436 Mr. Lubbock on the Heat of Vapours 



tain in nature, or that the absolute heat cannot be represented by 

 so simple a function of the temperature or sensible heat. Recourse 

 must then be had to more complicated expressions. U, on the 

 contrary, my formula represents the observations of the temper- 

 ature of vapours with accuracy, its origin in a simple theoretical 

 notion of the quantity of absolute heat, and its simplicity, are great 

 additional recommendations in its favour. The formula which I 

 have obtained does, I believe, represent the observations better 

 than any hitherto devised; at low temperatures and pressures it 

 deviates a little, but a very slight error in the observed pressures 

 may account for this discrepancy. Dalton says that it is next to 

 impossible to free any liquid entirely from air; of course if any 

 air enter, it unites its force to that of the vapour. Moreover, 

 when the pressures are small, the variation of temperature becomes 

 great for a small variation of pressure; so that the agreement of 

 theory with observation may be considered as complete, even if 

 the absolute amount of the error of the calculated temperature is 

 then more considerable. 



My formula has also been compared with the observations of Dr. 

 Ure, on the vapour of alcohol, aether, petroleum, and oil of tur- 

 pentine, recorded in the Philosophical Transactions for 1818*. 



I think that the comparisons contained in this treatise afford suf- 

 ficient evidence that my formula is established, and that the devia- 

 tions of the calculated results from those of observation are within 

 the limits of the errors of the latter ; but this point I leave to be 

 decided by those more conversant with the nature of the experi- 

 ments. It would not militate against mj' views if it were found ne- 

 cessary to take in an additional term and to make 



F=C+Z)(l+«fl)+^(l + «6)2 + &c. 



but the expressions for the temperature and density in terms of the 

 pressure would not be quite so simple, although more pliable. 



As the same principles must be applicable to the constitution of 

 the atmosphere, I have examined the observations made by M. 

 Gay Lussac in his aeronautic ascent from Paris, and which are 

 published by M. Biot in the Conn, des Temps. My calculated 

 temperatures may be considered as identical with the temperatures 

 regidarisees of M. Biot, which are given by that distinguished 

 philosopher as representing the condition of the atmosphere di- 

 vested of the irregularities and errors incidental to observations 

 made under circumstances so difficult and so disadvantageous. 

 But the altitude to which man can ascend is so limited, that observa- 

 tions of the temperature made in aeronautic ascents will never fui'- 



[* Dr. Ure's paper containing these observations was reprinted in Phil. Mag., First, 

 Series, vol. liii. p. 38, et sey.— Edit.] 



