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As o = fi, we see that when there is no transmitted wave the intensity of the reflected wave is precisely equal to that of the incident one. This is what might bo expected: it is, however, noticed here because a most illustrious analyst has obtained a different result. (Poisson, MdmoireB de VAcademie des Sciences, Tome X.) The result which this celebrated mathematician arrives at is, That at the moment the transmitted wave ceases to exist, the intensity of the reflected becomes precisely equal to that of the incident wave. On increasing the angle of incidence this intensity again diminishes, until it vanish at a certain angle. On still farther increasing this angle the intensity continues to increase, and again becomes equal to that of the incident wave, when the angle of incidence becomes a right angle.

It may not be altogether uninteresting to examine the nature of the disturbance excited in that medium which has ceased to transmit a wave in the regular way. For this purpose, we will resume the expression,

«f>, m Be-"'' sin -yfr = Be'"'* sin (Jy + ct) •„ .{

or if we substitute for B, its value given by the last of the equations (10); and for a', its value from (II); this expression, in the case of oidinary elastic fluids where 7^ = 7", A,, will reduce to

ft = 2a/*s cos e. e~ * v ^ sin(iy + e<), X being the length of the incident wave measured perpendicular to its own front, and 6 the angle cf incidence. We thus see with what rapidity in the case of light, the disturbance diminishes as the depth x below the surface of separation of the two media increases; and also that the rate of diminution becomes less as 0 approaches the critical angle, and entirely ceases when 6 is exactly equal to this angle, and the transmission of a wave in the ordinary way becomes possible.

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AT THE COMMON SURFACE OF TWO.' NON-'"
CRYSTALLIZED MEDiA.

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From the Tmnsactioni of the Cambridge Philosophical Society, 1838.
[Read December 11, 1837.]

ON THE LAWS OF THE REFLEXION AND REFRACTION
OF LIGHT AT THE COMMON SURFACE OF TWO
NON-CRYSTALLIZED MEDIA.

M. Caucht seems to have been the first who saw fully the utility of applying to the Theory of Light those formula? which represent the motions of a system of molecules acting on each other by mutually attractive and repulsive forces; supposing 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 phenomena, 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 fjafer method to take some general physical principle as the br.sis of our reasoning, rather than assume certain modes of action, which, after all, may be widely different from the mechanism employed by nature; more especially if this principle indude in itself, as a particular case, those before used by M. Cauc ly 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 *i*f way the elements of any material system may act upon each 1.

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 immediately apply the general method given in the M&anique Analytique, and which appears to be more especially applicable to problems that relate to the motions of systems composed of an immense number of particles mutually acting upon each other. One of the advantages of this method, of great importance, is, that we are necessarily led by the mere process of the calculation, and with little care on our part, to all the equations and conditions which are requisite and sufficient for the complete solution of any problem to which it may be applied.

The present communication is confined almost entirely to the consideration of non-crystallized media; for which it is proved, that the function due to the molecular actions, in its most general form, contains only two arbitrary coefficients, A and B; the values of which depend of course on the unknown internal constitution of the medium under consideration, and it would be easy to shew, for the most general case, that any arbitrary disturbance, excited in a very small portion of the medium, would in general give rise to two spherical waves, one propagated entirely by normal, the other entirely by transverse, vibrations, and such that if the velocity of transmission of the former wave be represented by >JA, that of the latter would be represented by y'/>'. But in the transmission of light through a prism, though the wave which is propagated by normal vibrations were incapable itself of affecting the eye, yet it would be capable of giving rise to a;i ordinary wave of light propagated by

A transverse vibrations, except in the extreme cases where -5 = 0,

or B ~ a vei7 *ar£e 1uant^*y i which, for the sake of simplicity,

may be regarded as infinite; and it is not difficult to prove that the equilibrium of our medium would be unstable unless

A 4

25 > J • We are therefore compelled to adopt the latter value of

A

Ts , and thus to admit that in the luminiferous ether, the velocity

of transmission of waves propagated by normal vibrations is very great compared with that of ordinary light,

The principal results obtained in this paper relate to the tensity of the wave reflected at the common surface of two

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