296 Prohahle Errors of Calculated Lhikage Values 



Comparing these values with the probable errors, gi ven by formulae (1), 

 (2) and (3), of the values obtained by crossing F^ with the double re- 

 cessive we see that the latter are always smaller. When P is nearly 1 

 the accuracies are nearly equal, but when P is small the direct method 



is — -p times as accurate as the indirect, i.e. ^ times as many zygotes 



obtained by the indirect method must be counted, in order that it 

 should give a result as accurate as the direct method. When P = J, 

 the ratio of the probable errors is only 3 : 2. 



Hence the ratios calculated from Pg are nearly as reliable as those 

 obtained from Pi x the double recessive in the case of coupling or weak 

 repulsion, but with strong repulsion they are somewhat unreliable. 

 Hence Bridges' stricture(5) on the unreliability of values derived from 

 Pa results is only justified in the case of strong repulsion. 



Moreover, since its numbers vary as the square of the cross-over 

 value, the double recessive class in F^ is a more sensitive indicator of 

 repulsion than any class derived from the cross Pj x double recessive. 

 Thus the enumeration of Pg is somewhat more sensitive as a test for 

 linkage, and about equally accurate as a measure of its degree in the 

 case of coupling, though not of repulsion. 



Differential mortality is eliminated by the above method under the 

 same conditions as by the direct method. This may be seen at once 

 from the fact that the coefficient of association is unaltered when {aB) 

 and {ah) are diminished in the same ratio. 



It may be remarked that where there is incomplete coupling or 

 repulsion in unequal degrees (in other words finite but unequal cross- 

 over values) in both sexes, the above method of evaluating t gives t =pqy 

 where p and q are the cross-over values in the two sexes. 



To return to Punnett's sweet pea experiment quoted above : from 

 formula (7) the probable error of P is 



/2^ 

 V ¥i 



,„„ , _7743 X -2257 .__, 



•"^^-/ 2-5486 X 6952 '"'••""^«"- 



Hence the cross-over value is 12*00 + '28 7o- 



From formula (9) the approximate probable error of X is 



/7'3^ 

 Hence a; = 7-333 + 197. 



6745 X 8-33 a / ' %l^^^^ ^ or -197. 



