BIPARENTAL INHERITANCE IN PARAMECIUM 397 



that conjugation is by no means always successful in producing 

 rejuvenescence" (p. 87). But I have shown in the paper ('13) 

 which precedes this one that there is no ground for supposing 

 that these would have died if conjugation had not occurred; in 

 our Experiment 1, for example, none of those that were prevented 

 from conjugating died, the deaths being hmited to those that did 

 conjugate; and the other experiments give evidence in the same 

 direction. This takes away all ground (if there ever was such 

 ground) for trying to exclude the cases in which both members of 

 the pairs died. What we must inquire, so far as deaths go, is, 

 whether the number of complete pairs that survive (or, if we pre- 

 fer, the number of complete pairs that die) is less than would be 

 expected if the deaths were due to causes that had no relation to 

 the pairing. 



To answer this question, we must know, first, how many com- 

 plete pairs would probably have occurred among the survivors 

 (or the non-survivors), if the deaths had taken place at random. 

 In Miss Cull's case, cited above, we must ask: How many com- 

 plete pairs would have survived among the 103 hnes (out of 186), 

 if the deaths had occurred at random? Would the number have 

 been greater or less than 38 (the' actual number)? Or: How 

 many complete pairs would have died among the 83 deaths (out 

 of 186), if the deaths had no relation to the pairing? 



To deal with tnis and similar cases, we are compelled to take 

 up this general problem : Suppose that we have a given number of 

 pairs, from which a given number of individuals are drawn at 

 random; what is the most probable number of cases where both 

 members of pairs will be drawn? We may realize such a case 

 concretely by throwing a lot of serially numbered tickets into a 

 hat, there being two tickets bearing each number (these constitu- 

 ting a pau'), then drawing out a certain number of the tickets. 

 What we wish is a formula for determining how many entire pairs 

 (both members) we shall probably get for any given number of 

 tickets taken from the hat. This will at the same time determine 

 how many pairs will be left. The question may be put algebraic- 

 ally thus: 



