504 Captain A. G. McKendrick. [ Nov. 30, 
would tend to be too long. (I have presumed that, in this experiment, the 
number of bacteria was sufficient to take up all the amboceptor. I shall 
discuss this in Section VIII.) 
V. The Relation between y and x which gies a Maximum Velocity.— 
& = ¥(2—2)-(t—2), © (e)=542- ae) 
hs ONG Cy dy \dt Ce C2 a2 
ad (dz 
when oF (5 
(z.e., When increase of velocity per increment in y is zero), then 
2y = «fz+cz, 
and this equation is satisfied when 
Ya CR. = C27, 2 aC ey, 
z.€. at “points of diversion.” 
This conclusion is made use of in the method of finding the approximate 
value of c, as described at the end of Section I. 
VI— When the Reaction is performed in Two Stages (Supersensitisation 
phenomena).—Let y be > cz. The first part of the experiment follows the 
equation ; 
= —(e=2) 
a ie aN 
When saturation has been accomplished, 
_— 
oe 
I 
8 
a Ie 
| 
x 
dt — 
If z for complete lysis was % at the commencement of the reaction, it is. 
after the first part of the experiment equal to y/c. 2 (call this 2). 
If complement be now added, the reaction follows the equation 
~ — — —_— —" 
(The value y/c is retained as all the amboceptor has become attached.) 
When equilibrium has been reached, « = cz,?. 
Had the experiment been performed in the usual manner in the presence 
of both components, equilibrium would have been reached when 
2 ag 
t-te) 
6 C \C&% 
That is to say the “ point of diversion” would have been at 
Ms ay i= VORh 
