502 Miscellanea 



produced by a mother-plnnt, representing the maternal character in a line ; (2) the weights of 

 iiidividujil seeds, tiikcn from this inothcr-plaiit aiul sown; and (3) the mcan weight of the seeds 

 bonic liy ejicli rcsultant plant. The regression coefficicnt, which Professor .loliannscn regards 

 (without any vcrv adcquatc proof ) !Vs e<]ual to 0, is between tlie deviatiou of the induidual Irans 

 (2) and that of the luean character of the series of phvnts (3) resulting from tlieni. We bave 

 therefore (1) the maternal generation dcfined by the mean character of all the beans borne by a 

 plant; (2) a second generation, children of the maternal plant, each defined in the s;une way, by 

 the mean character of the beans it bears ; we have no third generation at all, and the regression 

 which Professor Joliannsen lias observcd seems to have littlc be;ii-ing tm the (piestion at issne, 

 which couUl only be detcrinincd by growing a third generation from reiiresentative oflspring of 

 the filial plant-s, doscribing cach plant of this generation as those of the two previous genorations 

 were described, in terms of the meiin character of its seeds, and then dotermining the correlation 

 between the characters so described in the two successive generatious, the children and grand- 

 children of the siiiglo plant originally used to determinc the line. 



The qnestion, which the table.s given do to sonic e.\tcnt answer, is the qucstion what relation 

 cxists between the character of two seeds from the same mothcr-plant, and the character of the 

 plants produced when tho.se seeds are sown. Kow it seems clcar that if we take small beans out 

 of a gcneral liarvest of seed, we shall be to some extent selecting the seeds of plants which lx)re 

 on an average small l;eans; biit what rca.son is there for supposing that the small and the large 

 seeds from one and the same plant will lead to groujjs of plants bearing respectively small and 

 large seeds ? The hypothesis involved in this supposition seems somewhat analogous to the view 

 that out of two cggs of a clutch, the smaller will produce a hen laying smaller eggs than that 

 produced from the larger; this may well be quite fallacious, and it may yet be true that out of 

 large mas.ses of eggs, small eggs produce on the wliole hens which lay small eggs. The absence of 

 relationshijj of marked kind between the weight of seed sown, and mean weight of seed produced 

 by the resulting plant, seems to have no bearing on the problem whether selection within the line 

 can produce a change of character. 



One further point we must notice ; the Uebersichtstabelle 4 (pp. 36 — 37) has been treated in 

 a quite illogitimate way, which wovdd make the coefficients of correlation and regression=0 

 between any two varialjles w-hatover. 



If, as Professor Johannsen believes, the individual differences between members of any one 

 generation were mere fluctuations, having no hereditary value, then a given generation ought as 

 he says to be as well dotcrmined by selection of its grandparents as by selection of its parents. 

 We cannot determine whether this is true of the average character of plants in Professor 

 Johannsen's experiments, because the necessary data are wanting; but we can determine 

 roughly the relation between three successive genorations of individual beans. The material has 

 been selected in such a way that the Standard de\iatious of the successive genorations have 

 clearly quite artiticial \alucs, so that the corrclations obtained are not very trustworthy ; further, 

 the exact weights of be<ins are not always given, .so that wo have licen obliged to place a bean 

 recorded as lying between say 400 and 450 mgrni. in the middle of its category. With these 

 qualifications, we find 



Correlation of Älothcr Bean and Offspring Bean r„, = 0-3481 +0-0080, 



Correlation of Grandmaternal Bean and Offspring Bean r(,2 = 0-2428 + 0-0086. 



If we wish to predict the weight of a given bean of the filial generation from the known 

 weight of its maternal Iwan, we must form a regi-ession equation, which becomes 



Probable weight of Offspring bean = 538-31 +0-2691 x weight of Maternal Bean (i). 



If wo wish to predict the weight of a filial bean from knowledge of the grandmatenial liean, 

 we obtain the regression equation 



Probable weight of Oflspring bcan = 41"-41 +01074 x weight of Grandmaternal Bean... (ii\ 



