271 



tion, if introduced into the differential equations (at that lime 

 unknown) which subsist at the confines of two media, would 

 probably explain the peculiar phenomena of metallic re- 

 flexion, such as change of phase, &c. Very soon after that 

 date the equations were discovered which hold good at the 

 common surface of two transparent media (see Proceedings 

 R. I. A. vol. i., p. 378) ; and it is certainly not a little singular that 

 these equations, with the help of the aforesaid expression for 

 the vibration, not only explain the change of phase, but lead 

 to the precise formulas which had been previously giveu for 

 the case of metallic reflexion (Transactions R. I. A. vol. xviii. 

 p. 71). The application of the equations, however, to this 

 case, cannot be regarded as legitimate without further proof; 

 and the hypothesis is attended by another difficulty, the na- 

 ture of which may be seen in the letter alluded to. 



On the whole,ProfessorMacCullagh did not consider him- 

 self warranted, as yet, in choosing between his two hypo- 

 theses, nor even in concluding that one or other of them must 

 be the right one. Before constructing any refined theory, he 

 thought it necessary that the formulas to which he had re- 

 ferred, and which, if they are correct, must be the foundation 

 of the theory, should be tested by experiments more accu- 

 rate than any that had yet been made, and this was a task to 

 which he hoped he should soon have leisure to devote him- 

 self. 



Professor Lloyd explained, that the hypothesis which he 

 had suggested had not been offered by him as an exact 

 physical representation of the optical constitution of metals ; 

 but rather as one which lent itself, with tolerable facility, to 

 mathematical expression, and the results of which might 

 possibly, by a suitable determination of the constants of the 

 formulas, be found to coincide with the phenomena, and 

 therefore with the results of a more rigid theory. 



Resolved, — That, in future, when the office of Secretary 

 of the Academy is vacant, the vacancy shall be filled up by 

 express election. 



