THE ROUNDING OF SAND GRAINS 647 



the water. On this account the surface of the liquid is in a state 

 of tension, and in order to move the molecule B to the surface 

 we would have to overcome this force. We may liken the con- 

 dition of the surface of the liquid to that of the stretched rubber 

 membrane of a ball. We have a pressure at right angles to the 

 surface, capillary pressure, causing a tension parallel to the sur- 

 face, surface tension. 1 



Let us now consider a grain submerged in a liquid and let us 

 note the action of the different forces upon it. The body will be 

 pulled down by the force of gravity, the magnitude of the pull 

 being determined by the difference in the specific gravity of the 

 solid and the liquid. If we consider water, then the force will be 

 equal to vg (d—i); where v is the volume, g the acceleration due to 

 gravity, and d the density of the solid. 



In moving through the liquid, the grain will carry down a thin 

 film of water held by adhesion. There is a certain friction devel- 

 oped in this movement which will not be friction between the 

 grain and the water, but friction of water with water. The friction 

 developed by a thin film of water sliding on water is "superficial 

 viscosity." The term "skin friction" is also applied to it. 2 This 

 is the friction especially considered in the flow of water through 

 pipes and conduits. In addition, through the downward move- 

 ment of the grain, the shape of the liquid is disturbed. Any 

 disturbance or change of shape in a liquid calls forth a resistance, 

 "viscosity." But even if the particle were moving in a "perfect 

 fluid," i.e., a fluid without any viscosity, its energy would gradu- 

 ally be dissipated in forming waves. 3 



To summarize then, a body moving through water must over- 

 come resistance due to three causes; (1) viscosity, (2) skin- 

 friction, and (3) wave-resistance. 



If we take a case in which the liquid has a definite velocity, 

 the conditions as outlined above will not change. In this case 

 the grain will be acted on by a force which is the resultant of the 

 velocity and gravity, and will have the direction of the diagonal 



1 Ganot, Physics, 122. 



2 Basset, Elementary Treatise on Hydrodynamics, 52. 

 ^ Ibid., 51. 



