138 CHEMICAL EQUILIBRIA 



reaches a maximum value when the two substances 

 are mixed in about equivalent quantities, to be re- 

 dissolved on further addition of casein. This action 

 is supposed to be due to a formation of a soluble 

 compound containing more casein relatively to the 

 precipitin than the precipitate. This case has not 

 been thoroughly examined, but a similar case was 

 observed by HAMBURGER, when he investigated the 

 precipitate from a mixture of normal horse serum 

 with immune serum from a calf. In this case it is 

 not the increasing dilution on adding increasing 

 quantities of horse serum which causes the observed 

 maximum of precipitate, but the calculation indicates 

 that at first a precipitate is formed from one molecule 

 of precipitinogen and one molecule of precipitin. 

 This precipitate gives with one or two molecules of 

 precipitinogen a new compound which is relatively 

 soluble. In this case, as in the three others observed 

 by HAMBURGER, the calculation gives a very good 

 agreement with the observation. 



In the study of agglutinins similar observations 

 have been made, namely that in some cases the 

 agglutination at first increases with the quantity of 

 agglutinin added, and then subsequently decreases 

 when the quantity of agglutinin is increased. In 

 general the agglutinins behave much in the same 

 way as the precipitins or the precipitinogens, and 

 it is therefore probable that the agglutination is a 

 special manifestation of the precipitation. 



The formation of precipitates plays an important 

 r61e in the modern development of the doctrine of 



