5Q8 PHILOSOPHICAL TRANSACTIONS. [aNNO 1722. 



Isaac Newton's first and second solutions, and likewise with experience; for, 

 in his second solution, he supposes the jet of water narrower in diameter at a 

 small distance from the hole, than in the hole itself, in the ratio of 21 to 25; 

 therefore the section of the jet at that distance, is to the hole itself, as 21 X 

 21 to 25 X 25, that is, as 1 to \/2 nearly. And since the same quantity of 

 water flows in a given time, either through the section of the hole, or that of 

 the contracted jet, and consequently the velocities of the water in these sections 

 are reciprocally as the sections themselves, the velocity of the water in the hole 

 will be to the velocity of that in the contracted jet, as 1 to y'2; consequently 

 if the velocity in the contracted jet be such, as that the water can rise to the 

 whole height of that contained in the vessel, the velocity of the water will not 

 be greater in the hole itself, than what can raise it to half the height; these 

 two solutions therefore are consistent with each other and experience; for if by 

 either of the solutions, from the given velocity with which water is supposed 

 to pass either through a hole, or contracted jet, by calculation the quantity of 

 water to run out be found ; the same will be found to agree nearly with the 

 quantity of water discovered by experiments; and even Sir Isaac Newton's own 

 experiment, taking a hole whose diameter is f parts of an inch, agrees with 

 this calculation ; as also several other experiments with holes of smaller dia 

 meters, made at London; it is true, the experiments made by the accurate 

 Poleni differ somewhat from these, but yet they give a less quantity of water 

 than according to this calculation, and never a greater, because probably the 

 vessels were narrower in proportion to the size of the holes. 



There still remains one animadversion more, or rather scruple, p. 101, 102, 

 arising hence, that in corol. 17, theor. 3, of the abovementioned dissertation, 

 Dr. Jurin had supposed the motion or impetus of the blood to be greater in all 

 the capillary arteries taken together than in the aorta itself; to explain this, 

 Michelotti would fasten on the Doctor an hypothesis of a greater density of 

 blood in the capillary arteries than in the aorta. Dr. Jurin disowns any such 

 hypothesis, having deduced the corol. from the foregoing theor. which treats 

 of the motion of water running through any full pipe; whence it appears, that 

 the blood is no otherwise considered in his corollaries than as it is fluid, and 

 resembles water. But Michelotti's scruple appears to proceed from his taking 

 the impetus of the blood to be the quantity of its motion, produced by multi- 

 plying the velocity into the mass, running through in a given time; which is 

 quite different from Dr. Jurin's motion or impetus, he having in that theorem 

 supposed it equal to the motion of a mass of water, which runs out of a pipe 

 in any given time, and whose velocity is such, as in the same time to run over 

 a space equal to the length of the pipe. The aforesaid corol. easily flows from 



