If you already know what a nonius is, you can probably skip this post. But, if like us, you would have to look it up, we’ll tell you what we found out. It turns out, a translation mistake taught us a new word and some history we weren’t aware of.
Have a look at the adjacent graphic from a waveform display. What would you call the vertical red lines at positions 139 and 200?
We’d probably call them markers. Or maybe cursors. The manual, however, calls each one a “nonius”. It refers to them that way multiple times.
Oddly, the manual also has sentences like “Select one nonius and right-click, and then select ‘Remove Marker’ in the next window to delete the nonius.”
So, clearly, a nonius is the vertical line marker or cursor. But that, of course, begs a question…
What is a Nonius?
However, there was an earlier version used to improve measurements on astrolabes. A Portuguese navigator named [Pedro Nunes] created this type of astrolabe in 1542. The Latinized version of his name is [Petrus Nonius]. What are the odds of him inventing… oh wait, they named it after him. That does make more sense.
The nonius is a series of concentric circles traced on the instrument. Working towards the center, each circle has fewer divisions than the previous one. In fact, if the outer ring had 90 marks for 90 degrees, the next ring would have 89, and the following one would have 88.
The astrolabe’s line, the “alidade”, would cross all these circles but would be closest to one mark on one circle. Given that mark and that circle, you could look up the correct answer.
For example, the image shows such a system from [Nunes] himself. It shows the circle from 37 degrees to 38 degrees. You can see the 89th circle has only one mark for 37. The other marks are in other sectors of the outer ring. The 88th, for example, has two marks for 36 and 37.
On ring 65, the line runs right over the 27, which is hard to read because the line covers it up. With a table lookup, you’d find the correct value was 37º 23′ within 0.08′. Not bad. [Nunes] was considered one of the greatest mathematicians of his time.
But we had never heard of him, which goes to show that being a mathematician is not a good way to get lasting fame. [Charles V], [Nostradamus], and [John Calvin] were all born around the same time and, while not household names, are more likely to be known today than [Nunes].
And while this is interesting, it raises another question: Why did the GOWIN software instruction manual call the vertical marker line on a scope trace a nonius?
Why Nonius?
Our guess is that this is a translation mix-up: Chinese 游标 can mean either a computing cursor or a vernier. Or a nonius. Someone apparently selected the wrong English equivalent.
Of course, we figured it out. Plus, we learned a new word and a little history. So we aren’t complaining.
Astrolabes are pretty amazing. Navigation was so important that it drove many technological advancements. Of course, measuring things in general was also of keen interest to our forefathers.
Great article, AL! (sorry for the capital L, but this way it doesn’t look like AI).
I really like all mechanical measurement instruments, and deeply respect the people who designed and manufactured them. Can you imagine how people actually started making and calibrating calipers, back in the old days? That’s fascinating!
I like the word games you can play with Al’s name now that people are crashing out about AI. It’s pretty funny. You’d have to copy and paste the text to know what I’m talking about, but that’s the point!
I blame sans serif fonts. An uncivilised weapon for the modern time.
The Nonius in a (digital) calendar is a Marcus Bains Line!
No mention of transversal?
Now we know what a nonius is. And we do not yet how it works and how the lookup table was constructed, and why you state the precission. So more opportunities for insights.
Looks like my previous (probably self-) explanation of nonius as “a device for more exact reading of the scale bridging nine (nona in latin) parts of the scale” is not accurate:)
“On ring 65, the line runs right over the 27, which is hard to read because the line covers it up.”
Well also because of some resampling of the picture that happened from the source to the usage here. Which allows us to see not only some color fringes but also some moiré patterns the stem from aliasing.
And this is an interference phenomenon. Like the vernier scale and the nonius.
And linguistically an inference phenomenon?
There is probably a reason that the Chinese representation is the same for Nonius scales and Vernier scales as it is the same underlying principle to improve the reading accuracy, with Verniers being less cumbersome to implement and use, as well as the benefit of taking up less space plus being more direct to read. In some countries Vernier scales are actually called Nonius scales, just to add to the confusion.
In Afrikaans, a vernier is a “nonius skuifpasser” where “skuifpasser” would translate to something like “shifting fitter”. So I learned something, thanks!
In many languages, a vernier is in fact a “Nonius Scale” or “Nonius Rule”.
The French and by proxy the English speaking world calls it a Vernier, while the German, Dutch, and by proxy everybody else influenced by them calls it a Nonius.