104 Quantitative Analysis of Plant Growth 



Another suggestion is that the growth of a plant is similar to an 

 autocatalytic reaction, and that it can be expressed by the formula 



where A = the maximum dry-weight of the plant, x = the dry- weight 

 of the plant at any time t, t x = the time at which the weight of the 

 plant is half the final dry-weight, and K = a constant. This suggestion 

 was put forward by Robertson (24 and 25) and has received the support 

 of Eeed and Holland (21) and of Rippel(22 and 23). 



Finally Mitscherlich (14, 15 and 16) has attempted to apply to plant 

 growth as measured by dry-weight increase the following formula 



log (VA — \/y) = l°g v^4 — ex. 



In this formula n = a variable quantity indicating the probable 

 number of environmental factors, A = the maximum possible dry- weight 

 attainable by the plant in question, y = the dry- weight of the plant at 

 time x, the time x being expressed in vegetation periods (Vegetations- 

 abschnitten) of arbitrary length. 



A fuller consideration and criticism of these suggestions will be given 

 in subsequent chapters. 



In the present paper the primary objective is to attempt to obtain 

 a concrete idea of the growth and development of the plant. At the 

 outset it will be best to confine our attention to simple cases and we 

 propose to devote the first chapter to a consideration of an annual plant. 



Certain data are required: periodic dry- weight measurements of the 

 whole plant (and its various parts) at short intervals throughout its life, 

 starting from the seed at the time of sowing; corresponding periodic 

 leaf-area measurements; data with regard to light, temperature, and 

 water supply. To avoid the error due to individual variation, a large 

 number of plants should be used for each dry-weight measurement and 

 where possible uniform 'pure-line' material should be employed. 



There are various methods of presenting the results, and in the first 

 instance we shall use the relative growth-rate curve. The principle of the 

 proposed method of expressing rate of growth is analogous to that of 

 the method by which the rate of most reactions, both chemical and 

 physiological, are expressed, namely, amount of change per unit of 

 material per unit of time. Since the amount of material in the growing 

 plant is constantly changing, and since the relative rate of growth is 

 not constant, as the following analysis will show, to achieve mathe- 



