Mr. W. J. M. Rankine on the Mechanical Theory of Heat. 63 



at, ft 7 three constants, to be determined empirically for eacli 

 fluid. 



[The comparison of this formula with the experiments of 

 Regnault and Ure on the vapours of water, alcohol, aether, tur- 

 pentine, petroleum and mercury, was published in the Edinburgh 

 New Philosophical Journal for July 1849.] 



The first section of the paper contains the general theory of 

 the mutual conversion of heat and expansive power in all sub- 

 stances. The most important of the principles laid down is the 

 following, which is identical with that of M. Clausius : — 



If unity of weight of any substance pass through a variety of 

 changes of temperature and volumCj and at length return to its pri- 

 mitive volume and temperature j the algebraical sum of the vis viva 

 expended and produced, whether in the shape of expansion and 

 compression, or in that of heat, must be equal to zero. 



The expression obtained for the quantity of heat produced by 

 a given compression, or consumed by a given expansion, consists 

 of three terms. 



uThe first depends on the mere change of volume. 

 I) The second depends on certain changes of molecular arrange- 

 ment connected with change of volume only. 



The sum of those two terms is equivalent, in most cases, to 

 what M. Clausius calls " aiissere Arbeit" 



The third depends on other changes of molecular arrange- 

 ment, and corresponds to the '^ inner e Arbeit" of M. Clausius. 



The second section relates to real and apparent specific heat, 

 especially in perfect gases, that is to say gases which follow the 

 laws of Marriotte and Gay-Lussac. Real specific heat is the in- 

 crease of the vis viva of the atomic atmospheres for a rise of one 

 degree of temperature in unity of weight, and is equivalent, for 

 each substance, to a certain depth of fall. Apparent specific 

 heat is found by adding to the real specific heat that additional 

 heat which is consumed in producing changes of volume and 

 molecular arrangement. 



The apparent specific heat of a perfect gas at constant volume 

 is sensibly equal to its real specific heat. 



The apparent specific heat of a perfect gas under constant 

 pressure exceeds the real specific heat in a certain ratio, 1 + N : 1 ; 

 the fraction N being inversely proportional to the real spe- 

 cific heat of unity of volume of the gas, and probably a function 

 of its chemical constitution. The difference of those two specific 

 heats, ior unity of volume, is the same for all gases (as M. Clausius 

 also has shown). 



The value of 1 + N, as deduced from the velocity of sound, 

 lies between 1-4 and 1*410 for atmospheric air; for oxygen and 

 hydrogen, and probably for all simple gases, it is 1*436. «; » 



