THE SPACE RELATIONS OF ATOMS. 141 



its derivatives, which contain two carbon atoms, and exist 

 in four isomeric forms occurring in two pairs, thus : — 

 r- and /-borneol a rotation [a] D = + and — 37 . 

 r- and /-borneol j3 rotation ,, = + and -- 2>3°- 



Compounds containing three asymmetric carbon atoms 

 should present eight isomers belonging to four types, and 

 there have been actually prepared three types correspond- 

 ing to the formula C0 2 H(c7HOH) 3 CH 2 OH, viz., arabonic 

 acid, xylonic acid, and ribonic acid. The corresponding 

 acids with four asymmetric carbon atoms, C0 2 H(CHOH) 4 

 CH 2 OH, should exist in sixteen different forms belonging 

 to eight types ; of these, eight isomers belonging to five 

 types are known. 



When the formula containing the asymmetric carbon is 

 symmetrical the number of isomers is reduced, as identity 

 results between what may be called the right-left and the 

 left-right combinations, so that with the left-left and the 

 right-right compounds we have altogether only three isomers 

 for two asymmetric carbons ; it has already been seen that 

 this is the number of isomers presented by the symmetrically 

 constituted compounds, tartaric acid and hydrobenzoin. A 

 corresponding simplification results for more than two asym- 

 metric carbons. 



To determine which configuration to assign to each 

 isomer is often difficult, and to decide which of the two 

 enantiomorphic symbols belongs to the right-rotating and 

 which-' to the left-rotating compound is impossible. But 

 in the case of tartaric acid, e.g., we recognise the symbol 

 C0 2 H 



, as belonging, on account of its symmetry, to the 



C0 2 H 

 "inactive indivisible " type. This enables us to assign to 

 that type of tetrose, COH(CHOH) 2 CH 2 OH, which yields 

 inactive tartaric acid on oxidation, the symmetrical formula 

 H 2 COH 



; while the other type, yielding active tartaric acid, 



OCH 



10 



