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. [Illustration: Fig. 3.] 45. Or, again, let us take the inclined plane as represented in Fig. 3. Here we have a smooth plane and a weight held upon it by means of a power P, as in the figure. Now, if we overbalance P by a single grain, we shall bring the weight W from the bottom to the top of the plane. But when this has taken place, it is evident that P has fallen through a vertical distance equal to the length of the plane, while on the other hand W has only risen through a vertical distance equal to the height. Hence, in order that the principle of virtual velocities shall hold, we must have P multiplied into its fall equal to W multiplied into its rise, that is to say, P × Length of plane = W × Height of plane, or P/W = (Height.)/(Length.) _What Friction does._