Specific Heat of Elastic Fluids. 477 



212^ F. ; then the calorimeter at 32° F. under the same pressure. 

 The temperature of the calorimeter is raised t^ degrees, and ex- 

 periment shows that /' differs very little from t. 



3. An equal mass of the gas traverses, under a pressure of 

 10 atmospheres, the winding tube, in which it is heated to 

 212° F. ; but on reaching the orifice of the calorimeter at 32° F., 

 the gas expands, and the pressure falls below that of the atmo- 

 sphere in such a manner that it escapes from the calorimeter 

 with the same temperature and pressure as the surrounding 

 atmosphere. The temperature of the calorimeter is raised t" 

 degrees. 



According to the theories formerly recognised, the quantity of 

 heat disengaged by the gas in the experiment No. 3 should be 

 equal to that in No. 2, minus the quantity of heat absorbed by 

 the gas during the enormous expansion it has undergone, seeing 

 that its volume has increased tenfold ; but, on the contrary, ex- 

 periment shows that ^" has a value greater than t^ and t. 



It would be possible to bring forward more examples, but this 

 would involve an anticipation of what follows. I shall reserve the 

 discussion of this subject until the publication in a complete form 

 of my experiments upon the compression and expansion of gases. 



In any case, the examples already given will suffice to show 

 that great circumspection should be exercised in drawing con- 

 clusions from experiments in which elastic fluids are in a state 

 of motion, undergoing variations of elasticity, and effecting me- 

 chanical work frequently difficult to appreciate ; for the calorific 

 effects produced depend in a great measure upon the order and 

 mode in which these variations take place. 



Unfortunately, although it is easy to propound in a vague man- 

 ner a physical theory, it is very difficult to state it with precision 

 in such a manner as not only to include all the facts already 

 known, but likewise to deduce from it those which have hitherto 

 escaped observation. In this respect the theory of luminous un- 

 dulations, as established by Fresnel, is an isolated fact in phy- 

 sical science. The equation of problems relating to heat, regarded 

 under a mechanical point of view, leads, like all analogous pro- 

 blems, to an equation of partial differences of the second order, 

 between several variable quantities which are unknown functions 

 of each other. These functions represent the true elementary 

 physical laws, which it is necessary to know in order to arrive at 

 a complete solution of the problem. The integration of the 

 equation introduces arbitrary functions, the nature of which 

 should be sought for by comparing the results given by the 

 equation with those obtained by direct experiment, and with the 

 laws deduced from those experiments. In researches upon heat, 

 unfortunately, direct experimentation is rarely applicable to 



