associated with his memorable invention of the calculus of
Quaternions. It was to the creation of this branch of mathematics
that the maturer powers of his life were devoted; in fact he gives us
himself an illustration of how completely habituated he became to the
new modes of thought which Quaternions originated. In one of his
later years he happened to take up a copy of his famous paper on
Dynamics, a paper which at the time created such a sensation among
mathematicians, and which is at this moment regarded as one of the
classics of dynamical literature. He read, he tells us, his paper
with considerable interest, and expressed his feelings of
gratification that he found himself still able to follow its
reasoning without undue effort. But it seemed to him all the time as
a work belonging to an age of analysis now entirely superseded.

In order to realise the magnitude of the revolution which Hamilton
has wrought in the application of symbols to mathematical
investigation, it is necessary to think of what Hamilton did beside
the mighty advance made by Descartes. To describe the character of
the quaternion calculus would be unsuited to the pages of this work,
but we may quote an interesting letter, written by Hamilton from his
deathbed, twenty-two years later, to his son Archibald, in which he
has recorded the circumstances of the discovery:--

"Indeed, I happen to be able to put the finger of memory upon the year
and month--October, 1843--when having recently returned from visits
to Cork and Parsonstown, connected with a meeting of the British
Association, the desire to discover the laws of multiplication
referred to, regained with me a certain strength and earnestness
which had for years been dormant, but was then on the point of being
gratified, and was occasionally talked of with you. Every morning in