Ill 



them on any correct mechanical principles. With respect to y^ro- 

 payalion, the very first principles from which he sets out are such 

 as cannot be admilted ; with respect to ordinarfj reflection, he 

 partly accounted for them on correct principles, in the particular 

 case of ordinary media; and with respect to total reflection, his 

 beautiful empirical laws are well known, but he did not account 

 for them at all, even in the simple case of ordinary media, which 

 was the only one for which he had ever given them. Professor 

 Mac Cullagh, on the contrary, not only deduced the known laws 

 in all the three cases from mechanical principles of a nature so 

 simple and probable, as that they cannot but bear conviction of 

 their truth to any mind reflecting on them with anything like 

 the attention they undoubtedly deserve ; but he also gave the 

 general equations of the motion of the propagation of light, not 

 only in all known media, but also for all media which could ever 

 be discovered, or even conceived ; and with them he gave also the 

 general conditions which must be fulfilled at the common bound- 

 ing surface of every two not only known but conceivable media, 

 and which in every case give all the laws of reflection and of refrac- 

 tion, whether ordinary or total. Thus did he deliver to us and to 

 posterity a perfect and complete mechanical theory, — analytically 

 complete, — so that any one who in future may attempt to discover 

 in this region of science can only do so by treading in his steps, 

 and adopting his correct principles, but can never supersede them; 

 in fact he has discovered and handed down to us \X\e general prin- 

 ciples which must hold in all cases, and it remains for future in- 

 vestigators only to apply them 



" He himself applied them to the two most general cases of 

 propagation, viz., of polarized waves of undirainishing intensity 

 in a crystalline medium, and of that peculiar species of propagated 

 vibrations which take place in the rarer medium, in every case of 

 total rejicction at the surface either of an ordinary or of a crystal- 

 line medium; in the former case he arrived at all the laws of pro- 

 pagation in crystalline media which were discovered by Fresnel, 

 with one single variation, and that the very one on which he him- 

 self had long previously corrected Fresnel, viz., the vibrations of 

 the ether, which in place of being perpendicular to the plane of 



