427.
ON THE SCATTERING OF LIGHT BY SPHERICAL SHELLS, AND BY COMPLETE SPHERES OF PERIODIC STRUCTURE, WHEN THE REFRACTIVITY IS SMALL.
[Proceedings of the Royal Society, A, Vol. xciv. pp. 296—300, 1918.]
THE problem of a small sphere of uniform optical quality has been treated in several papers*. In general, the calculations can be carried to an arithmetical conclusion only when the circumference of the sphere does not exceed a few wave-lengths. But when the relative refractivity is small enough, this restriction can be dispensed with, and a general result formulated.
In the present paper some former results are quoted, but the investigation is now by an improved method. It commences with the case of an infinitely thin spherical shell, from which the result for the complete uniform sphere is derived by integration. Afterwards application is made to a complete sphere, of which the structure is symmetrical but periodically variable along the radius, a problem of interest in connexion with the colours, changing with the angle, often met with in the organic world.
The specific inductive capacity of the general medium being unity, that of the sphere of radius R is supposed to be K., where K — 1 is very small. Electric displacements being denoted by /, g, h, the primary wave is taken to be
so that the direction of propagation is along a; (negatively), and that of vibration parallel to z. The electric displacements in the scattered wave, so far as they depend upon the first power of (K — 1), have at a great distance the values
AnJ ' M'£. ' /V»'2
in which P = - (K - 1). eint [[/ e* <*-" efodycfe...................(3)
J J J
* PA& j¥ar/. Vol. XLI. pp. 107, 274,'447 (1871); Vol. xn. p. 81 (1881) ; Vol. XLVII. p. 375 (1889); Roy. Soc. Pros. A, Vol. LXXXIV. p. 25 (1910); Vol. xc. p. 219 (1914); Scientific Papers, Vol. i. pp. 87, 104, 518; Vol. iv. p. 397; Vol. v. p. 547 ; Vol. vi. p. 220. the feed of lubricant, represented by pJJ. Thus, altogether, for the work requiredter system.