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 deg., 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.