SEVERAL ASYMMETRIC CARBON ATOMS 119 

 The rotations corresponding are : 



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



AA o AA=2A + 



since in No. i the groups round the two carbon atoms are 

 reflected images of each other, and therefore produce equal 

 rotations, but in opposite senses. There arises, therefore, 

 an inactive type that is not capable of decomposition, 

 Nos. i and 4, which, however, is represented by only 

 a single substance, since i and 4 can be made to coincide 

 by rotation, and, therefore, symbolize one and the same 

 substance. The facts as to tartaric acid completely verify 

 the expectation, for we have : 



No. 2 and No. 3. The two active tartaric acids, together 



with racemic acid, their compound. 

 No. i or No. 4. Inactive undecomposable tartaric acid. 



Several asymmetric carbon atoms. In this case it is an 

 advantage to use, instead of Kekule's metallic model, that 

 of Friedlander, in which each carbon tetrahedron is 

 represented by four rubber tubes united in the centre, 

 whilst little sticks of wood inserted in the tubes render 

 possible mutual connexions, or serve to indicate the 

 attached atoms or groups by means of coloured balls on 

 the ends. The carbon atoms joined together, givin 

 a substance of the general formula, 



C(abc), C(de) 9 C(fgh), 



are expressible, according to Fischer's suggestion, by 

 ing c upwards about the axis a&, and h downwards about 

 the axis fg. Everything is then in one plane, and can be 

 shown upon paper. The 2 n = 2 3 = 8 possibilities for the 

 cases of triple asymmetry are then as follows : 



