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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, that 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. And long may 
these scienees continue to flourish in the University and in this Academy ! 
Independently of the magnitude and sublimity of their own proper 
objects,—independently of their direct value in Physical Science, as 
