234 FRANK R. LILLIE. 



crystallization dishes were placed i,ooo c.c. sea-water (A), 

 3,000 c.c. sea-water (B), i,ooo c.c. sea-water (C), 3,000 c.c. sea- 

 water (D). To each was added 2 c.c. of a washed egg-suspension 

 (about 3 per cent, to 5 per cent.). The sperm was then pre- 

 pared as follows: (i) one drop dry sperm to 3.3 c.c. sea-water at 

 9.43 A.M. = I per cent.; (2) i c.c. of sperm i to 99 c.c. sea- 

 water 9.43.30 A.M. = i/ioo per cent.; (3) i c.c. sperm i to 999 c.c. 

 sea-water 9.45.30 = i/iooo per cent. To A was added i drop 

 sperm 2(1/100 per cent.) at 9.43.45; to B one drop sperm 2(1/100 

 per cent.) 9.44; to C one drop sperm 3(1/1000 per cent.) 9.45.45; 

 to D one drop sperm 3(1/1000 per cent.) 9.45.45. An assistant 

 stirred in the sperm thoroughly as added. The sperm concentra- 

 tion in A was therefore i/ioo X 1/30 X i/iooo = 1/3,000,000 

 per cent.; in B it was 1/9,000,000 per cent.; in C 1/30,000,000 

 per cent.; in D 1/90,000,000 per cent. 1/3,000,000 per cent, 

 falls between 21 and 22 on the scale, and the others as shown. 

 The exact times of mixing the sperm are given because, as will 

 appear beyond, time is an extremely important factor with 

 reference to fertilizing power. 



To appreciate the extent of this dilution it may be said that 

 beyond a dilution of 1/10,000 per cent, (between 13 and 14 on 

 the scale) one can rarely find a single spermatozoon in the jelly 

 of the fertilized eggs. At about 1/2000 per cent. (11 on the 

 scale) the sperm suspension does not even appear opalescent. 

 We may therefore feel reasonably sure that beyond about 14 or 

 15 on the scale a single spermatozoon certainly suffices to com- 

 pletely fertilize an egg. 



In further elucidation of the curve I may say that the critical 

 (steep) part was covered by several determinations for each 

 point. Thus there are five determinations averaged for the 

 positions between 13 and 15. Seven between 15 and 18, five 

 between 18 and 20, and six between 20 and 21. The determina- 

 tions beyond 21 are single determinations. For the first part 

 of the curve up to 13, there are numerous determinations. There 

 are great variations in the single determinations compared with 

 one another; these averages must therefore be regarded only as 

 approximate values. With a sufficiently large number of deter- 

 minations the irregularities between 15 and 17 and between 19 



