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Vector-pseudoscalar mass splitting and Upsilon - eta b mass difference.

For the vector-pseudoscalar mass difference, we propose a new unified empirical formula which works very well for almost all known mesons whether or not they contain one light quark. For heavy mesons, we predict {Upsilon}{minus}{eta}{sub {ital b}}=55.0{plus minus}5.0 MeV and in particular {psi}{prime}{minus}{eta}{sub {ital c}}{sup {prime}}=96.5{plus minus}5.0 MeV without any additional parameters. This new relation seems also valid for the radially excited states of mesons. The well-known approximate relation {ital M}{sub {ital V}}{sup 2}{minus}M{sub P}{sup 2}{approx equal}0.56 GeV{sup 2} can be reproduced as a special case for a narrow region of the reduced mass. A problem concerning the difference in the hyperfine splittings of self-conjugate mesons with zero isospin and in other mesons is solved.