  The Fermion Spherical harmonics [$Y_\ell^{m}(\theta,\phi)$ for
half-odd-integer $\ell$ and $m$ - presented in a previous paper] are shown to
have the same eigenfunction properties as the well-known Boson Spherical
Harmonics [$Y_\ell^{m}(\theta,\phi)$ for integer $\ell$ and $m$]. The Fermion
functions are shown to differ from the Boson functions in so far as the ladder
operators $M_+$ ($M_-$) that ascend (descend) the sequence of harmonics over
the values of $m$ for a given value of $\ell$, do not produce the expected
result {\em in just one case}: when the value of $m$ changes from $\pm{1/2}$ to
$\mp{1/2}$; i.e. when $m$ changes sign; in all other cases the ladder operators
produce the usually expected result including anihilation when a ladder
operator attempts to take $m$ outside the range: $-\ell\le m\le +\ell$.
  The unexpected result in the one case does not invalidate this scalar
coordinate representation of spin angular momentum, because the eigenfunction
property is essential for a valid quantum mechanical state, whereas ladder
operators relating states with different eigenvalues are not essential, and are
in fact known only for a few physical systems; that this coordinate
representation of spin angular momentum differs from the abstract theory of
angular momentum in this respect, is simply an interesting curiosity. This new
representation of spin angular momentum is expected to find application in the
theoretical description of physical systems and experiments in which the
spin-angular momentum (and associated magnetic moment) of a particle is
oriented in space, since the orientation is specifiable by the spherical polar
angles, $\theta$ and $\phi$.
