460 BOTANICAL GAZETTE [DECEMBER 
which is insufficient to determine with certainty either the fact or 
the frequency of their occurrence. 
The mutations sought by the sugar-beet breeder are not neces- 
sarily morphologically distinguishable from other individuals of 
the variety. They are plants which have undergone constitutional 
alteration and hence possess new potential limits of physiological 
elasticity which they transmit to their progeny. 
The valuable plants of this class are those which transmit a 
higher sugar-producing capacity to their progeny than possessed 
by the variety regardless of their own qualities. In fact, we are 
hardly justified in assuming that the mutants themselves possess 
conspicuously high qualities. They are more likely to lie near the 
mean of the variety than at either limit of its range. This is illus- 
trated for a particular case in fig. 51. 
The frequency polygon A shows the actual distribution of 3784 
beets for percentage of sugar, while At shows a similar distribution 
of the hypothetical progeny of a supposed mutant. ‘Their means, 
represented by the vertical lines M and M*, are 17.67 and 18.67 
respectively, and hence differ by 1 per cent sugar. , The bulk of the 
mutant’s progeny in polygon A? lie between classes 17-21, which is 
about 22 times as great as the proportion lying above 21. Since 
the records of the progeny are an expression of the potentialities 
of the mutant, the mutant itself is 22 times as likely to lie between 
17-21 in the original population of polygon A as above this group. 
The possibilities of finding a mutant by taking a limited num- 
ber of roots from the material represented in polygon A are some- 
what greater in the classes above 21 than between 17-21. There 
are in polygon A about 100 times as many individuals in the classes 
17-21 as above 21. If the mutant were equally likely to appear in 
either group, the chances of finding it by taking an equal number of 
roots from each group would be o. or as great in classes 17-21 as M 
the population above 21. However, we found that the chances 
of the mutant’s lying in group 17-21 are 22 times as great as in the 
other group, therefore the possibilities of finding it by. drawing 
an equal number of roots from each group are not as 0.o1:1, but 
as 0.22:1, or about 1:4.5. If the whole polygon A were divided 
into two groups, so that all the roots containing 21 per cent sugar 
