42 DETERMINATION OF SPEED [CH. v. 



more or less elongated, threading itself along the 

 negative field : the direction of twist depending on 

 the sense of the field. 



There is no difficulty in determining the radius 

 of curvature r ; and the theory of normal deflexion 

 is the simplest possible, nothing more than stating 

 that the magnetic force H, acting on the current 

 element eu, is the necessary deflecting or centripetal 

 force, my?/r, required to overcome the mechanical 

 inertia of the particles ; i.e., 



mu 2 



- = jmeun., 



whence u= uKr ; 

 e 



or the ratio e/m is to the velocity of the particles as 

 the curvature of their path is to the intensity of 

 magnetic field which curves it. Prof. Schuster of 

 Manchester was among the first to make measure- 

 ments of this kind. 



The two factors on the right of this equation are 

 directly measurable (/u. being conventionally ignored 

 as usual, or a better mode of expression united 

 with H as induction-density) ; but the two factors 

 on the left are both unknown, hence neither can be 

 determined by this means alone,-an assumption 

 must be made about one or other of them, or else 

 another independent kind of experiment must be 

 made. 



Assume, as many experimenters did, that u is a 

 velocity appropriate to atoms flying in a gas of 

 ordinary temperature, then the value of e/m comes 

 out not so very far discrepant from the usual ionic 

 value, measured in liquid electrolysis, viz., 10 4 c.g.s. 

 Or, conversely, assume the usual ionic or electrolytic 



