378 MODERN THEORJES OF HEREDITY. 



heights. The same is done for each class of fathers {i.e., those 



62, 63, inches high).* It is then found that the mode 



for the height of the sons of the fathers in any one class lies 

 somewhere hetween the mode for all the fathers and the height 

 of that class oi father. For the 62-inch fathers the mode 

 of the sons' heights will lie between 62 and 69. If it is near 

 62, we should say there was a high degree of correlation ; if near 

 69. we should say only slight correlation was shown. Numeri- 

 cally, a mode of 63, 64, ... . 68. inches would show }, f, f, 

 ... -f, correlation. As a matter of fact, the correlation in 

 such cases is found to be approximately .5. (See Fig. 4.^ That 

 between grandfather and grandson is much less, and remoter 

 ancestors still less again. 



This must suffice for an indication of the methods employed 

 by the " biometrical " school of heredity. That the numerical 

 relations worked out in this way do exist there can be no doubt, 

 but whether they afford any insight into the nature of heredity 

 is another question. My own opinion is that the information 

 obtained is of very small value. It has become proverbial that 

 " .statistics can be made to prove anything." and it may be added 

 that they can be applied to almost any facts capable of mmierical 

 expression. We might, for instance, measure to tlie nearest 

 yard the distance between adjacent stations on the South 

 African Railways, and \Ao{ the re-uUs in the form of a curve,, 

 from which we might deduce the mode and the probable error 

 from the mode of anv one such measurement, but tlie value of 

 these rigiu-es would probably not be very large. My small 

 opinion of the value of the method must lie the excuse for a 

 very meagre account of the attenij^t to formulate laws of heredity 

 based on these statistical results. It may be added that it has 

 been foinul that, on the average, the correlation for certain 

 characters between a child and both its parents is about .5 or.6; 

 between a child and its four grandparents it is about .2 or a little 

 more, while it agrees with the eight preceding ancestors to the 

 extent of about .06 to .12. It is known, however, that these 

 relations often do not hold good.f 



* The curves for sons of fathers 64 inches and 77, inches high re- 

 siioctivelv are shown in Fig. 4 (6j inches represented hy the dotted curve, 

 and 73 inches by alternate dots and dashes). 



t It is perhaps desirable to state very l)rieHy tlie possible ex- 

 planation of the disagreement between the results obtained by the 

 biometrical method, and In- the Mendelian method. In the latter case 

 the most typical e.Kamples have involved single pairs of characters in 

 comparatively simple organisms. .\s we shall see, however, even in some 

 of these cases, what appear to be single characters may prove to be 

 really made up of several interacting characters, the relation between 

 which may be very complicated. There is evidence that in the higher 

 animals this may be much more often the case, and that what appear 

 simple characters in man, for instance, may in reality be complex blends 

 of quite a large number of simple characters. .Assuming that this is 

 actually the case, and that it is impossible to distinguish the simple 

 characters whicli form the complex (a very probable corollary\ a 



