18 



FRANK R. LILLIE. 



waters on own sperm, for the cloud phase is never passed in the 

 hetero-agglutination. 



In the second place, the duration of the iso-agglutination fol- 

 lows a very definite rule in relation to concentration of the 

 agglutinating substance which Richards and Woodward (1915) 

 have formulated by saying that the efficiency of the agglutinin 

 varies with the square root of the concentration. It is certain 

 that the duration of the agglutination is always greatly increased 

 with doubling of concentration, and in the lower concentrations 

 of I to 4 units nearly doubled. 



Table V. gives one set of results in which the egg- water of six 

 females of purpuratus was tested for duration of the reaction on 

 franciscanus sperm at four dilutions. 



TABLE V. 



DURATION OF HETEROAGGLUTINATION. EGG-WATERS OF Six PURPURATUS FEMALES 



ON FRANCISCANUS SPERM AT VARIOUS DILUTIONS. 



It will be seen that these figures do not follow any definite rule 

 with reference to duration of reaction and concentration, and 

 thus contrast in the most striking way with the iso-agglutina- 

 tion phenomena. This may be because the action at its optimum 

 is so slight on the individual spermatozoa of franciscanus as to 

 preclude any close agglutination. The indicator (i.e., the fran- 

 ciscanus sperm suspension) may thus appear to show the same 

 reaction at different dilutions of the egg-water. 



On the assumption that we are concerned with a single hetero- 

 active substance distinct from the true agglutinin, it should be 

 possible to remove this substance by treating the egg-water con- 

 taining it with franciscanus sperm without disturbing the iso- 



