1913] EAST—CROSSES OF NICOTIANA 185 
fluctuation is proportional to the size of the individual? Is it 
not true that favorable circumstances which force the corollas of 
N. forgetiana to become 5 mm. longer than usual will produce a 
10 mm. change in WN. alata grandiflora? 
If this is the correct way of looking at these two cases, then it 
is assuredly an error to plot the F, distribution—which includes 
both grandparental sizes—in classes of equal size. Assuming 
that our hypothetical size factors affect the individual as growth 
forces, it seems probable that they are not only cumulative but 
accelerative. Roughly one might imagine the effect on the 
individual to be something like a constant percentage. I do not 
believe these cases of size inheritance can be analyzed into their 
component factors and these factors given their proper weight 
(using the word factor in the general sense of elements or causes 
that produce a result) sufficiently well to give a precise value to 
the character determiners themselves. On the other hand, it is 
interesting to see just what is necessary in the way of class range 
to bring our F, corolla distribution to the normal distribution for 
four factors (n=4). Fortunately the corolla sizes were taken by 
millimeters, so this can be done. First I have smoothed the 
figures according to the regular method. The distribution in one- 
- millimeter classes i is then as follows (table IV, p. 186). 
Suppose now we begin at 24 mm. and take for this class a range 
of 4mm. Then let us increase our class range 1 mm. each time. 
This gives a simple arithmetical progression with an advancing 
difference of the second order, that is, the differences between the 
class ranges are constant. Compare the frequency distribution 
thus obtained with the expansion of (3-+3)*" where m is equal to 
4. This is done in table V, with an agreement among the figures 
that is very remarkable. If I were a biometrician, I probably 
could show that this agreement could not be due to chance—since 
by chance it could only occur once in some hundreds of thousands 
of times—and must therefore have some great significance. I 
should prefer to believe that I happened by chance upon a series 
of class ranges that fitted the normal frequency theory. But it 
must be emphasized that it was a constant increase in class range 
that produced the normal curve from the distorted skew curve. 
