105 



the subject on the same hypothesis, although never satisfied with it, 

 he succeeded in deducing all the laws from the simplest geometrical 

 considerations. In this first communication there was no new phy- 

 sical discovery, nor anythingwhich had not been previously known, 

 although there was abundance to show the original genius and power 

 of the author, as well as much purely mathematical, which was 

 perfectly new. On the same day he communicated also another pa- 

 per on the " Rectification of the Conic Sections," and that again 

 displayed no new results, but, like the other, simplicity and ele- 

 gance of method. Since that period, however, he did arrive at 

 several new and very beautiful theorems in that interesting subject, 

 the chief of which will be found published in his Examination Pa- 

 pers in the Dublin University Calendar. 



His next paper was read in the year he obtained fellowship, on 

 the 28th of May, 1832. It originated in a contest between Laplace, 

 Lagrange, and Sir James Ivory, in which the two latter denied the 

 truth of an approximate theorem in the subject of attractions dis- 

 covered by the former. In that paper Mac Cullagh showed, in the 

 most simple and elegant manner, that the objectors were wrong, and 

 that Laplace was right. 



His next paper was rea/1 on the 24th of June, 1835, and was en- 

 titled " Geometrical Propositions applied to the Wave Theory of 

 Light." In this again, although he displayed great originality, 

 acutencss, and geometrical elegance, he arrived at no physical 

 results which could be called strictly original, for his tivo cases of 

 •' Conical Refraction" had been previously discovered theoreti- 

 cally by Sir William Hamilton, and confirmed experimentally by 

 Dr. Lloyd. 



His first altogether original paper was read to the Academy 

 on the 22nd of February, 1836. In that paper, he linked together, 

 by a single and simple mathematical hypothesis, the peculiar and 

 unique laws which govern the motion of light in its propagation 

 through quartz; and having determined by observation of one set 

 of phenomena the value of a particular constant occurring in his 

 theory, he subjected that theory to the severe test of calculating 

 numerically Ihe results of another and wholly difltrent set of phe- 



VOL. IV. K 



