Accurate Polar Alignment

For simple visual observing without setting circles, you don't need to align a telescope's equatorial mount very well on the north celestial pole. Just plunk it down so that the polar axis (the right ascension axis) is aimed at Polaris as best you can judge by eyeballing it. The mount will then do its job.

For long-exposure astrophotography, however, the polar alignment must be a lot better.

The "declination drift method" is the most accurate way to accomplish this. The method is straightforward, but it does require some time and patience.

First aim the mount's polar axis roughly at Polaris. Now point the telescope at a star that's somewhat above the celestial equator and as close to south as you can judge by looking opposite Polaris. Put in a high-power eyepiece. If the eyepiece has cross hairs, center the star on them. Otherwise put the star on the north or south edge of the field and defocus it a little. Turn on the clock drive, and ignore any east-west drift.

If the star drifts south in the eyepiece, the polar axis is pointing too far east.

If the star drifts north, the polar axis is too far west.

Shift the polar axis left or right accordingly, until there is no more drift.

Now aim at a star that's near the celestial equator low in the eastern sky.

If the star drifts south, the polar axis points too low.

If the star drifts north, the polar axis points too high.

Again, shift the polar axis accordingly.

Now go back and repeat from the beginning, because each adjustment throws the previous one slightly off. When all visible drift is eliminated the telescope is very accurately aligned, and you can take long deep-sky exposures.

If your eastern sky is blocked, you can use a star low in the west and reverse the words "too high" and "too low" in the above instructions. If you're in the Earth's Southern Hemisphere, reverse the words "north" and "south."