165 
families of various sizes from 100 to 1000 are given in the 
following table^ and are calculated to allow a departure from 
the obseryed 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 individaals 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.Ö 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 
individnals 
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 Fg cul- 
tmes transgresses the limits indicated in this table. The 
family 09275 in which 656 individnals gave a ratio of 2.08 : 1, 
clearly presents a defect not dne to random sampling, and the 
cause of the deficiency was easily discovered. The parent of this 
family was classified as Bursa hursa-pastoris simplex, and was 
expected to produce only the parental characters in its offspring; 
but the progeny consisted of 443 B. hp. 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 afiected the 
offspring in a similar mahner, so that without doubt mauy of 
the heterozygotes were classified as B. bp. simplcx. 
Düring the early development of this family, it appeared 
to consist of about three B. hp. simpJex to one B. bp. tenuis, and 
