THE SPACE RELATIONS OF ATOMS. 495 



detected in substances containing less than two complex 

 radicals attached to A, though according to the general 

 rule many such substances should be asymmetrical. In 

 other words an asymmetric carbon atom 1 has never been 

 found sufficient to cause activity unless joined to at least 

 two other carbon atoms. 



(2) Two-dimensional molecules. Ethylene derivatives 

 were the first polyatomic compounds shown to have a plane 

 arrangement. The proof is due to Le Bel, who relied on 

 the fact that when we add R'" to each carbon atom in the 

 two isomeric substances having the formula CR'R" CR'R", 

 the resulting CR'R'R" CR'R'R" is, according to the 

 isomer taken, either inactive, or a mixture of two isomers 

 of equal and opposite activity in equal proportions. For 

 the formation of the active isomers in equal quantity can 

 only result from the fact that 2 R" is attached to half the 

 CR'R" CR'R" molecules on one side and to half on the 

 other, in corresponding positions. But in order that this 

 may be the case the molecules must present, when ap- 

 proached by the two R" groups in any direction, an atomic 

 arrangement exactly similar to that presented when the 

 approach is made in the opposite direction. Now there 

 are only two positions which possess such symmetry: (1) 

 The R'R" groups are in one plane, and the carbon atoms 

 occupy corresponding positions one on each side of this 

 plane ; (2) the whole arrangement is plane. 



But to the first kind of molecule the R'" groups could 

 attach themselves symmetrically only in the plane of the 

 R'R" groups and the result would be an inactive substance 

 only. Therefore the plane arrangement is the only one 

 admissible. That it satisfies all requirements is readily 

 shown. 



We then have for the two original isomers the two 

 formulae 



R R R R" 



I. C C II. C C 



R" R" R" R 



1 A carbon atom united to four, or a nitrogen atom united to five 

 different radicals is called an asymmetric atom. 



