110 THE SIDE-CHAIN THEORY 



then 2 X 40 parts of NaOH will unite with 2 X 36.5 parts of HC1, 

 and 3 X 40 NaOH with 3 X 36.5 HC1, etc. 



When this point was first investigated with toxin-antitoxin mix- 

 tures it was found that starting with an apparently neutral mixture 

 the injection of several multiples of this proved highly toxic; in other 

 words, whereas the original mixture was apparently perfectly innoc- 

 uous, a fatal result was obtained if from two to five times as much 

 toxin' was used, and this treated with corresponding multiples of 

 antitoxin. Upon first consideration such a result would seem entirely 

 contradictory to the idea that the toxin and antitoxin neutralize one 

 another in a chemical sense. Further investigation, however, has 

 shown that the contradiction is only apparent, and that the law of 

 multiples does hold good for the toxin-antitoxin interaction, but 

 that it is absolutely essential in such experiments to neutralize the 

 original mixture with such exactness that not even a minimal 

 fraction of toxin is present in excess of the antitoxin. If this is not 

 the case, one can readily conceive that even though the original 

 mixture were non-fatal, several multiples thereof might very readily 

 be so. It is hence imperative that the original mixture should be so 

 standardized that its injection does not cause the slightest symptom 

 of disease. If this is carefully done then it will be found that the 

 law of multiples actually does hold good, and this law, as a 

 matter of fact, forms the basis of Behring and Ehrlich's method of 

 standardizing the diphtheria antitoxin of the market, in which the 

 unavoidable source of error does not amount to more than from 

 0.1 to 1 per cent, (see Preparation of Diphtheria Antitoxin). 



If, now, we come to apply the law of multiples to the study of the 

 other antibodies, we find that the possible sources of error in the 

 concrete interpretation of the actual findings are still greater, and 

 it may not be out of place to refer in some detail to some of the 

 difficulties which have been here encountered and the manner in 

 which they have been met. We may say in advance, however, that 

 no observations have been made which would tend to exclude the 

 interaction between these antigens and their antibodies from the 

 law of multiples, as it has been established for toxin-antitoxin 

 mixtures. 



Starting with 1 c.c. of an emulsion of an agar slant culture of a 

 given organism in 15 c.c. of normal salt solution, and treating this 

 with an equal volume of an agglutinating serum in varying dilutions, 



