  The hyperspherical harmonics (HH) provide a complete basis for the expansion
of atomic wave functions, but even for two particles the number of harmonics
for a given order is not trivial and, as the number of electrons increases,
this degeneracy becomes absolutely prohibitive. We modify the method by
selecting a subset of the basis that, we feel, will yield the physically most
important part of the wave function, and test the idea on simple systems.
  In a previous work (with M. Haftel) of the singlet ground and first excited
states of the helium atom we found that the error in the binding energy of the
ground state was of the order of 1 part in 10,000 and that it decreased for the
first excited state.
  We now have applied our method to the equivalent triplet states. We report on
this work, and our results, and hope to draw attention to the interesting
accuracy that we obtain with the relatively simple wave functions of our
formulation.
