248 



The molecule thus possesses the symmetry of the group of the 

 second order 5. 



Another instance of a similar kind is found in the case of 

 methane- x ), and of tetra-methylene-derivztives of special configuration. 

 Let us imganine molecules such as: 



[CH.C(abc)]t or C[d-Cabc) z (l-C(abc) 2 ] 



which are represented by the models in fig. 165 and' 166: 



d'. 



Fig. 165. Fig. 166. 



Such molecules possess no less than jour or eight asymmetric carbon- 

 atoms, and also they have neither an inversion-centre nor a plane 

 of symmetry. Notwithstanding this, these compounds can never be 

 resolved into optically active antipodes, because both molecules have 

 a single quaternary mirror-axis A^ perpendicular to the plane of the 

 ring in the second, and placed vertically in the first formula. Having 

 thus a symmetry-element of the second order in their atomistic 

 arrangement, the configuration of the molecules must be congruent 

 with its mirror-image (group C 4 ), and therefore no fission of the 

 proposed kind can be possible. 2 ) 



1) G. Hart wall, Dissertation, Helsingfors, (1904). 



2) ' The groups (Cabc) are unsymmetrical, and thus are different from their 

 mirror-images. To avoid confusion, it is better therefore to discriminate them 

 pairwise by the prefixes d-, and /-; just because d-(Cabc) and l-(Cabc) are non- 



