168 THE LAWS OF 



2 sin 



4 n . ^ 4 w . 6 



TT 22.4 



2 sin 



2 2.4 

 &c &c &c 



But it is evident from the form of these equations, that if we 

 make generally -Z?, +1 = i*JB t , they will all be satisfied provided 

 the first is, and as by this means the first equation becomes 



S 1 - a* = Et- a 3 - 



there arises 

 2 sin 



7T 



Hence 



and the required value of p becomes 



a m (a 2 - 1) 2 (a 2 - / 



But whatever the density P on the inducing spherical sur- 

 face may be, we can always expand it in a series of the form 



