432 Notes. 



springs, therefore, in being each reduced the same angular quantity 

 as ACE is reduced, will oppose only double the resistance. In the 

 same manner it may be demonstrated that, in the succeeding in- 

 stants, the resistance opposed by the four springs in being closed 

 each the same angular quantity, as that by which ACE is closed in 

 one instant, is always to that opposed by the single spring ACB, in 

 the same instant, in the ratio of the velocities belonging to the two 

 bodies ; therefore a velocity double that required to close one spring 

 is sufficient to close four springs. Thus the number of springs closed, 

 which are 1 and 4, are as the squares of the velocities 1 and 2 neces- 

 sary to close them. 



We see then that the number of obstacles which bodies in mo- 

 tion are capable of overcoming increases as to the squares of the 

 velocities. But by the term force ought we to understand the num- 

 ber of obstacles ? Is it not much more natural to consider it as denot- 

 ing the sum of the resistances opposed by these obstacles ? For it is 

 not merely the number, but the value of each obstacle which des- 

 troys motion. Now in this case each instantaneous resistance being 

 evidently proportional to the quantity of motion destroyed by it, 

 (on which point all are agreed,) the sum of the resistances will be 

 proportional to the quantity of motion destroyed. If then by /orce, 

 we understand the *wm, and not merely the number of the resistances 

 which a moving body is capable of overcoming, the force is propor- 

 tional to the quantity of motion. From this principle it has likewise 

 been inferred that the number of resistances overcome are as the 

 squares of the velocities. The question then is in reality nothing 

 more nor less than a question about terms, and reduces itself to find- 

 ing the meaning of the word force. As to this point we are per- 

 fectly at liberty, provided we employ that which we take for the 

 measure of force agreeably to the idea which we attach to the 

 term force, we shall always arrive at the same results. We shall, 

 therefore, continue to take for the measure of forces the product of 

 the mass into the velocity ; and consequently by the force of a body 

 we understand the sum total of the resistances necessary to exhaust 

 its motion. 



II. 



On the Compressibility of Water. 



THE phenomenon of the transmission of sound through water and 

 other liquids had long indicated that they were capable of being 

 compressed. Canton, an English philosopher, clearly detected this 



