  We show that the solutions obtained in the paper `An exact solution for
arbitrarily rotating gaseous polytropes with index unity' by Kong, Zhang, and
Schubert represent only approximate solutions of the free-boundary
Euler-Poisson system of equations describing uniformly rotating,
self-gravitating polytropes with index unity. We discuss the quality of such
solutions as approximations to the rigidly rotating equilibrium polytropic
configurations.
