122 



PLANT PHYSIOLOGY 



sidered as the development of retardation, which shows itself 

 at first weakly but later with increasing importance, until growth 

 ceases. For the initial phase, Blackman applies the mathe- 

 matical formula for calculating compound interest, since, in 

 growth we are dealing with an increase in the number of cells 

 following a geometrical progression, in which one cell forms 

 2, 2 producing 4, then 8, 16, 32, 64, etc. Designating by the 

 letter A the final size of the section, and by a, the initial one; 

 by t, the time interval ; and by r, the rate of percentage increase : 

 the formula A = ae*"' is obtained, where e is the base of natural 



logarithms. Changing this formula to 

 a logarithmic form and converting the 

 natural into decimal logarithms, we 

 obtain 



90 



80 



10 



60 



gSO 



2 40 



30 



20 



10 







^ 



-z^-^ 



'T' 



\r 



y- 



-*.- 



2345 6789 



Fig. 28. — Growth curves 

 of roots of Vicia faba {after 

 Rippel) . 



2.3026 log — = rt, 

 a 



whence it is easy to compute the per- 

 centage of growth per day, the initial 

 and final size and the number of days 

 being known. 



Blackman's formula is applicable 

 only in a limited way to the initial 

 the exact moment of retardation is 



phase of the curve, for 

 very difficult to determine. Growth is based on the chemical 

 transformation of assimilated or reserve substances into living 

 protoplasm, and the latter begins to participate in the synthetic 

 reactions as soon as it is formed. Robertson has made an 

 attempt to apply to growth the formula of monomolecular 

 autocatalytic reactions, which should embrace the entire process 

 from beginning to end. If one considers the gradual retardation 

 of the reaction as being due to the accumulation of its end prod- 

 ucts, which does not always take place because of their rapid 

 removal, then the formula may be represented by 



where K is an empirical constant; x, the size reached in t days, 

 or other time units, from the beginning of growth; and A the 

 final size of the growing organ. By integrating and other trans- 



