490 
The Ohio Naturalist. 
[Vol. XV, No. 6, 
Emerson says (b), “A hurried examination of data, both 
published and unpublished, derived from my own studies of size 
in beans and maize, indicates that the F-l 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-l 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-l 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-l 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-l fruits approach more nearly the arithmetical 
than the geometrical mean between the parental sizes. Neither 
is it certain that all the F-l fruit-sizes can be made to approach 
more 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-l fruit-size to 
the geometrical or arithmetical means between these parents. 
Accordingly all available data upon F-l 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-l 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-l 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 true. This 
statement has been formulated not because it is well understood 
but because it may suggest principles of size inheritance which lie 
deeper than those now known and which, it is hoped, will be more 
full) - known in the light of future investigations. 
The inheritance of size of fruit in the F-2 generation has 
received even less study than the inheritance of size in the F-l 
generation. Groth seems to have been the only one to attempt 
an explanation. He has worked out a theoretical hypothesis, 
(b) See (20) page 57. 
