realizing the Advantages of the Air-Engine. 19 



A detailed mathematical investigation of the theory of air- 

 engines, with and without regenerators, is contained in the 

 third and fourth sections of a paper on Thermo-dynamics in 

 the Philosophical Transactions for 1854, Part L, together with 

 some numerical illustrations. 



Theoretical investigations of the duty of air-engines of dif- 

 ferent forms are contained in a paper by Mr Joule (Phil. 

 Trans., 1851), and in a series of papers in the American Jour- 

 nal of Science for 1853 and 1854, by Professor F. A. P. Bar- 

 nard, the first American author, so far as I know, who has 

 aided in the development of the consequences of the dynami- 

 cal theory of heat. 



Section II. — On the Actual Efficiency of Thermodynamic 

 Engines : of Steam-Engines in particular. 



12. Causes of Waste of Heat and Power. — In considering 

 the waste of heat and power which constitutes the difference 

 between the actual performance and the maximum theoretical 

 performance of engines worked by heat, — as the object now in 

 view is to compare different kinds of engines together, it is not 

 necessary to take into account those causes of loss of power 

 which either are or might be made nearly alike in all kinds of 

 engines, such as the friction of the machinery ; those causes 

 alone will h$ considered which affect the relation between the 

 expenditure of heat and the action of the working elastic sub- 

 stance upon the piston, — in other words, the indicated power 

 of the engine ; and from these causes will be further excepted 

 the waste of power in forcing the working substance through 

 narrow valve-ports and passages, as this kind of waste arises 

 only from an error in mechanism. As thus restricted, the 

 causes of waste of heat and power may be divided into five 

 classes— first, Imperfect communication of heat from the 

 burning fuel to the working substance ; second, Imperfect 

 abstraction of the heat, which constitutes the necessary loss 

 explained in the preceding section ; third, The communication 

 of heat to or from the working substance at improper periods 

 of the stroke ; fourth, Any expenditure of heat in elevating 

 the temperature of the working substance ; fifth, Imperfect 



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