You can use your finderscope (finder) to accurately polar-align your equatorial mount. This is more accurate than a rough alignment using the mechanical scales on your mount or roughly pointing the whole mount towards Polaris.
To use your finder as a polar finder is a three-step process. First, the optical axis of the finder must be aligned to the mechanical polar axis of your equatorial mount. Second, Polaris will be centered in the finder (polar axis pointing towards Polaris). Since Polaris is nearly one degree away from the true north celestial pole (NCP), the last step will offset the finder’s view and the polar axis to get true polar alignment.
The alignment of the optical axis of the finderscope with the mechanical polar axis of the mount can be done either at night with Polaris or (perhaps more easily) during the daytime on a distant building or landmark. If you do align during the day, use the latitude adjustment screws and the tripod to level the polar axis to make it easier to do.
NOTE: Any star can be used to get the finder optical axis and polar axis aligned. Polaris is chosen for convenience and also because it will be used in the second step.
You’ll flip the mount several times and recenter Polaris (or the landmark) in the finderscope each time, successively getting closer to alignment of the finderscope and polar axis.
Working with Polaris, start by setting up your mount as you would for polar alignment. The Dec setting circle should read 90 degrees. Unclamp the RA and rotate the mount until the telescope and finder are all the way to the left or right, Dec axis horizontal. Get Polaris in the field of view of the finder and centered in the crosshairs by moving the mount (using fine adjustment screws). Now move (flip) the mount all the way to the opposite side (180 degrees or 12 hours RA away from the original position). Note the shift of Polaris off the crosshairs. Actually the finderscope and the crosshairs themselves have rotated in a small semicircle around where the polar axis points. You can see where that is by looking through the finderscope as you rotate the mount, watching for the center of motion. Clamp the mount and turn the three setscrews around the finderscope to move the crosshairs over this pivot point. Recenter Polaris by only moving the mount.
Even with the telescope positioned 180 degrees away around
the mount, the telescope (and finderscope) should still be
pointing at the same object in the sky.
Repeat the flipping-setscrew-recenter Polaris procedure. Each time you go from one side to the other, the off-center distance of the crosshairs from the pivot point will be smaller. After three or four repeats, the crosshairs won’t move when you flip the mount. You will be pointing at Polaris. Your polar finderscope optical axis is now pointing in the same direction as the polar axis.
(If you did this during the day with a landmark, now wait until dark. Set up your mount as you would for polar alignment. The Dec setting circle should read 90 degrees. Use the latitude scale and adjustment screws to center Polaris in the finder.)
When rotating the scope and finder 180 degrees around the polar axis,
the crosshairs will rotate around where the polar axis is pointing
(this pivot point is the "X" in the right-hand figure). Adjusting the
finder and the equatorial mount until an object remains centered in the
crosshairs during the rotation aligns the finderscope with the
telescope's polar axis.
Steps one and two are done and the polar axis of the telescope is aligned with Polaris, but as any star atlas will reveal, the true pole lies about ¾-degree away towards the last star in the Big Dipper’s handle (Alkaid). To make this final adjustment, the telescope mount will need to be offset from Polaris towards the actual NCP.
Since Polaris makes a complete rotation around the NCP once a day, how far should the mount be moved and in what direction? One easy way is approximation. Guesstimate the direction by using Alkaid. Guesstimate the amount by knowing the field of your finderscope and dividing it by the ¾-degree distance of Polaris from the pole.
Example: On August 1, at 8PM, Alkaid is above and to the left of Polaris in the 10 o’clock position. You have a 6-degree field-of-view finderscope. Starting with Polaris on the crosshairs, use the fine adjustment screws to shift the mount in altitude (latitude) and azimuth up and left by one-eighth finder field (6 divided by 0.75).
The true North Celestial Pole (NCP) lies less than a degree away from Polaris in the direction of Alkaid, the last star in the handle of the Big Dipper (Ursa Major).
Now use the setting circles to check how close the polar axis alignment is to the NCP. Unclamp the axes and swing the scope’s tube to a bright star of known RA and Dec near the celestial equator. Turn (set) the RA setting circle to this star’s RA. Now move the tube until the RA setting circle reads 2 hours 31 minutes and the Dec circle reads +89 degrees 15 minutes. These are the coordinates of Polaris and the Pole Star should now be in the finder’s crosshairs. If it’s off, once again move the mount in latitude (altitude) and azimuth to center Polaris.
Now you have a polar alignment for your scope within a fraction of a degree of the NCP. This is excellent for visual purposes and short-exposure photographs piggybacking on the main tube. However, guiding corrections and field rotation will still be problems for long-exposure astrophotography, which demands the most precise polar alignment.
NOTE: At the completion of this process, Polaris may very well not appear in the center of your main scope's eyepeice field. This is because the optical axis of the finder and the polar axis are now parallel. But the finder's optical axis and the main tube's optical axis may not be parallel. So centering a star in your finder won't necessarily center it in your eyepiece. To overcome this, once you've achieved polar alignment, you can realign the finder with the main tube optics to return the finder to normal operation with the main scope.