This article, published in the *Transactions of the Royal Society of Edinburgh* in 1919, by R. A. Fisher, explores the correlation between relatives under the assumption of Mendelian inheritance. Fisher aims to analyze the biometrical properties of a population where inheritance follows Mendelian principles, with the goal of understanding human variability more accurately. He emphasizes the importance of measuring variability using the square of the standard deviation, which he terms the variance. Fisher discusses the correlation between father and son, noting that if the correlation is \( r \), the variance of sons is \( 1 - r^2 \) of the variance of the general population. He also examines the contributions of different ancestors to the variance, concluding that the total variance attributed to ancestors cannot exceed half of the total variance. Fisher then delves into the effects of dominance and environmental factors on correlations between relatives. He shows that dominance reduces certain relationship correlations and that the effects of dominance and environmental factors can be separated. He introduces the concept of epistacy, where the effects of different Mendelian factors may not add linearly, and discusses the statistical implications of this phenomenon. The article also addresses assortative mating, where individuals with similar genetic traits mate more frequently, and its impact on the variance and correlations within a population. Fisher provides mathematical expressions to determine the equilibrium frequencies of different genetic phases under assortative mating and multiple allelomorphism, extending the analysis beyond strictly Mendelian inheritance to include polymorphic factors. Overall, Fisher's work provides a comprehensive framework for understanding the genetic and statistical properties of populations under Mendelian inheritance, contributing significantly to the field of genetics and statistics.This article, published in the *Transactions of the Royal Society of Edinburgh* in 1919, by R. A. Fisher, explores the correlation between relatives under the assumption of Mendelian inheritance. Fisher aims to analyze the biometrical properties of a population where inheritance follows Mendelian principles, with the goal of understanding human variability more accurately. He emphasizes the importance of measuring variability using the square of the standard deviation, which he terms the variance. Fisher discusses the correlation between father and son, noting that if the correlation is \( r \), the variance of sons is \( 1 - r^2 \) of the variance of the general population. He also examines the contributions of different ancestors to the variance, concluding that the total variance attributed to ancestors cannot exceed half of the total variance. Fisher then delves into the effects of dominance and environmental factors on correlations between relatives. He shows that dominance reduces certain relationship correlations and that the effects of dominance and environmental factors can be separated. He introduces the concept of epistacy, where the effects of different Mendelian factors may not add linearly, and discusses the statistical implications of this phenomenon. The article also addresses assortative mating, where individuals with similar genetic traits mate more frequently, and its impact on the variance and correlations within a population. Fisher provides mathematical expressions to determine the equilibrium frequencies of different genetic phases under assortative mating and multiple allelomorphism, extending the analysis beyond strictly Mendelian inheritance to include polymorphic factors. Overall, Fisher's work provides a comprehensive framework for understanding the genetic and statistical properties of populations under Mendelian inheritance, contributing significantly to the field of genetics and statistics.