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of his discovery of Conical Refraction. This is admitted to have been one 

 of the most remarkable scientific predictions that was ever made — one 

 which announced, on the foundation of pure mathematical calculation, 

 a physical phenomenon which was suggested by no analogy, and seemed 

 beyond the boundaries of probability ; but which, as you know, was 

 completely verified by the experiments of Professor Humphrey Lloyd. 



In 1 837 Hamilton was elected President of this Academy, on the death 

 of Dr. Bartholomew Lloyd, who had occupied the chair for the two years 

 succeeding the death of Brinkley. His inaugural address gave evidence 

 of his power to direct the operations of a learned society constituted as 

 ours is. He showed that he entered into the working of all its depart- 

 ments, and could sympathize with the labours of all its members. For 

 eight years, during which he held this office, he exerted himself in every 

 way to increase the usefulness of the Academy, and to sustain its honour ; 

 and, when he resigned the Presidentship, he received the cordial thanks 

 of the Academicians "for his high and impartial bearing in the chair, 

 and for his untiring efforts to advance the interests of the body." 



"We have already mentioned Hamiltox's paper on a " General Method 

 in Dynamics." In this memoir, starting from the idea of a characte- 

 ristic function, analogous to that employed in his essay on Systems of 

 Rays, he succeeded in giving a system of complete and rigorous inte- 

 grals of the celebrated differential equations of motion of a system of 

 bodies. This achievement gained for him the Medal of the Royal So- 

 ciety, and the recognition of the greatest European mathematicians. 

 The next great work of Hautltox of which we have to make mention, 

 is his paper on "Algebra considered as the Science of pure Time," a 

 treatise of a peculiar and semi-metaphysical kind. His object in the 

 composition of it was to establish the foundations of algebra as a science, 

 rather than to improve its processes as an art, or to perfect its symbol- 

 ism as a language. With this was connected his theory of conjugate 

 functions, or algebraic couples, to which he was conducted in his attempts 

 to explain some remarkable results stated by my brother, Mr. John 

 Graves, in a paper upon imaginary logarithms. "We now, in this rapid 

 summary, pass on to his last great invention — that of the Calculus of 

 Quaternions. Its elaboration has occupied the last twenty- two years of 

 his life. During that time he has employed this new and powerful 

 organon in discussing questions in almost every branch of mathematics. 

 Most of his attention has, no doubt, been given to geometrical appli- 

 cations. But he has not failed to record in our "Proceedings" results 

 of researches, showing that the new calculus adapts itself to the require- 

 ments of physical science. He has shown how perfectly it enables us 

 to conceive and express, in its peculiar language, the mathematical 

 problem of determining the orbits and perturbations of bodies governed 

 in their motions by the Newtonian law of force. He has also shown 

 that quaternion equations may be advantageously employed in the dis- 

 cussion of Fresnel's wave surface. 



I have not attempted to make a complete catalogue even of all his 

 most important works ; I have said nothing of his papers on Fluctuating 



E. I. A. PEOC. VOL. IX. 2 T 



