232 Resistance of Liquids to Solid Bodies moving an them. 
tion; and that if the boat was urged to a velocity of ten, or twelve 
miles an hour, the wave entirely subsided, the bow of the boat be- 
ing gradually raised out of the water as the velocity increased, and 
that a less proportional force was required to move her at the great- 
er, than at the lesser velocities. 
These were all received as startling facts, and caused much theo- 
retical speculation; but they are only such effects as should natur- 
ally result from the laws of resistance, which have been determined 
with considerable accuracy, and some of the effects intimated long 
ago, by the French philosophers, to wit; by D’Alembert, in 1743; 
by La Place, in 1776; by Bossut, in 1778; by La Grange, in 
1786 ; by Coulomb, in 1800, and by many others at different times 
in other countries. 
La Grange ascertained, that a wave of water, where it was one 
foot deep, moved 5.495 feet per second, and that the velocity of 
waves of water of different depths, are as the square roots of the 
depths; consequently, the wave in a canal which is four feet deep, 
will move 10.99 feet per second, or about seven and a half miles 
an hour. As the time in which a pendulum performs its oscillations 
is in a certain proportion to its length, and not in proportion to the 
magnitude or intensity of the force which first caused its motion ; 
so the velocity of waves, being a similar motion, is in a certam pro- 
portion to the depth of the water, and not to the impulse of the boat 
which produces them. We ought therefore to expect, as the legiti- 
mate consequence of the long established premises—that as the velo- 
city of the wave in a canal depends only on the depth of the water, 
the boat, when urged with a greater velocity, must pass ahead of the 
wave, which will then subside—the cause of its rise and continuance 
having ceased to act. 
We here refer to ordinary circumstances, where the breadth of 
the canal is three or four times the breadth of the boat, so that the 
wave has its natural action, and not to a canal so narrow, that the 
boat necessarily pushes the water before her like a piston. 
The partial rising of the boat out of the water at great velocities, 
is caused by the inertia and the mutual attraction of the particles 
of the liquid, and because the air opposes comparatively, very little 
resistance, or about seven hundred times less than water. 
If we take a solid body whose specific gravity is equal to, or great- 
er than that of water, and put it into the water very slowly, we per- 
ceive but very little resistance ; but strike the water with great ve- 
