165 



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 



Obser 



^ed ratios 





individuals 



theoretically referable to 75 % 



referable to ratio 3 : 



1 



100 



60.34 % to 85.54 % 



1.52 : 



1 



to 5.91 : 



1 



200 



64.87 % to 82.97 % 



1.85 : 



1 



to 4.87 : 



1 



300 



66.84 % to 81.70 % 



2.02 : 



1 



to 4.46 : 



1 



400 



68.00 % to 80.90 % 



2.13 : 



1 



to 4.23 : 



1 



500 



68.78 % to 80.33 % 



2.20 : 



1 



to 4.08 : 



1 



600 



69.35 % to 79.91 % 



2.26 : 



1 



to 3.97 : 



1 



700 



69.80 % to 79.57 % 



2.31 : 



1 



to 3.89 : 



1 



800 



70.14 % to 79.29 % 



2.35 : 



1 



to 3.82 : 



1 



900 



70.43 % to 79.07 % 



2.38 : 



1 



to 3.77 : 



1 



1000 



70.68 % to 78.87 % 



2.41 : 



1 



to 3.73 : 



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. 



Düring the early development of this family, it appeared 

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



