354 
The logarithmic curve has a historical interest, being 
the first skew frequency curve ever studied, namely by 
D. Mc Alister !), on F. Galtons‘instigation®) 
(Originally the name of ,Curve of Facility“ was given 
to it) Kapteyn supposes that this type ,,probably 
represents one of the most important classes occurring in 
nature“*). Even Pearson, in spite of his antagonism 
against Kapteyns method in general, has no theoretical 
objections to this special curve, and discards it on account 
only of the unfavourable results of a series of testing- 
proofs ‘). 
It is curious that the physiological considerations which 
led Galton to his discussion of the , Law of the Geometric 
Mean“ should have impressed Pearson so deeply, that 
he also chose his test-objects from this domain and not 
from that of variability. Mc. Alister's treatment of 
the logarithmic curve is purely mathematical Nobody 
seems to have tried earnestly its use in variation statistics. 
So there remained a gap to be filled up. Feeling a 
favourable disposition towards this curve because of the 
simplicity of its basis, I have been looking for instances. 
Which are the characteristics that induce us to suppose 
a logarithmic distribution? . 
The skewness must be positive, that is, the ascent must 
be steeper than the descent. 
The Median (Med) must be not the arithmetic but the 
geometric mean of the values q, and q; (25th and 75th 
1) The Law of the Geometric Mean. Proc. Roy. Soc. XXIX. 1879. p. 367. 
=) Geometric Mean in Vital and Social Statistics. Proc. Roy. Soc. 
XXIX 1879. p. 365. 
‘) Skew Frequency Curves p. 22. 
4) K. Pearson. ,Das Fehlergesetz und seine Verallgemeinerungen 
durch Fechner und Pearson’. À Rejoinder. Biometrika IV. 1905. 
p. 193—194. 
