APR K.] CHARGE IN RAPID MOTION 225 



and is the formula appropriate to his experiments. All 

 this is in fact deducible at once by the usual Lagrangian 

 dynamical method from Mr. Heaviside's expression 

 Electrical Papers, vol. ii., p. 514 for kinetic energy; viz. 



an expression equivalent to ~ V? multiplied by the following 

 quantity : 



a 



r being the squared speed ratio u 2 /v 2 . 



In Larmor's original treatment of electrical inertia, Phil. 

 Trans. 185A (Aug. 1894), pp. 806-818, there was no reason 

 whatever for anticipating velocities greater than one-tenth 

 of light, so a simple inertia theory seemed amply sufficient 

 at that time; the mass being a permanent constant 

 associated with the electron and dependent on its 

 structure. 



It is the hope of seeing somewhat into structure that 

 has made the recent experiments on its modification at 

 high speeds so interesting. 



Professor J. J. Thomson's corresponding formula for 

 momentum is quoted above in the text, page 133, and 

 simplified ; and in simplified form it may be re-quoted : 



It amounts to this, that the mass of an electric charge 

 e on a small non-conducting sphere of radius a, moving 

 with a speed u = v sin 0, is 



which we have tabulated on page 145 (see also page 133) 

 in the form 



L.E. 



