182 Proceedings of Royal Society of Edinburgh. [sess. j 
by interchanging the positions of any two of the radicals. Now we 
cannot directly interchange the positions of two radicals by any 
method such that we can be sure which radicals have been inter- 
changed, but we can act upon one radical so as to increase or diminish 
its k, and if, for example, the k of B is increased so as to be greater 
than that of A, we have now a new compound, (C)A 1 B i r i A 1 , 
in which A 2 is the modified B, and B 1? r i? A 1 are the original 
A, r, A respectively. But we see that we have changed the order in 
which the radicals (arranged in order of values of k) are united to the 
asymmetric carbon atom. If the original compound is represented 
by (1) in the figure above, the new compound corresponds to (2). 
If therefore the original compound were right-handed, the new one 
will be left-handed, and vice versa. The change of sense of rotation 
is thus an indication that a change has been effected in the value of 
the k of a radical such as to change the order of the radicals. 
We do not know very many cases of such change, but we know 
enough to illustrate the foregoing. In right-handed tartaric acid 
there are two asymmetric carbon atoms, but as these are perfectly 
similar in all respects we need only look at one. This is then our 
(C), and our A, B, T, A, are (arranging them provisionally in order 
of mass) -CH(OH)— CO— OH, -CO— OH, -OH, and -H. By 
treatment with acetyl chloride, tartaric acid is converted into diacetyl- 
tartaric acid. Here the radicals are (preserving the order of union 
to the asymmetric carbon atom) -CH(0 — CO — CH 3 ) — CO — OH, 
-CO — OH, -0 — CO — CH 3 , and -H. Now the diacetyl- tartaric acid 
from right-handed tartaric acid is left-handed. We shall assume 
that addition to a radical increases the value of k, and that there- 
fore the k of -CO — OH is greater than that of -OH, and that k is 
increased when -OH is converted into -O — CO — CH 3 ; making these 
assumptions, we find then that the k of -0 — CO — CH 3 is greater 
than that of -CO — OH. Again, we can convert right-handed tartaric 
acid into its ethyl ether. Here, preserving the old order, we have 
the radicals -CH(OH)— CO— 0—C 2 H 5 , -CO— 0—C 2 H 5 , -OH, and 
-H. This ether is right-handed. From it, by the action of acetyl 
chloride, we can obtain diethyl diacetyl-tartrate. Here we have 
the radicals -CH(0 — CO — CH 3 )— CO — O — C 2 H 5 ,-CO — 0 — C 2 H 5 , 
-0 — CO — CII 3 , and -H. This ether is also right-handed, but only 
to a small extent. We thus see that the k of -0 — CO — CIT 3 is less 
