SQUARES OF ELLIPSOIDAL SURFACE HARMONIC FUNCTIONS. 137 



It is obvious that this process is considerably simpler and more elegant from the 

 point of view of theory, but to carry these operations through for all the integrals 

 given above would entail a good deal of algebra. I think indeed that the work 

 might not be very much less than what I have already done. 



Mr. HOBSON has further remarked that all the integrations may be avoided by the 

 following theorem : 



If F, (f, 77, ) be a solid spherical harmonic function of f, rj, of degree n, 



Considering, however, how simple are the integrals involved in his first method, it 

 may be doubted whether this would save trouble. 



VOL. com. A. 



