600 PROCEEDINGS OF THE AMERICAN ACADEMY. 



upon the theory of compressible atoms, has probably not before been 

 emphasized. 



From these examples it is clear why the density must usually be taken 

 at about the boiling point in order to obtain additive values for tlie mo- 

 lecular volumes of organic substances, as Kopp found. Those substances 

 which possess a high boiling point, or by inference great pressure of 

 cohesion, would be expected to be in a highly compressed state. When 

 compared at the same temperature, the molecular volumes of the more 

 compressed material will therefore be smaller than the molecular volumes 

 of the less compressed material ; but by heating the more compressed ma^ 

 terial it may be expanded until the thermal expansion at a definite point 

 replaces the volume lost by this cohesive compression. The higher the 

 boiling point, the greater must be the cohesive compression, and the higher 

 will be the rise of temperature needed to counteract it. This corresponds 

 exactly with the fact. In many cases (those of fat acids, esters, and 

 ethers) it happens that the required rise of temperature not only varies 

 in the same direction as the boiling points, but also closely corresponds in 

 magnitude with their difference. In others, especially the alcohols, alde- 

 hydes, halides, and aromatic compounds, the deviations are considerable. 

 In the case of butyl alcohol, for example, the liquid must be heated under 

 pressure to a point about 35° above its boiling point in order that it may 

 attain the volume required by Kopp's rule, being five per cent too small 

 in volume * at its boiling point. 



Deviations of this kind seem to indicate clearly that although in general 

 a substance possessing a higher boiling point must be heated to a higher 

 temperature in order that the molecular volume may become a precisely 

 additive quantity, the exact temperature needed is determined by the 

 concerted action of too many variables to be precisely determined. The 

 fact that in a minority of cases the boiling point itself is a suitable point 

 of comparison seems to be accidental. 



The existence of irregularities in the above described relation of 

 density to boiling point might have been predicted by the logical ap- 

 plication of the idea of compressible atoms ; for evidently chemical af- 

 finity causing atomic rearrangement within the molecule might cause a 

 change of atomic compression, and hence of density, without greatly 

 affecting the cohesive attraction, thus leaving the boiling point un- 

 changed. Accordingly, the usual relation between boiling point and 

 density might be marred in some cases. 



* See Ostwald's Lehrbucli, 1, 3G9 (1891). 



