In previous studies (1, 2, 3), methods of comparative titration of the specific and nonspecific activities of serum and antigen in the complement-fixation reaction were described, and a formula providing a quantitative and qualitative differentiation of the reactions was presented, . The purpose of the present paper is to describe a modification of the formula which increases both its accuracy and the range of reaction over which it can be applied. The formula expresses the ratio of the amount of complement fixed by immune serum and antigen to that fixed by normal serum and antigen in titrations of complement made with preliminary incubation in the presence of these reagents. This ratio indicates the quantitative difference in reaction between the normal and immune serum with a given antigen: the qualitative difference can be determined by comparing these ratios with those which represent the variation in the reaction of different normal sera with the same antigen.