328 Mr KELLAND, ON THE TRANSMISSION OF LIGHT 



displacement, and not at all on the position of the front of the wave. 

 If, indeed, it could restrict the hypothesis by adding that the force 

 put in play by a displacement in any direction in the front of a 

 wave is independent of the position of that front, or remains constant 

 whilst that front is made to revolve about the line of displacement, 

 it would coincide with what M. Fresnel had established above. 



It will be seen then that I object not to the supposition that 

 the force put in play is independent of the position of the plane of 

 the wave, but to the converse, that if a displacement be resolved 

 parallel to x, y, %, the forces put in play will be the same as if the 

 wave was in each individual case perpendicular to yss, xz, xy re- 

 spectively. 



It is clear that such an hypothesis takes for granted, what I 

 should not think Fresnel could mean, that the force on each particle 

 in any direction is of the same form as if that particle alone were in 

 motion in that direction. 



It will not suffice to urge in answer to these objections, that 

 however they might apply to motion in general, in the particular 

 instance of vibrations the nature of the arrangement is such as to 

 render them invalid. On no hypothesis, that I can conceive, would 

 the force due to a displacement in the direction of transmission be 

 the same as that in a perpendicular direction, and when the law of 

 force is that of the inverse square of the distance, far from being 

 identical, they are of a directly opposite character; and the effects 

 which they produce, instead of being analogous, are totally different 

 even in form ; the one being an oscillation, the other a progression. 

 But this is not the only objection which I adduce. M. Fresnel de- 

 termines by his construction the two directions in which a vibration 

 taking place the law of transmission is satisfied. He finds the force 

 in eacli of these directions, by supposing the whole force put in play 

 to be resolved into two; one in the direction itself, and the other, 

 perpendicular to the front of the wave. The former of these he 

 assumes as the force which produces vibration, the latter he omits 

 altogether. 



