472 Intelligence and Miscellaneous Articles. 



timeless than O'l second; the pressure increases then for several 

 seconds, at first rather rapidly, but then more slowly, and the more 

 so the greater the divergence of the gas from Mariotte's law. The 

 pressure attains a maximum, and then very slowly decreases until the 

 initial temperature is set up. 



This result is easily explained on thermodynamic principles. The 

 moment inequality of pressure begins to be set up, part of the gas 

 eddies about; there has been a lowering of temperature in the ex- 

 panded part, an increase in the compressed part. The vis viva of 

 the part in motion is gradually converted into heat, and consequently 

 the pressure increases. If the sides were impervious to heat, equi- 

 librium would be established without any external work being brought 

 into play, or any heat taken from or given to the surrounding bodies. 

 The temperature would then be lower than the original temperature ; 

 and the difference would be greater the greater the divergence from 

 Mariotte's law. But the sides impart heat to the cold part of the 

 gaseous mass, and take it, on the contrary, from the heated part, 

 without there being an exact compensation between the two effects. 

 The final result is that the mass receives a little heat from without ; 

 hence, when a mixture of all the gases is effected, the temperature is 

 a little higher than the original temperature, which it only acquires 

 after a tolerably long time. 



These observations complete a celebrated experiment in which 

 Mr. Joule investigated the ultimate thermal condition of a gas which 

 had expanded without external work. This effect, which it is almost 

 impossible to observe in the water surrounding the reservoirs, is 

 clearly manifested in ray experiments. Without the necessity of a 

 very great pressure, they furnish an undoubted proof of the sponta- 

 neous cooling which a gaseous mass undergoes, and exhibit various 

 accessory circumstances. We know that this cooling indicates the 

 existence of a molecular attraction in gases, and that the correspond- 

 ing loss of heat is equal to the production of a certain quantity of 

 internal work. The calculation of this amount of work under 

 given conditions is an interesting application of thermodynamic 

 formulae. 



Treating a series of problems on this question, I have rediscovered 

 the principal circumstances observed in my experiments. I have 

 made a numerical calculation for carbonic acid, using an empirical 

 formula which connects the pressure, the volume, and the tempera- 

 ture. This formula was enunciated by Mr. Rankine ; and Mr. Joule 

 and SirW. Thomson used it in their researches on the issue of gases 

 through small apertures. I have merely changed the constants of 

 this formula, so that it might satisfy the experimental data of M. 

 Regnault relative to the compressibility and expansion of carbonic 

 acid gas. — Comptes Rendus, March 9, 1868. 



