LIQUID SPHEROID OF FINITE ELLIPTICITY. 
219 
Now, as long as the spheroid continues stable for such zonal harmonic disydace- 
ments when the liquid is supymsed perfect, the frequencies of these oscillations will 
none of them vanish ; hence, their amplitude cannot be increased indefinitely by the 
attractions of bodies remaining in the equatorial plane of the syfiieroid ; and the only 
way in which this can take y^lace is under the influence of the tide generating force 
due to a satellite whose orbit is inclined at a considerable angle to the equatorial 
plane of the spheroid, the effect being greatest if their ydanes be yDeryDendicular. There 
is still the possibility that, contrary to our hypothesis in § 20, a perfect liquid spheroid 
may first become unstable for some displacement symmetrical about the axis ; and, 
unless this question be fully decided, we are not in a y^osition to say that such is 
not the case, and that Laplace’s hyy^othesis is wholly unfounded. 
2 F 2 
