MisceUanea öOS 



Tliis shows UH at onco tUut fruui l'rcif'c.s.soi- .Idhamiscii'.s own data tlie iimtonial bean i.s inoro 

 than twico as influential as the grandmatornal beaii in settliiig thc woight of tlie filial generation. 



If WC correlato the selected matornal and grandtnaternal beans, wo find the corrclution, 

 r,,, = 0'2532; and from this and the preccdiiig corrolations we find the double rcgrcssion fornmla 



Probable weight of Offspring bean 



-330'71 +0-2373X weight of Matornal Rcan+0'0731 x weight of Grandmaternal Bcan...(iii), 



showing again the prodominant influence of the matornal bean. 



If we were to calculate the mean weights of each ari-ay of oft'spring mcaus from (i), (ii) aud 

 (iii), we sliould oxpect the meau errors of the results to be in the ratio of 



Vl-)-V, Vl-'->. iiiiil Y^ 



-'•^2 + 2>-o 



(pr in this case as 



1-014 : l-OÖO : 1. 



We have applied (i) (ii) and (iii) to the G5 array.s of offspring given liy Professor Johaunson, 

 and the mean errors are 



44-3; 45-5, and 42-8 

 or in the ratio of 



1-035 : 1-OCO : 1. 



These numbers are, perhaps, as close as we could expect, and they sliow that we do in fact 

 get better results from a knowledge of maternal bean than from knowledge of grandmaternal 

 bean, and botter residts from a knowledge of lioth togcther than from a knowledge of either 

 alone. 



We hold therefore that Professor Johannsen's results prove : 



(1) That tbere is a regression from parcnt to oftspring, leadiug to the inference that 

 parental oorrelatiou has for Pkaseolus vulgaris a value elosel}' identical with that found for 

 other animals and plants, when we compare mean parental and meau ülial characters; 



(2) That when we compare the characters of indi\idual seeds in successive generations the 

 correlation between a seed aud its parental seed is so much greater than that between a seed and 

 its graudparental seed (both belonging to the sanie pure anoestral liue) as to give stroug evidence 

 that characters arisiug in one geucration within tlie line are inherited, and do therefore atiiird 

 a basis ou which selectiou may act. 



W. F. R. W. AND K. P. 



II. Addendum to " Graduation and Analysis of a Sickness Table" 



(Biometrika, Vol. ii. p. 2(JÜ). By W. Palin Elderton. 



On p. 261 it is stated that Gompcrt;;' hypothcsis may be viewed as the quotient of two 

 normal curves, and it will be interesting to see liow Makeham's useful modification of 

 Gompertz' theory may be .stated from the same point of view. Makeham's hypothesis is that 

 the force of mortality may be represented as .1 + /Je', which, from our point of view, means 

 that if we take a normal curve a.s the exposed we get {A+Bc') yf)e~'''''''^ for the deaths, and 

 this can be thrown into the form of two normal curves of the same Standard deviation, viz., 



• o" V 277 (7 V 27r 



64—2 



