100 GERT BONNIKH 



to find only the ordinary low percentage (4,3 %) and the ordinary 

 high percentage (about 22 % ). As lurlhermore it seemed not to be of 

 any special interest to have a precise location of these supposed genes 

 I did not consider the fact that in some cultures I had a badly deter- 

 mined endpoint in the piece of the X chosen (i. e. that lying between tan 

 and forked). It is therefore in a number of cases only possible to say 

 that the length of the pieces of the X with respect to which the excep- 

 tional females are homozygous has a value lying between two widely 

 differing limits. In other cases the difference between these limits is 

 much smaller. Such are for instance the cases from tables 11 — 16. 

 And from this we may see at once that there really exists some sort of cor- 

 relation between the length of the Ä' and the percentage of exceptions. 

 In order to analyze the results in more detail let us begin with the 

 following considerations. In both the tables 11 and 12 the left limit 

 of the A' part lies between cut and vermilion and the right limit lies to 

 the right of forked and probably coincides with the right hand end 

 of the whole chromosome. The difference between the two percentages 

 from these tables is not less than 4,94 %, but the mean error of this 

 difference is on the other hand as large as 1,7 % and three times this' 

 error makes 5,i. We may therefore believe that the percentage from 

 tables 11 and 12 belong to the same category and if we thus add the 

 figures from 11 and 12 we have a total of 1794 with the percentage of 

 exceptions 14, i6 db 0,82 as is mentioned at the bottom of table 12. 



If any mathematical relation exists between the percentage of ex- 

 ceptions (which may be called y) and the length of the piece of X 

 (which may be called z) with respect to which the exceptional females 

 are homozygous, it is to be believed that this relation is of a very 

 complicated kind. But as is usual in mathemathics complicated rela- 

 tionships may often as a first approximation be given in a simple form 

 for instance as a linear equation. Let us therefore suppose as this first 

 approximation of the relation between y and z that i/ = a + Az. Since 

 we have found that flies not homozygous for any part of X give the 

 low percentage it follows that when z = we shall have y = 4,3. 

 Thus a = 4,3. 



Of the other experiments there are two in which we have a rather 

 good determination of the endpoints of the parts of X used, viz. the 

 experiments from tables 14 and 16. It is therefore convenient to use 

 these experiments for the determination of k. In table 14 the endpoints 

 of the part of X lie, the first between eosin and echinus and the second 

 between vermilion and garnet. The minimum length of the part of 



