270 



one mecliuni into the other, takes place ahruplly at their 

 conimou surface ; and he had thought it not unlikely that the 

 supposition ofagradual change of elasticity, taking place with- 

 in a vert/ small space at one or both sides of the surface of a 

 metal, might afford an explanation of the peculiar phenomena 

 of metallic reflexion. Such a supposition would be mathe- 

 matically equivalent to the hypothesis that an immense num- 

 ber of films, of which the refractive powers vary between 

 given limits according to some law, compose a very thin 

 stratum at the surface of a polished metal ; and it would 

 be in accordance with the inference drawn by Professor 

 Mac CuUagh from certain formulas (Transactions R. I. A., 

 vol. xviii. p. 70) that the law of equivalent vibrations is not 

 observed in metals; an inference which, indeed, originally 

 suggested to him the hypothesis in question. He had not 

 yet compared the hypothesis with his formulas, but it was 

 easy to see that it would explain the non-existence of an 

 angle of complete polarization for metals, as well as the ge- 

 neral fact of elliptical polarization ; and perhaps the metallic 

 briUiancy, difference of colour, &c. might be occasioned by 

 the great number of reflexions in the variable stratum at 

 the surface, and the endless variety of interferences pro- 

 duced by them. 



The above was only one of the conjectures which had 

 been formerly made by Professor Mac Cullagh in relation to 

 this subject, and it was mentioned on this occasion chiefly on 

 account of its analogy with the view taken by Professor Lloyd. 

 Another and very different hypothesis, which was the first 

 that had occurred to him, as being immediately suggested by 

 the imaginary form which he had assumed for the velocity 

 of propagation in a metal, will be found stated in the Comptes 

 Rendus of the French Academy, torn, viii., p. 962, in a letter 

 to M. Arago, dated May 11, 1839. It consisted in supposing 

 the amplitude of the vibration within the metal to be propor- 

 tional to acertain exponential of which the value is there given, 

 accompanied with the remark that this expression for the vibra- 



