5Q6 PHILOSOPHICAL TRANSACTIONS. [aNNO 1722. 



Since this motion then was what the Doctor always meant by the motion of 

 running waters, as plainly appears by all his propositions, he thought he might 

 justly allege, that this motion had not hitherto been defined by any one, as far 

 as he knew; no mathematician having even so much as hinted at it; the Doctor 

 is therefore surprised, that neither Michelotti nor John Bernoulli were aware 

 that in the preface to that dissertation, so often cited and so much censured by 

 Michelotti, he did not so much as mention the velocity with which water runs 

 out at a hole, much less the velocity determined by Bernoulli. 



In order to define the said motion, the Doctor needed no other than his 

 third general theorem ; but since he thought the property of the Newtonian 

 hyperbolic curve, in which Sir Isaac Newton forms the cataract of the descend- 

 ing water, not unworthy the consideration of geometricians, he would by the 

 bye premise some things about it, as taken from prop. 36, lib. 2, Princip. 

 Mathem. Philos. Nat. 



For, it is plain that such a cataract should be formed by water descending 

 freely, and accelerated in the manner of all other heavy bodies, witliout any 

 other water surrounding it. And even if the cataract of water be surrounded 

 with a hollow crust of ice, exactly answering to its figure, and by reason of 

 its extreme polish making no resistance to it; the cataract of water will not in 

 the least press on the ice, but only touch it and descend quite freely; whence 

 no alteration will be produced either in the figure, or velocity of the descending 

 cataract. But if the circumambient ice be dissolved, there is no manner of 

 occasion for such a strong battery as Michelotti, p. 128, 129, 130, and likewise 

 John Bernoulli, have raised to break down the Doctor's slender cataract; since 

 Sir Isaac Newton himself has quite dissolved it, when he says, Princip. p. 304, 

 Liquescat jam glacies in vase, &c. 



The Doctor does not deny, but that there is some difference between the 

 case as laid down by Sir Isaac Newton, and by himself; for the cylinder of ice 

 which the former supposes to descend with a given uniform velocity, and to dis- 

 solve as soon as it touches the surface of the water, contained in the vessel, 

 that the vessel may be always kept equally full, the Doctor has omitted, and 

 instead of it has supposed an infinite surface of water, that by that means he 

 might represent the whole solid or hyperbolic cataract : yet this position alters 

 nothing, either in the velocity or motion of the running water. 



What S. Michelotti says, p. 127, that the Doctor begs the question; and a 

 little lower, that the question therefore ceases, and that the whole demonstra- 

 tion becomes an hypothesis; this the Doctor does not understand: for in loc. 

 citat. the question was not about the velocity of the effluent water, nor was 

 there any demonstration adduced to prove that velocity; but the only thing the 



