V31 PHILOSOPHICAL TRANSACTIONS. [aNNO 1745. 



Why therefore are we to take it for granted, or to have it imposed on us bv 

 way of principle or axiom, that the third effect is not greater, when the time, in 

 wliich it is produced by the pressure of the same, or equal springs, is longer, nay 

 infinitely longer ? 



But we are told that all the force, which resided in the spring, while bent, is 

 now, on the unbending of the spring, communicated to the body moved. What 

 then was that force, or what kind of force was that, which resided in the spring, 

 while bent, and without motion ? Was it a bare pressure, or a moving force } 

 A vis mortua, or a vis viva ? It must be acknowledged, it was a vis mortua, a 

 bare pressure, and nothing more. But the force communicated to the body, 

 and which now resides in the body in motion, is a vis viva, a moving force. This 

 therefore is not the same force, nor a force of the same kind, as that which re- 

 sided in the bent spring. 



It will be said however, that the force of the bent spring is entirely exhausted 

 in giving the body its moving force. What then is it that is to be understood by 

 these words, the force of the spring is entirely exhausted? If the meaning be, 

 that the spring could not possibly give that same body any greater moving force, 

 than what it has already given, it is allowed : but this does not prove, that the 

 same spring, bent afresh to the same degree, or an equal spring equally bent, 

 cannot give a greater force to a greater body. 



But if the meaning of these words be, that the spring cannot give a greater 

 moving force to any body whatever, that this is taking for granted the very point 

 which is in dispute. For the opposite party pretend, that a body of 4 times the 

 bulk, will receive twice the moving force in twice the time, from the pressure of 

 the same spring in unbending itself, or in exhausting all its force. 



It is plain therefore, that the followers of Mr. Leibnitz have no right to say, 

 a body has such or such a force, because such or such a spring has put it in mo- 

 tion by unbending itself, or can be bent by it. This is not a position to be 

 taken for granted, but stands in need of a demonstration, which nobody has as 

 yet attempted to give, at least from any uncontroverted principle; and, till this 

 be done, the laying down any such position can have no other effect, than to 

 perplex the controversy more and more, without hopes of ever coming to an end 

 of it. 



For which reason Dr. J. takes a quite different method in what follows, and 

 lays down nothing, by way of principle or axiom, but what is allowed of by all 

 the world, or at least has never yet been contradicted a priori. 



Axiom 1 . — When a bent spring, by unbending itself, pushes a body before it, 

 the greater the body is, the more slowly will the spring unbend itself. 



jixiom 1. — The more any spring is bent, the greater is its pressure. 



