106 Quantitative Analysis of Plant Growth 



shorter intervals were available, until we gain knowledge of a mathe- 

 matical law according to which the rate changes, we cannot determine 

 the rate at any given time. 



It might be suggested that allowance could easily be made for the 

 continuous increase in the dry- weight during the week by assuming that 

 this takes place at a uniform rate, and consequently that by means of 

 the following logarithmic formula the rate could be determined : 



log W — log W o = r, 



where W = the dry-weight at the end of the week, and W Q = the dry- 

 weight at the beginning of the week. 



In curve A, Fig. 1, this allowance has been made. In Curve B the 

 ordinates are relative growth-rates calculated by our method, that is, 

 without making allowance for the continuous increase during the week. 

 These curves show similar variations in relative rate from week to week. 

 The more complicated method, however, does not achieve accuracy as 

 it rests on the assumption that the rate remains constant during the 

 week, an assumption manifestly incorrect since the rate varies from 

 week to week. Both methods are purely conventional and only approxi- 

 mate to accuracy, and nothing definite is to be gained by adopting the 

 more complicated procedure. 



The relative rate of plant growth at any time may be taken as an 

 expression of the efficiency of the plant at that time in producing dry 

 matter. It must be remembered from what we have said above that 

 the actual value of the figures for the growth-rate is only an average of 

 the changing rate during a week. They are, however, valid for purposes 

 of comparing the rate of a plant's growth from week to week. 



The gist of the method described above of presenting the results of 

 growth experiments has been previously briefly put forward by Kidd 

 and West (9). 



CHAPTER I. 



THE RELATIVE GROWTH-RATE CURVE FOR MAIZE. 



The most complete set of data for one plant is to be found in a series 

 of papers published in Germany many years ago under the general 

 direction of U. Kreusler(H), n, and 13). From among the many results 

 recorded, we have chosen those for maize, since the growth of this plant 

 was studied in four successive years. The data include not only weekly 

 dry-weight measurements and corresponding leaf-area measurements, 



