254 PROF. K. PEARSON ON THE MATHEMATICAL THEORY OF EVOLUTION. 
(6.) Collateral Heredity— page. 
(a.) Stature in Man. Tables VI.-VIII. 281 
(&.) Conclusions—(Elder and Younger Sisters, Divergent Values of Correlation 
Coefficient, Correlation in Head Index, &c.). 282 
(7.) Special Case of Three Correlated Organs. 286 
(8.) Doub'e Regression and Biparental Inheritance. 
(a.) General Formulas and Comparison witb Theory of Midparent, Effect of Assor- 
tative Mating. 288 
( b .) Effect of Assortative Mating on Cross Heredity. 288 
(c.) Biparental Inheritance of Stature in Man, Tables (XII. —XIV.). 290 
(d.) Conclusions—Prepotency of Father. 291 
(9.) On some Points connected with Morbid Inheritance— 
(a.) The Skipping of Generations. 292 
(b.) General Formulas for Four Correlated Organs. 294 
(e.) Antedating of “ Family Diseases ”. 295 
(d.) On Skewness of Disease Curves. 297 
(10.) Natural Selection and Panmixia— 
(a.) Fundamental Theorem of Selection. 298 
( b .) Edgeworth’s Theorem in Correlation. 301 
(c.) Selection of Parentages, Correlation, Coefficients for Ancestry of p Genera¬ 
tions . 302 
(d.) Secular Natural Selection and Steady Continuous Selection ; the Focus of 
Regression . 306 
(e.) Foeus of Regression stable during Selection— 
(i.) Steady Selection cannot be secular or produce “ truer breeding ” . 308 
(ii.) Panmixia and Uniparental Regression .. 309 
(iii.) Panmixia and Biparental Regression .. 310 
(iv.) Panmixia for Human Stature with and without Assortative 
Mating. 311 
(v.) Effect of Panmixia on Variation. 312 
(/.) Progression of the Focus of Regression with Natural Selection— 
(i.) General Remarks on Progression and Fixedness of Character . . 314 
(ii.) Panmixia and Biparental Selection. 315 
(iii.) Panmixia for Human Stature. 317 
(iv.) Concluding Remarks on Progression and Fixedness of Character . 317 
(1.) Introductory. 
There are few branches of the Theory of Evolution which appear to the mathematical 
statistician so much in need of exact treatment as those of Regression, Heredity, and 
Panmixia. Round the notion of panmixia much obscurity has accumulated, owing to 
the want of precise definition and quantitative measurement. The problems of 
regression and heredity have been dealt with by Mr. Francis Galton in his epoch- 
making work on £ Natural Inheritance,’ but, although he has shown exact methods of 
dealing, both experimentally and mathematically, with the problems of inheritance, it 
does not appear that mathematicians have hitherto developed his treatment, or that 
