40G 



PROFESSOR KELLAND ON FKESNEL'S FORMULjE FOR THE 



Now, before we proceed to- apply analogous reasoning to the case of M'aves 

 whose vibrations take place in the plane of x y, it must be remarked, that, when 

 the motion arrives at the siu-face, a sudden change takes place. But this sudden 

 change, which occurs necessarily at the first instant the light falls on the surface, 

 will in all the future part of the motion materially affect, not only the vibrations 

 beyond the surface, but those also above it ; and the change which takes place is 

 nothing else than that of twisting a vibration which previously had been perpen- 

 dicular to the direction of motion, so as to cause it no longer to be so. Now, I 

 have shewn in the Transactions of the Cambridge Philosophical Society, vol. vi. 

 p. 180, that a motion perpendicular to the front of the wave cannot be transmit- 

 ted as a vibration along with the wave. The assumption that it can be so trans- 

 mitted gives rise to the result that the velocity is an impossible quantity. In 

 other words, some part of the expression which we assumed to be a function of 

 sines and cosines depends on possible, as sines and cosines do on unpossible, ex- 

 ponentials. 



To apply this conclusion to the case in question, we must observe, that, if 

 we reckon along the axis of y, whatever be the motion in question, its value must 

 be a reciprocating one ; and fui-ther, it is necessary that, whatever value it has for 

 one value of y at a particular time, the same will it have for another value of y 

 at some other time : hence the function which expresses the motion must be a 

 ch-cular function of y and t, but a possible exponential function of x. The motion 

 thus introduced will consequently be a vibration transmitted along the axis of y, 

 and consequently the direction of motion is parallel to the axis of x. 



We proceed then to deduce the equations of motion of a particle situated near 

 the common surface of the media, on the hypothesis that the light consists of vi- 

 brations in the plane of incidence. As a preliminary step, partly for the purpose 

 of exhibiting the correctness of the method employed, I have deduced the equa- 

 tions of motion of a particle situated at such a distance from the surface that the 

 vibrations transmitted along the axis of x do not affect the forces. Afterwards I 

 have deduced the general equations corresponding to a particle situated at the 

 common surface. 



