234 
MR. J. LARMOR OR A DYRAMICAL THEORY OF 
at the limit of the molecular range, this intensity being uniform in direction and a 
function of the distance only. The force due to this is along the direction cf 
the polarization ; which is therefore the local part to be added on to the electric 
force as ordinarily defined—namely, to that arising from the density p throughout 
the medium and the density <t on its external surface, and so everywhere derivable 
from a potential by the theory of gravitational mass-distributions. The value of 
the coefficient X of the above analysis should thus be |7r for a fluid but it may 
deviate from this value somewhat in the case of a solid, especially of course if it be 
crystalline. 
20. The mathematical principles, on which the above formula for the relation 
between inductive capacity and density is based, were flrst given by Poissox for the 
corresponding problem in magnetic polarization. The explicit application to electric 
polarization, on the lines of Faraday’s ideas, was made by Lord Kelvix and 
Mossotti. The investigation of the formula which has been implicitly given by 
Maxwell (‘"Treatise,” § 313), expressed in terms of the cognate problem of 
conduction, is however valid only for the case in which the coefficient of polarization 
of the medium is small compared with unity, that is, only for gaseous media. The 
same formula, viewed as a relation between refraclive index and density for trans- 
porent media, was obtained by LoRENTzt and was shown by him to be experimentally 
valid in an approximate way over the wide range of density including the licjuid and 
gaseous states ; though for the small changes of density induced in a liquid by 
alterations of pressure and temperature tlie effect of the change in the internad 
energy and mutual configuration of the molecules may considerably mask the direct 
effect of the slight change of density.^ For gases, however, in which the molecules 
are more isolated and the changes of density greater, the refraction is found to be 
in accordance with the formula. The investigation of Lorentz§ was probably tire 
first 6‘ffectlve attempt to introduce the molecular constitution of the medium into 
the electric theory of light, and so arrive at laws of refraction and dispersion. The 
form of the refraction constant was really settled by statical considerations akin to 
those here given ; but the theory of electric propagation employed by him at that 
* Tlie fact that the values of the refractive index for liquids are slig'htly in excess of what Lorextz’s 
formula ■would give by computatiun from the valaes for their vapours, may be an indication that this 
averaged field of molecular action is slightly elongated instead of spherical. 
t H. A. Lorextz, “ Ueber die Beziehung zwischen der Fortpflauzungsgeschwiiidigkeit des Lichtes uud 
der Kdrperdichto.” ‘ Wied. Arm.,’ 9, 1879, p. 641. 
I For these small changes, the Lorextz refraction function (m" — 1) j (_m~ + 2) is approximately 
proportional to that of GtEADSTOXE and Dale, their ratio (rn + l)/(m“ + 2) being nearly constant; but 
it docs not appear why the latter function happens to be usuallj' more nearly proportional to the 
density than the former. The results of Roxtgex and Zehnder, ‘ Wied Ann.,’ 44, 1891, on the effects 
of pressure on vmrious fluids, make the two formulre in default in opposite directions by about equal 
amorrnts. 
§ ‘ Yerhandl. der Akad. Amsterdam,’ 18 ; abstract in ‘ Wied Ann.,’ 9, 1872, pp. 641-665. 
