744 
MR. J. LARMOR ON A DYNAMICAL THEORY OF 
Young-Sellmpaer type, involving perhaps change of effective inertia, vhich will 
take a more complete account of the sympathetic interaction which occurs between 
the electric vibrations of the molecules and the vil^rations of the medium, when their 
periods are very nearly alike. 
The sum of the orders of the differential coefficients in any term of the energy 
must usually be even; a term in which it is odd would introduce unilateral quality 
into the medium, typified by such phenomena as rotatory polarization; and it is 
known from the facts and principles of crystalline structure that such terms can be, 
when existent at all, only of a very minute residual kind. 
When we come to discuss the problem of reflexion, the surface-terms derived from 
the variation of the energy-function must be retained, and they should be adjusted so 
as to maintain the continuity of the manifestations of energy in crossing the interface. 
But the dispersional terms will introduce into the variational equation surface- 
integrals involving not only 8^, S 77 , 8^, but also 8 {d^jdx), 8 [d^^jdx^), . ; and we 
cannot even attempt to make all these independent terms continuous across the 
interface. We therefore cannot follow in our analysis the complete circumstances of 
the problem of reflexion. This is not cause for surprise, because the essence of the 
method of continuous analysis consists of averaging the molecular discreteness of the 
medium; and we are now trying to fit this analysis on to conditions at an interface 
Avhere the law of the discreteness changes abruptly or rather very rapidly. 
35. In a problem of this kind the procedure by the method of rays asserts a marked 
superiority. The interfacial layer being assumed for other reasons to be very thin 
compared with a wave-length, the displacement of the medium must be continuous 
across it. And it may be fairly assumed that there is no sensible amount of degrada¬ 
tion of energy in this very thin superficial layer; so that the principle of continuity 
of energy gives the remaining interfacial condition. The result of these hyjDotheses 
will be that, so far, the law of reflexion of each homogeneous portion of the light 
depends on its own index, and not on the amount of the dispersion in its neighbour¬ 
hood. The assumption of continuity of energy is the same thing as recognizing that 
the continuity of the dispersional pait of the stress at the interface is maintained by 
surface forces of molecular character, which absorb no energy, and which need not be 
further specified for the present purpose,—thus forming an instance of a perfectly valid 
application of a surface-traction principle of the same kind as that of Nedmanx and 
Kirchhoff (§ 10). 
This explanation is based on MacCullagh’s theory of reflexion. If, merely for 
further illustration, we take Fresnel’s analysis of that problem, the medium is thereby 
assumed to be labile, and we must employ a stress condition at the interface as well 
as the energy condition. Now it is exactly in the insufficient specification of the 
stress near the surface that the trouble with respect to the dispersional terms came 
in ; thus, if Fresnel’s theory were the tenable one, it would be a matter of some 
difficulty to get from it a clear view of reflexion in its relation to disiJersion. 
