358 
so that 
Ar Te Herr IE 
À is known from the beginning. 
After looking up in Kapteyn's table 1b the two 
values R; and R, corresponding to the two ©'s we find 
M and h thus: 
s R — R  _R-R, 
Mot 0) loge lon 6 
Xi 
M = — = + log.À + log.i = — à + log.x;: 
Finally, the equation of the analytical curve itself becomes 
h mod D h*(log.x — M) 
AA ete LS 
For my series of pappus cells Ï obtained the constants 
M = 1.1802;: h —:8:47; 
and the equation 
DGA “mod ne 8.47*(log.x — 1.1802)° 
VOTE 2x 
It will be noted that this set of constants differs widely 
from that obtained by the general solution, In fact, in 
the case q — O the parameters M and h have an altered 
meaning. (See Kapteyn, p. 20, footnote). 
My Tables 1 and 2 give the comparison between the 
observations and the two solutions, General (Sol. 1) and 
Logarithmic (Sol. 2). With the latter, Ï had expected more 
than the twofold coincidence promised. But I had certainly 
not expected a harmony even better than that obtained by the 
general solution, especially at the ends of the curve. There 
are somewhat smaller differences, and more points of contact. 
Ï conclude almost with certainty, that, in the case of 
my pappus cells, the logarithmic curve is the true one, 
so that the growth of these cells has been governed by 
this law: Increase directly proportional to the length 
already acquired. 
[I 
