We generalize Schwinger's original mass formula to the case of an additiona
l isosinglet mixing with the nonet mesons. We then make further generalizat
ion to either (i) an arbitrary number of additional isosinglets mixing with
nonet mesons, or (ii) an arbitrary number of mesons mixing with an additio
nal isosinglet. In the former case, we present an explicit relation, while
in the latter case, we show by numerical example that the new mass formula
is only weakly affected by the inclusion of additional mesons, and hence ho
lds with good accuracy for each of the 3 X 3 mass sub-matrices. (C) 1999 El
sevier Science B.V. All rights reserved.