353 
coincidence between the two curves. Strictly speaking, 
there is equal frequency in five intervals, including also 
the interval past x.. 
Finally, by the aid of the constants, a theoretical value 
of © is to be computed for each x, and to be compared 
with the data. 
Kapteyn's method is open to criticism, because of 
the arbitrary choice of the four x's. By taking other 
points, we shall obtain other constants. I have given 
some instances of this fact on p. 26—27 of my disser- 
tation ‘). But, although mathematicians will assert that 
we Can imagine better-fitting curves than Kapteyn's, 
still they cannot but consider it greatly to his credit that 
his method alone throws some light on the causes of 
variation, by very simple and yet correct reasoning *). 
If an empirical curve is normal itself, we have to do 
" ler RARE dire 
with the case F(x) — x, and Far 1. This implies that 
an increase of x has been independent of x. 
Among the cases in which an increase does depend on 
x, the most simple one is a direct proportionality to the 
measure already attained, and it is this which leads to a 
logarithmic distribution. The condition 
l — 
FE aN 
is satisfied by 
SENS 
Consequently the curve generated under these circum- 
Stances is a skew curve, from which a normal one is 
obtained when we substitute every x by its logarithm. 
Hence the name. 
1) Statistische onderzoekingen bij Senecio vulgaris L. Groningen 1914. 
‘) À. ©. Holwerda, Frequentiecurven. Diss. Utrecht 1913. 
p. 167 —168. 
