£8 Mr. Vince's Observations on the Theory 
to the magnitude of the orifice ; whereas it is manifest from 
experiment, that the velocity at the orifice, the depth of the 
fluid being the same, depends upon the proportion which the 
magnitude of the orifice bears to the magnitude of the bottom 
of the vessel, supposing, for instance, the vessel to be a cylin- 
der standing on its base ; and in all cases the velocity, cceteris 
paribus , will depend upon the ratio between tlie magnitude of 
the orifice and that of the 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 
upon this subject are those of D. Bernouilli and M! d'Alem- 
bert ; the former deduced his conclusions from the principle 
of the conservatio virium vivarum, or as he calls it, the equali - 
tas inter descensum actualem ascensumque potentialem, where by 
the descensus actualis he means the actual descent of the centre 
of gravity, and by the ascensus potentials 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'Alem- 
bert leads immediately to that assumed by D. Bernouilli, 
and consequently they both deduce the same fluxional equa- 
tion, the fluent of which expresses the relation between the 
velocity of the fluid at the orifice, and the perpendicular alti- 
tude of the fluid above it. How far the principles here as- 
sumed can be applied in our reasoning upon fluids, can only be 
determined by comparing the conclusions deduced from them 
with experiments. 
The fluxional equation above mentioned cannot in general 
be integrated, and therefore the relation between the velocity 
