Significance of the Efficiency Index of Plant Growth . 99 
activity in the production of new material. 1 It is clear that owing 
to the marked fluctuation of the index over even such a short period 
as 24 hours some such convention is essential if we are to compare 
the activity of different plants. 
It has further been suggested in criticism that “the essential 
idea of the ‘ Substanzquotient ’ put forward by Noll and his pupils 
is far preferable, as it simply states the ratio of final weight to 
seed weight divided by time, and makes no assumption as to the rate 
at which the addition to dry material has been made.” In relation to 
this criticism it must be pointed out at once that the last statement 
cannot be accepted. A formula in which the final weight is 
divided by seed weight and by time implies that there is a linear 
relation between time and weight ( i.e ., that the increase of weight 
is an arithmetical progression) just as definitely as does the formula 
I put forward carry the implication that the relation between time 
and weight is a logarithmic one (i.e., that the increase of weight is 
of the nature of a geometrical progression). A simple formula is 
no less based on theory than a more elaborate one. 
The question as to which formula is the more suitable is 
simply the question as to which hypothesis most closely fits the 
facts. That plants do to a large extent add new material on the 
compound interest principle can hardly be denied. It would seem 
also that annual plants when growing under favourable conditions 
add the main mass of their material at a rate which constantly 
increases with time (see for example, Fig. 4 of Dr. Brenchley’s 
in the forthcoming paper already cited). A formula which takes 
this mode of increase into account by assuming an average or 
conventional index, would seem then more satisfactory as a 
comparative measure of efficiency than one which implies the 
addition of new material at a constant rate. 2 
The authors have also criticised the exhibition in the original 
paper of the data from Gressler’s work on Helianthus. The times 
chosen for the various species were those for which it appeared 
that the geometrical increase of dry weight was most marked. 
They served to bring out the marked difference in the economic 
rate at which these plants were working during these periods. The 
1 The use of the term “ constant ” can on this ground be defended as 
literally correct, since for any given experiment and any given period the 
index is an absolute constant, albeit a hypothetical one. 
2 It may be that to some plants growing under unfavourable conditions, or 
with a long period of slow growth in the latter part of their development, 
the simple “ arithmetical ” formula would more aptly apply. Even in these 
cases, however, for purposes of comparison with other plants the compound 
interest formula may conveniently be used. 
