Prof. Powell's Note on the Theory of Light. 373 



ject which have been pursued by several mathematicians, and 

 especially by M. Cauchy, so far as they have come to my 

 knowledge ; so various, however, are the channels through 

 which such researches are made public, that some of them, 

 especially those which appear on the Continent, often escape 

 attention. In this way I now find I have omitted to notice 

 some of the later investigations of the distinguished mathema- 

 tician just named. 



M. Cauchy has favoured me with a letter, in which, ac- 

 knowledging the receipt of a copy of my work, he adds a 

 brief mention of these later investigations, to which I had not 

 referred in my volume, with a request that I would take an 

 opportunity of supplying my readers with this further in- 

 formation. As it may be some time before a work on abstract 

 science reaches a second edition, perhaps the best course I 

 can pursue is to offer a very brief statement of the points in 

 question through the medium of this Journal. 



It appears then, that subsequently to the researches of 

 which I have given abstracts, M. Cauchy published in August 

 1836, at Budweiss, a lithographed memoir entitled Memoire 

 sur la Theorie de la Ltimiere, &c, which bears much on the 

 subject of the general theory, and the phaenomena to which 

 it relates, as considered in my tract. 



The main heads of this investigation are as follows : — 



1. The general equations of motion of the aether : 2nd. Co- 

 lour, or the dispersion : 3rd. The motion of light penetrating 

 to a small depth into the interior of opake bodies : 4th. The 

 transition from the formulae obtained under the third head, to 

 those which represent vibratory motion in general in an 

 aethereal fluid : 5th and 6th. The case of media in which the 

 propagation of light takes place in the same manner in every 

 direction, whether round any point, or round every axis 

 parallel to a given straight line : 7th. The propagation of 

 plane waves in transparent bodies. 



The consequences have been further followed out by the 

 author in other memoirs published since. 



In the second volume of the Comptes Rendus, 1836 (1st 

 semestre), p. 365, M. Cauchy has observed that the intensity 

 of the light penetrating to a small depth x in the interior of 

 an opake body, decreases in proportion to a negative expo- 

 nential of the form s— cx . 



Exponentials of the same kind are found entering into 

 many of the formulae included in the memoir of August 1836 ; 

 and setting out from these formulae, he shows (p. 84 of that 

 memoir) how in a coloured glass the thickness necessary to 

 produce the extinction of a luminous ray may vary with the 

 nature of the colour. 



