OF THE ROYAL IRISH ACADEMY, 1846. 457 



and the Neosophcrs, starting originally from opposite extremities 

 of the field of Truth. But, whatever may have been its origin, 

 we may now derive from it lessons not only of mutual forbear- 

 ance, but of mutual instruction. The mathematician may imbibe 

 from the antiquarian the taste which will lead him to explore, 

 with reverence, the early history of the efforts of those master- 

 minds in Science, whose very failures are fraught with philosophic 

 interest, and to trace the progress of discovery up to the first dawn 

 of thought ; and he will return from the investigation with clearer 

 views of the human mind itself, and of the means by which it 

 attains Truth. The antiquarian may learn from the man of 

 science those habits of precise thought, and exact reasoning, which, 

 in the mysterious twilight that surrounds the fascinating objects 

 of his pursuit, he is apt to think inapplicable ; and both may learn 

 from the cultivator of literature to value and to acquire that magio 

 power which language confers upon thought. 



Having said thus much in vindication of the constitution of the 

 Academy, suffer me, in the next place, to consider how far it has 

 been effective in attaining the ends proposed. For this purpose, 

 it will be requisite to take a brief survey of the recent advance- 

 ment 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 

 occupied 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 pre-eminent, 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 Hamilton 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 reflexion and refraction, by 



