AV. Palin Eldehton 



475 



Tlie follinvini^ hiiinictric illustratioiis ai'o, of rmirsc, not (■xli.-iustivc, but they 

 may serve to indicate soiir" casrs wluTcin wc liavc fouiid a piarliral iircil i\ir such 

 tables as arc iiow ])iiblislic(l. 



Illustration 1. 



As oxatiiplo of the iise of llic Table I. cif powcis, wc will tiiid tlic cuefficicnt of 

 parental ciirrolation bctwceii tiio sire aiid 'l'.V.)i ^ otfspring in greyhovinds. The 

 categorics .stdected were some black in foat colour aiid iio black in coat colour. 

 The followiug table resultud : 



Sire. 





O 



Tho nietliod of dealing with characters not c|uantitativoly measnrablc was 

 adopted* and by using Sheppard's tablesf the following ei|uatic)n for the correlation 

 coefficient ?• was found : 



(/) (?•) = •O02,726r" + -O.DT.UOr" + ■Ol7,192r' 



+ •(W;?,Ö78?'^ + -OSS,;«! r' + •134,717r= 



+ )•- -.560,386=0 (i). 



The derived fnnction is : 



(/>' (r) = Ol 9,082;-« + -342,894r' 4- -085,960^ + 334,312?-^ 



+ -2G4,993?---' + -269,434/- 4-1 (ii). 



We can now find r by Newton's rule. We see froni (i) that r is less than -.56 

 and the r- term being plus shows ns that it nuist be less than -ö2. Now take out 

 the first seven powei-s of -.52 from Table I. and evaluate (i) by ninltiplication on an 

 arithmonietcr, we find without cleai-ing product figures from machine: 



(^(-.52) = -016,384. 



Similarly, 

 He nee 



f (•52) =1-278,466. 



</>C52)/<^'C52) = -0128 



and the noxt approximatiuii to the root is 



-52 --0128 = -.5072. 



If we bad kept jiowers of r up to the eighth instead of the seventh, the 

 actual value of the root would be .5070. We thus see that the above process 

 gives the root true to three figures, aniply sufficient for biometric purposes. 



* Phil. Trans., Vol. 195 a, pp. 1—17. 

 t Biomctrikii, Vol. ii. p. 18'2 et seq. 



