F. L. Engledow 111 



The investigation began in 1913. Prior to that year the material was 

 in the hands of Professor Biffen. 



A certain amount of sterility was encountered, but as the details 

 given below make clear,its incidence was neither selective nor sufficiently 

 heavy to bias the numerical results recorded. 



In the F^ a few plants failed to mature by harvest time, and conse- 

 quently they were not measured. These again were not selective, but 

 included all three of the length types found in F^. 



The Fs plants were kept unthreshed during 1914 — 19, and it is 

 hoped to raise an F^ in 1920. 



II. The Observations and the Method of Measurement. 



The class-intervals of measurement are, throughout : 

 For glumes, 1*0 mm. ; for grains, 0*5 mm. 

 As a fact, the glumes were measured to 0*5 mm., but on this basis the 

 frequency distribution, in the case of Polish, covered a range of 45 classes. 

 Hence to facilitate statistical work and to smooth out the irregularities 

 introduced into such a distribution by very small classes, the observa- 

 tions were regrouped into 1*0 mm. classes. As a result of this regrouping 

 a non-integral {x'b) number of individuals is to be found as the class 

 frequency in some parts of the tables of observations. 



In all the generations one ear per plant was harvested and one 

 glume per ear was measured. The grain situated nearest to that glume 

 was measured also. Either glume of the median spikelet on either side 

 of the rachis (i.e. any one of a specified set of four glumes) was selected 

 for measurement. 



The acceptance of one glume-length as a characteristic of the ear 

 concerned, was justified by a separate investigation. It was first estab- 

 lished that the glumes of the median group of four spikelets on an ear, 

 were all of practically the same length. Thus the average of this set of 

 eight glumes (from four spikelets) could be regarded as a characteristic 

 of the ear. Next, for every F^ plant (total 492 plants) these eight 

 glumes (and with them the corresponding eight grains) were measured. 

 The frequency distribution of the deviation of every single measure- 

 ment from the mean of the set of eight to which it belonged, was then 

 compiled, regard being paid to the sign of the deviation. The mean 

 quartile deviation of the distribution was 0'401 mm. by direct calcula- 

 tion and 0'435 mm. when calculated from the standard deviation of the 

 distribution on the assumption of normality. That is to say, fifty per 



8—2 



