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added to each of these tubes. After shaking well, incubation is continued for
another 30 minutes, and the laking judged as before. The readings of these tubes
should support the preliminary titre, or indicate the necessity for some slight
modification.
This titration may be further illustrated by the table below

In the above description it will be noted that—
(a) the saline solution is used so that the mixtures in each tube amount
to 3 volumes before the red cells are added ;
(b) the front row tubes contain complement and sensitised red cells only,
and since serum is absent they have no place in the test proper ; but
(c) since the 4th or back row tubes contain one volume serum and one
volume of a complement dilution, these tubes are represented by the front row
tubes (controls) in the test proper; and, similarly,
(d) since the 3rd row tubes in the titration contain serum, complement
and dilute antigen, these tubes are represented by the two diagnostic rows of
tubes in the test proper ;
(e) the second row of tubes gives a measure of the anti-complementary
property of the antigen.
It will be apparent from the above notes why the 3rd and 4th rows of tubes in
the titration of complement are of such great importance.
2. Construction of a table to convert unit volumes of dilutions of guinea-pig serum
into units or doses of complement.—It may be helpful first to define clearly the meaning
of the terms used.
Guinea-pig serum is generally used in these fixation tests as the source of supply
of complement which is quantitatively estimated by titration as described above.
The unit dose (minimum hæmolytic dose) of complement is that quantity
(in guinea-pig serum) which is just sufficient to lake completely in 30 minutes the
unit volume of 3 per cent. red cells sensitised with 5 M.H.D. of amboceptor.
The standard unit volume for this test is .11 c.c. The titre indicates the number
of doses of complement present in the unit volume of undiluted guinea-pig serum.
As this serum is used diluted with .9 per cent. saline, the titre can also be expressed
as that factor which indicates the number of times the serum must be diluted to
give a solution containing one dose of complement per volume. For example, a
titre 60 means there are 60 doses of complement in one volume of the guinea-pig
serum, and it also denotes the dilution factor 60, since by diluting the serum 60
times the solution will contain one dose per volume.
When the titre is known the serum can be diluted to contain a given number of
doses per volume, or the doses per volume contained in a known dilution can be
calculated. Thus from the above definition of titre the following formula is derived ;
and, if any two of its terms are known, the third can readily be found: Titre = doses
per volume of guinea-pig serum dilution multiplied by the dilution factor (= d x f).
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