( 343 ) 



111 ciiiiiïc^jiK'iicc dl' the (lis|il;ir;'nu'iits (1), tat' clectiie ilciisity will 

 havo (•lianj^od l'nun r, to 



a ~ 

 Heiuo, thoro will ho an clcctrir hiroo 



2 A + 1 a ' d.l 



(F = vftlofity (if light) along tlic suiracc ami, as the iK'iisity 

 (lifl'crs from &■ by an iiiHnitoly small aiiKmnt, \V(> may write im' 

 the force per unit area 



,,/,(/, + !) o-^ an 



2 /i + 1 a ' dl 



'i'lic i'(iiiatl(ni nt' motion licconies 



.. Yi, ,„ 8 n , ^,., //(/, + !) <;2 9 Yi. 



^ ' d / 3 / 2 A + 1 rt ' 8 / 



ami the fivi|iieiu'y ni, is (Ictormincd by 



^ 2 A + 1 « 



Thus, we see that the fiequency is tlie same for all motions 

 corresponding to a harmoiiic of order //, no matter what particular 

 harmonic of this order may be chosen. 



If we put /' = 1, we ot)tain tlie frecjuency of the slowest vibra- 

 tions; A= 2 corresponds to the first of the higher types of motion, 

 and so on. However each of the difj'erent types includes a certain 

 number of difK'erent modes of motion. 



In the motion we have considered there is a kinetic energy 



V i', 



r=u.r^{^yu.., 



d 01 being an element of the sphere, and the integration extending 

 all over the surface. 



In virtue of the properties of spherical harmonics we may also 

 write 



