# NavList:

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

**Re: Comments on the units**

**From:**George Huxtable

**Date:**2006 Apr 7, 23:33 +0100

If you look at some astronomical instruments of the mid-1700s, you will often find that they have been engraved with two scales, each with its own vernier. One scale has the familiar 90degrees to the right-angle. The other has 96 units! Why on earth 96? I hear you ask. It was to allow really accurate division of the scale. Scales were divided by hand in those days, not by machine. The work was done by an expert artisan, using a beam-compass. The job was done like this, for a quadrant (quarter of a circle). It's easy to mark off a 60-degree arc around a circle, by just marking a chord across it that's exactly equal to the radius. The resulting triangle is equilateral, so its angles are exactly 60 degrees. School geometry stuff, that many will remember. Well, if you mark off a 60 degree arc on a circle that's marked with 96 units (not 90 degrees) to the right angle, that 60 degree arc will correspond to exactly 64 units, and there will be an arc of exactly 32 units left over to make up the rest of the quadrant. The next thing that it's easy to do precisely is to bisect an angle, by striking arcs from either end of a chord. And (of course) 64 and 32 are numbers that simply call out to be bisected, again and again. In that way, the 96-unit arc could be precisely divided. On the other hand, a 90-degree arc could be divided into 60 and 30 degrees, but quickly you find yourself having to divide an angle by three or by five to get to degrees; a much more intractable operation. Once you had that precise scale of 96 units, with its vernier, you could easily work out what a scale value, in units, each degree marking should correspond to, and then transfer it across. Attempts were made to persuade astronomers to measure, and make predictions, measured in those 96ths units, but I don't think it ever caught on. There's a good account, that I've borrowed from, of many aspects of scale division in- "Dividing the circle" by Allan Chapman. Second edition was published by Wiley in 1995. It's a really down-to-earth account, from a practical viewpoint, which I like. Many studies of early instruments concern themselves with stylistic matters that involve art-history more than technology. George. ============== contact George Huxtable at george---.u-net.com or at +44 1865 820222 (from UK, 01865 820222) or at 1 Sandy Lane, Southmoor, Abingdon, Oxon OX13 5HX, UK.