DAVIS. — A ra PLANE FOR THERMODYNAMIC CYCLIC ANALYSIS. 643 



of tlie F J' corner is the same as before; but the lines within are en- 

 tirely changed. 



The efficiency lines for type B are shown in Figure 11. The line 

 /* = 1 is still a part nf the curve E =^ 0, but the other part of this 

 curve is now well out in the plane. It is the locus of those figure-of- 

 eight cycles wiiose (algebraic) area is zero. Cycles to the left of it have 

 negative areas, and any negative efficiency whatever is possible for any 

 value of P (P> 1). An extraordinary pro[)erty of the curves of this 

 family is that any vertical line cuts each of them twice if at all ; their 

 turning points lie on the above mentioned locus of first order cycles.* 

 As P increases indefinitely, Q also increases indefinitely, logarithmically. 

 The other end of each curve has the corresponding type A efficiency 

 line as an asymptote. This may be explained by regarding an isother- 

 mal cycle as made up of an adiabatic cycle together with a first order 

 cycle of the type of Figure 1 (see Figure 2). The efficiency of the 

 type A part is independent of Q and is very much higher than that of 

 the triangular part that goes with it. Therefore, for small values of Q, 

 the efficiency of the whole cycle is small, because a great part of the 

 heat supplied is made use of under the unfavorable conditions of the 

 first order cycle. But as Q increases, P being kept constant, this low 

 efficiency part of the heat supplied l)ecomes less and less important in 

 comparison with the rest, and the efficiency of the cycle approaches as 



* For the E-type-B formula cm be written 



1 _P <c - E 



Differentiating and eliminating E, gives as the derivative 



l-P < -p < '^ 



9Q ^ K-J. Q Cp Ta 



S)P K P >i:zl im 



log, P < -1 + P x: 



(b) 



The condition that tliis vanish is 



l_p -c _p . _^^o. 

 or 



K—l K—l 



Q=Cp Ta (P "- - 1) = Cp (T, P < - r.) = iT,QB)j,^^ (see eq. b of note on 

 p. 640). ' " 



