70 Mr. Mac Cullagh on the Laws of 



upon it ; and therefore, in the beginning of this paper, a particular account has 

 been given of the manner in which it was originally suggested. If we wished to 

 give a reason for this hypothesis, we might say, that the motion of a particle of 

 ether, at the common surface of two media, ought to be the same, to whichsoever 

 medium the particle is conceived to belong ; and as the incident and reflected vibra- 

 tions are superposed in one medium, and the refracted vibrations in the other, we 

 might infer that the resultant of the former vibrations ought to be the same, both 

 in length and direction, as the resultant of the latter. At first sight this reason- 

 ing appears sufficiently plausible ; but it will not bear a close examination. For 

 as the argument is general, it would prove that the principle of the equivalence 

 of vibrations is true for metals,* as well as for crystals, which it certainly is not. 



* A few days after this paper was read, I found reason to persuade myself, that, in metals, the 

 vibrations parallel to the surface are equivalent, but not those perpendicular to it ; and that, in metals 

 as well as in crystals, the vis viva is preserved. This persuasion was founded on a system of formulse 

 which I had invented for expressing the laws of metallic reflexion and refraction ; and which seem 

 to represent very satisfactorily the experiments of Brewster, Phil. Trans. 1830. As metalhc and 

 crystalline reflexion are kindred subjects, and will one day be brought under the same theory, how- 

 ever distinct they may now appear, it will not be out of place to insert the formula; for metals here. 

 These formulae are not proposed as true, but as likely to be true ; and they will be found to express, 

 at least with general correctness, all the circumstances that have hitherto been regarded as anoma- 

 lies in the action of metals upon light. 



I suppose that, for every metal, there are two constants, m and ^, of which the first is a number 

 greater than unity, and the second is an angle included between and 90°. The number m I call 

 the modultis, and the angle y^ the characteristic of the metal. Both m and ^ vary with the colour 



of the light, and the ratio is probably the index of refraction. From Brewster's experiments 



it appears that M diminishes from the red to the violet; and therefore I should suppose that cosy 

 diminishes in a greater ratio, in order that the index of refraction may increase as in transparent 

 substances. 



Put (, for the angle of incidence, and t, for the angle of refraction, so that 



sint, M 



sin ij cos X 



and let ix be a variable determined by the condition 



(xii.) 



__ cos t| 



These two relations combined will give 



i, = l + (l-^-i^^)tan',, (xiv.) 



