HIS book may be regarded as a fifth edition of a Treatise on the Mathe-THIS Theory of of on matical Theory of the Motion of Fluids, which was published in 1879. The second edition, largely remodelled and extended, appeared under the present title in 1895, and was followed by a third in 1906, and a fourth in 1916. In this issue, as in the two preceding ones, no change has been made in the general plan and arrangement, but the work has again been carefully revised, occasional passages have been rewritten, and some important additions have been made, relating chiefly to recent investigations.

A word or two may be said with regard to certain departures from general usage which are to be found in the book. The use of the reversed sign for the velocity-potential (4), which was adopted in the 1895 edition and is here continued, was not altogether an innovation, and has strong arguments of a physical kind to recommend it. It appears so much more natural to regard the state of motion of a dynamical system, in any given configuration, as specified by the impulses which would start it, rather than by those which would stop it, that the altered definition of the function would seem to require no further justification. It has also the advantage that the analogies with other branches of Mathematical Physics are rendered more complete.