THE SPACE RELATIONS OF ATOMS. 137 



that the four valences are directed towards the corners of 

 a tetrahedron, with the carbon atom in the centre. . . ." 1 



" Practically our ideas, so far as they concern the asym- 

 metric carbon, amount to the same thing ; explanation of 

 the two isomers by means of the tetrahedron and its image, 

 disappearance of this isomerism when two groups become 

 identical through the resulting symmetry and identity of 

 the two tetrahedra" {Atonic im Raume, p. 2, 1894). As to 

 whether an asymmetric atom — to the exclusion of an 

 asymmetric group — is necessary for optical activity, Van't 

 H off from the first regarded this question as settled in the 

 affirmative by the test of experiment ; as to why an asym- 

 metric group should not be equally effective he offers no 

 theory. With regard to the question whether an asymmetric 

 atom is sufficient to cause optical activity Van't Hoff will 

 admit of no exceptions ; the apparent exceptions are due in 

 his view entirely to the difficulty of " doubling " the inactive 

 mixture. 



The rioht- and left-handed relation of the isomers 

 CR'R"R'"R 1V in their action on light and their crystalline 

 form has already been discussed. 



It is to be noted, further, that all the molecular dimen- 

 sions being equal in the two isomers, we must expect a kind 

 of isomerism distinguished by a near approach to identity. 

 Accordingly we find that both isomers possess the same 

 specific gravity, critical temperature, boiling-point, melting- 

 point, latent heat of fusion and vaporisation ; in short, all 

 the physical properties depending on molecular dimensions 

 and attractions are the same. 



As regards chemical properties, we find equal stability, 

 the same speed of formation, equilibrium when equal 

 quantities of each are present together, and equal heat of 

 formation. This quantitative proof raises to mathe- 



] Kekule had already suggested this arrangement of the carbon-valences, 

 as we have seen ; but the great advance made by Van't Hoff was that he 

 showed the practical bearing of this hypothesis on optical isomerism, on 

 geometrical isomerism, and on ring-formation, in every case bringing the 

 hypothesis to the test of experiment. 



