136 MR. A. W. BENNETT ON THE RATE OF GROWTH OF THE 
two terminal zones again into two parts, the uppermost of these (C—L) increased be- 
tween 10 a.m. on Sept. 27th and 9 a.m. оп Sept. 29th, from 9:8 to 11:35 in., or 15:8; 
the lowermost of them from 8:8 to 9°95 in., or only 13 per cent of its original length. 
In ealeulating what Sachs terms the ** Grand Curve of Growth " of the plant *, I have 
pursued a somewhat different plan to that adopted by this high authority. In his 
‘Text-book’ (p. 737) he gives the following instructions for the construction of such a 
eurve:—** If the increments of growth during successive equal times are drawn as 
ordinates, with the intervals of time as abscissze, a curve will be obtained which, starting 
from the axis of abscissæ, reaches a maximum of elevation and returns again to the 
axis.” In constructing these curves, it appeared to me that results of greater value 
would be obtained if, instead of the aetual inerement for any given time, the propor- 
tionate increase in relation to the length at the commencement of the interval were 
taken as the ordinate. Ву this means it seems to me that the energy of growth of 
each particular portion of the stem at any particular time will be represented by the 
altitude of the curve. Thus, supposing a stem increases during two successive equal 
intervals of time from 4 to 5 and from 5 to 6 inches, the energy of growth will not 
be equal to the two intervals, but will be less in the latter interval in the proportion of 
4to 5; inasmuch as it will have increased during the former interval 25 per cent., during 
the latter interval only 20 per cent. of its length at the commencement of that interval. 
It will be evident that though my grand eurves of growth will agree with Prof. Sachs's 
in their general features, they will differ in minor particulars, and will in general be 
less abrupt. In constructing the curves from the data already given, I have first of 
all divided the increment during each interval of time by the length at the commence- 
ment of the interval, in order to get the proportionate increase as above indicated, 
and then the result by the number of hours in the interval, in order to reduce the times 
to a uniformity, the length of the intervals between the observations varying greatly, 
owing to my engagements. It is obviously, then, indifferent on what scale the curve 
is constructed, 4. е. what is taken as the unit of measurement. In the diagram which 
accompanies this (р. 137), each unit of 1 inch on the ordinates represents an increase of 
1 per cent. per hour; while an inch on the line of abscissee represents a period of 12 
hours. In accordance with Prof. Sachs's plan I have placed each ordinate in the centre 
of the abscissa to which it belongs. The two accompanying curves have thus been 
obtained, one exhibiting the variation of the energy of growth for the two terminal 
portions, the other for the remainder of the flower-stalk. Тһе general result is seen 
to be that the terminal portion exhibits a considerably greater energy during the whole 
of the time with the exception of the first few hours. 
А second series of observations was made on another flower-stalk; but I have not 
thought it worth while to record the results in detail, in consequence of an accidental 
injury (to which the slender and delicate stems are extremely liable when undergoing 
measurement), which both retarded the growth and caused it to be somewhat irregular. 
The eurves construeted in the same manner showed a striking resemblance to those in 
the previous instances, but with two abrupt depressions caused by the injury referred to. 
* See * Arbeiten des botanischen Instituts in Würzburg, 1873, Heft 2, t. i. 
