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The spacings between bound-state levels of the Schr\"odinger equation withthe same principal quantum number $N$ but orbital angular momenta $\ell$differing by unity are found to be nearly equal for a wide range of powerpotentials $V = \lambda r^\nu$, with $E_{N \ell} \approx F(\nu, N) - G(\nu,N)\ell$. Semiclassical approximations are in accord with this behavior. Theresult is applied to estimates of masses for quarkonium levels which have notyet been observed, including the 2P $c \bar c$ states and the 1D $b \bar b$states.Comment: 20 pages, latex, 3 uuencoded figures submitted separately (process  using psfig.sty

Spacings of quarkonium levels with the same principal quantum number