98 Dr. L. Silberstein on Molecular 



all events an interaction of an electric nature between 

 neighbouring atoms, precisely on account of the displace- 

 ments of their electrons ; there may also be other inter- 

 actions about whose nature we are as yet entirely in the 

 dark. On these grounds we must expect greater or smaller 

 deviations [from the additive law] from which one may one 

 day be able to draw some conclusions concerning the struc- 

 ture of a molecule." But, as far as I know, no such 

 investigation has been undertaken up to date, no doubt 

 because of the excessive complexity of the problem when 

 treated in its full extent — that is, together with the ques- 

 tions of " valency" and of all the dynamical properties of a 

 molecule considered as a system of atoms carrying electrified 

 particles. Nor would I pretend to solve the full problem. 

 But what I propose is a much more modest task, and one 

 which does not seem entirely hopeless or useless, viz. : To 

 investigate, with the simplest assumptions possible, the 

 mutual action of the atoms of a molecule only so far as 

 the oscillations of their dispersive particles {electrons) * are 

 concerned, and taking the molecule as being a comparatively 

 fixed constellation of the atoms. In short, to treat the 

 optical side of the question detached from all its other 

 aspects. In doing so one is fully aware that such a division 

 of the problem is artificial and physically illegitimate. 

 Yet, the solution of the limited, and therefore easy, problem 

 may turn out to have the value of a first approximation 

 at least, preparing the way for obtaining the successive 

 approximations. 



2. Atomic Interaction ; General Equations, 



Let each of the atoms A lt A 2 , etc., like or unlike, contain 

 ■a single dispersive particle which (without prejudicing the 

 values of its e, m) will, for the sake of shortness, be called 

 an "electron." Let —e ly —e 2 , etc., m l9 m 2 , etc. be the 

 charges and the masses of the electrons contained in 

 A x , A 2 , etc., and let lf 2 , etc. be the positions of equi- 

 librium of the electrons within their atoms, and r 1? r 2 , etc. 

 the vectorial displacements of the electrons from these 

 positions. We shall assume throughout that all these points 

 Oi, centres — as we may call them — of the atoms contained 



* Some of the most authoritative physicists! believe to have strong 

 reasons for suspecting that the dispersion electrons have much to do, 

 or even are identical, with the " valency electrons". It may well be so. 

 But, true to my above limitation of the problem, I shall purposely 

 ignore the possible " valency "-role of the dispersive particles. 



