360 
On 268 capitula from as many plants ÎÏ measured the 
length of all these short bracts, a total of 3685. Their 
empirical curve showed unmistakable positive skewness. 
50 J tried a Jlogarithmic curve obtained with two values 
of x:near! qirand-qg. "(x = 13 x, —17) “But'thisiproved 
decidedly not to be the true one. It remained below the 
empirical curve in the terminal parts and above it in the 
middle: in short, it ran too steeply. The cause was 
obvious: the empirical curve had a long ,,tail“, due to the 
transitional leaflets being no true bracts but of greater 
length than these. 
Ï now wanted to make out if perhaps a logarithmic 
curve would agree with the parts where no influence of 
these plus-variates is yet felt Kapteyn's method does 
not provide for this case, as it deals only with homoge- 
neous material. So ÏI had to look for a solution myself, 
and Ï succeeded by reasoning as follows. 
Let there be, mixed up with every 100 typical indivi- 
duals, a number of a which differ from the type: together 
100 + a. If a curve were constructed only of the typical 
individuals on such a scale that it included with the line 
of abscissae an area 100, then it might coincide completely 
with a theoretical curve of this same area 190. By now 
adding the nontypical individuals, the area of the empirical 
curve becomes 100 + a; but its left part (where none of 
these plus-variates occur) continues to coincide with the 
theoretical curve, of which the area is only 100. 
If we now choose two values x, and x, in the region 
where only typical individuals occur, and if ©, and @, 
represent the percentage of observations in the whole 
material below these values, then of the fypical individuals 
AE FX Q, lie below x;, and et Le ®, below x. 
These reduced ©'s are to be the values of the probability 
integral for x, and x, in the theoretical curve that represents 
