226 Royal Society. 



the propagation and double refraction of light in crystallized media, 

 as well as in ordinary, v.'ith some of those of total reflexion at the 

 hounding surfaces of ordinary media, but he did not account for 

 them on any correct mechanical principles ; with respect to propa- 

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

 cannot now be admitted : with respect to ordinary reflexion, he partly 

 accounted for them on correct princij^les, in the particular case of 

 ordinary media, which was the only one for which he had ever given 

 them. Professor MacCuUagh, on the contrary, not only deduced 

 the known laws in all the three cases from mechanical principles of 

 a nature so simple and probable, that they cannot but bear con- 

 viction of their truth to any mind reflecting on them, with anything 

 like the attention they deserve, but he also gave the general equa- 

 tions of the propagation of light not only for all known media, but 

 also for all media which could ever be discovered or even conceived. 

 And with these he gave also the general conditions which must be 

 fulfilled at the common bounding surface of every two, not only 

 known, but conceivable media, and which in every case give all the 

 laws of reflexion and of refraction, whether ordinary or total. 



Thus did he deliver to his hearers and to posterity a perfect and 

 complete mechanical theory ; that is to say, analytically complete : 

 so that any one who in future may attempt to discover in this re- 

 gion of science, can only do so by treading in his steps, and adopt- 

 ing his principles, but can never supersede them. In fact, he has 

 discovered and handed down the general principles which must liold 

 in all cases. It remains for future investigators only to apply them. 

 He himself apj)lied them to the two most general cases of propaga- 

 tion, viz. of polarized waves of undiminishing intensity in a crystal- 

 line medium, and of that peculiar si)ecies of propagated vibrations 

 which take place in the rarer medium in every case of total reflexion 

 at the surface either of an ordinary or of a crystalline medium. In 

 the former case he arrived at all the laws of propagation in crystal- 

 line media which were discovered by Fresnel, with one single varia- 

 tion, and that the very one on which he himself had long previously 

 corrected Fresnel, viz. the vibrations of the aether, in jilace of coming 

 out to be perpendicular to the plane of polarization, as Fresnel had 

 supposed, came out on the contrary to be parallel to that plane, as 

 MacCullagh himself had supposed. 



He was enabled by discoveries of his own, to deduce again in a far 

 easier manner, all the beautiful geometrical laws of crystalline re- 

 flexion and refraction, which he had formerly laid before the Royal 

 Irish Academy in 1837, and for which that body awarded him the 

 honorary distinction of the Conyngham Medal, which I have Ijefore 

 alluded to. And they fully confirmed the acute prophecy then made 

 by his sagacious mind, on finding to his astonishment, that a law of 

 reflexion depended for its existence on the existence of a huvof pro- 

 j)agation ; when he said that the law of vis viva which he bad as- 

 sumed at the outset could not be a fundamental but rather a se- 

 condary law, and remarked that perhaps the next step in physical 

 optics would be the deduction, as parts of one system, of all the laws 



I 



