In applying Rayleigh's method, our approach will be to cut our manifold into an infinite number of infinitely skinny tubes. A crude estimate shows that we can get a lower bound for the lowest eigenvalue of a tube as long as its cross-section grows more or less exponentially. Thus to get a lower bound for the lowest eigenvalue of a manifold it suffices to show that it can be cut into infinitely skinny tubes in such a way that the cross-section of each and (almost) every tube grows more or less exponentially. This result complements the known fact that the rate of exponential growth of a manifold gives an upper bound for the bass note. Here we have a sort of converse: A definite rate of exponential growth gives a lower bound for the bass note, provided that the growth can be ``correlated'' by means of tubes.