1919] on Ether and Matter 459 



inertia is explicable (or supposed to be explicable) in terms of the 

 magnetic field surrounding the current, i.e. really (as I think) in terms 

 of a property of the ether of space. It exactly simulates inertia ; 

 but is it an imitation or is it the same thing ? Can it be said 

 that an electric charge possesses inertia in its own right, and retains 

 it always, as matter does, whether it be moving or whether it be 

 stationary 1 



The question was brilliantly answered by your Professor of 

 Natural Philosophy, Sir J. J. Thomson, so long ago as 1881. He 

 calculated the inertia or quasi " mass " of an electric charge e, on a 



sphere of radius a, and showed that it was m = — ^ • 



3a 



The fji need not be attended to now, though it is really the most 

 important of all— being a great etherial constant of utterly unknown 

 value"' — but for our present purpose the /x merely signifies that the e 

 must be measured in electromagnetic not electrostatic measure, 

 when the formula is interpreted numerically with /x = 1. 



At the date 1881 this expression for true electric inertia, though 

 an interesting result, seemed too absurdly small to have any practical 

 significance. Take a sphere like a football, 20 centimetres or 

 8 inches in diameter ; charge it till it is ready to give more than an 

 inch spark, say up to 60,000 volts ; then calculate the inertia or 

 equivalent mass corresponding to the charge. If I have done the 

 arithmetic right it comes out one-third of a millionth of a millionth 

 of a milligramme (3 x lO""'). Absurdly small ! Yes, but not zero. 

 And whenever a quantity is not nothing, there is no telling what im- 

 portance may not have to be attached to it sooner or later. Nothing 

 real can be so small as to be really negligible in the long run as 

 knowledge progresses. Something at present unforeseen may bring 

 it into prominence. So it has turned out in this case. The infini- 

 tesimal result of nearly forty years ago to-day dominates the horizon. 

 It was in some sort the dawn of a new era in physics. 



Consider it further. Clearly the inertia depends not on the 

 charge only, but on its concentration. The radius of the sphere 

 occurs in the denominator of the expression. The same charge on a 

 sphere 2 centimetres in diameter would have ten times the inertia ; 

 on a sphere as small as an atom the inertia would be a hundred 

 million times bigger still. But then even that is small ; moreover 

 an atom could scarcely be expected to hold such a charge. Never- 

 theless, allowing only a reasonable potential, it might seem that 

 atomic inertia could be sensibly increased by an electric charge. But 

 no, even on a sphere as small as an atom the concentration turns 

 out insufiicient ; the effect is still excessively minute. Yet as 

 electric inertia at given potential depends on linear dimensions, 



* I have guessed that it is a density of 10^^ grammes per c.c. -j- 47r. See 

 The Ether of Space, Appendix 2 ; also the Phil. Mag. for April, 1907. 



