BIPARENTAL INHERITANCE IN PARAMECIUM 413 



0.00224, while the probabihty that the deviation will be less than 

 this is 0.99776. Hence the chances are 445 to 1 against a devia- 

 tion so great as is actually observed, if the distribution of deaths is 

 independent of the pairing. 



Thus it appears that as further deaths take place, the tendency 

 for both members of a pair to die, if one dies, becomes greater; 

 after seven days the chances were but 39 to one against so great 

 a deviation as occurs, while after twenty days the chances against 

 the actual result are more than ten times as great as they were. 

 It is therefore clear that among those who died in the interval 

 between the seventh and the twentieth days there were a greater 

 number of mates of those that had previously died, than could 

 be expected as a matter of chance. This is clear when the exact 

 figures are considered. At the end of seven days there were left 

 154 individuals, including 134 that were still paired, while 20 

 were odd (their mates dead). Now, in the next thirteen days 

 there died 19 more, and of these 19, no less than 14 were mates of 

 those that had already died (or that died during the entire twenty 

 days), while but 5 fall to the 134 paired individuals! It is clear 

 that whatever is causing the death of one individual of a pair 

 has a strong tendency to cause likewise the death of its mates; 

 the mates are much more alike in this respect than are two lines 

 taken at random. And in accordance with what has previously 

 been set forth, we may make the same statement for the sur- 

 vivals. Whatever tends to cause one individual of a pair to 

 survive has likewise a strong tendency to cause the survival of its 

 mate — the numerical relations as to survival being identical with 

 those above set forth for the deaths. 



Third case. After thirty days Miss Cull found that out of 

 the 186 lines, 83 had died out, including 28 pairs. We have al- 

 ready dealt with this case, but may here recapitulate the facts. 

 By our formula (1), the average number of pairs obtained when 

 83 are drawn from 186 is 18.39, from whence it may be concluded 

 that the most probable number of pairs is 18. The excess over 

 the most probable number has therefore now grown to 10 pairs, 

 though at the end of 20 days the excess was but 6 pairs. This 



