360 HISTORY OF MECHANICS. 



make this change was the commencement of one of the most obstinate 

 and curious of the controversies which form part of the history of 

 mechanical science. The celebrated Leibnitz was the author of the 

 uew opinion. In 1686, he published, in the Leipsic Acts, "A short 

 Demonstration of a memorable Error of Descartes and others, concern- 

 ing the natural law by which they think that God always preserves 

 the same quantity of motion ; in which they pervert mechanics." The 

 principle that the same quantity of motion, and therefore of moving 

 force, is always preserved in the world, follows from the equality of 

 action and reaction ; though Descartes had, after his fashion, given a 

 theological reason for it ; Leibnitz allowed that the quantity of moving 

 force remains always the same, but denied that this force is measured 

 by the quantity of motion or momentum. He maintained that the 

 same force is requisite to raise a weight of one pound through four 

 feet, and a weight of four pounds through one foot, though the mo- 

 menta in this case are as one to two. This 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 produced 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 dis- 

 tinction 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 subject ; or rather, as Bernoulli says, 13 made him think for him- 

 self, which ended in his proving directly that which Leibnitz had de- 

 fended by indirect reasons. Among other arguments, he had pretended 

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

 forces be adhered to, a perpetual motion would be possible. It is easy 

 to collect many cases w T hich admit of being very simply and conve- 

 niently 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 

 account is taken of the time of producing the effect, we may conve- 

 niently use similar methods. 



But it was not till a later period that the question excited any 

 general notice. The Academy of Sciences of Paris in 1724 proposed 



13 Op. iii. 40. 



