Manchester Memoirs, Vol. Ixv. (192 1), No. 2 5 



in efficiency with different values of n and r in (5) and (6) 

 respectively. 



Several interesting points appear from an examination of 

 these curves. With reference first to the dotted lines it will 

 be observed that in the cases when p=i.i, 2 and 3, there is a 

 definite minimum efficiency for each, and that as p increases 

 there is a tendency for this minimum to disappear until, as 

 shown for the values p = g and 14 there is no evidence of either 

 a minimum or maximum point. In each of these cases also 

 the efficiency tends to a limit when n=i.<\, which limit is also 

 the same (as may easily be verified) as the Diesel engine 

 formula for efficiency, namely, 



1 p 8 -i , s 



r ' =I ~ *R x ifcT) " - - " (7) 



It is natural to expect, therefore, that the same limit obtains 

 when p=i in (5), but on plotting the graph it is evident that 

 there is no such limit arrived at by any approximation of 

 n to § as close as it may be desired to make it. The limiting 

 efficiency of (5) when p— 1 and n=i.4 instead of being in the 

 neighbourhood of 65.2 per cent, as it is in the limiting case of 

 (7) when p=i and r=i4, appears to approach a value in the 

 neighbourhood of 38 per cent. Glancing at the dotted curve 

 for p= 1.1 it is apparent that, as n approaches the value 1.4 the 

 efficiency increases very rapidly to the limiting value of (7). 



The reason for this difference in limiting efficiencies in the 

 two cases when p>i and when p= 1 is readily understood from 

 the temperature -entropy diagram of Fig. 4. Here the cross- 

 shaded portion represents the cycle of Fig. 1 when p=i.o. In 

 this case as n approaches 8 the adiabatic expansion line and 

 the compression line tend to coincide. This also occurs in 

 the limiting cases of the Carnot, Constant Volume and 

 Constant Pressure Cycles, as the amount of heat given per 

 cycle approaches the zero value. This does not mean, how- 

 ever, that the limiting efficiency is the same for the particular 

 cycle under consideration as it is for these. Efficiency on the 

 T<fi diagram is given by the ratio of areas representing there 

 the work done and the heat given, the nature of which ratio 

 can generally be inferred from an examination of the diagram. 

 It is apparent at once from Fig. 4, that as the pv n line of the 

 cross-shaded area tends to approach the pv% line, the area 

 approaches to a limit somewhere in the neighbourhood of 

 half that in the Carnot or the Constant Volume or Constant 

 Pressure cycles, while the heat given will tend to become 

 approximately the same in all cases. This means that the 



