Quantitative Analysis of Plant Growth . 203 
ing material” and also that the rate per unit of “growing material” 
decreases throughout the life cycle owing to the disappearance of 
a catalyst as growth proceeds. Such a formula, which fits the 
facts only approximately and explains the falling off in rate per unit 
dry-weight as being due to the disappearance of a catalyst, obviously 
does not help us much in an analysis of plant growth, and we agree 
with Enriques (5) that the similarity between an autocatalytic 
reaction and the growth of a plant is a purely superficial one, the 
falling off in rate per unit dry-weight being due rather to 
increasing differentation into productive and non-productive tissues. 
dW 
The formula -^-=rW, or in its integrated form W—W 0 e rt , 
originally put forward by V. H. Blackman (1) with the idea that it 
was an important physiological constant, involves the assumption 
that dry-weight (W) is a measure of “ growing material.” It has been 
shown that the rate per unit dry-weight, r, is not a constant (3 & 6). 
Suggested Procedure in the Study of Growth Bate. 
Before we can determine constants for a plant which have any 
physiological significance and which are comparable with physico¬ 
chemical constants we require a much more detailed analysis of 
the growth throughout the whole life-cycle. To this end we 
consider that the best procedure is to calculate the rates in relation 
to various units of the plant from data collected at frequent 
intervals. In this way we obtain a number of parallel records of 
rates throughout the life-cycle. By a careful comparison of these 
with each other and with the records of environmental factors we 
may hope to disentangle the problems of plant growth and proceed 
to the evaluation of constants. More in detail our technique and 
terminology are as follows 
(1) . Primary Data. Measurements of dry-weight and leaf- 
area at intervals of a week or less accompanied by measurements 
of respiration, assimilation, transpiration and chemical analysis of 
the plant tissue, and continuous records of the various environ¬ 
mental factors likely to affect growth. In order that these data 
when collected may be of real value it is necessary to adopt a sound 
statistical procedure, e.g., utilisation of material as uniform as 
possible, large samples and calculation of probable errors. 
(2) . Significant Secondary Relations. The presentation of the 
results so obtained through the complete life-cycle in four series 
of numbers which can, if desired, be put in the form of graphs— 
“Relative Growth Rate," “Leaf Area Ratio," “ Unit Leaf Rate" 
and “ Relative Leaf Growth Rate." 
