VOL. LXXXV.] PHILOSOPHICAL TEANSACTIONS. 473 



length of the pipe, or making it an increasing cone, under certain limitations, 

 is a circumstance which, I confess, I can give no satisfactory reason for. 



The above-mentioned experiments were made principally with a view to ascer- 

 tain how far the theory of the motion of fluids can be applied; and the inquiry 

 has led to several circumstances which I believe have not been observed before. 

 That the theory is not applicable in all cases is manifest; but that it brings 

 out conclusions in many instances which agree very well with experiment is 

 undoubtedly true. This tends to show, either that the common principles of 

 motion cannot be applied to fluids, and that the agreement is accidental; or 

 that under certain circumstances and restrictions the application is just. Which 

 of these is the case, is not perhaps easy for the mind to satisfy itself about. 

 Nothing however which is here said, is done with any view to detract from the 

 merit of those celebrated authors. They have manifested uncommon penetra- 

 tion, and carried their inquiries on the subject to an extent, that nothing farther 

 can be hoped for or expected ; and if they had done nothing else in science, this 

 alone would have ranked them among the very first mathematicians. The fault 

 has been non artificis sed artis. 



Mr. Maclaurin, in his Treatise on Fluxions, has given a most admirable 

 illustration of the theory of Sir Isaac Newton. It is there a very principal 

 inquiry to determine the ratio of the force which generates the velocity of the 

 descending surface of the fluid to the force of gravity. Now according to that 

 theory, the pressure on the bottom of the vessel is wholly taken off at the 

 instant of time at which the water begins to flow ; and as this conclusion cannot 

 be admitted, we may hence learn, says the author, that this theory is not to be 

 considered as perfectly exact. It appears therefore to be an important point to 

 determine, what is the pressure of the fluid on the bottom of a vessel, compared 

 with its whole weight at the time the fluid is running out. This may be deter- 

 termined to a great degree of accuracy by experiments constructed in the follow- 

 ing manner. 



Let ABCD (fig. 16) be a pair of scales, and o the fulcrum ; at the end of the 

 arm c suspend a cylinder e, having an orifice rs, immediately under which place 

 a weight iv, so that the upper surface may be in the vena contracta, or at so 

 small a distance below it that gravity can have produced no sensible effect on the 

 effluent fluid. Stop the orifice ry, and fill the cylinder with a fluid, and balance 

 it by a weight w in the other scale. Then open the orifice, and the fluid will 

 run out and strike w, and then be caught in the scale d. Now when the orifice 

 is opened and the fluid flows out, the pressure on the bottom of the cylinder is 

 diminished, part of the fluid now not being supported, notwithstanding which 

 the equilibrium is still continued; which shows that the action of the fluid 

 against w is exactly equal to the loss of weight in the cylinder by the motion of 



VOL. XVII. 3 P 



