634 PROCEEDINGS OF THE AMERICAN ACADEMY. 



In obtaining the formulae upon which the following discussion is 

 based, it will be assumed that the working substance is a perfect gas. 

 The analytic expression of this assumption is the two equations 



pv = RT, 



where ^ is a constant, and 



a 



&,='" 



where k is a constant.* Of the four constants R, Cp, (7„, and k, two 

 must be given to determine the nature of the perfect gas ; the two which 

 will be used in the formulae of this paper are Gp and k. The only 

 other symbols which will be needed are the physical constants g and J, 

 the parameters p^ and T^, the variables P and Q, and the symbol ( T^^ V, 

 E or IF) which represents the property under consideration. For con- 

 venience of reference the formulae are collected in Table 1 ; they are 

 easily obtained by the ordinary methods. f It should be noticed that 

 not one of them happens to involve the parameter ^„, a simplification 

 which has resulted from the choice of P as a coordinate. Each of these 

 formulae (except the ^-type-^ one) can be explicitly solved for Q. In 

 the accompanying figures, values of Q have been calculated with con- 

 siderable care, usually for some twenty-five diff'erent values of P, and it 

 is hoped that the resulting curves, especially on the working charts, are 



* The gas law alone is not enougli ; if both are given it follows at once that 

 Cp and (7„ are themselves constants. 



t The Te formulae for types A and B were obtained by following pressures and 

 temperatures up the compression line, across the top, and down again, by means 

 of the usual equations. Te for the regenerative type is independent of the param- 

 eters. The work was as follows (see Figure 2) : 



Tf=T,; :. Ta = Te + -^. (a) 



Op 



But the equation of the adiabatic d e gives 



1 K 1 (C <C — 1 



T^i p^ = Te pe~^, or T,i = Tc P~^; (b) 



therefore, etc. The V equations are special cases of equation (208), p. 151, of 

 Professor Peabody's " Thermodynamics of the Steam Engine " [4th ed. 1900]. 

 The E equations were obtained from the amounts of heat involved in the various 

 transformations, and the IF equations are of the form W= J QE. 



