  Using scaling rules valid in the liquid drop model of nuclei, as well as
universal rules associated with exchanges of stability in families of
equilibrium configurations, we constructed closed formulae in terms of the
atomic and mass numbers Z and A and the angular momentum L, which represent the
properties of nuclei rotating synchronously (with `rigid' moments of inertia),
as calculated numerically using the Thomas-Fermi model of [5,6]. The formulae
are accurate in the range of mass numbers where the transition to rapidly
elongating triaxial `Jacobi' shapes takes place. An improved set of formulae is
also provided, which takes account of the decreased moments of inertia at low
angular momenta. The formulae should be useful in guiding experimental searches
for the Jacobi transition. In the second part of the paper we discuss
qualitatively some aspects of the dynamics of nucleus-nucleus fusion, and
outline a possible way of estimating cross-sections for the synthesis of
superheavy nuclei.
