Mechanical Theory of Circular and Elliptic Polarization. 411 
laws, from certain principles* of his own, helped out, if need be, by 
proper relations among his constants ; especially if, to allow greater 
scope for such relations, the number of constants be increased by 
the hypothesis of two coexisting systems of molecules, an hypothesis 
which M. Cauchy has already considered with his usually generality, 
but without making any precise ‘application of it. (Hzercices d’Ana- 
lyse et de Physique Mathématique, tom. i. p. 33.) 
Perhaps one cause why M. Cauchy’s views on the subject of double 
refraction have met with such general acceptance, may be found 
in the fact, that a theory setting out from the same principles, and 
leading, by the same relations among constants, to formulas iden- 
tical in every respect with his earlier results, was advanced inde- 
pendently, and nearly at the same time, by M. Neumann of Kénigs- 
berg (Poggendorff’s Annals, vol. xxv. p. 418). A coincidence so 
remarkable would be looked upon, not unreasonably, as a strong 
* In applying these principles to the question of reflexion and refraction 
at the surface of an ordinary medium (Comptes Rendus, tom. ii. p. 348), 
M. Cauchy has arrived at the singular conclusion, that light may be greatly 
increased by refraction through a prism, at the same time that it is almost 
totally reflected within it. Supposing the refracting angle of the prism to 
be very little less than the angle of total reflexion for the substance of 
which it is composed, a ray incident perpendicularly on one of the faces 
will emerge making a very small angle with the other face; and as the re- 
flexion at the latter face is nearly total, it is self-evident that the intensity 
of the emergent light, as compared with that of the incident, must be very 
small. M. Cauchy, however, finds, by an elaborate analysis, that a prodi- 
gious multiplication of light [“ wne prodigieuse multiplication de la lumiére”’] 
takes place, the emergent ray being nearly six times more intense than the 
incident when the prism is made of glass, and nearly nine times when the 
prism is of diamond. This result was,in a general way, actually verified 
experimentally by himself and another person ; so easy it is, in some cases, 
to see anything that we expect to see. Had the result been true, it would 
have been a very brilliant discovery indeed ; for then we should have been 
able, by a simple series of refractions, to convert the feeblest light into one 
of any intensity we pleased; but the very absurdity of such a supposition 
should have taught M. Cauchy to distrust both his theory and his experi- 
ment. Far from doing so, however, he considers the fact to be perfectly 
established, and to afford a new argument against the system of emission. 
“Ici,” says he, “ un rayon, réfléchi en totalité, est de plus transmis avec ac- 
croissement de lumiére ; ce qui est un nouvel argument contre le systéme 
démission.” The system of emission has at least this advantage, that by 
no possible error could such a conclusion be deduced from it. For if all 
the particles of light be reflected, certainly none of them can be refracted. 
The truth is, that M. Cauchy mistook the measure of intensity in the 
hypothesis of undulations, supposing it to be proportional simply to the 
square of the amplitude of vibration ; whereas it is really measured by the 
vis viva, or by that square multiplied by the quantity of ather put in motion, 
a quantity which in the present case is evanescent, since the corresponding 
volumes of zther, moved by the ray within in the prism and by the emergent 
ray, are to each other as the sine of twice the angle of the prism to the 
sine of twice the very small angle which the emergent ray makes with the 
second face of the prism. The intensity of the emergent light is therefore 
very small, as it ought to be, though the amplitude of its vibrations is con- 
siderable, 
2E2 
