6 W. J. M. Rankine on the Means of 



appears that the heat expended in overcoming external pres- 

 sure is equivalent to only 



56,085 foot-pounds, 

 leaving 



690,825 foot-pounds 



for the mechanical equivalent of the heat which disappears in 

 overcoming the mutual attraction of the particles of the water. 



On the contrary, the latent heat of expansion of a permanent 

 gas consists almost entirely of heat which disappears in over- 

 coming the external pressure, that which disappears in over- 

 coming the mutual attraction of the particles of the gas being 

 comparatively very small ; in fact, in all practical calculations 

 respecting air-engines, the latter quantity may be altogether 

 neglected without sensible error, and the latent heat of expan- 

 sion of the air treated as the exact equivalent of the mecha- 

 nical work performed by it in the act of expanding. 



For example, — the product of the volume, in cubic feet, of 

 one pound of air, at the temperature of 650° Fahrenheit, by its 

 pressure in pounds per square foot, is 59,074 foot-pounds. If 

 that pound of air be expanded under pressure, to 1J times its 

 original volume, and be still maintained at the constant tem- 

 perature of 650°, by being supplied with heat from an ex- 

 ternal source, the work performed by it in expanding, will be 

 59,074 x hyperbolic-logarithm of 1J = 23,953 foot-pounds ; 

 and this quantity will also be sensibly equal to the mecha- 

 nical equivalent of the heat supplied, and which disappears 

 during the expansion. 



In considering the performance of any thermo-dynamic 

 engine, it is evident that the heat which disappears in pro- 

 ducing increase of volume under pressure, is to be regarded 

 as the real source of power ; as it is a portion of this heat 

 which is actually converted into mechanical work, while the 

 heat expended in producing elevation of temperature, produces 

 merely a tendency to the development of power. 



6. Mode of Operation of Thermo-dynamic Engines in 

 general. — The mode of operation of an elastic substance in 

 performing mechanical work by the agency of heat, reduced to 

 its simplest form, consists in the continued repetition, either 



