BIPARENTAL INHERITANCE IN PARAMECIUM 395 



sible to determine how frequently, on the average, this will occur. 

 This would enable us to determine further in how large a propor- 

 tion of the cases both members of pairs should be represented 

 among the survivors, in this case where the distribution of deaths 

 has no relation to the pairing. 



On the other hand, if the weakness and death are due to the 

 fact that one member (the 'male') of a pair does not reproduce 

 well, then it would be unusual for both members of a pair to show 

 weakness or death; from this cause acting alone it would never 

 occur. There would probably, of course, be acting also other 

 causes of weakness or death, that were independent of the pairing, 

 so that we should sometimes find that both members of a pair 

 die or are weak, owing to chance causes, but the number of cases 

 where both members die would be smaller, in proportion to the total 

 number of deaths, than if the distribution of deaths were purely 

 random so far as the pairing goes. For one of the chief causes for 

 the deaths would affect only one member of each pair. Thus 

 among the sur\ivors there would be a greater proportion of cases 

 where only one member of the pair exists than would be the case 

 if sexual differentiation played no part in the matter. 



This gives us a method of testing the matter. If, owing to 

 sexual differentiation, one member of the pair is more liable to 

 weakness or death than the other, then the number of cases where 

 both members of the pair survi\^e will be found less than would be 

 probable if the distribution of deaths were due to causes that were 

 independent of the pairing. 



To take a concrete case. Miss Cull ('07) found that out of the 

 progeny of 93 pairs (186 lines), there remained at the end of a 

 month 103 lines, and among these 103 lines were representatives 

 of both members in 38 pairs. Is this number of entire pairs 

 still living less than would be expected if the distribution of 

 deaths had no relation to the pairing? 



The same question may be dealt with by taking up the cases 

 that die, in place of those that survive. Thus, in the case cited 

 above, out of the progeny of the two members of 93 pairs (186 

 lines), 83 lines had died out, including 28 cases where both mem- 

 bers of the pairs had died. Is this number of pairs dead less than 



