spherical Wave of LigJit. 73 



+/[/2(-'--'-)(« + 4'" + "'^"'^ ^\ {^.r){x + c)'"-^ - K(x.r){x + ^)™+'} 



The limits between which the integrals are to be taken 

 correspond to the values and w of 0, and depend upon 

 whether the point is within or without the sphere. The 

 expression for f^^x-r^y is to be the expansion beginning 



2^,,^"->sin/{^(T + /) - r- r + i]lr"-^^, 

 that for f^ipcr^v" is to be selected out of that beginning 



2/^,X~Tsin/{/^(T + /) - c-r^-i)\r"^^, 

 and that for 0i(x.r) is made up of that part of the preceding 

 which does not contain j, and the expansion beginning 



2^,.^"sin/{^(T ^t)-c-r^ /}/r"+\ 

 where T stands for the time at which the displacement 

 reached the surface of the sphere of radius c and t the further 

 time before the secondary wave reaches Q. 



2 denotes summation for different values of ii and will 

 be generally omitted, and s and c will be written for 



We expand these by the method previously explained 

 so as to get solutions of the differential equations, these 

 solutions will also satisfy the condition of no condensation 

 if r„= -a,,. 



Substitute these expressions in the argument of our 

 integral, and write 



