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Your hypothesis is far nearer the truth than Mr. Hume's. Two factors must be kept in view — (a) a fixed period, and (b) a fixed rate of development nicely adjusted to it. Almost unthinkably long as is a Mahayug, it is still a definite term, and within it must be accomplished the whole order of development, or to state it in occult phraseology: the descent of Spirit into matter and its return to the re-emergence. A chain of beads, and each bead a world — is an illustration already made familiar to you. You have already pondered over the life impulse beginning with each Manvantarato evolve the first of these worlds; to perfect it; to people it successively with all the aerial forms of life. And after completing on this first world seven cycles — or revolutions of development — in each kingdom as you know — passing forward down the arc — to similarly evolve the next world in the chain, perfect it, and abandon it. Then to the next and next and next — until the sevenfold round of world-evolutions along the chain is run through and the Mahayug comes to its end. Then chaos again — the Pralaya. As this life-impulse (at the seventh and last round from planet to planet) moves on it leaves behind it dying and — very soon — "dead planets."
Mahayuga in Hinduism is a cycle that lasts for 4,320,000 years. The Master is probably not using the term in this specific way since he is talking about the length of a round, which lasts much longer.