222 CHARGE IN RAPID MOTION [APR K. 



There is no question but that the lines of force bend 

 back towards the equator, as stated by me in 1902, but I 

 assumed that this deflexion of the lines would entail their 

 moving up nearer to the equator of the sphere, so as to 

 leave the poles bare of charge, in order that the lines 

 might still continue radial. I admit that the lines of force 

 need not continue radial close to the sphere; but, in so 

 far as the sphere changes its shape, there should still be 

 some unimportant redistribution of the charge as the 

 speed increases. Mr. Searle calculates that whereas a 

 sphere at rest acts as if its charge were at a central 

 point, this equivalent point opens out into a uniformly 

 charged line, forming a medial and small portion of its 

 diameter, when the sphere is in motion ; as the velocity 

 increases, the length of this line gradually increases also, 

 until the speed equals that of light, when it fits the sphere 

 exactly. But this leaves out of account a distortional 

 change in the sphere itself, to which I will presently refer. 



The fact is that the behaviour of a charged body moving 

 at enormous speed may be treated exactly in the manner of 

 elementary potential theory for a charged ellipsoid at rest. 



It is doubtful whether the term " inertia " remains useful 

 under these conditions: it is perhaps best to reserve it 

 for the ordinary case when mass is constant ; for, as 

 Mr. Searle points out, three different estimates of inertia 

 can be made: one the ratio of force to acceleration, 

 another the ratio of momentum to velocity, and a third 

 as the ratio of kinetic energy to half the square of 

 velocity. In ordinary matter, as is well known, and for 

 slow electric motions, these three estimates are one and 

 the same; but for violent electric motions they become 

 different; though it should be realised how small the 

 difference is, until the speed of light is very closely ap- 

 proached ; so that in no material case of great velocity or 



