of the Motion and Resistance of Fluids. 27 
liquids. Under the circumstances, therefore, of an indefinite 
number of bodies acting upon each other by repulsive powers, 
or by absolute contact under the uncertainty of the friction 
which may take place, and of what variation of effects may be 
produced under different degrees of compression, it is no won- 
der that our theory and experiments should be so often found 
to disagree. 
Sir Isaac Newton seems to have been well aware of all 
these difficulties, and therefore in his Principia he has de- 
duced his laws of resistance, and the principles upon which the 
times of emptying vessels are founded, entirely from experi- 
ment. He was too cautious to trust to theory alone, under all 
the uncertainties to which he appears to have been sensible it 
must be subject. He had, in a preceding part of that great 
work, deduced the general principles of motion, and applied 
them to the solution of problems which had never before been 
attempted ; but when he came to treat of fluids, he saw it was 
necessary to establish his principles upon experiments ; prin- 
ciples, not indeed mathematically true, like his general prin- 
ciples of motion before delivered, but, under certain limita- 
tions, sufficiently accurate for all practical purposes. 
The principle to be established in order to determine the 
time of emptying a vessel through an orifice at the bottom, is 
the relation between the velocity of the fluid at the orifice and 
the altitude of the fluid above it. Most writers upon this sub- 
ject have considered the column of fluid over the orifice as the 
expelling force, and from thence some have deduced the velo- 
city at the orifice to be that which a body would acquire in 
falling down the whole depth of the fluid; and others that ac- 
quired in falling through half the depth, without any regard 
E 2 
