Titrations of complement under the conditions of the test for syphilis were made to determine the effect of the fixation period and of the different reagents, separately or in combination, upon the form of the curve representing the degree of hemolysis fifteen minutes after the addition of sensitized cells; the reaction-mixture was kept in a water bath at 37°C.

The form of the hemolytic curve was practically constant when relatively small amounts of complement were required for 50 per cent hemolysis and the concentration of serum constituents in the titration was not too low; it varied, however, when large amounts of complement were necessary for 50 per cent hemolysis. In titrations made in the presence of tissue-extract and of serum from patients with syphilis the form of the hemolytic curve varied with the concentrations of complement and of the antigen.

Under all the different conditions of these comparative titrations the experimental data could be closely approximated by the alternation formula of von Krogh with suitable constants. This furnished a means of interpolation for the 50 per cent hemolysis point. Linear interpolation may be used if log X is plotted against log , where X is the concentration of complement and Y is the degree of hemolysis.

In titrations of complement in the presence of antigen and of serum from persons with syphilis there was a linear relation between the amounts of complement and of serum required for 50 per cent hemolysis when the proper amounts of antigen were provided to yield the maximal reactions with the given quantities of serum, as well as between the quantities of complement and of antigen necessary for 50 per cent hemolysis when sufficient serum was used to yield the maximal reaction with the given quantities of antigen.

When antigen is present in too great an excess, the intensity of the reaction diminishes and may even disappear completely; but, with a considerable excess of serum, the reaction appears not to change appreciably; that is, does not diminish.

The relationships observed in these studies between serum and complement and between antigen and complement constitute a fundamental basis for the quantitative determination of the reaction.

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