26 The Contract of Practice and Jheory. 



arose, and arises every day almost, from the glaring and 

 obvious discrepancy between the heat supply required by 

 Carnot's law for an engine and that really necessary, the latter 

 varying from somewhat over twice to fifteen or twenty times 

 the former, in different engines. Yet in spite of this discrepancy 

 between the results of Practice and those of Theory no tolerably 

 good reason can be given for doubting either Joule's experi- 

 ments or Carnot's law, though the discrepancy is so great as at 

 first sight to appear a flat and emphatic contradiction by facts 

 of the whole of modern thermodynamical theory from beginning 

 to end. There are other discrepancies too. Carnot's law says 

 that the hotter the boiler steam, the more economical in fuel 

 will the engine be. In addition it says that using naphtha 

 vapour, or mercury vapour, or a mixture of gas and air, or any- 

 thing else makes no difference. Forty or fifty years ago, 

 however, many people had serious doubts as to whether fifty 

 pound steam was a bit more economical than fifteen. Later 

 on, gas engines, it is true, gave some countenance to Carnot's 

 law, for the temperature of explosion in them is very high ; but 

 then naptha and ammonia engines contradicted it, for in them 

 the boiler temperature may be, with equally economical results, 

 much lower than in a steam engine using the same pressure. 



Now, what is anyone to think of all this ? Joule's experi- 

 ments have been confirmed in a multitude of ways over and 

 over again. Carnot's law is closely connected with the rule 

 that perpetual motion is a practical impossibility ; and yet the 

 results got by their application to the case of the__ steam and 

 other heat engines seem to be, on the face of the thing, totally 

 at variance with all the known facts. 



I have chosen this example because it is a very conspicuous 

 one of the consequences of not carefully attending to what it is 

 that a theoretical rule does not say, and fixing one's attention 

 wholly on what it does say. I will repeat the rule, as I gave it 

 applied to the case of i8o lbs. steam before : — 



" If you want twenty pounds worth of work out of steam in 

 the engine, you must supply not less than about a hundred 

 pounds worth of work in the form of heat to the boiler." 



