CH. xm.] VARIATION OF INERTIA 133 



Lectures on Electricity and Matter, p. 44, as 



/ 11 



mu = electric momentum = 



where sin = ^/-y ; and we may express it in a fairly 

 simple form thus : 



The momentum of a particle of electricity moving 

 at excessive speed is greater than the momentum 

 of the same particle estimated on the hypothesis 

 that its mass is constant, in a numerical ratio given 

 by the following expression ; where the ratio of the 

 speed to that of light, u/v 9 is expressed as the sine 

 of a certain angle : 



4 sm 2 sin 20 



We will call this the ratio <(#). It is the measure 

 of the spurious or extra inertia due to rapid motion ; 

 the ratio of the mass at speed u to the stationary 

 mass. We may also write it, rather more conveniently 

 perhaps for calculation, thus : 



3l ~~ 2GOs20 2 2 ~ COS 2e 



l-cos20~sin20 l-cos20/ 



Now the highest speeds measured by Kaufmann 

 were such as the following : 



2'36, 2'48, 2-59, 272, 2*85 times 10 10 cm. per sec. 



while the speed of light is well known to be 3*0 x 1C 10 

 cm. per sec. ; so the ratios u/v, corresponding to the 

 above observed speeds, are respectively 



787, '817, '863, '907, '95. 



These numbers therefore represent the values of sin #, 

 to be inserted in the above formula for obtaining the 



