.99317·5 9.99317·2
40 9.99316·3 9.99315·6 9.99315·4 9.99315·1
50 9.99314·1 9.99313·5 9.99313·2 9.99312·9
56 0 9.99312·0 9.99311·4 9.99311·1 9.99310·8
10 9.99309·8 9.99309·2 9.99309·0 9.99308·7
20 9.99307·7 9.99307·1 9.99306·8 9.99306·5
30 9.99305·6 9.99304·9 9.99302·7 9.99304·4
40 9.99303·4 9.99302·8 9.99302·5 9.99302·3
50 9.99301·3 9.99300·7 9.99300·4 9.99300·1
57 0 9.99299·1 9.99298·5 9.99298·2 9.99298·0
10 9.99297·0 9.99296·4 9.99296·1 9.99295·9
20 9.99294·9 9.99294·3 9.99294·0 9.99293·8
30 9.99292·7 9.99292·1 9.99291·8 9.99291·7
40 9.99290·6 9.99290·0 9.99289·7 9.99289·5
50 9.99288·5 9.99287·9 9.99287·6 9.99287·4
58 0 9.99286·3 9.99285·7 9.99285·4 9.99285·3
10 9.99284·2 9.99283·6 9.99283·3 9.99283·1
20 9.99282·1 9.99281·4 9.99281·2 9.99281·0
30 9.99279·9 9.99279·3 9.99279·1 9.99278·8
40 9.99277·8 9.99277·1 9.99276·9 9.99276·7
50 9.99275·7 9.99275·0 9.99274·8 9.99274·6
59 0 9.99273·5 9.99272·9 9.99272·6 9.99272·5
10 9.99271·4 9.99270·7 9.99270·5 9.99270·3
20 9.99269·3 9.99268·6 9.99268·3 9.99268·2
30 9.99267·1 9.99266·4 9.99266·2 9.99266·0
40 9.99265·0 9.99264·3 9.99264·0 9.99263·9
50 9.99262·9 9.99262·2 9.99261·9 9.99262·7
60 0 9.99260·7 9.99260·0 9.99259·7 9.99259·6
10 9.99258·6 9.99257·9 9.99257·6 9.99257·4
20 9.99256·5 9.99255·8 9.99255·5 9.99255·3
30 9.99254·3 9.99253·7 9.99253·3 9.99253·1
40 9.99252·2 9.99251·5 9.99251·2 9.99251·0
50 9.99250·1 9.99249·4 9.99249·0 9.99248·8
61 0 9.99247·9 9.99247·2 9.99246·9 9.99246·7
10 9.99245·8 9.99245·1 9.99244·8 9.99244·5
20 9.99243·6 9.99243·0 9.99242·6 9.99242·4
30 9.99241·5 9.99240·8 9.99240·5 9.99240·2
40 9.99239·3 9.99238·7 9.99238·3 9.99238·1
50 9.99237·2 9.99236·6 9.99236·2 9.99235·9
62 0 9.99235·0 9.99234·4 9.99234·0 9.99233·8

[page] 33

TABLE X.
Numbers to be subtracted from the Logarithms in TABLE IX. when the Moon's Distance from the Sun is observed.
App. Alt. of the Sun's Center. Number to be subtracted.
°
3 2,8
4 1,9
5 1,4
6 1,1
7 0,9
8 0,8
9 0,7
10 0,7
12 0,7
14 0,7
16 0,7
18 0,7
20 0,7
21 0,8
22 0,8
24 0,8
25 0,8
26 0,9
28 0,9
29 1,0
30 1,0
32 1,0
33 1,1
34 1,1
36 1,1
37 1,2
38 1,2
40 1,2
41 1,3
42 1,3
44 1,3
46 1,4
48 1,4
49 1,4
50 1,5
52 1,5
54 1,5
55 1,6
56 1,6
58 1,6
60 1,6
62 1,6
63 1,7
64 1,7
66 1,7
68 1,7
69 1,8
70 1,8
72 1,8
74 1,8
76 1,8
78 1,8
79 1,8
80 1,8
82 1,8
84 1,8
86 1,8
88 1,8
90 1,8
TABLE XI.
Numbers to be subtracted from the Logarithms in TABLE IX. when the Moon's Distance from a Star is observed.
App. Alt. of the Star. Numbers to be subtracted.
°
3 2,7
4 1,8
5 1,3
6 0,9
7 0,7
8 0,6
9 0,5
10 0,4
11 0,3
12 0,3
13 0,2
14 0,2
15 0,1
16 0,1
20 0,1
25 0,1
26 0,0
&c.
TABLE XII.
The Moon's Parallax in Altitude.
D's App. Alt. The Moon's Horizontal Parallax.
53′ 54′ 55′ 56′ 57′ 58′ 59′ 60′ 61′ 62′
D. M. M. M. M. M. M. M. M. M. M.
0 53 54 55 56 57 58 59 60 61 62
5 53 54 55 56 57 58 59 60 61 62
10 52 53 54 55 56 57 58 59 60 61
15 51 52 53 54 55 56 57 58 59 60
18 50 51 52 53 54 55 56 57 58 59
20 50 51 52 53 54 54 55 56 57 58
22 49 50 51 52 53 54 55 56 56 57
24 48 49 50 51 52 53 54 55 56 57
26 47 48 49 50 51 52 53 54 55 56
28 47 48 49 49 50 51 52 53 54 55
30 46 47 48 48 49 50 51 52 53 54
32 45 46 47 47 48 49 50 51 52 53
34 44 45 46 46 47 48 49 50 51 52
36 43 44 44 45 46 47 48 48 49 50
38 42 43 43 44 45 46 46 47 48 49
40 40 41 42 43 44 44 45 46 47 48
42 39 40 41 42 42 43 44 45 45 46
44 38 39 40 40 41 42 42 43 44 45
46 36 37 38 39 40 40 41 42 42 43
48 35 36 37 37 38 39 39 40 41 42
50 34 35 35 36 37 37 38 39 39 40
51 33 34 35 35 36 36 37 38 38 39
52 32 33 34 34 35 36 36 37 38 39
53 31 32 33 34 34 35 35 36 37 38
54 31 32 32 33 33 34 35 35 36 37
55 30 31 31 32 33 33 34 34 35 36
56 29 30 31 31 32 32 33 34 34 35
57 28 29 30 30 31 32 32 33 33 34
58 28 29 29 30 30 31 31 32 32 33
59 27 28 28 29 29 30 30 31 31 32
60 26 27 27 28 28 29 29 30 30 30
61 26 26 27 27 28 28 29 29 30 30
62 25 25 26 26 27 27 28 28 29 29
63 24 24 25 25 26 26 27 27 28 28
64 24 24 24 24 25 25 26 26 27 27
65 23 23 23 24 24 24 25 25 26 26
66 22 22 22 23 23 24 24 24 25 25
67 21 21 21 22 22 23 23 23 24 24
68 20 20 21 21 21 22 22 22 23 23
69 19 19 20 20 20 21 21 21 22 22
70 18 18 19 19 19 20 20 20 21 21
71 18 18 18 18 19 19 19 19 20 20
72 17 17 17 17 18 18 18 18 19 19
73 16 16 16 16 17 17 17 17 18 18
74 15 15 15 15 16 16 16 16 17 17
75 14 14 14 14 15 15 15 15 16 16
76 13 13 13 14 14 14 14 14 15 15
77 12 12 12 13 13 13 13 13 14 14
78 11 11 11 12 12 12 12 12 13 13
79 10 10 10 11 11 11 11 11 12 12
80 9 9 10 10 10 10 10 10 11 11
81 8 8 9 9 9 9 9 9 10 10
82 7 7 8 8 8 8 8 8 8 9
83 7 7 7 7 7 7 7 7 7 8
84 6 6 6 6 6 6 6 6 6 7
85 5 5 5 5 5 5 5 5 5 5
86 4 4 4 4 4 4 4 4 4 4
87 3 3 3 3 3 3 3 3 3 3
88 2 2 2 2 2 2 2 2 2 2
89 1 1 1 1 1 1 1 1 1 1
90 0 0 0 0 0 0 0 0 0 0

E

[page] 34

TABLE XIII. For computing the Effects of Parallax on the MOON's Distance from the SUN or a STAR, by Mr. LYONS's Method.
Parallax in Altitude or Distance. Apparent Distance:
Add the Difference of the two Numbers taken out of this Table, if the Apparent Distance is less than 90°, and subtract it if above.
10° 11° 12° 13° 14° 15° 16° 17° 18° 19° 20° 21° 22° 23° 24° 25°
M
5 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0
8 3 3 2 2 2 2 2 2 2 2 1 1 1 1 1 1
10 5 5 4 4 4 3 3 3 3 2 2 2 2 2 2 2
11 6 5 5 4 4 4 4 3 3 3 3 3 3 3 2 2
12 7 6 6 5 5 4 4 4 4 3 3 3 3 3 3 3
13 8 8 7 6 6 5 5 5 5 4 4 4 3 3 3 3
14 10 9 8 7 7 6 6 6 6 5 5 4 4 4 4 4
15 11 10 9 8 8 7 7 6 6 6 5 5 5 4 4 4
16 13 11 10 9 9 8 8 7 7 6 6 6 6 5 5 5
17 14 13 12 11 10 9 9 8 8 7 7 6 6 6 5 5
18 16 14 13 12 11 10 10 9 9 8 8 7 7 6 6 6
19 18 16 15 14 13 12 11 10 10 9 8 8 8 7 7 7
20 20 18 16 15 14 13 12 11 11 10 9 9 9 8 8 7
21 22 20 18 17 15 14 13 12 12 11 10 10 10 9 9 8
22 24 22 20 18 17 16 15 14 13 12 12 11 11 10 10 9
23 26 24 22 20 18 17 16 15 14 14 13 12 11 11 10 10
24 29 26 24 22 20 19 18 17 16 15 14 13 12 11 11 10
25 31 28 26 24 22 21 19 18 17 16 15 14 13 12 12 11
26 34 31 28 26 24 22 21 19 18 17 16 15 14 13 13 12
27 36 33 30 28 26 24 22 21 19 18 17 16 15 15 14 13
28 39 35 32 30 28 26 24 22 21 20 19 18 17 16 15 14
29 42 38 34 32 30 28 25 24 22 21 20 19 18 17 16 15
30 45 41 37 34 32 29 27 25 24 22 21 20 19 18 17 16
31 48 44 39 37 34 31 29 27 25 24 23 22 21 19 18 18
32 51 46 42 39 36 33 31 29 27 25 24 23 22 21 20 19
33 54 49 44 41 38 35 33 31 29 27 25 24 23 22 21 20
34 57 52 47 44 41 38 35 33 31 29 27 25 24 23 22 21
35 60 55 50 46 43 40 37 35 33 31 29 27 25 24 23 23
36 64 58 53 49 45 42 40 37 35 33 31 29 27 26 25 24
37 67 61 56 52 48 45 42 39 37 35 32 31 29 28 26 25
38 71 65 59 55 51 47 44 41 39 36 34 32 31 29 28 27
39 75 68 62 58 53 50 46 43 41 38 36 34 32 31 29 28
40 79 72 66 61 56 52 49 46 43 40 38 36 34 32 31 30
41 83 76 69 64 59 55 51 48 45 42 40 38 36 34 33 32
42 87 80 73 67 62 58 54 50 47 44 42 40 38 36 35 33
43 91 84 76 70 64 60 56 53 49 47 44 42 39 38 36 35
44 96 88 80 73 67 63 59 55 52 49 46 43 41 39 38 36
45 100 92 83 77 70 66 61 58 54 51 48 46 43 41 40 38
46 105 96 87 80 74 69 64 60 57 54 51 48 45 43 42 40
47 109 100 91 84 77 72 67 63 59 56 53 59 47 45 43 42
48 114 104 95 87 80 75 70 65 61 58 55 52 50 47 45 43
49 119 109 99 91 83 78 73 69 64 61 57 55 52 49 46 45
50 124 113 103 95 87 81 76 71 67 63 60 57 54 51 48 46
51 129 117 107 98 91 85 79 74 69 66 62 59 56 53 50 49
52 134 121 111 102 95 89 83 77 72 68 65 61 58 55 53 51
53 139 126 115 106 98 92 86 80 74 71 67 64 60 58 55 53
54 144 131 120 110 102 95 89 83 77 73 70 66 63 60 57 54
55 149 136 124 114 106 99 92 86 80 76 70 69 65 62 59 57
56 155 141 129 119 110 103 96 89 83 79 75 71 68 65 62 59
57 160 146 133 123 114 107 99 93 86 82 77 74 70 67 64 61
58 166 151 138 127 118 110 103 96 90 85 80 76 73 69 66 63
59 172 156 143 133 123 115 106 100 93 88 83 79 75 72 68 65
60 178 162 148 137 128 119 110 103 97 91 86 82 78 74 70 67
61 184 167 153 141 131 122 113 107 100 94 89 85 80 76 72 69
62 190 173 158 145 135 125 117 110 103 97 92 87 83 79 75 72

[page] 35

TABLE XIII. For computing the Effects of Parallax on the MOON's Distance from the SUN or a STAR, by Mr. LYONS's Method.
Parallax in Altitude or Distance. Apparent Distance:
Add the Difference of the two Numbers taken out of this Table, if the Apparent Distance is less than 90°, and subtract it if above.
26° 27° 28° 29° 30° 31° 32° 33° 34° 35° 36° 37° 38°
M
5 0 0 0 0 0 0 0 0 0 0 0 0 0
8 1 1 1 1 1 1 1 1 1 1 1 0 0
10 2 2 2 1 1 1 1 1 1 1 1 1 1
11 2 2 2 2 2 2 2 2 1 1 1 1 1
12 3 2 2 2 2 2 2 2 2 2 2 1 1
13 3 3 3 3 2 2 2 2 2 2 2 2 2
14 4 3 3 3 3 3 3 2 2 2 2 2 2
15 4 4 4 4 3 3 3 3 3 3 3 2 2
16 5 5 5 4 4 4 4 3 3 3 3 2 2
17 5 5 5 5 4 4 4 4 4 4 3 3 3
18 6 6 6 5 5 5 5 4 4 4 4 3 3
19 6 6 6 6 5 5 5 5 5 4 4 4 4
20 7 7 7 6 6 6 6 5 5 5 5 4 4
21 8 7 7 7 7 6 6 6 6 5 5 5 5
22 9 8 8 7 7 7 7 6 6 6 6 5 5
23 9 9 9 8 8 7 7 7 7 6 6 6 6
24 10 9 9 9 9 8 8 7 7 7 7 6 6
25 11 10 10 10 9 9 9 8 8 8 7 7 7
26 12 11 11 10 10 9 9 9 9 8 8 7 7
27 13 12 12 11 11 10 10 10 9 9 9 8 8
28 14 13 13 12 12 11 11 10 10 9 9 8 8
29 15 14 14 13 13 12 12 11 11 10 10 9 9
30 16 15 15 14 14 13 13 12 12 11 11 10 10
31 17 16 16 15 15 14 14 13 13 12 11 11 11
32 18 17 17 16 16 15 15 14 14 13 12 11 11
33 19 19 18 17 17 16 16 15 14 14 13 12 12
34 21 20 19 18 18 17 17 16 15 14 14 13 13
35 22 21 20 19 19 18 17 17 16 15 14 14 13
36 23 22 21 20 20 19 18 17 17 16 15 14 14
37 24 23 22 21 21 20 19 18 18 17 16 15 15
38 26 24 23 22 22 21 20 19 19 18 17 16 16
39 27 26 24 24 23 22 21 20 20 19 18 17 17
40 29 27 26 25 24 23 22 21 21 20 19 18 18
41 30 29 27 26 25 24 23 23 22 21 20 19 19
42 32 30 29 28 27 26 25 24 23 22 21 20 20
43 33 32 30 29 28 27 26 25 24 23 22 21 21
44 35 33 32 30 29 28 27 26 25 24 23 22 22
45 36 35 33 32 30 29 28 27 26 25 24 23 23
46 38 36 35 33 32 30 29 28 27 26 25 24 24
47 40 38 36 35 33 32 30 29 28 27 26 26 25
48 42 40 38 36 35 33 32 31 30 29 28 27 26
49 43 41 39 38 36 35 33 32 31 30 29 28 27
50 45 43 41 39 38 36 35 33 32 31 30 29 28
51 47 45 43 41 39 38 36 35 33 32 31 30 29
52 49 47 45 43 41 39 38 36 35 33 32 31 30
53 50 48 46 44 42 41 39 38 36 35 33 32 31
54 52 50 48 46 44 42 41 39 38 36 35 33 32
55 54 52 49 47 45 44 42 41 39 38 36 35 33
56 56 53 51 49 47 45 44 42 41 39 38 36 35
57 58 55 53 51 49 47 45 44 42 41 39 37 36
58 60 57 55 53 51 49 47 45 44 42 40 38 37
59 62 59 57 55 53 51 48 47 45 43 41 40 38
60 64 61 59 56 54 52 50 48 47 45 43 41 40
61 66 63 61 58 56 54 52 50 48 46 44 43 41
62 69 66 63 60 58 56 54 52 50 48 46 44 43

E 2

[page] 36

TABLE XIII. For computing the Effects of Parallax on the MOON's Distance from the SUN or a STAR, by Mr. LYONS's Method.
Parallax in Altitude or Distance. Apparent Distance:
Add the Difference of the two Numbers taken out of this Table, if the Apparent Distance is less than 90°, and subtract it if above.
39° 40° 41° 42° 43° 44° 45° 46° 47° 48° 49° 50° 51°
M
5 0 0 0 0 0 0 0 0 0 0 0 0 0
8 0 0 0 0 0 0 0 0 0 0 0 0 0
10 1 1 1 1 1 1 1 1 1 1 1 0 0
11 1 1 1 1 1 1 1 1 1 1 1 0 0
12 1 1 1 1 1 1 1 1 1 1 1 0 0
13 2 2 2 2 2 1 1 1 1 1 1 1 1
14 2 2 2 2 2 2 2 1 1 1 1 1 1
15 2 2 2 2 2 2 2 2 2 1 1 1 1
16 2 2 2 2 2 2 2 2 2 2 2 2 1
17 3 3 3 3 3 3 2 2 2 2 2 2 2
18 3 3 3 3 3 3 3 3 3 2 2 2 2
19 4 3 3 3 3 3 3 3 3 3 3 3 3
20 4 4 4 4 3 3 3 3 3 3 3 3 3
21 5 4 4 4 4 4 4 4 4 3 3 3 3
22 5 5 5 5 4 4 4 4 4 3 3 3 3
23 5 5 5 5 5 5 4 4 4 4 4 3 3
24 6 6 6 6 5 5 5 5 5 4 4 4 4
25 7 6 6 6 6 6 5 5 5 5 5 4 4
26 7 7 7 7 6 6 6 6 6 5 5 5 5
27 8 7 7 7 7 6 6 6 6 5 5 5 5
28 8 8 8 8 7 7 7 7 7 6 6 6 6
29 9 9 9 8 8 7 7 7 7 6 6 6 6
30 9 9 9 9 8 8 8 8 7 7 6 6 6
31 10 10 10 9 9 8 8 8 8 7 7 7 6
32 10 10 10 10 9 9 9 9 8 8 7 7 6
33 11 10 10 10 10 10 9 9 8 8 7 7 7
34 12 11 11 11 10 10 10 10 9 9 8 8 7
35 13 12 12 11 11 11 10 10 9 9 8 8 8
36 13 13 13 12 11 11 11 11 10 10 9 9 9
37 14 13 13 12 12 11 11 11 10 10 10 10 10
38 15 14 14 13 13 12 12 12 12 11 11 11 11
39 16 15 15 14 14 13 13 13 13 12 12 11 11
40 17 16 16 15 15 14 14 14 13 13 12 12 12
41 18 17 17 16 15 15 14 14 14 13 13 12 12
42 19 18 18 17 16 15 15 15 14 14 13 13 13
43 20 18 18 17 16 16 15 15 14 14 13 13 13
44 20 19 19 18 17 16 16 16 15 14 13 13 13
45 21 20 20 19 18 17 17 16 15 14 14 13 13
46 22 21 20 19 19 18 18 17 16 15 14 14 14
47 23 22 22 21 20 20 19 18 17 16 15 15 15
48 24 23 23 22 22 21 20 19 18 17 16 16 16
49 26 24 24 24 23 22 21 20 19 18 17 17 17
50 27 26 26 25 24 23 22 21 20 19 18 18 18
51 28 27 26 25 24 23 22 22 21 20 19 18 18
52 29 28 27 26 25 24 23 22 21 20 19 19 18
53 30 29 28 27 26 25 24 23 22 21 20 19 19
54 31 30 29 28 27 26 25 24 23 22 21 20 19
55 32 31 30 29 28 27 26 25 24 23 22 21 20
56 33 32 31 30 29 28 27 26 25 24 23 22 21
57 35 33 32 31 30 29 28 27 26 25 24 23 22
58 36 35 33 32 31 30 29 28 27 26 25 24 23
59 37 36 34 33 32 31 30 29 28 27 26 25 24
60 38 37 35 34 33 32 31 30 29 28 27 26 25
61 40 38 36 35 34 33 32 31 30 29 28 27 26
62 41 40 38 36 35 34 33 32 31 30 29 28 27

[page] 37

TABLE XIII. For computing the Effects of Parallax on the MOON's Distance from the SUN or a STAR, by Mr. LYONS's Method.
Parallax in Altitude or Distance. Apparent Distance.
Add the Difference of the two Numbers taken out of this Table, if the Apparent Distance is less than 90°, and subtract it if above.
52° 53° 54° 55° 56° 57° 58° 59° 60° 120 65° 115 70° 110 75° 105 80° 100 85° 95 90° 90
M
5 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
8 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
10 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
11 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
12 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
13 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0
14 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0
15 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0
16 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0
17 2 2 2 1 1 1 1 1 1 1 0 0 0 0 0
18 2 2 2 2 2 2 2 2 2 1 1 0 0 0 0
19 3 2 2 2 2 2 2 2 2 1 1 0 0 0 0
20 3 2 2 2 2 2 2 2 2 1 1 1 0 0 0
21 3 3 3 2 2 2 2 2 2 1 1 1 0 0 0
22 3 3 3 3 3 3 2 2 2 2 1 1 0 0 0
23 3 3 3 3 3 3 3 3 2 2 1 1 0 0 0
24 4 3 3 3 3 3 3 3 3 2 1 1 1 0 0
25 4 4 4 3 3 3 3 3 3 2 1 1 1 0 0
26 5 4 4 4 4 4 3 3 3 3 2 1 1 0 0
27 5 5 5 4 4 4 4 4 3 3 2 1 1 0 0
28 6 5 5 5 5 5 4 4 4 3 2 2 1 0 0
29 6 5 5 5 5 5 4 4 4 3 2 2 1 0 0
30 6 5 5 5 5 5 4 4 4 4 3 2 1 0 0
31 6 5 5 5 5 5 5 5 4 4 3 2 1 0 0
32 6 5 5 5 5 5 5 5 5 4 3 2 1 0 0
33 6 6 6 5 5 5 5 5 5 4 3 2 1 0 0
34 7 6 6 6 6 6 5 5 5 4 4 2 1 0 0
35 8 7 7 6 6 6 6 6 5 4 4 2 1 0 0
36 8 8 7 7 7 7 6 6 6 5 4 3 2 1 0
37 9 9 8 8 8 7 7 7 6 5 4 3 2 1 0
38 10 10 9 9 9 8 8 7 7 5 4 3 2 1 0
39 11 10 10 9 9 9 8 8 7 5 4 3 2 1 0
40 11 11 10 10 9 9 8 8 8 6 5 3 2 1 0
41 12 12 11 10 10 10 9 9 8 6 5 3 2 1 0
42 12 12 11 11 10 10 9 9 9 7 5 4 2 1 0
43 12 12 11 11 10 10 9 9 9 7 5 4 2 1 0
44 12 12 11 11 11 10 10 9 9 7 6 4 2 1 0
45 13 12 12 11 11 11 10 10 9 7 6 4 2 1 0
46 13 13 12 12 12 11 11 10 10 8 7 5 3 1 0
47 14 14 13 12 12 12 11 11 10 8 7 5 3 1 0
48 15 14 13 13 12 12 12 11 11 9 7 5 3 2 0
49 16 15 14 14 14 13 13 12 11 9 7 5 3 2 0
50 17 16 15 15 14 13 13 12 12 10 8 6 4 2 0
51 17 16 16 15 15 14 14 13 12 10 8 6 4 2 0
52 17 17 16 16 15 15 14 14 13 10 8 6 4 2 0
53 18 18 17 16 16 15 14 14 13 10 8 6 4 2 0
54 19 18 17 17 16 16 15 15 14 11 9 7 4 2 0
55 19 18 18 17 17 16 16 15 14 11 9 7 4 2 0
56 20 19 18 18 17 16 16 15 15 12 9 7 5 2 0
57 21 20 19 19 19 18 17 16 15 12 9 7 5 2 0
58 22 21 20 20 19 18 17 16 16 13 10 7 5 2 0
59 23 22 21 21 20 19 18 17 17 13 10 7 5 2 0
60 24 23 22 22 21 20 19 18 18 14 11 8 5 3 0
61 25 24 23 23 22 21 20 19 18 15 11 8 5 3 0
62 26 25 24 23 22 21 20 19 19 16 12 9 6 3 0

[page] 38

TABLE XIV. For turning Degrees and Minutes into Time, and the contrary.
D H M
M M S
1 0.4
2 0.8
3 0.12
4 0.16
5 0.20
6 0.24
7 0.28
8 0.32
9 0.36
10 0.40
11 0.44
12 0.48
13 0.52
14 0.56
15 1.0
16 1.4
17 1.8
18 1.12
19 1.16
20 1.20
21 1.24
22 1.28
23 1.32
24 1.36
25 1.40
26 1.44
27 1.48
28 1.52
29 1.56
30 2.0
31 2.4
32 2.8
33 2.12
34 2.16
35 2.20
36 2.24
37 2.28
38 2.32
39 2.36
40 2.40
41 2.44
42 2.48
43 2.52
44 2.56
45 3.0
46 3.4
47 3.8
48 3.12
49 3.16
50 3.20
51 3.24
52 3.28
53 3.32
54 3.36
55 3.40
56 3.44
57 3.48
58 3.52
59 3.56
60 4.0
61 4.4
62 4.8
63 4.12
64 4.16
65 4.20
66 4.24
67 4.28
68 4.32
69 4.36
70 4.40
71 4.44
72 4.48
73 4.52
74 4.56
75 5.0
76 5.4
77 5.8
78 5.12
79 5.16
80 5.20
81 5.24
82 5.28
83 5.32
84 5.36
85 5.40
86 5.44
87 5.48
88 5.52
89 5.56
90 6.0
91 6.4
92 6.8
93 6.12
94 6.16
95 6.20
96 6.24
97 6.28
98 6.32
99 6.36
100 6.40
101 6.44
102 6.48
103 6.52
104 6.56
105 7.0
106 7.4
107 7.8
108 7.12
109 7.16
110 7.20
111 7.24
112 7.28
113 7.32
114 7.36
115 7.40
116 7.44
117 7.48
118 7.52
119 7.56
120 8.0
121 8.4
122 8.8
123 8.12
124 8.16
125 8.20
126 8.24
127 8.28
128 8.32
129 8.36
130 8.40
131 8.44
132 8.48
133 8.52
134 8.56
135 9.0
136 9.4
137 9.8
138 9.12
139 9.16
140 9.20
141 9.24
142 9.28
143 9.32
144 9.36
145 9.40
146 9.44
147 9.48
148 9.52
149 9.56
150 10.0
151 10.4
152 10.8
153 10.12
154 10.16
155 10.20
156 10.24
157 10.28
158 10.32
159 10.36
160 10.40
161 10.44
162 10.48
163 10.52
164 10.56
165 11.0
166 11.4
167 11.8
168 11.12
169 11.16
170 11.20
171 11.24
172 11.28
173 11.32
174 11.36
175 11.40
176 11.44
177 11.48
178 11.52
179 11.56
180 12.0
181 12.4
182 12.8
183 12.12
184 12.16
185 12.20
186 12.24
187 12.28
188 12.32
189 12.36
190 12.40
191 12.44
192 12.48
193 12.52
194 12.56
195 13.0
196 13.4
197 13.8
198 13.12
199 13.16
200 13.20
201 13.24
202 13.28
203 13.32
204 13.36
205 13.40
206 13.44
207 13.48
208 13.52
209 13.56
210 14.0
211 14.4
212 14.8
213 14.12
214 14.16
215 14.20
216 14.24
217 14.28
218 14.32
219 14.36
220 14.40
221 14.44
222 14.48
223 14.52
224 14.56
225 15.0
226 15.4
227 15.8
228 15.12
229 15.16
230 15.20
231 15.24
232 15.28
233 15.32
234 15.36
235 15.40
236 15.44
237 15.48
238 15.52
239 15.56
240 16.0
241 16.4
242 16.8
243 16.12
244 16.16
245 16.20
246 16.24
247 16.28
248 16.32
249 16.36
250 16.40
251 16.44
252 16.48
253 16.52
254 16.56
255 17.0
256 17.4
257 17.8
258 17.12
259 17.16
260 17.20
261 17.24
262 17.28
263 17.32
264 17.36
265 17.40
266 17.44
267 17.48
268 17.52
269 17.56
270 18.0
271 18.4
272 18.8
273 18.12
274 18.16
275 18.20
276 18.24
277 18.28
278 18.32
279 18.32
280 18.40
281 18.44
282 18.48
283 18.52
284 18.56
285 19.0
286 19.4
287 19.8
288 19.12
289 19.16
290 19.20
291 19.24
292 19.28
293 19.32
294 19.36
295 19.40
296 19.44
297 19.48
298 19.52
299 19.56
300 20.0
301 20.4
302 20.8
303 20.12
304 20.16
305 20.20
306 20.24
307 20.28
308 20.32
309 20.36
310 20.40
311 20.44
312 20.48
313 20.52
314 20.56
315 21.0
316 21.4
317 21.8
318 21.12
319 21.16
320 21.20
321 21.24
322 21.28
323 21.32
324 21.36
325 21.40
326 21.44
327 21.48
328 21.52
329 21.56
330 22.0
331 22.4
332 22.8
333 22.12
334 22.16
335 22.20
336 22.24
337 22.28
338 22.32
339 22.36
340 22.40
341 22.44
342 22.48
343 22.52
344 22.56
345 23.0
346 23.4
347 23.8
348 23.12
349 23.16
350 23.20
351 23.24
352 23.28
353 23.32
354 23.36
355 23.40
356 23.44
357 23.48
358 23.52
359 23.56
360 24.0

[page 39]

TABLE XV.

PROPORTIONAL

LOGARITHMS.

[page] 40

TABLE XV. Proportional Logarithms.
S h. m. h. m. h. m. h. m. h. m. h. m. h. m. h. m. h. m.
0° 0′ 0° 1′ 0° 2′ 0° 3′ 0° 4′ 0° 5′ 0° 6′ 0° 7′ 0° 8′
4.3345 2.2553 1.9542 1.7782 1.6532 1.5563 1.4771 1.4102 1.3522
1 4.0334 2.2481 1.9506 1.7757 1.6514 1.5549 1.4759 1.4091 1.3513
2 3.7324 2.2410 1.9471 1.7734 1.6496 1.5534 1.4747 1.4081 1.3504
3 3.5563 2.2341 1.9435 1.7710 1.6478 1.5520 1.4735 1.4071 1.3495
4 3.4314 2.2272 1.9400 1.7686 1.6460 1.5506 1.4723 1.4061 1.3486
5 3.3345 2.2205 1.9365 1.7663 1.6443 1.5491 1.4711 1.4050 1.3477
6 3.2553 2.2139 1.9331 1.7639 1.6425 1.5477 1.4699 1.4040 1.3468
7 3.1883 2.2073 1.9296 1.7616 1.6407 1.5463 1.4688 1.4030 1.3459
8 3.1303 2.2009 1.9262 1.7593 1.6390 1.5449 1.4676 1.4020 1.3450
9 3.0792 2.1946 1.9228 1.7570 1.6372 1.5435 1.4664 1.4010 1.3441
10 3.0334 2.1883 1.9195 1.7547 1.6355 1.5421 1.4652 1.4000 1.3432
11 2.9920 2.1822 1.9162 1.7524 1.6338 1.5407 1.4640 1.3989 1.3423
12 2.9542 2.1761 1.9128 1.7501 1.6320 1.5393 1.4629 1.3979 1.3415
13 2.9195 2.1701 1.9096 1.7479 1.6303 1.5379 1.4617 1.3969 1.3406
14 2.8873 2.1642 1.9063 1.7456 1.6286 1.5365 1.4606 1.3959 1.3397
15 2.8573 2.1584 1.9031 1.7434 1.6269 1.5351 1.4594 1.3949 1.3388
16 2.8293 2.1526 1.8999 1.7412 1.6252 1.5337 1.4582 1.3939 1.3379
17 2.8030 2.1469 1.8967 1.7390 1.6235 1.5324 1.4571 1.3929 1.3371
18 2.7782 2.1413 1.8935 1.7368 1.6218 1.5310 1.4559 1.3919 1.3362
19 2.7547 2.1358 1.8904 1.7346 1.6201 1.5296 1.4548 1.3910 1.3353
20 2.7324 2.1303 1.8873 1.7324 1.6185 1.5283 1.4536 1.3900 1.3345
21 2.7112 2.1249 1.8842 1.7302 1.6168 1.5269 1.4525 1.3890 1.3336
22 2.6910 2.1196 1.8811 1.7281 1.6151 1.5256 1.4514 1.3880 1.3327
23 2.6717 2.1143 1.8781 1.7259 1.6135 1.5242 1.4502 1.3870 1.3319
24 2.6532 2.101 1.8751 1.7238 1.6118 1.5229 1.4491 1.3860 1.3310
25 2.6355 2.1040 1.8721 1.7217 1.6102 1.5215 1.4480 1.3851 1.3301
26 2.6185 2.0989 1.8691 1.7196 1.6085 1.5202 1.4468 1.3841 1.3293
27 2.6021 2.0939 1.8661 1.7175 1.6069 1.5189 1.4457 1.3831 1.3284
28 2.5863 2.0889 1.8632 1.7154 1.6053 1.5175 1.4446 1.3821 1.3276
29 2.5710 2.0840 1.8602 1.7133 1.6037 1.5162 1.4435 1.3812 1.3267
30 2.5563 2.0792 1.8573 1.7112 1.6021 1.5149 1.4424 1.3802 1.3259
31 2.5421 2.0744 1.8544 1.7091 1.6005 1.5136 1.4412 1.3792 1.3250
32 2.5283 2.0696 1.8516 1.7071 1.5989 1.5123 1.4401 1.3783 1.3242
33 2.5149 2.0649 1.8487 1.7050 1.5973 1.5110 1.4390 1.3773 1.3233
34 2.5019 2.0603 1.8459 1.7030 1.5957 1.5097 1.4379 1.3764 1.3225
35 2.4894 2.0557 1.8431 1.7010 1.5941 1.5084 1.4368 1.3754 1.3216
36 2.4771 2.0512 1.8403 1.6990 1.5925 1.5071 1.4357 1.3745 1.3208
37 2.4652 2.0467 1.8375 1.6970 1.5909 1.5058 1.4346 1.3735 1.3199
38 2.4536 2.0422 1.8348 1.6950 1.5894 1.5045 1.4335 1.3726 1.3191
39 2.4424 2.0378 1.8320 1.6930 1.5878 1.5032 1.4325 1.3716 1.3183
40 2.4314 2.0334 1.8293 1.6910 1.5863 1.5019 1.4314 1.3707 1.3174
41 2.4206 2.0291 1.8266 1.6890 1.5847 1.5007 1.4303 1.3697 1.3166
42 2.4102 2.0248 1.8239 1.6871 1.5832 1.4994 1.4292 1.3688 1.3158
43 2.4000 2.0206 1.8212 1.6851 1.5816 1.4981 1.4281 1.3678 1.3149
44 2.3900 2.0164 1.8186 1.6832 1.5801 1.4969 1.4270 1.3669 1.3141
45 2.3802 2.0122 1.8159 1.6812 1.5786 1.4956 1.4260 1.3660 1.3133
46 2.3707 2.0081 1.8133 1.6793 1.5771 1.4943 1.4249 1.3650 1.3124
47 2.3613 2.0040 1.8107 1.6774 1.5755 1.4931 1.4238 1.3641 1.3116
48 2.3522 2.0000 1.8081 1.6755 1.5740 1.4918 1.4228 1.3632 1.3108
49 2.3432 1.9960 1.8055 1.6736 1.5725 1.4906 1.4217 1.3623 1.3100
50 2.3345 1.9920 1.8030 1.6717 1.5710 1.4894 1.4206 1.3613 1.3091
51 2.3259 1.9881 1.8004 1.6698 1.5695 1.4881 1.4196 1.3604 1.3083
52 2.3174 1.9842 1.7979 1.6679 1.5680 1.4869 1.4185 1.3595 1.3075
53 2.3091 1.9803 1.7854 1.6661 1.5666 1.4856 1.4175 1.3586 1.3067
54 2.3010 1.9765 1.7929 1.6642 1.5651 1.4844 1.4164 1.3576 1.3059
55 2.2931 1.9727 1.7904 1.6624 1.5636 1.4832 1.4154 1.3567 1.3051
56 2.2852 1.9690 1.7879 1.6605 1.5621 1.4820 1.4143 1.3558 1.3043
57 2.2775 1.9652 1.7855 1.6587 1.5607 1.4808 1.4133 1.3549 1.3034
58 2.2700 1.9615 1.7830 1.6568 1.5592 1.4795 1.4122 1.3540 1.3026
59 2.2626 1.9579 1.7806 1.6550 1.5578 1.4783 1.4112 1.3531 1.3018
60 2.2553 1.9542 1.7782 1.6532 1.5563 1.4771 1.4102 1.3522 1.3010

[page] 41

TABLE XV. Proportional Logarithms.
S h. m. h. m. h. m. h. m. h. m. h. m. h. m. h. m. h. m.
0° 9′ 0° 10′ 0° 11′ 0° 12′ 0° 13′ 0° 14′ 0° 15′ 0° 16′ 0° 17′
0 1.3010 1.2553 1.2139 1.1761 1.1413 1.1091 1.0792 1.0512 1.0248
1 1.3002 1.2545 1.2132 1.1755 1.1408 1.1086 1.0787 1.0507 1.0244
2 1.2994 1.2538 1.2126 1.1749 1.1402 1.1081 1.0782 1.0502 1.0240
3 1.2986 1.2531 1.2119 1.1743 1.1397 1.1076 1.0777 1.0498 1.0235
4 1.2978 1.2524 1.2113 1.1737 1.1391 1.1071 1.0773 1.0493 1.0231
5 1.2970 1.2517 1.2106 1.1731 1.1386 1.1066 1.0768 1.0489 1.0227
6 1.2962 1.2510 1.2099 1.1725 1.1380 1.1061 1.0763 1.0484 1.0223
7 1.2954 1.2502 1.2093 1.1719 1.1374 1.1055 1.0758 1.0480 1.0219
8 1.2946 1.2495 1.2086 1.1713 1.1369 1.1050 1.0753 1.0475 1.0214
9 1.2939 1.2488 1.2080 1.1707 1.1363 1.1045 1.0749 1.0471 1.0210
10 1.2931 1.2481 1.2073 1.1701 1.1358 1.1040 1.0744 1.0467 1.0206
11 1.2923 1.2474 1.2067 1.1695 1.1352 1.1035 1.0739 1.0462 1.0202
12 1.2915 1.2467 1.2061 1.1689 1.1347 1.1030 1.0734 1.0458 1.0197
13 1.2907 1.2460 1.2054 1.1683 1.1342 1.1025 1.0730 1.0453 1.0193
14 1.2899 1.2453 1.2048 1.1677 1.1336 1.1020 1.0725 1.0449 1.0189
15 1.2891 1.2445 1.2041 1.1671 1.1331 1.1015 1.0720 1.0444 1.0185
16 1.2883 1.2438 1.2035 1.1665 1.1325 1.1009 1.0715 1.0440 1.0181
17 1.2876 1.2431 1.2028 1.1660 1.1320 1.1004 1.0711 1.0435 1.0176
18 1.2868 1.2424 1.2022 1.1654 1.1314 1.0999 1.0706 1.0431 1.0172
19 1.2860 1.2417 1.2016 1.1648 1.1309 1.0994 1.0701 1.0426 1.0168
20 1.2852 1.2410 1.2009 1.1642 1.1303 1.0989 1.0696 1.0422 1.0164
21 1.2845 1.2403 1.2003 1.1636 1.1298 1.0984 1.0692 1.0418 1.0160
22 1.2837 1.2396 1.1996 1.1630 1.1292 1.0979 1.0687 1.0413 1.0156
23 1.2829 1.2389 1.1990 1.1624 1.1287 1.0974 1.0682 1.0409 1.0151
24 1.2821 1.2382 1.1984 1.1619 1.1282 1.0969 1.0678 1.0404 1.0147
25 1.2814 1.2375 1.1977 1.1613 1.1276 1.0964 1.0673 1.0400 1.0143
26 1.2806 1.2368 1.1971 1.1607 1.1271 1.0959 1.0668 1.0395 1.0139
27 1.2798 1.2362 1.1965 1.1601 1.1266 1.0954 1.0663 1.0391 1.0135
28 1.2791 1.2355 1.1958 1.1595 1.1260 1.0949 1.0659 1.0387 1.0131
29 1.2783 1.2348 1.1952 1.1589 1.1255 1.0944 1.0654 1.0382 1.0126
30 1.2775 1.2341 1.1946 1.1584 1.1249 1.0939 1.0649 1.0378 1.0122
31 1.2768 1.2334 1.1939 1.1578 1.1244 1.0934 1.0645 1.0374 1.0118
32 1.2760 1.2327 1.1933 1.1572 1.1239 1.0929 1.0640 1.0369 1.0114
33 1.2753 1.2320 1.1927 1.1566 1.1233 1.0924 1.0635 1.0365 1.0110
34 1.2745 1.2313 1.1921 1.1561 1.1228 1.0919 1.0631 1.0360 1.0106
35 1.2738 1.2307 1.1914 1.1555 1.1223 1.0914 1.0626 1.0356 1.0102
36 1.2730 1.2300 1.1908 1.1549 1.1217 1.0909 1.0621 1.0352 1.0098
37 1.2722 1.2293 1.1902 1.1543 1.1212 1.0904 1.0617 1.0347 1.0093
38 1.2715 1.2285 1.1896 1.1538 1.1207 1.0899 1.0612 1.0343 1.0089
39 1.2707 1.2278 1.1889 1.1532 1.1201 1.0894 1.0608 1.0339 1.0085
40 1.2700 1.2272 1.1883 1.1526 1.1196 1.0889 1.0603 1.0334 1.0081
41 1.2692 1.2266 1.1877 1.1520 1.1191 1.0884 1.0598 1.0330 1.0077
42 1.2685 1.2259 1.1871 1.1515 1.1186 1.0880 1.0594 1.0326 1.0073
43 1.2678 1.2252 1.1865 1.1509 1.1180 1.0875 1.0589 1.0321 1.0069
44 1.2670 1.2245 1.1858 1.1503 1.1175 1.0870 1.0585 1.0317 1.0065
45 1.2663 1.2239 1.1852 1.1498 1.1170 1.0865 1.0580 1.0313 1.0061
46 1.2655 1.2232 1.1846 1.1492 1.1164 1.0860 1.0575 1.0308 1.0057
47 1.2648 1.2225 1.1840 1.1486 1.1159 1.0855 1.0571 1.0304 1.0053
48 1.2640 1.2218 1.1834 1.1481 1.1154 1.0850 1.0566 1.0300 1.0049
49 1.2633 1.2212 1.1828 1.1475 1.1149 1.0845 1.0562 1.0295 1.0044
50 1.2626 1.2205 1.1822 1.1469 1.1143 1.0840 1.0557 1.0291 1.0040
51 1.2618 1.2198 1.1816 1.1464 1.1138 1.0835 1.0552 1.0287 1.0036
52 1.2611 1.2192 1.1809 1.1458 1.1133 1.0831 1.0548 1.0282 1.0032
53 1.2604 1.2185 1.1803 1.1452 1.1128 1.0826 1.0543 1.0278 1.0028
54 1.2596 1.2178 1.1797 1.1447 1.1123 1.0821 1.0539 1.0274 1.0024
55 1.2589 1.2172 1.1791 1.1441 1.1117 1.0816 1.0534 1.0270 1.0020
56 1.2582 1.2165 1.1785 1.1436 1.1112 1.0811 1.0530 1.0265 1.0016
57 1.2574 1.2159 1.1779 1.1430 1.1107 1.0806 1.0525 1.0261 1.0012
58 1.2567 1.2152 1.1773 1.1424 1.1102 1.0801 1.0521 1.0257 1.0008
59 1.2560 1.2145 1.1767 1.1419 1.1097 1.0797 1.0516 1.0252 1.0004
60 1.2553 1.2139 1.1761 1.1413 1.1091 1.0792 1.0512 1.0248 1.0000

F

[page] 42

TABLE XV. Proportional Logarithms.
S h. m. h. m. h. m. h. m. h. m. h. m. h. m. h. m. h. m. h. m. h. m. h. m.
0° 18′ 0° 19′ 0° 20′ 0° 21′ 0° 22′ 0° 23′ 0° 24′ 0° 25′ 0° 26′ 0° 27′ 0° 28′ 0° 29′
0 0000 9765 9542 9331 9128 8935 8751 8573 8403 8239 8081 7929
1 9996 9761 9539 9327 9125 8932 8748 8570 8400 8236 8079 7926
2 9992 9758 9535 9324 9122 8929 8745 8568 8397 8234 8076 7924
3 9988 9754 9532 9320 9119 8926 8742 8565 8395 8231 8073 7921
4 9984 9750 9528 9317 9115 8923 8739 8562 8392 8228 8071 7919
5 9980 9746 9524 9313 9112 8920 8736 8559 8389 8226 8068 7916
6 9976 9742 9521 9310 9109 8917 8733 8556 8386 8223 8066 7914
7 9972 9739 9517 9306 9106 8913 8730 8553 8384 8220 8063 7911
8 9968 9735 9514 9303 9102 8910 8727 8550 8381 8218 8061 7909
9 9964 9731 9510 9300 9099 8907 8724 8547 8378 8215 8058 7906
10 9960 9727 9506 9296 9096 8904 8721 8544 8375 8212 8055 7904
11 9956 9723 9503 9293 9092 8901 8718 8542 8372 8210 8053 7901
12 9952 9720 9499 9289 9089 8898 8715 8539 8370 8207 8050 7899
13 9948 9716 9496 9286 9086 8895 8712 8536 8367 8204 8048 7896
14 9944 9712 9492 9283 9083 8892 8709 8533 8364 8202 8045 7894
15 9940 9708 9488 9279 9079 8888 8706 8530 8361 8199 8043 7891
16 9936 9705 9485 9276 9076 8885 8703 8527 8359 8196 8040 7889
17 9932 9701 9481 9272 9073 8882 8700 8524 8356 8194 8037 7887
18 9928 9697 9478 9269 9070 8879 8697 8522 8353 8191 8035 7884
19 9924 9693 9474 9266 9066 8876 8694 8519 8350 8188 8032 7882
20 9920 9690 9471 9262 9063 8873 8691 8516 8348 8186 8030 7879
21 9916 9686 9467 9259 9060 8870 8688 8513 8345 8183 8027 7877
22 9912 9682 9464 9255 9057 8867 8685 8510 8342 8181 8025 7874
23 9908 9678 9460 9252 9053 8864 8682 8507 8339 8178 8022 7872
24 9905 9675 9456 9249 9050 8861 8679 8504 8337 8175 8020 7869
25 9901 9671 9453 9245 9047 8857 8676 8502 8334 8173 8017 7867
26 9897 9667 9449 9242 9044 8854 8673 8499 8331 8170 8014 7864
27 9893 9664 9446 9238 9041 8851 8670 8496 8238 8167 8012 7862
28 9889 9660 9442 9235 9037 8848 8667 8493 8326 8165 8009 7859
29 9885 9656 9439 9232 9034 8845 8664 8490 8323 8162 8007 7857
30 9881 9652 9435 9228 9031 8842 8661 8487 8320 8159 8004 7855
31 9877 9649 9432 9225 9028 8839 8658 8484 8318 8157 8002 7852
32 9873 9645 9428 9222 9024 8836 8655 8482 8315 8154 7999 7850
33 9869 9641 9425 9218 9021 8833 8652 8479 8312 8152 7997 7847
34 9865 9638 9421 9215 9018 8830 8649 8476 8309 8149 7994 7845
35 9861 9634 9418 9212 9015 8827 8646 8473 8307 8146 7992 7842
36 9858 9630 9414 9208 9012 8824 8643 8470 8304 8144 7989 7840
37 9854 9626 9411 9205 9008 8821 8640 8467 8301 8141 7987 7837
38 9850 9623 9407 9201 9005 8817 8637 8465 8298 8138 7984 7835
39 9846 9619 9404 9198 9002 8814 8635 8462 8296 8136 7981 7832
40 9842 9615 9400 9195 8999 8811 8632 8459 8293 8133 7979 7830
41 9838 9612 9397 9191 8996 8808 8629 8456 8290 8131 7976 7828
42 9834 9608 9393 9188 8992 8805 8626 8453 8288 8128 7974 7825
43 9830 9604 9390 9185 8989 8802 8623 8451 8285 8125 7971 7823
44 9827 9601 9386 9181 8986 8799 8620 8448 8282 8123 7969 7820
45 9823 9597 9383 9178 8983 8796 8617 8445 8279 8120 7966 7818
46 9819 9593 9379 9175 8980 8793 8614 8442 8277 8117 7964 7815
47 9815 9590 9376 9172 8977 8790 8611 8439 8274 8115 7961 7813
48 9811 9586 9372 9168 8973 8787 8608 8437 8271 8112 7959 7811
49 9807 9582 9369 9165 8970 8784 8605 8434 8269 8110 7956 7808
50 9803 9579 9365 9162 8967 8781 8602 8431 8266 8107 7954 7806
51 9800 9575 9362 9158 8964 8778 8599 8428 8263 8104 7951 7803
52 9796 9571 9358 9155 8961 8775 8597 8425 8261 8102 7949 7801
53 9792 9568 9355 9152 8958 8772 8594 8423 8258 8099 7946 7798
54 9788 9564 9351 9148 8954 8769 8591 8420 8255 8097 7944 7796
55 9784 9561 9348 9145 8951 8766 8588 8417 8253 8094 7941 7794
56 9780 9557 9344 9142 8948 8763 8585 8414 8250 8091 7939 7791
57 9777 9553 9341 9138 8945 8760 8582 8411 8247 8089 7936 7789
58 9773 9550 9337 9135 8942 8757 8579 8409 8244 8086 7934 7786
59 9769 9546 9334 9132 8939 8754 8576 8406 8242 8084 7931 7784
60 9765 9542 9331 9128 8935 8751 8573 8403 8239 8081 7929 7782

[page] 43

TABLE XV. Proportional Logarithms.
S h. m. h. m. h. m. h. m. h. m. h. m. h. m. h. m. h. m. h. m. h. m. h. m.
0° 30′ 0° 31′ 0° 32′ 0° 33′ 0° 34′ 0° 35′ 0° 36′ 0° 37′ 0° 38′ 0° 39′ 0° 40′ 0° 41′
0 7782 7639 7501 7368 7238 7112 6990 6871 6755 6642 6532 6425
1 7779 7637 7499 7365 7236 7110 6988 6869 6753 6640 6530 6423
2 7777 7634 7497 7363 7234 7108 6986 6867 6751 6638 6529 6421
3 7774 7632 7494 7361 7232 7106 6984 6865 6749 6637 6527 6420
4 7772 7630 7492 7359 7229 7104 6982 6863 6747 6635 6525 6418
5 7769 7627 7490 7357 7227 7102 6980 6861 6745 6633 6523 6416
6 7767 7625 7488 7354 7225 7100 6978 6859 6743 6631 6521 6414
7 7765 7623 7485 7352 7223 7098 6976 6857 6742 6629 6519 6413
8 7762 7620 7483 7350 7221 7096 6974 6855 6740 6627 6518 6411
9 7760 7618 7481 7348 7219 7093 6972 6853 6738 6625 6516 6409
10 7757 7616 7479 7346 7217 7091 6970 6851 6736 6624 6514 6407
11 7755 7613 7476 7344 7215 7089 6968 6849 6734 6622 6512 6406
12 7753 7611 7474 7341 7212 7087 6966 6847 6732 6620 6510 6404
13 7750 7609 7472 7339 7210 7085 6964 6845 6730 6618 6509 6402
14 7748 7607 7470 7337 7208 7083 6962 6843 6728 6616 6507 6400
15 7745 7604 7467 7335 7206 7081 6960 6841 6726 6614 6505 6398
16 7743 7602 7465 7333 7204 7079 6958 6840 6725 6612 6503 6397
17 7741 7600 7463 7330 7202 7077 6956 6838 6723 6611 6501 6395
18 7738 7597 7461 7328 7200 7075 6954 6836 6721 6609 6500 6393
19 7736 7595 7458 7326 7198 7073 6952 6834 6719 6607 6498 6391
20 7734 7593 7456 7324 7196 7071 6950 6832 6717 6605 6496 6390
21 7731 7590 7454 7322 7193 7069 6848 6830 6715 6603 6494 6388
22 7729 7588 7452 7320 7191 7067 6946 6828 6713 6601 6492 6386
23 7726 7586 7450 7317 7189 7065 6944 6826 6711 6600 6491 6384
24 7724 7583 7447 7315 7187 7063 6942 6824 6709 6598 6489 6383
25 7722 7581 7445 7313 7185 7061 6940 6822 6708 6596 6487 6381
26 7719 7579 7443 7311 7183 7059 6938 6820 6706 6594 6485 6379
27 7717 7577 7441 7309 7181 7057 6936 6818 6704 6592 6484 6377
28 7714 7574 7438 7307 7179 7055 6934 6816 6702 6590 6482 6376
29 7712 7572 7436 7304 7177 7052 6932 6814 6700 6589 6480 6374
30 7710 7570 7434 7302 7175 7050 6930 6812 6698 6587 6478 6372
31 7707 7567 7432 7300 7172 7048 6928 6810 6696 6585 6476 6371
32 7705 7565 7429 7298 7170 7046 6926 6809 6694 6583 6475 6369
33 7703 7563 7427 7296 7168 7044 6924 6807 6692 6581 6473 6367
34 7700 7560 7425 7294 7166 7042 6922 6805 6691 6579 6471 6365
35 7698 7558 7423 7291 7164 7040 6920 6803 6689 6578 6469 6364
36 7696 7556 7421 7289 7162 7038 6918 6801 6687 6576 6467 6362
37 7693 7554 7418 7287 7160 7036 6916 6799 6685 6574 6466 6360
38 7691 7551 7416 7285 7158 7034 6914 6797 6683 6572 6464 6358
39 7688 7549 7414 7283 7156 7032 6912 6795 6681 6570 6462 6357
40 7686 7547 7412 7281 7154 7030 6910 6793 6679 6568 6460 6355
41 7864 7544 7409 7279 7152 7028 6908 6791 6677 6567 5459 6353
42 7681 7542 7407 7276 7149 7026 6906 6789 6676 6565 6457 6351
43 7679 7540 7405 7274 7147 7024 6904 6787 6674 6563 6455 6350
44 7677 7538 7403 7272 7145 7022 6902 6785 6672 6561 6453 6348
45 7674 7535 7401 7270 7143 7020 6900 6784 6670 6559 6451 6346
46 7672 7533 7398 7268 7141 7018 6898 6782 6668 6558 6450 6344
47 7670 7531 7396 7266 7139 7016 6896 6780 6666 6556 6448 6343
48 7667 7528 7394 7264 7137 7014 6894 6778 6664 6554 6446 6341
49 7665 7526 7392 7261 7135 7012 6892 6779 6663 6552 6444 6339
50 7663 7524 7390 7259 7133 7010 6890 6774 6661 6550 6443 6338
51 7660 7522 7387 7257 7131 7008 6888 6772 6659 6548 6441 6336
52 7658 7519 7385 7255 7129 7006 6886 6770 6657 6547 6439 6334
53 7655 7517 7383 7253 7127 7004 6884 6768 6655 6545 6437 6332
54 7653 7515 7381 7251 7124 7002 6882 6766 6653 6543 6435 6331
55 7651 7513 7379 7249 7122 7000 6881 6764 6651 6541 6434 6329
56 7648 7510 7376 7246 7120 6998 6879 6763 6650 6539 6432 6327
57 7646 7508 7374 7244 7118 6996 6877 6761 6648 6538 6430 6325
58 7644 7506 7372 7242 7116 6994 6875 6759 6646 6536 6428 6324
59 7641 7503 7370 7240 7114 6992 6873 6757 6644 6534 6427 6322
60 7639 7501 7368 7238 7112 6990 6871 6755 6642 6532 6425 6320

F 2

[page] 44

TABLE XV. Proportional Logarithms.
S h. m. h. m. h. m. h. m. h. m. h. m. h. m. h. m. h. m. h. m. h. m. h. m.
0° 42′ 0° 43′ 0° 44′ 0° 45′ 0° 46′ 0° 47′ 0° 48′ 0° 49′ 0° 50′ 0° 51′ 0° 52′ 0° 53′
0 6320 6218 6118 6021 5925 5832 5740 5651 5563 5477 5393 5310
1 6319 6216 6117 6019 5924 5830 5739 5649 5562 5476 5391 5309
2 6317 6215 9115 6017 5922 5829 5737 5648 5560 5474 5390 5307
3 6315 9213 6113 6016 5920 5827 5736 5646 5559 5473 5389 5306
4 6313 6211 6112 6014 5919 5826 5734 5645 5557 5471 5387 5305
5 6312 6210 6110 6013 5917 5824 5733 5643 5556 5470 5386 5303
6 6310 6208 6108 6011 5916 5823 5731 5642 5554 5469 5384 5302
7 6308 6206 6107 6009 5914 5821 5730 5640 5553 5467 5383 5300
8 6306 6205 6105 6008 5913 5819 5728 5639 5551 5466 5382 5299
9 6305 6203 6103 6006 5911 5818 5727 5637 5550 5464 5380 5298
10 6303 6201 6102 6005 5909 5816 5725 5636 5549 5463 5379 5296
11 6301 6200 6100 6003 5908 5815 5724 5635 5547 5461 5377 5295
12 6300 6198 6099 6001 5906 5813 5722 5633 5546 5460 5376 5293
13 6298 6196 6097 6000 5905 5812 5721 5632 5544 5459 5375 5292
14 6296 6195 6095 5998 5903 5810 5719 5630 5543 5457 5373 5291
15 6294 6193 6094 5997 5902 5809 5718 5629 5541 5456 5372 5290
16 6293 6191 6092 5995 5900 5807 5716 5627 5540 5454 5370 5288
17 6291 6190 6090 1993 5898 5806 5715 5626 5538 5453 5369 5287
18 6289 6188 6089 5992 5897 5804 5713 5624 5537 5452 5368 5285
19 6288 6186 6087 5990 5895 5803 5712 5623 5530 5450 5300 5284
20 6286 6185 6085 5989 5894 5801 5710 5621 5534 5449 5365 5283
21 6284 6163 6084 5987 5891 5800 5709 5620 5533 5447 5364 5281
22 6282 6181 6082 5985 5891 5798 5707 5618 5531 5446 5362 5280
23 6281 6179 6081 5984 5889 5796 5706 5617 5530 5445 5361 5279
24 6279 6178 6078 5982 5888 5795 5704 5615 5528 5443 5359 5277
25 6277 6176 6077 5981 5886 5793 5703 5614 5527 5442 5358 5276
26 6276 6174 6076 5979 5884 5792 5701 5613 5526 5440 5357 5275
27 6274 6173 6074 5977 5883 5790 5700 5611 5524 5439 5355 5273
28 6272 6171 6072 5976 5881 5789 5698 5610 5523 5437 5354 5272
29 6271 6169 6071 5974 5880 5787 5697 5608 5521 5436 5353 5271
30 6269 6168 6069 5973 5878 5786 5695 5607 5520 5435 5351 5269
31 6267 6166 6067 5971 5877 5784 5694 5605 5518 5433 5350 5268
32 6265 6165 6066 5969 5875 5783 5692 5604 5517 5432 5348 5266
33 6264 6163 6064 5968 5874 5781 5691 5602 5516 5430 5347 5265
34 6262 6161 6063 5966 5872 5780 5689 5601 5514 5429 5346 5264
35 6260 6160 6061 5965 5870 5778 5688 5599 5513 5428 5344 5262
36 6259 6158 6059 5963 5869 5777 5686 5598 5511 5426 5343 5261
37 6257 6156 6058 5961 5867 5775 5685 5596 5510 5425 5341 5260
38 6255 6155 6056 5960 5866 5774 5683 5595 5508 5423 5340 5258
39 6254 6153 6055 5958 5864 5772 5682 5594 5507 5422 5339 5257
40 6252 6151 6053 5957 5863 5771 5680 5592 5506 5421 5337 5256
41 6250 6150 6051 5955 5861 5769 5679 5591 5504 5419 5536 5254
42 6248 6148 6050 5954 5860 5768 5677 5589 5503 5418 5335 5253
43 6247 6146 6048 5952 5858 5766 5676 5588 5501 5416 5333 5252
44 6245 6145 6046 5950 5856 5765 5674 5586 5500 5415 5332 5250
45 6243 6143 6045 5949 5855 5763 5673 5585 5498 5414 5331 5249
46 6242 6141 6043 5947 5853 5761 5671 5583 5497 5412 5329 5248
47 6240 6140 6042 5946 5852 5760 5670 5582 5496 5411 5328 5246
48 6238 6138 6040 5944 5850 5758 5669 5580 5494 5409 5326 5245
49 6237 6136 6038 5942 5849 5757 5667 5579 5493 5408 5325 5244
50 6235 6135 6037 5941 5847 5755 5666 5578 5491 5407 5324 5242
51 6233 6133 6035 5939 5846 5754 5664 5576 5490 5405 5322 5241
52 6232 6131 6033 5938 5844 5752 5663 5575 5488 5404 5321 5240
53 6230 6130 6032 5936 5843 5751 5661 5573 5487 5402 5320 5238
54 5228 6128 6030 5935 5841 5749 5660 5572 5486 5401 5318 5237
55 6226 6126 6029 5933 5839 5748 5658 5570 5484 5400 5317 5235
56 6225 6125 6027 5931 5838 5746 5657 5569 5483 5398 5315 5234
57 6223 6123 6025 5930 5836 5745 5655 5567 5481 5397 5314 5233
58 6221 6121 6024 5928 5835 5743 5654 5566 5480 5395 5313 5231
59 6220 6120 6022 5927 5833 5742 5652 5564 5478 5394 5311 5230
60 6218 6118 6021 5925 5832 5740 5651 5563 5477 5393 5310 5229

[page] 45

TABLE XV. Proportional Logarithms.
S h. m. h. m. h. m. h. m. h. m. h. m. h. m. h. m. h. m. h. m. h. m. h. m.
0° 54′ 0° 55′ 0° 56′ 0° 57′ 0° 58′ 0° 59′ 1° 0′ 1° 1′ 1° 2′ 1° 3′ 1° 4′ 1° 5′
0 5229 5149 5071 4994 4918 4844 4771 4699 4629 4559 4491 4424
1 5227 5148 5070 4993 4917 4843 4770 4698 4628 4558 4490 4422
2 5226 5146 5068 4991 4916 4842 4769 4697 4626 4557 4489 4421
3 5225 5145 5067 4990 4915 4841 4768 4696 4625 4556 4488 4420
4 5223 5144 5066 4989 4913 4839 4766 4695 4624 4555 4486 4419
5 5222 5143 5064 4988 4912 4838 4765 4693 4623 4554 4485 4418
6 5221 5141 5063 4986 4911 4837 4764 4692 4622 4552 4484 4417
7 5219 5140 5062 4985 4910 4836 4763 4691 4621 4551 4483 4416
8 5218 5139 5061 4984 4908 4834 4762 4690 4619 4550 4482 4415
9 5217 5137 5059 4983 4907 4833 4760 4689 4618 4549 4481 4414
10 5215 5136 5058 4981 4906 4832 4759 4866 4617 4548 4480 4412
11 5214 5135 5057 4980 4905 4831 4758 4686 4616 4547 4479 4411
12 5213 5133 5055 4979 4903 4830 4757 4685 4615 4546 4477 4410
13 5211 5132 5054 4977 4902 4828 4756 4684 4614 4544 4476 4409
14 5210 5131 5053 4976 4901 4827 4754 4683 4612 4543 4475 4408
15 5209 5129 5051 4975 4900 4826 4753 4682 4611 4542 4474 4407
16 5207 5128 5050 4974 4899 4825 4752 4680 4610 4541 4473 4406
17 5206 5127 5049 4972 4897 4823 4751 4679 4609 4540 4472 4405
18 5205 5125 5048 4971 4896 4822 4750 4678 4608 4539 4471 4404
19 5203 5124 5046 4970 4895 4821 4948 4677 4607 4538 4469 4402
20 5202 5123 5045 4969 4894 4820 4747 4676 4606 4536 4468 4401
21 5201 5122 5044 4967 4892 4819 4746 4675 4604 4535 4467 4400
22 5199 5120 5043 4966 4891 4817 4745 4673 4603 4534 4466 4399
23 5198 5119 5041 4965 4890 4816 4744 4672 4602 4533 4465 4398
24 5197 5118 5040 4964 4889 4815 4742 4671 4601 4532 4464 4397
25 5195 5116 5039 4962 4887 4814 4741 4670 4600 4531 4463 4396
26 5194 5115 5037 4961 4886 4812 4740 4669 4599 4530 4462 4395
27 5193 5114 5036 4960 4885 4811 4739 4668 4597 4528 4460 4394
28 5191 5112 5035 4959 4884 4810 4738 4666 4596 4527 4459 4393
29 5190 5111 5034 4957 4882 4809 4736 4665 4695 4526 4458 4391
30 5189 5110 5032 4956 4881 4808 4735 4664 4594 4525 4457 4390
31 5187 5108 5031 4955 4880 4806 4734 4663 4593 4524 4456 4389
32 5186 5107 5030 4954 4879 4805 4733 4662 4592 4523 4455 4388
33 5185 5106 5028 4952 4877 4804 4732 4660 4590 4522 4454 4387
34 5183 5105 5027 4951 4876 4803 4730 4659 4589 4520 4453 4386
35 5182 5103 5026 4950 4875 4801 4729 4658 4588 4519 4452 4385
36 5181 5102 5025 4949 4874 4800 4728 4657 4587 4518 4450 4384
37 5179 5101 5023 4947 4873 4799 4727 4656 4586 4517 4449 4383
38 5178 5099 5022 4946 4871 4798 4726 4655 4585 4516 4448 4381
39 5177 5098 5021 4945 4870 4797 4724 4653 4584 4515 4447 4380
40 5175 5097 5019 4943 4869 4795 4723 4652 4582 4514 4446 4379
41 5174 5095 5018 4942 4868 4794 4722 4651 4581 4512 4445 4378
42 5173 5094 5017 4941 4866 4793 4721 4650 4580 4511 4444 4377
43 5172 5093 5016 4940 4865 4792 4720 4649 4579 4510 4443 4376
44 5170 5092 5014 4938 4864 4791 4718 4648 4578 4509 4441 4375
45 5169 5090 5013 4937 4863 4789 4717 4646 4577 4508 4440 4374
46 5168 5089 5012 4936 4861 4788 4716 4645 4575 4507 4439 4373
47 5166 5088 5011 4935 4860 4787 4715 4644 4574 4506 4438 4372
48 5165 5086 5009 4933 4859 4786 4714 4643 4573 4505 4437 4370
49 5164 5085 5008 4632 4858 4784 4712 4642 4572 4503 4436 4369
50 5162 5084 5007 4931 4856 4783 4711 4640 4571 4502 4435 4368
51 5161 5082 5005 4930 4855 4782 4710 4639 4570 4501 4434 4367
52 5160 5081 5004 4928 4854 4781 4709 4638 4569 4500 4433 4366
53 5158 5080 5003 4927 4853 4780 4708 4637 4567 4499 4431 4365
54 5157 5079 5002 4926 4852 4778 4707 4636 4566 4498 4430 4364
55 5156 5077 5000 4925 4850 4777 4705 4635 4565 4497 4429 4363
56 5154 5076 4999 4923 4849 4776 4704 4633 4564 4495 4428 4362
57 5153 5075 4998 4922 4848 4775 4703 4632 4563 4494 4427 4361
58 5152 5073 4997 4921 4847 4774 4702 4631 4562 4493 4426 4359
59 5150 5072 4995 4920 4845 4772 4701 4630 4560 4492 4425 4358
60 5149 5071 4994 4918 4844 4771 4699 4629 4559 4491 4424 4357

[page] 46

TABLE XV. Proportional Logarithms.
S h. m. h. m. h. m. h. m. h. m. h. m. h. m. h. m. h. m. h. m. h. m. h. m.
1° 6′ 1° 7′ 1° 8′ 1° 9′ 1° 10′ 1° 11′ 1° 12′ 1° 13′ 1° 14′ 1° 15′ 1° 16′ 1° 17′
0 4357 4292 4228 4164 4102 4040 3979 3919 3860 3802 3745 3688
1 4356 4291 4227 4163 4101 4039 3978 3919 3859 3801 3744 3687
2 4355 4290 4226 4162 4100 4038 3977 3918 3858 3800 3743 3686
3 4354 4289 4224 4161 4099 4037 3776 3917 3857 3799 3742 3685
4 4353 4288 4223 4160 4098 4036 3975 3916 3856 3798 3741 3684
5 4352 4287 4222 4159 4097 4035 3974 3915 3856 3797 3740 3683
6 4351 4285 4221 4158 4096 4034 3973 3914 3855 3796 3739 3682
7 4350 4284 4220 4157 4095 4033 3972 3913 3854 3795 3738 3681
8 4349 4283 4219 4156 4093 4032 3971 3912 3853 3794 3737 3680
9 4347 4282 4218 4155 4092 4031 3970 3911 3852 3793 3736 3679
10 4346 4281 4217 4154 4091 4030 3969 3910 3851 3792 3735 3678
11 4345 4280 4216 4153 4090 4029 3968 3909 3850 3792 3734 3677
12 4344 4279 4215 4152 4089 4028 3967 3908 3849 3791 3733 3677
13 4343 4278 4214 4151 4088 4027 3966 3907 3848 3790 3732 3676
14 4342 4277 4213 4150 4087 4026 3965 3906 3847 3789 3731 3675
15 4341 4276 4212 4149 4086 4025 3964 3905 3846 3788 3730 3674
16 4340 4275 4211 4147 4085 4024 3963 3904 3845 3787 3729 3673
17 4339 4274 4210 4146 4084 4023 3962 3903 3844 3786 3728 3672
18 4338 4273 4209 4145 4083 4022 3961 3902 3843 3785 3727 3671
19 4336 4271 4207 4144 4082 4021 3960 3901 3842 3784 3727 3670
20 4335 4270 4206 4143 4081 4020 3959 3900 3841 3783 3726 3669
21 4334 4269 4205 4142 4080 4019 3958 3899 3840 3782 3725 3668
22 4333 4268 4204 4141 4079 4018 3957 3898 3839 3781 3724 3667
23 4332 4267 4203 4140 4078 4017 3956 3897 3838 3780 3723 3666
24 4331 4266 4202 4139 4077 4016 3955 3896 3837 3779 3722 3665
25 4330 4265 4201 4138 4076 4015 3954 3895 3836 3778 3721 3664
26 4329 4264 4200 4137 4075 4014 3953 3894 3835 3777 3720 3663
27 4328 4263 4199 4136 4074 4013 3952 3893 3834 3776 3719 3663
28 4327 4262 4198 4135 4073 4012 3951 3892 3833 3775 3718 3662
29 4326 4261 4197 4134 4072 4011 3950 3891 3832 3774 3717 3661
30 4325 4260 4196 4133 4071 4010 3949 3890 3831 3773 3716 3660
31 4323 4259 4195 4132 4070 4009 3948 3889 3830 3772 3715 3659
32 4322 4258 4194 4131 4069 4008 3947 3888 3829 3771 3714 3658
33 4321 4256 4196 4130 4068 4007 3946 3887 3828 3770 3713 3657
34 4320 4255 4192 4129 4067 4006 3945 3886 3827 3769 3712 3656
35 4319 4254 4191 4128 4066 4005 3944 3885 3826 3768 3711 3655
36 4318 4253 4189 4127 4065 4004 3943 3884 3825 3768 3710 3654
37 4317 4252 4188 4126 4064 4003 3942 3883 3824 3767 3709 3653
38 4316 4251 4187 4125 4063 4002 3941 3882 3823 3766 3709 3652
39 4315 4250 4186 4124 4062 4001 3940 3881 3822 3765 3708 3651
40 4314 4249 4185 4122 4061 4000 3939 3880 3821 3764 3707 3650
41 4313 4248 4184 4121 4060 3999 3938 3879 3820 3763 3706 3649
42 4311 4247 4183 4120 4059 3998 3837 3878 3820 3762 3705 3649
43 4310 4246 4182 4119 4058 3997 3936 3877 3819 3761 3704 3648
44 4309 4245 4181 4118 4056 3996 3935 3876 3818 3760 3703 3647
45 4308 4244 4180 4117 4055 3995 3934 3875 3817 3759 3702 3646
46 4307 4243 4179 4116 4054 3993 3933 3874 3816 3758 3701 3645
47 4306 4241 4178 4115 4053 3992 3932 3873 3815 3757 3700 3644
48 4305 4240 4177 4114 4052 3991 3931 3872 3814 3756 3699 3643
49 4304 4239 4176 4113 4051 3990 3930 3871 3813 3755 3698 3642
50 4303 4238 4175 4112 4050 3989 3929 3870 3812 3754 3697 3641
51 4302 4237 4174 4111 4049 3988 3928 3869 3811 3753 3696 3640
52 4301 4236 4173 4110 4048 3987 3927 3868 3810 3752 3695 3639
53 4300 4235 4172 4109 4047 3986 3926 3867 3809 3751 3694 3638
54 4298 4234 4171 4108 4046 3985 3925 3866 3808 3750 3693 3637
55 4297 4233 4169 4107 4045 3984 3924 3865 3807 3749 3693 3636
56 4296 4232 4168 4106 4044 3983 3923 3864 3806 3748 3692 3635
57 4295 4231 4167 4105 4043 3982 3922 3863 3805 3747 3691 3635
58 4294 4230 4166 4104 4042 3981 3921 3862 3804 3746 3690 3634
59 4293 4229 4165 4103 4041 3980 3920 3861 3803 3746 3689 3633
60 4292 4228 4164 4102 4040 3979 3919 3860 3802 3745 3688 3632

[page] 47

TABLE XV. Proportional Logarithms.
S h. m. h. m. h. m. h. m. h. m. h. m. h. m. h. m. h. m. h. m. h. m. h. m.
1° 18′ 1° 19′ 1° 20′ 1° 21′ 1° 22′ 1° 23′ 1° 24′ 1° 25′ 1° 26′ 1° 27′ 1° 28′ 1° 29′
0 3632 3576 3522 3468 3415 3362 3310 3259 3208 3158 3108 3059
1 3631 3576 3521 3467 3414 3361 3309 3258 3207 3157 3107 3058
2 3630 3575 3520 3466 3413 3360 3308 3257 3206 3156 3106 3057
3 3629 3574 3519 3465 3412 3359 3307 3256 3205 3155 3105 3056
4 3628 3573 3518 3464 3411 3358 3306 3255 3204 3154 3105 3056
5 3627 3572 3517 3463 3410 3358 3306 3254 3204 3153 3104 3055
6 3626 3571 3516 3463 3409 3357 3305 3253 3203 3153 3103 3054
7 3625 3570 3515 3462 3408 3356 3304 3253 3202 3152 3102 3053
8 3624 3569 3514 3461 3408 3355 3303 3252 3201 3151 3101 3052
9 3623 3568 3514 3460 3407 3354 3302 3251 3200 3150 3101 3052
10 3623 3567 3513 3459 3406 3353 3301 3250 3199 3149 3100 3051
11 3622 3566 3512 3458 3405 3352 3300 3249 3198 3148 3099 3050
12 3621 3565 3511 3457 3404 3351 3300 3248 3198 3148 3098 3049
13 3620 3565 3510 3456 3403 3351 3299 3247 3197 3147 3097 3048
14 3619 3564 3509 3455 3402 3350 3298 3247 3196 3146 3096 3047
15 3618 3563 3508 3454 3401 3349 3297 3246 3195 3145 3096 3047
16 3617 3562 3507 3454 3400 3348 3296 3245 3194 3144 3095 3046
17 3616 3561 3506 3453 3400 3347 3295 3244 3193 3143 3094 3045
18 3615 3560 3506 3452 3399 3346 3294 3243 3193 3143 3093 3044
19 3614 3559 3505 3451 3398 3345 3294 3242 3192 3142 3092 3043
20 3613 3558 3404 3450 3397 3345 3293 3242 3191 3141 3091 3043
21 6312 3557 3503 3449 3396 3344 3292 3241 3190 3140 3091 3042
22 3611 3556 3502 3448 3395 3343 3291 3240 3189 3139 3090 3041
23 3610 3555 3501 3447 3394 3342 3290 3239 3188 3138 3089 3040
24 3610 3555 3500 3446 3393 3341 3289 3238 3188 3138 3088 3039
25 3609 3554 3499 3446 3393 3340 3288 3237 3187 3137 3087 3099
26 3608 3553 3498 3445 3392 3339 3288 3236 3186 3136 3087 3038
27 3607 3552 3497 3444 3391 3338 3287 3236 3185 3135 3086 3037
28 3606 3551 3497 3443 3390 3338 3286 3235 3184 3134 3085 3036
29 3605 3550 3496 3442 3389 3337 3285 3234 3183 3133 3084 3035
30 3604 3549 3495 3441 3388 3336 3284 3233 3183 3133 3083 3034
31 3603 3548 3494 3440 3387 3335 3283 3232 3182 3132 3082 3034
32 3602 3547 3493 3439 3386 3334 3282 3231 3181 3131 3082 3033
33 3601 3546 3492 3438 3386 3333 3282 8231 3180 3130 3081 3032
34 3600 3545 3491 3438 3385 3332 3281 3230 3179 3129 3080 3031
35 3599 3545 3490 3437 3384 3332 3280 3229 3178 3129 3079 3030
36 3598 3544 3489 3436 3383 3331 3279 3228 3178 3128 3078 3030
37 3598 3543 3488 3435 3382 3330 3278 3227 3177 3127 3078 3029
38 3597 3542 3488 3434 3381 3329 3277 3226 3176 3126 3077 3028
39 3596 3541 3487 3433 3380 3328 3276 3225 3175 3125 3076 3027
40 3595 3540 3486 3432 3379 3327 3276 3225 3174 3124 3075 3026
41 3594 3539 3485 3431 3379 3326 3275 3224 3173 3124 3074 3026
42 3593 3538 3484 3431 3378 3325 3274 3223 3173 3123 3073 3025
43 3592 3537 3483 3430 3377 3325 3273 3222 3172 3122 3073 3024
44 3591 3536 3482 3429 3376 3324 3272 3221 3171 3121 3072 3023
45 3590 3535 3481 3428 3375 3323 3271 3220 3170 3120 3071 3022
46 3589 3535 3480 3427 3374 3322 3270 3220 3169 3119 3070 3022
47 3588 3534 3480 3426 3373 3321 3270 3219 3168 3119 3069 3021
48 3587 3533 3479 3425 3372 3320 3269 3218 3168 3118 3069 3020
49 3587 3532 3478 3424 3372 3319 3268 3217 3167 3117 3068 3019
50 3586 3531 3477 3423 3371 3319 3267 3216 3166 3116 3067 3018
51 3585 3530 3476 3423 3370 3318 3266 3215 3165 3115 3066 3018
52 3584 3529 3475 3422 3369 3317 3265 3214 3164 3114 3065 3017
53 3583 3528 3474 3421 3368 3316 3265 3214 3163 3114 3065 3016
54 3582 3527 3473 3420 3367 3315 3264 3213 3163 3113 3064 3015
55 3581 3526 3472 3419 3366 3314 3263 3212 3162 3112 3063 3014
56 3580 3525 3471 3418 3365 3313 3262 3211 3161 3111 3062 3014
57 3579 3525 3471 3417 3365 3313 3261 3210 3160 3110 3061 3013
58 3578 3524 3470 3416 3364 3312 3260 3209 3159 3110 3060 3012
59 3577 3523 3469 3415 3363 3311 3259 3209 3158 3109 3060 3011
60 3576 3522 3468 3415 3362 3310 3259 3208 3158 3108 3059 3010

[page] 48

TABLE XV. Proportional Logarithms.
S h. m. h. m. h. m. h. m. h. m. h. m. h. m. h. m. h. m. h. m. h. m. h. m.
1° 30′ 1° 31′ 1° 32′ 1° 33′ 1° 34′ 1° 35′ 1° 36′ 1° 37′ 1° 38′ 1° 39′ 1° 40′ 1° 41′
0 3010 2962 2915 2868 2821 2775 2730 2685 2640 2596 2553 2510
1 3009 2962 2914 2867 2821 2775 2729 2684 2640 2596 2552 2509
2 3009 2961 2913 2866 2820 2774 2729 2683 2639 2595 2551 2508
3 3008 2960 2912 2866 2819 2773 2728 2683 2638 2594 2551 2507
4 3007 2959 2912 2865 2818 2772 2727 2682 2638 2593 2550 2507
5 3006 2958 2911 2864 2818 2772 2726 2681 2637 2593 2549 2506
6 3005 2958 2910 2863 2817 2771 2725 2681 2636 2592 2548 2505
7 3005 2957 2909 2862 2816 2770 2725 2680 2635 2591 2548 2504
8 3004 2956 2909 2862 2815 2769 2724 2679 2635 2591 2547 2504
9 3003 2955 2908 2861 2815 2769 2723 2678 2634 2590 2546 2503
10 3002 2954 2907 2860 2814 2768 2722 2678 2633 2589 2545 2503
11 3001 2954 2906 2859 2813 2767 2722 2677 2632 2588 2545 2502
12 3001 2953 2905 2859 2812 2766 2721 2676 2632 2588 2544 2501
13 3000 2952 2905 2858 2811 2766 2720 2675 2631 2587 2543 2500
14 2999 2951 2904 2857 2811 2765 2719 2675 2630 2586 2543 2499
15 2998 2950 2903 2856 2810 2764 2719 2674 2629 2585 2542 2499
16 2997 2950 2902 2855 2809 2763 2718 2673 2629 2585 2541 2498
17 2997 2949 2901 2855 2808 2763 2717 2672 2928 2584 2540 2497
18 2996 2948 2901 2854 2808 2762 2716 2672 2627 2583 2540 2497
19 2995 2947 2900 2853 2807 2761 2716 2671 2626 2583 2538 2496
20 2994 2946 2899 2852 2806 2760 2715 2670 2626 2582 2538 2495
21 2993 2946 2898 2852 2805 2760 2714 2669 2625 2581 2538 2494
22 2993 2945 2898 2851 2805 2759 2713 2669 2624 2580 2537 2494
23 2992 2944 2897 2850 2804 2758 2713 2668 2624 2580 2536 2493
24 2991 2943 2896 2849 2803 2757 2712 2667 2623 2579 2535 2492
25 2990 2942 2895 2848 2802 2756 2711 2666 2622 2578 2535 2492
26 2989 2942 2894 2848 2801 2756 2710 2666 2621 2577 2534 2491
27 2989 2941 2894 2847 2801 2755 2710 2665 2621 2577 2533 2490
28 2988 2940 2893 2846 2800 2754 2709 2664 2620 2576 2533 2489
29 2987 2939 2892 2845 2799 2753 2708 2663 2619 2575 2532 2489
30 2986 2939 2891 2845 2798 2753 2707 2663 2618 2574 2532 2488
31 2985 2938 2891 2844 2798 2752 2707 2662 2618 2574 2530 2487
32 2985 2937 2890 2843 2797 2751 2706 2661 2617 2573 2530 2487
33 2984 2936 2889 2842 2796 2750 2705 2660 2616 2572 2529 2486
34 2983 2935 2888 2842 2795 2750 2704 2660 2615 2572 2528 2485
35 2985 2935 2887 2841 2795 2749 2704 2659 2615 2571 2527 2485
36 2981 2935 2887 2840 2794 2748 2703 2658 2614 2570 2527 2484
37 2981 2933 2886 2839 2793 2747 2702 2657 2613 2569 2526 2483
38 2980 2932 2885 2838 2792 2747 2701 2657 2612 2569 2525 2483
39 2979 2931 2884 2838 2792 2746 2701 2656 2612 2568 2525 2482
40 2978 2931 2883 2837 2791 2745 2700 2655 2611 2567 2524 2481
41 2977 2930 2883 2836 2790 2744 2699 2655 2610 2566 2523 2480
42 2977 2929 2882 2835 2789 2744 2698 2654 2610 2566 2522 2480
43 2976 2928 2881 2835 2788 2743 2698 2653 2609 2565 2522 2479
44 2975 2927 2880 2834 2788 2742 2697 2652 2608 2564 2521 2478
45 2974 2927 2880 2833 2787 2741 2696 2652 2607 2564 2520 2477
46 2973 2926 2879 2832 2786 2741 2696 2651 2607 2563 2520 2477
47 2973 2925 2878 2831 2785 2740 2695 2650 2606 2562 2519 2486
48 2972 2924 2877 2831 2785 2739 2694 2649 2605 2561 2518 2485
49 2971 2924 2876 2830 2784 2738 2693 2649 2604 2561 2517 2485
50 2970 2923 2876 2829 2783 2738 2692 2648 2604 2560 2517 2474
51 2969 2922 2875 2828 2782 2737 2692 2647 2603 2559 2516 2473
52 2969 2921 3874 2828 2782 2736 2691 2646 2602 2558 2515 2472
53 2968 2920 2873 2827 2781 2735 2690 2646 2601 2558 2515 2472
54 2967 2920 2873 2826 2780 2735 2689 2645 2601 2557 2514 2471
55 2966 2919 2872 2825 2779 2734 2689 2644 2600 2556 2513 2470
56 2965 2918 2871 2825 2779 2733 2688 2643 2599 2556 2512 2470
57 2965 2917 2870 2824 2778 2732 2687 2643 2599 2555 2512 2469
58 2964 2916 2869 2823 2777 2732 2687 2642 2598 2554 2511 2468
59 2963 2916 2869 2822 2776 2731 2686 2641 2587 2553 2510 2467
60 2962 2915 2868 2821 2775 2730 2685 2640 2596 2553 2510 2467

[page] 49

TABLE XV. Proportional Logarithms.
S h. m. h. m. h. m. h. m. h. m. h. m. h. m. h. m. h. m. h. m. h. m. h. m.
1° 42′ 1° 43′ 1° 44′ 1° 45′ 1° 46′ 1° 47′ 1° 48′ 1° 49′ 1° 50′ 1° 51′ 1° 52′ 1° 53′
0 2467 2424 2382 2341 2300 2259 2218 2178 2139 2099 2061 2022
1 2466 2424 2382 2340 2299 2258 2218 2178 2138 2099 2060 2021
2 2465 2423 2381 2339 2298 2258 2217 2177 2137 2098 2059 2021
3 2465 2422 2380 2339 2298 2257 2216 2176 2137 2098 2059 2020
4 2464 2422 2380 2338 2297 2256 2216 2176 2136 2097 2058 2019
5 2463 2421 2379 2337 2296 2256 2215 2175 2136 2096 2057 2019
6 2462 2420 2378 2337 2296 2255 2214 2174 2135 2096 2057 2018
7 2462 2419 2378 2336 2295 2254 2214 2174 2134 2095 2056 2017
8 2461 2419 2377 2335 2294 2253 2213 2173 2134 2094 2055 2017
9 2460 2418 2376 2335 2294 2253 2212 2172 2133 2094 2055 2016
10 2460 2417 2375 2334 2293 2252 2212 2172 2132 2093 2054 2016
11 2459 2417 2375 2333 2292 2251 2211 2171 2132 2092 2053 2015
12 2458 2416 2374 2333 2291 2251 2210 2170 2131 2092 2053 2014
13 2458 2415 2373 2332 2291 2250 2210 2170 2130 2091 2052 2014
14 2457 2415 2373 2331 2290 2249 2209 2169 2130 2090 2052 2013
15 2456 2414 2372 2331 2289 2249 2208 2168 2129 2090 2051 2012
16 2455 2413 2371 2330 2289 2248 2208 2168 2128 2089 2050 2012
17 2455 2412 2371 2329 2288 2247 2207 2167 2128 2088 2050 2011
18 2454 2412 2370 2328 2287 2247 2206 2167 2127 2088 2049 2010
19 2453 2411 2369 2328 2287 2246 2206 2166 2126 2087 2048 2010
20 2453 2410 2368 2327 2286 2245 2205 2165 2126 2086 2048 2009
21 2452 2410 2368 2326 2285 2245 2204 2165 2125 2086 2047 2009
22 2451 2409 2367 2326 2285 2244 2204 2164 2124 2085 2046 2008
23 2450 2408 2366 2325 2284 2243 2203 2163 2124 2085 2046 2007
24 2450 2408 2366 2324 2283 2243 2202 2163 2123 2084 2045 2007
25 2449 2407 2365 2324 2283 2242 2202 2162 2122 2083 2044 2006
26 2448 2406 2364 2323 2282 2241 2201 2161 2122 2083 2044 2005
27 2448 2405 2364 2322 2281 2241 2200 2161 2121 2082 2043 2005
28 2447 2405 2363 2322 2281 2240 2200 2160 2120 2081 2042 2004
29 2446 2404 2362 2321 2280 2239 2199 2159 2120 2081 2042 2003
30 2445 2403 2362 2320 2279 2239 2198 2159 2119 2080 2041 2003
31 2445 2403 2361 2320 2279 2238 2198 2158 2118 2079 2041 2002
32 2444 2402 2360 2319 2278 2237 2197 2157 2118 2079 2040 2001
33 2443 2401 2359 2318 2277 2237 2196 2157 2117 2078 2039 2001
34 2443 2401 2359 2317 2277 2236 2196 2156 2116 2077 2039 2000
35 2442 2400 2358 2317 2276 2235 2195 2155 2116 2077 2038 2000
36 2441 2399 2357 2316 2275 2235 2174 2155 2115 2076 2037 1999
37 2441 2398 2357 2315 2274 2234 2194 2154 2115 2075 2037 1998
38 2440 2398 2356 2315 2274 2233 2193 2153 2114 2075 2036 1998
39 2439 2397 2355 2314 2273 2233 2192 2153 2113 2074 2035 1997
40 2438 2396 2355 2313 2272 2232 2192 2152 2113 2073 2035 1996
41 2438 2396 2354 2313 2272 2231 2191 2151 2112 2073 2034 1996
42 2437 2395 2353 2312 2271 2231 2190 2151 2111 2072 2033 1995
43 2436 2394 2353 2311 2270 2230 2190 2150 2111 2072 2033 1994
44 2436 2394 2352 2311 2270 2229 2189 2149 2110 2071 2032 1994
45 2435 2393 2351 2310 2269 2229 2188 2149 2109 2070 2032 1993
46 2434 2392 2350 2309 2268 2228 2188 2148 2109 2070 2031 1993
47 2433 2391 2350 2309 2268 2227 2187 2147 2108 2069 2030 1992
48 2433 2391 2349 2308 2267 2227 2186 2147 2107 2068 2030 1991
49 2432 2390 2348 2307 2266 2226 2186 2146 2107 2068 2029 1991
50 2431 2389 2348 2307 2266 2225 2185 2145 2106 2067 2028 1990
51 2431 2389 2347 2306 2265 2225 2184 2145 2105 2066 2028 1989
52 2430 2388 2346 2305 2264 2224 2184 2144 2105 2066 2027 1989
53 2429 2387 2346 2304 2264 2223 2183 2143 2104 2065 2026 1988
54 2429 2387 2345 2304 2263 2223 2182 2143 2103 2064 2026 1987
55 2428 2386 2344 2303 2262 2222 2182 2142 2103 2064 2025 1987
56 2427 2385 2344 2302 2262 2221 2181 2141 2102 2063 2025 1986
57 2426 2384 2343 2302 2261 2220 2180 2141 2101 2062 2024 1986
58 2426 2384 2342 2301 2260 2220 2180 2140 2101 2062 2023 1985
59 2425 2383 2342 2300 2260 2219 2179 2139 2100 2061 2023 1984
60 2424 2382 2341 2300 2259 2218 2178 2139 2999 2061 2022 1984

G

[page] 50

TABLE XV. Proportional Logarithms.
S h. m. h. m. h. m. h. m. h. m. h. m. h. m. h. m. h. m. h. m. h. m.
1° 54′ 1° 55′ 1° 56′ 1° 57′ 1° 58′ 1° 59′ 2° 0′ 2° 1′ 2° 2′ 2° 3′ 2° 4′
0 1984 1946 1908 1871 1834 1797 1761 1725 1689 1654 1619
1 1983 1945 1908 1870 1833 1797 1760 1724 1689 1653 1618
2 1982 1944 1907 1870 1833 1796 1760 1724 1688 1652 1617
3 1982 1944 1906 1869 1832 1795 1759 1723 1687 1652 1617
4 1981 1943 1906 1868 1831 1795 1759 1722 1687 1651 1616
5 1981 1943 1905 1868 1831 1794 1758 1722 1686 1651 1616
6 1980 1942 1904 1867 1830 1794 1757 1721 1686 1650 1615
7 1979 1941 1904 1867 1830 1793 1757 1721 1685 1650 1614
8 1979 1941 1903 1866 1829 1792 1756 1720 1684 1649 1614
9 1978 1940 1903 1865 1828 1792 1755 1719 1684 1648 1613
10 1977 1939 1902 1865 1828 1791 1755 1719 1683 1648 1613
11 1977 1939 1901 1864 1827 1791 1754 1718 1683 1647 1612
12 1976 1938 1901 1863 1827 1790 1754 1718 1682 1647 1612
13 1975 1938 1900 1863 1826 1789 1753 1717 1681 1646 1611
14 1975 1937 1899 1862 1825 1789 1752 1717 1681 1645 1610
15 1974 1936 1899 1862 1825 1788 1752 1716 1680 1645 1610
16 1974 1936 1898 1861 1824 1788 1751 1715 1680 1644 1609
17 1973 1935 1898 1860 1823 1787 1751 1715 1679 1644 1609
18 1972 1934 1897 1860 1823 1786 1750 1714 1678 1643 1608
19 1972 1934 1896 1859 1822 1786 1749 1714 1678 1643 1607
20 1971 1933 1896 1859 1822 1785 1749 1713 1677 1642 1607
21 1970 1933 1895 1858 1821 1785 1748 1712 1677 1641 1606
22 1970 1932 1894 1857 1820 1784 1748 1712 1676 1641 1606
23 1969 1931 1894 1857 1820 1783 1747 1711 1676 1640 1605
24 1968 1931 1893 1856 1819 1783 1746 1711 1675 1640 1605
25 1968 1930 1893 1855 1819 1782 1746 1710 1674 1639 1604
26 1967 1929 1892 1855 1818 1781 1745 1709 1674 1638 1603
27 1967 1929 1891 1854 1817 1781 1745 1709 1673 1638 1603
28 1966 1928 1891 1854 1817 1780 1744 1708 1673 1637 1602
29 1965 1928 1890 1853 1816 1780 1743 1708 1672 1637 1602
30 1965 1927 1889 1852 1816 1779 1743 1707 1671 1636 1601
31 1964 1926 1889 1852 1815 1778 1742 1706 1671 1635 1600
32 1963 1926 1888 1851 1814 1778 1742 1706 1670 1635 1600
33 1963 1925 1888 1850 1814 1777 1741 1705 1670 1634 1599
34 1962 1924 1887 1850 1813 1777 1740 1705 1669 1634 1599
35 1962 1924 1886 1849 1812 1776 1740 1704 1668 1633 1598
36 1961 1923 1886 1849 1812 1775 1739 1703 1668 1633 1598
37 1960 1923 1885 1848 1811 1775 1739 1703 1667 1632 1597
38 1960 1922 1884 1847 1811 1774 1738 1702 1667 1631 1596
39 1959 1921 1884 1847 1810 1774 1737 1702 1666 1631 1596
40 1958 1921 1883 1846 1809 1773 1737 1701 1665 1630 1595
41 1958 1920 1883 1846 1809 1772 1736 1700 1665 1630 1595
42 1957 1919 1882 1845 1808 1772 1736 1700 1664 1629 1594
43 1956 1919 1881 1844 1808 1771 1735 1699 1664 1628 1593
44 1956 1918 1881 1844 1807 1771 1734 1699 1663 1628 1593
45 1955 1918 1880 1843 1806 1770 1734 1698 1663 1627 1592
46 1955 1917 1880 1843 1806 1769 1733 1697 1662 1627 1592
47 1954 1916 1879 1842 1805 1769 1733 1697 1661 1626 1591
48 1953 1916 1878 1841 1805 1768 1732 1696 1661 1626 1591
49 1953 1915 1878 1841 1804 1768 1731 1696 1660 1625 1590
50 1952 1914 1877 1840 1803 1767 1731 1695 1660 1624 1589
51 1951 1914 1876 1839 1803 1766 1730 1694 1959 1624 1589
52 1951 1913 1876 1839 1802 1766 1730 1694 1658 1623 1588
53 1950 1913 1875 1838 1802 1765 1729 1693 1658 1623 1588
54 1950 1912 1875 1838 1801 1765 1728 1693 1657 1622 1587
55 1949 1911 1874 1837 1800 1764 1728 1692 1657 1621 1587
56 1948 1911 1873 1836 1800 1763 1727 1692 1656 1621 1586
57 1948 1910 1873 1836 1799 1763 1727 1691 1655 1620 1585
58 1947 1909 1872 1835 1798 1762 1726 1690 1655 1620 1585
59 1946 1909 1871 1835 1798 1762 1725 1690 1654 1619 1584
60 1946 1908 1871 1834 1797 1761 1725 1689 1654 1619 1584

[page] 51

TABLE XV. Proportional Logarithms.
S h. m. h. m. h. m. h. m. h. m. h. m. h. m. h. m. h. m. h. m. h. m.
2° 5′ 2° 6′ 2° 7′ 2° 8′ 2° 9′ 2° 10′ 2° 11′ 2° 12′ 2° 13′ 2° 14′ 2° 15′
0 1584 1549 1515 1481 1447 1413 1380 1347 1314 1282 1249
1 1583 1548 1514 1480 1446 1413 1379 1346 1314 1281 1249
2 1582 1548 1514 1479 1446 1412 1379 1346 1313 1281 1248
3 1582 1547 1513 1479 1445 1412 1378 1345 1313 1280 1248
4 1581 1547 1512 1478 1445 1411 1378 1345 1312 1280 1247
5 1581 1546 1512 1478 1444 1411 1377 1344 1311 1279 1247
6 1580 1546 1511 1477 1443 1410 1377 1344 1311 1278 1246
7 1580 1545 1511 1477 1443 1409 1376 1343 1310 1278 1246
8 1579 1544 1510 1476 1442 1409 1376 1343 1310 1277 1245
9 1578 1544 1510 1476 1442 1408 1375 1342 1309 1277 1245
10 1578 1543 1509 1475 1441 1408 1374 1342 1309 1276 1244
11 1577 1543 1508 1474 1441 1407 1374 1341 1308 1276 1243
12 1577 1542 1508 1474 1440 1407 1373 1340 1308 1275 1243
13 1576 1542 1507 1473 1440 1406 1373 1340 1307 1275 1242
14 1576 1541 1507 1473 1439 1406 1372 1339 1307 1274 1242
15 1575 1540 1506 1472 1438 1405 1372 1339 1306 1274 1241
16 1574 1540 1506 1472 1438 1404 1371 1338 1306 1273 1241
17 1574 1539 1505 1471 1437 1404 1371 1338 1305 1273 1240
18 1573 1539 1504 1470 1437 1403 1370 1337 1304 1272 1240
19 1573 1538 1504 1470 1436 1403 1370 1337 1304 1271 1239
20 1572 1538 1503 1469 1436 1402 1369 1336 1303 1271 1239
21 1571 1537 1503 1469 1435 1402 1368 1335 1303 1270 1238
22 1571 1536 1502 1468 1435 1401 1368 1335 1302 1270 1238
23 1570 1536 1502 1468 1434 1401 1367 1334 1302 1269 1237
24 1570 1535 1501 1467 1433 1400 1367 1334 1301 1269 1237
25 1569 1535 1500 1467 1433 1399 1366 1333 1301 1268 1236
26 1569 1534 1500 1466 1432 1399 1366 1333 1300 1268 1235
27 1568 1534 1499 1465 1432 1398 1365 1332 1300 1267 1235
28 1567 1533 1499 1465 1431 1398 1365 1332 1299 1267 1234
29 1567 1532 1498 1464 1431 1397 1364 1331 1298 1266 1234
30 1566 1532 1498 1464 1430 1397 1363 1331 1298 1266 1233
31 1566 1531 1497 1463 1429 1396 1363 1330 1297 1265 1233
32 1565 1531 1496 1463 1429 1396 1362 1329 1297 1264 1232
33 1565 1530 1496 1462 1428 1395 1362 1329 1296 1264 1232
34 1564 1530 1495 1461 1428 1394 1361 1328 1296 1263 1231
35 1563 1529 1495 1461 1427 1394 1361 1328 1295 1263 1231
36 1563 1528 1494 1460 1427 1393 1360 1327 1295 1262 1230
37 1562 1528 1494 1460 1426 1393 1360 1327 1294 1262 1230
38 1562 1527 1493 1459 1426 1392 1359 1326 1294 1261 1229
39 1561 1527 1493 1459 1425 1392 1359 1326 1293 1261 1229
40 1561 1526 1492 1458 1424 1391 1358 1325 1292 1260 1228
41 1560 1526 1491 1458 1424 1391 1357 1325 1292 1260 1227
42 1559 1525 1491 1457 1423 1390 1357 1324 1291 1259 1227
43 1559 1524 1490 1456 1423 1389 1356 1323 1291 1259 1226
44 1558 1524 1490 1456 1422 1389 1356 1323 1290 1258 1226
45 1558 1523 1489 1455 1422 1388 1355 1322 1290 1257 1225
46 1557 1523 1489 1455 1421 1388 1355 1322 1289 1257 1225
47 1556 1522 1488 1454 1421 1387 1354 1321 1289 1256 1224
48 1556 1522 1487 1454 1420 1387 1354 1321 1288 1256 1224
49 1555 1521 1487 1453 1419 1386 1353 1320 1288 1255 1223
50 1555 1520 1486 1452 1419 1386 1352 1320 1287 1255 1223
51 1554 1520 1486 1452 1418 1385 1352 1319 1287 1254 1222
52 1554 1519 1485 1451 1418 1384 1351 1319 1286 1254 1222
53 1553 1519 1486 1451 1417 1384 1351 1318 1285 1253 1221
54 1552 1518 1484 1450 1417 1383 1350 1317 1285 1253 1221
55 1552 1518 1483 1450 1416 1383 1350 1317 1284 1252 1220
56 1551 1517 1483 1449 1416 1382 1349 1316 1284 1252 1219
57 1551 1516 1452 1449 1415 1382 1349 1316 1283 1251 1219
58 1550 1516 1482 1448 1414 1381 1348 1315 1283 1250 1218
59 1550 1515 1481 1447 1414 1381 1348 1315 1282 1250 1218
60 1549 1515 1481 1447 1413 1380 1347 1314 1282 1249 1217

G 2

[page] 52

TABLE XV. Proportional Logarithms.
S h. m. h. m. h. m. h. m. h. m. h. m. h. m. h. m. h. m. h. m. h. m.
2° 16′ 2° 17′ 2° 18′ 2° 19′ 2° 20′ 2° 21′ 2° 22′ 2° 23′ 2° 24′ 2° 25′ 2° 26′
0 1217 1186 1154 1123 1091 1061 1030 0999 0969 0939 0909
1 1217 1185 1153 1122 1091 1060 1029 0999 0969 0939 0909
2 1216 1184 1153 1122 1090 1060 1029 0998 0968 0938 0908
3 1216 1184 1152 1121 1090 1059 1028 0998 0968 0938 0908
4 1215 1183 1152 1120 1089 1058 1028 0997 0967 0937 0907
5 1215 1183 1151 1120 1089 1058 1027 0997 0967 0937 0907
6 1214 1182 1151 1119 1088 1057 1027 0996 0966 0936 0906
7 1214 1182 1150 1119 1088 1057 1026 0996 0966 0936 0906
8 1213 1181 1150 1118 1087 1056 1026 0995 0965 0935 0905
9 1213 1181 1149 1118 1087 1056 1025 0995 0965 0935 0905
10 1212 1180 1149 1117 1086 1055 1025 0994 0964 0934 0904
11 1211 1180 1148 1117 1086 1055 1024 0994 0964 0934 0904
12 1211 1179 1148 1116 1085 1054 1024 0993 0963 0933 0903
13 1210 1179 1147 1116 1085 1054 1023 0993 0963 0933 0903
14 1210 1178 1147 1115 1084 1053 1023 0992 0962 0932 0902
15 1209 1178 1146 1115 1084 1053 1022 0992 0962 0932 0902
16 1209 1177 1146 1114 1083 1052 1022 0991 0961 0931 0901
17 1208 1177 1145 1114 1083 1052 1021 0991 0961 0931 0901
18 1208 1176 1145 1113 1082 1051 1021 0990 0960 0930 0900
19 1207 1175 1144 1113 1082 1051 1020 0990 0960 0930 0900
20 1207 1175 1143 1112 1081 1050 1020 0989 0959 0929 0899
21 1206 1174 1143 1112 1081 1050 1019 0989 0859 0929 0899
22 1206 1174 1142 1111 1080 1049 1019 0988 0958 0928 0898
23 1205 1173 1142 1111 1080 1049 1018 0988 0958 0928 0898
24 1205 1173 1141 1110 1079 1048 1018 0987 0957 0927 0897
25 1204 1172 1141 1110 1079 1048 1017 0987 0957 0927 0897
26 1204 1172 1140 1109 1078 1047 1017 0986 0956 0926 0896
27 1203 1171 1140 1109 1078 1047 1016 0986 0956 0926 0896
28 1202 1171 1139 1108 1077 1046 1016 0985 0955 0925 0895
29 1202 1170 1139 1108 1076 1046 1015 0985 0955 0925 0895
30 1201 1170 1138 1107 1076 1045 1015 0984 0954 0924 0894
31 1201 1169 1138 1106 1075 1045 1014 0984 0954 0924 0894
32 1200 1169 1137 1106 1074 1044 1014 0983 0953 0923 0893
33 1200 1168 1137 1105 1074 1044 1013 0983 0953 0923 0893
34 1199 1168 1136 1105 1074 1043 1013 0982 0952 0922 0892
35 1199 1167 1136 1104 1073 1043 1012 0982 0952 0922 0892
36 1198 1167 1135 1104 1073 1042 1012 0981 0951 0921 0891
37 1198 1166 1135 1103 1072 1042 1011 0981 0951 0921 0891
38 1197 1165 1134 1103 1072 1041 1011 0980 0950 0920 0890
39 1197 1165 1134 1102 1071 1041 1010 0980 0950 0920 0890
40 1196 1164 1133 1102 1071 1040 1009 0979 0949 0919 0889
41 1196 1164 1132 1101 1070 1040 1009 0979 0949 0919 0889
42 1195 1163 1132 1101 1070 1039 1008 0978 0948 0918 0888
43 1195 1163 1131 1100 1069 1039 1008 0978 0948 0918 0888
44 1194 1162 1131 1100 1069 1038 1007 0977 0947 0917 0887
45 1193 1162 1130 1099 1068 1037 1007 0977 0947 0917 0887
46 1193 1161 1130 1099 1068 1037 1006 0976 0946 0916 0886
47 1192 1161 1129 1098 1067 1036 1006 0976 0946 0916 0886
48 1192 1160 1129 1098 1067 1036 1005 0975 0945 0915 0885
49 1191 1160 1128 1097 1066 1035 1005 0975 0945 0915 0885
50 1191 1159 1128 1097 1066 1035 1004 0974 0944 0914 0884
51 1190 1159 1127 1096 1065 1034 1004 0974 0944 0914 0884
52 1190 1158 1127 1096 1065 1034 1003 0973 0943 0913 0883
53 1189 1158 1126 1095 1064 1033 1003 0973 0943 0913 0883
54 1189 1157 1126 1095 1064 1033 1002 0972 0942 0912 0883
55 1188 1157 1125 1094 1063 1032 1002 0972 0942 0912 0882
56 1188 1156 1125 1094 1063 1032 1001 0971 0941 0911 0882
57 1187 1156 1124 1093 1062 1031 1001 0971 0941 0911 0881
58 1187 1155 1124 1092 1062 1031 1000 0970 0940 0910 0881
59 1186 1154 1123 1092 1061 1030 1000 0970 0940 0910 0880
60 1186 1154 1123 1091 1061