154 



THE RATE OF GROWTH 



[CH. 



cent. ; there is no great difference between such short intervals and 

 actual continuity, but there is a deal of difference between continuous 

 payment and payment (say) once a year*. Certain sunflowers 

 (Helianihus) were found to grow as follows, in thirty-seven days: 



Compound interest rate (%) 



Weight (gm.) 



Continuous 



Discontinuous 



Giant sunflower 

 Dwarf sunflower 



Seedling 



0033 

 0035 



Plant 



17-33 

 14-81 



Per day Per wk. Per day Per wk. 



170 119 18-5 228% 



16-4 114 17-7 214% 



When the yeast population is allowed to run its course, it yields 

 a simple S-shaped curve ; and the curve of first differences derived 



Fig. 31. The growth of a yeast-population. After Per Ottestad. 



from this is, necessarily, a bell-shaped curve, so closely resembling 

 the Gaussian curve that any difference between them becomes a 

 deUcate matter. Taking the numbers of the population at equal 

 intervals of time from asymptotic start to asymptotic finish, we 

 may treat this series of numbers like any other frequency distribu- 

 tion. Finding in the usual way the mode and standard deviation, 



* Cf. V. H. Blackman, The compound interest law and plant growth, Ann. of 

 Botany, xxxiii, pp. 353-360, 1919. The first papers on growth by compound 

 interest in plants were by pupils of Noll in Bonn: e.g. von Kreusler, Wachstum der 

 Maispflanze, Landw. JB. 1877-79; P. Gressler, Suhstanz-quotienten von Helianthus, 

 Diss. Bonn, 1907 etc. 



