SLOW AND RAPID GROWTH 
equations (table i) are seen to be very close to the observed values with few 
exceptions; the values, therefore, may be assumed to be approximately 
correct. 
A series of values more nearly corresponding to the observed lengths 
may be obtained by the means employed in another study (Reed, 1920 b) 
of this kind, but the simpler equation gives satisfactorily close values and 
its use will contribute to clarity of discussion. 
160- 
A, 
A 
/ 'O ° 
) 
0 5 10 15 ZO 
Timt in- WeeK% 
Fig. I. Curves showing mean length of apricot shoots during one season. 
AAA, Observed lengths of shoots on pruned trees. 
, Length of shoots calculated from X2 = 218(1 — e^-^^O- 
0000, Observed lengths of shoots on unpruned trees. 
, Length of shoots calculated from xi = 100(1 — e~-^^^). 
The differential equation, dx/dt = k{a — x), represents rate of growth, 
i.e., amount of elongation in unit time. If we get the weekly increments in 
length, we shall have the observed increments in unit time expressed as a 
rate per week, and can compare them with values calculated from the above 
differential equation. Since there are inevitable fluctuations in the actual 
growth rate, it will be better to use ''adjusted" values, 5, of the observed 
increments. This is a slope method of determining the observed values of 
