n8 MOLECULAR STRUCTURE 



separately, which we may write A and B, A and B. 

 The rotations then are : 



No. i No. 2 No. 3 No. 4 



A + B -A+B A-B=-(-A+B) -A-B 



= -(A + B). 



These possibilities are easily realized by combining an 

 acid and base, each of which occurs in two opposite active 

 modifications, such as lactic acid and coniine. The four 

 possible salts then are : 



No. i No. 2 No. 3 No. 4 



A+B -A + B A-B -A-B. 



cMactic acid. t?-coniine Z-lactic acid. c?-coniine c?-lactic acid, i-coniine Macticacid. ^-coniine 



As an example of this fourfold isomerism in a single body 

 the dibromocinnamic acids may be chosen : 

 C 6 H 3 CHBrCHBrCOOH. 



The two asymmetric carbon atoms are distinguished by 

 underlining. It is well known that Liebermann succeeded 

 in obtaining from cinnamic acid, C 6 H 5 CHCHCOOH, by 

 addition of bromine, an inactive mixture or racemic com- 

 pound which could be split up into the pair of the one type. 

 The other pair was obtained in a similar way from allo- 

 cinnamic acid, which is isomeric with cinnamic acid. 



Inactive undecomposable type. A separate discussion is 

 required for the case, which may be regarded as a special 

 case of the above, in which the atoms or groups attached to 

 the two carbon atoms are similar in pairs, i. e. 



E t = E 4 , E 2 = E 5 , E 3 = E 6 , 

 as in tartaric acid, 



COOHCHOHCHOHCOOH, 

 in which 



Ej = E 4 = H, E 2 = E 5 = OH, E 3 = E 6 = COOH. 



The four former symbols then become : 



E 3 E,, E 3 E 3 



E t CE 2 E 2 CE 1 E] CE 2 EgCEj 



Ej CE 2 EjCEg EgGEj E 2 CE^ 



E 3 E 3 E 3 E 3 



