OX TJCE THEORY OF THE STEAM-ENGINE. 573 



engines, in the process of change of volume and temperature, while 

 following the series of changes which gives the means of transformation 

 of heat into power with final restoration of the fluid to its initial condition, 

 showing that such a complete cycle must be traversed in order to deter- 

 mine what proportion of the heat energy available can be utilised by 

 conversion into mechanical energy. This is one of the most essential of 

 all the principles comprehended in the modern science. This ' Carnot 

 Cycle ' was afterward represented graph ically by Clapeyron. 



Carnot shows that the maximum possible efficiency of fluid is attained, 

 in heat-engines, by expanding the working fluid from the maximum 

 attainable temperature and pressure down to the minimum temperature 

 and pressure that can be permanently maintained on the side of conden- 

 sation or rejection, i.e., if we assume expansion according to the hyper- 

 bolic law, by adopting as the ratio of expansion the quotient of maximum 

 pressure divided by back pressure. He farther shows that the expansion, 

 to give maximum efficiency, should be perfectly adiabatic. These prin- 

 ciples have been recognised as correct by all authorities from the time of 

 Carnot to the present time, and have been not infrequently brought 

 forward as new by minor later writers unfamiliar with the literature of 

 the subject. Introducing into the work of Carnot the dynamical relation 

 of heat and work, a relation, as shown by other writings, well under- 

 stood if not advocated publicly by him, the theory of the steam-engine 

 becomes well defined and substantially accurate. The Count de Pambonr, 

 writing in 1835, and later, takes up the problem of maximum efficiency 

 of the steam-engine, shows the distinction to be drawn between the 

 efficiency of fluid and efficiency of machine, and determines the value of 

 the ratio of expansion for maximum efficiency of engine. He makes this 

 ratio equal to the quotient of maximum initial pressure divided by the 

 sum of the useless internal resistances of the engine, including back 

 pressure and friction, and reduced to equivalent pressure per unit of area 

 of piston. This result has been generally accepted, although sometimes 

 questioned, and has been demonstrated anew, in apparent ignorance of the 

 fact of its prior publication by De Pambour, and by more than one later 

 writer. De Pambour, applying his methods to the locomotive particu- 

 larly, solved the problem, since distinctly known by his name, Given the 

 quantity of steam furnished by the boiler in the unit of time, and the 

 measure of resistance to the motion of the engine : to determine the 

 speed attainable. 



Professor Thomas Tate, writing his ' Mechanical Philosophy,' in 1853, 

 gives the principle stated above a broader enunciation, thus : ' The pres- 

 sure of the steam, at the end of the stroke, is equal to the sum of the 

 resistances of the unloaded engine, whatever may be the law expressing 

 the relation of volume and pressure of steam.' 



Professor Clansius, as has been already stated, applied the modern 

 theory of the steam-engine to the solution of the various problems which 

 arise in the practice of the engineer, so far as they can be solved by the 

 principles of thermodynamics. His papers on this subject were printed 

 in 1856. The Count de Pambour had taken a purely mechanical mode 

 of treatment, basing his calculations of the work clone in the cylinder of 

 the steam-engine upon the hypothesis of Watt, that the weight of steam 

 acting in the engine remained constant during expansion, and that the 

 same assumption was applicable to the expanding mass contained in 

 engine and boiler during the period of admission. He had constructed 



