SPHEROIDS, AND ON THE OCEAN TIDES UPON A YIELDING NUCLEUS. 21 
Spheroid with Rigidity of Iron (7’8 X 10 8 ). 
Lunar Semidiurnal Tide. 
Modulus 
of 
relaxation. 
Yiseosity. 
Reduction 
of 
ocean tide. 
Acceleration 
of 
high water. 
Hrs. 
min. 
Hrs. 
min. 
Fluid 0 
0 
0 
•ooo 
3 
6 
0 
30 
140 
•420 
1 
47 
1 
0 
280 
•573 
1 
7 
2 
0 
560 
•647 
0 
36 
3 
0 
840 
•665 
0 
25 
Elastic oo 
GO 
•679 
0 
0 
Fortnightly Tide. 
Days 
hrs. 
Days. 
hrs. 
Fluid 0 
0 
0 
•ooo 
3 
10 
0 
6 
1,700 
•294 
2 
11 
0 
12 
3.400 
•470 
1 
18 
1 
0 
6,700 
•602 
1 
1 
2 
0 
13,500 
•657 
0 
13 
3 
0 
20,200 
•669 
0 
9 
Elastic oo 
OO 
•679 
0 
0 
10. The influence of inertia. 
In establishing these results inertia has been neglected, and I will now show that 
this neglect is not such as to materially vitiate my results. 4 ' 
Suppose that the spheroid is constrained to execute such a vibration as it would do 
if it were a perfect fluid, and if the equilibrium theory of tides were true. Then 
the effective forces which are, according to D’Alembert’s principle, the equivalent of 
inertia, are found by multiplying the acceleration of each particle by its mass. 
Inertia may then be safely neglected if the effective force on that particle which has 
the greatest amplitude of vibration is small compared with the tide-generating force 
on it. In the case of a viscous spheroid, the inertia will have considerably less effect 
than it would have in the supposed constrained oscillation. 
Now suppose we have a tide-generating potential wr % S cos (vt-\-7]), then, according 
to the equilibrium theory of tides, the form of the surface is given by 
ar='~ S cos (vt ~\~rj) ; 
ar 2 g 
* In a future paper (read on December 19th, 1878) I shall give an approximate solution of the problem, 
inclusive of the effects of inertia. 
