1897-98.] Dr Walker on the Velocity of Graded Actions. 25 
actions occurring in aqueous solution, so far at least as the type of 
the reaction is concerned; although the degree of dissociation 
greatly influences the numerical value of the velocity constant. 
It was the study of such a transformation in aqueous solution that 
led to the following considerations with respect to the velocity of 
graded actions. 
Let the chemical system A pass into the system C through the 
intermediate system B ; and let the actions he irreversible. If the 
action A->B is indefinitely faster than the action B->C, then the 
total action A->C will proceed at a rate determined solely both 
as to type and numerical value by the rate of B->C ; and if A->B 
is indefinitely slower than B->C, the rate of A->C will he that 
of A->B. Should the rates of the two actions he comparable 
with each other, the rate of A->C will fall under no simple type, 
and will differ essentially from that of any pure reaction. A case 
of this kind was studied by Harcourt and Esson, the pioneers in 
the field of reaction velocity, and a very complete mathematical 
treatment is given in an appendix to their paper by Esson.* This 
paper, although frequently cited, has been altogether neglected 
from the point of view of graded reactions. The process studied 
by them was the reduction of potassium permanganate by oxalic 
acid. In presence of manganese sulphate it takes place in two 
stages, which they express by the equations, 
2KMn0 4 + 3MnS0 4 + 2H 2 0 = K 2 S0 4 + 2H 2 S0 4 + 5Mn0 2 , 
Mn0 2 + H 2 S0 4 + H 2 C 2 0 4 = MnS0 4 + 2H 2 0 + 2C0 2 . 
These actions take place at comparable rates, and mathematical 
formulae are given for them which accord very well with the results 
of experiment. 
The simplest case to consider is that in which both actions are 
unimolecular. For a pure unimolecular reaction the expression for 
the velocity constant is, as given above, 
m = ^ log f 
A 
A -s' 
To bring this into a form comparable with that of the graded 
reaction we rearrange it as follows : — 
z = A(l 
* Phil. Trans., clvi. 216, 1866. 
