[ r33 ] 



LXXXVI. The Longitudinal and Transverse Mass of an 

 Electron. By W.F. G. Swann, JD.Sc, A.R.C.S., As- 

 sistant Lecturer in Physics at the University of Sheffield*. 



IN his paper on " Recent Theories of Electricity " (Phil. 

 Mag. February 1911) Prof. L. T. More refers in a note, 

 page 214, to the difficulty of realizing the existence of a 

 transverse mass for an electron when the velocity is zero, in 

 view of the fact that, as he remarks, transverse mass is 

 defined as mass due to a change in direction only. I think 

 that the following method of deducing the expressions for 

 the masses, while of course it rests on the same funda- 

 mental bases as those hitherto employed in former investi- 

 gations, has the advantage or bringing out more clearly the 

 real meaning of the masses, and further it does not involve 

 the consideration of a curvilinear motion at all f . 



We first define force as equal to the rate of increase of 

 momentum produced by it in the direction in which it acts. 



Let us find the component 

 accelerations X, //., v produced 

 by the unit forces in the three 

 coordinate directions X, Y, Z 

 at the instant when the electron 

 is moving in any direction OA 

 with velocity p, q, r. Let 

 U, Y, W be the components of 

 the momentum of the electron 

 expressed as functions of p, q, r. 

 According to our definitions of 

 the unit forces we have 



i=^ = ^n ?£ ^x^i 7 , 



"dt ^p ' "dt Bp' 



.,, • « . . , . BY . 3W 



with similar expressions involving -~ — and -=■ — , 



so that 



dp d? br 



* Communicated by the Author. 



t The point raised by Professor More may also be met, by observing- 

 that the expression deduced for the transverse mass by the method 

 adopted by Abraham (see ' Ions, Electrons, and Corpuscules,' by Abraham 

 & Langevin) is independent ot the radius of curvature of the curve 

 which the electron is supposed to describe, so that it holds for an infinite 

 radius of curvature, i, e. for a rectilinear motion. 



