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34 is lowered, will exactly equal the large weight, multiplied into that through which it is raised.

This principle, known as that of virtual velocities, enables us to perceive at once our true position. We see that the world of mechanism is not a manufactory, in which energy is created, but rather a mart, into which we may bring energy of one kind and change or barter it for an equivalent of another kind, that suits us better—but if we come with nothing in our hand, with nothing we shall most assuredly return. A machine, in truth, does not create, but only transmutes, and this principle will enable us to tell, without further knowledge of mechanics, what are the conditions of equilibrium of any arrangement.

For instance, let it be required to find those of a lever, of which the one arm is three times as long as the other. Here it is evident that if we overbalance the lever by a single grain, so as to cause the long arm with its power to fall down while the short one with its weight rises up, then the long arm will fall three inches for every inch through which the short arm rises; and hence, to make up for this, a single kilogramme on the long arm will balance three kilogrammes on the short one, or the power will be to the weight as one is to three.

45. Or, again, let us take the inclined plane as represented in Fig. 3.