On the Construction of Graphs and Tables for Evaluation of the Quantitative Complement-Fixation Reactions and Reaction Ratios

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Abstract
As a means of obtaining a measure of reactivity of sera with antigens the complement-fixation reactions have been used extensively. The aim of investigations in this laboratory has been to develop a quantitative basis for expressions of this relative reactivity with a specific antigen. Hemolysis of sensitized sheep cells has been used as the indicator of modification of complement activity in the presence of various amounts of antigen and a given serum. Several systems have been studied, and a quantitative measure in the form of an index has been employed in the case of the tuberculous, syphilitic, and gonococcal antisera reacting with prepared antigens (1, 2). Tables have been developed to facilitate evaluations, and the object of the present communication is to indicate the procedures used in their construction. As a preliminary, the fundamental relations are developed below. Let x be the number of units of complement used in a reaction mixture, and y be the degree of hemolysis obtained.

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