¹The MS. of this paper was finally prepared for press by Dr. Sorby during his last illness. It contains the details and complete account of his work, of which preliminary accounts were published in the first two volumes of the Mineralogical Magazine under the following titles:— ‘On a simple method of determining the index of refraction of small portions of transparent minerals.’ 1877, vol. i, pp. 97–98. Presidential address. [Determination of refractive indices in mineral plates, etc.] 1877, vol. i, pp. 193–208, with plate VII. ‘On the determination of minerals in thin sections of rocks by means of their indices of refraction.’ 1878, vol. ii, pp. 1–4. ‘Further improvements in studying the optical characters of minerals.’ 1878, vol. ii, pp. 103–105. The method he describes for determining refractive indices is identical in principle, though worked out in far greater detail, with that given by the Due de Chaulnes in 1767 for singly-refracting substances; but, as may be gathered from a remark in the last of the papers quoted above, the method was devised quite independently by Dr. Sorby. The paper is now published with the aid of a grant from the Government Publication Grant administered by the Royal Society. An obituary notice, with portrait, of Dr. Sorby appeared in the last number of this magazine (vol. xv, p. 180).