In a recent paper, Innanen and Papp (1977) have introduced and discussed the behaviour of a function they called the “super angular momentum,” ht2. This quantity, although not formally an integral of motion in the classical definition, is nevertheless a straightforward generalization of the classical total angular momentum. The super angular momentum, together with the other two classical invariants, the total energy E, and the Z component of the angular momentum hZ lead to the introduction for each homogeneous stellar system of a new collision-free distribution function and fo, β and γ are constants. The function f satisfies the fundamental equation of stellar dynamics and shows that the velocity dispersions of stellar systems cannot be isotropic, but rather that

1. (a) the velocity dispersion in the radial direction is constant (i. e. “isothermal”) and

2. (b) the velocity dispersions in the tangential directions follow the law

That is, the tangential components are “isothermal” at the centre of the system, and decay according to the above equation so as to leave a purely radial distribution in the outer parts.