245 



are present or not, we can now at once infer that every chemical 

 molecule must be considered to be resolvable into enantiomorphously 

 related components, when the stereometrical configuration of its atoms 

 possesses only axial symmetry. 



If, however, the configuration of the molecule be such, that it has 

 either axes of the second order, or one or more planes of symmetry, 

 there is no possibility of antipodes occurring; the case, where there 

 exists a symmetry-centre in the chemical molecule is, of course, 

 also included. 



Properly speaking, only the cases where a single asymmetrical 

 carbon-atom, or more generally: a single plurivalent asymmetrical 

 atom, is present in a chemical molecule, fall under the simple idea 

 of Van 't Hoff-Le Bel's theory, because only in such cases 

 is the dissymmetry of the molecule immediately evident, at least, 

 if we disregard for the moment the highly exceptional and very 

 improbable case of an arrangement which will accidentally appear 

 abnormally symmetrical. When, however, several asymmetrical atoms 

 in the molecule are present, and especially when we have to deal 

 with so-called cyclic compounds, or with such possessing double 

 bonds in their molecules, the symmetry of the stereometrical con- 

 figuration must be studied carefully, so as to be certain that the 

 conclusions drawn about the eventual occurrence of antipodes are 

 really right. Many erroneous statements on this subject are to be 

 found in works on chemistry ; and although the full discussion of this 

 matter cannot be given here, this being more the special subject 

 of text-books on stereochemistry, rather than that of the present 

 volume, - - yet it seems desirable to treat some important cases 

 here more in detail, because of the great significance of these views, 

 and for the purpose of illustrating the general applicability of the 

 doctrine of symmetry as developed in the previous chapters, also 

 to problems of the kind just mentioned. 



18. Before recapitulating these, it is perhaps better first to 

 make a few remarks on the optical activity of carbon-compounds 

 which possess only one asymmetrical carbon-atom. 



The theory of Van 'tHoff and Le Bel has been tested experi- 

 mentally in a great number of cases, and its correctness has been 

 fully confirmed. 



In all the compounds investigated, the asymmetrical carbon-atom 

 was always linked to at least one other carbon-atom; and the 

 question may arise, whether the conclusions drawn from that theory 



