:;54 



THE AMERICAN XA Ti'R. I LIS T 



[Vol. L 



This method makes no assumption as to an independent 

 action of the different factors in reducing viability. It 

 does assume, however, that for individuals with the same 

 combination of factors there is the same degree of via- 

 bility in the two experiments ; this is not always true, since 

 under different conditions of food, etc., individuals of the 

 same genetic type may have very different degrees of via- 

 bility; moreover, there are sometimes "invisible" factors 

 present in one experiment but not in the other which influ- 

 ence viability and which are linked with the factors that 

 are being studied. The assumption, nevertheless, is un- 

 avoidable. But it can be shown mathematically that any 

 errors in the calculated values, due to assumptions made 

 in following the formulas of either the first or the second 

 method, are greatly reduced by using a combination of 

 the two methods; namely, by making "contrary crosses," 

 calculating the linkage value in each of them by means of 

 the first method, and then taking the square root of the 

 product of these two values. 



In a cross involving three or more factors no formula 

 corresponding to the one first given is possible, and before 

 it is possible to use a formula corresponding to the second 

 method, an increasingly large number of different kinds 

 of crosses must be made, according to the number of fac- 

 tors involved. Still another method is, therefore, neces- 

 sary ia order to obtain fairly accurate results from crosses 

 involving many factors, except in the rare case that these 

 factors have very little differential effect on viability. 

 The method devised is as follows : 



The female, heterozygous for many factors, whose 

 gametic output it is desired to study, is back-crossed, not 

 to a multiple recessive male, but to one homozygous for all, 

 or nearly all, the dominant factors (these are, in the case 

 of flies, mostly the normal allelomorphs). All the off- 

 spring appear alike, then, in that they all show the domi- 

 nant characters of their father (except in the case of sex- 

 linked factors, which are transmitted by the father to his 

 daughters only), and so all should be of the same viability, 

 except for the insignificant effect of the recessive factors 



