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Essays in Biochemistry 



no simpler than the application of rule 4. Moreover, the information 

 so obtained is frequently less detailed. In example 6 we find a sym- 

 metry number of two for either XVa or XVc, which is too low for the 

 superposition of four identical groups. This result provides no in- 

 formation about the disposition of the a groups which can or cannot 

 be differentiated. Finally we shall find that the use of symmetry 

 numbers encounters difficulties from yet another source. 



We have thus far assumed, quite unrealistically, that molecules can 

 be represented by rigid bodies. The rotation around single bonds, in 

 particular, has presented a problem also in classical stereochemistry, 

 where it has been met by various devices, including the suggestions 

 that the symmetry properties of a molecule be determined for a prop- 

 erly selected conformation or for a time average of all conformations. 12 

 The first of these devices has been used in this discussion thus far; 

 the second can be applied to example 8. In examples 9 and 10, how- 

 ever, it is no longer possible to derive the correct answer if we merely 

 consider the symmetry properties of some rigid representation of the 

 whole molecule. We shall still find it possible, however, to apply 

 rule 4. ' 



Example 8, cyclohexane derivatives (XX). If one tests the chair 

 form XXa for the steric equivalence of the two carbon atoms labeled 

 a' and a", one obtains on rotation arrangement XXc which is obviously 

 different. However, the original compound is accompanied by an 

 equal amount of XX6 which yields XXd, when subjected to the 



XXa 



XXb 



XXe 



XXc 



XX d 



XX f 



corresponding motion. Since XXd can be superposed on XXa, and 

 XXc on XXb, the actual compound which contains equal parts of 

 XXa and XXb meets the superposition test even if the individual 

 molecules do not. It follows that the two a groups or b groups, re- 



