1908.] 



Theory of Ancestral Contributions in Heredity. 



65 



family borne on one or more plants. I tried to identify it by the general look of its seeds, 

 but although the F 2 cotyledons produced from the different types of yellows are often 

 strikingly like their yellow grandparents, I did not succeed. The only drawback, 

 however, which this accident entails is the impossibility of employing these families for 

 the purpose of determining the percentage of greens from crosses from the several green 

 and yellow parent forms. The total result from the F 2 families not classifiable by parent 

 forms has been incorporated in the grand total ; as also has a plant which is recorded 

 as having been "accidentally left behind between 216 and 28 and not belonging to 

 either/' There were 161 yellow and 50 green seeds on it (see Summary after Table VI). 

 Fortunately, all the plants from crosses between the pure yellow and extracted green were 

 grown on a plot by themselves, so that there can be no question as to the parentage of a 

 plant like this. 



The Percentages of Greens in F \ produced f rom the several Yello w and Green 



I have classified all the F 2 families, from the cross between the pure yellow 

 and extracted green, into groups according to their yellow grandparents, and 

 also according to their green grandparents, where this was possible (see 

 previous section), and have determined the proportions of greens in each of 

 these groups with a view to finding out whether the close approximation to 

 25 per cent., viz., 24 - 88 per cent., which was the proportion of greens^ in 

 the whole population (including those families which could not be classified 

 into groups), was also exhibited in each of these groups. The percentage of 

 greens, calculated from the total numbers of yellows and green in the 

 classifiable families is 24 - 82. Now it is quite conceivable that this total 

 proportion may be compounded of widely divergent proportions, ranging 

 perhaps from 10 to 40 per cent., and each, possibly, characteristic of families 

 from particular yellow or green grandparents. In order to find out whether 

 the deviations which might be expected to, and do, occur, are significant, or 

 attributable to chance, it is necessary to calculate the Probable Error of the 

 percentage. Half the deviations should fall inside and half outside the 

 Probable Error in the phis or minus direction ; and deviations greater than 

 four times the Probable Error should not occur often. The Probable 

 Error of the ratio, expressed as a percentage, of any part to a whole (in this 

 case the ratio of the greens in a generation to the total number of seeds in 

 that generation) is calculated by the following formula, which . I have used 

 here : — 



Parent-forms. 



100 0-67449 x 



x 



in which x is the whole (or the total number of seeds) and a is the part (or 

 the number of greens). The table on the next page shows that of the 



VOL. LXXXI. — B. F 



