2 The Plant World. 



Galton found that the diameters bore an almost simple direct 

 proportion to the weights. The figure illustrates very nicely 

 the well known law of regression which may be expressed as 

 follows: Adult offspring, taken as a whole, deviate in the same 

 way as their parents from the mean of the race, but in a lesser 

 degree. That is, if one weie to pick an extreme parent from a 

 population one could expect, according to the law, that the off- 

 spring would also be extreme, but to a lesser extent than the 

 parent. Therefore, by continued selection, one might shift the 

 type of the race on that line along which selection was being con- 

 tinued. Regression in the case figured amounted to one-third. 

 In other words, a selection of three parental units is necessary to 

 effect a one unit change in the offspiing. 



Apparently the original idea of Johannsen was to test out 

 this law in pure lines as well as in populations. For this purpose 

 he secured a quantity of beans of one variety which were appar- 

 ently quite uniform. The average weight was 495 mg. per seed. 

 A number of beans (286) were selected out, most of them nearly 

 the mean in weight, but the extremes of the variety were also 

 represented. The weights of the offsprings (seeds) of these 

 classes were determined and the results showed a regression 

 similar to that obtained by Galton with sweet peas (see Fig. 2). 

 In this instance the regression was only about one-sixth. 



The first filial generation from the original individual beans 

 was grown in 1901, and to continue the experiment, a certain 

 number of the pure lines were grown in 1902. The lines of 1902 

 were a continuation of those inaugurated in 1900. The data of 

 the pure lines were used not only alone but also in connection 

 with the study of the "population" i. e. the variety taken as a 



.175 inches. Now it is apparent that a single point upon the squared paper may represent 

 not only the value of y but of x also. The position of the upper cross in Fig. 1 indicates 

 that the parent seeds of that class had a diameter of .15 inches while the filial seeds had a 

 diameter of 153 inches. When one plots the parental and filial classes of any character, 

 as found in a random sample of the race, then one presumably obtains a picture that ex- 

 presses the relation of the offspring to the parents as far as the character in question is con- 

 cerned. Galton "smoothed" his filial results, evidently by applying the best fitting straight 

 line to the crosses seen in Fig. 1. The crosses of a 'smoothed ' table would therefore, lie 

 along the dotted line of Fig. 1. Johannsen's observed results evidently approximate more 

 closely to the theoretical straight line joining the means than Galton's. If the offspring 

 had followed the lead of the parents exactly and had there been no regression, the crosses 

 would have coincided with the Une of 45 degrees. 



