140 Kleinere Mitteilungen. 
§ 2. 
A more exact consideration of these tables leads us on to other ground. 
It is remarkable that the groups of which table I is composed, are quite 
different to those of table II; viz: that the periods of length fluc- 
tuation do not agree with those of breadth fluctuation in the 
self-same plant. The periodicity of the length fluctuation proceeds thus 
independantly of that of the breadth fluctuation: The curves of frequency 
of length and of breadth are thus independant of each other. Length 
and breadth of leaf are therefore two distinct qualities. The 
shape of the leaf is due to the cooperation of two different qualities unlike 
each other. This opinion is also strengthened by other data. The following 
correlation table serves this purpose (table III). 
In this table, relating to a smaller specimen of C. Uganda, both 
measurements have been so represented that one may trace how many 
times a combination of a definite length occurs with a definite breadth. 
This table, therefore, leads to the following considerations. If the 
leaf-formation were an expression of a single property, then for each length 
there would have to occur a definite breadth: this is then the simplest 
presentment in the matter; for so, it would generally be held that the 
relation between length and breadth must generally be constant. The table 
now is in entire opposition to such a view. By a breadth of 4c. m. there 
are possible combinations with 21 different lengths, extending from 6 to 
18 c.m.; the relations of length and breadth varying here from 1,5 to 4,5. 
A length of 17 c. m. may indeed have as many as Io different 
breadths. Examples, such as the table offers many of, do not appear to 
me to favour the view that length and breadth are one and the same 
property. 
Briefly stated; if length and breadth really formed together one single 
property of the leaf, this table would be obliged to present the appearance 
of an ideal correlation table; in that case, the numbers would have to 
extend diagonally across the table, at the very least, their maxima must 
do so. Now, in our table, those maxima are printed in heavy type: again 
there is no question of correlation here. 
In such cases I am strongly opposed to the opening up of a mathe- 
matical possibility of a so-called “imperfect” correlation. The biometricians 
have indeed gone somewhat wrong in this direction. By mathematical 
treatment two totally distinct phenomena have been represented as a 
single phenomenon, viz: 
wy the connection of the properties originated in this way as being 
the expression of one and the same inherited property (true correlation); 
2'y the about same method of reaction under the same circumstances 
by totally differing properties. 
The first case furnishes the true correlation and the true ideal 
correlation table, where no formulae are needed to reveal them. 
