224 PHILOSOPHICAL TRANSACTIONS. [aNNO 1746. 



which there is no controversy with the Leibnitzians, and which being the same 

 with those given by Wolf, are here omitted. 



Theor. 10. — Actions, by which the same effect is produced, are as the velo- 

 cities. It is on this theorem that the whole matter turns : if it be true, the 

 Leibnitzian doctrine is to be embraced ; if not, it is to be rejected : therefore its 

 demonstration must be scrupulously examined. It is divided by Wolf into 3 

 cases : but as the 2d and 3d depend on the first, we shall need only consider this 

 one. Mr. W. says, " when moveables are equal, and the same effect is pro- 

 duced in different times, the velocities will be reciprocally as the times in which 

 it is produced ; that is, a body, which produces an effect in the time \t, is moved 

 with the velocity 2v, when another, which produces the effect in the time t, is 

 moved with the single velocity v ; and so on. Now it is evident that a uniform 

 action is double, which produces the same effect in half the time, triple which is 

 subtriple, and so on." 



But do you say, Mr. Wolf, that this is evident ? What if I should deny it ? 

 What if I should say that any action, which produces the same effect, is the 

 same, in whatever time it produces it ? This is the very supposition of Leibnitz, 

 of which, in his letter to Bernoulli in 1 6g6, he says he has not discovered a 

 method of demonstrating a priori, and in his letter to yourself in 1711, he says 

 is still to be demonstrated. And yet you do not endeavour to demonstrate it, but 

 say it is evident. Now I deny its being evident, and thus your demonstration 

 falls to the ground, and the supposition along with it. 



But before substituting a new one, let us consider a little what is understood 

 by action, and what by effect. Wolf, after the example of Leibnitz, has omitted 

 the definition of action. He only distinguishes what is a pure action, viz. that 

 which is free from all impediment ; and what is a uniform acfion, viz. that which 

 increases in proportion to the time : but what he means by action itself is no- 

 where determined. But till this is done, nothing can be demonstrated, as Ber- 

 noulli advised Leibnitz long since. 



If I might venture to supply this defect, I would ascribe the same definition 

 to action, which Wolf has given of effect ; since there seems to be no other 

 difference between action and effect, than that action, if I may so speak, is an 

 effect in fieri, and effect an absolute action, or one that is perfected. For in 

 Wolfs example, a vis viva is that which transfers a moveable through a space ; 

 therefore the action of a vis viva is the translation of a moveable through a space ; 

 and the effect of a vis viva, is also the translation of a moveable through a space ; 

 or rather, an effect is a moveable already transferred through the same space. 



But generally an action is the preceder of an effect : or rather, an action is 

 that by which any thing is effected ; but an effect is the thing itself which is ef- 

 fected. For example, if I write a page, my action will be the writing of a page, 



