1910.) The Chemical Dynamics of Serum Reactions. 503 
continue for a sufficient period of time. One hour at 37° C. is insufficient ; 
under such conditions the bulges in the / form are much more developed, but 
the curve is not calculable by equation (8), as the system is not in equilibrium. 
I have found that incubation for two hours at 37° C., followed by 12 hours in 
the ice box, is sufficient for practical purposes. 
The variables y, x, and z, have now been fully observed ; and the surface 
obtained by the equation of equilibrium agrees in every detail and in all its 
singular properties with the form obtained from experiment. | 
IV. y and ¢ varying. Complement absent (« = 0); effect z constant. This 
leads us into a different domain of serum reactions, viz., agglutination. 
Equation (1) loses its fraction dependent on concentration of complement, 
and becomes . 
WAD 2 
OZ Ui pe 
Bae eek. Vince ie 072 
On integration =a = or yt = (16) 
dj Ree cZ—Y 
The appended table is taken from Arrhenius,* and I have added as a fourth 
‘column results calculated from the right hand of equation (16)— 
y ¢ (minutes). | yt |  e2/ {cz—y). 
0 008 140 eG) 1°11 
0-006 | 150 tf O90 0°95 
0 0055 165 Oro. || 0-912 
0 -005 180 ie eOROOR! | 0 *888 
0-004 210 0:84. | 0°83 
0-0035 240 | Orea | 0-80 
0-008 300 0:90 | 0°784 
0 -0022 420 0°92 0°75 
0-002 480 || 0-96 0°74 | 
| | 
e—10:6058 ee —- 0-03. 
These constants were obtained by solving simultaneous equations obtained 
by introducing observed values of y and ¢ in equation (16). 
Arrhenius considers that there is an experimental error in the first value 
of yt, due to the fact that the liquids were not immediately brought to a 
constant temperature, and considers yf to be constant (mean for last eight’ 
values = 0:90). I would suggest that the discrepancy lies in the later figures. 
Agglutination is measured by the eye. When the reaction is fast the flocculi 
are larger and are more easily observed. When the reaction is slow 
agglutination occurs in smaller, more discrete particles, and observed times 
_ * Loe. cit., p. 104. 
