426 Frof. Thomson on tlie Dynamical Theory of Heat. 



65. Hence we conclude, that the heat evolved by any fluid ful- 

 filling the gaseous laws is proportional to the work spent in com- 

 pressing it at any given constant temperature ; but that the 

 quantity of work required to produce a unit of heat is not con- 

 stant for all temperatures, unless Carnot's function for different 

 temperatiu'es vary inversely as 1 4- E^ ; and that it is not the 

 simple mechanical equivalent of the heat, as it was unwarrant- 

 ably* assumed by ]\Iayer to be, imless this function have pre- 

 cisely the expression 



^ = •^•1^1? ^^)- 



This formula was suggested to me by Mr. Joule, in a letter 

 dated December 9, 1848, as probably a true expression for /i, 

 being requii'ed to reconcile the expression derived from Carnot's 

 theory (which I had communicated to him) for the heat evolved 

 in terms of the work spent in the compression of a gas, with the 

 hj-pothesis that the latter of these is exactly the mechanical 

 equivalent of the former, which he had adopted in consequence 

 of its being, at least approximately, verified by his own experi- 

 ments. This, which will be called Mayer's hypothesis, from its 

 having been first assumed by Mayer, is also assumed by Clausius 

 without any reason from expei'iment ; and an expression for fi 

 the same as the preceding, is consequently adopted by him as 

 the foundation of his mathematical deductions from elementary 

 reasoning regarding the motive power of heat. The preceding 

 formula? show, that if it be true at a particular temperatm'e for 

 any one fluid fulfilling the gaseous laws, it must be true for 

 eveiy such fluid at the same temperature. 



66. Of the various experimental researches which might be 

 suggested as suitable for testing Mayer's hypothesis, it appears 

 from the preceding formula, that any which would give data for 

 the determination of the values of //, through a wide range of 

 temjieratiu'cs would, with a single accurate determination of J, 

 afford a complete test. Thus an experimental determination of 

 the density of satm-ated steam for temperatm'cs from 0° to 230° 

 Cent, would complete the data, of which a part have been so 

 accurately determined by Regnault, for the calculation of the 

 values of /i between those wide limits, and would contribute 

 more, perhaps, than any set of experimental researches that could 

 at present be proposed, to advance the mechanical theory of heat. 



67. The values of yu., given in Table I. of my Account of Car- 



* In violation of Cai-not's important principle, that thermal agency and 

 mechanical effect, or mechjfnical agency and thermal effect, cannot be re- 

 garded in the simple relation of cause and effect, when any other eflfect, 

 such as the alteration of the density of a body, is finally concerned. 



