( 644 ) 



is not satisfied, this will certainly not be the case for T=z x / l T k . 

 Still, it would be too hazardous to assert that it has now been 

 incontestable proved that e.g. for the system ether-anthraquinone no 

 temperature maximum can occur. For we have had to make use 

 of the supposition that TV depends linearly on ,c, and though this 

 supposition may possess some degree of probability for critical tem- 

 peratures that differ much, it is just with substances which — as 

 ether and anthraquinone-lie closer together, that there is some ground 

 for expecting a deviation from the straight line. Only very few ex- 

 perimental data are at our disposal. As such may e. g. be used 

 the determinations on the increase of the plaitpoint temperature by 

 addition of little volatile substances, made by Smits, Cextnerszwer 

 and Büchner. For by means of the formula given I »v van der Waals 1 ) 



dT dTk_ 49 jrfTV 1 dpi |» 



Tdx Tf-d.c 45 ( Tylx 7 pkdx 



in which we need only pay regard to the principal terms (those 



dT k 



with 1\), we may calculate the value of — — from those directly 



J kdx 



measured. If we now calculate by the aid of the thus found 



dT k 

 value of——— and the supposition of rectilinearitv, TV, i.e. the 

 I kdx 



value of r l\ for the admixed substance, we find the data collected in 



the following table. (P. 645). 



From this appears that the values calculated in this way at least 



for some substances, and particularly for anthraquinone according to 



the determination by Smits, are not inconsiderably lower than double 



the melting point temperature. It may, therefore, be considered highly 



probable that these lines are convex seen from below, and so the 



dT k 

 absolute value of — — will be larger than might be expected trom 

 1 kdx 



the supposition of rectilinearity. With our imperfect knowledge of 



the further course of the plaitpoint line, and hence a fortiori of the 



line for Tk an estimation as to this will, naturally, remain very 



uncertain ; but yet it seems to me that something about this may 



be ascertained in the following way. We have on the side of the 



ether : 



/ dT k \ f da db\ 



\TkdxJ r — Q \adx bdx) x = ' 



i) These Proc. VII, p. 272 and 296. 



