Inbreeding, gene frequency variance, and their corresponding effective population numbers are now commonplace terms in population genetics. The concepts and much of the theory are classical (Wright, 1921, 1931; Fisher, 1930). More recent refinements and extensions of the theory by Crow and associates (Crow, 1954; Crow and Morton, 1955; Kimura and Crow, 1963a, b) have been primarily concerned with distinguishing between the inbreeding effect on heterozygosity and on the variance of gene frequencies which are so intimately connected in finite populations. The purpose of the present paper is to relate the two in a way which the author thinks is meaningful and easy to grasp. Further, correlational measures are made compatible with probability measures of identity by descent and a simple basis is provided for the analysis of the variance of gene frequencies in experimental or natural populations. The procedure is to work with the variance of a linear function and to incorporate the role that the inbreeding and coancestry of individuals play in this variance. First, let us develop this role. We let aij index the jth allele in the ith individual and introduce a measure of frequency xij defined by