ON THE TIIKOIIV OF Till: .STEAM-E.N(ilNE. 



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and o.^tiinateF tlio amonut of licat demanded and of fuel consumed in 

 their operation, assuming no other expenditure of heat than that required 

 ill an engine fr ;> f .on losses by conduction and radiation. Ho next, in a 

 simihir manner, apphe *ho theory to tlio steam-engine, proves tho fact of 

 the condensation of steam ihiring tho period of expansion, estimates the 

 amount of heat, fuel, and , ttfnu oxpended, and the tpiantity of work done, 

 and determines thns tho eliiciency of the engine. Ho makes a Sjjecial case 

 of the engine using su{)erheaied steam, as well as that of tho 'jacketed' 

 engine, considers tho supi^rheated steam-engine, and tlio binary vapour- 

 engine, and reconstructs \)e Panibour's problem. Applying the theory 

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

 steam pressure and in tho ratio of expausiou adopti'c ,, and including both 

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

 tlie efficiency of tho stea'u, and the probable consumption of fuel (assum- 

 ing a somewhat h>w elliciency of boiler), whicli table re[iresents tho limit 

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

 proached as the conditions of nractico approximate to those of tho ideal 

 cases taken, but which can never bo reached. 



As Rankine was not aware of tho often enormous diflference i)roduced 

 in the performance* of the steani-engino by the extra thermodynamic phe- 

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

 results of his calculations must be taken v>'itli the qualitication just stated 

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

 actual performance. The *'act 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 largo amount. 



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

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

 tions, and tho work of later engineers, and of physicists working upon tlie 

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

 the limitations set to tho 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 sizo of steam-engine, from 

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

 and all exjienses 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. Ho studied the action of explosive gas-engines, 

 and calculated the explosive energy of liquids heated under pressure. 

 Besides all this, llankine 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 largo 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. 



