tion. The transformation of mechanical effect into heat involves no losses except those resulting from imperfect installation, and these may be so completely avoided that Dr. Joule was able by this method to determine the equivalent values of the two forms of energy. But, in attempting the inverse operation of effecting the conversion of heat into mechanical energy, we find ourselves confronted by the second law of thermo-dynamics, which says that, whenever a given amount of heat is converted into mechanical effect, another but variable amount descends from a higher to a lower potential, and is thus rendered unavailable.
In the condensing steam-engine this waste heat comprises that communicated to the condensing-water, while the useful heat, or that converted into mechanical effect, depends upon the difference of temperature between the boiler and condenser. The boiler-pressure is limited, however, by considerations of safety and convenience of construction, and the range of working temperature rarely exceeds 120° C., except in the engines constructed by Mr. Perkins, in which a range of 160° C., or an expansive action commencing at fourteen atmospheres, has been adopted with considerable promise of success, as appears from an able report on this engine by Sir Frederick Bramwell. To obtain more advantageous primary conditions we have to turn to the caloric or gas engine, because in them the co-efficient of efficiency, expressed by t' may be greatly increased. This value would reach a maximum if the initial absolute temperature t could be raised to that of combustion, and t' reduced to atmospheric temperature, and these maximum limits can be much more nearly approached in the gas-engine worked by a combustible mixture of air and hydrocarbons than in the steam-engine.
Assuming, then, in an explosive gas-engine a temperature of 1,500° C., at a pressure of four atmospheres, we should, in accordance with the second law of thermo-dynamics, find a temperature after expansion to atmospheric pressure of 600° C., and therefore a working range of 1500° - 600° 900°, and a theoretical efficiency of 1,500 274 about one half, contrasting very favorably with that of a good expansive condensing steam-engine, in which the range is 150 30 120° C, and the efficiency 150 274 7. A good expansive steam-engine is therefore capable of yielding as mechanical work two-seventh part of the heat communicated to the boiler, which does not include the heat lost by imperfect combustion, and that carried away in the chimney. Adding to these the losses by friction and radiation in the engine, we find that the best steam-engine yet constructed does not yield in mechanical effect more than one seventh part of the heat-energy residing in the fuel consumed. In the gas engine we have also to make reductions from the theoretical efficiency, on account of the rather serious loss of heat by absorption into the