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order of Jheris amara, grown on the sand, deviates entirely, being 
a semi-curve. For the culture on fertile earth, however, this same 
character gives a symmetrical curve. In fig. V this latter is very 
flat and extended in length, as the observations were divided over 
a great number of intervals in order to allow a comparison of the 
two curves. If, however, the observations are arranged to a number 
of groups equal to that of the other figures, the curve thus obtained 
is not different from those of the other characters. For this culture 
the median is 58, the quartile 17.25 and the variability-coefficient 
— 0.32, the minimum number of side-branches being 1, the maxi- 
mum 162. 
With this character now, bad nutrition does not result in a simple 
shifting of the curve to the left, accompanied by greater or smaller 
ê QO 
changes in the values of J/, Q and ar as in the other cases, but 
here the symmetrical curve changes into a semi-curve of which the 
apex lies at zero. 
We can explain the origin of this semi-curve in the following way. 
The lower limit for the number of branches of the third order 
of Jberis amara is 0. Since the plant also blooms on the principal 
stem and on the branches of the second order, it may exist without 
branches of the third order. Under favourable nutritive conditions 
the development of the plant is so vigorous that in all individuals 
branches of the third order are formed, but in greatly diverging 
numbers, as is shown by the curve of fig. V for this culture. With 
unfavourable nutrition, however, also individuals arise in which no 
branches of the third order are originated and as nutrition becomes 
worse the number of these individuals will become greater. Hence 
we see that with the very bad nutrition of the sandy soil, a great 
number of plants has no branches of the third order and so has 
reached the lower limit, the other specimens bearing a greater or 
smaller number of these side-branches, as is shown by fig. V for 
this culture. This leads us to the conviction that the semi-curve for 
this character is a necessary consequence of the fact that by the 
unfavourable nutritive conditions the variation-curve is shifted in 
such a way that it strikes against the lower limit of the whole 
range of variation of this character, a great many of the individuals 
showing this lower minimum value. 
Also with Anethum graveolens a great difference is noticed in the 
shape of the curves of the number of umbel-rays in the two cultures, 
fig. VI. The curve of the well-fed plants is nearly symmetrical, while 
