G92 AJagneiic Properties of Systems of Corpuscles. 



Substituting these 

 (2) takes the form 



dz 

 Substituting these values for x and ;: in ^^^~^ ^ttj '^^'g see that 



^ = Acos{7iayt±8t)6"'^~y~^' 



thusj to use the language of spectrum analysis, instead of a 

 single line of frequency ?ico Ave have two lines whose fre- 

 quencies are nco-hS and nco — S respectively: it is easy to 

 show that these lines are circularly polarized in opposite 

 senses. 



18. Let us now consider the effect at right-angles to the 

 magnetic force, and first take the component of the magnetic 

 force parallel to cC ; we have 



_ ^ /dy d^l ^dz d 1\ 



Along the axis of ?/ the only terms we need consider are those 

 in which the differentiation is entirely with regard to y' \ 

 picking out this term we have, when there are n corpuscles, 



,, .-i>-^y) 



" = ^7^2^ —r^' 



in this equation some constants have been omitted which do 

 not affect the argument. 



y — 7} cos ht — f sin ht. 



Substituting the values for z, 77, and f given above, we 

 find that a contains terms of the following ty[)es : — 



co^ [nwt -Vnht) , cos (na)t±{n — 2) ht), cos (ncot±{n— 4:) ht), 

 and so on, the last term being- 

 cos {;)2cot + 2Bt) if 71 is even, 

 cos {7io}t±Bt) if n is odd. 

 The equation for the magnetic force parallel to z is 

 _ ^ /d.v d 1 dy d 1\ 

 ^ ~ ^\di </ r' " ~dt d^' vr 



along the axis of y this reduces to terms proportional to 



"dt-y —r — 



