292 Mr. C. K. Akin on the Compressibility of Gases. 

 which in the case of M. Regnault's experiments, for all of which 

 <7 = 3 metres, and 0^=1*5 metre, 



becomes, by specializing, 



, n ID 

 r= 2 H "'' 



So that, finally, we arrive at the results presented in the following 

 Table :— 



Gas. tr-l. 



Atmospheric air 0-000094 



Nitrogen 0-000091 



Carbonic acid 0000144 



Hvdrogen | 0-00000/ 



It appears also, on inspection of formula (I.), that there does 

 not exist, as implicitly assumed by M. Regnault in choosing the 

 variables of his empirical formulae, any generally valid relation 

 between the proportion of pressures and the proportion of volumes 

 in gases altogether independent of the absolute magnitudes of the 

 volumes. For, even if the law of Boyle held good, and adopting for 

 k its simplest expression, contained in formula (II.), the above rela- 

 tion would still be dependent also on the difference of volumes; 

 so that to the same ratio of pressures different ratios of volumes 

 might correspond, according to the values of the differences 

 of the latter. But the bearing of this last observation, as well as 

 the influence of the [k r — 1) on the final results of M. Regnault's 

 calculations, could only be fully explained after premising some 

 other statements, which are now to follow. It will be well, how- 

 ever, to state at once that it is not intended to resume the above 

 subject, as what is to be brought forward in the very next sen- 

 tences is of so much greater numerical importance, that it would 

 appear superfluous, on comparison, to bestow any more lines on 

 the present matter. 



2. The particular method adopted by M. Regnault in the inves- 

 tigation here under review has been incidentally spoken of already 

 in the preceding article ; it consisted simply in this — a compres- 

 sing of different masses of gases of like initial volume, but varying 

 density, to the same amount =| the primitive volume, noting at 

 the same time the corresponding pressures. But since it was the 

 aim of these researches, the insufficiency of the Boylean law being 

 once made patent, to determine empirically some other general 

 formula by means of which the pressure could be calculated on 

 knowing the density, or conversely*, the following subsidiary pro- 

 cesses were resorted to for the purpose. The known values of (3 



* At least in cases where the temperature is not very different from that 

 at which the actual measurements were made. 



