B— CHEMISTRY 



55 



From this point of view the optical activity of hving matter is an 

 inevitable consequence of its property of growth. 



The question how an original bias could have arisen provokes an 

 inquiry into the probable degree of variation from exact equality to be 

 expected in the numbers of d- and /-molecules when a given number of 

 molecules of a dissymmetric compound are produced under undirected 

 conditions. 



It is very well known that the most probable distribution of d- and 

 /-molecules is that in which the numbers of the two kinds are exactly 

 equal. The probability of the occurrence of this exact distribution, where 

 the numbers are large, is, however, very small, and is greatly exceeded by 

 the sum of the probabilities of the other distributions. An exactly equal 

 distribution will practically never occur, and it is of interest to know the 

 average degree of inequality to be expected for a given number of 

 molecules. 



This is easily calculated for a relatively small number, for example, 

 100,000. Plotting the probabilities of obtaining given numbers of 

 ^-molecules, as ordinates, against the numbers, as abscissas, a symmetrical 

 curve is obtained — 



49,500 



50,000 

 Fig. 8. 



50,500 



100,000 

 (/-molecules. 



which just becomes distinguishable from the base-line at about 49,500 

 and rises to a maximum at, of course, 50,000 J- molecules. The ordinate 

 of 49,894 divides the half-area into two equal portions. If, therefore, a 

 number of groups of 100,000 molecules of a dissymmetric compound are 

 produced under conditions vmder which the probability of formation of 

 d- and /-molecules is equal, half the groups will contain an excess of more 

 than 212 molecules of one enantiomorph or the other. We may regard 

 this proportion of o-2i per cent, as expressing the degree of statistical 

 dissymmetry (which we may call k) to be expected when 100,000 dis- 

 symmetric molecules are produced under unbiassed conditions. 



As we take larger and larger numbers of molecules the average difference 

 between the numbers of d- and /-molecules produced becomes, of course, 

 absolutely greater, but relatively less. 



