43. To impress this truth still more strongly, let us take quite a different machine, such as the hydrostatic press. Its mode of action will be perceived from Fig. 2. Here we have two cylinders, a wide and a narrow one, which are connected together at the bottom by means of a strong tube. Each of these cylinders is provided with a water-tight piston, the space beneath being filled with water. It is therefore manifest, since the two cylinders are connected together, and since water is incompressible, that when we push down the one piston the other will be pushed up. Let us suppose that the area of the small piston is one square centimetre,[3] and that of the large piston one hundred square centimetres, and let us apply a weight of ten kilogrammes to the smaller piston. Now, it is known, from the laws of hydrostatics, that every square centimetre of the larger piston will be pressed upwards with the force of ten kilogrammes, so that the piston will altogether mount with the force of 1000 kilogrammes--that is to say, it will raise a weight of this amount as it ascends. Here, then, we have a machine in virtue of which a pressure of ten kilogrammes on the small piston enables the large piston to rise with the force of 1000 kilogrammes. But it is very easy to see that, while the small piston falls one metre, the large one will only rise one centimetre. For the quantity of water under the pistons being always the same, if this be pushed down one metre in the narrow cylinder, it will only rise one centimetre in the wide one. Let us now consider what we gain by this machine. The power of ten kilogrammes applied to the smaller piston is made to fall through one metre, and this represents the amount of energy which we have expended upon our machine, while, as a return, we obtain 1000 kilogrammes raised through one single centimetre. Here, then, as in the case of the pulleys, the return of energy is precisely the same as the expenditure, and, provided we ignore friction, we neither gain nor lose anything by the machine. All that we do is to transmute the energy into a more convenient form--what we gain in power we lose in space; but we are willing to sacrifice space or quickness of motion in order to obtain the tremendous pressure or force which we get by means of the hydrostatic press. _Principle of Virtual Velocities._ 44. These illustrations will have prepared our readers to perceive the true function of a machine. This was first clearly defined by Galileo, who saw that in any machine, no matter of what kind, if we raise a large weight by means of a small one, it will be found that the small weight, multiplied into the space through which it is lowered, will exactly equal the large weight, multiplied into that through which it is raised.