170 GENETICS AND EUGENICS 



more difficulties than it has cleared away. The second expla- 

 nation is that the map-distances indicate proportionate 

 numbers of breaks in the linkage chain between points, not 

 proportionate numbers of changes of relation between genes 

 at particular points. Thus, suppose genes AB C D E of a link- 

 age system meet their allelomorphs, a b c d e, in a cross and 

 gametes are later formed by the cross-bred as follows, (1) 

 A B c d e, (2) A B c d E, and (3) A b c D e. Assuming that 

 the arrangement is linear, we must suppose that one break in 

 the linkage chain has occurred in (1), two breaks in (2), and 

 three breaks in (3). But if we did not have genes BCD 

 under observation, and merely noted the relation of A to E, 

 we should infer that in case (1) and in case (3) a single cross- 

 over had occurred, but that in case (2) no crossover had oc- 

 curred. We should on that basis underestimate the amount 

 of breaking in the linkage chain. Accordingly the construc- 

 tion of maps on the basis of short distances summated is 

 justifiable, provided the arrangement is linear, as it seems 

 to be. But it must be borne in mind that the map distances 

 do not correspond with cross-over percentages (although 

 they are based on them) except in the case of very short 

 distances. Map distances often exceed 50, but cross-over 

 percentages can not do so, as already pointed out. To get 

 a distinctive name for the map units, Haldane has called 

 them units of Morgan or simply ** morgans." Haldane has 

 computed a formula for converting cross-over percentages 

 into ** morgans" and vice versa. He finds that the two cor- 

 respond only for very low values (5 or less) and diverge 

 more and more as the observed cross-over percentages ap- 

 proach 50. Haldane's formula may be stated thus. If three 

 genes. A, B, and C, occur in a common linkage group, and 

 the cross-over percentages are known between A and B and 

 between B and C, we may predict with a probable error of 

 not over two per cent, what cross-over percentage will be 

 found to occur between A and C. Calling the cross-over 

 percentage between A and B, m, and that between B and C, 

 n, the cross-over percentage between A and C will lie be- 



