Sf/ stews of Corpuscles Jeser/'him/ C'lrciday ( h'hits. ^87 

 From (2) and (.')) we liavc 



d ( dz (l'/\ ITT, '"^ / 2 , "A 



{0/- + --) -O/o-^-'o )} +//„ ^-^~o ,7^. 



wluM-e Vo, Co, ""'^^ '^ are the values of y, z, and their dif- 

 ferential coefficients when ^ = 0. Hence, if we retain in the 

 expression for a. only those terms whose mean values do not 

 vanish, we have 



/ 



or 





dz 

 'Jdt- 



^djf _ 1 lie 

 '^ dt ~ 2 m 



\\\\l\Vl\ u 



djh d^ 



[^i'-i-'-'sym'M-i^->)}{j^,^£:.)i. 



Si 



nee 





we see that tlie orbit is equivalent to a little magnet whose 

 moment is 



The part of the moment which depends upon the external 

 magnetic force is 



and the mean value of this is 



4 m '-^^ ^~" ^'^ ^ ^^' 



where y^ and z^ are the mean values of y^ and z^ round the 

 orbit. 



If we consider a large number of particles describing 

 orbits, the phases of the particles in their orbits being 

 uniformly distributed, we can see that the total moment of 

 their equivalent magnets will be zero ; for consider a 

 number of similar orbits which only differ from each other 

 by the position of the particle when the magnetic force is 

 first applied. For all these orbits ^^ + 'i^ is the same; so 

 that if there are n orbits the sum of the second term inside 



2Z2 



