426 H. S. JENNINGS AND K. S. LASHLEY 



The 6 members at fissions must likewise be paired with the 

 6 at 1 fission, giving 36 in which the difference is 1 ; we thus enter 

 this 36 beneath the difference 1, in table 40. In the same way 

 we successively pair the 6 (at fissions) with all the other totals 

 of table 38, entering the products under the proper differences in 

 table 40; this gives the first row of 'number of pairings' in this 

 table. 



We proceed in the same way with the remainder, each 'total' 

 of table 38 giving under the difference the entry found by the 

 formula ^ n (n — 1), and successively under the other differences 

 the product of this total with each of those following it. This 

 gives, for the entire first week, table 40. We next sum the num- 

 ber of pairings for each difference, as in the last row, and get their 

 total sum (1770). A control for the accuracy of the work up to 

 this point is given by the fact that this total sum must be equal 

 to ^ n (n — 1), where n is the total number of diverse lines (in 

 this case 60). 



Next we multiply each difference of table 40 by the sum of the 

 'total pairings^' under it, and add these products, giving the total 

 sum of differences for all the pairings. In the present case this 

 total sum is 3270. Dividing this by the total number of pairings 

 (1770), we find that the average difference between members, 

 when all possible matings are made, is 1.8474. 



In the same way we may if we desire find the average differ- 

 ence between the most rapidly dividing members ('females') 

 of pairs; and between the slowest members ('males'). 



Carrying out these operations for the five weeks of Experiment 

 1 (table 29 of the paper on the effect of conjugation, page 379), 

 and for certain combinations of these periods, we obtain the 

 results given in table 41. 



The results given in table 41 are surprising. In' every case the 

 difference between the members of actual pairs is not greater, but 

 less, than the average difference between two individuals taken at 

 random. 



Thus we find, for the rate of reproduction, as for the distribu- 

 tion of deaths, and of surviA^als, that the two individuals do not 

 resemble each other less, but more, than the average individuals. 



