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 connection with the colours, changing with the angle, often met with in the organic world.
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A 1918 study studied this question.