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

 surface-form being 



r=+2*C w .................................... (i), 



we assume, for the velocity-potential, 



{ v n fan + 11 



(+i)+j!m}S. ........................... (). 



where the coefficients have been adjusted so as to make d(j>/dr=0 for r=b. 

 The condition that 



for r = a, gives 



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



47ryp 3 T oo47rypa 

 ~~ * 



where p is the mean density of the whole mass. Hence, putting </ 

 we find 



The pressure-condition at the free surface then gives 



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



rf r n +<^n=o .............................. (viii), 



