Steam-Engine. 427 



Having thus brought into an equation all the different ele- 

 ments from which this expenditure of heat results, we are able 

 to analyse the several effects produced by them. In the first 

 place, according to the experiments of Clement, Southern, and 

 Despretz, before mentioned, c' is sensibly constant at all tempe- 

 ratures at which we have yet been able to make observations, 

 and accordingly the expenditure will be always the same. As 

 to the elastic force F, we know that it augments according as 

 the temperature is raised. But It will be seen by the formula 

 that the density w', and consequently the expenditure of heal, 

 increases in proportion to F. Consequently if we take away the 

 factor (1 + /' . 0,00208), arising from the dilatation produced by 

 the increase of temperature, the expenditure necessary to pro- 

 duce the force F will be exactly proportional to this force, and 

 we shall neither gain nor lose any thing by giving it a greater 

 or less energy. But the influence of the factor (l + I' . 0,00208,) 

 which increases as the temperature is raised, diminishes the 

 expenditure in question, in proportion as the temperature be- 

 comes higher ; for if we operate, for instance, at 212, this factor 

 becomes 1,44096 ; and if at 320, it becomes 1,66560 ; so that 

 the relative expenditure in this last case, compared with that in 

 the first, with the same elastic force, is nearly in the ratio of 

 144 to 166, or nearly of 6 to 7. Such then is the saving of heat 

 that may be made in the formation of steam in the extremes of 

 temperature at which we have as yet operated. Accordingly if it 

 were true that high pressure engines have, over those of the ordi- 

 nary kind, an advantage as great as has been alleged, it must be 

 sought in something else beside the saving of fuel. But in order 

 to judge correctly of these engines it is necessary to take into 

 consideration another element, namely, the ulterior developement 

 of elastic power, which the steam thus formed is capable of fur- 

 nishing, when, after having been employed with its primitive 

 energy in the first cylinder, it is made to pass into another larger 

 cylinder where it dilates, undergoing a reduction of temperature 

 at the same time, in such a manner as always to fill the space 

 into which it is received, until at length it is condensed into water, 

 when it no longer has an elastic force, either equal or inferior to 

 the pressure of the atmosphere. Jt is manifest that this ulterior 

 developement of force must, in order that the whole effect may 

 be appreciated, be added to the mechanical power at the 



