Si/stems of Corpuscles describing Circular Orbits. 075 



Honce y the z component of the magnetic force at P, 

 calculated on the assumption that the velocity of the particle 

 is uniform, is given by the equation 



r=-eaa,^sm^^+cos^^|p. 



r' being written for PQ. 

 Writinij r for OP we have 



/ = a ( cos 6^-r- + sin ^ ^- I - 4- :; — : ( cos ^ ^ + sm 6' -7- 



r \ dx dij) r 1 . 2 \ dx dy J r 



hence, writing ^ for cos ^ -r- + sin ^ -r- , we have 

 ' ^ dx dy^ 



7=-eaa)|d--a32l + -^^^3l_ 1 . ^ (2) 

 ' L^ r 1 .1 r J ^^ 



To pass to the solution in which the acceleration of the 

 particle is taken into account we must express 7 in terms of 

 the time. 



Now 6 = dot when t the time is measured from the instant 

 when the particle is on the axis of a; ; hence, substituting the 

 exponential values for the cosine and sine, we have 



If we introduce two new variables f and 97, defined by the 

 equations 



then d d _ d ^ d d _^ d ^ 



dx dy d^ dx dy drj' 



thus , r „. d 



-V d^'^ dvi 



- 3.,}„-@V„„.-,K(|)-. 



drj 



Hence to deduce from (2) the value of the magnetic force 

 when we take into account the acceleration of the particle, 



w^e must write in that expression instead of -S"- 



