TWO ASYMMETRIC CARBON ATOMS 117 



prepared compound. This position may be chosen so that 

 the six groups combined with the two carbon atoms lie 

 opposite one another in pairs, as in Fig. 23. 



Number of isomers in multiple asymmetry. From the 

 standpoint thus adopted the number of isomers is only 

 increased by single linkage with a second carbon atom 

 when a new asymmetric grouping is so introduced, as e. g. 

 in a compound of the general type 



C (Rj^RgRgj C (R 4 R 5 R 6 ). 



The number of isomers in this case is two on account of the 

 one carbon atom, and is doubled by the presence of the other, 

 consequently four. In the same way, if n such carbon atoms 

 unite the number becomes 2 n . 



The arrangement and behaviour of these isomers may, 

 in the case of two asymmetric carbon atoms, be made clear 

 by the use of Kekule's wire model, and may be represented 

 on a plane by appropriate projection. Taking for that 

 purpose Fig. 23 as starting-point, R 1? R 2 ,R 4 , and R 5 lie on the 

 plane of the diagram ; then R 3 may be brought into it by 

 rotation upwards, about an axis passing through R : Ro, and 

 R 6 by rotation downwards about an axis passing through 

 R 4 R 5 . We thus get the substance represented by the 

 formula No. i following, and the three isomers are 

 Nos. 2, 3, and 4 : 



JVb. i No. 2 No. 3 A T o. 4 



RS R.3 J**3 R.S 



RI OjA< 2 rv^O-bv^ jttj Ort 2 jLv 2 Oi\^ 



R 4 CR 5 R 4 CR 5 R-CR 4 R 5 CR 4 



R 6 R 6 R 6 R 6 



It appears from this mode of representation that the four 

 isomers are arranged in pairs 2 and 3, i and 4, each group 

 including two configurations behaving as opposite reflected 

 images, and are thus the expression of optical antipodes 

 like those that occur with a single asymmetric carbon atom. 

 This behaviour is still more easily understood by con- 

 sidering the optical rotation due to each carbon atom 



