24

26

28

30

3.54.8 0.3 0.3 0.4

4.39.3 0.5 0.5 0.5
5.22.4 0.6 0.7 0.7
6. 3.9 0.8 0.9 0.9
6.43.7 1.0 1.1 1.2
7.21.5 1.2 1.3 1.4

120 5
135 10
150 13

7.57.2 1.5 1.6 1.7 Op.180 15 13 II

8.30.7 1.8 1.9 2.0

9. 1.6 2.0 2.2 2.3

Inf. C. 6 11 19

The aberration of the Sun in longitude is always 20". The 9.29.9 2.3 2.5 2.7 apparent place is given in the Nautical Almanac, and 9.55.4 2.7 2.9 3.1 by adding 20" the Sun's true longitude will be obtained.

Table XL. contains the equation of the equinoxes in longitude to be applied with its sign to the mean longitudes of all the heavenly bodies. Thus on July 16, 1830, when the longitude of the moon's ascending node was 5s. 12° 38' the equation of the equinoxes was-5". 3.

The correction in Table XLI. corresponding to the Argument of Longitude being found, and its logarithm added to the fog secant (less radius) of the star's latitude, will be the log. of the star's aberration in longitude, to be applied with its sign to the mean longitude. The logarithm of the correction in Table XLI. corresponding to the Argument of Latitude added to the log. sine of the star's latitude will be the aberration of the star in latitude, to be applied with its sign to the mean latitude. Example. Required the Aberration of a Pegasi, July 16, 1830?

long. 3s. 23° 22′.

* long. 11. 21. 07.

Arg. long. 4. 02. 15. Table 41.+10". 7 log. 1.02938. Arg. lat. 1s. 2°. 15′ Tab. 41.-16". 9 log. 1.22789 *Latitude 19° 25/

Sec. 0.02543.

Sine 9.5217

28

23

21

0 19.17 16.60 9.59 30 1 19.17 16.43 9.30 29 2 19.16 16 .269.00 3 19.15 16 .08 8.70 27 4 19.1315.90 8.40 26 5 19.10 15 71 .10 25 619 .0715 .517 .80 24 719.03 15.31 7 49 8 18 .99 15.117.18 9 18 .94 14 .90 6 .87 10 18 .88 14 .69 6.56 11 18 .82 14 12 18 .75 14 13 18 .68 14 14 18 .60 13 15 18 .52 13 16 18 .43 13 .32 4 .64 17 18 .3413 .08 4.31 18 18 .23 12 .83 3 .99 19 18 .13 12 .58 3 .66 20 18 .02 12 .32 3 .33

PART II.
R. A. + Long.
Arg. R. A. +3 signs.
0. 6. 1. 7. 2. 8.
I+ I+ +
oo".83 0.72 0.41 30
I o .83 o .71 o .40 29
20 .83 0.70 0.39 28
30.83 0.69 0.38 27
40.82 0.69 0.36 26
5 0.82 0 .68 o .35 25
6 0.82 0.67 0.34 24
70.82 0.66 0.32 23

22

9

20

10

.47 6 .24 .25 5.92 .025 .61 .79 5.28 .56 4 .96

19

18

17

16

14

15

15

14

16

17

0.79 0.57 0.20 14
0.79 0.56 0.19 13
18 0.79 0.55 o .17 12
19 0.78 0.54 0.16
20 o .78 0.53 0.14 10

22

O .77 0.52 0.13

O .77 0.51 0.12
23 0.76 0 .500 .10
24 0.76 0.49 0.09
25 0.75 0.47 0.07

26 0.74 0.46 0.06
27 0.74 0.45 0.04

II

28 0.73 0.44 0.03 2
29 0.72 0.43 0.01
30 0.72 0.41 0.00 0

+ + + D 11. 5. 10. 4.19. 3.

To find the Aberration of a Star in Right Ascension.-Find the Equations in Part I. and II. corresponding to the arguments of R. A. at the top of those tables, and connect them according to their signs, and to the log. of this sum or difference add the log. secant (less radius) of the star's declination, the sum will be the log. of the aberration in Right Ascension in seconds of a degree, which divided by 15 will be reduced to time, to be applied to the mean R. A.

To find the Aberration of a Star in Declination.-Increase the former arguments of R. A. by 3 signs, and connect together the corresponding equations of Part I. and II. to the log. of which add the log. sine of the star's declination, the sum will be the log. of arc 1st. With the arguments at the top of Part III. find in the Table arcs 2d and 3d. These three arcs connected with their signs will be the aberration in declination, to be applied to the mean declination.

EXAMPLE. Required the Aberration in R. A. and Dec. of a Pegasi, July 16, 1830? By Table 8. R. A.=22h. 56′ 13′′=11s. 14°. 5'. Dec. 14° 18′ N. and by Ñ. A. long. 3s. 23° 22'.

Nutation in Right Ascension and Declination to be applied to the mean values.

o 8.33 7.21 4.16 30
I 8.33 7.14 4.04 29
28 .327 .06 3 .91 28
38.32 6.99 3.78 27
48.31 6.91 3 .65
5 8.30 6 .82 3 .52

.12

26

25 68.28 6.74 3.39 24 7 8 .27 6 .65 3.25 23 8 8.25 6 .56 3.12 22 9 8 .23 6.47 2.99 21 10 8 .20 6.38 2 .85 20 11 8.18 6 .29 2.71 19 128 .156 .19 2.57 18 13 8 6 .09 2.44 17 14 8.08 5.99 2.30 16 15 8 .05 5.89 2.16 15 16 8 .015 .79 2.02 17 7.97 5.68 1.87 13 7.92 5.57.73 12 19 7.88 5.46 1.59 11 207.83 5.35 1.45 10 21 7.785 .241 .30 22 7.72 5.13 1.16 237.67 5,01 1 .02 24 7.61 4.90 0.87 25 7.55 4 .78 0.73 26 7.49 4.66 o .58 4 27 7.42 4.54 0.44 28 7.35 4.41 0.29 2 29 7.29 4.29 0.15 307.214.16 0.00

18

6

9876543

1.22 1.06 0.61 30

I .22

I .22

I .05 0.59 29

31.22 1 .02

4I .22 I .01

0.57 28
0.55 27

o .53 26

51 .22 I .00 o .52 25 5

61.21

I .21

I .21

9.20 ΤΟ I .20

0.99 0.50 24
0.97 0.48 23
0.96 0.46 22
o .950 .44 | 21

123

10 .7 15.5 19 3 .4 II .015 .6 18

333

o .93 0.42 20 ΙΟ
0.92 0.40 19 II 3 .I
1.19 0.91 0.38 18 12
13 1.19 0.89 0.36
14 I .18 0.88 o .34 16
151.18 0.86 o .32 15

22

1.12 o .73 0.15

17

98765

13 3 7 11.2 15.717 14 4 .01 .4 15.7 16 15 4 .2 11 .6 15 .8) 15 4 .5 11.8 15.9 14 4 .8 12.0 16.0 13

14

16

13

17

18

16 .0 12

II

19

5 .312 .4

16.1

II

10

20

21

4

26

+

+ +

D

+

11. 5. 10. 4. 9. 3.

43

210

83

7.2 13.6 16 .3 7 .4 13

.7 16 .4

7 .7 13 .916 .4 7.9 14.016 .4 .2 14.2 16.4

+ +

11. 5. 10. 4. 9. 3.

To find the Nutation of a Star in Right Ascension. Find in Parts I. II. the Equations corresponding to the arguments of R. A. at the top of the tables, connect them according to the signs, and to the log. of the sum or difference add the log tangent of the star's dechnation, the sum will be the log. of an arc, to which apply the equation of the equinoxes, Part III. corresponding to the long. of the 's node (page 3, N. A.) the sum or difference will be the Nutation in Right Ascension in seconds of a degree, which divided by 15 will be reduced to seconds of time.

To find the Nutation of a Star in Declination.-Increase the arguments of R. A. Parts I. II. by 3 signs, and connect the corresponding equations of those tables, which will be the nutation of declination. Note. In putting the R. A. of the star equal to 3 signs, the nutation in declination will be the equation of the obliquity of the ecliptic.

EXAMPLE. Required the Nutation of a Pegasi, in R. A. and Decl. July 16, 1830 ?
R.A.Tab.8. 11s. 14° 5'

If the Declination of the Star was South, the argument of Part I. II. of Right Ascen

To find the Augmentation of the Moon's Semidiameter, by the altitude of the Nonagesimal, and the apparent distance of the Moon therefrom.

+

3.30

3. o

2.40
2.20

PART III.

Argument 's Parallax in Lat.

O' 10/ 20/ 30' 40' 50' 60'

6° oo".000".30 0.60 0.921".24 1".57 1.91
5. 0
0 .000 .250 .500 .771 .041 .321 .61
4. 0
0 .000 .200 .410 .620 .85 1.081 .32
0 .000 .170 .360 .550 .750 .961 .17
0 .000 .150 .310 .480 .650 .83 1 .02
0 .000 .130 .280 .430 .590 .750 .93
0 .000 .120 .240 .380 .520 .670 .83
0 .000 .100 .210 .330 .460 .590 .73
0 .000 .090 180 .28 o .3go.5io.63
0 .000 .070 .150 .230 .320 .430 .54
0 .000 .050 .110 .180 .260 .350 .44
0 .000 .040 .080 .130 .190 .260 34
0 .000 .020 .050 .090 .130 180 .24
0 .000 .000 .020 .040 .060 .100 .15

2. O
1.40

I.20
1. O

0.40

0.20

0.0 North.

o .05
o .06

.2

0 .07

0 .08

111. 565. 377. 74 19 12. 705. 487. 78 131. 845. 587. 83 141. 985. 697. 87 152. 125. 797. 91

18

17

16

0.10

15

0.30
0 .000 .020.030 .040 .03 0.02 +
0.40 0 .000 .030 .050 .060 .060 .060 .05
I. O 0 .000 .040 .080 .110 .130.140 .15
0 .000 .060 .110 .160 .190 .220 .24
0 .000 .080 .150 .210 .260 .300 .34]
2. O 0 .000 .090 .180 .260 .330 .390 .44
0 .000 .110 .210 .300 .390 .470 .54
2.400 .000 .130 .240 .350 .460 .550 .63
0 .000 .140 .280 .400 .520 .630 .73
0.000 .170 .330 .480 .620 .750 .88
4. 0
0 .000 .190 .370 .550 .720 .871.03
5. o 0 .000 .240 .470 .700 .911 .121.32
6. o
0 .000 .290 .570 .841 .11 .371.61
+ + + + + +
0' 10/ 20' 30/ 40' 50/ 60'
C's Horiz. Semi. Diam.

3. 0
3.30

Pre. Eq. 40" 50" 0" 10" 20" 30" 40" 50" 0" 10" 20" 30" 40" 50" arguments at the

0.160.149.12 0.10 0.08 0.06 0.04 0.02 0.00 0.02 0.04 0.060.090.11
0.320.280.240.200.16 0.12 0.08 0.040.00 0.04 0.08 0.130.170.21

top, and connect them according to their signs. With this sum or difference, take out the

In

the

0.480.42 0.360.300.240.18 0.12 0.060.000.060. 130.190.260.32 corresponding cor0.640.56 0.48 0.41 0.33 0.25 0.16 0.080.000.08 0.170.250.340.43 rection P. II. 0.80 0.70 0.61 0.51 0.41 0.31 0.21 0.100.000.100.210.320.430.53 occultations, 0.96 0.840.73 0.610.490.370.25 0.120.000.13 0.25 0.38 0.51 0.64 correction P. III. is to be found with 1.120.98 0.85 0.710.570.430.290.150.000.150.290.440.600.75 the 's Par. in lat. 1.281.120.970.81 0.65 0.490.330.170.000.170. 0.340.51 0.68 0.86 1.441.26 1.090.91 0.73 0.550.37 0.190.000.190.380.570.770.96 true lat. at the side. at the top, and her 1.60 1.411.21 1.01 0.82 0.620.41 0.210.000.210.420.630.85 1.07 but in solar Eclip1.761.551.331.120.90 0.680.450.230.000.230.460.700.941.18ses, this p. is noth1.92 1.69 1.451.22 0.98 0.1 740.490.250.000.25 0.51 0.761.021.28ng. Connect these 2.08 1.831.571.32 1.06 0.800.540.270.000.270.550.831.111.39three parts, and 2.241.97 1.701.421.140.860.58 0.290.000.290.590.891.191.50 with the sum enter the side col2.402.111.821.52 1.220.92 0.62 0.310.00 0.31 0.630.95 1.28 1.60 umn of P. IV., and 2.56 2.251.94,1.62 1.31 0.98 0.66 0.33 0.00 0.34 0.67 1.02 1.361.71 find the 's Horiz. Semi. Dia. at the top; the corresponding cor. applied, with its sign, to the sum of the three first parts, will give the Aug. of the 's S. D.

II

12

13

14

15

16

Thus in Ex. 1, Prob. 5, Appendix. The Alt. Nonag. is 2s. 7° 59', Dis. Nonag. (D.+P.) 20° 46', S. D. by N. A. 16' 27". 7. Hence Arg. P. I. are 2s. 7° 59' 20° 46', that is, 2s. 23° 45' and 1s. 17° 13', to which correspond+8" 18+6".01 + 14" 19. This gives in P. II. +0" 21., P. III. is 0". The sum of the three parts is 14. 4, with which and the S. D. 16' 27". 7. P. IV. is nearly +08; this connected with 14.4 gives the Aug. of 's S. D. 15" 2, as in Prob. VI. Appendix.

Equation of Second Differences to be applied to the mean longitude or latitude with a sign contrary to that of the mean of the second differences.

22.2 26.6 31.1 35.5 39.9 44.4 48.8
23.5 28.2 32.9 37.6 42.3 47.0 51.7
29.7 34.6 39.6 44.5 49.5 54.4
31.1 36.3 41.5 46.7 51.9 57.0

53.3

36.4

50.4

62.

16.2

21.6

16.9

22.5

17.5

12.0 18.1

18.6

27.1 32.5 37.9 43.3 48.7 54.1 59.5 28.1 33.7 39.4 45.0 50.6 56.2 61.9 67.5 23.3 29.1 35.0 40.8 46.6 52.4 58.3 64.1 199 24.1 30.1 36.1 42.1 48.1 54.2 60.2 66.2 722 24.8 31.0 37.2 43.4 49.6 55.8 62.0 68.2 74.4 25.5 31.8 38.2 44.6 50.9 57.3 63.7 19.6 26.1 32.6 39.1 45.7 52.2 58.7 65.2 26.7 33.3 40.0 46.7 53.3 60.0 66.7 27.7 34.6 41.5 48.4 55.4 62.3 69.2 76.1 83.1 35.6 42.8 49.9 57.0 64.2 71.3 78.4 85.6 36.5 43.7 51.0 58.3 65.6 72.9 80.2 87.5 37.0 44.4 51.9 59.3 66.7 74.1 81.5 834 37.4 44.9 52.3 59.8 67.3 74.8 82.2 37.5 45.0 52.5 60.0 67.5 75.0 82.5 900

649

70.0 76.4

71.7 783

73.3 800

0.1 0.1 0.2 0.3 0.3
0.3 0.4 0.5 0.7
0.4 0.6 0.8 1.0
0.3 0.5 0.8 1.0 1.3
0.2 0.2 02
0.3 0.6 1.0 1.3 1.6
0.2 0.3
0.4 0.8 1.1 1.5 1.9 0.0 0.1 0.1 0.2 0.2 0.2 0.3 0.3
0.4 0.9 1.3 1.8 2.2 0.0 0.1 0.1 0.2 0.2 0.3 0.3 0.4
0.5 1.0 1.5 2.0 2.5 0.0 0.1 0.1 0.2 0.2 0.3 0.3 0.4
0.5 1.1 1.6 2.2 2.7 0.1 0.1 0.2 0.2 0.3 0.3 0.4 0.4
0.6 1.2 1.8 2.4 3.0 0.1 0.1 0.2 0.2 0.3 0.4
1.3 1.9 2.6 3.2 0.1 0.1 0.2 0.3 0.3 0.4
0.1 0.1 0.2
0.1 0.1 0.2
0.1 0.2 0.2
0.1 0.2 0.2
0.1 0.2 0.3
0.1 0.2 0.3

0.0 0.0
0.0 0.0
0.1 0.1 0.1
0.1 0.1 0.1
0.1 0.1 0.2
0.1 0.2 0.2

0.0

0.0

0.0

0.0

0.0

0.0

0.1

0.1 0.1

0.1 0.2

00000

0.9

0.3

0.3

0.4

04

05

0.4 0.5
05 0.5 0.6

05