ON THE THEORY OF THE STEAM-ENGINE. 575 



and estimates the amount of heat demanded and of fuel consumed in 

 then* operation, assuming no other expenditure of heat than that required 

 in an engine free from losses hy conduction and radiation. He next, in a 

 similar manner, applies the theory to the steam-engine, proves the fact of 

 the condensation of steam during the period of expansion, estimates the 

 amount of heat, fuel, and steam expended, and the quantity of work done, 

 and determines thus the efficiency of the engine. He makes a special case 

 of the engine using superheated steam, as well as that of the ' jacketed ' 

 engine, considers the superheated steam-engine, and the binary vapour- 

 engine, and reconstructs De Pambour's problem. Applying the theory 

 of the steam-engine to a considerable number of cases, differing in the 

 steam pressure and in the ratio of expansion adopted, and including both 

 condensing and non-condensing engines, he constructs a table exhibiting 

 the efficiency of the steam, and the probable consumption of fuel (assum- 

 ing a somewhat low efficiency of boiler), which table represents the limit 

 of efficiency under the assumed conditions, a limit which may be ap- 

 proached as the conditions of practice approximate to those of the ideal 

 cases taken, but which can never be reached. 



As Rankine was not aware of the often enormous difference produced 

 in the performance of the steam-engine by the extra thermodynamic phe- 

 nomena involved in its operation, he does not indicate the fact that the 

 results of his calculations must be taken with the qualification just stated 

 above, and his figures are still sometimes supposed to represent those of 

 actual performance. The fact is, however, that the consumption of steam 

 and of fuel in actual practice always considerably exceeds those obtained 

 by the solution of the thermodynamic problem, and, often, as already 

 stated, exceeds that quantity by a very large amount. 



Since the time of Rankine's and Clausius' investigations, the thermo- 

 dynamic theory of the steam-engine has received no important modifica- 

 tions, and the work of later engineers, and of physicists working upon the 

 general subject, has been confined to the study, experimental or other, of 

 the limitations set to the application of this theory by the influence of 

 other physical phenomena. 



Rankine's work included the construction of a remarkably exact, 

 though hypothetical, equation expressing the relation of temperatures 

 and pressures of vapours, based upon his theory of ' molecular vortices,' 

 a comparison of the efficiencies of air and steam-engines working between 

 the same limits of temperature, and an exceedingly beautiful method of 

 graphically determining the most economical size of steam-engine, from 

 the commercial point of view, the quantity of power required being given, 

 and all expenses being calculable. He defined and outlined the science 

 of ' energetics,' established the beginnings of a system of graphical 

 thermodynamics, including the representation of the action of steam in 

 the compound engine. He studied the action of explosive gas-engines, 

 and calculated the explosive energy of liquids heated under pressure. 

 Besides all this, Rankine performed an enormous amount of work in 

 mathematical physics, in hydrodynamics, in hydromechanics, in the theory 

 of naval architecture, and in the application of mechanics to general 

 engineering. Several important text-books, a large volume on ship- 

 building, and other works, with an unknown number of papers, published 

 and unpublished, form a monument to the power and industry of this 

 wonderful man and remarkable genius, that may be looked upon as perhaps 

 the greatest wonder of the intellectual world. 



