3897 - 98 .] Dr Walker on the Velocity of Graded Actions. 31 
I am indebted to my colleague, Dr John M'Cowan, for the solu- 
tions of some special cases where the integration can be performed ; 
but, as they do not correspond to any cases hitherto realised, and, 
in addition, show no special features different from those exhibited 
by the two successive unimolecular reactions, I refrain from giving 
them here. 
In the example given above of the transformation of ammonium 
cyanate into urea, the processes of electrolytic dissociation and 
association take place so rapidly, compared with the processes of 
urea-formation and decomposition, that they may be neglected, as 
far as the form of equation goes, for expressing the rate of the 
reaction. By a combination of chemical and electrical measure- 
ments (Walker and Kay, Jour. Chem. Soc ., 1897, 489) we can 
determine at any moment the value of x + y and of y , and so can 
ascertain the value of n, an equilibrium experiment having pre- 
viously given the ratio of n' to n. 
It should be noted that we cannot, strictly speaking, compare the 
values of n and n' in the above equation for urea-formation, since 
they are of different dimensions, their ratio being altered by a 
change in the unit of volume. In general we can only compare 
together the constants of reactions of the same order, as reactions 
of different orders depend on the volume in different ways. This 
observation suggests a possible method for ascertaining the rate of 
very rapid reactions otherwise inaccessible. For instance, it would 
be of great interest to determine the rate of any case of electrolytic 
dissociation or association, but the rapidity with which these re- 
actions proceed precludes any direct measurement. Suppose a 
graded action could be found in which the first stage was the 
union of two ions to form an undissociated molecule and the 
second stage a comparatively slow transformation of the undis- 
sociated molecule into something else. Here we should have a 
very rapid bimolecular reaction followed by a measurable uni- 
molecular reaction. In solutions of ordinary concentrations the 
rate of the total transformation would be that of the pure uni- 
molecular reaction; but, if we could follow the course of the 
graded action in extremely dilute solution, we might be able to 
discover a disturbing effect of the preliminary bimolecular reaction, 
and ascertain thereby approximately its rate. This is so, because 
