330 
H. S. REED 
dxjdt and has been applied to statistical problems by McEwen and Michael 
(1919). Its usefulness depends upon the fact that the slope of the chord of a 
simple curve is approximately equal to that of the tangent at the point 
midway between the extremities of the chord. The values of 5 are obtained 
from I (observed length at time / + i — observed length at time / — i), 
which represents the average rate between time t -\- \ and time t — \. 
Figure 2 shows the values so obtained compared with the calculated rate. 
They show that the rate is at a maximum at the inception of the growth 
period and follows the course of a curve decreasing exponentially to the 
end of the period. 
25 
IS 
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Time in. WeeK«> 
Fig. 2, Curves expressing rate of growth of apricot shoots. 
AAA, Observed growth increments {S) of shoots on pruned trees. 
, Values of dxjdt = .11(218 — X2). 
0000, Observed growth increments (5) of shoots on unpruned trees. 
, Values of dxjdt = .11(100 — X\). 
