440 SURFACE WAVES. [CHAP. IX 



The numerical results given above for the case n = 2 shew 

 that, in a non-rotating liquid globe of the same dimensions and 

 mean density as the earth, forced oscillations having the cha 

 racters and periods of the actual lunar and solar tides, would 

 practically have the amplitudes assigned by the equilibrium-theory. 



243. The investigation is easily extended to the case of an 

 ocean of any uniform depth, covering a symmetrical spherical 

 nucleus. 



Let b be the radius of the nucleus, a that of the external surface. The 

 surface-form being 



we assume, for the velocity-potential, 



{ r n /,, + 11 



f*+ 1 &amp;gt;P+*^}* ........................... (ii), 



where the coefficients have been adjusted so as to make d&amp;lt;j)/dr = for r=b. 

 The condition that 



for r=a, gives 



t 



For the gravitation -potential at the free surface (i) we have 



where p is the mean density of the whole mass. Hence, putting # = 

 we find 



The pressure-condition at the free surface then gives 



-A 



: (vii). 



The elimination of S n between (iv) and (vii) then leads to 



j:r + n a n=0 (viii), 





