April, 1915.] The Inheritance of Size in Tomatoes. 491 



based on linear dimensions, to show complete segregation of size 

 characters, varying in the Mendelian fashion from the larger to 

 the smaller parent. He assumes a cross between two toinatoes 

 with the linear dimensions 4x4x4 and 9x9x9 respectively, and gets 

 an F-1 hybrid which is ()x()xG. He assumes factors for length, 

 width, breadth and shape. Shape inodifies the dimensional 

 factors, while each of the three dimensional factors modifies the 

 other two, from which it can be seen that this is a multiple factor 

 hypothesis. If all the tomato fruits were perfect spheres, this 

 explanation would be more tenable; but, as noted before, the 

 extreme irregularity of shape causes any explanation, founded on 

 linear dimensions, to be liable to considerable error. 



The results presented in this paper, showing apparently such 

 unusual dominance of the red currant size factors, cannot be 

 interpreted by Groth's hypothesis. However, a Mendelian 

 explanation has been worked out which agrees fairly well with 

 the facts. This explanation is given in the following paragraph, 

 as it seems to be the best possible interpretation of these results 

 at the present time. 



As noted before, Nilsson-Ehle in his work on tri-hybrid red 

 wheat found in the second generation 63 grains of varying redness 

 to one white wheat grain. From this he reasoned that the red 

 grains possessed three independent color factors each of which 

 was able to give the red color to the wheat. In the F-2 tomato 

 generation 44 plants have been grown and the segregation of size 

 characters has been so incomplete as to warrant the assumption 

 of at least four size factors. The small size factors of the red 

 currant seem to be incompletely dominant oyer the large size 

 factors of the yellow pear, because, when an equal number of 

 large and small size factors are present, as in the F-1 generation, 

 the geometrical mean between the parents is realized. As the 

 number of small size factors increases or decreases from the number 

 present in the F-1 generation so will the weight of the resulting 

 fruit vary more or less from the geometrical mean. This varia- 

 tion will not be large, as the small size factors, however few, are 

 incompletely dominant over any number of large size factors. 

 There should be occasional returns to both parent sizes, the 

 frequency depending upon the number of factors concerned. If, 

 with further experiments, no such original joarental size is ever 

 attained, there is evidently more than multiple factors involved. 



SUMMARY. 



1. A more accurate representation of the .size of tomato 

 fruits can be obtained from their weights than from their linear 

 dimensions. 



2. The size of fruit of the F-1 generation of the currant-pear 

 cross is the geometrical mean between the parental sizes. 



