	Die Theorie der ColleetivgegenstŠnde.	157

normal frequency curve may be obtained by running a continuous

curve through the point-binomial
(9 ± -)' when n is fairly large, so

a more general form of the probability curve may be obtained by
running a continuous curve through the general binomial (p ± q)fl.
As the great and only true test of the normal curve is: Does it
really fit observations and measurments of a symmetrical kind, so
the best argument for the generalised probability curve deduced in
this paper is that it does fit, and fit surprisingly accurately obser-
vations of an asymmetrical character. Indeed, there are very few
results which have been represented by the normal curve which do
not better fit the generalised probability curve, - a slight degree of
asymmetry being probably characteristic of nearly all groups of
measurmentsÇ. In diesen Worten zeigt sich die klare Erkenntniss,
dass Asymmetrie als Regel vorauszusetzen und dementsprechend das
gewšhnliche Fehlergesetz durch ein asymmetrisches zu ersetzen sei.
Zugleich wird die Erfahrung als einziger PrŸfstein anerkannt.
Pearson stellt sich somit das nŠmliche Problem wie Fechner; er
erstrebt jedoch die Lšsung mit anderen HŸlfsmitteln.
	Die stetige Curve, welche der discreten, durch Entwicklung von
(p ± q)" nach dem binomischen Satze resultirenden Werthenreihe zur
Seite steht, findet Pearson mittelst einer ihm eigenthiimlichen Me-
thode bestimmt durch

Px =po(1 +	C exp(- ix). 	(3O

Dass hierbei in der That die erwŠhnte Hypothese, die hier in der
Annahme von Elementarursachen (È contributory causes an Stelle
der positiven und negativen Elementarfehler besteht, den Ausgangs-
punkt bildet, erhellt aus den Worten: ÈSo long as we remain in
ignorance of the nature and number of contributory causes in phy-
sics and biology, so long as we do find markedly skew distributions,
it seems to me that we must seek more general results than flow
from the assumption that p = q and n = co. The form of curve
given above is suggested as a possible form of skew frequency cur-
ves. Its justification lies essentially, like that of the normal curve,
in its capacity to express statistical observationsÇ.
