Notes on some Points in the Theory of Light. 209 



p. 432). The remark, however, did not meet with much at- 

 tention from mathematicians, who were, perhaps, not dis- 

 posed to scrutinize too closely any hypothesis which gave 

 transversal vibrations as a result. Besides, the hypothesis 

 appeared to go much further, as it offered prima facie expla- 

 nations of a great variety of phenomena ; it was one to which 

 calculation could be readily applied, and therefore it naturally 

 found favour with the calculator ; and as to M. Poisson's objec- 

 tion, it was easily removed by a change of terms, for when the 

 elastic solid was called an " elastic system" there was no longer 

 anything startling in the announcement that the motions of the 

 ether are those of such a system. The hypothesis was there- 

 fore embraced by a great number of writers in every part of 

 Europe, who reproduced, each in his own way, the results of 

 M. Cauchy, though sometimes with considerable modifications. 

 Every day saw some new investigation purely analytical some 

 new mathematical research uncontrolled by a single physical 

 conception put forward as a " mechanical theory " of double 

 refraction, of circular polarization, of dispersion, of absorption ; 

 until at length the Journals of Science and Transactions of 

 Societies were filled with a great mass of unmeaning formulas. 

 This state of things was partly occasioned by the great number 

 of " disposable " constants entering into the differential equa- 

 tions of M. Cauchy and their integrals ; for it was easy to in- 

 troduce, among the constants, such relations as would lead to 

 any desired conclusion; and this method was frequently 

 adopted by M. Cauchy himself. Thus, in his theory of double 

 (or rather triple) refraction, given in the works already cited 

 (p. 145), he supposes three out of his nine constants to vanish, 

 and assumes, among the other six, three very strange and im- 

 probable relations, by means of which each of the principal 

 sections of his wave-surface (considering only two out of its 

 three sheets) is reduced to the circle and ellipse of Fresnel's 

 law; and the tLree principal sections being thus forced to coin- 

 cide, it would not be very surprising if the two sheets were 

 found to coincide in every part with the wave-surface of Fres- 



p 



