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nature, had, nevertheless, a common origin in a higher and more 

 ultimate law, from which they were but particular deductions. In 

 this paper he succeeded in deducing from a single physical hypo- 

 thesis, and from strictly mechanical principles, all the known laws 

 of crystalline propagation, reflection, and refraction. 



This new theory he has since applied to the hitherto undisco- 

 vered laws of total reflection, and had succeeded in completely 

 solving the problem in the particular case of an ordinary medium. 

 This he has noticed in difierent places in the third volume of the 

 Proceedings of the Academy. He had also succeeded in deve- 

 loping the whole problem in the general case, although in its com- 

 plete form his theory was never published. 



While he was thus discovering the true laws of that branch of 

 physical science, he saw that a false theory on the same subject was 

 proposed on the continent, and that, from the great name of its ori- 

 ginator, it was gaining ground even in his own University. He 

 immediately came forward and exposed the many errors and incon- 

 sistencies of that theory. This refutation will be found in the Pro- 

 ceedings of the Academy, Vol. II., page 189. 



During all this period he also read before the Academy some 

 highly original papers on purely mathematical subjects. Of these 

 his paper " On Surfaces of the Second Order," published in the Pro- 

 ceedings, Vol. III., would have sufficed, had he written nothing else, 

 to establish his reputation as a mathematician. 



In 1838 Professor Mac Cullagh received from the Royal Irish 

 Academy the Cunningham Medal, for his paper " On the Laws of 

 Crystalline Reflection and Refraction." On presenting him with 

 that medal. Sir William Hamilton, who was then our President, 

 delivered an Address, which is printed in the Proceedings, and 

 which contains a concise account of the then existing state of sci- 

 ence, and a just tribute to the value of Mac Cullagh's discoveries. 



In 1842 a still further recognition of his merits was made by 

 the Royal Society, who awarded him the Copley Medal for his in- 

 vestigations in the theory of Light. On this occasion he had 

 among his competitors for this high honour, Bessel, Dumas, and 

 Murchison. 



But it would be a great error to estimate the services which 

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