Evaporation and Dissociation. 211 



value of the expression +-, will be greater, and the vapour- 

 density less, than that of a theoretical gas. 



The formula which we find to represent the relations of 

 temperature and pressure at constant volume, p'=vt — a, repre- 

 sents these facts. The reciprocal of the vapour-density is 

 the product of pressure and volume, divided by the product 

 of the absolute temperature into half the molecular weight, or 



1 _ pv 2_ 



vap. dens. - t mol. wt.' 

 Now while at small volumes the rate of diminution of volume 

 of a substance increases more and more slowly with rise of 

 pressure, there is no limit conceivable to the pressure which 



may be applied. Hence the value of the expression ^-~ 



vv 

 must ultimately be greater than unity. The relation of —— 



to the pressure for ether has been calculated by means of our 

 equation for a few isothermals, and is shown in the annexed 

 figure. From the direction of the lines, it would appear that 

 if produced to still higher pressures, the product pv would 

 reach and exceed unity. This state has indeed been reached 

 by Natterer in compressing the so-called permanent gases at 

 temperatures far above the critical points. 



It is possible, by means of our equation, to follow these lines 

 into the unrealizable state, at low temperatures, where pressure 

 becomes negative. An example is given at 150°. It is ob- 

 vious that those isothermals which include negative pressures 



will intersect each other at the zero of pressure and -^— , and 



t 



will form loops in the negative region. This is shown on PI. IV. 



It has recently been suggested by Wroblewski (Wien. 

 Monatsb. der Chemie, 1886, p. 383), in a paper from the con- 

 clusions of which we differ in every point, that the minimum 

 values of pv mapped against pressure form a curve con- 

 tinuous with the vapour-pressure curve. This is distinctly 

 not the case. The curve is cut by the vapour-pressure 

 curve at the critical point. It is, however, approximately 

 continuous with the curve shown on plate ix. in our previous 

 paper on this subject, representing the pressures corresponding 

 to the inferior apices of the serpentine isothermals. The mini- 

 mum product of pressure and volume probably does not occur 

 at volumes corresponding to these apices, but at slightly lower 

 volumes. We have proved this to be the case at high tempe- 

 ratures, and it is probably also the case at lower temperatures. 



In conclusion, we should state that we have purposely 



P2 



