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effective in attaining the ends proposed. For this purpose, it will be 

 requisite to take a brief survey of the recent advancement of knowledge 

 in this country, so far as it has been influenced by this Academy. And 

 if, in the brevity with which the necessary limits of this Address compel 

 me to glance over the subject, I should appear to have overlooked, or 

 not to have assigned its due weight to any portion of our labours, you 

 will, I trust, attribute this to its true cause. 



" The prominent place which the Mathematical Sciences have occu- 

 pied in our Transactions, may be dated from the time when Brinkley 

 was enrolled amongst our Members. But it is to the labours of your 

 late President, and your late Secretary, in this department, thfit the 

 Academy, in a .great measure, owes the high place which it holds 

 among the Scientific Bodies of Europe. Of these labours, it might, 

 perhaps, be rash to single out any portion as preeminent, had not the 

 Academy itself, and the Royal Society of London, by the awards of 

 their highest honours, marked out the researches of Sir William Hamil- 

 ton, and Professor Mac Cullagh, in connexion with the wave-theory of 

 light, as of especial value. The theoretical discovery of Conical 

 Refraction, by Sir William Hamilton, the theory of Crystalline Re- 

 flexion and Refraction, by Professor Mac Cullagh, and the general 

 Dynamical Theory of Light by the same author, mark an era in this 

 branch of science not inferior to that of Fresnel. 



" Time will not permit me to do more than allude to the new 

 branch of Analysis, which has recently engaged so much of the atten- 

 tion of Mathematicians, and which originated in the Theory of Qua- 

 ternions of Sir William Hamilton, and has received an important 

 modification and development in the Triplet theory of Professor 

 Graves. As a member of the University, I rejoice to be able to add, 

 that worthy successors, even to such men as I have named, are arising 

 there ; and that the recent union of the mathematical strength of Cam- 

 bridge and of Dublin, in the Mathematical Journal which was so 

 long and so ably supported by the former University, is likely to give a 

 new impulse to this branch of science amongst us. AnA long may 

 these sciences continue to flourish in the University and in this x^cademy ! 

 Independently of the magnitude and sublimity of their own proper 

 objects, — independently of their direct value in Physical Science, as 



