ON THE LAWS OF THE REFLEXION AND REFRACTION 

 OF LIGHT AT THE COMMON SURFACE OF TWO 

 NON-CRYSTALLIZED MEDIA. 



M. CAUCHY seems to have been the first who saw fully 

 the utility of applying to the Theory of Light those formulae 

 which represent the motions of a system of molecules acting on 

 each other by mutually attractive and repulsive forces ; sup- 

 posing always that in the mutual action of any two particles, the 

 particles may be regarded as points animated by forces directed 

 along the right line which joins them. This last supposition, if 

 applied to those compound particles, at least, which are separable 

 by mechanical division, seems rather restrictive ; as many phe- 

 nomena, those of crystallization for instance, seem to indicate 

 certain polarities in these particles. If, however, this were not 

 the case, we are so perfectly ignorant of the mode of action of 

 the elements of the luminiferous ether on each other, that it 

 would seem a safer method to take some general physical princi- 

 ple as the basis of our reasoning, rather than assume certain 

 modes of action, which, after all, maybe widely different from 

 the mechanism employed by nature ; more especially if this 

 principle include in itself, as a particular case, those before used 

 by M. Cauchy and others, and also lead to a much more simple 

 process of calculation. The principle selected as the basis of the 

 reasoning contained in the following paper is this : In whatever 

 way the elements of any material system may act upon each 

 other, if all the internal forces exerted be multiplied by the 

 elements of their respective directions, the total sum for any 

 assigned portion of the mass will always be the exact differential 

 of some function. But, this function being known, we can imme- 

 diately apply the general method given in the Mtfcanique Analy- 

 tique, and which appears to be more especially applicable to 



