G. U. YuLB 133 



negative value wc cannot be sure that iicverthcless j AB \ C\ and j AB \ 7 | arc not 

 bolh zero. Some given attribute might, fbr iiistance, be inherited neither in the 

 male line nor the fcmale iine ; yet a niixed reeord might exhibit a considerabic 

 apparent iuheritance. Suppose for instance that 50 "/o oi' the fathers and of tho 

 sons exhibit the attribute, but only 10 % of the mothers and daiighters. Thcn 

 if thcre be no iuheritauce in either line of descent the reeord must givo 

 (approximately) 



fathers with attribute and sons with attribute 25 °/^ 



„ „ „ without „ 25 7o 



„ without „ „ with „ 25 % 



without „ 25% 



mothers with attribute and daughters with attribute 1 7„ 

 , „ „ „ „ without „ 9 °/o 



„ without „ „ „ with „ 9 % 



„ without ,, 81 %. 



If these two records be mixed in equal proportions we get 



parcnts with attribute and ofifspring with attribute 13°/^ 



„ „ „ ,. „ without „ 17% 



„ without „ „ „ with „ 17°/„ 



„ „ „ „ „ without „ 53% 



Here 13/30 = 43^ "/„ of the offspring of parents with the attribute possess the 

 attribute thcmselves. but only 30°/_ of offspring in general, i.e. thcre is quite 

 a large but illusory iuheritance created simply by the mixture of the two distinct 

 records. A similar illusory association, that is to say an association to which the 

 most obvious physical meaning must not be assigued, may very probably oceur in 

 any other case in which different records are pooled together or in which only 

 one reeord is made of a lot of heterogeneous material. 



Consider the case quite generally. Given that j J.5 | ] and | ^5 | 7 | are both 

 zero, find the value oi{AB). From tlie data we have at once 



tAR^\- (^^)(-^'y) _ [(Ä)-(AC)][ { B)-(BC)] 

 ^^SC)J^C)(BC) 



Addins 



{AB) = 



(C) • 



N(AC)(BO-(A)(C)(BC)-(B)(C')(AC) + (A)(B)(C) 

 (C)[i\r-(C')] 



