556 THE NATURE OF THE GROWTH RATE 



The Reliability of Various Criteria for Determination of the Growth 



. Rate. 



It will be well to discuss certain questions which will arise in the 

 mind of the reader. He desires to know, for example, whether the 

 growth rate will conform to a differential equation when we use some 

 other criterion, e.g. weight, as a measure of growth. An examination 

 of all possible measures of growth should be made, especially in view 

 of the statement sometimes heard that growth is a process so complex 

 that no single equation can successfully represent it. 



It should be noted at the outset that every measure which is a 

 mean of separate determinations of mass or volume is accompanied 

 by an inevitable error. This error is made up of two separate errors. 

 The first is due to the fact that the individuals measured were not 

 truly representative of the population, i.e. they did not constitute a 

 good "random sample"; the second is due to the errors which arise 

 in the use of the measuring device (meter stick or balances). If the 

 errors are of a purely random nature they will largely offset one another 

 in a large series, but in a small series they may materially affect the 

 mean. We need not expect, therefore, to find , agreement between 

 observed and calculated values as close as the physical chemist ob- 

 tains with his material. A difference of not more than 10 per cent 

 of the calculated value may be regarded as sufficiently accurate to 

 inspire confidence in the results. 



Kreusler has recorded the growth of several varieties of maize at 

 7 day intervals. Height of plant, green weight (entire plant), and 

 dry weight (entire plant) were determined on fairly large samples 

 of plants. I have found that the growth rate of the different varieties 

 determined by Kreusler follows the equation previously used 



- = kx{a — X) 

 dt 



The determinations made upon one variety (Hiihner-mais) will be 

 given as an illustration. Those who are interested may profitably 

 compute the growth rates of the other varieties which Kreusler fol- 

 lowed. Reference to Table V shows undoubted errors in the weight 

 of the samples at various dates. These can only be due to the use of 

 too small a number of plants to give a true representation of the 



