318 Douhleness in Stocks 



in passing that the proportion of single and double plants among self- 

 bred offspring of eversporting forms presumably indicates the proportion 

 of single and double-carrying ovules in the parents, since the % gametes 

 are being tested, so far as appears, against a uniform standard — the 

 double- carrying pollen grain. A survey of the numbers recorded (see 

 Table III), especially where the totals are fairly large, whether obtained 

 as the result of a considerable sowing from one individual or by summing 

 the results of small sowings from many individuals, leads to the con- 

 clusion that the real ratio of single to double is either exactly 7 : 9, or 

 that it lies somewhere between this and equality. The proportion is 

 in fact such as we might expect from imperfect gametic coupling 

 where two pairs of allelomorphs are concerned. Coupling on a 7 : 1 

 basis for example gives the precise ratio 7:9; a 15 : 1 series gives 

 7*5 : 8'5 and the next higher term in the series a still nearer approach 

 to equality. On the whole the balance of evidence seems to point to 

 a 15 : 1 series, but very large numbers would be required to enable us 

 to decide this point with certainty, and until these are available we 

 may conveniently represent the ratio of the two forms by the general 

 expression 



7 -H a; single : 9 — a; double, 



where x has some value less than 1. We may suppose that the value 

 for X is probably the same in all the strains investigated and that the 

 considerable divergences occurring in many cases where the numbers 

 are small are not real but the outcome of a topographical scheme of 

 distribution of the different % gametes, in consequence of which the 

 flower unit may not afford an average sample. It is as though 

 the arrangement of the % gametes were regulated by some coarse 

 mechanism, so that in regard to such small regions as a single fruit 

 or part of a fruit, there may be great irregularity of grouping. With 

 a view to avoiding any effect of unconscious selection in the samples 

 sown, the practice was adopted of sowing all the seeds belonging to 

 some definite unit or area, as e.g. all from one fruit, or from one side 

 of the fruit, or if fewer still were required the necessary number were 

 taken in order from one end of the pod, and not selected at random 

 from the mixed seed of many pods. Several cases selected for further 

 sowings on account of the aberrant result obtained in the first instance 

 from small samples, later gave totals in accordance with expectation. 

 It is this irregularity of distribution which renders it difficult to 

 determine whether the higher or the lower of the ratios given above 

 should be accepted as correct. 



