30 
Proceedings of Royal Society of Edinburgh. [sess. 
overlooked if observations near the beginning of the action 
were not considered. In this case the disturbing influence of the 
second reaction is briefly that z , instead of being equal to 
l-e~ mt is approximately equal to l-l'01e~ m \ in general to 
1 - (^ + 7 ^Je~ mt . The effect of rapid disturbing actions is, as 
may be seen from the tables, most evident near the beginning of 
the reaction, which only assumes an appearance of regularity as 
the process goes on. Now, “ initial disturbances ” play a large 
part in known cases of reaction velocity, and it seems to me not 
improbable that some of them are due to the actions considered 
not being simple actions, but graded actions, with one stage very 
much more rapid than the other. 
When the actions are reversible and some of them other than 
unimolecular, the differential equations do not often permit of a 
simple solution. Thus, for example, the transformation of urea 
into ammonium cyanate is chemically 
NH 4 CNO $ NH 4 - + CNO' CO(NH 2 ) 2 . 
Let the total mass be A as before, composed of x in the first stage 
(undissociated cyanate), y in the second stage (dissociated cyanate), 
and 2 : in the third stage (urea) ; and let the constants be 
m for NII 4 CNO NII 4 ' + CNO'' 
m' for NH 4 - + CNO' -> NH 4 C5TO 
n for NH 4 ' + CNO' -=> CO(NH 2 ) 2 
n' for CO(NH 2 ) 2 NH^ + CNO'. 
The differential equations are then 
dx , 9 
^ = mx -my 1 
dz 
dt =n y nz - 
From a knowledge of the composition of the solution when 
equilibrium occurs we get the ratio of m to m', and of n to n'. We 
are then in possession of all the information necessary to express, 
as before, 2 in terms of t , and it is only difficulties in the integration 
that present an obstacle. 
