the Eartlis Magnetic Field. 87 



that the time taken by the corresponding particle in going 



1 2 



V(# 2 ~#l) 



from xi to x 2 ' is e ll H v -\ K^ — -? but the time taken in 



going from x 2 to #/ is e 1 ^ ^-^ . lnus, not only 



is the average velocity altered, but the alteration depends on 

 the direction. In the case of uniform translatory motion, 

 however, the principle leads to the result that, on the whole, 

 the various motions so adjust themselves that, if a piece of 

 matter at rest produces no magnetic field, that piece of matter 

 will produce no field when in uniform translatory motion. It 

 is reasonable to suppose, however, that in cases other than those 

 of uniform translatory motion this compensation will not 

 necessarily be exact. If n is the number of corpuscles per c.c, 

 V the average velocity of a corpuscle, X the mean free path, 

 t the time which elapses between two collisions, s the number 

 of collisions suffered by a corpuscle per second, and if: further, 

 suffix (1) refers to the direction of motion of the element of 

 matter, and suffix (2) to the opposite direction, the resultant 

 current density due to the want of symmetry referred to is 

 of the order 



a — nesfYxfi — V 2 f 2 ) = nes(\i — X 2 ) = nesBX, 



where SX = Xx — X 2 . 



Since sX = Y we may write a = neY8X/X. 



Taking n = !0 24 , e = 10- 20 E.M.U., V = 10 7 cm./sec.*, 



we find that, in order to produce a current density of 

 10~ 9 e.m.u., we must have 8X/X = 10 -20 . Now the first term 

 which we might expect to be involved in the expression for 

 BKJX is a term of the order //0, since terms independent of 

 the acceleration, and depending only on the velocity, must 

 not exist, owing to the fact that they would involve magnetic 

 fields for matter moving with uniform translatory velocity. 

 fjG is of the order 10 ~ 10 however, i. e. far greater than we 

 require. Indeed, a term of the order (f/G).(v 2 /C 2 ), that is 

 10 — 18 , is amply sufficient to account for the necessary value of 

 SX/X, and indeed leaves a good margin. 



It may be argued that, in raising the question of the 

 possibility of a want of symmetry in the expulsion of electrons, 

 or in the mean free paths of the electrons, we have given no 

 suggestion of a physical basis for the existence of such a 



* This value of V is calculated for a temperature 0° C. by taking- the 

 mean kinetic energy of the corpuscle as equal to that of the hydrogen 

 molecule. 



