212 Notes on some Points in the Theory of Light. 



by proper relations among his constant^ ; especially if, to allow 

 greater scope for such relations, the number of constants be in- 

 creased by the hypothesis of two coexisting systems of mole- 

 cules, an hypothesis which M. Cauchy has already considered 

 with his usual generality, but without making any precise ap- 

 plication of it.* 



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 



total reflexion for the substance of which it is composed, a ray incident perpendi- 

 cularly on one of the faces will emerge, making a very small angle with the other 

 face ; and as the reflexion 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 prodigious 

 multiplication of light [" une prodigieuse multiplication de a Zumiere"~\ 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 ano- 

 ther 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 ex- 

 periment. Far from doing so, however, he considers the fact to be perfectly esta- 

 blished, and to afford a new argument against the system of emission. " Ici," says 

 he, " un rayon, re"flechi en totalite, est de plus transmis avec accroissement de 

 lumiere; ce qui est un nouvel argument centre le systeme d'emission." The sys- 

 tem 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, cer- 

 tainly none of them can be refracted. 



The truth is, that M. Cauchy mistook the measure of intensity in the hypothe- 

 sis 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 ether put in motion, a quantity which in the 

 present case is evanescent, since the corresponding volumes of ether, 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 emer- 

 gent light is therefore very small, as it ought to be, though the amplitude of its 

 vibrations is considerable. 



* Exercices d 1 Analyse et de Physique Mathematiqiie, torn. i. p. 33, 



