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.LXVIT. Mutual Electromagnetic Mass. 



To the Editors of the Philosophical Magazine. 

 Gentlemen, — 



IN the September number o£ the Philosophical Magazine* 

 Dr. L. Silberstein draws attention to the problem of the 

 mutual mass of two electrical charges placed close together. 

 In a recent paper of my own, " Electromagnetic Inertia and 

 Atomic Weight,''' I had overlooked the fact that Dr. Silberstein 

 bad already calculated formulae giving this mutual mass 

 precisely, and I had obtained an approximate formula for one 

 of the special cases. While very willing to concede all priority 

 to Dr. Silberstein in this connexion, perhaps I may be per- 

 mitted to make one or two remarks about my paper. Its 

 object was not the calculation of mutual mass, but the 

 application of the idea to some points of nuclear structure in 

 the atom, as in fact its title indicates. Being unaware of 

 Dr. Silberstein's calculation, 1 made an approximate one 

 myself, by very obvious and simple mathematics. This 

 approximation was all that I required, and its deduction forms 

 an inconsiderable part of my paper. A numerical error in 

 a coefficient, due, as I find from my manuscripts, to the 

 transposition at one stage of a factor 2 in a fraction, does 

 not affect my reasoning, which only dealt with orders of 

 magnitude. I had no necessity for the exact formulae in 

 the applications I was making. 



It would be int. 'resting to trace the first appreciation of 

 the existence of mutual mass, — the term employed both by 

 Dr. Silberstein and myself. I am sure it is not so recent as 

 Dr. Silberstein's note seems to imply. For example, many 

 years ago Dr. Oliver Heaviside determined approximately 

 the effect of an external field on the mass of a charged par- 

 ticle, — the calculation being reproduced in his collected papers, 

 — and evidently at that time fully appreciated the mutual 

 effect of two charged particles. But he did not, however, 

 make the precise calculation which Dr. Silberstein has since 

 given U s. 



Believe me, Gentlemen, 



Yours very truly, 

 J. W. Nicholson. 

 King's College, Strand, W.C. 



