Over a certain range there is a linear relationship between the amount of complement required for 50 % lysis and the amounts of one of the variables in the primary reaction mixture of a complement-fixation test when the third variable is present in a quantity sufficient to allow maximum fixation.

If this linear relationship were maintained as the concentration of the selected variable is progressively reduced, there would also be a linear relationship between the logarithms of the amounts of complement fixed and the logarithms of the amounts of the selected variable; in this case, the line with logarithmic co-ordinates will necessarily have unit slope.

When the fixation of small amounts of complement by several virus systems is measured, an approximately linear relationship using logarithmic co-ordinates has been demonstrated, but in many cases the line does not have unit slope. In this range, therefore, there is not a linear relationship when arithmetic co-ordinates are used.

A new design for a complement-fixation test is proposed, using isohaemolytic curves.