BIPARENTAL INHERITANCE IN PARAMECIUM 411 



of pairs that will be obtained if successive drawings are made is 

 by formula (1), 2.G8. Five actual drawings of 32 tickets out of 

 186 gave respectively 4, 2, 1, 2, 4 pairs; the average being thus 

 2.6; very close to what the theory calls for. 



The observed number 6 is therefore greater than would be 

 expected, not less, as the theory of sexual differentiation would 

 expect. By formula 3, the probability for 2 pairs is found to be 

 0.27233; that for 3 is 0.26808; for 6 is 0.02013. The observed 

 number (6) deviates from the most probable number (2) by 4; 

 we require to know what is the probability that there should be 

 so great a deviation as this. By our rule (5) (Appendix), we 

 find that the total probability for a deviation as great as 4 is 

 0.0248, while for deviations less than 4 it is 0.9752, so that the 

 chance is 39.3 to 1 against there being a deviation so great as that 

 observed, if the distribution of deaths is independent of the pair- 

 ing. 



Thus, so far as this case goes the probability is very strong 

 that the distribution of deaths is not independent of the pairing. 

 But its dependence is of a character the reverse of what the 

 theory of sexual differentiation requires; the number of pairs is 

 greater, not less, than we should expect from a random distribu- 

 tion of deaths. Thus it appears that the members of the pairs 

 are more alike, not less alike, in this respect, than would be antici- 

 pated. The drawing of further conclusions may be deferred until 

 other cases are examined. 



Second case. After twenty days, ]Miss Cull found that 51 

 Hues had died, out of 186, and among these were 13 pairs. 



By formula (1) the most probable number of pairs is found to 

 be 7, the average number if a great number of drawings were made 

 being 6.892. Five drawings of 51 tickets out of 186 gave respec- 

 tively 6, 9, 8, 8, 8 pairs, the average being 7.8, which is very close 

 to theory; the excess of nearly 1 showing what may happen when 

 but few drawings are made. 



The observed number of 13 pairs exceeds the most probable 

 iiumber by 6, pairs. WTiat is the probability that there should 

 be so great a deviation as this from the most probable number of 

 pairs? 



