PKESIDENT's address. SECTION CJl. 517 



a less degree.* Professor Karl Pearson has shown, however, that the 

 Galton regression value holds good only for certain cases,! a point 

 to which we shall later recur. 



This fact of regression implies, on the one hand, that the full 

 hereditary transmission of any gift is ordinarily highly improbable, 

 ?-nd, on the other hand, that imperfection or disease is also likely to 

 be inherited only partially.; 



5. Ance&tral Inheritance. — Although regression toward average 

 values is a tendency expressed with great precision when many cases 

 are considered, it in no way limits what has been called by Galton 

 anceMral inheritance, a generalisation of considerable value. Galton's 

 observation is to the effect that in regard to any inherited character, 

 the two parents contribute on the average one-half of the in- 

 herit-ed faculty, each thus contributing one-fourth; the four grand- 

 parents contribute among them one-quarter, thus each one-sixteenth, 

 and so on. Hence, we get the series — 



i + i + i + xV + etc. .._ = 1, 



a^ is necessary. Professor Karl Pearson found, however, that while a 

 series of this ty]je holds good, the series as just given probably 

 requires modification, as hereunder, viz. : — - 



Galton's co-efiicients ... 0"5 0"25 0'125 &c. 



Pearson's co-efficients ... 0-G214 O'lOSS 0-0630 &c. 



It is further to be noted that modification through reduction 

 of the number of ancestors may aSect the result. Biooks, for example, 

 pointed out that if a definite population had for ten generations 

 married first cousins, the total ancestry of any person would be 

 thirty-eight instead of an otherwise possible total of 2,048, and in 

 the case of the present ruler of Gennany, the probable number of 

 his ancestors in the twelfth generation back were not more than 

 533, though the theoretical total possible was 4,096. 



Professor Karl Pearson also points out that in the existing state 

 of our knowledge we can hope only to reach the -prohahle character 

 regarding offspring of any given ancestrj' by the application oi the 

 statistical method, since the causes, a. h, c, &c., which have been 

 isolated are not followed by a single effect x, but by any one of the 

 effects X, y, z, &:c., hence, a determination of the frequency with which 

 each of these follow is an essential of the problem. 



6. The Mendelian Theory. — One of the most interesting of recent 

 applications of the statistical method is its use in testing the Men- 

 delian Theoiy. In fact, in interpreting the whole series of facts 

 relating to reproduction, the application of the statistical method has 

 been productive of results of great impoi-tance. In 1866, Mendel 

 published what is now widely regarded as one of the greatest of 

 biological discoveries. His work was overlooked till his doctrine was 



rediscovered independently in 1900 by the botanists Correns, De Vries, 



■ • 



* Stated more rigorously, the fact may be thus pxpressed. If the frequency of 

 any particular character be unimodal, the average value of the character for the sons 

 of fathers of any definite measure of peculiarity exhibit it in less degrt-e. If the 

 frequency be not unimodal the statement is much more complex and the question of 

 the dominant element comes in. 



t Wee Phil. Ttaw. A., vol. 203, pp. 53-8G, in particular pp. 82-3. 



X Fathers with a mean stature of 72 inches had sons of the average height of 

 70"8 inches, while tho.se of 66 inches had sons of the height of 6S'3, that is, one set 

 regressed downicard, the other upicard toward the mean. 



