C. Cool and A. N. Koopmans 
39 
(2) Countings of Pastinaca sativa. 
Variation of the number of umbel rays of the terminal umhel. 
In Table I are arranged, according to the increasing numbers of umbel rays, 
terminal umbels of two groups of plants growing in different places ; the first group 
of 341 plants came from clayey and peaty waysides in the neighbourhood of Delft 
(Holland), the second of 335 plants for the greater part from sheltered, for the 
smaller part from exposed spots in the duneland not far from the village of Lisse 
(Holland). The countings were made in the months of July and August of the 
year 1912. 
In counting, a large number of fasciations were observed in the umbels. Among 
515 plants, of which both the terminal and lateral umbels were counted, 167 were 
observed to have fasciations. As many rays were taken into account as there 
would have been, if no fasciation had occurred. Plate I, figures 1 and 2, shows 
some very interesting fasciations. 
Variation of the number of umbel rays of the lateral umhels of the first order and 
correlation of the numbers of umbel rays of terminal iimbels and that of lateral 
umbels. 
The countings of umbel rays of lateral umbels have been combined in two 
different ways. In the first place lateral umbels belonging to plants with the 
same number of rays in the terminal umbel have been united into groups ; and in 
the second place those which belonged to plants with the same number of lateral 
umbels. 
In Table II, 3836 lateral umbels of 515 plants have been divided into groups, 
each of which has been placed in a horizontal row and contains all the lateral umbels 
of plants with the same number of rays in the terminal umbels. 
The mean number of umbel rays of the lateral umbels is greater than that of 
the terminal umbels. For that reason terminal and lateral umbels are considered 
separately. 
In Table III the lateral umbels are divided into groups in such a way that all 
the lateral umbels of plants with the same number of lateral umbels are arranged 
in one horizontal row. 
The distribution of the number of iimbel rays of the 3836 lateral umbels is 
represented graphically in Fig. 3. 
The distribution, which is given in the first and the last column of Table III and 
which gives the number of lateral umbels per plant, has not been studied in detail 
because it is of no importance for this investigation. The constants /3i = 0-144 
and 3-485, the "critical function" =0-208 and the curve which will fit best 
to this distribution is a Pearson curve of Type IV. 
