Sept, i, 1921 
Rate of Culm Formation in Bromus inermis 
815 
COMPOUND INTEREST LAW 
The compound interest law applied by Blackman 1 to plant growth 
deals with processes in which any rate of change varies as the quantity 
which is changed. This law evidently applies in the present case, as 
the larger the brome-grass plant the larger the peripheral ring which 
produces new culms. This law is expressed symbolically as 
W, = lV 0 e rt 
where W x is the final weight or measure of the plant, W„ the initial 
weight or measure, r the rate of interest, t the time involved, and e the 
base of the natural system of logarithms. Obviously 
_log IT.-log W„ 
l log e 
The rate of interest, r, appears to Blackman as an important physio¬ 
logical constant, for it represents to him the efficiency index of the plant 
as a producer of new material. 
Similar efficiency indexes were calculated for culm formation in 
Bromus inermis for the four initial culmages for the various dates. 
Each index, or interest rate, indicates comparative average rate of 
growth per day for the period of growth to each respective date, using 
the proper initial culmage as the base in each of the four cases. The 
indexes are presented in Table IV. 
Table IV .—Efficiency indexes of culm formation with four-initial culmages as determined 
by the compound interest law 
Growth period. 
One 
initial 
culm. 
Two 
initial 
culms. 
Three 
initial 
culms. 
Four 
initial 
culms. 
O. 090 
O. 076 
0. 037 
IO . 
0. 013 
16. 
. 124 
• °93 
. 072 
. 087 
.038 
21. 
• I IO 
. 091 
.079 
•973 
•073 
. 072 
• 090 
' . 070 
•075 
•075 
. 067 
. 061 
• 065 
• 070 
• 065 
• 067 
. 064 
•059 
•055 
•059 
•055 
•059 
• 056 
•055 
• OOo 
•059 
.052 
. OOO 
• °57 
.056 
•055 
• 052 
. 064 
- o6l 
• 054 
• 050 
68. 
•059 
•057 
• 054 
.052 
. 048 
• °53 
.051 
• 047 
78. 
• °53 
• 049 
• 048 
4 . 046 
•045 
84. 
• 0^6 
•054 
. 049 
• 044 
• 047 
•043 
1 Blackman, V. H. the compound interest law and plant growth In Ann. Bot 
P-353~36o. 1919. 
v. 33, no. 131, 
