172 GENETICS AND EUGENICS 



percentage between A and C should be either 23.7 or 5.1, 

 according as the hnear arrangement is ABC or ACB. 



Measurement of linkage. It will be observed that as the 

 strength of linkage increases, the cross-over percentage de- 

 creases. With a cross-over percentage of 50, there is no 

 linkage. With a cross-over percentage of 0, the linkage is 

 complete, two characters so related behaving as allelomorphs. 

 Accordingly we depend upon the observed cross-over per- 

 centage both for the detection of linkage and for the measure- 

 ment of its strength. But unfortunately the linkage strength 

 varies inversely as the cross-over percentage. This makes 

 the cross-over percentage directly considered, a rather poor 

 measure of linkage strength. It is really the amount by 

 which the cross-over percentage falls below 50 that measures 

 directly the strength of linkage. Thus with cross-over per- 

 centages of 50, 40, 30, 20, 10, and 0, we should have linkage 

 strengths of 0, 10, 20, 30, 40, and 50. We should then have 

 a standard for measuring linkage strength directly, on a 

 scale of 50. But as we are more accustomed to grading on a 

 scale of 100, it seems preferable to double the values indicated 

 above. We then have grades of linkage strength on a scale 

 of 100, as follows: 



Accordingly, to estimate the strength of linkage in a particu- 

 lar case, we multiply by 2 the difference between the ob- 

 served cross-over percentage and 50. 



But suppose the observed cross-over percentage were 

 greater than 50, what then.^ Such an occurrence would not 

 indicate linkage, a tendency of characters to remain grouped 

 as they were, but an opposite tendency, to assume new group- 

 ings. No such tendency has been observed. If it should be, 

 it would need a different name and method of measurement. 



