VOL. XXXII.] PHILOSOPHICAL TRANSACTIONS. SQQ 



this theorem ; since in a given time an equal mass of blood runs through the 

 aorta and capillary arteries, and the length of the tube, consisting of the aorta 

 and capillary arteries, is greater than the aorta alone. This the Doctor has the 

 rather observed, because not only Michelotti, but other mathematical writers, 

 in treating of forces, which either put into motion the liquor, contained in 

 pipes filled with it, or stop its efflux, consider only the mass and velocity of the 

 effluent fluid, without regarding the length of the pipes; for, cseteris paribus, 

 a fluid is with greater difficulty, either thrown out of a full pipe, or stopped in 

 its efflux, the longer the pipe is; since the whole mass of fluid contained in 

 the pipe must be put into motion before any part can flow out at the orifice; as 

 also the entire mass be necessarily stopped, to hinder the efflux of any part just 

 ready for it. 



* The principles of Bernoulli's demonstration of the velocity of water run- 

 ning out of a hole of a full vessel, are, that the lowest drop of the liquor, or 

 that immediately incumbent on the hole of the vessel, is considered as pressed 

 on, or, as he calls it, animated by a certain accelerating gravity, which is to 

 the natural gravity, as the height of the water, or of the whole liquor, incumbent 

 on the hole of the vessel, to the height of the small drop; that is, as the abso- 

 lute weight of the column of water, insisting on the hole of the vessel, to the 

 absolute weight of the drop; for thus, nothing remains but to find how great 

 a velocity the drop, animated by that greater gravity, may acquire, when it 

 falls through a line equal to its height; that is, after it has got quite out of the 

 hole; for it is pressed on by the whole column of water, consequently animated 

 by the greater gravity, so long as any of the drop, which he supposes a small 

 solid column, remains above the hole.' 



The weakness of this foundation appears thus; since Bernoulli makes use of 

 nothing to animate, as he calls it, the lowest drop with the aforesaid accele- 

 rating gravity, but pression alone, or the weight of the column of water in- 

 sisting on the hole: let all the water, surrounding that column, be supposed 

 to be frozen, and the column to fall without any resistance along the smooth 

 surface of the ice; then as long as the hole is shut up, the small drop next the 

 hole will be pressed on by the whole weight of the incumbent column of water, 

 in the manner Bernoulli supposes. Now let the hole be opened, and a free exit 

 be given to the water. What will then be the consequence? will the lowest 

 drop be urged or animated by the accelerating gravity, which is to the natural 

 gravity, as the height of the whole water incumbent on the hole, to the height 

 of the drop? by no means; but it will be urged only by its own natural acce- 

 lerating gravity ; for, as soon as the lowest drop begins to descend, though 

 with an infinitely small velocity, it will no longer be urged by the weight of the 



