where L = 2,7rabc - 5 - r - r > ............... (26)
2 2 ?
with similar expressions for M and .AT.
If the ellipsoid be of revolution the case is simplified*. For example, if it be of the elongated or ovary form with eccentricity e,
e2); .................................... (27)
(29)
For the sphere (e = 0) L = M = N=* ............ . ................ (30)
o
In the case of a very elongated ovoid, L and M approximate to the value Z while N approximates to the form
vanishing when e = 1. It appears that, when K' ' JK is finite, mere elongation does not suffice to render A and B negligible in comparison with G. The limiting value of G : A is in fact ^ (I+K'/K). If, however, as for a perfectly conducting body, K' = oo , then C becomes paramount, and the simplified values already given for this case acquire validity f.
Another question which naturally presents itself is whether a want of equality among the coefficients A, B, C interferes with the relation between attenuation and refractive index, explained in my paper of 1899."{:. The answer appears to be in the affirmative, since the attenuation depends upon Az + B2 + Oz, while the refractive index depends upon A + B + G, so that no simple relation obtains in general. But it may well be that in cases of interest the disturbance thus arising is not great.
The problem of an ellipsoidal particle of uniform dielectric quality can be no more than illustrative of what happens in the case of a molecule ; but we may anticipate that the general form with suitable values of A, B, G still applies, except it may be under special circumstances where resonance occurs and where the effective values of the coefficients may vary greatly with the wave-length of the light.
* See the paper of 1897.
t But the particle must still be small relatively to the wave-length within the medium of which it is composed.
J An equivalent formula was given by Lorenz in 1890, (Euvres Scientifiques, t. i. p. 496, Copenhagen, 1898. See also Schuster's Theory of Optics, 2nd ed. p. 326 (1909). f 25")