LIQUID SPHEROID OF FINITE ELLIPTICITY. 
213 
Forced Tides. 
22. We now revert to the applications of the methods of this paper to the investiga¬ 
tion of the tides produced on the surface of the spheroid by the influence of periodic 
variations of pressure over the surface of the liquid, or by the attractions of disturbing 
bodies in the neighbourhood of the spheroid. 
In this connexion, the equations found in §§ 9, 10 will be required, viz., if at the 
surface 
^3 —Ihip = (/r) sin {s(^ + '2o)Kt — e„/) . . . (88), 
and 
h = (/r) sin {s^ + 2o)Kt — e„y') .... (89), 
then C(b,*) will be given in terms of by the relation 
4/cD^P„ {v) 
sD^P„ (v)I(k — 1) + sec® « . + {v)Ik 
?3(0 (90), 
where, as in (12), (15), 
and 
Also, from (39), we have 
K cos a 
12^0 
^ y/{l — sin® «) ’ 
^ = cot a 
4«:D"P„ {v) % (^) 
(91). 
J 
O', k) 
sDdb (r)/(« — 1) + sec®«. V {p)Ik 
- A^,,,)T,/(z.) . (92). 
The value of i/> at any point of the surface being 
[i/;] = (v) (p.) sin {s(j) -f 2o)Kt — /) .... (93), 
is determined in terms of by the last equation (92). 
23. An interesting case occurs when k = 1. The period of the tides will then be 
half that of a complete revolution of the liquid, and they may therefore be called 
“ semidiurnal ” with reference to the spheroid. Except in the case Avhen 5=0, 
equation (90) gives 
3-''^C,.,-K/(0 = W.-.(94); 
also, from (92), A,/T,/ (v) = 0, and, therefore, [v/;] = 0 : hence, it is evident that tp 
must also vanish throughout the liquid. 
