Miscellanea 
169 
assumption is just as large or small as the weight we choose to give to the three Gaussian 
conditions by which the normal cm-ve is usually supported. 
Further, when the assumptions have been made what is the result ? Why, we are not 
really a bit forwarder than on the simple assumption that the general frequency-curve is : 
2/ = <^(*') 
where ^ (x) is perfectly arbitrary. Both (i) and (ii) involve an arbitrary function and therefore 
can be made to give the most general frequency distribution which is conceivable! I pointed 
this out years ago in criticising Professor Edgeworth's solution*. 
Mathematically Kapteyn and Edgeworth seem to me to follow entirely the same path. 
But biologically there is a very serious flaw in Kapteyn's preliminary reasoning. He asserts 
that "the frequency -curve is generated under the influence of causes the effect of which is 
proportional to / " (p. 16). No causes that we are awai'e of in biological or indeed 
r \x) 
sociological investigations lead to a mathematical relationship of this kind. The relationshi[)s, 
which actually arise between the characters and between characters and environments, are not 
causative, but correlational, and this is a fundamental distinction which Kapteyn entirely 
overlooks. 
Accordingly I personally am unable to see any real distinction between Kapteyn and 
Edgewortli. They both obtain a form of equation which is no more nor less general than 
y=<^ (.«■), but it is put into a form which enables them to prostrate themselves before the 
Gaussian fetish. 
(6) Professor Kapteyn assei'ts that in propounding as a general form of frequency-curve 
the equation 
\ du .v-\-a, 
y dx f{x) ^ ' 
I am simply adopting the general difl^erential equation of his curve (i). I am afraid I should 
look upon it as nothing more than stating in a convenient form the general result y = (f){x), 
for it contains the perfectly arbitrary function f{.v). There is nothing more in it than this, 
and I should not value in the least the discovery that (iii) was the general form of frequency- 
curve ! But if (iii) really embraces Professor Kapteyn's curve and he wishes to claim priority 
for this find, I have only to say that I can give him, if he desires it, conclusive evidence that 
(iii) has been habitually discussed in my lectures on statistics for at least five or six years, 
if not longer ! 
My custom has been to follow exactly the lines indicated in my memoir on Skew 
Correlation t. Namely, to give (iii) and then assume that f{.r) could be expanded in the 
form f{x) = S{CnX"'). I then determine the values of the constants c„ by a finite difference- 
equation between the moments. 
The Drapers' Memoir referred to above was only published in 1905, but if Professor Kapteyn 
looks at Biometrii-a, Vol. ii. p. 281, issued in June, 1903, he will see the general formula(e) 
for c„ in terms of the moments given, and this was at a time anterior to my knowledge of 
Professor Kaj^teyn's paper. 
In the question of an important discovery, priority by the usual scientific courtesy turns 
on priority of publication. 
Professor Kapteyn's memoir is dated October, 1903. My formida was published in June, 
1903, showing that I was then using the expression: 
1 dy _ x + a 
y dx~ f{x) 
* Phil. Mag., Jan. 1901, p. 111. 
t Drapers'' Research Memoirs, Biometric Series ii. Pulau and Co. 
Biometrika y g2 
