Doubt about a computation in Jules Verne

Question

In his Aventures de trois Russes et de trois Anglais dans l'Afrique australe (The Adventures of Three Englishmen and Three Russians in South Africa), Jules Verne describes in some detail the geodetic techniques of his age. His research for this book was solid, but he was no scientist himself (for instance, for his characters' outcome of measuring an arc of a meridian, he reuses an actual result, but taken at a different latitude, so it's not correct there; see Pierre Bacchus, “Jules Verne et l'astronomie” for this and other Vernian imprecisions).

There is something else I can't understand: it looks like an error, but I may be wrong myself, or misunderstand Verne's reasoning. In chapter 20, Verne tells of the main characters that

Ils obtinrent par la latitude du Scorzef 19° 37′ 18″, 265, valeur approchée jusqu’aux millièmes de seconde, c’est-à-dire à un mètre près. Il était impossible de pousser plus loin l’exactitude. Ce résultat les confirma dans la pensée qu’ils se trouvaient à moins d’un demi-degré du point septentrional de leur méridienne...

that is,

They got, for the latitude of [the summit of mount] Scorzef, 19° 37′ 18.265″, a value precise up to thousandths of seconds [of arc], that is, up to a metre. It was impossible to push the exactness further. This result confirmed their thought, that they were less than half a degree from the northernmost point of their meridian (= the arc of meridian they intended to measure).

This is my own translation, since for some reason the one linked above is somewhat abridged, lessening the precision of the characters' result (“They had found the latitude of Mount Scorzef to be 19°, 37´, which result confirmed their opinion that they were less than half a degree from the northern extremity of their meridian...”).

Now, one thousandth of a second of arc seems to me to correspond to 1/(360 * 60 * 60 * 1000) = 1/1,296,000,000 of a round angle. So, taking 40,000 km as the length of a great circle on Earth, one thousandth of a second of arc corresponds to 40,000,000/1,296,000,000 metres, or about 3 centimetres, almost two orders of magnitude less than Verne's metre.

Am I missing something? (Perhaps the best SE site for this question? I was also thinking HSM.SE or even the one about French language, in case there is some subtlety in à un mètre près.)

Answer 1

Your reasoning is sound, your calculation correct.

It's easy judgement, if one recalls that originally the nautical mile was defined as the length corresponding to one arc minute at the equator.

So even with a coarse memory of a nautical mile being a bit less than 2km, a milli-arc second (1/60000 of an arc minute) means it's quite a bit less than a metre accuracy. Using todays definition and more accurate knowledge of the Earth's circumference, your calculation is precise. Or with the nautical mile 1852 metres in a mile or arc minute and 60000 mili-arc seconds therein, thus the given accuracy of the position is 1852m/60000 or about 3cm precision.

Yet the possibly strange part about the text is really "they were (...) North of the meridian they intend to measure". That's a thing which is virtually impossible unless that word has another more limited meaning or the left-out part of the text specifies that they only measure a part of the meridian, a meridian arc with a well-defined Northern end point.

Usually a meridian is the virtual line on the globe which goes from the North pole to the South pole, thus the longitudinal lines. One cannot be "North" of that, there is no point North of the North pole. This statement would only make sense, if they intend to refer to a certain latitude, thus a parallel, a circle parallel to the equator (but which is thus not a great circle).