St/stcms of Corpu.^cU's di'i^cr/'lt'nii/ Circular Orbits* G91 



ip,v . (I ip'/ .. d , ivz ,. d 



— {r~ lor . - ' tor—, and- • - tor - 



V /• cLc \r ay \r ax 



in that expression, so that as far as this term is coiiccrned, 

 (I) reduces to 



thu^ along the axis of x where y and z both vanish we need 

 only consider terms for which m = n=Oy and along the axis 

 of// those for which l-—7i = 0. 



17. L(;t d-, 7/, z denote the coordinates of one of the cor- 

 puscles, the y component of the magnetic force at the point 

 [.c\ y\ z') is given by the equation 



^ (dz d \ dx d 1\ ,.x 



where r' is the distance between (cc, y, z) and {x\ y\ z'), and 

 ^ denotes that the sum of the corresponding expressions for 

 all the corpuscles is to be taken. If r is the distance of 

 x' y' z' from the origin of coordinates (the centre of the 

 orbit) then 



11/^^ d d\\ 1 / d d , d\n 



Along the axis of x the only terms we need consider are 

 those in which the differentiation is entirely with regard to 

 cr' ; hence, confining ourselves to these terms, we see from 

 § 5 that if there are ?i corpuscles regularly spaced round 

 the orbit, the term in /3 with which we are concerned will be 

 of the form 



'"-1 /dV'-K'iP^ 



dz X-' (dY-^e^''-y^ (.. 



dt' l.t.\).ii-\.\dx'l r ' • -^^ 



Now X is of the form A cos wt-{-V> sin coi, 

 while if ^ 1 H^ 



z = ^ cos St-\-r) sin Bt, 



where f = A' cos cot -j- W sin wty 



71 = k!' cos (Sit + V>" sin wt. 



