88 
BOTANY: OSTERHOUT AND HAAS 
rapidly as time goes on. We must therefore conclude that photosynthesis 
belongs in a different category. 
The key to the situation is furnished by the figures in the second column 
of table 1 which show that if the reaction is catalyzed by a substance, it 
must be produced more rapidly at first and then more and more slowly. - It is 
also evident that this substance must be limited in amount and that when 
its production ceases the rate of photosynthesis stops increasing and becomes 
constant. We may assume that the rate of photosynthesis is proportional 
to the amount of the catalyst, which we will call C. The figures suggest that 
this substance may be produced in the manner characteristic of a monomo- 
lecular reaction. We may therefore assume that C is produced by a substance 
A, under the influence of sunlight, according to the monomolecular reaction: 
A -»C. 
We may now proceed to test this assumption by calculating the amount of 
photosynthesis which is to be expected after the lapse of a given time. 
According to the ordinary equation for a monomolecular reaction, 
C = A - Ae 
-KT 
in which T is time, e is the basis of natural logarithms, and K is the velocity 
constant of the reaction. 
If the rate of photosynthesis is directly proportional to the amount of C, 
we may, for convenience, put 
Rate of photosynthesis = ^ = C; 
dl 
hence 
On integration this becomes 
A K K 
When the rate has become constant we find that a unit amount of photo- 
synthesis is produced in 20.4 minutes (average of the last 3 periods in table 
1), hence the rate of photosyn theses at that time is 1 -~ 20 .4 = 0.049. This 
is by assumption equal to C when A is completely transformed into C and 
this is in turn equal to A at the beginning of the reaction. Hence A at the 
start = 0.049. We may substitute this value in the equation and find the 
value of K by trial. If we put K = 0.049 we get the values given in table 1. 
Better agreement with the observed values is obtained by taking lower 
values of K. This produces a gradual falling off in subsequent values, but 
it is possible that this might actually occur if the experiment could be con- 
tinued for a sufficient length of time. 
