from, the Physico- Chemical Standpoint. 335 



number. This correspondence in values is, however, only a 

 rouo-h one. The ratio of atomic number to atomic weight for 

 calcium is found to be 1 : 2*00. For strontium it is 1 : 2*31; 

 for barium it falls to 1 : 2*45 ; for radium it is still smaller, 

 1 : 2*57; and with uranium it reaches 1 : 2 59. In order to 

 connect the number of positive charges in an atom with the 

 atomic weight, therefore, it is necessary to provide some 

 mechanism which will decrease the ratio of charge to mass 

 from 1 : 2 to 1 : 2'59. 



This can be done in the following way. The mass of an 

 electrical charge depends upon the velocity with which the 

 charge is moving, provided that this velocity be made 

 approximate to that of light. In the model atom suggested 

 above, it w T as assumed that the positive electrons were moving 

 in their orbits ; and if the further assumption be made that 

 these charges revolve at speeds comparable with that of light, 

 then the masses of the charges will vary according to the 

 velocity with which they move*. 



In the calcium atom, the positive electrons maybe assumed 

 to be travelling comparatively slowly; and as the series is 

 ascended through strontium, barium, and radium, the intra- 

 atomic velocities may be assumed to increase; with the result 

 that each positive charge will gain in mass, and thus the 

 ratio of charge to mass could be brought into accordance with 

 the known data. 



For example, the atomic number of radium-B is £2, whilst 

 its atomic weight is 214. If the intra-atomic charges were 

 movino- within the radium-B atom v\ ith the same velocity as 

 those of calcium, then the atomic weight of radium-B would 

 be 164; so that it is necessary to calculate the velocity which 

 will raise the mass of these charges from 164 to 214. This 

 can be done by means of the Lorenz equation : — 



m _ 1 



in which m is the mass of the charge moving at a low 

 velocity; m is the mass of the same charge at the required 

 velocity, v • and c is the velocity of light. Taking m as 

 164 and m as 214, the equation yields t = 0'64, when the 

 velocity of light is taken as unity. 



This velocity may appear very high; but there is experi- 

 mental proof that negative elect ronst emerging from the 



* The same question has been approached from a different standpoint 

 by Conistock, Phil. Mag. [6] xv. p. 1 (1908). 



t Owing to the assumptions made above, it is difficult to deduce intra- 

 atomic velocities from the speed of the a-particles. 



