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Prof. G-. G. Stokes on the Foci of Lines [June 21^ 



li mi nary notice, and defer to a subsequent occasion a detailed account of 

 the whole subject, as known from observation. In that paper 1 purpose 

 to show how the indices can be accurately determined in minerals of 

 different structure, to point out how closely observation agrees with 

 theory, and to describe a number of anomalies met with in particular 

 specimens. 



X. " On the Foci of Lines seen through a Crystalline Plate. M 

 By & Gr. Stokes, M.A., Sec. E.S. Received June 21, 1877. 



At the Soiree o: the Royal Society on the 25th of April Mr. Sorby 

 showed me the method he had recently devised for discriminating between 

 minerals by focusing a microscope over a delicate image of cross lines, 

 which image was viewed, first directly, and then through a crystalline 

 plate, having previously been adjusted to be at the distance of the lower 

 surface of the plate. "With glass and singly refracting substances the 

 alteration of the focus produced by the interposition of the plate affords 

 a measure of its refractive index. But with a plate cut from a doubly 

 refracting crystal, not only is there more than one focal distance, but for 

 one at least of the pencils there is (except in special cases) no true 

 focus, but the foci of the two systems of cross lines are found at two dif- 

 ferent depths, or else there is no sharply denned image at all. according 

 to the orientation of the hues relatively ro lines fixed in the crystalline 

 plate. ACoreover the result obtained on applying the formula which, for 

 a singly refracting plate, gives the refractive index from the measured 

 displacement of the focus is often widely d iff erent from what is known 

 to be the refractive index of the crystal., for the pencil under examina- 

 tion, in a direction perpendicular to the plate. 



The phenomena will be described in detail by Mr. Sorby in his own 

 paper. My object is to show how they flow from the known laws of 

 double refraction, as consequences of which they will necessarily come 

 under review *. 



* [It seemed pretty certain that some of the phenomena must hare been noticed 

 before, though I am not aware that they have been described, or their theory worked 

 out in any detail. I find that Prof. Clifton has been in the habit of using an instru- 

 ment somewhat similar to l£r. Sorby 's. which was procured several years ago for the 

 Museum of the University of Oxford, and that he was familiar with such things as the 

 low apparent index of calcite for the extraordinary pencil nearly in the direction of 

 the axis, and the astigmatism in general of a pencil refracted across a plate otherwise 

 than by ordinary refraction ; and. further, that he utilized these phenomena for the 

 instruction of students as to the general form of the wave-surface. 2s o one, however, 

 so far as I know, before ~Mr. Sorby. had applied the phenomena to the practical dis- 

 crimination of minerals, or had worked them out quantitatively and in detail ; and it 

 is my desire to complete the subject, by supplying the mathematical theory, that must 

 be my excuse for offering to the Society an investigation which in itself consists merely 

 in easy deductions from well-known principles. 



It is perhaps hardly necessary to refer to a paper by Dr. Quincke in Poggendorff s 



