The fact that for two or more real positive quantities there exist three well-known algebraic means, the Arithmetic, the Geometric, and the Harmonic, which stand in a fixed order of magnitude independent of the quantities operated on, suggests the question whether there may not be other algebraic means that stand in a definite order of magnitude with reference to those just named and to one another. The following paper supplies an affirmative answer to the question. The results given in the first section are, so far as I know, novel; some of those in the second section are well known, but I hope some freshness may be apparent in their treatment here.