R. P. Gregory 79 



have been used as parents : their offspring are shown in the following 

 table : 



Cross 



Pure short-styled X Self 



Pure short-styled ? x Long- sty led s 



Long-styled? x Pure short-styled <r 



Totals — 789 



Several thousand plants have been raised from crosses of (long- 

 styled X long-styled), all the offspring being long-styled. 



Heterozygous short-styled plants. 



The results of crosses in which heterozygous short-styled plants 

 were used are shown in the accompanying table (p. 80). 



Although the results are in general harmony with simple expec- 

 tation, yet the observed numbers diverge rather widely from the 

 calculated ones'. The divergences are, moreover, in opposite directions 

 according as the cross is of the type {DR x DR) or of the type 

 (DR X R) and the reciprocal form. The heterozygous short-styled 

 plants, self-fertilized, show a deficiency of short-styled offspring as 

 compared with the expected ratio of 3 short : 1 long ; the same plants, 

 crossed either way with long-styled plants, give an excess of short-styled 

 offspring. In the former case the divergence from the ratio 3 : 1 is 

 more than twice as great as the probable error of a random sampling 

 taken from a population mixed in that ratio ; and an equally great 

 divergence occurs in the results of the crosses {DR x R) and {R x DR) 

 taken together-. 



1 The results of two experiments, each of which would have the effect of slightly 

 increasing the divergence, have been excluded from the totals given in the Table (p. 80). 

 In each case a long-styled plant ? was crossed by a short-styled <? ; the j parents 

 were known to be heterozygous, but the offspring, 9 in the one case, 5 in the other, 

 consisted of short-styled plants only. The cases are excluded owing to the possibility 

 that the two short-styled plants were behaving in a manner similar to that of the 

 abnormal case described on p. 84. One other very aberrant family has also been 

 excluded, owing to the possibility of error. This family was produced from a mating 

 (F^ ? X long-styled <J ) and consisted of 27 short-styled and 9 long-styled plants (expected 

 equality). 



- The probable error for random sampling of TV individuals of two kinds mixed 



w NpQ 

 in the proportion p : q is given by the formula p.e. = -6745 - — ^ . The errors given in 



the table show the probable departures from the exact ratios 3 : 1 and 1 : 1 respectively 

 for the numbers concerned. I am indebted to Mr A. B. Bruce, of the Cambridge 

 University Department of Agriculture, for this formula. 



