H. S, REED 553 



The data for the second cycle were similarly treated. The values 

 were all diminished by 79 cm. The value of a was taken as 56 and 

 that of h as 85. The mean value of K was determined to be 0.0423 

 and from this the values of x — 79 were calculated by the same gen- 

 eral formula as for the other cycle. The agreement between the cal- 

 culated and observed values is quite good. A graphical representa- 

 tion of the values is shown in Fig. 3. 



It thus appears that between April 17 and September 4 the growth 

 of this population of Juglans nigra trees fell into two distinct cycles 

 and that the rate of growth for each cycle followed closely the course 

 of an autocatalytic reaction. 



A similar type of growth rate was also found for the Juglans nigra 

 trees from which the laterals had been removed at the beginning of 

 the season. It has been shown (Reed and Holland) that the smaller 

 members of a population have a type of growth rate similar to that 

 of the larger individuals. That is, both groups were found to corre- 

 spond to the equation which states that the growth in unit time is 

 proportional to the product of the height at that time and the amount 

 yet to grow, multiplied by a constant. 



The growth rate of the Juglans regia trees was likewise studied. 

 Here again it is advisable to deduct a constant amount from each 

 height measurement in order to bring the base line near the point of 

 origin of the part of the growth curve studied. In this case Xi = x — 50. 

 The value of a was found by approximations to be 153.2 cm. and h 

 = 96. We therefore have 



log r^ =K{t -96) 



153.2 — xi 



Table IV shows the observed values of Xi, the various values of K, 

 and the calculated values of Xi with the meaji value of K. The root- 

 mean-square deviation is 3.5 cm. The smallness of this divergence 

 becomes apparent when we note that the probable errors of the mean 

 values of x (Table III) are greater than 3.5 except in the first six cases. 

 A graphic representation is given in Fig. 4. 



It will be noted that the data for the growth rate of Juglans regia 

 extend from June 5 to October 15. There appears to be but one 

 growth cycle between these dates. This period begins close to the 



