310 A. W. Witkowski on the 



These numbers are represented in a graphical form on 

 PL II. by means of so-called curves of compressibility 

 (abscissas = pressures, ordinates = isothermal values of 7j=pv ; 

 the axis of abscissas through the point 0*1). It may be well 

 to remark that, on assuming Boyle's law to hold for all 

 pressures and temperatures, these curves would be straight 

 lines parallel to the axis of abscissas. 



Every one of these curves shows a minimum of the pro- 

 duct pv for a certain value of p (depending on the tempera- 

 ture of the corresponding isothermal). This expresses the 

 fact, verified for many gases at higher temperatures, that with 

 increasing pressure the compressibility exceeds at first that 

 given by Boyle's law until a maximum is reached, afterwards 

 it diminishes indefinitely. In the vicinity of the critical point 

 the curves of compressibility run downwards very steeply ; at 

 points where liquefaction occurs their course is vertical. 



§ 18. Comparison with other Gases. — The general proper- 

 ties of atmospheric air as regards expansion and compressi- 

 bility are quite analogous — apart from the large difference of 

 critical temperatures — with those of other gases which have 

 been investigated hitherto in this respect. It is interesting to 

 inquire whether this resemblance of properties is merely a 

 qualitative one, or whether it is more deeply rooted ; in other 

 words, is it possible to calculate beforehand the properties of a 

 gas, assuming the properties of another to be known ? — this is 

 the thesis of van der Waals. Wroblewski, in his memoir on 

 the Compressibility of Hydrogen, asserts the possibility of such 

 predictions. Take for any one gas the critical pressure for 

 the unit of pressure ; for the unit of temperature its critical 

 temperature (absolute) : then Wroblewski's theorem asserts 

 that the dependence between the temperature and that value 

 of the pressure for which the product pv is a minimum, is the 

 same for all gases. A more general theorem is due to 

 L. Natanson, namely, that all gases have a common character- 

 istic equation, i. e., a common relation (not necessarily that of 

 van der Waals) between pressure, temperature, and volume, 

 provided that these elements be measured by means of units 

 specially adapted to the nature of every gas; the critical 

 elements form one of the infinitely numerous groups of such 

 units. 



The critical elements of air are given by Olszewski as 

 follows : — crit. pressure = 39 atm. ; crit. temperature = — 140° 

 Cent. These data are also confirmed by my own experiments ; 

 I should only consider — 141° as a nearer approximation to 

 the true value of the critical temperature. A comparison of 

 atmospheric air with other gases may be best effected on the 



