Space occupied by Atoms. 347 



This law — of Avogadro — is, as I yet hope to show, of funda- 

 mental interest in connexion with the notion of osmotic 

 pressure. The above proposition also furnishes a very simple 

 method for determining the molecular weight from the specific 

 gravity of a solution. 



The study of the co-volumes of solids led to values which 

 were mostly not greater thau half the molecular co-volumes 

 of homogeneous liquids. Now since in the case of some such 

 compounds as racemic acid &c. the molecular volume was 

 undoubtedly doubled, but was accompanied by twice as great 

 a co-volume as in the case of other solid compounds, the 

 assumption did not appear too bold that in general the 

 apparent halving of the co-volume during the passage from 

 the liquid to the solid state was to be attributed to a doubling 

 of the molecular weight — an assumption supported by the 

 fact that during the passage from the solid to the liquid state 

 the increase of volume is proportional to the decrease in the 

 degree of association of the liquid *. On this is based the only 

 reliable method of determining the molecular toeights of homo- 

 geneous solids. 



As regards the effect of temperature on the co-volume, 

 the law of Charles-Gay-Lussac-Dalton applies to all three 

 states of aggregation. Especially in the case of the solid 

 elements (including most metalloids) did I supply the proof 



that the coefficient of expansion of the co-volume is — . 



If the known co- volume per oramme-molecule for the 

 gaseous state — 22,400 c.c. — be divided by the molecular 

 co-volume at 0° for the liquid state, we obtain the intrinsic 



pressure -g. Using this method, I calculated the intrinsic 



pressure for most organic liquids to be between 800 and 1000 

 atmospheres; for gold in the solid state, 176,000 atmos.; 

 and for the diamond, 5,460,000 atmos. These intrinsic 

 pressures were, for an element obeying Dulong and Petit's 



law, equal to exactly three times the value C — , where C 



. dv dv 



stands for the atomic heat and -=- for the rate of change of 



volume with temperature j\ 



The intrinsic pressures of the metals were found to follow the 



* Cf. my Grundriss der Physik. Chem. pp. 207 &: 208. 



f Richards has (I. c. Bd. xl. p. 174), unlike myself, calculated the 

 intrinsic pressure not by the aid of van der Waals' equation, but by 

 putting Cdt=iLdv — an assumption which is not permissible, since the 

 heat has to do work other than that involved in overcoming the internal 

 pressure. 



