820 
MR. J. LARMOR ON A DYNAMICAL THEORY OF 
with free periods, which may be done by imposing an elastic restoring force on each.'"' 
In this latter case however the difficulty of representing the nature and origin of the 
restoring force detracts very seriously from the efficiency and validity of this mode of 
representation. Fortunately the simpler and more definite case is all we now 
require; when the mass is all concentrated in the beads, Lagrange finds that the 
velocity of propagation of a wave whose length contains n beads is Vq sin -A jTTj‘2iiA 
For the ca,se of an ordinary light-wave there are about 10® molecules in a wave¬ 
length, so that the dispersion for an octave should by this formula be about 
-^( 77 / 2000 )’ of the velocity, which is enormously smaller than the corresponding 
disjDcrsion, usually about one per cent., of actual optical media. 
Thus we must conclude that, while the present form of MacCullagh’s theory 
ascribes refraction to the defect of elastic reaction of the molecules, and dispersion to 
the influence of their free periods, so also the elastic-solid theory must ascribe refrac¬ 
tion to loading by the mass of the molecules, and dispersion to the influence of their 
free periods. In these respects the two theories run parallel, and there is not much 
to choose between them ; a model constructed on either basis would fairly represent 
the phenomena of dispersion. The latter ascribes the influence of the matter to 
nodules of mass, in the rethereal, not by any means the material or gravitative 
sense, supposed distributed through the medium ; the former finds its cause in the 
properties of the nuclei of intrinsic strain, or electrons. On either view, Fresnel’s 
laws of reflexion are a first approximation obtained by neglecting dispersion, and are 
as we know departed from by a medium which produces anomalous dispersion of 
the light, even for wave-lengths which suffer no sensible absorption.j 
* Gf. Lord Kelvin, ‘Baltimore Lectures,’ 1884. 
t Lagrange, ‘Mec. Anal.’ ii., 6, § 30; Rayleigh, ‘Sound,’ § 120; Route, ‘ Djnamics,’ vol. 2, § 402. 
+ The most definite form which the Young-Sellmeier type of theory has yet assumed is that of 
Lord Kelvin (‘Baltimore Lectures,’ 1884). The author begins with an illustrative molecule, con¬ 
sisting of a core of veiy high inertia joined by elastic connexions to a chain of outlying satellites of 
which the last onb' is in connexion with the Eether. The core being thus practically unmoved, the 
whole system is so to speak anchored to it, and the mass of the core does not come into account. Such 
an illustration gives very vivid representations of absorption and fluorescence. After working out the 
formula for the index of refraction in the manner of Lagrange’s dynamics of linear systems, a trans¬ 
formation is suggested by consideration of the zeros and infinities of the function representing the 
index, which gives a priori a result whose validity is far wider than any special illustration, in the form 
= 1 -h 
'-H 
p I 
1 
D 
+ 
w^hei'e T is the period of the waves, atj, . . . are the free periods of the molecule, and the coefficients 
gj, 22 • • • dejiend on the distribution of the energy of the steadily vibrating molecule amongst these 
periods. On this theory the mther is 7iot simply loaded by the molecule, but the coefficient q depends 
on the manner in which the molecule is anchored in space; the theory is accordingly in difficulties with 
regard to double refraction and reflexion (Zoc. cit., Lecture xvi.), of which the foi’mer is not a dispersional 
phenomenon. 
The analogous electric theory explained above appears to be free from these difficulties. The 
