# NavList:

## A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding

**Re: Coordinates on Cook's maps**

**From:**George Huxtable

**Date:**2007 Apr 20, 00:01 +0100

I wrote- | > Halving an | > angle with the compass is easy, and Alex replied- | Really?? | Would you explain me just how to halve a given angle | with a compass? (No ruler/straightedge!! The same | famous Bird who said: there is NO WAY to draw a straight line | between two given points. And this is true.) | Is this taught in the British schools? All right. Lets assume we have a precisely-drawn arc, struck from a centre, more than 60 degrees long, with some arbitrary radius, defined by the setting of a beam compass. Mark an arbitrary starting point near one end of that arc. Without changing the setting of the beam compass, strike a short arc, centred at that starting point. Where it crosses the main arc is at exactly 60 degrees along that arc. That wasn't specified in Alex's challenge, but it gives us an arc we are going to halve, by a method we can use to halve any arc, not just one of 60 degrees. Set the beam compass to be, by eye, slightly more than the half-arc we plan to mark off, and with it, strike a trial arc from both the start point and the 60-degree end point. Those arcs should intersect at two points. Joining those points by a straight line, that line crosses our 60-degree arc exactly at its mid point. That's the way it would have been taught in British schools, 60 years ago. What the supposed problem is, in joining two points by a straight line, that Alex quotes from Bird, I don't understand. But if he objects to that straight line for some reason, then let the radius of the beam compass be reduced a bit, and a new pair of arcs drawn from the start and end points, to cross closer together than before. Adjust the radius still further, by a trial-and-error process, until the two arcs just cross where they cross the 60-degree arc, at the one point. That marks the exact half-angle, in this case 30 degrees from either end. In practice, the trial arcs would be drawn so lightly as to be almost invisible, and only the final mid point would be shown in bold. Will that do, Alex? =================== In Navlist 2634, Alex wrote- "So I study the question myself using the information available to me: I examine certificates of the sextants sold on e-bay:-) Unfortunately, they did not supply certificates in the first half of the XIX century, so I can only study recent history of division. Interestingly, many mid XX century sextants have quite large corrections in their certificates (30" to 45"). Which means of course that the manufactures simply DO NOT CARE to make a perfect arc." Well, I don't regard non-zero errors on the calibration certificate as anything much to worry about, as long as there was a smooth variation between them (though it would be hard to know for sure that that was the case). It's an easy matter to guess an adjustment to apply, based on the certificate that's pasted into the box. But it's an interesting question as to how precise the test instrument (at Kew, say) really was. Imagine that it got known, say, that the collimator to test for a nominal 60 degrees happened to positioned 20 seconds high. Might a sextant maker be tempted, then, to make all the instruments he sent to Kew to read, correspondingly, 20 seconds high at 60 degrees, so that their certificates came out spot-on? Just a thought.... George. contact George Huxtable at george@huxtable.u-net.com or at +44 1865 820222 (from UK, 01865 820222) or at 1 Sandy Lane, Southmoor, Abingdon, Oxon OX13 5HX, UK. --~--~---------~--~----~------------~-------~--~----~ To post to this group, send email to NavList@fer3.com To unsubscribe, send email to NavList-unsubscribe@fer3.com -~----------~----~----~----~------~----~------~--~---