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of the first to recognise his wonderful mathematical powers, and to 
guide his early investigations. 
These early investigations, which had reference chiefly to Geo- 
metrical Optics, were gradually developed into an elaborate “ Theory 
of Systems of Eays,” which was communicated to the Eoyal Irish 
Academy in 1828. In the third supplement to this essay, he pre- 
dicted from theory the existence of the two species of Conical Eefrac- 
tion, the experimental verification of which has given so much addi- 
tional probability to the hypothesis of luminiferous undulations. 
His next great papers were entitled “ On a General Method in 
Dynamics,” and appeared in the Philosophical Transactions in 
1833-34. In these he developed the principle of Yarying Action, 
the discovery of which constitutes one of the most important steps 
which dynamical science has yet made. In these investigations, 
both optical and dynamical, the novel and remarkable feature is the 
discovery of the existence of a single function (adapted to each 
particular problem), from wliich, if known, the complete solution 
of the problem is to be found by differentiation alone. These papers 
soon gave him a European fame, and procured for him the honorary 
diploma of all the most important scientific societies abroad, as well 
as at home. Though much has been done, especially by Jacobi, in 
extension of Hamilton’s results, it has been almost entirely confined 
to their analytical aspect ; the physical discoveries which must 
abundantly flow from them have, as yet, been barely sought for. 
Put perhaps Hamilton was most widely known by his splendid 
invention of ‘‘ Quaternions.” A profound general principle in optics 
or dynamics is heard of only by the few who can understand it ; 
but a new mathematical method is, at least in its elements, acces- 
sible to all. Little has yet been done to disseminate elementary 
knowledge of this important Calculus. Hamilton’s “ Lectures on 
Quaternions” (1853) is adapted only to a high class of readers ; but 
it is to be hoped that his posthumous work, to which he devoted the 
last six years of his life, and which (under the title of “ Elements 
of Quaternions”) is announced for speedy publication, will put 
within the reach of the intelligent beginner a branch of mathematics 
which for simplicity of conception, symmetry, variety of expres- 
sion, and almost irresistible power, may well challenge comparison 
with any yet devised. 
