CONFIRMATION OP THE UXDULATORY THEORY. 127 



particles of the etlier. The length of one of those undulations \vlv oh 

 produce light, is a very small quantity, its mean value being l-50,000th 

 of an inch ; but in the previous investigations of the consequences of 

 the theory, it had been assumed that the distance from each other, of 

 the particles of the ether, which, by their attractions or repulsions, 

 caused the undulations to be propagated, is indefinitely less than this 

 small quantity ; so that its amount might be neglected in the cases 

 in which the length of the undulation was one of the quantities which 

 determined the result. But this assumption was made arbitrarily, as a 

 step of simplification, and because it was imagined that, in this way, a 

 nearer approach was made to the case of a continuous fluid ether, 

 which the supposition of distinct particles imperfectly represented. It 

 was still free for mathematicians to proceed upon the opposite assump- 

 tion, of particles of which the distances were finite, either as a mathe- 

 matical basis 'of calculation, or as a physical hypothesis; and it 

 remained to be seen if, when this was done, the velocity of light would 

 still be the same for different lengths of undulation, that is, for different 

 colors. M. Cauchy, calculating, upon the most general principles, the 

 motion of such a collection of particles as would form an elastic medium, 

 obtained results which included the new extension of the previous 

 hypothesis. Professor Powell, of Oxford, applied himself to reduce to 

 calculation, and to compare with experiment, the result of these 

 researches. And it appeared that, on M. Cauchy's principles, a varia- 

 tion in the velocity of light is produced by a variation in the length of 

 the wave, provided that the interval between the molecules of the 

 ether bears a sensible ratio to the length of an undulation. 19 Professor 

 Powell obtained also, from the general expressions, a formula express- 

 ing the relation between the refractive index of a ray, and the length 

 of a wave, or the color of light. 20 It then became his task to ascer- 

 tain whether this relation obtained experimentally ; and he found a 

 very close agreement between the numbers which resulted from the 

 formula and those observed by Fraunhofer, for ten different kinds of 

 media, namely, certain glasses and fluids. 21 To these he afterwards 

 added ten other cases of crystals observed by M. Piudberg. 22 Mr. 

 Kelland, of Cambridge, also calculated, in a manner somewhat different, 

 the results of the same hypothesis of finite intervals ;" and, obtaining 



19 Phil. Mag. vol. vi. p. 266. 20 Ib. vol. vii. 1835, p. 266. 



11 Phil. Trans. 1835, p. 249. M Ib. 1SS6, p. 17. 



M Camb. Trans, vol. vi. p. 153. 



