Blackman . — The Compound Interest Law and Plant Growth. 355 
in title in the Proceedings of the society) entitled ‘ Uber die Substanz- 
quotienten pflanzlicher Entwickelungsstadien In the next two years three 
of his pupils, Gressler, 1 Hackenberg, 2 and Kiltz, 3 published inaugural disser- 
tations dealing with the determination of the ‘ Substanzquotienten ’ of 
various plants. 
From these papers it becomes clear that the c Substanzquotient ’ is the 
factor which relates the dry weight at the end of any period of growth with 
the dry weight at the beginning of that period. Taking Gressler’s results 
with Helianthus uniflorus giganteus we find that in five successive weeks the 
average dry weight in grammes of a number of plants was 0-0454, 0*147, 
0-508, 1*653, 17*33, 30*35, 46-2, 66-1, 88*9. Dividing the second by the 
first, the third by the second, and so on, we find that the successive weekly 
‘substance-quotients’ were 3-25, 3*45, 3'24> 3\5 6 > 3*°» I *75, 1# 4» 1 ' 3 - 
The successive, weekly dry weights clearly exhibit at first a progression 
which is approximately geometrical ; later, however, the rate of increase falls 
off, the series becoming an arithmetical one. 
The ‘ substance-quotient ’ per week is obviously a clumsy and in- 
accurate method of expressing these results. What is required is some 
simple method of relating the plant’s activity in the production of new 
material to time and to the initial weight of the seedling. Hackenberg and 
Kiltz merely state their results as ‘ substance-quotients ’ per week, but in 
calculating the average £ substance-quotient ’ over a period of many weeks 
Gressler treats his results as a discontinuous geometric series. The formula 
which would then apply is W 1 ~ W 0 (1 +r) t , where W 1 = the final weight, 
W 0 = the initial weight, r = the rate of interest, and t — time. Gressler’s 
results for Helianthus calculated in this way per week and per day are 
shown in columns 5 and 6 of the accompanying table. 
Seedling Final Time tRate of Interest Rate of Interest 
weight . weight, jjavs (- Discontinuous ). ( Continuous ). 
Grm. Grm. ' per week, per day. per week, per day. 
II. uniflorus giganteus 
0.0327 
17*33 
37 
227.6% 
i 8*5% 
ii9*°% 
17.00 
% 
It. nanus 
0.0348 
14.805 
37 
214*3 % 
i7*7% 
ii4*5 % 
16.36 
% 
It. cucumer if olius nanus 
0.00106 
0.401 
56 
no*o % 
H*2% 
74*i % 
10.59 
% 
H. macrophyllus giganteus 
0-0241 
6.772 
32 
243*3 % 
J 9*3 % 
123*4% 
17.63 
% 
H. arboreus giganteus 
0.0192 
14.680 
40 
219.6% 
i8-i% 
116.1% 
16.59 
% 
Treatment of the results in this way would, however, only be satisfac- 
tory if the additional material were added discontinuously at the end of 
each day or week. It is obvious, however, that during the daylight period the 
plant is adding new material continuously, and during rapid growth the plant 
1 P. Gressler: Ueber die Substanzquotienten von Helianthus Annuus. Inaug. Diss., Bonn, 
1-29, Tables I-V, 1907. 
2 H. Hackenberg: Ueber die Substanzquotienten von Cannabis sat iva xmd Cannabis gigantea. 
Inaug. Diss., Bonn, 1-27, 1908. Also Beihefte zum Bot. Centralbl., xxiv, pp. 45-64, 1908. 
8 H. Kiltz : Versuche uber den Substanzquotienten beim Tabak und den Einfluss von Lithium auf 
dessen Wachsthum. Inaug. Diss., Bonn, 1908 (seen only in abstract, Bot. Centralbl., cx, p. 455, 
1909). 
