9 



families of various sizes from 100 to 1000 are given in the 

 following table, and are calculated to allow a departure from 

 the observed ratio, equal to three times the probable error. The 

 adoption of three times the probable error as a crtrerion of 

 significant differences is purely arbitrary, and about three families 

 in one-thousand having the given number of individuals could 

 be expected to transgress the limits indicated in the table, and 

 such departures would still be due only to the errors of random, 

 sampling. Some biometricians accept 2.5 times the probable error 

 as the limit within which results may not be confidently claimed 



to be significant. 



Table IV. 



Number of Observed percentages Observed ratios 



individuals theoretically referable to 75 % referable to ratio 3 : 1 



100 60.34 % to 85.54 % 1.52 : 1 to 5.91 



200 64.87% to 82.97% 1.85:1 to 4.87 



300 66.84 % to 81.70 % 2.02 : 1 to 4.46 



400 68.00 % to 80.90 % 2.13 : 1 to 4.23 



500 68.78 % to 80.33 % 2.20 : 1 to 4.08 



600 69.35 % to 79.91 % 2.26 : 1 to 3.97 



TOO 69.80 % to 79.57 % 2.31 : 1 to 3.89 



800 70.14 % to 79.29 % 2.35 : 1 to 3.82 



900 70.43 % to 79.07 % 2.38 : 1 to 3.77 



1000 70.68 % to 78.87 % 2.41 : 1 to 3.73 



1 

 1 

 1 

 1 

 1 

 1 

 1 

 1 

 1 

 1 



Only one of the ratios for the leaf-characters in the F 3 cul- 

 tures transgresses the limits indicated in this table. The 

 family 09275 in which 656 individuals gave a ratio of 2.08 : 1, 

 clearly presents a defect not due to random sampling, and the 

 cause of the deficiency was easily discovered. The parent of this 

 family was classified as Bursa bursa-pastoris simplex, and was 

 expected to produce only the parental characters in its offspring ; 

 but the progeny consisted of 443 B. bp. tenuis and 213 B. bp. simplex, 

 thus demonstrating that the parent was a heterozygote in which 

 the normally dominant tenuis characters failed to appear. The 

 relative impotency of the tenuis character which allowed it to 

 remain undeveloped in the parent, seems to have affected the 

 offspring in a similar manner, so that without doubt many of 

 the heterozygotes were classified as B. bp. simplex. 



During the early development of this family, it appeared 

 to consist of about three B. bp. simplex to one B. bp. tenuis, and 



