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FOR COMPUTING THE FINAL EFFECT OF PARALLAX ON THE DISTANCE

BETWEEN THE MOON AND THE SUN, OR A FIXED STAR.

Arg. Par. in Alt. or Dist.

Argument. 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.

60° 65° 70°

75°

80°
53°

55°
54°
56°

85°
59°

90° 570 120 115 110 105 | 100

90°

52°

58°

95

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A P P E N D I X,

CONTAINING

THE METHOD

OF FINDING

THE APPARENT TIME OF THE RISING AND SETTINO

OF THE SUN, MOON, AND FIXED STARS ;

THE TIME OF THE BEGINNING AND END OF

TWILIGHT, ITS DURATION, 8:c.

INTRODUCTION.

An observation of the rising or setting of the Sun, affords a ready

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N method of ascertaining time at sea. This method is, however, disaffected by an error arising from the uncertainty of the horizontal refraction at that time: but this error diminishes with the latitude and declination; and, in most cases, will seldom exceed half a minute. The rising or setting of a fixed star may, also, be applied to the same purpose.

The time of the Moon's rising is necessary to be known, in order to determine if a certain observation of that object will be visible, and to be prepared for such an observation.

Also, many observations may be taken with accuracy during the twilight, such as altitudes of the brightest of the stars, for determining the apparent time at the ship; the distance between the Moon and a star, for the longitude, &c. Upon these accounts, therefore, it is thought proper to subjoin this Appendix, in order to render this work still more useful.

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0 0 0 0 0 0 0 0 0 0 0 0 21 1 1 1 1

1 1 0 01010 4 2 2 2 2 2 1 1 1 0 6 2 2 2 2 2 2 2 2

1 8 3 3 3 | 3 3 2 11 0 10 4 4 4 4 4

2 2 1 0 12 5 5 5 5

3 2 1 146 5 5 4

2 16 7

4 3 2 0 18 8 8 7

5 29 9 8 8

-4 2 0 22 10 10 10 919 8 64 3 10 24 111 11 11 10 10 9 8 77 5 3 26 12 12 12 11 1 10 9 8 530 28 13 13 13 12 12 11 10 8 6 4 30 14 14 14 14 13 13 11 9 32 15 15 15 15 14 14 12 10 740 34 16 16 16 16 16 15 13 11 8 5 36 117 117 118 17 117 116 115 12 9 50 38.118 118 19 19 18 17 16 13 1060 40 20 20 21 21 20 19 17

15 11 6 0 41 121 21 22 121 121 20 18 15 11 6 0 42 21 22 22 22 22 21 19 16 12 7 43 22 22 23 23 23 22 20 17 12 7 0 44 23 23 24 24 24 22 21 18 13 7 45 24 24 25 25 25 23 22

19 13 8 46 24 25 26 26 26 24 23 20 14 9 47 25 26 27 27 27 26 24 29 15 9 48 26 27 28 28 28 27 25 22 16 10 49 27 28 29 29 29 28 26 23 16 10 50 28 29 30 31 30 30 27 24 17 13 0 51 29 30 31 32 32 31 29 26 19 11 0 52 30 31 32 133 133 32 30 27 20 11 53 31 32 33 34 34 34 32 29 21 12 54 32 34 35 36 36 36 34 30 22 13 55 34 35 36 37 38 38 (36 32 24 14 56 35 37 38 39 40 40 38 34 125 15 57 36 38 40 41 42 42 40 36 27 17 58 38 40 42 43 44 44 43 39 30 19 59 39 42 44 45 46 47 46 42 32 20 60 41 43 46 47 49 50 49 45 35.22

00 30 6° 9° 1120 115° (180 (20° 22°123° 23°

21

20 9 8 8 8 7

2 10 9 9 87105 4 2 24 11 10 10 10 9 8 26 12 11 11 10 10 9

2 28 13 12 12 11 10 9 8 6 30 14 13 13 12 11 10 917 32 15 14 14 13 12 11 95 3 34 16 15 15 14 13 12 110 8

3 36 17 16 16 15 14 12 11 64 38 18 18 17 16 15

13 11

9 4 40 20 19 18 17 16 14 12 10 7 4 41 21 20 18 17 16 14 12 10 7 42 20 19 18 17 15 13 11 43 122 121 20 19 17 15 13 11 44 123 22 21 20 16 16 14 11 8 45 24 23 22 20 18 16 14 11 46 24 124 122 21 19 17 15 12 8 47 25 24 23 21 19 17 15 129 48 26 25 24 22 20 18 15 13 49 27 26 25 23 21 18 16 13 9 50 28 127 25 24 22 19 16 13 9 5 0 51 29 128 126 24 22 20 17 14 9 52 30 29 27 25 123 21 1 11+ 10 6 53 31 30 28 26 24 22 118 15 10 6 0 54 32 131

29 27 124 22 18 15 10 6 55 34 32 30 28 25 23 19 16 10 6 56 35 33 31

23 26 23 19 116 11 6 57 36 35 112 50 27 124 20 17 11 6 58 38 36 33 31 29 25 20 17 11 6 59 39 37 35 32 29 126 21 18 11 60 41 38 36 33 30 27 92 18 11

0° / 5° 6° 9° 12° 15° 15° 120° 22° 23° 23°

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THE TIME ANSWERING TO A CHANGE OF ALTITUDE OF ONE DEGREE

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4 10
4 11
4 12
4 15
4 17
4 19
4 22

14 16 18

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4 10 4 13 4 16 4 19 4 23 4 27 4 32 4 37 4 43 4 49 4 57 5 5

20 22 24 26 28 30 32 34 36 38

4 13 4 13 4 13 4 14 4 15 4 17 4 19 4 22 4 24 4 26 4 30 4 35 4 39 4 44 4 50 4 57 54 5 12 5 21 5 31

2 4 4 4 6 4 8 4 10 4 13 4 16 4 19 4 23 4 27 4 32 4 38 4 44 4 50 4 58 5 6 5 14 5 19 5 24 5 29 5 35 5 41 5 47 5 54 6 1 6 8

4 20 4 30 4 34 4 39 4 44 4 50 4 57 5 5 5 13 5 22

4 17 4 21 4 25 4 29 4 31 4 40 4 45 4.52 5 0 5 of 5 16 5 21 5 26 5 32 5 38 5 44 5 50 5 57 6 4 6 11 6 20 6 28 6 38 6 47 6 58

7 7 18 7 30

43 7 57 8 14

4 17 4 17 4 18 4 18 4 20 4 22 + 24 4 27 4 29 4 32

36 4 41 4 45 4 51 4 57 5 5 5 12 5 21 5 32 5 42 5 55 6 1 6 9 6 13 6 26 6 33 6 44 6 55

4 19
4 23
4 27
4 31
4 36
4 42
4 48
4 55
5 3
5 11
5 20
5 25
5 30
5 36
542
5 48
5 54
6 1
6 8
6 16
6 25
6 34
6 44
6 54
7 5
7 16
7 28
74;
7 55
8 10
8 27

4 22 4 23 4 24 4 25 4 26 4 28 4 30 4 33 4 36 4 39 4 43 4 48 4 53 4 59 5 6 5 14 5 23 5 32 5 43 5 56 6 10 6 18 6 27 6 36 6 45 6 55 7 6 7 19

34 50

4 6 4 6

7 4 8 4 10 4 12 4 14 4 16 4 19 422 4 26 4 30 4 35 4 40 4 45 4 52 4 59 5 8 5 16 5 26 5 31 5 36 5 42 5 49 5 55 6 1 6 8 6 16 6 25 6 34 6 44 6 55 7 6 7 18 7 30 743 7 58 8 14 8 30 8 48 120

5 13 5 18 5 23 5 28 5 33 5 39 5 45 5 52 5 59

6

4 29 4 30 4 30 4 31 4 33 4 35 4 37 4 40 4 43 4 47 4 52 4 57 5 3 5 10 5 17 5 25 5 35 5 46 5 58 6 13 6 29 6 38 6 48 6 59 r 10 723

34

52 8 8 8 27 8 47 9 11 9 37 10 7 10 43 11 25 12 15 13 18 14 38

4 37 4 37 4 38 4 39 4 41 4 43 4 46 4 49 4 52 4 57 5 2 5 7 5 14 5 21 5 30 5 39 5 50 6 3 6 17 6 34 6 54 7 4 7 16 7 30 7 44 8 0 8 18 8 37 9 0 9 25 9 54 10 28 11 11 58 12 57 14 14 15 58

40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

33 5 39 5 45 5 51 5 58 6 5 6 12 6 20 6.99 6 38

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30°

TO FIND THE TIME ANSWERING TO A GIVEN CHANGE OF ALTITUDE

AT THE HORIZON.

Rule. To the Prop Log. of the time, answering to the latitude and declination, add the P.log. of the given change of altitude, and the constant log. 9.5229, the sun will be the P. log. of the time required.

EXAMPLE Required the interval of time between the risiog of the upper and lower limbs of the Sun, August 12th, 1804, in lat, 57° N. Time answering to lat. and declination,

8' 21" P. L. 1.3336 Sun's diameter,

31 41 P. L. 0.7544 Constant log.

9.5229

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PROBLEM I.

To find the Apparent Time of the Rising or Setting of the Sun.

RULE.

Reduce the Sun's declination to the meridian of the given place, by Problem v. page 107; to the log. tangent of which add the log. tangent of the latitude, the sum will be the log. cosine of an arch; which, reduced to time, will be the approximate time of the rising of the Sun, and its complement to 12 hours will be that of Sun setting, the latitude and declination being of the same name; but if of contrary names, the above arch, reduced to time, will be the approximate time of Sun setting, and its complement to 12 hours that of Sun rising.

Take the number fron Table A, answering to the latitude and declination, which is to be added to the approximate time of Sun rising or setting, if the declination is increasing, and of the same name with the latitude, or decreasing, and of contrary names; otherwise, it is to be subtracted therefrom.

Enter Table B, with the latitude and declination, and take out the corresponding time, which is that answering to a change of altitude at the horizon of 1o. Now, find the proportional part of this time, answering to the sum of the horizontal refraction, and dip of the horizon; which is to be subtracted from the approximate time of Sun rising, and added to that of Sun setting. Hence, the apparent time of the rising or setting of the Sun will be obtained.

REMARKS. The time of the half countinuance of an object above the horizon, may also be found by either of the following methods :

1. To the secant of the latitude add the secant of the declination, and the co-sine of their difference, or sum, according as the latitude and declination are of the same, or of a contrary name; and the sum being found in Table 1. the corresponding time will be that of the half continuance of the object above the horizon.

When the latitude and declination are of the same name, the sum of the three logs. may exceed the limits of the table. In this case, the co-sine of the sum is to be taken, and the complement to 12 hours of the time corresponding to the sum of the three logs. will be half the continuance of the object above the horizon.

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II.

To the co-tangent of the latitude add the co-tangent of the declination, the time answering to this sum, found in Table xLvIII. being added to six hours, when the latitude and declination are of the same name, or subtracted from 6 hours when of a contrary denomination, will give the time of the half continuance of the object above the horizon.

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