THE ELECTRIC AND LUMINIFEROUS MEDIUM. 
•235 
time was the one developed in von Helmholtz’s early memoirs on electrodynamics, 
and it would appear that fliscrepancies come in throug’h treating the mther as 
polarized like a material dielectric; at any rate his final result {loc. cit. p. 654) 
seems to give the refractive index a value greater than unity for free mther, and one 
only infinitesimally different for a ponderable medium. A mathematical investigation 
has been given by Lord Rayleigh, in which the range of density over which these 
statical computations are valid is tested by finding for certain cases the complete 
expressions in a statical theory, of which they form the first rough approximations. 
The result is rather unfavourable to Lorentz’s formula, so much so as perhaps to 
excite surprise at its close agreement with the facts when the range of density is so 
great as that between the liquid and gaseous states of the same substance. There 
is thus room for the statistical method under which the subject has here been 
apj)roached,t in that it explains the wide range through which the formula proves 
to be valid as a first approximation ; while it at the same time recognizes that when 
the change of density is itself small, but is accompanied by other kinds of physical 
change, the influence of the latter on the polar molecule may be sufficiently important 
to prevent its exact verification.J On the specific influence of temperature, cf. § 72 
infra. 
21. In thus basing a theory of refraction equivalents on the value of the inductive 
cajiracity, it has been tacitly assumed that the dispersion of the medium is small; 
hence the results apply certainly only in the cases in which there is approximate 
agreement between the inductive capacity and the square of the refractive inde.x.§ 
When dispersion in ahsolutely non-conducting media is taken into account, as in the 
previous memoir, § 11, and infra, § 23, the formula however still holds, the constant k, 
equal to/'/P of § 24, now involving the period of the light. 
The fact that for gases, and a large class of denser bodies as well, the inductive 
capacity is approximately ecjual to the square of the refractive index, shows that in 
them the polarization of the molecules can completely follow the rapid alternations of 
electric force which belong to the light waves. Thus we can conclude that when the 
Rayleigh, On the influence of obstacles arranged in rectangular order on the properh'cs of a 
medium,” ‘ Phil. Mag.,’ 34, 1892 (2), p. 481. 
f Since this was written, I have found that the analytical method here employed is essentially the 
same as that of Clausius ( Mechanische Warmetheorie,’ 2, 1879) the fundamental in)portance of the 
ideas involved, and the discussion here given of the value of A, in the case of fluid media, may perliap.s 
justify the retention of the above independent statement. 
+ A theory precisely similar to the above of course applies to determinations of molecirlar magneti¬ 
zation in solutions of iron or other salts; strictly it is not the coeffcicnt of magnetization v, but 
that is proportional to the density of the magnetic molecules. The values of k are however 
usually so small that this constant is practically equal to a-. 
§ This accords with the conclusion drawn by Lixde from an experimental examination of the subject, 
Wied. Ann.,’ 5G, 1S95, pp. 546-70 (see p. 566). [Philip, ‘ Zeitsch. Phys. Chem.,’ 1897, finds that the 
Clausils foiiniila is quite inapplicable to mixtures of substances with abnormally high values of K.j 
O Tir O 
^ xl w 
