It may be shown that the configurations which realize the extrema of the $M_{\rm B}$ and M at fixed J coincide, see Harrison et al. (1965) for the static case, and Friedman et al. (1988) for uniformly rotating configurations.

.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.

We note a misprint in this Lemma text as printed in Friedman et al. (1988), who use dots to denote a derivative with respect to $\lambda$ : the dot over the right bracket in $(\dot \Omega \dot J + \dot \mu \dot N\dot{)}\ne 0$ is missing.

.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.