372 Quantitative Analysis of Plant Growth 



inconsiderable for the periods of slow increase or decrease, at the time 

 of most rapid growth the formula ultimately adopted is approximately 

 double the true value; whence it must be apparent that any quantitative 

 study of the growth rates is materially influenced by the choice of the 

 measure of growth rate. Nor can the difficulty of calculation explain 

 the choice, for with the aid of a table of natural logarithms the correct 

 value is more quickly calculated than any of its approximations ; indeed 

 it is surprising that the experience of calculating one series did not bring 

 conviction on this point. One can only explain the choice by the mis- 

 taken impression, which is emphasised above, that the use of the log- 

 arithmic formula involved the assumption that the relative rate of in- 

 crease is independent of the time; an assumption which as the authors 

 state, is manifestly incorrect. 



This conclusion is confirmed by an apparently disconnected dis- 

 cussion, with which the paper opens, of the general mathematical formulae 

 which have been suggested to represent the growth history of annual 

 plants; among them there is ascribed to Blackman the view that this 

 growth history can be represented by an exponential curve, that is to 

 say, by a constant relative growth rate. Whether this view of the growth 

 history of annual plants has ever been advocated, I am unable to say, 

 but there can be no doubt that in advocating the use of accurate methods 

 for measuring relative growth rate, Blackman (l) is amply justified. 



Summary. 



The methods of calculation formulated by Briggs, Kidd and West 

 for the analysis of plant growth are inaccurate, (i) in introducing a 

 large exaggeration when the plant is increasing in mass, (ii) in applying 

 to periods of varying length, a method of calculation which thereby 

 becomes self-inconsistent. 



The correct measure for the mean value of the relative growth rate 

 over any period, long or short, is that advocated by Blackman under 

 the name of the "efficiency index." 



REFERENCES. 



(1) Blackman, H. V. (1919). The compound interest law and plant growth. Annals 



of Botany, xxxin. 353. 



(2) Brenckley, W. E. (1920). On the relations between growth and the environ- 



mental conditions of temperature and bright sunshine. Annals of Applied 

 Biology, vi. 211. 



(3) West, C, Briggs, G. E., and Kidd, F. (1920). Methods and Significant Relations 



in the quantitative analysis of plant growth. Neiv Phytologist, xix. 200. 



(4) Briggs, G. E., Kidd, F., and West, C. (1920). A quantitative analysis of plant 



growth. Parti. Annals of Applied Biology, vn. 103. 



