of Crystalline Reflexion and Refraction, communicated to 

 the Academy in December, 1839 (Proceeding's, vol. i. p. 374). 

 This was followed soon after by a general Theory of Total 

 Reflexion (Proceedings, vol. ii. p. 96), founded on the same 

 principles. The latter theory, forming a new department 

 of physical optics, and involving the solution of questions 

 not previously attempted, was analytically complete when it 

 was communicated to the Academy in May, 1841 ; but its 

 geometrical development has since required my attention 

 from time to time, and has not yet been brought to that de- 

 gree of simplicity of which it appears to be susceptible 

 (see Proceedings, vol. ii. p. 174). Indeed I have found that, 

 in this instance, the geometrical laws of the phenomena are 

 by no means obvious interpretations of the equations re- 

 sulting from the analytical solution of the problem ; and in 

 endeavouring to verify such supposed laws I have often been 

 led to algebraical calculations of so complicated a nature that 

 it has been impracticable to bring them to any conclusion, 

 and I have been obliged, from mere weariness, to abandon 

 them altogether. On returning, however, to the investigation, 

 after perhaps a long interval of time, I have usually per- 

 ceived some mode of eluding the calculations, or of directly 

 deducing the geometrical law ; and when the theory comes 

 to be published in its final form, no trace of these difficulties 

 will probably appear. 



From the causes above-mentioned, combined with fre- 

 quent absence from Dubhn, the researches which I had 

 entered upon, respecting the action of metals upon light, 

 have been hitherto interrupted ; and as it may still be some 

 time before they are resumed, I venture, in the meanwhile, 

 to submit to the Academy the results already spoken of, 

 which were obtained on the first trial of the instrument, and 

 which afford the best data th can yet be had for compari- 

 son with theory. 



The results, it must be confessed, are those of very 

 2k2 



