158 



the same laws, ox*, if not the same, what may seem to be more 

 exact laws, from certain principles* of his own, helped out, 

 if need be, by proper relations among his constants ; espe- 

 cially if, to allow greater scope for such relations, the number 

 of constants be increased by the hypothesis of two coexist- 



* 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. Sup- 

 posing the refracting angle of the prism to be very little less than the angle of to- 

 tal reflexion for the substance of which it is composed, a ray incident perpendicu- 

 larly 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 prodigieiise multiplication de la lumi&re"^ 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 sup- 

 position 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 esta- 

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

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

 Inmidre ; ce qui est un nouvel argument contre 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. 



