the Inertia of Electric Convection. 231 



retained is not affected by the relative distances of the electrons. 

 For the purpose of this paper it is not therefore necessary to 

 go beyond the above expression. 



The correction to self-induction for a conductor of length I 



and uniform cross-section A will be - ^- or 



2 A 



l{l + 2*(ir— l)}/3NAa, 



where k is that fraction of the total current which is conveyed 

 by the positive electricity. If both kinds of electrons take 

 equal parts in conveying the current, the correction becomes 



7/6NAa. 



The correcting term increases in importance with diminish- 

 ing cross-section, and might be made large, if the cross-section 

 could be reduced so as to be comparable with molecular 

 dimensions. 



6. We must now enter into a discussion of the numerical 

 quantities involved. In the case of metallic conductors we 

 may, in the absence of contrary evidence, reasonably take N 

 to be of the order of magnitude of the number of molecules 

 per unit volume. Taking the molecular distance to be 10 — s 

 this gives N=10 24 . 



As regards the linear quantity a, observations made on, 

 cathode rays determine it, in my opinion, and in any case 

 fix a lower limit. The deflection of these rays by the magnet 

 shows that the moving electron has itself a mass or is carried, 

 by a small mass. J. J. Thomson adopts the latter view, but 

 it seems to me to be more natural to take the inertia of the 

 cathode particle to be the magnetic inertia of the electron. 

 If m is the mass, real or apparent, of the particle carrying 

 the negative charge, we may determine the ratio q/m. 

 Measurements of this quantity were first made by myself in 

 1881) *, and since then more accurate determinations by my 

 original method or by other and better methods have been 

 carried out by J. J. Thomson, Kaufmann,, Lenard, and 

 Wiechert. Taking the latter's estimate as being deduced 

 from the most direct method, I shall use l'3x 10 7 in electro- 

 magnetic measure for the value of q/m. If q, as was assumed 

 by me and afterwards proved by J. J. Thomson, is the same 

 quantity as that carried by the ion in a liquid, we know that in 

 the case oi e.g. hydrogen q/m! =10*, if m' denote the mass of 

 an atom of hydrogen. Now from the density p of the gas and 

 the number W of hydrogen molecules per unit volume, we 



* Bakerian Lecture, Proc. Roy. Soc. vol. xlvii. p. 526 (1890). ...."] 



