Relative Retardation between Components of a Stream of Light. 79 



" On the Relative Retardation between the Components of a 

 Stream of Light produced by the Passage of the Stream 

 through a Crystalline Plate cut in any Direction with 

 respect to the Faces of the Crystal." By JAMES WALKER, 

 M.A. Communicated by Professor R. B. CLIFTON, F.R.S. 

 Received February 29 Read March 10, 1898. 



The relative retardation between the components of a stream of 

 light produced by the passage throngk a crystalline plate can, as is 

 well known, only be determined in finite terms in a limited number 

 of special cases. Tn general it is necessary to be content with an 

 approximate solution, and those hitherto published have, as far as I 

 have ascertained, never been carried beyond terms of the second 

 order with respect to the sine of the angle of incidence of the light, 

 while they do not readily lend themselves to a further approxima- 

 tion. The following method of dealing with the problem, which, 

 except for the labour of calculation, can easily be extended to 

 terms of any order, may then be of practical use, and, as leading to 

 an interesting relation between the corresponding terms in the 

 development of the roots of a certain biquadratic equation, of some 

 interest. 



1. Let the pla.ne of the paper represent the plane of incidence, OT 

 represent the normal to the front of the incident plane wave, OP and 

 OP' the normals to the fronts of the two corresponding refracted 

 waves ; then if OM, ON, and ON' represent the spaces these waves 

 would traverse in unit time, planes through. M, N, and N' perpendi- 

 cular to OT, OP, and OP' respectively will represent the position* 

 that the fronts of the waves would occupy in unit time after leaving- 

 0, and these planes will, by Huygens' principle, intersect tl e 

 surface of the crystalline plate in one straight line, projected on the 

 plane of the figure in the point C. 



Let OT, OP, and OP' meet the second surface of the plate in the 



VOL. LXIIf. 



