( 179 ) 



will bc ubtaiiK'd in case of a quick cuuliiig — iii(lcpciKlciit ul' the 

 situation of the beating- temperature. 



The velocity of cooling as mentioned in Case III — V, is supposed 

 to be such that the liquid finds no occasion to alter its mixing- 

 proportion ajft acquired at a higher temperature. Should the VGlocity 

 of cooling be less, this only results in the differences between the first 

 acquired congealing-point and point H being smaller than in a case 

 of very quick cooling. The deviations remain however in the same 

 direction. 



It is therefore possible to determine with perfect accuracy the 

 apparently curious phenomena of congelation, with a knowledge of 

 the lines G F^ F D and F E. On the other hand it would be pos- 

 sible, from observation of the congealing temperatures, after the 

 substance « or I'j having gone through a sharply defined way, to 

 conclude to the situation of different points of these lines, conse- 

 quently to determine their direction, if this were not possible along 

 other ways. 



The phenomena described here, may appear not only in tautomeric 

 substances, but in all substances which in the liquid state, give two 

 modifications that are apt to transformation. 



Consequently many optic isomers that show equilibrium at higher 

 temperatures, come under this head. There however the matter can 

 often become complicated, it being possible that after the transfor- 

 mation of the d or the ^form, the racemic form deposes in the solid 

 condition. It is however easy to take this into account. 



Physics. — ^Variation of volume and of jjra^nKre in niixuKj'. 

 By Prof. J. D. VAi^^ der Waals. 



The supposition of Mr. Ajiagat (C. K. 11 Juillet IS'JN), that in 

 a mixture every gas can be considered to occupy the volume which 

 it would occupy separately under the same pressure and at the 

 same temperature, comes to the same thing as supposing, that 

 mixing under a constant pressure does not cause variation of 

 volume, and that there would be no question of either positive or 

 negative contraction. As at great densities (of liquids), mixing is 

 generally accompanied by contraction, the thesis, also in case of 

 slight densities, can only be meant as an approximation. For slight 

 densities this thesis can be tested by means of the characteristic 

 equation of a mixture. 



