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347
this difference may be disregarded. — The cultures were run in
three parallel series, one jar in each. The seeds were put for
germination on filter-paper in Petri-basins on the 10th of June,
the seedlings planted on the 17th of June. As the absorption of
Ihe seedlings during the first fortnight may certainly be disregarded
in comparison with the contents of a jar, the continuous renewal
was begun two weeks after planting, as the supply of distilled
water was limited. The plants grew very well, though the later
appearance of a physiological disease, which will be discussed
below, caused a decrease in their turgescence. The roots of the
plants in VII showed the usual stunted appearance, many times de-
scribed as occurring in solutions showing lack of calcium. A late
infection of green aphides was checked through sprinkling with
distilled water. The plants were harvested on the 21st of August,
dried and weighed, each plant separately. The average dry-weight
per plant in relative values (Compare BaurE 1918 [4], p. 365) for
each parallel series were plotted in curves, over the ratio Ca: Na, each
point with its mean error! (figures 1, 2 and 3). The jar with the
least mean error of each ratio was selected to give a new series,
the relative values of which also were plotted in a curve (fig. 4).
The average curve for the three parallel series was caleulated and
plotted in the same way (fig. 5).” — The second experiment was
carried out in England in 1923 under somewhat different con-
ditions, yet, according to the author’s opinion, not too different
to exclude the possibility of comparing the general aspect of the
production curves of the two experiments. (Compare the discussion
* The mean error, u, of the arithmetical mean of n different figures will be
/ 2 Y
— _, where [4*|] means the sum of
n(n—1)
obtained by using the formula: u= + |
the squares of the actual deviations from the mean.
* This average curve was caleulated in the usual way, its ordinates in each
point being taken as the relative value of the arithmetical mean of the corre-
sponding average dry-weights of the three parallel series. The so called weighed
averages with their weighed mean errors of the three series were also calculated,
each average dry-weight of the parallel series being given a "weight^ equal to
the inverted square of its mean error. But as firstly no reasons for a greater
probability à priori for the different parallel series could be found, and secondly
all these weighed averages were nearly equal to the arithmetical ones, in fact
their difference was in all cases less than i of the mean errors given in the
curve, (except in VII, where the weighed average was less than the arithmetical),
the author considers his curve to represent the facts as nearly as possible. (Cl.
BaureE 1918, [4] p. 384.)
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