Sept, i, 1921 
Growth in Branches of Young Pear Trees 
859 
The data presented in Table V show that the lengths of the laterals 
arranged in basipetal order form some sort of a descending series. The 
lengths of the first half dozen laterals descend very rapidly; indeed, 
from that point down there is no marked decrease in values in the pruned 
series, though the unpruned series shows a second descent from about 
lateral XVIII. In data of this kind it is frequently advantageous to 
use S instead of the observed values of y. In this case S is computed 
from 
7x-i + y x +1 
2 
when y represents length of the lateral and a: represents its ordinal posi¬ 
tion on the mother shoot. Thus the value of S for any given lateral 
represents the average of the preceding and the following laterals. As 
McEwen and Michael ( 6 ) have pointed out, this takes advantage of the 
fact that the slope of a chord of a simple curve is approximately equal 
to the slope of the tangent at the point midway between the extremities 
of the chord. Its use enables one to smooth out inequalities due to 
errors of sampling or to other causes. In comparing the various values 
of S it is convenient to employ logarithms of the values, as was done 
in making the graphs shown in figure 3, because of the wide range of 
the figures and of the difficulty in using a satisfactory scale. It is 
obvious that these graphs would descend in a comparatively straight 
