Reclining/Declining

[GinnyandHalB]

Robert,

I think I've read all the responses to your question.  I would like to make
you aware of an approach that I've used for many years.  It involves a
coordinate transformation from horizon coordinates ( I use +X for South, +Y
for East and +Z toward the Zenith) to dial coordinates ( +X is the path of
steepest descent).  Once the transformation equations are established they
are used to transform the style and Sun vectors from horizon to dial
coordinates.  The transformed style vector gives the style height and the
substyle distance directly.  The hour-line angle is the cross product of the
cross product of the Sun and style vectors in dial coordinates, and the
normal to the dial which defines the plane of the dial.

Details can be found in my article in Vol. 5 No. 3 of "The Compendium -
Journal of the the North American Sundial Society".

Please let me know if I can provide further information.  However, I will be
in China for the next three weeks.

Harold Brandmaier