Resistance of Liquids to Solid Bodies moving in them. 233 
locity, and we find the resistance to be nearly as great as when we 
strike a solid rock, because it requires a certain time for the particles 
of any liquid to move among themselves; and if the boat moved 
with a very great velocity, she would of course, rise entirely out of 
the water, and slide on it as though it were ice. 
If the boat and water were covered with clarified oil, she would, 
from the same cause, descend under the water; because the oil 
would cause a resistance about seventeen times greater than the wa- 
ter; and if the water and boat could be practically covered with al- 
cohol without mixture, the boat would have a small tendency to rise 
at great velocities, because the resistance of alcohol would be but 
one third of the resistance of water. ‘The laws of the resistance of 
liquids, in all the various circumstances in relation to it, have not 
been ascertained with the accuracy and precision which the present 
state of knowledge of other subjects seems to require; this may be 
owing in part, to some hasty generalizations of the early philoso- 
phers, and also to the abstruse nature of the subject. It is now gen- 
erally admitted, that the direct perpendicular resistance of a plane 
surface moving in a liquid of indefinite extent, and in a direction at 
right angles to the plane, is nearly equal to the product of the square 
of the velocity, the density of the liquid, and the area of the plane. 
This may be rigorously exact within certain limits, but may not be 
true when the velocities are very small or very great. It has also 
been admitted that when the plane is inclined to the direction of its 
motion, the resistance is proportional to the square of the sine of the 
angle of inclination. ‘This has been denied, and the resistance sta- 
ted to be proportional to the sine of the angle of inclination. Is it 
necessarily true, that this oblique resistance is proportional to the 
sines, or some other lines relating to circles or to some power of them ? 
And is it not possible that the proportion may have a nearer relation 
to some of the properties of a parabola or an ellipse, than to those 
of a circle? 
In 1778, Bossut and Condorcet made many experiments to as- 
certain the resistance of liquids. ‘The reservoir of water was two 
hundred feet long, one hundred feet wide, and eight and a half feet 
deep. ‘They used a solid in the form of a cube, whose side was five 
feet ; it was sunk four feet in the water, and to one of the sides were 
attached successively, triangular prows or bows of various angles, 
from twelve to one hundred and sixty eight degrees, and it was 
moved with different velocities, through a space of ninety six feet. 
Vou. XXVIII.—No. 2. 30 
° 
