Before explaining the principle upon which the gas-engine and every other hot-air engine depends, I shall remind you of a few data with which most of you are already familiar.  The volume of every gas increases with the temperature; and this increase was the basis of the air thermometer—­the first ever used.  It is to be regretted that it was not the foundation of all others; for it is based on a physical principle universally applicable.  Although the volume increases with the temperature, it does not increase in proportion to the degrees of any ordinary scale, but much more slowly.  Now, if to each of the terms of an arithmetical series we add the same number, the new series so formed increases or decreases more slowly than the original; and it was discovered that, by adding 461 to the degrees of Fahrenheit’s scale, the new scale so formed represented exactly the increment of volume caused by increase of temperature.  This scale, proposed by Sir W. Thomson in 1848, is called the “scale of absolute temperature.”  Its zero, called the “absolute zero,” is 461 deg. below the zero of Fahrenheit, or 493 deg. below the freezing point of water; and the degree of heat measured by it is termed the “absolute temperature.”  It is often convenient to refer to 39 deg.  Fahr. (which happens to be the point at which water attains its maximum density), as this is the same as 500 deg. absolute; for, counting from this datum level, a volume of air expands exactly 1 per cent. for 5 deg., and would be doubled at 1,000 deg. absolute, or 539 deg.  Fahr.

Whenever any body is compressed, its specific heat is diminished; and the surplus portion is, as it were, pushed out of the body—­appearing as sensible heat.  And whenever any body is expanded, its specific heat is increased; and the additional quantity of heat requisite is, as it were, sucked in from surrounding bodies—­so producing cold.  This action may be compared to that of a wet sponge from which, when compressed, a portion of the water is forced out, and when the sponge is allowed to expand, the water is drawn back.  This effect is manifested by the increase of temperature in air-compressing machines, and the cold produced by allowing or forcing air to expand in air-cooling machines.  At 39 deg.  Fahr., 1 lb. of air measures 121/2 cubic feet.  Let us suppose that 1 lb. of air at 39 deg.  Fahr. = 500 deg. absolute, is contained in a non-conducting cylinder of 1 foot area and 121/2 feet deep under a counterpoised piston.  The pressure of the atmosphere on the piston = 144 square inches x 14.7 lb., or 2,116 lb.  If the air be now heated up to 539 deg.  Fahr. = 1,000 deg. absolute, and at the same time the piston is not allowed to move, the pressure is doubled; and when the piston is released, it would rise 121/2 feet, provided that the temperature remained constant, and the indicator would describe a hyperbolic curve (called an “isothermal”) because the temperature would have remained equal throughout.