150 



FAMILY STUDIES IN BUILD. 



independent factors, on the other, involved. We have seen, in each 

 of the various matings, that the result is, on the whole, more closely 

 in accord with the 3-factor hypothesis than that of 2 factors. But 

 this is not to insist that never more than 3 independent factors are 

 involved in build, or never less than 3. 



An attempt was made to apply Dr. Sewall Wright's formula 

 (Castle, 1922, p. 22). Using the data of tables 12, 27, and 31, the 

 value for n (the number of factors) was calculated by the formula 



N = 



D 2 



8 (^-crx 2 ) 



where D is the difference between the means of parental pure races, <?i 

 is the standard deviation of Fi, and <r 2 is standard deviation of F 2 . 



20 



15 



10 



26 



28 



30 



32 



34 



36 



38 



40 



42 



44 



46 



48 



50 



Fig. 52. — Polygon of distribution of frequencies of build of offspring of S X M matings (from 

 Appendix table VII), sexes separate and combined. See also legend to fig. 50. 



Substitution for the letters of their values given n=(39.20 — 28.50 ) 2 

 -7-8 [ (6.78) 2 — (5.02) 2 ] =0.69. We can only conclude that, owing to 

 small numbers, this formula is not applicable here. 



Returning, then, to our conclusion that the assumption of at least 

 3 gametic factors for some, probably most, cases of build accords best 

 with the results of the various matings, we may inquire what is the 

 nature of these factors. It seems probable that two of them may 

 correspond to dystrophies of the pituitary and thyroid glands respec- 



