490 The Ohio Naturalist. [Vol. XV, No. 6, 



Emerson says (b), "A hurried examination of data, both 

 piibHshed and unpubHshed, derived from my own studies of size 

 in beans and maize, indicates that the F-1 sizes are nearer the 

 average than the geometric means between the parent sizes." 

 When all of the available data of Emerson is considered, a part of 

 the F-1 sizes show a near approach to the geometric mean and a 

 part to the average. He made a cross between the Black Mexican 

 and Tom Thumb varieties of corn and obtained an F-1 hybrid 

 whose weight was the exact geometric means between the parent 

 weights. The breadth of the hybrid seeds, however, show a 

 closer approach to the arithmetical than to the geometrical mean. 



A very extensive series of experiments have been conducted 

 at the New Jersey Experiment Station upon the quantitative 

 inheritance of characters in peppers. Part of the F-1 sizes 

 approach the arithmetical and part approach the geometrical 

 mean between the parents. 



From the data enumerated above and from the other available 

 data, it appears that there has not as yet been a sufficient amount 

 of work done to enable a definite statement to be made, as to 

 whether the F-1 fruits approach more nearly the arithmetical 

 than the geometrical mean between the parental sizes. Neither 

 is it certain that all the F-1 fruit-sizes can be made to approach 

 m.ore nearly to one than to the other of these two means. The 

 suggestion came to the mind of the writer of this paper that per- 

 haps there was some correlation between the relative difference 

 of parental fruit-sizes and the approach of the F-1 fruit-size to 

 the geometrical or arithmetical means between these parents. 

 Accordingly all available data upon F-1 size inheritance was 

 studied. This examination seemed to indicate that when two 

 varieties are crossed which differ greatly in fruit-size (the fruit- 

 size of one parent being probably about two, three or more times 

 the size of fruit of the other parent), the resulting F-1 fruit-size 

 will be nearer to the geometrical than the arithmetical mean; but 

 when two parents similar in fruit-size are crossed, the size of fruit 

 of the F-1 offspring will approach more nearly to the arithmetical 

 than the geometrical mean. There are some exceptions to this 

 statement but as a general rule it was found to be ti'ue. This 

 statement has been fonnulated not because it is well understood 

 but because it may suggest principles of size inheritance which lie 

 deci)cr than those now known and which, it is hoped, will be more 

 fulh' known in the light of future investigations. 



The inheritance of size of fruit in the F-2 generation lias 

 received even less study than the inheritance of size in tlic F-1 

 generation. Groth seems to have been the only one to attempt 

 an explanation. He has worked out a theoretical h\-i)othesis, 



{b) See (20) page 57. 



