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22 . CARNOT. 
pieces, by the aid of which forces of all sorts ordinarily 
produce effects which their direct action could not bring 
about. ‘Take, for instance, the stone-mason with his 
hand on the handle of a very simple machine, the winch 
of the lifting-jack or the roller ; he turns about enormous 
blocks, or inclines them to suit his convenience, or raises 
them to the summit of the highest buildings, when, with- 
out the machine, he could not stir them a hair’s breadth. 
At sight of these effects, the ignorant make great out- 
cry at the marvel; they persuade themselves that ma- 
chines multiply force, and this false idea, radically false, 
leads them into fantastic and generally very complicated 
conceptions, which take away an immense quantity of 
capital every year, in pure loss, from agriculture, and 
manufacturing industry, and commerce. 
With a force of any nature whatsoever, that which 
must be valued in money, that which the fabricator buys 
from the engineer, may be easily referred to a very sim- 
ple effect, of which every one has a clear idea. Let the 
force be supposed directly applied to the raising of a 
weight ; the height to which the force raises the weight 
in a certain time is observed, and these two data from 
experiment, the weight and the height, multiplied together 
form a product which is the exact value of the force em- 
ployed. This product, indeed, for a given time and the 
same height, cannot be augmented or diminished with- 
out the force augmenting or diminishing in the same 
proportion ; so that, for example, if it becomes double, 
triple, or decuple, it is the result of the force being mul- 
tiplied by two, three, or ten. 
The product, which gives the direct measure of a 
force, serves equally to measure it when it exercises its 
action against a resisting body by an intermediate ma- 
