402 Proceedings of the Royal Society of Edinburgh. [Sess. 
from one side. If the distribution given by Mr Leake be divided into six 
portions containing each four of the units and fitted to (3 + 1) 3 (1 + 3) 2 , we 
have the following comparison : — 
Actual +5 12 55 168 95 31 15 1*5 
Theoretical 0 10 69 152 109 32 4 
This is a very good fit, considering the nature of the experiments, for 
the data do not admit of any very accurate analysis. The length of the 
vegetative period is dependent on the season, and the original crossings 
have obviously been selected, so that any better result could hardly be 
hoped for. 
It is to be noted in this connection that the standard deviation of 
(3_l_l)m (i_j_3)«, i s constant if m + n = a constant, so that it affords a strict 
means of comparison between symmetrical and skew distributions if 
dominance holds. The degree of mixture of race cannot, however, be 
compared by this means, if blending holds in one case and dominance in 
another. The simplest case is that of the races blending with regard to 
four qualities, and is represented by (l + l) 4 . The same when mixed 
dominance holds is (3 + 1) (1+3); the extreme range is the same in both 
instances by hypothesis, yet in the former case yu 2 =l, an d in the latter 
/ul 2 = 15, so that between two equally mixed races a 50 per cent, difference 
might be observed. 
Concerning cases 3 and 4 there are no data, so that further discussion is 
at present unnecessary. 
Some remarks may be made in conclusion regarding the methods which 
should be observed in making experiments. Though no race is approxi- 
mately pure, it is most probable that the extremes of each race are more 
pure than the members between. In making cross-fertilisation experiments, 
then, the extremes should be chosen, as in that way the mixtures will 
be much more easily analysed mathematically. When, as in Mr Leake’s 
experiments, individuals are chosen from each race by special selection, it 
is hardly likely that results will be obtained which give much hope of 
satisfactory analysis. 
[Table 
