sept, i, 19 j i Growth in Branches of Young Pear Trees 861 
These figures clearly betoken certain biological relationships which 
must be of prime importance in attempting to understand the laws of 
development in higher organisms. They make it possible to extend the 
ideas on integration and differentiation which formed such a considerable 
part of Herbert Spencer’s (ij) "Principles of Biology.” The figures 
presented show that the length of a lateral is some sort of a function of 
its ordinal position on the branch which bore it. That the length of a 
given lateral is as much an expression of the properties of the branch as 
the angles of a crystal are of the properties of a salt there can be no 
reason to doubt. This is not to say that the equation giving the length 
of a lateral will necessarily disclose the physiological factors determining 
it, but it does banish the idea that form and function are so variable as 
to be outside of the realms of exact science. 
The series of correlations reported on a subsequent page are further 
evidence of a functional relationship between the various laterals with 
due regard to the factors which may reside in the mother shoot. The 
representation of their relative length by a mathematical equation is 
not, therefore, due to chance or to the fortunate choice of an equation. 
Future work in this important field on subjects such as those investi¬ 
gated by Pearl (7) and by Johnson (4) should afford information of the 
utmost value. 
variability in the length of laterals 
The biological constitution of the population under consideration was 
next investigated. The nature and amount of variability existing in 
the population was used as an indicator of its genetic character. The 
laterals on the pruned shoots served as a basis for the inquiry, because 
of the larger number in the population. 
A graph in figure 4 shows the coefficient of variability of the first 15 
laterals produced on the pruned mother shoots. The coefficients of 
variability of these means increases somewhat irregularly from 23.18 for 
lateral I to 359.90 for lateral XIII and falls to 159.52 for lateral XV. 
This indicates that the laterals produced from the distal end of the 
mother shoot are less variable in length than those produced nearer the 
proximal end of the shoot. This increased variability can not be attrib¬ 
uted to the smallness of the group or to a poor sample, because lateral 
XIII comprised a population of 172 individuals. 
The fact that minimum variability occurs in the members at the distal 
end of the shoot has previously been noted in Ceratophyllum (7). On 
Ceratophyllum the whorls of leaves borne at the distal end of the shoot 
may be considerably younger than those borne at the opposite end. 
On the pear shoots the distal lateral is likely to be the oldest on the mother 
shoot, though in many cases the difference in age is very slight. The 
position of the lateral upon the parent axis appears to be more of a factor 
than age in determining variability in length. 
