178 Sir Oliver Lodge 



on 



Hence i£ we wish for a single expression to serve in the 

 electrical case, for an election e revolving round a nucleus 

 with unbalanced charge Ne, and with b as a radius of dis- 

 continuity or distance at which break-away occurs, some 

 such law as this might be suggested, 



N^/r y( r 2 -b 2 ) 





it being understood that the first term ceases to apply after 

 the snap. The frequency corresponding to the direct-distance 

 law will be given by the square root or' the ratio of the force 

 at unit distance to the revolving mass, or 



, 9 , 2 Ne 2 . 2 fie 2 



So ^3=^N (1) 



07T 



In the early stages, at small distances, the speed of the 

 electron would keep on increasing with the radius until it 

 became 2iTnb : and as soon as the speed is high the balance 

 of force equated to the centrifugal reaction must be disturbed, 

 by reason of the force term diminishing while the inertia 

 term increases, under the influence of a factor ^/(l — v 2 jc 2 ) as 

 multiplier and divisor respectively; hence sooner or later a 

 break is inevitable. We shall be able to calculate the value 

 of this factor in some critical cases later on. 



When snap occurs at distance r — b under an inverse square 

 law, the critical condition would be 



Ne 2 



N<? 2 3 



So, still, n 2 b z = 2Tr = q- 



where a is the radius of an electron, c the velocity of light, 

 and where for the present the j3 factor involving v 2 /c 2 is 

 ignored. 



If the particle now flies away, the energy of escape is half 

 the energy from infinity under an inverse square law, so 



\m(2irbnf=\nh, 



or h/27r = mvb, which according to Planck is constant or 



