232 FRANK R. LILLIE. 



dry sperm, the initial variation due to the method cannot be 

 very great in relation to the tremendous range of variation in 

 fertilizing capacity of sperm due to other causes. Indeed it is a 

 vanishing quantity. 



Eggs. — Egg concentration is a factor of relatively slight 

 significance within the limits of the experiments, as will appear 

 from the facts to be presented. Within a very wide range it 

 does not affect the result measured in percentage of fertilized 

 eggs. It is measured roughly by allowing washed eggs to settle 

 for half an hour in a loo-c.c. graduated cylinder, and expressing 

 the quantity there settled as a percentage of the entire fluid. 

 There is of course for every concentration of sperm an egg con- 

 centration that is above the optimum for percentage of fertiliza- 

 tion. But, as will be seen from the tables, such egg concentration 

 lies beyond the concentration used in most experiments. 



In most cases segmentation of the eggs was used as the criterion 

 of fertilization, but membrane formation was also used in some 

 cases, especially in high concentrations of sperm where many 

 eggs failed to segment owing to polyspermy. 



Formulation of Results. — The fertilizing power of sperm suspen- 

 sions is expressed in curves whose ordinates are percentages of 

 fertilization, and the abscissae a geometrical series of dilutions 

 of I per cent, sperm in powers of 2. This method was adopted 

 for the abscissae because of the method of successive half dilu- 

 tions used in many experiments, and because the enormous range 

 of fertilizing power made it impossible to compare results on 

 one scale with an arithmetical progression. When it is realized 

 that the fertilizing power may cease at 1/156 of i per cent., or 

 extend to 1/90,000,000 the necessity of the geometrical series in 

 the abscissae will become apparent. 



2. The Optimum Curve of Dilutions. 



We may begin with the optimum curve of dilutions (Curve i), 

 because this answers most completely, and probably fully, to the 

 current expectation that a single spermatozoon suffices for the 

 fertilization of an egg. This curve is prepared from data of ex- 

 periments calculated to bring eggs and sperm together in the 

 freshest possible condition of the sperm. In general measured 



