F. F. Blackman. 
30 
change in the test-tube and in the cell. The law of mass-action 
states that the amount of chemical action going on at any moment 
at a given spot is proportional to the quantity or mass of the 
reacting substances that are present. Katalytic agents naturally 
obey this law ; if a double amount of enzyme is present in a solution 
it converts twice as much substance in a given time as a single 
amount would. Now, even with the acceleration produced by a 
katalytic enzyme all ferment actions are slow and if a reaction is 
started with a definite amount, say, of invertase, and a definite 
amount of cane-sugar in a beaker, it is many hours before all the 
sugar is “ inverted.” The inversion of the sugar is at first fast, 
and so the amount of the sugar rapidly decreases; from this it 
follows by the law of mass that the rate of inversion will now fall 
off also, and so it does, tailing off more and more as the amount of 
sugar becomes diminished. 
If half t\\Q total sugar be inverted in the first hour, then i the 
remainder (=^) will be inverted in the second hour, ^ the new 
remainder (=:^), in the third hour, in the fourth hour, and so on 
never reaching absolute completion in theory, but coming near 
enough to it in practice. This march of the conversion can be 
graphically represented from these data by a regular falling 
“ logarithmic ” curve showing the rate of inversion at any moment. 
From analogy with the action of colloidal Platinum as a 
katalytic agent, it is held that the enzyme unites temporarily with 
the sugar molecule, and the water molecule, and that this so-called 
“ active system ” at once splits up, regenerating the enzyme and 
leaving the sugar so acted upon by the water that it is inverted 
from cane-sugar to glucose and levulose. The rate of the compound 
process of inversion must depend upon the rate of formation of the 
“ active system ” and the rate at which it splits up again. The 
amount of enzyme in the solution remains by definition unchanged, 
so that the rate will come to depend only upon the amount of cane- 
sugar present. A constant fraction of the total number of sugar 
molecules present (50% per hour in this assumed case) unites with 
enzyme to form the active system. Here the enzyme is assumed in 
excess, and the sugar is the limiting factor to the rate of inversion. 
One can however for a time produce a different balance of 
activity in the solution. Suppose that at the beginning, cane-sugar 
molecules are very abundant and enzyme particles are very few. 
Then the number of active systems formed (in the hour) will be 
limited by the scarce enzyme and many of the sugar molecules will 
