	Die Theorie der Co11ectivgegenstnde.	159

X at 	xa
	Px =	1 ± )	(i -	(31)

und
	p = p0 cos'°tJ . exp(- VJ) ; x = a tang , 	(32)
wo je nach dein Werthe gewisser Constanten die eine oder die an-
dere Function in Kraft tritt. Zur Rechtfertigung sagt er: »Until
we know very much more definitely, than we do at present, how the
size of an organ in any individual, say, depends on the sizes of the
same organ in its ancestors, ore what are the nature of the causes
which lead to the determination of prices, or of income, Or of mor-
tality at a given age, I do not se that we have any right to select
as our sole frequency curve the normal type
in preference to the far more general
	x"",
i=/(1±)		i) -,

which not only includes the former, but supplies the element of
skewness which is undoubtedly present in many statistical frequency
distributions. As we may look upon the former as a limit to a coin-
tossing series, so the latter represents a limit to teetotum-spinning
and card-drawing experiments. It is not easy to realise why nature
or economics should, from the standpoint of chance, be more akin
to tossing than to teetotum-spinning or card-dealing. At any rate,
from purely utilitarian and prudent motives, we are justified so long
as the analysis is manageable, in using the more general form. It
will always give us a measure of the divergence of particular statistics
from the normal type, and in many cases of skew frequency, it can
be used when it would be the height of absurdity to apply the nor-
mal curve at all."
	Der kritische Werth, von dem die Anwendbarkeit des einen oder
anderen Curventypus abhängt, ist in der Schreibweise Pearson's:

2i(34 - t4) 4- 3112 , 	(33)
WO	i,, 14 die sogenannten Momente der Vertheilungstafel oder
Iläufigkeitscurve bezüglich des arithmetischen Mittels sind. Diese
