iv Preface. 



In his earlier Optical Memoirs, Prof. Mac Cullagh 

 aimed chiefly at elucidating, by means of geometrical 

 theorems, the physical theory of Fresnel. This is the 

 principal object of the Memoirs I. -IV. in the present 

 volume. In V. occurs the first notice of a problem 

 which subsequently occupied so large a space in Prof. 

 Mac Cullagh' s researches, namely, the investigation 

 of the laws according to which polarized light is re- 

 flected and refracted at the surface of a crystalline 

 medium. This problem is discussed at length in XI. 

 and XIV. In the former of these memoirs he deduces 

 a solution of the problem from certain assumed phy- 

 sical principles. In the second he seeks to establish 

 the theory upon a strictly mechanical basis by means of 

 the general dynamical equation of Lagrange. These, 

 which are the principal memoirs treating of the general 

 question, are supplemented by Memoirs XVI. XIX., 

 in which the same problem is discussed. Two other 

 important questions, namely, metallic reflexion and the 

 double refraction of quartz, which required a peculiar 

 mode of treatment, are considered in Memoirs VI., 

 VII., XV., XVII., XXI. 



Prof. Mac Cullagh' s contributions to pure Geo- 

 metry, excluding, as has been said, all those theorems 

 which have been introduced by the author as auxiliary 

 to his Optical researches, form the second Part of the 

 present volume. The first of these is a Memoir on 



