VOL. XLIV.] PHILOSOPHICAL TRANSACTIONS. '221 



it, more in the received tbrm, though in fact they both coincide. For nothing 

 is more evident than that moving actions ought to be measured by their immediate 

 effects. If therefore the lengths gone through, and the velocities, unless any 

 one will obstinately have the velocity to be rather the cause, are the eifects of an 

 immediate action, and indeed the only ones, of which one does not depend on 

 the other, the moving actions will necessarily be in a ratio compounded of the 

 lengths and the velocities : ajud so, in equal times, in the duplicate ratio of the 

 velocities." 



Now in this answer it is plain that Bernoulli approves of the 2d demonstration 

 in appearance, but in reality condemns it, though with the greatest caution and 

 modesty. For he not only hints that the velocity is rather the cause than the 

 eftect of an action, but he restrains his assent to this condition, that one of the 

 effects mentioned by Leibnitz, viz. of the velocity and the length gone through, 

 does not depend on the other, or is not included in the other. Now as it is very 

 evident, that the length gone through does depend on the velocity, and is included 

 in it, it is plain that the demonstration is faulty in the opinion of Bernoulli. 



Leibnitz, in his next letter, gave a distinct and copious answer to many otherff 

 things, but to these tacit objections of Bernoulli he answers lightly, dissembling 

 their force, and as if treating of something else, only just says, " But as I now 

 estimate an action by the compound ratio of its principles, power and time ; so 

 I had estimated it a little before by the compound ratio of what it performs ; an 

 extensive or material effect, viz. of the length, which I usually call an effect xar' 

 i^oyriv, and an extensive or formal effect. For it is required that much should 

 be performed and soon. You see now that both the estimations agree together." 



By the obscurity of this answer, whether it be affected or natural to Leibnitz, 

 it is easily seen that he would have the velocity to be taken for the effect of an 

 action, which Bernoulli had hinted was rather the cause, but that he dared not 

 name it openly, though he understands it under the name of an intensive or 

 formal effect, which the action performs. Besides, as to Bernoulli's other ob- 

 jection, though the velocity is in the highest degree the effect of an action, as 

 well as the length gone through ; yet as one of these effects depends on the 

 other, and is included in it, and certainly the length gone through depends on 

 the velocity, an action ought not to be measured by both those effects ; as to 

 this, I say, he observes a profound silence. 



The second demonstration therefore seems to be given up by Lebinitz, as well 

 as Bernoulli ; and indeed in all their subsequent letters there is not the least 

 mention of it. Besides, that first demonstration, which comes to the same with, 

 the other, viz. a true with a false one, it seems not wholly free from exception, 

 either with Bernoulli or with Leibnitz himself. For Bernoulli, though he had 

 declared in April, that it quite satisfied him, that he acquiesced in it, and that 



