20 



Scientific Proceedings (117). 



the independent variable, complement, and y is the proportion 

 of cells which are hemolyzed. Possibly a more convenient 

 nu t hod still is the use of the coordinate paper shown in Fig. 2, 

 where log [v/(i — y)] is directly compared with log x.. In the 

 case of the nomogram a straight edge is laid between the values of 

 yi and yi on the lines AB and CD respectively and the point where 

 it crosses the line EF marked. A line is then drawn between the 

 values of X\ and .r 2 on EF and CD respectively and this line is 

 moved parallel to itself until it passes through the point where the 

 first line crosses EF. It will then intersect the line OP at the 

 value of n required to satisfy this pair of values. In the use of 

 the coordinate paper the values are plotted directly and the slope 

 measured. This second method has the advantage over the first 

 of being dependent on all values of x and y and not merely upon 

 a pair of values. 



The Wassermann reaction is in the last analysis an estimation 

 of complement after certain procedures are performed. This 

 method is, it is believed, the nearest to an absolute measure of 

 complement which has yet been devised and has a precision under 

 favorable conditions of 3 per cent, or better. 



The reaction between syphilitic antibody-antigen complex and 

 complement appears to follow the same law, wherein the logarithm 

 of the proportion between the amount of complement absorbed 

 to that unabsorbcd varies linearly with the logarithm of the 

 amount of antigen antibody complex present, the slope of the 

 graph in this case ranging round 1 or a little higher. 



If these considerations are valid, one can make certain state- 

 ments as to the Wassermann procedure which are at variance 

 with the theory of the reaction as ordinarily conceived. In the 

 first place, the estimation of complement should be performed 

 under such conditions as to bring the amount of hemolysis in the 

 neighborhood of 50 per cent., which corresponds to the value 

 log [y/(i — y)] = Q. 'The precision of measurement of comple- 

 ment by using this point can be calculated to be and is in fact at 

 least 10 times as great as the precision obtainable by the common 

 methods. In the second place, a true measure of the amount of 

 syphilitic antibody antigen complex is given, not by the absolute 

 amount of complement absorbed, but by the proportion which 



