## Saturday, June 16, 2018

### Davis Mark 3 Sextant Part 1 — How to read the Angle Scales

This is one of several notes with associated videos on the use of the Davis Mark 3 sextant. We have a more general book on How to Use Plastic Sextants, but now we are focusing in on the Mark 3.  The reason for this focus is a bigger challenge we set for ourselves in our new booklet that teaches mariners how to use a sextant and find position at sea with no previous training at all. In fact, to the extent we succeed, you do not need this article or video! Just get the book and open it when you need it. To that end, we put together a kit that includes one of these sextants, this new booklet, and a few other things to serve as a GPS Backup Kit.

But for now, however, we address those who, for whatever reason, wish to use a Mark 3 sextant. There is a manual that comes with the Mark 3, rather detailed even, but it is our experience from teaching cel nav for so many years to so many thousands of students that the stock manual is not enough. So our GPS Backup Kit includes the book below, which explains how to use the Mark 3, which must start with how to read the scales, the subject at hand.

Back and front covers of our new book, available in print or ebook format.

Later we address how to calibrate the sextant and take sun and star sights, but now we just look at how to read the scales.  Below is the angle the sextant measures, called sextant height (Hs).

Below is a picture of the Mark 3 with parts identified. There are two adjustment screws (#1 and #2) which we discuss later. The angle we measure Hs will be in the form 39º 20', which is about what the one below is set to.

We read the degrees part of the angle from the arc scale, and the minutes part of the angle from the vernier scale at the bottom of the index arm that slides along the arc. A vernier scale is a way to estimate fractional positions between two lines. The linear version we use today was invented by Pierre Vernier in the 1630s, likely based on a circular version used by Portuguese navigators in the late 1500s. The vernier scale has interval separations slightly larger than those on the scale it is interpolating. In the picture below we see that 30 intervals on the vernier scale span 31 intervals on the arc scale.

Start by looking at sample A below (click the pic for a better view). This is a reference showing what 0º 0' looks like. The checks we make for sextant calibration at each sight (index error) will be just a slight variation of this alignment, as discussed below.

 Click the image for a bigger view.
The degrees part of any sight is read from the arc scale relative to the 0' mark on the vernier scale. In sample B we see from the degrees scale that the angle is bigger than 32º, but somewhat less than halfway to 33º. In other words the minutes part of the angle will be less than 30' It is always valuable to estimate what the minutes are before actually checking to see what they are. In this case, for example, you might decide is this just a bit bigger than 32 or is it almost 33 or is it near halfway, just below or above halfway, and so on.

Use the vernier scale to to get a better measure by finding which of the tic marks on the vernier scale most closely lines up with any of the degree marks above it. Zooming in on the image (which we do with a small magnifying glass when underway) we see that 20' or 22' could be considered aligned, with 18' or 24' definitely not aligned. Note too that the out of alignment marks will be off in the opposite direction on either side of the best aligned one... or maybe two, as in this case.  We called this one 22, but you could argue in this case that 21' might be best, since 20 and 22 were pretty close.

In Sample C this is a little easier with the degrees being almost 32, but not quite, so degrees part is 31º and the minutes alignment is best at 46'. Again, notice that the 45' and 57' are off in opposite directions.

A possible blunder to make in these measurements is to count the degrees scale backwards. In sample C that would be reading the angle as just bigger than 28º. It pays to double check we are doing that right. In other configurations it could be more misleading.

Another challenge we face is when it looks like the degrees line up exactly as in sample D. It would be a mistake to call this 28º 00' and go on.  When the degrees line up very closely (as they will with all of the index error measurements) then we must turn to the vernier scale to see if it is large minutes or small minutes that line up. Small minutes alignment means you are just over 32º; large minutes alignment means you are just under 32º and the actual degrees part is 31º, not 32º. Zooming in on D we see that 4' is the best alignment, so the angle is 32º 4'.

The next three samples are what we see when measuring the index correction, discussed later. In sample E we can see from the degrees scale alone that we are just above 0º and checking the vernier we see the amount above is 6', with 4' and 8' off in opposite directions. This value of Hs would be 0º 6'. When doing an index correction measurement we would call this 6' "On the scale."

In sample F we have similar case, but in this one it is easier to see that both 4' and 6' are equally unaligned but they are better than all the others, so this would be called 5' On the scale.

In sample G we cannot tell from the 0º alignment if this is above or below 0, so we check the vernier to find that the 52' mark is best aligned, and again we check that the alignment on either side is off in the opposite directions.  With these large minutes aligned, we have effectively -1º + 52' = -8'.  In other words, this alignment is just 8' Off the scale, which is how we would record it.

For index corrections we have then either small minutes aligned which are called "On the scale" or we have large minutes aligned and we subtract that from 60' and call the result "Off the scale."

That is how the scales are read. This must be done carefully if we want to get out the full potential of the Mark 3 sextant. A small magnifier helps.  Also we stress multiple places that whenever possible we should not rely on just one measurement. For good work we should take 3 or 4 sights each time so we can average the results.

We will add more articles and videos on the use of this sextant, but they will now assume we know how to read it.

#### 10 comments:

Axelle said...

Hello,

We just bought a Mark 3 sextant but for some reason we can't make the vertical adjustment work: even when the screw is completely loose, a vertical line appears twice (1 on the mirror, 1 in the real world).

How important is this adjustment ? Do you know how we could fix this ?

Thank you !

Aaron said...

Hi,

I bought a Mark 3 to learn on. For sun sights, the index shades seem to work well. I see a nice outline of the sun that doesn't hurt to look at. But the horizon shades don't seem strong enough or something. I can't see the outline of the sun because it's lost in all the bright light. (I used both horizon shades). I have stopped using it because I'm worried it might not be good for my eyes.

Has anyone else experienced this? Any advice on how to use it correctly?

Thanks!

David Burch said...

To Axelle, I apologize for missing your question. I think we finally have this set up so we get a notice. By vertical error, i think you refer to what we have called side error. some side error is not crucial, but if too much it won't work. We have notes on adjustments in the book cited and also in another book called How to Use Plastic Sextants. Step one is check for perpendicularity. Then it will be an interactive process using both side error and index error. It is unlikely, but not impossible that the mirror is glued in crooked.

David Burch said...

To Aaron, on other sextants, the horizon shades are primarily for removing glare from the water. If there is no glare on the water, these should not be needed. But on the Mk 3 these second shades are right in front of the eye piece so all light goes through them, meaning they can be used as extra shading in general. The general procedure would be use both of the index shades and then add one or two of the "horizon" shades as needed. If all 4 do not block the sun enough, then maybe they are deficient, or you may have to wait till the sun is lower and less bright. You could also jury rig a homemade solar index shade which would replace the two index shades. That is discussed at the end of this article: http://davidburchnavigation.blogspot.com/2018/09/solar-index-correction-method-for.html and also in our book How to use pastic sextants.

Unknown said...

Thanks for the above explanation of how to read the vernier calibration I now understand it's application. I have the Davis manual but the instructions are vauge to me and difficult to grasp the concept. The examples you have given are a great.
aid.
Yes I get it now.

David Burch said...

Thanks for your note. The book shown has very detailed notes on use of the instrument beyond those covered here.

Unknown said...

I think that I have found a couple on typos in the sample calculations in the book.If these are errors, has an addendum been issued? I will be glad to send you my list, if still needed.

I expected a work form for the sight reduction calculations, but was disappointed not to find one. It would serve as a checklist and guide through the process. Has a suitable form just for this been developed? Ideally, the form would be the same size as the book to fit with it in the case.Would one of the standard Starpath Forms serve? Which one would you recommend?

There is an excellent article in the blog about determining Long from sunset of the upper limb which only requires a watch, almanac, and probably very dark glasses. Could the book almanac be used? Why not time both the upper and lower limbs?

Thanks,
Jim Long

David Burch said...

Hi Jim, thanks for your comments. There is an errata for the latest printing with news about the book. You can send your observations to helpdesk@starpath.com and we will have a look. Thanks.

The examples in the book are all presented in a form of sorts, but a separate blank form for the various operations covered seems a good idea. We will look into that and then post it at the page above. I don’t think any of our other forms would be that much help, since the backup methods are so compacted.

As for finding Lon from sunrise or sunset, the backup almanac would do the job, but the analysis is not covered in the book, because that calls for learning a full sight reduction which we do not do in this backup approach. When doing that technique, upper or lower or even better both can be used. You can also use sunrise/sunset tables that might be found in tide tables. That approach is covered in our book on Emergency Navigation

Robert Garrigós said...

Hi David, I was also looking for the errata, but the page your pointed us to doesn't contain the errors in the calculations I've also found in page 17. In the table 5-2, Lat, as z + Dec, should be 35° 80,6', not 36° 80,6' (thus 36° 20,6', not 37° 20,6'). The error comes from the final Ho, which should be 75° 14,0', not 74° 14,0'.

David Burch said...

Thanks very much Robert. You are right of course about that error. The errata is at the bottom of page support page, which includes several resources that might be of interest if you have not seem them. This is a little book, but it still took us a while to get what i hope are most of the typos removed. It is now in the 7th printing.