i H. xiv.] AT HIGH SPEEDS 143 



was wanted was the transverse inertia, or the inertia 

 appropriate to a deflecting force at right angles to 

 the line of motion. This is to be obtained from the 

 expression for the tran verse force, derivable from the 

 expression for the energy in the ordinary manner by 

 Lagrange's dynamical equations : at high speeds its 

 value comes out different ; and when the formula 

 supplied for it by Dr. Abraham was subsequently 

 applied by Kaufmann in his calculations, it was found 

 to correspond very nearly with the view that the 

 whole of the inertia is electric. 



This formula, which in fact applies to any solid 

 aggregation of electricity stratified spherically, is 

 that the transverse inertia of a flying particle, m, is 

 to the inertia of the same particle stationary or 

 moving slowly, m , in the following ratio : 



m 



where /3 is the ratio of the velocity of the particle 

 to the velocity of light. 



This formula is not identical with that employed by 

 Thomson, possibly because the latter worked with a 

 different idea of an electron, though it gives numerical 

 results not exceedingly different. Primarily, how- 

 ever, it was employed not so much as an absolute 

 expression, as a form of function to be verified : 

 though it was used absolutely too. Kaufmann was 

 ultimately satisfied by finding out that his observed 

 mass varied if anything more rapidly, not less rapidly, 

 than theory required ; so that if the particles con- 

 tained any outstanding inertia of a non-electrical 

 character, such unexplained inertia must have a 

 negative value, which presumably would be absurd. 



I do not myself find that Abraham's function 



