the Earth's Magnetic Field. 85 



Increase in the rate of absorption to the rear, we have an 

 explanation of the current, and the extremely small order 

 of the effect necessary may be gathered from the following 

 consideration. 



To fix our ideas, suppose an atom emits a corpuscle 2p 

 times per second, with a velocity of 10 7 cm. /sec. For a 

 resting molecule there is no resulting current, because the 

 emission is perfectly symmetrical. Suppose, however, that 

 owing to the motion of the matter, the emission p in the 

 direction of motion is altered in favour of that direction by 

 a fraction k of its value. The effect will be equivalent to a 

 current density of the order of magnitude <r = kp^e\ x 10 7 , 

 where e is the electronic charge, and is equal to 10 ~ 20 e.m.u., 

 A, the mean free path of a corpuscle, and N the number of 

 atoms per c.c. Taking N = 10 23 , and A,= 10~ 7 cm., we see 

 that in order to obtain a current density of 10 ~ 9 e.m.u. it is 

 necessary to have kp = 10~ 12 . Now k must be a function of 

 the centripetal acceleration, and of the velocity v of the 

 element of matter, and even though, to satisfy the conditions 

 of uniform translatory motion, we imagine it to be of such 

 a form as to contain no terms of the type vjC or v 2 jC 2 (C 

 being the velocity of light), or at any rate of such a form 

 that the other alterations in the matter brought about by the 

 motion prevent any such terms appearing in the final ex- 

 pression for the magnetic field, we may nevertheless expect 

 terms of the order //C, fv/G 2 , &c. to occur. 



Considering a case where k is of the order //C, L e. 10 ~ 10 , 

 we see that it is not necessary that p should be greater than 

 10 ~ 2 , so that the expulsion of one electron from an atom in 

 100 seconds would be sufficient to ensure that the variation 

 in this quantity, resulting from the motion, would account 

 for the earth's field. 



In spite of the smallness of the necessary value of p, it 

 maybe argued that it would correspond to a very radioactive 

 substance, since one gram of radium only expels 10 10 cor- 

 puscles in one second. It must be remembered, however, 

 that we are not here dealing with the complete expulsion of 

 corpuscles from the matter. The chance of a corpuscle 

 leaving an atom, due to the comparatively large pull exerted 

 by an adjacent atom, and remaining in the vicinity of the 

 atoms, is enormously greater than the chance that the cor- 

 puscle will get away altogether, so that the above values of 

 p must not be looked upon as being inconsistent with radio- 

 active phenomena. Indeed, values of p enormously greater 

 than that which it has been necessary for us to assign are 

 tolerated, for example, in the particular theory of metallic 



! 



