xii CONTENTS 



CHAPTER PACK 



XIII. CORRELATION . * . -453 



I. Meaning of Correlation 453 



II. Calculation of Coefficients of Correlation . . . . 455 



III. The Correlation Table 458 



IV. The Correlation Coefficient 459 



V. The Regression Coefficient 466 



VI. Studies in Speed Records 6f Trotters . . . . .468 



References 472 



XIV. HEREDITY .".".' 473 



I. How Characters behave in Transmission .... 473 



II. Statistical Methods of Study of Heredity .... 478 



III. The Regression Table 479 



IV. Like Parents beget Unlike Offspring and, conversely, Like 



Offspring may be begotten by Unlike Parents . . . 482 

 V. Regression. In general, the Offspring is More Mediocre 

 than the Parents; that is, Whatever the Parentage, the 

 Offspring exhibits a Strong Tendency to regress toward the 



Mean of the Race 484 



VI. The Measure of Heredity . . . . . . .486 



VII. The Mean of the Offspring not necessarily the Same as the 



Mean of the Parentage ....... 490 



VIII. Extremes of a Race relatively Less Productive than the 



Means 491 



IX. Progression. Parents in general produce a Few Individuals 



More Extreme than the Race 492 



X. The Exceptional Individual arises either from Mediocrity 



or from the Exceptional Parent 499 



XI. Fraternal Variability, Offspring of Same Parents not 



Identical ... 500 



XII. Characters tend to combine in Definite Mathematical 



Proportions 504 



XIII. Mendel's Law of Hybrids 513 



XIV. The Law of Ancestral Heredity 525 



XV. Limit to the Reduction of Variability ..... 534 



XVI. Power of Selection to permanently modify Types by the 



Establishment of Breeds 537 



XVII. Breeding True, or Stability of a Character established by 



Selection 541 



XVIII. Duration of Varieties, Breeds, and Family Strains . . 544 



References 547 



XV. PREPOTENCY 551 



I. Data from the Trotting Records illustrating Prepotency . 551 



II. Prepotency in Sex ......... 567 



III. Influence of Age on Prepotency ...... 573 



IV. Influence of Constitutional Vigor upon Prepotency . . 573 

 References . <. 575 



