VOL. XXXII.] PHILOSOPHICAL TRANSACTIONS. 597 



Doctor intended was, from that velocity to deduce the equation of the Newto- 

 nian hyperbolic curve; for the Doctor had already determined the velocity of 

 the effluent water, or rather assumed it, viz. by supposing what Sir Isaac 

 Newton had done, viz. that water by the force of gravity falls freely, and in 

 falling is accelerated. 



Here the Doctor takes notice of an error, Michelotti, p. 112, 113, would 

 rashly fasten on Sir Isaac Newton, Huygens, and Mr. Keill, viz. that they 

 have supposed the force, by which the whole motion of the effluent water may 

 be produced, equal to the weight of a cylindrical column of water, whose base 

 is the hole, and height double that of the water contained in the vessel; this 

 Sir Isaac Newton had briefly but perspicuously demonstrated in the second 

 corol. of the aforesaid prop. And another demonstration of it might be 

 deduced from considering the entire hyperbolic cataract, which is equal to this 

 cylinder, and whose entire weight is spent on the descent of the water; but 

 that is unnecessary, since the same thing follows very evidently from Bernoulli's 

 own proposition, which Michelotti so often commends and so strenuously 

 defends. This will easily appear, if, laying aside for a while the consideration 

 of the column of water, incumbent on the hole, and making the calculation, 

 he would, from the mass of water running out at the hole in any given time, 

 and from the velocity with which Bernoulli has determined water to run out, 

 determine the motion of the water, and then find the weight which, by the 

 force of gravity, falling freely in the same given time, may produce the same 

 quantity of motion ; he will find this weight equal to that of double the column 

 of water incumbent on the hole, just as Sir Isaac Newton had determined it in 

 that corol. But the same weight, suspended at one arm of a balance, will be 

 kept in equilibrio by the impetus of the water, at its very first efflux out of the 

 hole, impinging in a continued stream on the other equal arm of the balance, 

 and falling down immediately after the impulse, which will easily appear on 

 making the calculation. 



Dr. Jurin would here also remove a prejudice which Michelotti, p. 113, and 

 others labour under. Sir Isaac Newton had demonstrated, prop. 37, lib. 2, 

 Princip. first edit, that water runs out at a hole in the bottom of a vessel with 

 that velocity, with which it might rise to half the height of the water con- 

 tained in the vessel. Experience is said to contradict this, by which it is dis- 

 covered, that the effluent water rises to the whole height; and Sir Isaac Newton 

 himself in the solution of the same problem, prop. 36, lib. 2, the second edit, 

 ascribes to the water that velocity with which it might rise to its whole height; 

 consequently he seems to contradict himself. But if this matter be accurately 

 and judiciously considered, it will be found to agree very well both with Sir 



