NavList:

Bill wrote:

"It seems to me that once seen it is simple, but putting the technique into
words is challenging."

 

I agree. I think of navigation manuals as early examples of "technical writing". In the most common modern manifestation of this art, I think we've all been subjected to truly awful computer manuals and, with any luck, to some really good ones --it all depends on the author.

 

I think you've hit the nail on the head, too, by pointing out that it's easier to do once you've seen it, so maybe the trick is to describe how it looks...

 

Let's suppose I am measuring the altitude of the Sun, and it's near 45 degrees. I set my sextant to 45 degrees, and aim it at the horizon holding it more or less vertically. Now suppose I slowly rotate the sextant keeping the Sun in the field of view until the handle of the sextant is horizontal. Through the horizon glass, I can now see a spot in the sky to the side of the Sun that is just about 45 degrees away from the Sun. I could keep on rotating (keeping the Sun in view and leaving the index arm at 45) until the sextant is completely upside down (sounds painful!). I should find that I am looking straight up at the zenith through the hoizon glass. And I should see the Sun's reflected image straight up, too. I can keep on rotating and bring the Sun back down to the horizon on the opposite side. If we try it, it's not hard to see that the instrument has gone through a complete rotation around the axis that points to the Sun's apparent place in the sky. The Sun's reflected image in the sextant has been carried around the sky in a big circle with a radius of 45 degrees. For proper altitude measurement, we need to use the same motion to examine a small portion of this same big circle. When you swing the sextant to get the right altitude, the idea is to move the Sun's image through that small portion of this large circle that just grazes the horizon, sweeping first left and then right. By adjusting the micrometer until the Sun's image touches the horizon only for an instant as it is swept past, we guarantee that we are measuring the proper vertical altitude of the Sun.

 

By the way, the "wrong" method where the sextant is rocked about the line of sight does work to an extent in some cases. But it's not general, and the "correct" method is as easy and it's general so I can't see any reason not to use it.

 

And:

"I am assuming the axis of rotation (along the line of sight to the body)
would pass through the index mirror.  Is that correct?"

 

It could do that, but I think for most people it would pass through a spot behind the telescope or even through the observer's head. The axis of rotation points to the the observed body, but the axis may lie some inches outside the frame of the instrument. This works because the objects we're observing are so far away.