52 
MR. LUBBOCK ON THE TIDES. 
which quantity is 9-5307813. The determination of Laplace, by other means, 
of the same quantity is 9-5385031 = log- tan 19° 4'. Bernoulli took this con- 
stant — 9-60286 = log-. — , without explaining- how he obtained it. Newton 
determined — = . * ■ , making the mass of the moon much too great. 
ily d T J 1 O 
19° 4' — 18° 45' = 19' or l m 16 s in time. A difference therefore of about 
one minute in the sum of the intervals when the moon passes the meridian 
at 4 h 20 m and at 10 h 20 m would remove altogether the discrepancy between 
my determination and that of Laplace. 
The following Table shows the differences between the times of higli water 
calculated by M. Dessiou with the constants 3 h 47 ra ‘8, l h 20 m and 9-5307813, 
according to the formula Phil. Trans. 1831, p. 387, line 17, and the times given 
by observation, and also the differences between the times calculated (with the 
correct establishment) by means of the Table of Bernoulli given in the An- 
nuaire for 1829, p. 40, and the same times given by observation. 
Moon’s 
Transit. 
Observed. 
Calculated 
with the 
constants 
above. 
Error of 
Calculation. 
Calculated 
from the 
Table in the 
Annuaire. 
Error of 
Calculation. 
h 
m 
h 
m 
h 
m 
h 
h 
m 
m 
12 
0 
3 
47-8 
3 
47-8 
0 
3 
oo 
0 
0 
30 
3 
43-5 
3 
40-7 
— 
2-8 
1 
0 
3 
36-6 
3 
33-2 
— 
3-4 
1 
30 
3 
23 
3 
25-6 
+ 
2-6 
2 
0 
3 
1 5’5 
3 
18-1 
+ 
2-6 
3 
14-3 
— 
1-2 
2 
30 
3 
10-9 
3 
10-9 
0 
3 
0 
3 
7-8 
3 
4 
— 
3-8 
3 
30 
3 
4-9 
2 
58 
— 
6-9 
4 
0 
2 
58-4 
2 
53-1 
— 
5-3 
2 
CO 
— 
12-6 
4 
30 
2 
50 
2 
49-7 
— 
0-3 
5 
0 
2 
48-5 
2 
48-5 
0 
5 
30 
2 
49-5 
2 
50-1 
+ 
0-6 
6 
0 
2 
52-8 
2 
55-3 
+ 
2-5 
2 
45-3 
— 
7-3 
6 
30 
3 
2-2 
3 
4-7 
+ 
2-5 
7 
0 
3 
18-2 
3 
18 
— 
0-2 
7 
30 
3 
33-5 
3 
33-3 
— 
0-2 
8 
0 
3 
46-4 
3 
47-1 
+ 
0-7 
3 
Cn 
O 
CO 
+ 
4-4 
8 
30 
4 
0 
3 
58-3 
— 
1-7 
9 
0 
4 
9 
4 
4-9 
— 
4-1 
9 
30 
4 
9-9 
4 
7-7 
— 
2-2 
10 
0 
4 
9'5 
4 
7-3 
— 
2-2 
4 
10-8 
+ 
0-7 
10 
30 
4 
6-9 
4 
4-5 
— 
2*4 
11 
0 
4 
2-5 
4 
0-1 
— 
2-4 
11 
30 
3 
54-6 
3 
54-4 
— 
0-2 
