NavList:

Robin Stuart, last week you described some variation observations recorded in logbooks in 1797 and 1824. And you noted that these were quoted to the nearest minute of arc.

I've also seen logbooks the first couple of decades of the 19th century with regular, and seemingly "over-precise", recorded values for compass variation apparently based on careful observation. By 1840 at least, there are no more reported variation observations in any logbooks I've seen. It seems that the observations for variation were normal practice in an era when there were insufficient records of the variation globally that could be trusted by navigators. They were encouraged to shoot their own estimates as often as possible, and I would guess that there were sailing "agencies" (local corporations) in various ports collecting all this data for use by their members. It seems that hydrographic data like that were treated as trade secrets by some commercial groups, as valuable as knowledge of good "fishing grounds", but in later decades the responsibility for compiling and also distributing this information passed to government agencies (and no doubt at different dates in each navigation culture but probably close to 1830 or 1840 in the more familiar navigation cultures).

As for those minutes of arc in the computations and records of the variation, I don't think we can read much into that precision for two reasons. First, there were only vague concepts of accuracy and precision in this era, and navigators were inclined to include extra digits for no good reason, especially --it seems-- if the examples in standard navigation manuals included extra digits. Also, I believe this was a natural outcome of the use of sexagesimal numbering in angles. If you want an output of a calculation to display a little more detail than the nearest whole degree, today we might calculate a value to the nearest tenth of a degree (or maybe less... see my PS). But in that era, the only acceptable choice after degrees was minutes --a jump of 60. Surely some navigators understood that the numerical value of those minutes had no significance, but then again, many probably just assumed that a number is a good number if it's recorded. I suppose it's a bit like Google Maps today providing 15 digits of precision after the decimal point in latitudes and longitudes, which many users will happily record and report (even though that 15th digit reflects "atom level" definition of a position). It's also similar to the somewhat over-done precision in lunars clearing calculations in that same period. It's quite common to see everything worked out to the nearest second of arc in lunars. Why? Because seconds come after minutes, so that's the only choice! ...something like that.

Incidentally, since I brought this up a few weeks back in the context of low-grade longitude determination, I would add that I am quite sure that these navigators were not observing variation for longitude. They needed good, daily observation of the variation so that they could get good direction info from their magnetic compasses. Variation for the sake of variation. :)

Frank Reed
Clockwork Mapping / ReedNavigation.com
Conanicut Island USA

PS: Abour a quarter of a century ago, I was helping a programming team design some software for the options pricing business in Chicago. There are various rates of change in pricing that can be calculated, and sometimes there was a desire to go beyond two significant figures in those calculations. For example, a calculation might yield an option "delta" of 0.52. That's fine, but maybe we want just a little more... (we see the same thinking in celestial navigation when we ask for tenths of a minute of arc in altitude corrections even though we may not expect better than whole minute of arc quality in the process). Going beyond those two sig figs in the delta is simple enough: add a digit. So we would have 0.523 or 0.521 for those "deltas". But that gets distracting, and really we only want a nudge beyond the two significant figures. But our standard decimal numbering system doesn't have a nudge. You have to add a whole factor of ten in precision if you want anything more, right? But why not change the numbering system to get that nudge? We did this by adding a little superscript + or - (and an implied "null" in between). It worked well enough, but it was right at the end of manual trading anc computation. I'm sure those deltas were being computed to fifteen significant figures just a few years later [not "2.5" years... but "a few" :) ].