22 MODES OF RESEARCH IN GENETICS 



curve fitting knows that this process always runs 

 a grave danger of becoming perfectly futile. Be- 

 cause if one increases the number of constants 

 until it is equal to the number of classes of objects 

 (ordinates) to be fitted, the "fit" is bound to be 

 perfect, but also meaningless, because in no 

 sense a true graduation. This danger is par- 

 ticularly grave in Mendelian work because there 

 the number of classes or categories in the observed 

 ratios is usually small, so that constants and 

 ordinates may very easily become of the same 

 order of magnitude. In this event agreement 

 between observation and theory, however close, 

 affords no critical evidence whatever as to the 

 qualitative validity of the theory. (Cf. infra, 

 p. 29.) 



It has been shown by Yule, 1 Pearson, 2 and his 

 students, and Hatai 3 that statistically the con- 

 sequences of the distribution of hereditary specifici- 

 ties in accordance with Mendel's law are in 

 essential agreement with the statistical results of 

 the law of ancestral heredity. This result is at 

 the present time chiefly of interest in that it 

 furnishes the complete proof that hereditary 

 differences are distributed in accordance with 



1 Yule, G. U. "New Phytologist," 1902. 



8 Cf. particularly Pearson, K., "Math. Cont. etc. XII," "On a 

 Generalised Theory of Alternative Inheritance, with Special Reference 

 to Mendel's Laws." Phil. Trans., A. 203, pp. 53-86, 1904. 



3 Hatai, S. "The Mendelian Ratio and Blended Inheritance." 

 Amer. Nat., Vol. XLV, pp. 99-106, 1911. 



