VOL. XLIII.] PHILOSOPHICAL TKANSACTIONS. 131 



for the springs are equal, and are now equally bent ; and the moving forces, 

 which are the causes of those effects, are wholly consumed in producing them ; 

 and therefore, by virtue of the principle above laid down, those causes must be 

 equal ; that is, the moving forces of the 1 bodies must be equal. 



But their antagonists reply, that this principle is not admitted by them, except 

 the times of producing those effects are equal ; and that they are not so in the 

 case before us ; for the greater body takes up a longer time in producing its effect, 

 or in bending its spring. 



If therefore the Leibnitian party pretend, that equal effects, when produced in 

 unequal times, do always arise from equal causes, they must not impose this on 

 their opponents by way of principle or axiom, but must demonstrate it. Till 

 this be done, there will be room to doubt, at least, whether the two bodies have 

 equal moving forces, though they bend equal springs to the same degree. For 

 the larger and slower of these two bodies will bend the one spring more slowly ; 

 and consequently will be resisted for a longer time, than the smaller and swifter 

 body will be resisted in bending the other spring to the same degree. 



May not therefore the total resistance of a spring be greater, if that resistance 

 continues for a longer time ? And if the total resistance be greater, must not the 

 moving force, which is destroyed and consumed by that resistance, be also greater ? 

 Is there not reason then to doubt, whether the moving forces of these two bodies 

 be equal, though they bend equal springs to the same degree? 



In like manner, when a spring, already bent to some certain degree, does, by 

 unbending, drive before it a body which gives way to its pressure, is there not 

 room to doubt, whether the pressure of the spring may not produce a greater 

 effect, when that pressure continues for a longer time ? 



That pressure may be said to produce three effects, all of which may, if we 

 please, be considered as different from one another. 1 . The pressure carries the 

 body through a certain space ; by which space the length of the bent spring is 

 increased, in returning to its natural situation. 1. The pressure gives to the 

 body a certain quantity of motion. 3. It gives the body a certain moving force. 



Now, the first of these effects is greater, when the pressure acts for a longer 

 time. For, if the pressure of a bent spring, by acting for one second on the 

 body 1 , carry that body 1 through the space 1 ; the pressure of the same, or of 

 an ecjual spring equally bent, by acting for 2 seconds on the same body 4, will 

 carry that body 4 through the same space 1. 



Likewise the 2d effect is greater, when the pressure continues for a longer 

 time. For in the case just now mentioned, the body 4 will have twice the 

 quantity of motion that the body 1 has ; though these two quantities of motion 

 arise from the pressure of the same, or, which is all one, of equal springs 

 equally bent. 



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