474 PHILOSOPHICAL TRANSACTIONS. [|aNNO l/QS. 



the fluid through the orifice. In order therefore to find the diminution of the 

 weight on the bottom of the cylinder, we have only to find a weight equivalent 

 to the momentum of the fluid against w. 



Let AB (fig. 17) be a lever flat on the upper side, suspended by an horizontal 

 axis CD; L a scale hanging from it, which is to be balanced by a weight w; e is 

 the cylinder suspended to something immoveable at m, having its orifice rs as far 

 distant from ab as before it was from the weight in the scale; and let the orifice 

 and scale be equi-distant from cd. Stop the orifice, and fill the cylinder; then 

 on opening the orifice, let one person, by means of a cock at v on a pipe which 

 goes into a reservoir xyz, keep the fluid in the cylinder exactly at the same alti- 

 tude, and another put such a weight w into the scale l as shall keep ab exactly 

 in the same position ; then the weight lu is equivalent to the momentum of the 

 fluid against ab, together with the momentum of the fluid entering the top of 

 the cylinder through the pipe. To determine what weight is equivalent to this 

 latter momentum, take away the cylinder e and weight m, and bring ab up to 

 the pipe, and let the fluid act on it, and find what weight (i) put into the scale 

 will now keep ab horizontal, and this weight {v) will be equivalent to the mo- 

 mentum of the fluid flowing into the cylinder; hence w — z; is a weight equiva- 

 lent to the momentum of the fluid issuing out of the cylinder at the vena con- 

 tracta, and consequently equivalent to the diminution of the pressure on the 

 bottom after the opening of the orifice. In order to keep the fluid accurately at 

 the same altitude, I should propose to have a floating gage v (fig. 18) with a wire 

 standing perpendicularly on it, and entering a cylinder w attached to the side of 

 the vessel, and of a bore just large enough to give it a free motion; then the 

 cock must be opened and adjusted to give it such an aperture as will keep the top 

 of the wire on a level with the top of the cylinder. 



Or we may find the diminution of the pressure on the bottom on opening the 

 orifice in this manner. In fig. 16, take away the scale d and balance the cylinder 

 when filled, and let the end c of the beam be made flat at the point from which 

 the vessel is suspended. Then open the orifice of the vessel, having the same 

 provision before to keep it filled to the same altitude, and place such a weight at 

 c as shall preserve the equilibrium during the time the fluid is in motion, and 

 this weight is equivalent to iv in the former case. This method is the more 

 simple of the two; but the other includes a circumstance of some consequence, 

 that is, that the momentum of the efiiiient fluid is exactly equivalent to the 

 weight which the vessel loses. Having thus examined all the circumstances pro- 

 posed respecting the emptying of vessels, I proceed next to the consideration of 

 the doctrine of the resistance of bodies moving in fluids. 



When a body moves in a fluid, each particle, in theory, is supposed to act on 

 it undisturbed by the rest, or the fluid is conceived to act as if each particle, after 



