256 



tar ic acid and tartaric acids mentioned above, not only two active 

 and one inactive form besides the racemic compound, but two active 

 and two inactive isomerides. A carbon-atom as found here in the 

 midst of the molecule of trioxyglutaric acid, is called a pseudo-asym- 

 metrical carbon-atom. 



As to the number of isomerides which can be expected when the 

 number of asymmetric and pseudo-asymmetric carbon-atoms in 

 the molecule is known, the following data may suffice. 



If n be the number of true asymmetric carbon-atoms in the mole- 

 cule, N a the number of the possible optically active isomerides, 

 Nj that of the possible inactive and non-resolvable isomerides, and 

 N r the number of racemic compounds, we have in the various cases 

 the following relations: 



a) If no reduction of the number of isomerides occurs, neither 

 by "internal compensation", nor by the presence of a pseudo-asym- 

 metric carbon-atom in the molecule, then generally: 



N a = 2 n , and N r = J N a = J. 2", while N t = 0. 



b) If internal compensation occurs, without the influence of a 

 pseudo-asymmetric carbon-atom, then: 



N a = 2- J , N r = J. 2-', and N t = 2~ 2 ~*- 



c) If there be a pseudo-asymmetric carbon-atom, these numbers 

 become : 



n 1 n 1 n 1 



N a = 2 n ~ 1 2~*~; N r = ^ (2-* 2~^~); and Nt = 2~*~. 



22. In the case considered here, the impossibility of the fission 

 of the mesotartaric acid and of the two inactive trioxyglutaric acids 

 was an immediate consequence of the existence of a symmetry- 

 plane in their atomistic arrangement. The same, however, must 

 occur if the arrangement has a mirror-axis or a symmetry-centre 

 among its symmetry-elements. Such cases can occur, as soon as 

 asymmetric carbon-atoms are units of a cycle of atoms. A few selected 

 instances may further explain this. 



If there be only a single asymmetrical carbon-atom in the ring, 

 the influence produced by that atom is in principal features the 

 same as that in open-chain compounds with a single asymmetric 

 atom. In such cases the plane of the ring can, of course, never be a 

 symmetry-plane of the molecule, and the number of isomerides is two, 

 not counting the racemic compound. If, however, there be two or more 

 asymmetric carbon-atoms, more detailed examination is necessary. 



