399 
Centesimal Grades, quartile-limits). Consequently, the 
two Quartiles must be unequal, @ > Q ; their ratio 
& must be the same as ne or nee 
Med must also be the geometric mean of every pair 
of Grades equidistant from 50 °/,. This will be understood 
from what follows. Two points on the line of abscissae 
of the normal z-curve, equidistant from its Mean (M), 
will include equal frequencies on either side of M. These 
two values, however, are the logarithms of the corres- 
ponding x's, and M — log.Med; thus in the skew curve 
the two x's including equal frequencies on either side of 
Med, will bear equal ratios to Med. 
Here we see the importance of the Median, which is, 
in fact, the Geometric Mean of the whole series. Neither 
the Arithmetic Mean (lying to the right of it) nor the 
Mode (to the left) are of importance in the logarithmic curve. 
The indications just mentioned were present in two 
frequency series from the material which I had collected 
for my dissertation, namely 300 plants of Senecio vulgaris L. 
For particulars about my material Î refer to this publi- 
cation. Let it suffice here to say that although in these 
wildgrowing plants no strict homogeneity was to be expected, 
I found in none of the studied characters a marked hetero- 
geneity. Î am quite sure that all the individuals belonged 
to one and the same subspecies. 
For most of the characters I had taken only one measure 
per plant. These series were not numerous enough for 
analysis, but only for the computation of coefficients for 
variability and skewness. Fortunately, a few series were 
represented by more measures, and among these were 
the two instances which I am going to describe. 
ist. Top Cells of Pappus. 
The pappus hairs are composed of a small number of 
cell-rows, generally 4. As a rule, two of these reach 
