236 Influence of Environment on Plants 
Galton, and others the statistical examination of individual differ- 
ences in animals and plants has become a special science, which is 
primarily based on the consideration that the application of the 
theory of probability renders possible mathematical statement and 
control of the results. The facts show that any character, size of 
leaf, length of stem, the number of members in a flower, etc. do not 
vary haphazard but in a very regular manner. In most cases it is 
found that there is a value which occurs most commonly, the average 
or medium value, from which the larger and smaller deviations, the 
so-called plus and minus variations fall away in a continuous series 
and end in a limiting value. In the simpler cases a falling off occurs 
equally on both sides of the curve; the curve constructed from such 
data agrees very closely with the Gaussian curve of error. In more 
complicated cases irregular curves of different kinds are obtained 
which may be calculated on certain suppositions. 
The regular fluctuations about a mean according to the rule of 
probability is often attributed to some law underlying variability* 
But there is no such law which compels a plant to vary in a par- 
ticular manner. Every experimental investigation shows, as we have 
already remarked, that the fluctuation of characters depends on 
fluctuation in the external factors. The applicability of the method 
of probability follows from the fact that the numerous individuals of a 
species are influenced by a limited number of variable conditions’. 
As each of these conditions includes within certain limits all possible 
values and exhibits all possible combinations, it follows that, accord- 
ing to the rules of probability, there must be a mean value, about 
which the larger and smaller deviations are distributed. Any cha- 
racter will be found to have the mean value which corresponds with 
that combination of determining factors which occurs most frequently. 
Deviations towards plus and minus values will be correspondingly 
produced by rarer conditions. 
A conclusion of fundamental importance may be drawn from 
this conception, which is, to a certain extent, supported by experi- 
mental investigation®. There is no normal curve for a particular 
character, there is only a curve for the varying combinations of 
conditions occurring in nature or under cultivation. Under other 
conditions entirely different curves may be obtained with other 
variants as a mean value. If, for example, under ordinary conditions 
the number 10 is the most frequent variant for the stamens of Sedum 
spectabile, in special circumstances (red light) this is replaced by the 
number 5. The more accurately we know the conditions for a par- 
1 de Vries, Mutationstheorie, Vol. 1. p. 35, Leipzig, 1901. 
2 Klebs, Willkiirl. Ent. Jena, 1903, p. 141. 
3 Klebs, ‘* Studien iiber Variation,” Arch. fiir Entw. 1907. 
