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



this case, it will presently be proved to be necessary to depart 

 from what are conventionally called the pressure and density of 

 a gaseous mass ill daily practice, and to exchange at least one or 

 other, density or pressure as habitually understood, for one 

 different from either. For since it is known, in the first place, 

 that, consequent upon the action of gravity, each separate layer 

 of infinitesimal vertical extent, an aggregate of which only forms 

 a finite mass, has its own particular density and pressure, it will 

 follow as a first consequence that only such densities and pres- 

 sures as in a given mass coexist in the same infinitesimal layer 

 can be considered as congruous or correlative within the mean- 

 ing of the Boylean law; whilst such densities and pressures as 

 belong to different layers must be connected by some more com- 

 plicated formula, dependent on the magnitude of the mass which 

 separates the layers considered. Practically, however, what 

 is denominated the pressure of a gaseous mass is the pressure 

 of its lowest-situated layer, which is in contact with the liquid 

 employed for evaluating the pressures in the manometer, this 

 last pressure being generally alone accessible to measurement ; 

 but for density, on the other hand, following the extended defi- 

 nition of the term, is taken the mean of the densities of all 

 the component layers, or the mass divided by the volume — and 

 this also in the sense of density of the integer mass. Since this 

 last density, however, is necessarily identical with that of some 

 medium layer situated between the top and bottom of the mass, 

 considered as made up of a continuous pile of infinitesimal hori- 

 zontal layers, whilst the pressure, before adverted to as generally 

 viewed in the light of that of the mass considered as a whole, 

 belongs, in fact, to the layer at the bottom only, it must be evi- 

 dent that these two, pressure and density as just described, are 

 not correlatives in the sense which is implied by the Boylean 

 law. Hence the necessity, as bottom-pressure and mean density 

 are generally alone measurable, to take one or other of the 

 two couples, pressure and density at the bottom, or mean pres- 

 sure and mean density, as characteristic of a gaseous mass — at 

 least whenever it is desired to apply to such the law of Boyle, 

 which above was shown to be inapplicable to the densities and 

 pressures of different layers promiscuously combined. 



The precaution enjoined in the preceding sentences it is cer- 

 tainly needless to take in ordinary applications of the Boylean 

 law, for reasons which are sufficiently evident : in the case of M. 

 Regnault's experiments, however, to neglect it will entail appre- 

 ciable numerical errors, as shall now be shown. For this pur- 

 pose it will be necessary to quote a formula (the demonstration 

 of which shall be given in an Appendix) exhibiting the actual 

 relation between ordinary pressures and volumes (the former 



