166 Essays in Biochemistry 



of the paper and which passes through the center of the C-C bond, 

 XV6 results. Similarly, rotation of XVc around an axis which lies 

 within the plane of the paper and which bisects and is perpendicular 

 to the C-C bond yields XVd. The conclusions which can be drawn 

 from these two operations are identical since both demonstrate the 

 steric equivalence of C and C", of b' and b", of a' and a"", and of a" 

 and a'", respectively. As no other motions produce indistinguishable 

 arrangements we can conclude that the following pairs can be differ- 

 entiated: a' from a", a' from a"', a" from a"", and a"' from a"". 

 The steric inequalities could have been deduced also by considering 

 example 6 a special case of example 3, which shows that a' and a" 

 can be differentiated as well as a'" and a"". The remaining relation- 

 ships between the a groups follow, then, from consideration of the 

 steric equalities already established. The molecule arranged as in 

 XVa possesses two planes of symmetry, as in XVc a plane and a center 

 of symmetry. As the a groups lie outside these symmetry elements, 

 the prevailing steric inequalities are predicted also by rule 1 which, 

 however, gives no information about the groups which cannot be 

 differentiated unless further symmetry considerations are applied. 

 Structure XVa has a twofold simple axis, and XVc a twofold simple 

 axis as well as twofold alternating axes. The results obtained, there- 

 fore, are clearly inconsistent with rule 2. The compound contains two 

 meso carbon atoms. Rule 3, therefore, predicts correctly two of the 

 steric inequalities of the a groups but fails to disclose the two others. 

 Moreover, it does not indicate the presence of identical substituents 

 which cannot be differentiated. 



Example 7, Cabc-Cabc (XVI and XVII). Again, as in examples 

 4 and 5, the results to be expected depend on the configurations of 

 the asymmetric centers. Application of our criterion to the meso 

 compound XVI shows that all pairs of identical substituents as well 

 as the two central carbon atoms can be differentiated, whereas this 

 is impossible with the optically active forms since XVTIa on rotation 



a' be' a' b c' a" b" c* 



\!/ \i/ \i/ 



c' c c 



c" c" c 



b a" a" b c" a' b c' 



XVI XVIIa XVIIb 



