202 Mr. C. G. Darwin on 



moving slower than it would if its mass were constant. This 

 gives the attractive force more time in which to exert its 

 effect, and analysis shows that in some cases the particle is 

 unable to escape. 



The variability of mass is of course not the only effect of 

 rapid motion. It is observed experimentally, and is also a 

 consequence of the general electromagnetic theory. If we 

 proceed strictly on this theory as it stands at present there 

 will also be a large radiation of energy due to acceleration, 

 and in addition to this an aberration of force due to the time 

 which is required for electromagnetic effects to be propagated 

 from one body to the other. When the particles are very 

 close together it is impossible to separate out all these effects 

 and ascribe one part to variation of mass and another to 

 radiation, but in the earlier stages it would seem justifiable 

 to do this. If the positive nucleus has an infinite mass the 

 aberration effect disappears. For the nucleus will remain, 

 fixed during the whole time and hence the mechanical force 

 on the electron, no matter what its own motion, will be 

 — eEi/r 2 where e, E are the charges of electron and nucleus 

 and r is the distance. Of course the force on the nucleus is- 

 not the equal and opposite of this, but as it is powerless ta 

 produce any motion it is immaterial. Although its effect is 

 certainly not negligible the radiation will be neglected for 

 the present, and subsequently an attempt will be made to 

 estimate the change in the orbits. It does not appear pos- 

 sible that any of the neglected effects could tend to cause a 

 separation of the particles, so that we have to conclude that 

 in certain cases a coalescence of charges should take place,, 

 if the electromagnetic equations as given by Lorentz are 

 universally true. 



As formula for the mass we shall take that given by Lorentz 

 for the " deformable '' electron. Any of the other values 

 which have been worked out for electrons of various charac- 

 ters would give a similar result, but Lorentz's formula, besides 

 being apparently in best agreement with experiment, makes 

 possible a complete integration of the equations of motion. 



2. If c is the velocity of light, v the velocity of the electron 

 and m its mass at low velocity, then Lorentz's values for the 

 longitudinal and transverse mass are respectively 



m 



in = 



v 2\3/2 



' ('-» 



m 





