14 The Significance of Horticultural 1 \irietics. 
Hence the illusion of an increase in variability. The ex- 
planation is simply this that, as shown in the preceding 
section ( 1), we first find a minus variant of the new 
character, which, in accordance with the law of regres- 
sion, approaches not the character of the old species but 
the mean value of the new variety, as soon as it is iso- 
lated. And this takes place easily and swiftly since the 
new variety in this case behaves like an improved race 
on the cessation of selection or under reversed selection 
(Vol. 1, 14, p. 122). 
The progress made by this improvement and through 
the purification from the results of crossing is often so 
rapid that it can be expressed in terms of a geometrical 
series. This generalization does not attain to the rank 
of a law, but my meaning will become clearer by citing 
an example. HOFMEISTER sowed the seeds of plants of 
Papaver somniferum polycepJialiim, 1 which he had found 
growing between normal examples of the species. By 
selecting the fruits which were richest in supernumerary 
carpels, but without isolation, he effected the following 
increase in the number of abnormal examples in the suc- 
ceeding generations : 
Year: 1863 1864 1865 1866 1867 
Percentage of abnormal plants: 6% 17% 27% 69% 97% 
Geometric series: 8 16 32 64 (100) 
These figures, as we see, do not differ considerably 
from a geometric series. I do not lay much stress on 
the fact, but I have myself more than once obtained 
similar series of figures in breeding experiments. 
The limits that can be reached are as little under the 
control of the breeder as the starting-points that had to 
1 Allgememe Morphologic, p. 565. See our Fig. 27 on p. 138 of 
the first volume; also HOFFMANN, Bot. Zcitg., 1881, p. 397, and VER- 
LOT, Production et fixation des varietes, p. 88. 
