402 MR. K. PEARSON ON THE MATHEMATICAL THEORY OF EVOLUUION. 
converts the theoretical areas into the ordinates of the theoretical curve. For other 
petals, ordinates and areas practically coincide in value. 
(32.) Example XII.—Another example of a similar kind may be taken from 
Herr DE Vriss’ memoir (oc. cit., p. 202). He cultivated under the name of perwm- 
bellatum a race of Trifolium repens, in which the axis is very frequently prolonged 
beyond the head of the flower, and bears one to ten blossoms. In the summer of 
1892 he had a bed of such clover, produce of a single plant, and in July counted the 
extent of this variation on 630 flowers. In 325 cases the axis, according to DE VRIES, 
had not grown through the head of the flower, in 83 cases it had grown through and 
bore one blossom, in 66 cases two blossoms, and so on. The complete statistics are 
as follows :— 
High blossoms 0 1 2 8 4 5 6 7 8 9 10 
Frequency 6s BRS 83 66 51 36 36 18 7 6 1 1 
Taking moments in the manner of the earlier part of this memoir, I found as a first 
approximation to the frequency curve : 
y = 452842 we 2817 (10-69114 — a) 1528044, 
with the origin at °47813 to left of maximum ordinate. This first approximation 
seemed to justify three things : (1.) starting at ‘5 to the left of the maximum ordinate; 
(ii.) assuming a range, 11, which just covered the whole series of observations, 2.e., 
from ‘5 to 10°5; and (iii.) that the moments of the areas might be found from a value 
of p not far from °5. 
A second approximation was then made, and taking moments round the asymptotic 
ordinate, I found : 
ww, = 18680, yp’ = 7°77028, 
whence, in the manner of $16, we have: 
Xi = 1698182, X2 = 38781526, 
and ultimately : 
m, = — ‘493118, M, = 1°47797, 
and 
Yo = 4°65148. 
The equation to the frequency curve is therefore : 
y= 4°65148 go — 493118 (11 AA x) 147797 
The value found for p, 7.e., 493, justifies our calculation of the moments on the 
assumption that it was ‘5. 
