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normal. We should then have reason to speak ofnioléculesliquidogènes" 

 and "molecules gazogenes". It would then, however, be required that 

 the following equalities happened to be satisfied. In the first place 

 the two transformations would require the same amount of energy; 

 and in the second place the number of "molecules liquidogènes" in the 

 liquid state ^) at every temperature would have to be proportional with 



p(v V ) 



the value of — \ '' . The following equation would then hold : 

 a a _ 



pdT P(^— «i) v,v,p p{v,—v,) 



Not succeeding in deducing this course of the amount of the 

 liquidogène molecules from the thermodynamic rules and in accoun- 

 ting for the above mentioned accidental equalities I have relinquished 

 this idea, the more so as this supposition is unable to explain the 

 fact that the liquid volume can decrease below />. 



If we ask what kind of modification is required in the equation 

 of state with constant a and b in order to obtain a smaller vapour 

 tension, we may answer that question as follows. Every modification 

 which lowers the pression with an amount which is larger according 

 as the volume is smaller, satisfies the requirement mentioned. In 

 the following figure the traced curve represents the isothermal for 

 constant a and b ; the straight line AB, which has been constructed 

 according to the well known rule indicates the coexisting phases, 

 and the points C and D represent the phases with minimum pressure 

 and maximum pressure. The dotted curve has been constructed in 

 such a way that for very large volumes it coincides sensibly with 

 the traced curve, but for smaller \olumes it Ues lower, and the 

 distance is the greater according as the volume is smaller. Then 

 the point D' has shifted towards the right and the point C" towards 

 the left. For in the point exactly below D as well as in the point 



exactly below C the value of — for the dotted curve is positive; 



dv 



these points lie therefore on the unstable part of the modified iso- 

 thermal and the limits of the unstable region are farther apart. 

 But it is also evident — and this is of primary interest — that 

 if for the modified isothermal we trace again the straight line of 

 the coexisting phases according to the well know rule, this line 

 w^ill lie lower than the line AB. The area of the figure above AB 



1) Diminished with that number in the gaseous state. 



