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Dynamics which have been published by various investigators since the first edition appeared. I have moreover added some historical matter, and rewritten many sections. It is not necessary to specify these in detail, but perhaps I may mention that the new explanation of the transformation-theory of Dynamics in 125 sprang from a desire to do justice to the earliest great work of Hamilton sgenius: that the changes in 69 (the motion of a body about a fixed point under no forces) arose from my opinion that the Jacobian functions are preferable to theW eierstrassian in the numerical computations :and that I should have liked to give a fuller proof of Sundman stheorem (181), but thought it better to give only such an account as might impel the reader to consult Mr Sundman sown accessible and readable memoir. I wish again to record my obligations to the staff of the Cambridge University Press. E. T. WHITTAKER. Edinbdegh, A ugust, 1916.
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