{by volume 0.788 N + 0.197 O + 0.001 CO2 + 0.014 H2O
by weight 0.771 N + 0.218 O + 0.009 CO2 + 0.017 H2O

This law is, however, subject to some apparent exceptions. Carbon burned in protoxide of nitrogen, or laughing gas, N2O, produces about 38 per cent. more heat than the same substance burned in pure oxygen, notwithstanding that the work of decomposing the protoxide of nitrogen has to be performed. In marsh gas, or methane, CH4, again, the energy of combustion is considerably less than that due to the burning of its carbon and hydrogen separately. These exceptions probably arise from the circumstance that the energy of chemical action is absorbed to a greater or less degree in effecting molecular changes, as, for example, the combustion of 1 pound of nitrogen to form protoxide of nitrogen results in the absorption of 1,157 units of heat. Berthelot states, as one of the fundamental principles of thermochemistry, "that the quantity of heat evolved is the measure of the sum of the chemical and physical work accomplished in the reaction"; and such a law will no doubt account for the phenomena above noted. The equivalent heat of combustion of the compounds we have practically to deal with has been experimentally determined, and therefore constitutes a secure basis on which to establish calculations of the caloric value of fuel; and in doing so, with respect to substances composed of carbon, hydrogen, and oxygen, it is convenient to reduce the hydrogen to its heat-producing equivalent of carbon. The heat of combustion of hydrogen being 62,032 units, that of carbon 14,544 units, it follows that 4.265 times the weight of hydrogen will represent an equivalent amount of carbon. With respect to the oxygen, it is found that it exists in combination with the hydrogen in the form of water, and, being combined already, abstracts its combining equivalent of hydrogen from the efficient ingredients of the fuel; and hence hydrogen, to the extent of 1/8 of the weight of the oxygen, must be deducted. The general formula then becomes:

Heat of combustion = 14,544 {C + 4.265 (H-(O/8))},

and water evaporated from and at 212°, taking 966 units as the heat necessary to evaporate 1 pound of water,

lb. evaporated = 15.06 {C + 4.265 (H-(O/8))},

carbon, hydrogen, and oxygen being taken at their weight per cent. in the fuel. Strictly speaking, marsh gas should be separately determined. It often happens that available energy is not in a form in which it can be applied directly to our needs. The water flowing down from the mountains in the neighborhood of the Alpine tunnels was competent to provide the power necessary for boring through them, but it was not in a form in which it could be directly applied. The kinetic energy of the water had first to be changed into the potential energy of air under pressure, then, in that form, by suitable mechanism, it was used with signal success to disintegrate and excavate the hard rock of the tunnels. The energy resulting from combustion is also incapable of being directly transformed into useful motive power; it must first be converted into potential force of steam or air at high temperature and pressure, and then applied by means of suitable heat engines to produce the motions we require. It is probably to this circumstance that we must attribute the slowness of the human race to take advantage of the energy of combustion. The history of the steam engine hardly dates back 200 years, a very small fraction of the centuries during which man has existed, even since historic times.

The apparatus by means of which the potential energy of fuel with respect to oxygen is converted into the potential energy of steam, we call a steam boiler; and although it has neither cylinder nor piston, crank nor fly wheel, I claim for it that it is a veritable heat engine, because it transmits the undulations and vibrations caused by the energy of chemical combination in the fuel to the water in the boiler; these motions expend themselves in overcoming the liquid cohesion of the water and imparting to its molecules that vigor of motion which converts them into the molecules of a gas which, impinging on the surfaces which confine it and form the steam space, declare their presence and energy in the shape of pressure and temperature. A steam pumping engine, which furnishes water under high pressure to raise loads by means of hydraulic cranes, is not more truly a heat engine than a simple boiler, for the latter converts the latent energy of fuel into the latent energy of steam, just as the pumping engine converts the latent energy of steam into the latent energy of the pumped-up accumulator or the hoisted weight.

If I am justified in taking this view, then I am justified in applying to my heat engine the general principles laid down in 1824 by Sadi Carnot, namely, that the proportion of work which can be obtained out of any substance working between two temperatures depends entirely and solely upon the difference between the temperatures at the beginning and end of the operation; that is to say, if T be the higher temperature at the beginning, and t the lower temperature at the end of the action, then the maximum possible work to be got out of the substance will be a function of (T-t). The greatest range of temperature possible or conceivable is from the absolute temperature of the substance at the commencement of the operation down to absolute zero of temperature, and the fraction of this which can be utilized is the ratio which the range of temperature through which the substance is working bears to the absolute temperature at the commencement of the action. If W = the greatest amount of effect to be expected, T and t the absolute temperatures, and H the total quantity of heat (expressed in foot pounds or in water evaporated, as the case may be) potential in the substance at the higher temperature, T, at the beginning of the operation, then Carnot's law is expressed by the equation:

W = H (T - t)
T

I will illustrate this important doctrine in the manner which Carnot himself suggested.