683 
Also this construction is in a great measure indeterminate. This 
vagueness may be utilised to satisfy conditions of a non-mathematical 
character. 
The construction having been carried out in some way or other, 
for each value of / the conjugate value of z may be determined 
and the curve z= f(r) may thus be constructed, which will then 
show the shape of fig. 14. 
The reaction function looks as fig. 17. 
The transformation of the observed 
integral-curve into the theoretical one may 
Bir ol also be interpreted in this way: 
Fia 12. In the point «= #, the observed inte- 
gral-curve has for ordinate the total frequency of the values « Zw, 
i.e. the quotient of the whole number of individuals for which « < «,, 
divided by the number N of all the individuals. 
The theoretical ordinate pP, in the branch @#, represents the 
frequency of the values «<< a) as far as these are due to the branch 
Ff, of the function f, i.e. to the branch 1, ==, , of the reaction- 
Jy 
function. The final ordinate cC,, then represents the quotient of the 
whole number of values «<<, that is of all values due to the 
first branch, divided by N. 
From (C,, onwards the second branch of the reaction-function 
begins to play a part. New values of « now appear between 2, and 
ap (Ce). The number of values of w between «, and 2, which 
are thus added, amounts to N times the increase of the ordinate 
from C,, to P,. On the other hand the increase from P, to B, 
represents the quotient of the number of values w (a {er ej) as 
far as due to the second branch, divided by N. Accordingly the 
increase from B, to P, represents the Vt part of the number of 
values of «, which, lying between x, and wz), are due to the third 
branch. Hence the increase from P, to P;, or the segment P,P, 
represents the Nt: part of the number of values of « lying between 
wp and a, as far as due to both the second and the third branch. 
Adding to this the ordinate pP,, we obtain the V part of the 
total number of values of « that are inferior to «)». Now in the 
observed integral-figure this number was represented by the ordi- 
nate pP. Hence the relation 
pP=pP, + P,P; , 
which may also be written: 
pP = pP, — fae oF : 
