rilESIDENTIAL ADDRESS, 823 



Joule, Rankine, and their great Continental colleagues, it is true, settled once 

 and for all the broad laws of thermodynamics, but the Carnot cycle is a cycle 

 which is, as has been repeatedly shown, an impossible one in practice. Accord- 

 ingly actual engines have to operate upon imperfect cycles. The theory of these 

 imperfect cycles has been worlced out mostly during the last twenty-five years, 

 although Rankine made a beginning in dealing Avith the theory of the Joule air 

 engine. For the first time he showed the existence of what may be termed a 

 cycle of constant efficiency in the case of the Joule air engine. Assuming con- 

 stant specific heat for the working fluid, he calculates the efficiency of wliat we 

 now call a constant-pressure air engine between cei-tain limits of tem])eraturo, 

 and he gives the efficiency of the fluid where U = energy exerted and Hj = heat 

 received, and ;• = ratio of compi-essiou and expansion ;^ 



• H, rO-408' 



that is, lie indicates in this formula that the thermal efficiency is independent of 

 the maximum temperature as long as that maximum temperature exceeds the 

 temperature of adiabatic compression. He makes no statement, however, that 

 this engine is within a certain range independent of the maximum tempei'ature ; 

 that is, that increasing maximum temperature does not increase efficiency. 

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

 specific heat, 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 has been held by many scientific men, 

 and has prevented the minute investigation 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 efficiencies 

 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 thermodynamic laws, because it requires 

 accurate knowledge of the properties of the working fluid dealt with under con- 

 ditions rendering observation extremely difficult. The modern internal-com- 

 bustion motor is the successor to the air engine so fully discussed by eminent 

 engineers of fifty-five years ago; and the forebodings of even so eminent a man as 

 Faraday as to its ultimate success have proved unfounded. Great difficulties 

 have been encountered and many discrepancies have had to be explained, but a 

 minute study of the nature of the working fluid has rendered it more and more 

 possible to calculate the efficiencies to be expected under practical conditions. At 

 the present time we can deal with almost any cycle or any working fluid with some 

 fair approximation to an accurate result. Much work, however, is required before 

 all problems of the working fluid can be said to be solved with regard to any heat 

 engine. Indeed, it may be said that under modern conditions of the use of steam 

 even the properties of the working fluid — steam — have not yet been satisfactorily 

 determined. The mere question of specific heat, for example, of steam and its 

 variations of temperature and pressure is now under review, and important 



