182 Observation of the Origin of Varieties. 
The progress was uniform and regular and the sim- 
plest index of it is the series of successive seed-parents. 
The number of ray-florets in the terminal inflorescences 
of my selected plants in successive years was as shown 
in the table on page 179. 
The progress can be seen still better from the curves 
which I have plotted of the terminal inflorescences in the 
various generations. The reader is referred to the table 
on page 180 and Fig. 32 on page 181. The original plant 
of 1895 referred to as No. 1 arose from a seed which, 
as already stated, was obtained by exchange from a 
botanical garden. Indeed this particular lot of seed came 
from Groningen but produced a mixture the curve of 
which would obviously not have any special interest. The 
cultures of the subsequent years were every time the 
offspring of a single individual whose fertilization by its 
like had been insured as much as possible. 
The following considerations arise out of an inspec- 
tion of Fig. 32. 
The curve of 1897 was monomorphic like that of the 
typical examples of the 21-rayed race (Fig. 31 B, p. 169) ; 
but it was markedly asymmetrical, a fact which afforded 
a pretty strong indication that the race could be improved 
by selection in the plus direction. It confirmed the expec- 
tation based on the part-curve of the parent of this 
culture. 
The curve of 1898 relates to the offspring of the 34- 
rayed plant of 1897. In it new maxima appear. These 
conform with LUDWIG'S law, for they lie on the figures 
of the well-known BRAUN-SCHIMPER or FIBONACCI se- 
ries. One of them is at 34 (= 13 + 21) which belongs 
to the primary series ; the other is at 26 (= 5 + 8+ 13) 
which is one of the subsidiary numbers. The maximum 
