K. 1'kakson and A. Lkk ;}8r> 



lu'icdity is zero, and agaiii (b) wlu'ii tlic diganic foiTclatimis are zevn. Hencc vvc 

 niiglit, it' 1,2 ivpivscnt organs in (inu of a pair, and 1', 2' tliu saine Organs in the 

 other (if a imir nt' relatives, uxpect t,o lind : 



r,,- = c rn'V^w + c' r.wi\.„ 



?•,■. = c"jvy?-,v + c"'?-|,'?-,.j, 



whero c, c', c" and c" are al jiresctit. indrlcrniinate. 



Hencu : 



1 . , , s Ac'-n' + c"r..A (er.,,' + c"r,A 

 i ('V + r ,'=) = riv ^ 2 j + ' '2 (^ 2 j ■ 



Now if hrredity were constant i'm- all cliaracters, \ve shoiild have r„' = r.../, and 

 we sliould rcach the abovc pro]K).sition b}' [)iitting c = c' = c" = c" = •">. Thiis we 

 should expcot the c's to bc equal to '5 plus funotions of j-,,-, ?v, 7\., and ?-,v, which 

 vanish wlien ;■,,. = /•../ and ry,= )\w. What tlidsc t'iuictrions niay he it wnuld 

 probably be liard t<i drterniinr. I thcreturi' propose tu write siniply 



7-,,' = C' ('•„■'•,.,. + /WlO[ ^^.J) 



rv, = (n-/ n-a' + ''ir '"i-j) I 



and determini' the vahuvs oft'. These are given in the Talile VU. below. We see 



at once that C is ahvays greater than ■'), its mean value is -.^O.S:). ]f we ail(i])t 



this value we should have the fVillnwiug einpirical forniida to deteiniine a ci'oss 



lieredity coefticient : 



r„- = -5(>83 (/•„•)•,•.+?:,,■?•„) (vii). 



But i^inee the nunieiieal tactor is greater than 'ö, and r,,- and ?•._.,■ as a rule some- 

 what less, we ougijt to get ruiujh values of the cross eoerticients fnnii 



'■i.' = i(''iV + ''i.) (^'iii)- 



The values ealculated JVoni these euipirieal ibnnulae are given in Table VIII. 

 below with the differences. 



The probable ern)rs of these coeffioients of eross correlations are given in 

 Table VI. Formula (vii) gives 13 values above and 11 below tiie corresponding 

 probable errnr. Formula (viii) gives 11 above it and 13 below it. The niean 

 deviation of (vii) is 'Oiy and (viii) is also '019. Thus the fornmlae are practically 

 equally good so far. But (vii) gives 10 above and 14 below, whilo (viii) gives only 

 o above and 21 below the observed values. Thus as an empiricid formula (vii) is 

 somewhat better than (viii), which is really based on the equality of all inheritance 

 coefficients and theii' appruximatiou to a value of ■."), assumptions only roughlv 

 true. 



Practically either (vii) or (viii) would sutfice Cor niost purposes, and the nianner 

 in which they smootli the observed results, especially in niaking what we might 

 ä priori expeet, near equality* between the pairs of corresponding cross correlations 

 is itself an argument in their favour. Hence I should say that wlien the 



* See /{. ,S'. Prot'. Vol. «2, \u 411. 



