XVI. ON A DYNAMICAL THEORY OF CRYSTALLINE 

 REFLEXION AND REFRACTION. 



[Proceedings of the Royal Irish Academy, VOL. n. p. 96. Bead May 24, 1841.] 



PROFESSOR MAC CULLAGH read a supplement to his Paper 

 " On a Dynamical Theory of Crystalline Reflexion and Refrac- 

 tion." 



In his former Paper on that subject,* the author had given the 

 general principles for solving all questions relative to the propa- 

 gation of light in a given medium, or its reflexion and refrac- 

 tion at the separating surface of two media ; but he had applied 

 them only to the common case of waves, which suffer no dimi- 

 nution of intensity in their progress, and in which the vibration 

 may be represented by the sine or cosine of an arc multiplied 

 by a constant quantity. Some months after that Paper was read, 

 it occurred to bun that he might obtain new and important 

 results by substituting in his differential equations of motion a 

 more general expression for the integral, that is (as usual in 

 such problems), by making the displacements proportional to 

 the sine or cosine of an arc, multiplied by a negative exponen- 

 tial, of which the exponent should be a linear function of the 

 co-ordinates. Such vibrations would become very rapidly insen- 

 sible, and would, therefore, be fitted to represent the disturbance 

 which, in the case of total reflexion, takes place immediately 

 behind the reflecting surface ; and, the laws of this disturbance 

 being thus discovered, the laws of polarization in the totally 



* See Proceedings, 9th December, 1839 (supra, p. 146). 



