38 THE SCIENTIFIC PAPERS OF 



In applying this formula, to ascertain the power of an air- 

 engine, the value of the constant A is = 106, as shown by the 

 diagram, Fig. 3, Plate 5. 



If the object is to ascertain merely the relative .economy of 

 an engine, as compared with a perfect engine, it suffices to 

 determine 



1st. The total units of heat which are imparted to the working 

 fluid, and, 2nd, the units of heat which disappear in producing 

 useful effect ; and inasmuch as the former exceed the latter, so 

 the engine falls short of producing a full equivalent of mechanical 

 effect for the heat expanded. 



Take the example of an air-engine consisting of a working 

 cylinder, A, an air-pump B, and a reservoir D between them 

 (Fig. 4, Plate 5). To obtain the greatest effect, the admission of 

 air into the working cylinder should, under all circumstances, be 

 so regulated, that it may expand down to atmospheric pressure 

 before it is discharged. 



Supposing that nothing was known of the proportion between 

 the cylinders, of the working pressure, or of the rate of expan- 

 sion, but that the temperature of the air was known to be, 



60 Fahr. On entering the pump at m. 



130 On entering the vessel D, which would be the case 

 if compressed to half its original volume. 



710 On entering the working cylinder, which would be 

 the heat required to double its volume at con- 

 stant pressure, and 



570 On being discharged, having lost 140 in its expan- 

 sion down to the atmospheric pressure. 



Then the heat supplied by the fire would be = 710 130 = 

 580 Fahr. and the difference of temperature of the air, on 

 entering and on leaving the engine, would be = 570 60 = 

 510 Fahr. It follows, that 580 510 = 70 of heat have 

 been converted into their equivalent of mechanical effect, and 

 the duty performed by the engine, for every one unit (Fahr.) of 



70 

 heat employed, is = -^ 770 = 91 '2 Ibs. lifted 1 foot high. 



The expansive air-engine is, therefore, theoretically superior 

 to Boulton and "Watt's condensing engine, but inferior to a good 



