K. Pkahson and A. Lkk ;jsi 



thesü iis inost crrtiiiiily quostiDiiablc tlu' iiicin icsult. is ■•t.'):} + ■ÜU7, thc tstaiuhird 

 doviatioii being -OTl. Thus -4.') may, 1 tliink, lic juslifiably takcn in fuUire to 

 represent the apjjroxiiuatu valuc nf pmcutal liorudity, in cases where no dircct 

 observatioiis have becn niadu l'or thu characlcr and species uiidcr consideraiion. I 

 [)ivf'er, howovpr, tlu^ ^{i to 'ö of tbe best of tlio above series. 



I ni)\v pass to the |ii'i'dicl imi tdrmiilac, i.i'. the rcgrcssion lincs aiul planes, froni 

 which the iiniliablc \aluL' ot a cbaracter in Ibc oHspring niay be (l(,'tei'Miiiii'il wbcn 

 tlle value of tlic cliaiactcr in the iiarcntaL;!' is known. 



If tiie siibscript c donotc fbikl and jj parrnt; aiid iii. 1«' the mean, C the 

 character ; \ve havc for })rediction froni one parent : 



C, = ,n, + '^'^{Cp-m,) (iv) 



witli a Standard (ioviatioii for tlie array of value S,. = er,, VI — ''%• 

 If we piXMÜct froni two jjarL-nts y), and^)., tho fornnda is : 



^~PiP± ^P\ ^'~2hVz ^Pi 



with a Standard doviation for the array of 



-c- - o^f Y 1 - r- 



' P\PI 



Using these fornndao we have the fijllowing results* : 



A. Stafure. 

 For Son : 



(!) Probable Stature = 33"-7o + -^Iß (Father's Stature) ± 1""")6, 



(2) Probable Stature = IVr-Gr, + -.500 (Mother's Stature)! ± l"-ö9, 



(3) Probable Stature = 14"-().S + •40!) (Father's Stature) 



+ ■430 (Mother's Stature) ± l"-42. 

 For Ddughter : 



(4) Probable Stature = 3()"-.")() + •4y3 (Father's Stature) + l"--'il, 



(5) Pi-obable Stature = 29"-2S + -.554 (Mother's Stature) + 1""52, 



(6) Probable Stature = 10"-S2 + "SMe (Father's Stature) 



+ -431 (Mother's Stature) + l"-33. 



* The actual tablos of correlatiüii are yiveu iu the Appendix and fiom them it will be seen that all 

 possible pairs were used in each case for determiuing the eorrelation. Thus the Standard deviations 

 and means vary slightly from table to table, of course well within their probable errors. The formulae 

 here given were, however, obtained by using the means and Standard deviations which were adopted for 

 Table I. 



t If Father and Mother are to contribute iudifferently to Son's stature, the parental statures should 

 be in the ratio of about öOO to 51(i, which is very nearly the ratio of l'OBö to 1, and almost exactly equal 

 to the 1-083 to 1 of ratio of Father's to Ifother's average stature. 



Biometrika ii 49 



