Back Sight in Celestial Navigation

Running through some practice questions I encountered the following...

From Leonard Gray's 100 Problems in Celestial Navigation...

Problem 4-8
From our 0719 July 8, 1993 fix at 40deg 00'N, 42deg58'W, we continue on course 090deg at 6.0 knots. Our height of eye is still 9 feet, but we check the sextant and find that its I.C. is now -2'.0. We'd like another fix when the haze clears. The moon and sun are nearly opposite in the sky, so we won't get a sun-moon fix. We will rely on a running fix of the sun.

When the sun rises, the horizon under it is still obscured, and stays that way all morning, although it is clear in the opposite direction. We decide to get a backsight - point the sextant toward the horizon opposite the sun, and measure the angle from there past the zenith to the sun. Therefore, the body we are backsighting must be high enough so that 180deg - Hs is not beyond the range of our sextant (120deg or so). We get three backsights of the sun, and three hours later, when the sun has moved to the southwest, get three regular lower-limb sights.

BODY/GMT/Hs
Sun (backsight*)/14-10-05/109deg31'.6
Sun (backsight*)/14-11-46/109deg19'.5
Sun (backsight*)/14-13-23/109deg13'.6
Sun/17-01-39/57deg07'.3
Sun/17-03-20/56deg46'.9
Sun/17-04-55/56deg30'.0
*-Appears in the horizon glass to be a lower-limb sight.

There are two ways to work a backsight. We will use the easier, more logical one: apply the normal I.C. and dip corrections to Hs. subtract the result from 180deg, then apply the S.D. correction, but in reverse. If the sight appeared to be on the lower limb (as in this case), use the UL correction. If it looked like an upper-limb sight, use the LL correction. (For a star or a planet, apply the normal refraction correction in this third step.) What is our July 8 1413-1705 R.fix?

This appeared to make some interesting kind of sense but I couldn't get my head around visualizing how this sight could be taken to catch the sun while looking the opposite way. Was there something tricky in holding the sextant sideways or upside down to take this sight? Anyway that I held the sextant and imagining looking away to the opposite horizon couldn't resolve the sight in my mind. Time to google it in search of a diagram...

Nothing came up except the following...

From David Burch's Starpath School of Navigation, a forum conversation...

http://www.starpath.com/cgi-bin/ubb/ultimatebb.cgi?ubb=get_topic;f=16;t=000155

An excerpt from Bowditch's American Practical Navigator, on page 246...

http://msi.nga.mil/MSISiteContent/StaticFiles/NAV_PUBS/APN/Chapt-16.pdf

And another excerpt from the following - halfway down under heading of TAKING A SIGHT - this is also a very good primer on Celestial Navigation...

http://oceannavigation.blogspot.ca/2009/02/celestial-navigation-notes.html

And finally from Dutton's Nautical Navigation (15th Edition) by Thomas J. Cutler...

When the horizon is poorly defined and a star at high altitude is visible, it may be desirable to take both direct and back (over the shoulder) sights. In this latter technique, the observer faces away from the body and measures the supplement of the altitude (180deg - sextant reading = observed altitude). The arc that appears when "rocking" the sextant is inverted, with the highest point on the arc the position of perpendicularity; practice is required for accuracy in taking back sights. The results of the direct and back sights are compared and usually averaged.

This all represented a good amount of consistent explanation and background, but I was hoping to find a diagram so that I could 'see' how this sight was to be taken. A few emails out to some Celestial Navigation instructors that I knew with the following responses...

From Dominique Prinet of Vancouver Marine Courses -  (http://www.vancouvermarinecourses.com/) - who also has an excellent book on Celestial Navigation...

I had never heard of a back-sight. It seems that, when the sun is quite high up above the horizon, you can take the sight by looking the other way around, over your shoulder with the sextant, and see the sun just behind you and above your head. The sextant allows taking sights of up to 120˚ (2 x 60˚ because angles double after reflexion on a mirror, a “sextant” covering one sixth of a circle, or 60 ˚). So, if the sun is 70 ˚ above the horizon on one side, it’s 110 ˚ above the horizon from the other side. And the upper limb becomes the lower limb. Funny. It can be useful close to the equator, when the ocean horizon is on the side away from the sun, i.e. you are taking a sight with an island close by in the direction of the sun but a clear ocean-horizon away from the sun. I hadn’t thought of it.

From Clive Smith of Harbourfront Centre Sail and Power - (www.harbourfrontcentre.com/boating/) ...

Now I get it. Cool, never thought of doing this.  Yes, the catch is the sun has to be high enough so that you don't go past 120 degrees to get it. Then, as the author points out, your sight will be upside down because you have gone past your Zenith, the upper limb will look like the lower limb and you will have to apply the upper limb correction., etc. Very clever. I like it. Just for the hell of it, I will try this one of these days. Maybe on the Celestial Cruise next summer.

From Barrie Hudson of International Navigation School (www.learntonavigate.com) - who runs a great program on navigation...

Yes I know them. Make sure you are sitting in a chair because it is convenient for a backwards lean. See explanation by Cotter and calculation. I’ve used it when coasting in my keener days. Note recco. Stay away from angles smaller than 60 degrees for obvious reasons.

Barrie's explanation and calculation as follows...

The Explanation and Visual...

...and the Calculation.