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1916] . LAMB'S HYDRODYNAMICS 401
point for investigations in other subjects as well as in hydrodynamics. To almost all parts of his subject he has made entirely original contributions; and, even when this could not be claimed, his exposition of the work of others is often so much simplified and improved as to be of not inferior value. As examples may be mentioned the account of Cauchy and Poisson's theory of the waves produced in deep water by a local disturbance of the surface (§ 238) —the first satisfactory treatment of what is called in Optics a dispersive medium—and of Sommerfeld's investigation of the diffraction of plane waves of sound at the edge of a semi-infinite screen (§ 308).
Naturally a good deal of space is devoted to the motion of a liquid devoid of rotation and to the reaction upon immersed solids. When the solids are " fair " shaped, this theory gives a reasonable approximation to what actually occurs; but when a real liquid flows past projecting angles the motion is entirely different, and unfortunately this is the case of greatest practical importance. The author, following Helmholtz, lays stress upon the negative pressure demanded at sharp corners in order to maintain what may be called the electric character of flow. This explanation may be adequate in some cases; but it is now well known that liquids are capable of sustaining,negative pressures of several atmospheres. How too does the explanation apply to gases, which form jets under quite low pressure differences?* It seems probable that viscosity must be appealed to. This is a matter which much needs further elucidation. It is one on which Kelvin and Stokes held strongly divergent views.
The later chapters deal with Vortex Motion, Tidal Waves, Surface Waves, Waves of Expansion (Sound), Viscosity, and Equilibrium of Rotating Masses. On all these subjects the reader will find expositions which could hardly be improved, together with references to original writings of the author and others where further developments may be followed.
It would not have accorded with the author's scheme to go into detail upon experimenta] matters, but one feels that there is room for a supplementary volume which should have regard more especially to the practical side of the subject. Perhaps the time for this has not yet come. During the last few years much work has been done in connexion with artificial flight. We may hope that before long this may be coordinated and brought into closer relation with theoretical hydrodynamics. In the meantime one can hardly deny that much of the latter science is out of touch with reality.
* The fact that liquids do not break under moderate negative pressure was known to T. Young. "The magnitude of the cohesion between liquids and solids, as well as of the particles of fluid with each other, is more directly shewn by an experiment on the continuance of a column of mercury, in the tube of a barometer, at a height considerably greater than that at which it usually stands, on account oi the pressure of the atmosphere. If the mercury has been well boiled in the tube, it may be made to remain in contact with the closed end, at the height of 70 inches or more " (Young's Lectures, p. 626,1807). If the mercury be wet, boiling may be dispensed with and negative pressures of two atmospheres are easily demonstrated.
R. vi. 26