308 A. W. Witkowski on the 



strictly true, the expansion of air, subject to a constant pres- 

 sure of 1 a tin., would be independent of temperature. Now 

 this is known to be approximately the case ; but on the other 

 hand it is certain that the isothermals cannot converge strictly 

 to this point, since the pressure at one atmosphere has nothing 

 in common with the internal constitution of air. From some 

 experiments it would appear that the isothermals do not 

 intersect at all low pressures ; they come very near one 

 another, descending to a minimum at certain low pressures, 

 and probably return afterwards in a steep course towards 

 higher values. 



B. Compressibility at Low Temperatures, 



§ 16. Definitions. — It is now a simple matter to calculate 

 the compressibility of atmospheric air at any one of the nine 

 temperatures investigated above ; the compressibility at +16° 

 being assumed as known through the work of Amagat (§ 11). 



Let v denote the normal volume (at 0° and 1 atm.) of a 

 certain quantity of air. When heated or cooled to any 

 temperature 6, and submitted to a pressure of p atmospheres, 

 the air assumes a volume v. Admitting Boyle's and Charles's 

 law, we should write 



r 



Now, in reality, the product pv is not independent of the 

 pressure p, and its dependence on 6 is not a linear one. 

 Instead of the above, we must write : 



pv = V . v , . . (6) 



y(p0) denoting a certain function of p and 6, the values of 

 which are to be calculated. 



This we may do as follows : — Consider a volume v of air 

 in the normal state. Heat it, at constant pressure ( = 1 atm.) 

 to + 16° ; the volume increases to 



v (l-±y .16). 



At this temperature submit it to a pressure of p atmospheres, 

 then according to the notation of § 11 we obtain the volume 

 t? (l + y.l6) 

 p ; 



finally heat it at the constant pressure p to 6 degrees. 

 Denoting by a 16 and a e the coefficients of expansion corre- 

 sponding to the pressure p and to the ranges 0-16 and 

 0-0, we get 



tt (l + y.l6) l + 0.a Pt9 



p l^lQ ,a Pt iQ 



