342 On the Action of a Blast of Sand in cutting hard Material. 

 In the case of glass striking glass, we may take 

 d=d> = 150, 



\=144 x 8,000,000 = 1,152,000,000, 

 jo= 1,440,000; 

 .\ substituting in (4), we have 



1440000x8 



v— 



v/150x 1152000000 

 = 27 \ (feet per second). 



This would be the velocity just sufficient to crush the surface ; 

 to produce an appreciable effect would require a somewhat higher 

 velocity ; so that this value agrees very well with the result of 

 experience, which is that a blast caused by a pressure of 4 inches 

 of water is amply sufficient to cut glass. 



In the case of an ordinary solid body we have, by combining 

 the two effects, 



m </%d ■ _,_ v*d 



P= ~V7 V+ W 



which gives the pressure in terms of the velocity impressed on the 

 surface. It is important to notice that, so far as the strength of 



the body itself is concerned, the last term — produces no effect, 

 as this part of the pressure is balanced by the inertia of the sur- 

 face itself, and that the first term a/ — v will only hold so 



" V 9 

 long as it is less than the ultimate pressure which the material 

 will stand. When it is greater than this, the ultimate pressure 

 must be substituted for this term. 

 In the case of lead we have 



d'=712, 



X' = 720,000x144; 



but this will only be true so long as the pressure is less than 

 4000 x 144, this being the maximum pressure the lead will stand; 



.-. instead of \ /— v we substitute 576000; 



V 9 



71 o 



,\ p=b76000+~{u-vy 2 . 



r o4 • 



And if we take, as before, the pressure sufficient to crush the 

 glass, 



p = 1440000, I j 



