"Your sonnet which you showed me expressed much better than I could
express it the feeling with which I tried to write this book, and I
once intended to ask your permission to prefix the sonnet to my book,
but my friends persuaded me that I ought to tell my story in my own
prose, however much better your verse might be."

The first epoch-marking contribution to Theoretical Dynamics after
the time of Newton was undoubtedly made by Lagrange, in his discovery
of the general equations of Motion. The next great step in the same
direction was that taken by Hamilton in his discovery of a still more
comprehensive method. Of this contribution Hamilton writes to
Whewell, March 31st, 1834:--

"As to my late paper, a day or two ago sent off to London, it is
merely mathematical and deductive. I ventured, indeed, to call it
the 'Mecanique Analytique' of Lagrange, 'a scientific poem'; and
spoke of Dynamics, or the Science of Force, as treating of 'Power
acting by Law in Space and Time.' In other respects it is as
unpoetical and unmetaphysical as my gravest friends could desire."

It may well be doubted whether there is a more beautiful chapter in
the whole of mathematical philosophy than that which contains
Hamilton's dynamical theory. It is disfigured by no tedious
complexity of symbols; it condescends not to any particular problems;
it is an all embracing theory, which gives an intellectual grasp of
the most appropriate method for discovering the result of the
application of force to matter. It is the very generality of this
doctrine which has somewhat impeded the applications of which it is
susceptible. The exigencies of examinations are partly responsible