RESPONSES TO ENVIRONMENT BY PLANTS IN THE VEGETATIVE PHASE 527 



the percentage gain in dry weight per week on an arithmetical scale. 

 The rejoinder by Blackman ( 1920 ) was that if a single basic assump- 

 tion had to be made, then the weight of the evidence, particularly for 

 the vegetative phase, was that growth was an accumulatory process, 

 so that any calculation of the mean rate over appreciable time intervals 

 on a linear basis was liable to considerable error. Blackman agreed that 

 when the relative growth rate was calculated over short time intervals, 

 fluctuations in environmental factors would be reflected in variations in 

 the index, but he still held that over longer periods the mean index 

 did give some quantitative indication of the relative performance of 

 diflFerent plants. Fisher ( 1920-21 ) also pointed out with pungency that 

 if one wanted to find the average change in weight between two sam- 

 pling times, then the rate was best expressed as : 



1 dw d 



— — or — logeW. 

 w dt dt 



To these strictures Briggs et al. ( 1920-21c ) replied that they had put 

 forward both methods of calculation and that both methods were 

 perfectly proper. 



These authors (1920-21b) put into more precise terms the de- 

 pendency of the relative growth rate on both the level of photosynthe- 

 sis per unit of leaf surface and the assimilatory area. As the ash content 

 of most plants is small and does not appreciably alter with the stage of 

 development, the net gain in dry matter over each 24 hours is deter- 

 mined by the excess of carbon dioxide fixed during the day over that 

 respired during the night. Hence a measure of the net fixation per unit 

 leaf surface can be obtained if the leaf area is measured simultaneously 

 with the estimation of dry weight. Briggs et al. defined "unit leaf rate" 

 as the increase in dry weight per square centimeter of leaf per week, 

 taking as the leaf area the average of the area at the beginning and end 

 of the week. Here, again, in estimating unit leaf rate, the question 

 arose whether changes between sampling occasions should be taken 

 as exponential or not. If an exponential basis is assumed, then the mean 

 rate is best expressed as : 



W2 — Wi logp A2 — loge Al 



X 



t2 — ti A2 — Al 



where \V2 and Wi and Ao and Ai represent the weights and total leaf 

 areas at times ti and to. If the relationships are considered to be linear, 

 then the expression becomes : 



W2 - Wi _ A2 + Al 

 t2 — ti ■ 2 



