20 MR. DARWIN ON THE BODILY TIDES OP VISCOUS AND SEMI-ELASTIC 
Hence the apparent tides on the yielding nucleus are equal to the corresponding tides 
on a rigid nucleus reduced in the proportion of cos y tan e to unity, and there is an 
As these analytical results present no clear meaning to the mind, I have compiled 
the following tables. I take the two cases considered by Sir W. Thomson, where 
the spheroid has the rigidity of glass, and that of iron, and I work out the results for 
various times of relaxation of rigidity, for the semidiurnal and fortnightly tides. The 
last line in each division of each table is Thomson’s result. 
I may remind the reader that the modulus of relaxation of rigidity is the time 
in which the stress requisite to retain the body in its strained configuration falls 
to ’368 of its initial value. 
Spheroid with Rigidity of Glass (2’44 X 10 8 ). 
Lunar Semidiurnal Tide. 
Modulus of 
relaxation of 
rigidity 
(t). 
Coefficient of 
viscosity 
(ret x 10 _ln )- 
Ocean tide 
is tide on rigid 
nucleus 
multiplied by 
(cos x tan *)• 
High tide 
relatively to 
nucleus is 
accelerated by 
Hrs. 
Hrs. 
min. 
Fluid 0 
0 
•ooo 
3 
6 
1 
88 
•256 
1 
44 
2 
176 
•342 
1 
3 
3 
264 
•370 
0 
45 
4 
351 
•382 
0 
34 
5 
439 
•388 
0 
28 
Elastic oo 
OO 
•398 
0 
0 
Fortnightly Tide. 
Days. 
hrs. 
Days. 
hrs. 
Fluid 0 
0 
0 
•ooo 
3 
10 
0 
6 
500 
■099 
2 
21 
0 
12 
1,100 
•181 
2 
9 
1 
0 
2,100 
•285 
1 
16 
2 
0 
4,200 
•357 
1 
0 
3 
0 
6,300 
•379 
0 
16 
Elastic oo 
OO 
•398 
0 
0 
