254 



to make sure that the configuration thus obtained has no axis 

 of the second order, nor any symmetry-plane, nor a centre of 

 symmetry 1 ). If this be done, the compound will be such as to be 

 possibly resolved into enantiomorphous isomerides. But if one of 

 the symmetry-properties of the second order mentioned be found in 

 the model, the substance will not be resolvable into two enantio- 

 morphously related isomerides, not even if there were eventually 

 several asymmetric carbon-atoms present in it. A few instances 

 may be exemplified here to make this clear. 



21. The oldest known example of a compound which cannot 

 be resolved into enantiomorphous isomerides, although it possesses 

 several asymmetrical carbon-atoms, is. meso-tartaric acid: 



COOH 



*CHOH 



*CHOH 



COOH 



Evidently the one half of the molecule is here the mirror-image 

 of the other half; or what is the same thing: the stereometrical 

 configuration of atoms has here a plane of symmetry, and, therefore, 

 it cannot differ from its mirror-image. Formerly this was explained 

 by saying, that the rotatory effect of the one half of the molecule 

 was counterbalanced by that of the other half, and such molecules 

 were, therefore, said to be inactive and non-resolvable "by internal 

 compensation". The explanation given here is, however, better, because 

 it does not introduce any superfluous hypothesis, but elucidates 

 the fact merely as a direct consequence of 'the general doctrine of 

 symmetry. It simply states, that no enantiomorphism of stereome- 

 trical arrangement can ever occur, when the configuration of atoms 

 as a whole shows any symmetry-element of the second order 2 ). 



The same is true with trioxyglutaric acid: 



1 ) The "plane of indirect symmetry", as mentioned by Ladenburg and by 

 Groth in the discussion of the impossibility to resolve certain diketo-pipevazines 

 into antipodes, corresponds to no other operation than inversion. Such molecules 

 cannot be separated into enantidmorphous modifications, because they have an 

 inversion-centre, which is equivalent to a binary-axis of the second order; they 

 are, therefore, congruent with their mirror-images. It is quite superfluous to 

 introduce here any new name. 



2 ) A case similar to that of meso-tartaric acid, etc., has also been studied by 



