356 
the top. I had collected 275 capitula from as many plants, 
and on each of these [| measured the length (see Fig. 1, 
a—b) of 10 top cells at random, avoiding any preference. 
There exists a wide variability even among the pappus 
of a single flower, hardly less than the total variability 
of these cells. So my series of 2750 lengths may be said 
to represent a typical scheme of distribution for this kind 
of cells The curve was sufficiently fluent when I had 
divided the range of variation into 25 intervals. See Table 2. 
J had first applied the general solution according to 
L Kapteyn's method, and obtained an analytical 
curve which fitted properly. Its constants were 
M = 3.430; h — 0.581; k = — 94; q = +07. 
Wishing now to try a logarithmic curve, 
which represents the special case k — 0, q —0, 
[ found on p. 34 and 35 of the ,5kew Fre- 
quency Curves“* the formulae for the less 
special case q — 0 but k not O0. If a priori 
q is supposed to be 0, the equation contains 
only 3 parameters, for the solution of which 
only 3 values of x with their ©’s are required. 
The warranted coincidence is now but three- 
fold; if there is found a more complete harmony, 
it is a check on the correctness of the sup- 
Fig. 1.  POSition. 
Similarly, if also k is supposed to be 0, 
there remain no more than fwo constants to be solved, 
by means of only two values of x and ©. No more than 
twofold coincidence is warranted; but nobody will apply 
this solution unless a logarithmic distribution is suspected, 
and here, too, the correctness of the supposition will be 
proved by a more complete harmony. 
The formulae for this case are very simple. The con- 
a j fs # AGIR k x: 
stant À, being in general ---, now becomes —, 
i i 
