An equatorially mounted telescope has it easy. The telescope can
track the stars with a simple slow constant rotation about the polar
axis. This is called "equatorial tracking". An altazimuth mount rooted
firmly on the ground is simpler and surer but cannot easily track -
after all there's no polar axis. Instead tracking is a complicated
affair of ever varying drive rates in both altitude and azimuth.
The Earl of Crawford devised a clever way so that an altazimuth
telescope can simulate equatorially tracking. A cord is attached from a
point on the polar axis to the end of the telescope's tube. The
telescope tube is weighted in the rear to keep the cord tight. As the
telescope swings across the sky constrained by the cord, it describes
an equatorial tracking arc.
Here we see an altazimuthly mounted telescope with the Earl of
Crawford's tracking cord attached. The telescope is pointing at the
celestial meridian (aimed southward, if in the northern hemisphere,
aimed northward if in the southern hemisphere). The bottom of the
tracking cord is attached to a point along the polar axis. Because the
polar axis makes an angle of 45 degrees with respect to the horizon,
the scope must be situated at a latitude of 45 degrees on Earth.
Now let's swing the telescope across the sky, keeping the cord
tight. The telescope will simulate an equatorial tracking arc across
Ideally, the cord is attached to a point on the telescope's optical axis since it is this optical axis that ought to track equatorially. Attaching to the side of the tube causes tracking errors. That's because the optical axis is not coincident to the axis defined by the arm's attachment point to the telescope tube and the intersection of the three axes: the polar axis, the azimuth axis and the altitude axis.
The arc that the Crawford arm swings through is not the same arc
that the telescope's optical axis swings through. The 'Crawford' arc
can be calculated by lowering the telescope's altitude reading by the
angle the attachment point to the telescope's tube makes with the
intersection of the three axes.
Now let's check out where the telescope is pointed after two hours
of simulated equatorial tracking motion by the Earl of Crawford arm.
You can see an error in the tracking motion. In this case it is a
substantial six degrees. That means that an object will drift out of
the field of view in 10-20 minutes.
You can see this for yourself by performing this simple experiment. Attach a small telescope to the side of a Dobsonian telescope at some crazy angle, so that it is not pointed in the same direction as the Dobsonian. Point the Dobsonian on a bright star and note the field in the small auxiliary telescope. Wait a dozen minutes and re-aim the Dobsonian. Inspect the field of view through the eyepiece of the auxiliary telescope; you'll see that the field has drifted. That's the Crawford arm tracking error.
In the case of a telescope pointed at the celestial meridian, the change in altitude is minimal. If the Crawford's arm tracking speed is adjusted, the tracking error can be significantly reduced. In the image above, the Crawford arm can be moved further along, reducing the error to about a degree.
The Crawford arm was used on Lord Rosse's 72 inch Leviathan, perhaps taking advantage of the minimal altitude change.
This is why a Crawford arm for an equatorial table will only work when the arm is tied to the telescope's optical axis.
What to do? The essential problem is field rotation: the tube does not rotate to match the sky's twisting motion. If the tube cannot rotate, then perhaps the arm can.
If the arm is attached to a slippery rotating ring and pulled tight,
then perfect tracking is restored.
Another answer is to elevate the tube such that a line parallel to
the rod's attachment point to the telescope tube goes through the
center of rotation of both the azimuth and altitude axes. The tube's
off-center location will cause it to pull against the rod as it is
Yet another answer is to attach the arm to the optical axis that emerges from the back of the telescope tube. By adding a Declination clamp, we venture into the territory of the Morse Transformer, a wonderful analog equatorial to altazimuth calculator invented in the 1930's.As I showed with the Morse Transformer, another possibility is to clone the telescope's altazimuth axes, moving them to the side of the telescope. Then a Crawford arm can be attached directly to the cloned optical axis that intersects the cloned polar axis. You can see that the tracking mechanism moves with the rocker box but the polar axis that intersects altitude axis and the cloned azimuth axis stays aligned with the sky.
Google Sketchups: the Earl of Crawford arm study; the Morse Equatorial Transformer