ALLOTROPISM BASED ON THE THEORY OF DIRECTIVE VALENCY. 325 



tion need not be taken into account, as its formation is 

 dependent upon the temperature, and it can hardly be 

 regarded as a true allotrope. Any other graphic repre- 

 sentation indicating valency direction will be found to 

 yield either an unsymmetrical molecule or one of the forms 

 already figured. 



Phosphorus. 



In the case of phosphorus, we have an element whose 

 molecular weight calculated from its vapour density at 

 444*8° is 126*6, corresponding to the molecular formula P 4 .* 

 Mitscherlich, and Deville and Troost obtained the molecular 

 weight of 123*84 at the temperature of 515° and 1040° 

 {Roscoe and Schorlemmer). 



Determination of the molecular weight from the raising 

 of the boiling point of solutions of phosphorus in carbon 

 bisulphide, 2 and the depression of the freezing point of solu- 

 tions in benzene, 3 further prove that the molecule consists 

 of four atoms. 



If we regard phosphorus as a trivalent element we shall 

 have as the ordinary representation of the phosphorus 

 molecule P == P 



If now we assign valency direction to these bonds we 

 get twelve possible cases, assuming as in the case of sulphur 

 that the transference of electrons takes place only between 

 the atoms of the molecules. We obtain : — 



Case A. when the double bonds travel in the same direc- 

 tion (aa). This gives rise to three variations according as 

 the single bonds travel — 



1 Chapman, Journ. Chem. Soc. 1899, Trans. Vol. 75, p. 734. 



2 Beckinann, Zeitschr. Physik. Chemie, 1890, 5, p. 76. 



3 Hertz, ibid., 6, p. 358. 



