ANALYSIS TO THE DYNAMICAL THEOllY OF THE TIDES. 
231 
By the method here sketched I have calculated the first six roots of the period- 
equation for four different depths of the ocean corresponding to the values 
'io’ iVj "sj respectively, for hgjioi^a‘^. These depths are equivalent to about 
7260, 14520, 29040, 58080 feet respectively, and the results are embodied in the 
following tables :— 
Table I. 
i 
1 
j 
j 
Approximate value 
of computed 
from equation 
L. = 0. 
Corrected value 
of 
Period of 
o.scillation expressed 
in sidereal time. 
Corresponding 
period when there 
is no i-otation. 
h. 
m. 
h. 
ra. 
Depth 7,260 feet {kgjico^a^ = ; pja- - 
= T8093. 
n = 2 
•56230 
•44155 
18 
3-5 
32 
49 
w = 4 
•95036 
•96357 
12 
13-5 
17 
30 
n = 6 
1-4971 
1-5224 
9 
43-5 
11 
58 
rz. = 8 
2-2373 
2-2539 
7 
59-6 
9 
5 
n = 10 
3-1755 
3-1867 
6 
43-3 
7 
20 
n = l2 
4-3130 
4-3209 
5 
46-4 
6 
9 
i 
Depth 14,520 
feet = 
2^); p/o- 
= T8093. 
n = 2 
•69600 
•62473 
15 
11-0 
23 
12 
n = 4 
1-4202 
1-4368 
10 
0-7 
12 
23 
91 = G 
2-5032 
2-5168 
7 
33-8 
8 
28 
M = 8 
3-9798 
3-9882 
6 
0-5 
6 
26 
n = \0 
5-8544 
5-8600 
4 
57-4 
5 
11 
n = 12 
8-1283 
8-1322 
4 
12-5 
4 
21 
Depth 29,040 
feet (%/4mW = 
1^); p/o- 
= -18093 
• 
n = 2 
•96344 
•92506 
12 
28-6 
16 
25 
w = 4 
2-3599 
2-3707 
7 
47-6 
8 
45 
n = 6 
4-5155 
4-5224 
5 
38-6 
5 
59 
w = 8 
7-4649 
7-4691 
4 
23-5 
4 
33 
w = 10 
11-2123 
11-2150 
3 
35-0 
3 
40 
n = 12 
1 
15-7588 
15-7609 
3 
1-4 
3 
4 
i 
Depth 58,080 feet (/ip/4&>®a^ = 
i); p/o- 
= -18093. 
n = 2 
1-4983 
1 -4785 
9 
52-1 
11 
35 
71 = 4 
4-2393 
4-2453 
5 
49-4 
6 
11 
71 = 6 
8-5402 
8-5437 
4 
6-3 
4 
14 
71 = 8 
14-4352 
14-4371 
<> 
o 
9-5 
3 
13 
n = 10 
21-9275 
21-9293 
2 
33-8 
2 
36 
71 = 12 
31-0202 
31-0212 
2 
9-3 
2 
10 
