BIPARENTAL INHERITANCE IN PARAMECIUM 



425 



TABLE 39 



From table 39 it is found that the average difference between 

 the two members of the actual pairs is for the first week 1.533. 



To find the average difference between any two members (or 

 the difference that would exist if the animals were paired at 

 random), we must pair each member with every other. It will 

 be found that for any given number n of organisms, the number of 

 diverse pairings that can be made is 1 + 2 + 3 + ... up to 

 one less than the given number; this is equivalent to the expres- 

 sion ^ n {n — 1). Thus, for the 60 organisms of the first week, 

 the number of possible pairs is | (60 X 59) = 1770. 



To make all possible pairings we proceed as follows, taking 

 the 'totals' of table 38 as an example: Arrange a table for the 

 possible differences, as in the first row of table 40. Now, in table 



TABLE 40 



38 there are 6 members showing fissions. • If these 6 are paired 

 among themselves, the differences between them will likewise 

 be 0. The number of di^'erse pairings among the 6 is given by 

 the formula ^ 7i (n — 1); for n = 6 this gives 15 pairs. We enter 

 this 15 beneath the of table 40. 



