I].—An Essay towards a dynamical Theory of crystalline Reflexion and Re- 
Jraction. By James Mac Cuttacn, Fellow of Trinity College, Dublin. 
Read December 9th, 1839. 
SECT. I.—INTRODUCTORY OBSERVATIONS.—EQUATION OF MOTION. 
NEARLY three years ago I communicated to this Academy* the laws by which 
the vibrations of light appear to be governed in their reflexion and refraction at 
the surfaces of crystals. These laws—remarkable for their simplicity and ele- 
gance, as well as for their agreement with exact experiments—I obtained from a 
system of hypotheses which were opposed, in some respects, to notions previously 
received, and were not bound together by any known principles of mechanics, 
the only evidence of their truth being the truth of the results to which they led. 
On that occasion, however, I observed that the hypotheses were not independent 
of each other; and soon afterwards I proved that the laws of reflexion at the 
surface of a crystal are connected, in a very singular way, with the laws of double 
refraction, or of propagation in its interior ; from which I was led to infer that 
“all these laws and hypotheses have a common source in other and more intimate 
laws which remain to be discovered ;” and that “the next step in physical optics 
would probably lead to those higher and more elementary principles by which 
the laws of reflexion and the laws of propagation are linked together as parts of 
the same system.” This step has since been made, and these anticipations have 
been realised. In the present paper I propose to supply the link between the 
* Tn a paper “on the Laws of crystalline Reflexion and Refraction.” —Transactions of the Royal 
Trish Academy, vol. xviii. p. 31. 
} Ibid. p. 53, note. The note here referred to was added some time after the paper itself 
was read. 
VOL. XXI. D s 
