624 THE AMERICAN NATURALIST. [Vor. XXXIV. 
TABLE II. — CONSTANTS OF VARIATION. 
P. VULGARIS. P. VARIANS. 
DORSAL SPINES. | VENTRAL SPINES. | DomsAL SPINES. | VENTRAL SPINES. 
A 8.2819 2.9781 4-3137 1.6984 
€ 8145 4477 .8627 :4799 
M 8.3079 3.1391 4-4634 
G 8.2395 4.2158 
2 8379 :9137 
a 1.4666 4.5457 
m 3.1260 42.2128 
T 22357 114.5962 
yo 623.86 2127 33-25 
V 8.3632 10.6333 
c.v. 9.83% 15.03% 20.00% 28.26% 
mean ; e index of variability = root of average square devia- 
tion from arithmetic mean ; M, mode = abscissa of maximum 
ordinate (ym) of the theoretical curve; G, geometric mean ; 
8 = V A? — G? (see Duncker [99], p. 38) ; a, standard dimen- 
sion of abscissa ; m, T, exponents ; yo, ordinate of origin of 
theoretical curve; 6, abscissa to yo; c.v. coefficient of 
variation = IOO « : A 
The theoretical curves, the polygons of which are repre- 
sented in Pl. I, C, D, by dotted lines, belong to type IV, 
Pearson (95) ; they are of the form, 
y = yo (cos 0)*"e- tg 6, 
where ir b= -a means deviation from 6, and have been 
calculated by the method A (moments not modified) of 
Davenport (’99). 
From this table we get the following results. The dorsal 
spines are much more numerous in both species than the 
ventral ones, and their variability is 1.8 times higher than 
that of the latter. The mean values of the homologous 
characters are about twice as large in P. vulgaris as M 
P: varians ; neyertheless, the indices of variability are nearly 
equal in both species, in P. vulgaris even a little lower than 
