14 
THE REV. W. WHEWELL ON THE EMPIRICAL LAWS 
But we have found that h! varies as 
2-85 — 1*85 sin 2 1. 
Hence 1 — tan 2 1 = ; tan 2 ^ 
2*8o 57 5/ 
l = 30° 38'. 
Hence it appears that the amount of the effect of declination on the time H. W. 
at Liverpool corresponds to the effect on an equilibrium-spheroid at a place in lati- 
tude 30°. 
23. It will be convenient to express the double maximum of the semimenstrual 
inequality by a formula. The formula 60 m sin 2 & gives the following accordance with 
the excess above 82 m : 
Decl 
0°. 
3°. 
6°. 
9°. 
12°. 
15°. 
18°. 
21°. 
24°. 
27°. 
Obs. . . . 
0*2 
0-4 
1-6 
1-4 
1-3 
3-8 
5-5 
7-5 
10-3 
14-5 
Formula 
0 
0-2 
0-3 
1*4 
2-6 
4-0 
6-0 
7-7 
9-9 
12-4 
Hence 82 m + 60 m sin 2 & nearly expresses the double maximum. 
It appears also that the times when the inequality is 0 and max. are later as the 
declination is greater, the difference being about 15 m from decl. 0° to decl. 2 7 °, and ap- 
parently increasing as the square of the decl. or of sin decl. Now sin 2 2 7 = i nearly : 
lienee the correction of a is nearly /5 m sin 2 c>, and we have a = 65 m + 75 m sin 2 t$. 
24. The effect of lunar declination on the heights will be found in the same manner 
from Mr. Lubbock’s Table XVI. The mean of each column is obtained in the first 
line of the following Table. 
Table XVI. (b.) 
[Heights.] Mean of each column subtracted from the column. 
Decl 
0°. 
3°. 
6°. 
9°. 
12°. 
15°. 
18°. 
21°. 
24°. 
27°. 
Mean \ 
Height J 
15-74 
15-78 
15-77 
15-72 
15-54 
15-41 
15-23 
14-92 
14-74 
14-39 
J ’ sTransit . 
h m 
, 0 30 
1 30 
2 30 
3 30 
4 30 
5 30 
6 30 
7 30 
8 30 
9 30 
10 30 
11 30 
Remainder. 
+ 2-59 
+ 2-53 
+ 1-75 
+ 1-01 
— 0-70 
— 1-62 
— 2-66 
— 2-83 
- 1-61 
— 0-60 
+ 1-12 
+ 1-09 
Remainder. 
+ 2-64 
4 - 2-52 
+ 1-97 
4 - 0-69 
— 0-48 
— 2-10 
— 2-74 
- 2-66 
— 2-28 
— 0-37 
4 - 0-92 
4 - 1*93 
Remainder. 
4 - 2-30 
+ 2-73 
+ 1-95 
- 0-77 
— 0-53 
— 1-85 
— 3-00 
— 2-70 
— 2-11 
— 0-42 
4 - 1-03 
4 - 1-84 
Remainder. 
4 - 2-52 
4 - 2-57 
4 - 1-82 
+ 0-88 
— 0-74 
- 1-96 
— 2-86 
— 3-10 
— 1-72 
- 0-32 
4 - 0-84 
4 - 2-14 
Remainder 
4 - 2-65 
4 - 2-61 
4 - 1-99 
4 - 0-80 
— 0-54 
- 1-83 
— 3-08 
- 2-95 
- 1-89 
— 0-53 
4 - 0-95 
4 - 1-87 
Remainder. 
4 - 2-58 
4 - 2-51 
4 - 1-81 
4 - 0-84 
- 0-52 
— 1-81 
- 2-96 
- 3-02 
- 1-99 
— 0-41 
4 - M 2 
4 - 1-81 
Remainder. 
+ 2-27 
4 - 2-46 
4 - 2-03 
4 -MO 
— 0-70 
- 2-01 
- 2-88 
- 2-91 
- 1-90 
— 0-30 
4 - 0-99 
4 - 1-90 
Remainder. 
4 - 2-53 
4 - 2-32 
4 - 1-86 
4 - 1-03 
— 0-27 
— 1-86 
— 3-12 
— 3-01 
- 1-95 
— 0-40 
4 - 1-01 
4 - 1-87 
Remainder. 
4 - 2-18 
4 - 2-34 
+ 1-99 
4 - 1-21 
— 0-22 
- 1-75 
- 3-05 
- 3-10 
- 1-94 
— 0-21 
4 - 0-80 
4 - 1*78 
Remainder. 
+ 2-38 
4 - 2-40 
4 - 2-10 
4 - 1-21 
- 0-22 
- 1-61 
- 3-24 
— 3-20 
— 1-88 
- 0-39 
4 - 0-85 
4 - 1-60 
Greatest 1 
DifT . / 
5-42 
5-38 
5-73 
5-67 
5-73 
5-60 
5-37 
5-65 
5-44 
5-64 
Mean 
5-63 
