Researches in the Theory and Calculus of Operations. 247 



stitution of the matter; but the liberated force OA', a unit 

 of velocity thus generated, would carry the ball against non- 

 resistance on to infinity, at the rate of a unit of distance in 

 a unit of time ; the mass of the ball being unity, and count- 

 ing also as unity the sum of the atomic forces of each radius, 

 one destroyed and one liberated, and this indeed is the same 

 as regarding the entire sphere as one mammoth atom. But 

 cases will arise, for which it is necessary to explain the pro- 

 pagation or transmission through a line of atoms. The mole- 

 cular compression and reacting expansion begun at A, travels 

 along the diametral line of atomic forces, just like as in the 

 familiar experiment often exhibited of a file of suspended 

 balls : an extreme ball being raised and then dropped, the 

 impulse is successively communicated, each ball remains 

 quiescent, except the one at the other extreme of the file, 

 which alone moves in answer to the communicated impulse ; 

 but in the example of the solid sphere, the atom A' cannot 

 move without dragging the others after it. Q. E. D. 



The impulsive force of the blow and the reacting force of 

 the ball are in inverse relation together, and the mass of the* 

 mobile enters the operation as a factor (Freycinet), a force 

 of the first degree. Starting from rest, the following are a 

 few results: 



Velocity of striker. 

 1 



2 



1 



i 



2 

 1 

 2 



2 

 2 



Maes of body struck. 



1 

 1 



2 

 1 



2 



i 

 2 



m 



Distance moved. 

 1 



2 



i 

 i 



2 

 i 



4 

 1 



v 

 m 



Such would be the result of a single impulsion applied 

 to a movable body. In the case of a continued repetition of 



