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SCIENCE PROGRESS 



where F x ( = P x //3), F v , F z are components of force, 

 law would have the same form in S', viz. : 



This 



MO- 



F r , and two similar 



if 



?*> - fa' - **f)\ 



^ _ J 



PF,= $F y 

 PF,= /3F, 



(6) 



Now in the case of electromagnetic forces, which are believed 

 to-day to cover a very wide range of phenomena, equations (6) 

 are known to be satisfied by the measures of such forces made 

 by observers in different systems of reference, if Maxwell's 

 equations are taken as true. In this region, therefore, we have 

 a law of motion which satisfies the principle of Relativity ; 

 i.e. maintains an invariant form for different systems of refer- 

 ence. It satisfies Nature also ; for in systems for which v is 

 small, it degenerates to Newton's law 



d( 



HtV 1 



-) =F etc 

 dt) x ' 



and in its wider application it is known to be true in the case 

 of high-speed electrons and /3-particles. Its most obvious 

 deduction is the variability of mass ; for writing (5) in Newtonian 

 form 



L m d £) - F - etc - 



we see that m = fifi = fi/\/i —v l , which increases as v in- 

 creases, and attains an infinite value as v approaches unity, 

 i.e. the velocity of light. 



At this point it is natural to ask if to this variation of 

 inertial mass there is a corresponding and proportional change 

 in gravitational mass. If there were not, then a body passing 

 through a given point near a gravitating mass would experi- 

 ence the same gravitational force whether moving fast or slow, 

 but would not experience the same acceleration, since in the 

 first case its inertial mass would be greater. Now, as far as 

 the most careful experiments can tell us, the acceleration is 

 independent of the velocity, and so the gravitational force 

 must also change with the mass, i.e. with the relative motion 

 of the body. Hence gravitational forces should conform to 

 Relativity. Were we assured that these forces are of electro- 



