1889-90.] Professor Crum Brown on Optical Activity. 
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On the Relation of Optical Activity to the Character of 
the Radicals united to the Asymmetric Carbon Atom. 
By Professor Crum Brown. 
(Read June 2, 1890.) 
It is obvious that the amount of the optical activity of a given 
compound containing an asymmetric atom of carbon depends upon 
the amount of difference in character among the four radicals united 
to the asymmetric carbon atom, so that if two of them are very 
nearly equal we come very near to a compound of a symmetric 
carbon atom, in which the optical activity is zero. The question 
suggests itself, How are we to measure this difference of character ? 
We shall assume that there is a function, capable of numerical 
representation, derivable from the composition and constitution of 
the radical and the temperature of the substance, and that it is the 
difference between the values of this function in the case of two 
radicals which gives us the difference of character referred to. For 
the sake of brevity, we may call this function the k of the radical. 
The object of this paper is to show that, if there be such a function, 
there are methods by means of which we may hope to ascertain its 
value in each case. 
Let us represent the compound by the formula (C)ABrA, in 
which (C) represents the asymmetric carbon atom, and A, B, T, A 
the radicals united to it arranged in order of the values of k. How 
these radicals may be united to the asymmetric carbon atom in either 
of two ways. One of these ways — we have as yet no means of 
guessing which — corresponds to right-handed rotation, the other to 
left-handed rotation. The one form can be changed into the other 
