258 PLANT HYBRIDIZATION BEFORE MENDEL 



In like manner, where the pedigree reached up to the third 

 ascending generation, the total number of tricolor cases in the 

 offspring calculated, to those observed, was as 180 to 181. Thus 

 in both instances there was an almost perfect coincidence of the 

 observed data with the mathematical law. 



Galton did not rest content with the obtained results : 



"In order to satisfy myself," he says, "that the correspondence between 

 calculated and observed values was a sharp test of the correctness of 

 the coefficients, I made many experiments by altering them slightly, and 

 re-calculating. In every case there was a notable diminution in the ac- 

 curacy of the results. The test that the theory has successfully undergone 

 appeared on that account to be even more searching and severe than I 

 had anticipated." (p. 408.) 



Galton was thus able to demonstrate the possibility of calculat- 

 ing, on a statistical basis, the probable number of offspring in a 

 given case of color-inheritance, in a manner that satisfied the re- 

 quirements of a statistical law of descent. The fact that Galton's 

 constituted the only attempt during the pre-Mendelian period, to 

 arrive at a fully exact and quantitative scientific method of at- 

 tacking the question of inheritance, renders it noteworthy, even 

 although the method is statistical rather than genetic in character. 



Galton well sums up his views in words that are probably little 

 widely known, but that should be read, in order to realize that 

 the author of "Galton's Law" was not a mere mathematical ma- 

 chine, but a man of broad humanistic as well as utilitarian views. 



"It is hardly necessary to insist on the importance of possessing a cor- 

 rect law of heredity. Vast sums of money are spent in rearing pedigree 

 stock of the most varied kinds, as horses, cattle, sheep, pigs, dogs, and 

 other animals, besides flowers and fruits. The current views of the breed- 

 ers and horticulturists on heredity are contradictory in important re- 

 spects, and therefore must be more or less erroneous. Certainly no pop- 

 ular view at all resembles that which is justified by the present memoir. 

 A correct law of heredity would also be of service in discussing actuarial 

 problems relating to hereditary longevity and disease, and it might throw 

 light on many questions connected with the theory of evolution." 



As Goldschmidt says : 



"of course the significance of a biological law disappears for the law 

 of ancestral heredity. All that it shows is that it can be taken as a statis- 

 tical consequence of Mendelian number-ratios when, in a mixed popula- 

 tion, the members of which propagate among themselves, average values 

 are regarded." (2, p. 62.) 



Galton's Law has been thus fully treated because of its funda- 



