114 Glume- Length and Grain-Length in Wheat 



distribution (i.e. 11*5 mm. in Table IV). If this were so, then that part 

 of Table IV lying between 11 "5 mm. and 9*5 mm. (both values inclusive) 

 was the lower half of the distribution of all the plants of Kubanka type 

 in the F^. The upper half of the distribution was obtained by writing 

 down the frequencies symmetrical about 11*5 mm. to those of the lower 

 half From the distribution so completed the standard deviation (o-) 

 and number of observations {N) were found, and the mean M was, of 

 course, 11'5 mjn. The "normal" curve equivalent to this distribution 

 was calculated [see Yule (5) for formula and tables for use in calculation]. 

 By the same processes the normal curve for the distribution of the 

 Polish type of F^ was obtained. Subtraction of these two normal distri- 

 butions from the total F2 gave the distribution of the heterozygote or 

 intermediate type. Thus calculated, the frequencies of the F^ types 



were : 



KIP 



23-29% 57-76% 18-94%: 

 while the modes were : 



11*5 mm. 16*5 mm. 245 mm. 



This theoretical " dissection " was carried out for the sole purpose of 

 testing the i*eliability of mathematical analysis of the Fo as against the 

 far more lengthy and laborious genetic analysis by means of a com- 

 plete ^3. 



Clearly, the analysis of F^. into constituent genetic types necessitated 

 the raising of a complete F^. 



F,. 



The Fs plants were kept in " families," an F^^ family consisting of 

 all the plants raised from the grain borne by any one F^ " mother " 

 plant. From the nature of the Fs family the genetic type of the corre- 

 sponding F2 plant was judged. Thus an F3 family in which all the 

 plants were P, must have originated from a homozygously P plant of 

 the Fq ; similarly in the case of K. An F^ family containing plants of 

 two or more types, e.g. P, I, and K, or P and /, or / and K, or P and K, 

 must have come from an F^ plant that was heterozygous, i.e. an / plant. 



The sorting into types of the F3 families necessitated a definition of 

 the three types P, I, and K (the tri-modality of the F2 distribution 

 pointed to the existence of only three types). Measurement as opposed 

 to eye-judgment was intended to be the essence of this investigation, 

 and an attempt was made to set up measurable (quantitative) type 



1 



