No. 57:5] 



REDD PLICA II OX II YPO TIfi;sjs 



547 



All of these series must be considered as either primary 

 or secondary and therefore involving primaries of higher 

 intensity. In fact there is unpublished evidence that 

 many of them can not be simple primaries. A num- 

 ber of series of very high intensity are known, and will 

 appear in future publications. Therefore all the calcula- 

 tions that follow give results which are far too small. 



According to Trow, the minimal number of successive 

 cell divisions required to complete the series is given by 

 the expression mnp ■ • ■ where m, n, p, etc., are the larger 

 terms of the primary series involved. In the present case 

 the value of that expression is something over 76,000,- 

 000,000. However, Trow's formula seems to be wrong. 

 If a be the number of cell divisions required to produce 

 m cells, then 2 a = m. If this expression gives a value of 

 a which is not an integer, then the next higher whole 

 number is to be taken. In the case of the first series two 

 divisions are necessary to segregate the genes, and in the 

 following series one is required. The number of succes- 

 sive cell divisions required then is (a -f 1) + (h + 1) 

 -f (c + 1) -\ 1- 1, where b, c, etc., bear the same rela- 

 tion to n, p, etc., that a does to m. In the case of Droso- 

 phila the value of this expression is 56. As pointed out. 

 however, this value is certainly far too small. 



The total number of cells required is given by the 

 expression 2mnp ■ ■ • + 2np ■ ■ ■ +2mn • • • +2mp • • • 



+ 2m • • • -f 2n f- 2p h h ^nnp + 2mn + 2mp 



+ 2np + • • • + 2m + 2n + 2p . + 1. 



This gives a value considerably above 600,000,000,000— a 

 manifest absurdity. However, it is not necessary that all 

 these cells should be produced, since the ratios would not 

 be appreciably affected by some lines becoming crowded 

 out. It is necessary, on the other hand, that all of the 

 series shall be completed in every line which does live, 

 since every female DrosophUa* which is of the proper 

 constitution to be tested, shows linkage for every pair of 

 genes tested. 



