  Sachs has derived quaternion field equations that fully exploit the
underlying symmetry of the principle of general relativity, one in which the
fundamental 10 component metric field is replaced by a 16 component four-vector
quaternion. Instead of the 10 field equations of Einstein's tensor formulation,
these equations are 16 in number corresponding to the 16 analytic parametric
functions {\partial}x^{{\mu}'}/{\partial}x^{{\nu}} of the Einstein Lie Group.
The difference from the Einstein equations is that these equations are not
covariant with respect to reflections in space-time, as a consequence of their
underlying quaternionic structure. These equations can be combined into a part
that is even and a part that is odd with respect to spatial or temporal
reflections. This paper constructs a four-vector quaternion solution of the
quaternionic field equation of Sachs that corresponds to a spherically
symmetric static metric. We show that the equations for this four-vector
quaternion corresponding to a vacuum solution lead to differential equations
that are identical to the corresponding Schwarzschild equations for the metric
tensor components.
