106 AMERICAN BREEDERS MAGAZINE. 



between them equal sperms meet equal eggs, so that in each case 

 the resultant offspring should be exactly equivalent in all their heredi- 

 tary qualities and the coefficients 9.081 per cent and 9.063 per cent 

 must be measures of the non-hereditary variations or "fluctuations," 

 while the coefficient 12.63 per cent in the F 2 is the result of the con- 

 currence of hereditary and non-hereditary variations. 



The number of rows on the ear, which is used here as a measure 

 of the variability, is not in itself of great practical importance, of 

 course, but the general question of variability, which is illustrated by 

 this character, is of very great practical value.' The possibility of 

 attaining a fair degree of uniformity in the several desirable qualities 

 will favor a more definite specialization of the crop to meet particular 

 desired ends. Besides, any diversity in the qualities of the crop 

 necessarily means a lower value in regard to each desirable quality 

 than would be attainable if all individuals were brought up to a uni- 

 formly high standard. 



Another very practical point in regard to this second generation 

 and which emphasizes the importance of utilizing the F x plants for 

 the crop each year, is seen by a comparison of the yields per acre (see 

 Table 1) produced by the F 2 as compared with F v In both of the F 2 

 families the yield is less than the corresponding yield of the F t families, 

 and when taken together this difference amounts to 8 bushels per 

 acre. When considered in connection with the increased variability, 

 this serves to further illustrate the point made in the last paragraph, 

 namely, that the increased range of variation means a decreased yield. 



The results of all my investigations to the present time, which 

 seem to demonstrate that there are many distinct biotypes of corn 

 continually mingled together in complex hybrid combinations, and 

 that there is a stimulating effect of heterozygosis, may be summar- 

 ized in the following statements. The first four of these propositions 

 were demonstrated by data presented in my paper on "The composition 

 of a field of maize" ; the next four in "A pure-line method of corn 

 breeding"; and the present paper gives further proof of the correct- 

 ness of (6), (7) and (8), and adds the last four. 



(1) The progeny of every self-fertilized corn plant is of inferior 

 size, vigor and productiveness, as compared with the progeny of a 

 normally cross-bred plant derived from the same source. This is true 

 when the chosen parent is above the average conditions as well as 

 when below it. 



