418 Prof. Rowland on Spherical Waves of Light 



remains unaltered. Select three of these forms, and we can 

 thus write 



r 



h = {vyV»^ r ^- y;>-™, 



where Y„, Y^, Y^' are surface harmonics. 



These do not satisfy the equation of continuity, but the 

 series of derived vectors F m , G m , H m satisfy both the equation 

 of continuity and the equations of light. 



One of the best forms for these spherical harmonics is to 

 assume one of the axes in each of them parallel to one of the 

 coordinate axes. We can then write 



dV 



r/V 

 H =0 o n — ~e<e- Y V 



In this case the vector represented by the components F , 

 G , H is perpendicular to the surface V_ M == constant. 



Now the components of this vector do not satisfy the equa- 

 tion of continuity, and so, although it may represent the 

 vector potential on the electro-magnetic theory, it cannot 

 represent either the electric current or magnetic force, and is 

 almost without direct use on the elastic-solid theory. Hence 

 the derived vectors are of more general use. These are 



Hl «0..^-{^-^}««-0. 



G 2 =— c 2 G + -^, 



H 2 =-c 2 H + 



dJo u 

 dz ' 



