PNEUMATICS. 271 



364. The depth to which a ball penetrates into 

 wood, earth, &c. is nearly as its weight multiplied 

 into the square of its velocity. 



p 



Hence, since fl 2 = w 2 x~ 5 BlfyzypPi so that the 



effect of a shot is nearly as the quantity of gun- 

 powder. 



From the Table given by Dr HUTTON, Course of Ma- 

 thematics, vol. in. p. 272. the value of m may be 

 deduced nearly = 2000. 



The following proposition, which has been already 

 mentioned, is applicable to many researches in Me- 

 chanics and Hydrodynamics, and particularly to such 

 as are now treated of. 



365. When bodies, whether solid or fluid, act 

 on one another by impulse or percussion, in such 

 a manner that their action is subject to the law of 

 continuity, the sum which is made up, at any in- 

 stant, by multiplying every mass into the square 

 of its velocity, and adding all the products toge- 

 ther, is a constant quantity, or one which remains 

 always of the same magnitude. 



The sum thus made up is the vis viva of the bodies, 

 and this proposition is therefore called the conserva- 

 tion, of the v is viva. 



366. If 



