never 



s 



" IS 



Prof. Thomson on the Dynamical Theory of Heat. 107 



find 



"'"^ '=]/}'' J ' 



This shows that the work really produced, which always falls 

 short of the duty indicated by Carnot's theoiy, approaches more 

 and more nearly to it as the range is diminished; and ultimately, 

 when the range is infinitely small, is the same as if Carnot^s 

 theory required no modification, which agrees with the conclusion 

 stated above in § 22. 



27. Again, equation (8) shows that the real duty of a given 

 quantity of heat supplied from the source increases with every 

 increase of the range ; but that instead of increasing indefinitely 



in proportion to / fidt, as Carnot's theory makes it do, it 



•^T ... /»" 



reaches the value JH, but approximates to this limit, as / fidt 



increased without limit. Hence Carnot's remark* regarding the 

 practical advantage that may be anticipated from the use of the 

 air-engine, or from any method by which the range of tempera- 

 tures may be increased, loses only a part of its importance, while 

 a much more satisfactory view than his of the practical problem 

 is afforded. Thus we see that, although the full equivalent of 

 mechanical effect cannot be obtained even by means of a perfect 

 engine, yet when the actual source of heat is at a high enough 

 temperature above the sun-ounding objects, we may get more 

 and more nearly the whole of the admitted heat converted into 

 mechanical effect, by simply increasing the effective range of 

 temperature in the engine. 



28. The preceding investigation (§ 25) shows that the value 

 of Carnot's function, /l4, for all temperatures within the range of 

 the engine, and the absolute value of Joule's equivalent, J, are 

 enough of data to calculate the amount of mechanical effect of a 

 perfect engine of any kind, whether a steam-engine, an air-engine, 

 or even a thermo-electric engine ; since, according to the axiom 

 stated in § 12, and the demonstration of Prop. II., no inanimate 

 material agency could produce more mechanical effect from a 

 given quantity of heat, with a given available range of tempera- 

 tures, than an engine satisfying the criterion stated in the enun- 

 ciation of the proposition. 



29. The mechanical equivalent of a thermal unit Fahrenheit, 

 or the quantity of heat necessary to raise the temperature of a 



* "Account, &c." Appendix, Section IV. 



