Si/stems of Corpuscles descrihing Circular Orbits. 679 



due to the particles (1) (2) (3) respectively, 71 will be 

 ^iven by the expression already found, 72 "^^'^1^ he got from 



7i by writing cot-] for (ot, y^ by writing co^-f2- — for 



o)^, and so on. The total magnetic force parallel to z due to 

 the p particles will be 



71 + 72 + 73+ . . .7p- 



The term independent of the time will be the same in 

 7i? 72? -"9 hence for the p particles it will be 



2 d' 1 



5. Let us now consider the periodic terms. The term 

 corresponding to e'^'*^^ in 71 will in 72 be e'^^^'^ "^ p \ in 73 

 ^tn\^io --^^^r^iij 5Q Qj^^ hence the corresponding term in 

 71 + 72+73+ ••• will be 



f),— O— O— 



„ , mfowJ-t-— \ in(wt+2.—) in (u)t+3.—) . 



^tnuit^^ \ ^^; + gV pJ + e ^ ?y+...; 



now this expression vanishes unless n is a multiple of p, 

 when it equals pe^^'^K 



Hence the largest periodic term in the expression for the 

 magnetic force due to the p corpuscles will be that corre- 

 sponding to the term e^^^* in 7^, and its magnitude will be p 

 times this term ; referring to the expression for 71 w^e see that 

 the largest periodic term in the magnetic force due to the 

 p particles will be 



iptor ipuyr 





/ , p(tjr\ 



*^'--^n^r-=^^}- 



Similarly the x and 7/ components of the force due to the 

 p particles are given by the equations 



