i6 Dugald Clerk, The Work and Discoveries of Joule 



certain limits of temperature, and he gives the efficiency of 

 the fluid where U = energy exerted and iiZ^heat received, 

 and 7 = ratio of compression and expansion : — 



®t 



U t /t\o.4o8 



that is, he indicated in this formula that the thermal efficiency 

 was independent of the maximum temperature as long as that 

 maximum temperature exceeded the temperature of adiabatic 

 compression. He made no statement, however, that this 

 engine was within a certain range independent of the maxi- 

 mum temperature ; that was, that increasing maximum 

 temperature did not increase efficiency. Subsequent work 

 has shown that, on a simple assumption, such as constant 

 specific heat of *the working fluid, many engine cycles exist 

 of a practicable nature having high theoretical efficiencies 

 where the theoretical efficiency depends on one thing only — 

 the ratio of compression. Some misunderstanding has arisen 

 with regard to these imperfect cycles, and it has even been 

 thought that such imperfect cycles would be contrary to the 

 second law of thermodynamics. Lord Kelvin himself was of 

 this opinion in 1881. I vividly remember a conversation I 

 had with him at the Crown Iron Works, in Glasgow, over the 

 results I had obtained from one of my early gas engines. I 

 had then come to the conclusion that the "Otto" cycle as 

 ordinarily operated was a cycle of constant efficiency, and I 

 explained this to Lord Kelvin. He had not followed such 

 cycles, and his view then was that no such cycle could exist, 

 because he thought it was contrary to the second law of 

 thermodynamics. Some idea of this kind had been held by 

 many scientific men, and had prevented the minute investiga- 

 tion of imperfect cycles of different kinds, because of the 

 feeling that the whole question of efficiency was entirely 

 settled by the nature of the temperature limits ; that is, by the 

 maximum and minimum temperatures at the disposal of the 

 engineer. It is true that these values, as has been shown, 

 must always determine the extreme limit of possible efficien- 

 cies between certain temperatures, and in cycles of constant 

 efficiency the particular efficiency of the cycle is always less 

 than the efficiency of a Carnot cycle engine working between 

 the same limits of superior and inferior temperature. The 

 investigation, however, of these imperfect cycles is much more 

 difficult than the broad investigation of the general thermo- 



