The heritability, h I (2) , of a linear combination of phenotypes, I, when defined as the ratio of the variance of the genetic index, σ g⋆ (2) *, to the variance of the index, σ I (2) , is shown to be different from the square of the correlation, r HI (2) , between the index and an arbitrary linear combination of genetic effects, H. The gain in H fror selection on I is shown to be proportional to h I (2) . bHg⋆ for any index.