526 FRANK R. LILLIE 



The presence of the substance is shown by the agglutination of 

 sperm-suspensions of the same species. If a few drops of sea- 

 water containing this substance in sufficient concentration be 

 added to a 1 per cent sperm-suspension in a test-tube a flocculent 

 condition becomes apparent to the naked eye in a few moments. 

 The quaUtative aspects of the reaction were described quite fully 

 in the preceding paper of this series, and need not therefore be 

 repeated here. 



In my previous papers ('12 and '13) no attempt was made to 

 establish a quantitative method of study. But in order to carry 

 the subject farther it was necessary to determine how much of 

 the sperm agglutinating substance was produced by the ova under 

 various conditions. As noted in previous papers the reaction 

 is reversible. With high concentrations of the agglutinating 

 substance it may be several minutes before the agglutinated 

 masses break up and reversal is complete; with low concentrations 

 on the other hand the agglutinated masses are smaller and their 

 disintegration is correspondingly more rapid. It was therefore 

 possible to establish as a unit concentration of the agglutinating 

 substance the greatest dilution at which an unmistakable reaction 

 is given. Such a reaction lasts only a few seconds. It would be 

 obviously very tedious to establish the exact point at which the 

 reaction ceases in a long series of experiments, and in practice 

 I prepared a series o£ dilutions each member of which was one- 

 half of the preceding member, and the last one to give the re- 

 action was regarded as the unit concentration. The method is 

 as follows: Taking a given solution of the fertilizin a series of 

 dilutions is made. If these begin with (a) 1/100 (i.e., 99 parts 

 of sea-water plus 1 part of the solution) a half dilution of (a) is 

 made, (b) (i.e., 1/200); a half dilution of (b) follows (c) 1/400, 

 (d) 1/800, (e) 1/1600, (f) 1/3200, etc. If 1/1600 is negative, 

 1/800 may give a 4 to 6-second reaction; if 1/800 is negative 

 1/400 may give a 4 to 6-second reaction, etc; when the solution 

 was known to be strong it was usual to begin with a 1/100 dilution; 

 otherwise we might begin with a 1/10 dilution, followed by a 

 1/20, 1/40, etc., or 1/2 followed by 1/4, 1/8, 1/16, etc., the last 

 member of a series to give a positive reaction was accepted as 



