  Numerical results for the energy spectra of $N$ electrons on a spherical
surface are used as input data to determine the quasiparticle energies and the
pairwise ``Fermi liquid'' interactions of composite Fermion (CF) excitations in
fractional quantum Hall systems. The quasiparticle energies and their
interactions are then used to determine the energy spectra, $E$ vs total
angular momentum $L$, of states containing more than two quasiparticles. The
qualitative agreement with the numerical results gives a remarkable new
confirmation of the CF picture.
