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regular series of gradations,

A*», /*,» A* /*»;

T being the common thickness of each of these successive media.

Then it is clear we should have to replace the last system by

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But it is evident from the form of the equations on the right side of system (33), that the total effect, due to the last terms of their second members will be far less when n is great, than that due to the corresponding term in the.-second equation of system (29)*. If, therefore, we reject these second terms, and conceive the common interval T so small that the result due to the first terms may not differ very sensibly from that which would be produced by a single refraction, we should have to replace the system (29) by (30), and the intensity of the reflected wave would then agree with the law assigned by Fresnel. In virtue of this law, however highly refracting any substance may be, homogeneous light will always be completely polarized at a certain angle of incidence; and Sir David Brewster states

* Id fact, iu the system (33) each of the last terms -will, in consequence of the factors - jug*), &o. be quantities of the order 4; compared with the last term of (19/), and as their number is only n, their joint effect will be a quantity of the order - compared with that of the term just mentioned.

that this is the caae with diamond at the proper angle. Bat the phenomena observed by Professor Airy appears to him eniirely inconsistent with this result (Vide Canib. Phil. Trans., Vol. IV. p. 423); what immediately precedes seems to render it probable that considerable differences in this respect may be due to slight changes in the reflecting surface.

ON THE

PKOPAGATION OF LIGHT

IN CRYSTALLIZED MEDIA*

* From the Trataaetiom of Ae Cambridge Phtloiopkical Society, 1839. [Bead May 10, 1839.]

MEDIA.

In a former paper * I endeavoured to determine in what way a plane wave would be modified when transmitted from one non-crystallized medium to another; founding the investigation on this principle: In whatever manner the elements of any material system may act upon each other, if all the internal forces he multiplied by the elements of their respective directions, the total sums for any assigned portion of the mass will always be the exact differential of some function. This principle requires a slight limitation, and when the necessary limitation is introduced, appears to possess very great generality. I shall here endeavour to apply the same principle to crystallized bodies, and shall likewise introduce the consideration of the effects of extraneous pressures, which had been omitted in the former communication. Our problem thus becomes very complicated, as the function due to the internal forces, even when there are no extraneous pressures, contains twenty-one coefficients. But with these pressures we are obliged to introduce six additional coefficients; so that without some limitation, it appears quite hopeless thence to deduce any consequences which could have the least chance of a physical application. The absolute necessity of introducing some arbitrary restrictions, and the desire that their number should be as small as possible, induced me to examine how far our function would be limited by confining ourselves to the consideration of those media only in which the directions of th« transverse vibrations shall always be accurately in the front of the wave. This fundamental principle of Fresnel's Theory gives fourteen relations between the twentyone constants originally entering into our function; and it seems worthy of remark, that when there are no extraneous pressures, the directions of polarization and the wave-velocities given by our theory, when thus limited, are identical with those assigned by Fresnel's general construction for biaxal crystals; provided we suppose the actual direction of disturbance in the particles

* Supra, p. 343.

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