368 Quantitative Analysis of Plant Growth 



It is here fitting to remark that whatever assumptions are made as 

 to the variations of growth rate with time, the relative growth rate at 

 any instant is necessarily 



1 dm d . 



mit = dt l °z m < ra >; 



the value of R, calculated by formula II, therefore gives correctly the 

 average value of the relative growth rate over the period between the 

 two observations, whatever may be the nature of the changes in relative 

 growth rate over this period. This property of formula II, and the 

 precise definition of relative growth rate at any instant given by III 

 should be borne in mind in considering the confused and contradictory 

 use of the term in the ensuing quotations. 



For when we refer to the paper under discussion (4) to ascertain what 

 are the two methods of calculation, the merits of which are to be dis- 

 cussed, we find that the term relative growth rate is now applied to a 

 quantity calculated as a schoolboy is taught to calculate Simple Interest. 

 The justification of this procedure must be quoted in full ((4), p. 104). 



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 mathematical accuracy, the 

 increase should be measured over an infinitely short period. This procedure is mani- 

 festly impossible, and as we have no exact knowledge of the way in which the relative 

 rate of growth varies, over a given period we have adopted the following purely 

 conventional method of defining relative rate of growth. The relative rate of growth 

 of a plant during any given week of its fife-cycle, is the amount of dry matter which 

 100 gms. of diy matter taken at the beginning of the week adds during the week. 

 A week has been chosen since this is the usual interval between determinations of 

 dry weight in most experiments on growth in plants. It must be noticed that the 

 method does not pretend to mathematical accuracy', being merely an approximate 

 average for the week, but with such results as are at present available nothing more 

 accurate can be obtained." 



The most striking feature of th<s paragraph is the contrast between 

 the precision of the first definition of relative growth rate contrasted 

 with the inconsequent arbitrariness of the method proposed for its cal- 

 culation. Nothing could be more clear than to define relative growth 

 rate as "amount of change" (i.e. increase) "per unit of material per 

 unit of time"; the statement is equivalent to that of expression III. 

 But why, if so precise a definition can be given of the quantity we wish 



