88 HISTORY OF MECHANICS. 



was answered by the Abbe de Conti; who truly 

 observed, that allowing the effects in the two cases 

 to be equal, this did not prove the forces to be 

 equal ; since the effect, in the first case, was pro- 

 duced in a double time, and therefore it was quite 

 consistent to suppose the force only half as great. 

 Leibnitz, however, persisted in his innovation ; and 

 in 1695 laid down the distinction between vires 

 mortuce, or pressures, and vires vivce, the name 

 he gave to his own measure of force. He kept 

 up a correspondence with John Bernoulli, whom 

 he converted to his peculiar opinions on this sub- 

 ject; or rather, as Bernoulli says 13 , made him think 

 for himself, which ended in his proving directly 

 that which Leibnitz had defended by indirect rea- 

 sons. Among other arguments, he had pretended 

 to show (what is certainly not true,) that if the 

 common measure of forces be adhered to, a per- 

 petual motion would be possible. It is easy to 

 collect many cases which admit of being very 

 simply and conveniently reasoned upon by means 

 of the vis viva, that is, by taking the force to be 

 proportional to the square of the velocity, and not 

 to the velocity itself. Thus, in order to give the 

 arrow twice the velocity, the bow must be four 

 times as strong; and in all cases in which no ac- 

 count is taken of the time of producing the effect, 

 we may conveniently use similar methods. 



But it was not till a later period that the 

 13 Op. iii. 40. 



