M. Cauchy's Vim of the JJndulatory Theory of Light, 26S 



" that the difference of velocity does not depend on the mag- 

 nitude of vibration of each particle, for it is the same whether 

 the light be feeble or intense, that is, whether the vibration be 

 small or great. Nor does it depend on the relative vibration 

 of two contiguous particles, as that varies in the same propor- 

 tion as the last, with a variation of the intensity. The only 

 element which in conjunction with either of these will define 

 the undulation, is the time of vibration : and it is, in fact, the 

 time of vibration which distinguishes the different kinds of 

 light. It would seem natural, therefore, to seek for an expla- 

 nation of the difference of velocities in something which de- 

 pends not on space but on time." 



These observations occur in the appendix to the author's 

 profound paper on the double refraction of quartz in the 

 Cambridge Transactions 1831; and thus far are perfectly 

 general, and explain in the clearest manner the precise point 

 to which our investigation ought to be directed in any attempt 

 to remove the difficulty of the unequal refrangibility. 



These remarks, indeed, are introductory to a particular 

 suggestion for explaining the difficulty, thrown out by the 

 distinguished author. But it is not here intended to discuss 

 this and other conjectural causes which have been proposed, 

 and which may very possibly conspire to account for the re- 

 sult 



The essential point aimed at in any legitimate inquiry of 

 this nature is to show some relation between the length of an 

 undulation and the velocity of its propagation; or in other 

 words, that in transparent media the velocity of propaga- 

 tion of the waves is different for the different primary rays, 

 that is, for rays in which the lengths of the undulations are 

 different. 



But, as we have seen, in the ordinary view of the theory 

 of waves the equal refrangibility of all rays is a necessary con- 

 sequence. The course, then, to be pursued by any judicious 

 inquirer, and that, in fact, adopted by M. Cauchy, is that of 

 reviewing the first elements of the theory, viz., the particular 

 constitution of the hypothetical aethereal medium, and endea- 

 vouring so to modify them, that while they shall apply equally 

 to the conclusions deduced on the ordinary principles, and 

 referring to the other phaenomena of light, they shall also be 

 made to include results which will explain the phaenomena in 

 question. Now, the great desideratum, the establishment of 

 a relation between the length of a wave and the time or ve- 

 locity of its propagation, is supplied, as M. Cauchy has ex- 

 pressly remarked, " in general^'* in the formula before given. 



But, as was remarked at the beginning of these papers. 



