310 Morphology of the Fruit of Samjuinaria Canadensis 
inheritance in thoroughbred horses. It seems to me a good one and I shall 
use it throughout a series of studies on fertility in plants, modifying the terms 
involved as may be necessary but keeping always to the general idea of the 
definition. Mayer* used the same ratio in a study of symmetry and fertility in 
a Medusa. He used the term " coefficient of fertility." Coefficient of fecundity 
is perhaps a more suitable term, agreeing with Pearson's terminology. The 
coefficient of fecundity is a very useful constant. Its value lies between 0 and 1, 
and its form is therefore similar to that of some other statistical constants. 
TABLE 2. 
Constants for 1907 Collection of Sanguinaria. 
Average 
Standard 
Coefficient 
Character 
and 
Deviation and 
of 
Probable Error 
Probable Error 
Variation 
Length of Fruit in 3 mm. Uiiitst ... 
51-865 ±-268 
7-948 + -190 
15-32 
Ovules on First Placenta ... 
12-812 + -137 
4-052 + -097 
31-63 
Ovules on Second Placenta 
12-792 + -136 
4-024 ±-096 
31-46 
Ovules on First and on Second Placenta 
12-802+ -096 
4-038+ -068 
31-54 
Total Ovules per Fruit 
25-605 + -265 
7-850+ -187 
30-66 
Seeds on First Placenta 
9-717 + -134 
3-980 + -095 
40-96 
Seeds on Second Placenta ... 
9-795±-135 
3-991 + -095 
40-74 
Seeds on First and on Second Placenta ... 
9-756+ -095 
3-986 + -067 
40-85 
Total Seeds per Fruit 
19-512 ±-258 
7-660 + -183 
39-26 
Aborted Ovules on First Placenta 
3-095 + -086 
2-559+ -061 
82-68 
Aborted Ovules on Second Placenta 
2-997 + -088 
2-610 + -062 
87-09 
Aborted Ovules on First and on Second Placenta 
3-046 + -062 
2-585 + -044 
84-86 
Total Aborted Ovules per Fruit ... 
6-092 + -161 
4-785 ±-114 
78-55 
t Constants tabulated in units of 1 mm. 
In the present case the coefficient of fecundity is the ratio of the total seeds 
developing in the population to the total ovules produced. 
For the present series of data we have : — 
For 1906 series, c.F. = = -7710 + -0016 + 
29904 
For 1907 series, c.F. = -^^= -7621 + -0042, 
10242 ~ 
Difference, - '0089 ± "0045. 
* Mayer, A. G., Sci. Bull. Brook. Mus. Vol. i. 1901 ; see also C. B. Davenport, Biometrika, Vol. i. 
pp. 255, 256, 190-2. 
X It is known that if //g be the frequency of any class of individuals in a population of m individuals, 
the probable error of the frequency is given (Biometrika, Vol. ii. p. 274, 1903) by the formula 
i52/,,= -fi7449>/2/,x(l-|i). 
In the present case is the number of seeds developing in the population m, or total number of 
ovules. From the ab.solute probable error of the number of seeds developing calculated from this 
formula, the probable error of the coefficient of fecundity was obtained by taking the ratio of the 
absolute probable error to ?», the total number of ovules. 
