It's not always the case that half-way will work for you, and I wondered
why. I have a theory, of course <g>.

The basis of my theory is this (untested) assumption, but I think it's true:
because the two coordinate systems (alt-az and equatorial) are oriented so
differently, making a change to a single axis (alt or az) can affect
position in the other coordinate system along two axes (RA and Dec).

For example, if one axis (alt or az) is very close to correct, and the other
is not, you should avoid making changes to the one that is close to correct,
and concentrate on getting the other one close to correct, too. I haven't
had to do this kind of polar alignment for several months, so my experience
isn't fresh. I'm currently using a polar scope on an NJP 160, although I
have a 400 GTO coming and will have to re-learn these skills.

But as I recall, if one axis was close, and I made adjustments to two axes
(alt and az), the axis that was close to correct would oscillate
(overshoot). I would then move that axis to the mid position (between the
extremes of the oscillation), and then leave it alone and concentrate on
bringing the other axis close to correct position. Once both were of nearly
equal magnitude, I could then quickly get a good alignment by adjusting both
together.

I have even had situations where I have had to go _double_ the distance,
rather than half the distance, to get aligned in a reasonable number of
iterations. If memory serves, that tended to be the case when I was aligning
to stars on different sides of the meridian, but it has been a while and I'm
not entirely sure.

Ron Wodaski
http://www.newastro.com