It is shown for rationals a,b ≥ 1 that NC_a^NC_b = NC_a+b-1. As a consequence, if, for some k ≥ 1 and ε > 0, NC_k = NC_k+ε, then NC_k = NC. A similar development can be applied to circuits with unbounded fan-in. It is seen that AC_a^AC_b = AC_a+b, AC_a^NC_b = NC_a+b and NC_a^AC_b = AC_a+b-1. This shows for a ≥ 0 and b ≥ 1 that AC_a^AC_b = NC_a+1^AC_b and AC_a^NC_b = NC_a+1^NC_b. We then construct an oracle A for which ∀k, NCk^A ⊂ AC_k^A and, in fact AC_k^A - NC_k+ε^A ≠ ∅ for any ε < 1. Similarly, there is an A so that ∀k and ε < 1, NC_k+1^A - AC_k+ε^A ≠ ∅, and hence AC_k^A and NC_k+ε^A ⊂ NC_k+1^A. Combining, this yields an A such that, for all k and 0 < € < 1, the classes AC_k^A and NC_k+ε^A are incomparable.