1 .'}.S Mr. Herapath on Elastic Fluids. 



is to be understood when the compresshifr sides are individually 

 homogeneous; and also when the compressions do not [)ro- 

 duce any decomposition, combustion, &c. in the gas. 



Hence, if any gas, as oxygen, be compressed bv mercury, 

 the rise of temjierature should be 27 times greater than in an 

 equal volume of the same gas similarly compressed by water. 

 I here take it for granted, that the experiments of Mr. Dal- 

 ton are correct, from which I have (Annals for September 

 1821, p. 208,) computed the relative masses of particles of 

 water and mercury; and likev/ise that a due allowance has 

 been made for the temperatnre evolved by the condensation of 

 the aqueous vapour in the space containing one portion of the 

 gas. This allowance I conceive may be easily made by the 

 data I have heretofore published. 



Let philosophers try this very striking case; and, if the ex- 

 periments are too delicate to define precisely the amounts of 

 the elevations of temperature, they will, I think, at least per- 

 ceive enough to show that the general consequence I have 

 drawn of the superior rise of temperature liy mercury is cor- 

 rect; and consequently that the result of M. Laplace's theory 

 is erroneous, which makes equal compressions, however made, 

 produce the same rise of temperature. 



Ira M. Laplace's equation 1 [P = 27rHKg-c-] P is the 

 pi-essure or elasticity of the gas; 27r is double the ratio of 

 the circumference of a circle to its diameter ; " H est line 

 constante qui depend de la force repulsive de la clialeur, et 

 qui semble ainsi devoir etre la meme pour tons les gaz ;" K is 

 the integral of vj/s ds from to oo , s being an indefinitely small 

 distance from the envelope ; q is the density or rather number 

 of the particles of gas in a unity of space; and c is the caloric 

 of one particle. It is evident, therefore, that the factor 27rHK 

 is independent of the nature of the gas, and ought to be " la 

 meme pour tons les gaz." Hence we have universally 



P = A^V, 

 A being =27rHK, however different the gases. Now q being 

 the number of particles, and c the caloric of each, we have 



AC- = AgV=P, 

 putting C for the absolute caloric in a unity of space. In equal 

 volumes, therefore, of all gases under equal pressures, there 

 must be the same absolute quantity of caloric; and conse- 

 quently the same specific quantity. That is, the capacities for 

 caloric of equal volumes of all gases under equivalent pres- 

 sures and temperatures are the same — a conclusion notoriously 

 at variance with facts. 



It is extraordinary that this consequence, so very obvious 

 and absurd, should have escaped the penetration of such a 



mathematician 



