J. A. Harris 
477 
The first of these is clearly enough a radially symmetrical fruit with respect to 
number of ovules per locale. Any fruit in which the number of ovules is the 
same in each locule, as 6 — 6 — 6, or 7 — 7 — 7, is radially symmetrical with respect 
to this character. Tiiose in which the number of ovules differs from locule to 
locule are quite as obviously irregular or radially asymmetrical with respect to 
number of ovules. 
Admitting that fruits in which all the locules produce the same number of 
ovules are radially symmetrical, while those with at least one of the locules 
differing from the others in its number of ovules are radially asymmetrical, we 
may be either (a) content to divide our ovaries into two classes, radially sym- 
metrical and radially asymmetrical, or (b) get some measure of the amount of 
asymmetry in individual fruits so that the asymmetrical fruits may be subdivided 
for further analysis. 
The measure of asymmetry must be one for the individual fruit, not for 
a population. The measure must also be independent of the order in which the 
three locules of the fruit are taken, for there is no constant ditferentiation between 
them and they may be opened in any order. Two measures have occurred to me. 
First, the sum of the positive difference between the number of ovules in the 
locules of an ovary might be used. In a fruit of the formula 
(a) (6) (c) 
7—8—6, 
we have, taking all possible differences, 
a-b = -l, b-c = + 2, 
a - c = + 1,- c — a = - 1, 
b - a = + I, c-b = -2, 
Sum of positive differences = 4. 
Comparing a fruit of the formula 7 — 8 — 7 we find the sum i>f the positive 
differences = 2. The first is more asymmetrical than the second. This is obvious 
in the present case from mere inspection. 
The second measure is the square root of the mean square deviation of the 
number of ovules per locule from the mean number in the whole fruit. For the 
first illustration the mean number per locule is 7 and the deviations are 
a = 0, a- = 0, Coefficient of asymmetry =V| = -8165. 
b= + l, b'=l, 
c = -l, c'=l. 
For the second illustration : A = 7"3383, the deviations are 
a = - -3333, b = + -6666, c = - -3333, 
and the coefficient of asymmetry is 
/•33332 + -6666^ + -3333-' 
V 3 ^ 
Biometrika vii 61 
