726 
MR. j. LARMOR ON A DYNAMICAL THEORY OF 
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owing to the formation of compressional waves which carry away some of the energy, 
and to laws of reflexion quite irreconcilable with observation. 
11. Can then any justification be offered of Kirchhoff’s doctrine of extraneous 
surface-forces ? The parallel case which is appealed to for its support is that ot 
capillary forces at an interface betw^een tw'o fluids. Now on Gauss’ theory of capil¬ 
larity these forces are derived simply from the principle of energy ; each fluid beuig 
in equilibrium, its intrinsic energy is distributed throughout its interior wfith so to 
speak uniform volume-density; if we imagine the surface of transition to be sharp, 
and each fluid to retain its properties unaltered right up to it, the total energy will 
be simply the sum of the two volume-energies and will not depend on the surface at 
all; as a matter of necessity, however, there is a gradual transition from one fluid to 
the other across a thin surface-layer, and the energy per unit volume in this layer 
alters with the change of properties ; so that to the energy estimated as if the 
transition were sharp, there is to be made a correction which takes the form of a 
surface distribution of energy; and this latter term must reveal itself, according to 
Gauss’ well-known reasoning, in the phenomena of capillary surface-tension. The 
relation between the volume-densities of the energy in the two fluids is determmed 
by the proper balance of intrinsic hydrostatic pressure across the interface. Now if 
we adhere at all to the principle that the play of energy, as distributed throughout 
the masses in the field, is the proper basis for the interpretation of physical pheno¬ 
mena, the extraneous surface-forces of Kirchhoff must also be accounted for in some 
such way as the above; they must arise out of the influence of a layer of gradual 
transition between the media. But superior limits have been obtained to the thick¬ 
ness of such a layer in various ways, by actual measurement; such limits are found in 
the thickness of the thinnest possible soap-film, as measured by Reinold and Rucker, 
or in the thickness of the film of silvering which in Quincke’s experiments just 
suffices to extinguish the influence of the glass, on which it is deposited, on the 
jahenomena of surface-tension. The former limit is about one-fortieth of the wave¬ 
length of green light, the latter limit is well within one-tenth of the same wave¬ 
length."'* The quantity with v/hich to compare the surface-energy due to this 
transition is the energy contained in a wave-length of the light whose reflexion is 
under consideration. It is plain that such an amount of surface-energy as is here 
possible will not suffice to totally transform the circumstances of the reflexion, and 
therefore will not account for Kirchhoff’s extraneous forces. Furthermore, a layer 
of transition, of thickness of the same order of magnitude as the wave-length, would 
introduce a change of phase into the reflexion, such as we know, from Lord Rayleigh’s 
and Drude’s experiments on reflexion from absolutely clean surfaces of transparent 
media, does not exist, and such as even Rirchhoff’s own theory does not allow for. 
It is for these reasons that it is here considered that Neumann’s theory of light is, on 
* Reinold and Rucker, ‘Roy. Soc. Proc.’ 1877; ‘Phil. Trans.,’ 1883. Quincke, ‘Pogg. Ann.,’ 
vol. 137, 1869. Of. Lord Kelvin, “ Popular Lectures and Addresses,” vol. 1, p. 8. 
