390 MOTION AND RESISTANCE OP FLUIDS. 



base; and in all cases the velocity, cccteris paribus, will depend on 

 the ratio between the magnitude of the orifice and that of ffcc surface 

 of the fluid. Conclusions thus contrary to matter of fact show, either 

 that the principle assumed is not true, or that the deductions from it 

 are not applicable to the present case. The most celebrated theories 

 on this subject are those of D. Bernouilli and M. D'Alembert; the 

 former deduced his conclusions from the principle of the conserva- 

 tio virium vitarum, or as he calls it, the equalitas inter dcscensum 

 actualem ascensumque potentialem, where, by the descensus 

 actualis he means the actual descent of the ccsitre of gravity, and 

 by the ascensus potentiates, he means the ascent of the centre of 

 gravity, if the fluid which flows out could have its motion directed 

 upwards ; and the latter from the principle of the equilibrium 

 of the fluid. This principle of M. D'Alembert leads immediately 

 to that assumed by D. Bernouilli, and consequently they both de- 

 duce the same fluxional equation, the fluent of which expresses the 

 relation between the velocity of the fluid at the orifice, and the per- 

 pendicular altitude of the fluid above i f . How far the principles 

 here assumed can be applied in our reasoning on fluids, can only be 

 determined by comparing the conclusions deduced from them with 

 experiments. 



In order to determine whether there was any pressure of the fluid 

 against the sides of the pipes as it passed through in all their dif- 

 ferent situations, some small holes were pierced in them at different 

 parts. In the cylindrical pipes, and those in the form of increasing 

 cones, the fluid passed by the holes without being projected out, or 

 without having the least tendency to issue through them ; but in 

 the decreasing cones the fluid spouted out at the holes. In the 

 former cases therefore there was no pressure against the sides of the 

 pipes, but in the latter case there was. 



In respect to the motion of the fluid through any of the pipes, I 

 found no difference whether I stopped the pipe at the end of the 

 tube which enters into the vessel, in which case the motion began 

 when the tubes were empty, or whether at the other end, in which 

 case they were full at the commencement of the motion. That the 

 fluid should flow into the pipe faster than it would through an ori- 

 fice, may probably, in part at least, be owing to the adhesion of 

 the fluid to the pipe, and be thus explained. Though the horizon- 



