232 
MR. J. LARMOR OX A DYNAMICAL THEORY OF 
insignificant as to be far below the reach of experience : electrons may, it is true, 
also conceivably obliterate each other in the same way as these diffuse electrifications, 
but that is a contingency of negligible probability with which we are familiar in all 
kinds of molecular theory. 
Relations of Inductive Capacity and Optical Refraction to Density. 
18. Let the medium be free sether containing n similar molecules per unit volume; 
and suppose each molecule to be polarized to moment y by the field of electric force. 
This field is made up of the extraneous exciting field and that of the polarized 
molecules themselves ; the latter again consists of a part arising from the polarized 
medium as a whole and a part involving only the immediate surroundings of the 
point considered. If h denote this local part, and H the remainder of the total 
electric field, we have relations of the types p = Jc (H + h), % — np, h = \ . np, 
i denoting the intensity of the polarization, h a constant independent of the density 
of the material medium, and A a parameter which, as will appear, must be nearly 
independent of the density. These relations lead to i — hi (H + that is, since 
by the definition of the inductive capacity K, i' = (K — l)/47r. H with electrostatic 
units, they lead to SMtt. hi = (K — 1)/(K — 1 + Ttt/A) ; so that, p denoting density, 
(K — 1)/(K — 1 + Itt/X) p is constant for the same material medium. For fluid 
media at any rate, it will appear that X must be very nearly equal to so that for 
them Lorentz’s expression (K — i)/(K + 2) p should be approximately constant. 
When the dielectric is a compound one consisting of n molecules of one kind and 
n of another per unit volume, we have % = np fi- l^ — 5 and p = k (H + h), 
p z= h (H + /i), so that pjk = p jh — i' jikn fi- hn). Thus [hi fi- k'n) (Hfi- Xi'), 
so that, with the above value ^tt for X, 3/4:7 .{hi + hn) — (K — l). (K + 2). This 
formula gives an additive character to the refraction equivalent for a mixture ; and 
also for a compound body, provided in the latter case the moment p belongs to the 
individual atom, and is not sensibly afiected by the molecular grouping of the atoms. 
This investigation is of course not absolutely exact; but it is the first approxim¬ 
ation in a statistical theoiy, and the question presents itself how far it is a 
sufficient approximation. On examination, it will appear that the coefilcients k and k' 
are rightly taken to be numerical quantities independent of n and n, provided the 
distance between the effective poles of an atom or molecule is not a considerable 
fraction of the mean distance between adjacent molecules. The constancy of the 
value of X, when the component densities are altered, appears from considerations of 
dimensions. For the force due to a polarized molecule varies as pX (distance)”®: 
thus, as on change of density (distance)”® varies directly as density, the character of 
the arrangement of the molecules being supposed unaffected, the force due to the 
molecules surrounding the point is proportional to pX density, that is, it is equal 
