106 



nomena, and thence compared the results with observation, before 

 he gave the theory in its published form to the Academy. 



His next paper was also on the subject of Light, and in it again 

 he made a great advance beyond the knowledge of the time. It was 

 read to the Academy on the 9th of January, 1837, and was entitled, 

 " On the Laws of crystalline Reflexion and Refraction." The pro- 

 blem discussed in that paper was completely solved and reduced to 

 geometrical laws of the greatest simplicity and elegance, which 

 had been but partially solved by Fresnel, in the particular case 

 of ordmary media ; and even this limited solution depended on 

 inaccurate principles, and only gave the right results by a balancing 

 of opposite errors. The laws discovered by Mac Cullagh in this 

 paper were deduced ixomfour hypotheses, unestablished certainly, 

 but highly probable from their great simplicity and accordance with 

 all previous physical notions. The truth of these hypotheses was 

 then confirmed by their leading to results conformable to observa- 

 tion, but as yet they had not been accounted for on a single mecha- 

 nical principle. It was in reference to the results published in this 

 paper that Mr. Neumann, of Konigsberg, subsequently advanced a 

 claim of priority. The letter of Mr. Neumann to Sir William Ha- 

 milton, then President of the Academy, "will be found in the first 

 volume of the Proceedings ; and the masterly defence of his own 

 claims made by Professor Mac Cullagh, has been published in the 

 pages immediately succeeding. He has there shewn that he was 

 indebted to no man living for assistance on the subject of light, save 

 to Fresnel alone; and his vindication of himself is so complete, 

 that nothing more need be here said on the subject, except to re- 

 mark that the results of greatest importance had not been arrived 

 at by Mr. Neumann. Both had set out, independently of each other, 

 from the same principles, and both had completely solved the ques- 

 tion analytically, but the geometrical interpretation of the laws 

 had been given by Professor Mac Cullagh only. 



His next paper was presented to the Academy on the 9th of De- 

 cember, 1839". It was on *' The Dynamical Theory of Crystalline 

 Reflexion and Refraction." In this he verified all his preceding 

 predictions respecting the laws of propagation and reflection, by 

 showing that both sets of laws, although so widely different in their 



