Having defined compressed air, we must next define heat; for in dealing with compressed air, we are brought face to face with the complex laws of Thermodynamics. We cannot produce compressed air without also producing heat, and we cannot use compressed air as a power without producing cold. Based on the material theory of heat, we would say that when we take a certain volume of free air and compress it into a smaller space, we get an increase in temperature because we have the heat of one volume occupying less space, but no one at this date accepts the material theory of heat. Your distinguished director, Professor Thurston, in discussing "Steam and its Rivals," in the _Forum_, said: "The science of Thermodynamics teaches that heat and mechanical energy are only different phases of the same thing, the one being the motion of molecules, and the other that of masses." This is the accepted theory of heat. In other words, we do not believe that there is any such _thing_ as heat, but that what we call heat is only the sensible effect of motion. In the cylinder of an air compressor the energy of the piston is converted into molecular motion in the air and the result, or the equivalent, is heat. A higher temperature means an increased speed of vibration, and a lower temperature means that this speed of vibration is reduced. If I hold an open cylinder in my left hand and a piston in my right, and place the piston within the cylinder, I here have a confined volume of air at the temperature and the pressure of this room. These particles of air are in motion and produce heat and pressure in proportion to that motion. Now if I press the piston to a point in the center of the cylinder, that is, to one-half the stroke, I here decrease the distance between the cylinder head and the piston just one-half, hence each molecule of air strikes twice as many blows upon the piston and head in traveling the same distance and the pressure is doubled. We have also produced about 116 degrees of heat, because we have expended a certain amount of work upon the air; the air has done no work in return, but we have increased the energy of molecular vibration in the air and the result is heat. But what of this heat? What harm does it do? If I instantly release the piston which I hold at one-half stroke it will return to its original position, less only a little friction. I have, therefore, recovered all, or nearly all, the power spent in compressing the air. I have simply pressed a spring, and have let it recover. We see what a perfect spring compressed air is. We see the possibility of expending one horse power of energy upon air and getting almost exactly one horse power in return. Such would be the case provided we used the compressed air power _immediately and at the point where the compression takes place_. This is never done, but the heat which has been boxed up[1] in the air is lost by radiation, and we have lost power. Let us see to what extent this takes place.