Manchester Memoirs, Vol. Ixv. (192 1), No. 2 7 



knowledge, it has never been pointed out that this is due to 

 the peculiar nature of this approach of the efficiency to its 

 limiting value when the expansion and compression lines 

 coincide in the manner indicated, i.e., not by parallel approach 

 of the lines but by convergent approach. The effect of this 

 in reducing efficiency becomes damped more and more as the 

 amount of heat given increases, as appears clearly from the 

 dotted lines of Fig. 3. This is also the explanation why, with 

 extra heavy engine loads, efficiency is scarcely, if at alL 

 affected by water injection. 



The abrupt change in the character of the graphs (repre- 

 sented by the dotted lines of Fig. 3) which is apparent when 

 the curve for any value of p as close to unity as may be desired, 

 is compared with the curve for a value of p — unity, would 

 appear to indicate that the latter graph should be represented 

 not only by the dotted line shown but also by a vertical line 

 from an efficiency value of 38 per cent, to an efficiency value 

 of 65.2 per cent., when 11 = or 1.4. Examination of (5), 

 however, shows, as already observed, that this is not the case. 

 The true explanation is that as p approximates to unity, that 



portion of the graph represented by-r approaching an infinite 



value, is really a region of what may be termed li unstable " 

 efficiency, i.e., as p approaches unity a very slight change in 

 the value of n results in a large change in the value of the 

 efficiency. When, however, p = unity, there is no such unstable 

 portion in the curve. 



The above point is, perhaps, rendered more clear by 

 reference to Fig. 5. In Fig. 3 it will be observed that, in the 

 limit when p=i and 71=1.4, tne value of a is unitv. In the 

 curves of Fig. 5, however, the values of the variables con- 

 cerned have been so chosen that 0=1.1 when 71=1.4, r being- 

 taken as 10. The curves shown there for different values of 

 p indicate that the limiting case of Fig. 3 when p=i does not 

 apply here. It is interesting to note therefore .that the reason 

 for the theoretical minimum for the " nn " curves can be 

 traced in every case to the peculiarity of the limiting case of 

 Fig. 3. 



In Fig. 6 the curves showing the relationship between 

 y] and p are given for different values of n. The interesting- 

 point about these is the existence of a maximum efficiency 

 point in each case, the value of p at this maximum point 

 increasing as the value of n diminishes. 



Referring now to the full lines of Fig. 3 giving the rela- 



