Sand in cutting hard Material. 339 



(b) A soft body may cause pressure sufficient to crush a hard 

 body. 



The pressure necessary to force-in (to indent) the surfaces at 

 the point of contact will depend on two things — (1) the inertia 

 of the particles at the surface, (2) the support these particles 

 receive immediately from behind. 



1. The inertia will depend simply on the density; and if we 

 regard all bodies as liquids, we may express this part of the pres- 

 sure as similar to that of a jet against a surface. With liquid or 

 very soft bodies this will be the only source of pressure. And in 

 the case of hard bodies it seems probable that this part of the 

 pressure will depend on the same laws as for liquid bodies; for 

 there is close analogy between the flow of solids under pressure 

 and that of liquids. 



2. The support which the surface receives from behind will 

 depend on the elasticity of the material and on the density. In 

 the case of hard bodies such as glass, this will constitute almost 

 the entire source of pressure. If the body were compressible in 

 the same sense as gas, it would be the only source of pressure ; 

 but in the case of elastic but incompressible bodies the inertia 

 will affect the pressure, and it is assumed that it affects it in the 

 same way as in the case of a liquid. 



When a soft body such as lead strikes a hard surface such as 

 glass, if the velocity is sufficient, the inertia of the lead will cause 

 enough pressure to crush or penetrate the glass, however small 

 the projectile may be. 



It now remains to show more definitely how the pressure is 

 connected with the velocity and nature of the bodies in impact. 



In doing this I shall assume, first, that the bodies are elastic, 

 and, second, that they are incompressible fluids. 



By elastic bodies are meant bodies compressible in the same 

 sense as gas is compressible; ordinary bodies are not compressible, 

 and any calculations founded on their being so are necessarily 

 erroneous. If, however, the bodies are first treated as elastic 

 and then as fluid, and the results compounded, we shall probably 

 arrive very close to the truth ; at any rate we shall be able to 

 judge whether they may be treated as one or the other without 

 serious error : in this way we find that glass may be considered 

 as elastic, and lead as a liquid. 



Let A and B be two balls (for the sake of simplicity we will 

 first suppose them equal and of the same material), and let A 

 impinge on B with a velocity u. 



Then at the instant of impact, before the motion of the centres 

 of the balls has been affected, the only result will be the inden- 

 tation of the surfaces at C, the point of contact ; and it is clear 

 that the surface of contact will be halfway between A and B, and 



2 A2 



