130 PHILOSOPHICAL TRANSACTIONS. [aNNO 1745. 



is admitted by the other party ; without which, all reasoning on it is to no pur- 

 pose ; this conduct has been so little observed in the present dispute, that what 

 has been offered on the one side as an undoubted principle or axiom, has com- 

 monly been something that the opposite party does not admit, nay even absolutely 

 denies. 



Of this it were easy to produce a number of examples ; but two only may suf- 

 fice. Those who maintain that the moving force is as the weight into the ve- 

 Ibcity, lay down for a principle or axiom, that when two bodies meet one another 

 in contrary directions, if their moving forces be equal, neither body will prevail 

 over the other : and if their moving forces be unequal, the stronger will always 

 prevail over the weaker. 



This the Leibnitian party deny. They maintain, that one of these bodies may 

 prevail over the other, though their moving forces be equal : nay, that in many 

 cases the weaker will prevail over the stronger. 



It is therefore to no purpose to allege, that the principle above laid down is 

 founded on common sense ; or that it was always universally received, till this 

 dispute began : for since the opposite party now reject it, all reasoning upon it 

 can have no weight with them : we must have recourse to something else. 



On the other hand, those who adhere to Mr. Leibnitz's sentiment, lay down 

 for a principle, that equal effects always arise from equal causes ; provided the 

 causes be entirely consumed in producing those effects. 



This their opponents do not admit, unless in the case where those equal effects 

 are pro<luced in equal times : and therefore, till both sides shall agree in admitting 

 this principle, no argument can be drawn from it by one party, that will be of 

 any service to convince the other. 



But as this principle is chiefly used in reasoning on experimenis made with 

 springs, many of which have been produced by both parties, in support of their 

 opinions, it may be worth while more particularly to consider, what right there 

 is on the one side to impose this principle, and what reasons may be given on the 

 other for rejecting it. 



When one end of a spring, wholly unbent, leans against an immoveable sup- 

 port, and the opposite end is struck on by a body in motion, which, bending 

 the spring to some certain degree, thereby loses its whole moving force ; the 

 moving force of the body may be considered as the cause of bending the spring ; 

 and the bending of the spring as the effect of that cause which is wholly spent 

 and consumed in producing it. - 



Now if two unequal bodies, moving with unequal velocities, strike in this 

 manner on 2 equal springs, and each of them bend the spring it strikes on, ex- 

 actly to the same degree ; and by so doing, the moving force of each body be 

 entirely consumed^ here, say the Leibnitian writers, are 2 equal effects produced; 



