1906.] Offspring of Thoroughbred Chestnut Mares. 



397 



above than below the truth. In spite of this, however, the proportion of 

 Chestnut foals produced by the sires called DE is too small for any simple 

 Mendelian theory. The simple Mendelian expectation is half, or 1235 

 Chestnuts, the standard deviation being .y/2470/4, or about 24 - 8. The 

 observed deviation is —77, or more than 3 - l times the standard deviation, 

 and a reference to the Tables of the Probability Integral shows that the 

 chance of getting a deviation so great as this is only - 0009, or a little less 

 than one in a thousand. 



Chestnut Mares x Bay Horses. 





Colour and frequency of foals. 



Sire. 



Ch. 



Ch. 

 fto. 



Ch. 

 Bl. 



Ch. 

 B. 



B. 



B. 

 Br. 



Br. 



Br. 

 BL 



BL 



Totals. 



" DR " 



1118 



1 



1 



4 



1141 



68 



88 



4 



5 



2430 



" DD " 









■ 1 



308 



21 



44 





3 



377 





1118 



1 



1 



5 



1449 



89 



132 



4 



8 



2807 



The matings with Brovm horses, treated in the same way, give similar 

 results. 



Chestnut Mares x Brown Horses. 





Colour and frequency of foals. 



Sire. 



Ch. 



Ch. 

 B. 



Ch. 

 Br. 



B. 



B. Br. 



Br. 



Br. 

 BL 



BL 



Totals. 



"DR" 



233 



1 



1 



246 

 193 



25 

 19 



72 



74 



9 

 4 



9 

 5 



594 

 297 



"DD" 







233 



1 



1 



439 



44 



146 



13 



14 



S91 



Here the simple Mendelian expectation is 297 Chestnuts, so that the 

 observed deviation from the required result is — 64, the standard deviation 

 of the expected result being .y/594/4 = 122, or the observed result is even 

 more improbable than that given by Bay sires. 



If we attempt to consider some more complex Mendelian theory of the 

 relation between Chestnut and Bay or Brown, we must base our hypothesis 

 of the number of gametic determinants involved upon some separation of 



