  Within the newly formulated composite fermion hierarchy the filling fraction
of a spherical quantum Hall system is obtained when it can be expressed as an
odd or even denominator fraction. A plot of $\nu\frac{2S}{N-1}$ as a function
of $2S$ for a constant number of particles (up to N=10001) exhibits structure
of the fractional quantum Hall effect. It is confirmed that $\nu_e +\nu_h=1$
for all particle-hole conjugate systems, except systems with $N_e =N_h$, and
$N_e=N_h \pm 1$.
