IX REPULSION AND COUPLING 93 



pulsion for the same pair of factors is of the same intensity 

 — whether for instance two characters coupled on the 15:1 

 basis will exhibit repulsion on the 1:15 basis. The existing 

 evidence certainly favours such a view. Experiments made 

 during the present year (191 2) render it practically certain 

 that in the cretin case the coupling between the normal 

 flower and the fertile anther is on a 3 : i : i : 3 basis ; and 

 there is strong reason for supposing that the repulsion 

 between long pollen and purple is on a i : 7 : 7 : i basis. 

 In each of these two instances the coupling and repulsion 

 appear to be of the same intensity. In the higher series 

 very large numbers are needed to determine the intensity 

 of the repulsion. Thus for the series i AB 1127 Ab 1127 

 aB : I ab the double recessive is expected only once in 

 65,536 plants. It is unlikely that such cases will ever be 

 decided by direct experiment, but it may be asserted that 

 where the intensity of coupling is high, the evidence avail- 

 able certainly points to the intensity of repulsion being 

 high also. 



One more point of interest may be noted in connection 

 with these series. As the table shows it is possible where 

 coupling is concerned to express the various gametic series 

 by the general formula (« - i) AB : Ab : aB -.{n- i)ab, 

 where 2« is the total number of the gametes in the series 

 A plant producing such a series of gametes gives rise to a 

 family of zygotes in which 3;r — (2^^— i) show both of the 

 dominant characters and n^-(2n-i) show both of the 

 recessive characters, while the number of the two classes 

 which each show one of the two dominants is (2« - 1). 

 When in such a series the coupling becomes closer the 

 value of n increases, but in comparison with n^ its value 

 becomes less and less. The larger n becomes the more 

 negligible is its value relatively to «-. If, therefore, the 

 coupling were very intense, the series 3«^-(2«-i): 

 (2« - i) : (2« - i) : «^ - (2« - i) would approximate more 

 and more to the series 3^^ : o : o : «^, i.e. to a simple 3 : i 

 ratio. Though the point is probably of more theoretical 

 than practical interest, it is not impossible that some of the 



