High Tensions in Moving Liquids. 113 



the laws of rebound of a solid from a flat liquid and from a 

 flat solid surface. 



Let us suppose the flat face of the solid to be a square of 

 side a, and also that it does not pass discontinuously into the 

 rest of the surface, but by means of a thin strip of curved 

 surface passing tangentially into it all round, the sections of 

 the strip by planes normal to the side of the square being arcs 

 of radius r. Suppose the solid to move with the flat face 

 horizontal, and with horizontal velocity u and vertical ve- 

 locity v at the instant when it encounters a horizontal liquid 

 surface. To trace the effects of the encounter we had better 

 for a moment imagine u to be zero, so that we have first the 

 simple case of normal impact with velocity v. 



The first effect of the impact is to establish both motion and 

 compression in the water near the solid, and also to compress 

 the solid and diminish its motion. This goes on till the 

 instant when the face of the solid and the liquid in contact 

 with it are moving with the same velocity. But by this time 

 part of the energy imparted to the liquid by the compression 

 has changed itself into motion within the mass of the liquid ; 

 and apparently in all ordinary cases this part of the energy 

 is usually a large fraction, so that the liquid has only a little 

 compressional energy left with which to attempt to thrust the 

 solid body away from it ; and thus the rebound fails, the dis- 

 tinction between the encounter of two solids and that of a 

 solid and a liquid being that in the latter case a large fraction 

 of the available energy is soon changed into energy of motion 

 within the liquid. Under these circumstances it comes to 

 pass that, in consequence of the motion in the liquid, its sur- 

 face near the solid takes the form of a curved depression 

 tangential to the curved edges of the face. 



When the vertical velocity v is zero, the effect of impact 

 with only horizontal velocity can be studied separately. The 

 first effect is the establishment of intense tensile strain in both 

 solid and liquid. With viscous communication of motion to 

 the liquid and from the solid the tensile strain in the liquid 

 tends to relieve itself rapidly by generating motion within 

 the mass : but the solid for some little time must tend to restore 

 the strain as fast as the liquid relaxes it, so that we have a 

 short period of constant tension in the liquid near the solid. 



When both velocities u and v are in existence, a combina- 

 tion of the states of affairs just described occurs ; by the end 

 of some short time t the vertical velocity v is destroyed, and 

 the surface of the liquid contains a curved depression which is 

 tangential to the curved edge of the flat face of the solid ; 

 the depression moves with a velocity comparable but not 



Phil Mag. S. 5. Vol. 42. No. 251. July 1896. I 



