Theory of Matter and on Radiation. 197 



k= +], orbital, are to and fro vibrations in the plane of 

 the ring; &=+l, axial, are vibrations with one diameter 

 fixed. In all cases positive values of k mean waves travelling 

 forward, negative, backward. 



h=o 



Orbital 



k--±2 





k=o 



k=±Z 



Side view 



We are not at present concerned with the forces which 

 produce these vibrations, but only with the waves emitted 

 which we now proceed to examine. 



§ 8. At a great distance from the ring I find 



P = A=0, 



ne cot 6 



+ ? ^COS 6 .y/- 1 . B 6 V~l{ <?(«-£)+*} X Pj&J'nW sin $)e +=* ■ '** 



e=N= n^>te Ae ^ q{t _ ^;^ u ^ sin e)e ^ 



mty 



+ ^ Ce *=, . ,(.- e M_ (^ -10 sin tf^J,,,^ sin 0) 



e V - 1 . m^ 



V— 1 . mty 



n= -M= - — 2 ^-1 . Ae ^-i.fl{*- c") X P0*J'm(ll3 sin 0)* 



' S= — 00 



- !!£| C os V-l-Ce v = 1 -*('-e)*2°J , /«r'«(//8ain *)■« v ' = ~ w > 



?7> s=— oo 



^7 / I* \ 7T 



where >?i = & + sn, Z = -~ + & -j- sw, i/r = o)( £ — j { J + B -f - } — c/>. 



