144 
AGRICULTURE: REED AND HOLLAND 
It is plain that the amounts of invert sugar finally formed in four different 
flasks may vary, depending upon the amount of cane sugar originally present, 
yet the constant of autocatalysis remains the same and the time may be the 
same in each case. This relation exists because the quantity dx/dt is propor- 
tional to the quantity of cane sugar remaining, which may be represented by 
(a — x) where a is the original quantity of cane sugar at the beginning, i.e., 
when / = 0. 
The senior author has discussed the distribution of these plants in the 
several quartiles in a paper soon to be published (Reed, 1919), showing that 
said distribution is due to some agency operating to cause variability in height 
other than purely casual agencies which might be expected upon the basis of 
pure chance. The data presented in table 3, indicate that no difference in 
the growth constants exists which can account for the larger or smaller size of 
a part of the population. Whether the differences in the amount of material 
produced, i.e., the size of the plants, is to be referred to differences in amount 
or activity of the catalyst, or of the substrate, cannot be discussed upon the 
basis of the data now in hand. 
An additional point may be discussed in this connection, viz., ''Are the 
values of the growth constants more widely dispersed from their means in one 
quartile than in another?" We may take the standard deviations of the 
means as a measure of the dispersion of the individual values. Reference to 
table 3 shows that the standard deviations increase from the lower to the upper 
quartiles, which would seem to indicate that the growth rate of the larger 
plants fluctuates more from the mean than is the case in the smaller plants. 
Summary. — 1. Measurements of sunflower plants at intervals of seven 
days showed that their growth rate approximated closely the course of an auto- 
catalytic reaction. 
2. The close correspondence of the actual mean height of plants to that re- 
quired by the equation of autocatalysis is taken to indicate that the growth 
rate is governed by constant internal factors rather than by external factors 
which would be expected to be more casual in their influence. 
3. The growth rate showed no strong correlation either with temperature- 
summations, or with transpiration-summations. 
4. The value of the growth constant was not perceptibly different for the 
larger or smaller plants in this population. 
*Paper 56 from the University of California, Graduate School of Tropical Agriculture 
and Citrus Experiment Station, Riverside, California. 
Church, A. H., quoted in Cockerell, T. D. A., Amer. Nat., Lancaster, 49, 1915, (609). 
Elderton, W. P., Biometrika, London, 1, 1902, (153-163). 
Miyake, K., Soil Science, 2, 1916, (481-492). 
Pearl, R., and Surface, F. M., Zs. indukt. Ahstam.- Vererbungslehre, 14, 1915, (97-203). 
Reed, H. S., (1919), Amer. J. Bot., (in press). 
Roberston, T. B., Arch. Entwicklungsmechanik, 26, 1908, (108-118); Ibid., 37, 1913, (497); 
Berkeley, Univ. Cal. Puhl. in Physiology, 4, 1915, (211-288). 
Shull, G. H., Bot. Gaz., Chicago, 45, 1908, (103-116). 
