536 Mr. Rankine on the Centrifugal Theory of Elasticity, 



from which, making \o^ePo + T ^ dp . ='^ and 



^ Pa pyi-t^) 



CnM/ dir . X=n, the following value results for the hyper- 



bolic logarithm of the superficial atomic elasticity of the vapour 

 at sensible distances from the surface of the liquid :— - 



Iog.p,=^P-" (36) 



In the cases which occur in practice, the density of the vapour 

 is very small as compared with that of the liquid. Hence it fol- 

 lows, that in such cases the value of ^ depends chiefly on the 

 superficial atomic elasticity of the liquid, and that of 11 on its 

 density. The density is known to diminish with the tempera- 

 ture, but slowly. The superficial atomic elasticity, according to 

 equation (32), is expressed by 



i"o=;'i+yi;i>,)-/(i>o), 



where jt?i and/(Di) are obviously small as compared with/(Do), 

 a function of the density of the liquid, so that the variations of 

 Pq and of "^ with the temperature are comparatively slow also. 



Therefore when the density of the vapour is small as compared 

 with that of the liquid, the principal variable part of the loga- 

 rithm of its supei-ficial atomic elasticity, and consequently of its 

 whole pressure, is negative, and inversely proportional to the 

 absolute temperature ; and 



a — 



T 



(a and /3 being constants) may be regarded as the first two terms 

 of an approximate formula for the logarithm of the pressure. 



A formula of two terms, similar to this, was proposed about 

 1828 by Professor Roche. I have not been able to find his 

 memoir, and do not know the nature of the reasoning from 

 which he deduced his formula. It has since been shown, by 

 M. Regnault and others, to be accurate for a limited range of 

 temperature only. The quantity corresponding in it to t is 

 reckoned from a point determined empirically, and very different 

 from the absolute zero. 



Thus far the investigation has been theoretical. The next 

 step is to determine empirically what other terms are requisite 

 in order to approximate to the effect of the function /(D), and 

 of the variation of the functions "^ and fl. 



The analogy of the formulae for the dilatation of gases, the 

 obvious convenience in calculation, and the fact that the devia- 

 tions of the results of the first two terms from those of experi- 



