  Notation for spin coefficients for metrics of neutral signature in four
dimensions is introduced. The utility and interpretation of spin coefficients
is explored through themes in null geometry familiar from (complex) general
relativity. Four-dimensional Walker geometry is exploited to provide examples
and the generalization of the real neutral version of Pleba\~nski's (1975)
second heavenly equation to certain Walker geometries given in Law and
Matsushita [16] is extended further.
