500 Captain A. G. McKendrick. [Nov. 30, 
The constants were obtained as follows :— 
The summit of the observed curve (vide Chart 2) is shown as lying 
between 3and 4. Ichose y = 3 as the summit, and that the degree of lysis at 
this point was 92 per cent. The value of « is 0°24 throughout the whole 
curve. The summit conditions are given by equations (6) and (7). 
By equation (6) | OS G6 
we have c = 9/0°24, 
or Ci Fonnos 
By equation (7) = Oe 
2 = 3/37°5. 
Therefore z = 0°08 for 92 per cent. lysis. 
A comparison of observed and calculated values in Chart 2 shows more 
clearly than the figures do that all the singularities of the curve are fulfilled. 
III. x and z varying; amboceptor (y) constant. dz/dt = 0. Chart 3.— 
To find the constants in the (z, z) plane is much more difficult. A point of 
flexion may be found within the range of experiment. When little 
amboceptor is present it hes near the y axis. When much more amboceptor 
is present it is not seen; the curve is nearly flat; the point, as a matter of 
fact, lies beyond the line of complete lysis. 
The curve thus occurs in widely different forms. For low values of y it 
is almost entirely convex upwards, For high values of y it is concave 
upwards, in reality nearly flat, and] for intermediate values it assumes. 
an fform. Some of these forms are shown in Chart 3. 
The point of flexion can be found mathematically as follows. Re-arrange 
equation (8) 
e+ ce? = y2z+cx%y—); 
thus Os ee, 
de ytd3ceey-1—2cz 
aes 1 et el 90 dz 
da? (y+ 3c?2y-1—2cz)? du’ 
When = 0 (the point sought for), 
2 
either e = 0, which is obviously not the case, 
L 
or 6erzy-1 = 26, 1.2. y= sez. (11) 
Substituting this value of y in (8), we find 
gs Lee, (12) 
