220 - On the Measure of 
the estimation of the forces of moving bodies, 
itis, properly speaking, the doctrine of Galileo 
and of Newton. PA 
But we have seen that the same principle 
has been still farther extended, and applied to 
explain the phenomena of force producing 
changes of figure in masses of matter. 
No indications of force are more constantly 
presented to our notice than those which con- 
sist of mechanical changes of figure.—The 
fabrication of every thing that is useful or 
convenient to us is accomplished chiefly by 
the application of mechanical force to pro- 
duce change of figure. The grinding of 
corn, the expressing of oil from seed, the 
sawing of timber, the hammering and rolling 
of metals, the driving of piles,—are all ex- 
amples of moving force producing changes of 
figure; and although, in all these cases the 
effects produced are of a complicated kind, yet 
the moving forces by which they are produced 
may be estimated with tolerable’ precision. 
The force expended in driving piles into the 
earth,. has been.examined by many mathema- 
ticians. In this case, the whole force of a 
body m motion is supposed to be expended in 
driving the pile, and this quantity of force is 
understood to be as the height from which the 
body falls, or as the square of its velocity. 
