No. 404.] PALA MONETES VULGARIS HERBST. 625 
in P. varians. Judging from the coefficient of variation, 
however, we should find the numbers of ventral spines more 
variable than those of the dorsal ones, and the homologous 
characters only half as variable in P. vulgaris as in P. varians. 
Thus the coefficients of variation give quite different results 
from those obtained from the indices of variability, and only 
the latter ones, as Pl. I shows, correspond to the real con- 
ditions of variation in the four characters compared. There- 
fore, in our examples, the indices of variability alone, not the 
coefficients of variation, are morphologically significant, and the 
Sormer are similar in homologous characters, but independent of 
their mean values. 
The numbers of dorsal spines vary regularly, according to 
type IV of Pearson (95) in both species with negative asym- 
metry of the variation curves, that is, the modes are higher 
than the means. It is remarkable that the ordinate of origin 
of the curve of P. varians lies at 10.63 of the abscissa, even 
higher than the mean and the ordinate of origin of P. vuigaris. 
Since both species, wherever they occur, are represented by 
immense numbers of individuals, their range of variation in 
the character considered probably extends much farther than 
will be expected from the empirical results of the investiga- 
tions made by Weldon and myself. The variation curve in 
P. vulgaris is more symmetrical than that of P. varians, 
according to its small z-value. In both cases the agreement 
between the empirical series of variations and the theoretical 
one is thoroughly satisfying, the area of error between their 
two polygons remaining far behind its allowed upper limit, 
IOO 
A% = Fa 
The numbers of ventral spines vary irregularly, which may 
partly be due to their small variability. In P. varians we 
find a curve of type I (asymmetrical, limited to both sides), 
where, however, the value 5 8, — 6 8, — 9 is negative,’ and 
where, accordingly, the index of asymmetry of this curve has 
a different sign from its third moment about the mean. In 
1 For explanation of these symbols, see Davenport (99), or Duncker (99). 
