According to various books, one lays out the hour-line angles 
of a horizontal dial for the latitude, one lays out the hour-line 
angles of a direct-south vertical dial for the co-latitude, and 
one lays out the hour-line angles of a reclining direct-south 
dial for the co-latitude minus the angle of reclination.

I wonder if it would be simpler to say (for northern latitudes) that:
1) The style of the gnomon always points to the (ideal) north star
2) Hour-line angles are laid out by 
?D = ARCTAN (TAN t * SIN phi)
?where
?D = hour-line angle
?t = solar hour angle
?phi = angle of style to dial plate

This is the usual equation, but I have redefined phi.

John B


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