# NavList:

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

**Magnetic Variation on land**

**From:**Kieran Kelly

**Date:**2004 Feb 29, 15:12 +1100

I recently sent a post regarding finding compass variation on land using a sextant, artificial horizon and compass. It was a method based on the formula used by the explorer Augustus Gregory. Hav(180dd-Z)= sech secL cosS cos(S-p) Where >Z = Azimuth angle (not Azimuth) >h = altitude >L = latitude >p = polar distance (visible pole) >S = 1/2 (h+L+p) He was trying to solve for Z - the sun's Azimuth Angle. As both George Huxtable and Doug Royer have pointed out this is an expression for the azimuth angle of a body, to compare with its compass bearing and so obtain the compass error assuming that because the observer is on land there will be zero compass deviation. In simple terms, compass "error" becomes the difference between the calculated azimuth angle of the sun and the compass bearing of the sun. I showed these formulae to both Bruce Stark in the USA and George Bennet in Australia many years ago before I became involved in this list and they provided a lot of helpful analysis eg. George Bennett showed that the following formula gives the same results as the one above (albeit you need a calculator) cos C = (cos c - cos a cos b)/ sin a sin b Where c = Polar Distance a = co altitude b= co latitude We spent considerable time plugging numbers into these two formulae and always got the same results. However this is for a restricted navigational triangle based on the southern visible pole i.e. observer in the southern hemisphere. Bruce Stark pointed out at the time and I have since confirmed it that the exact method including formula used by Gregory was in an 1804 Mackay's navigator and a 1789 Moore as well as the formula I have already pointed to in Bowditch. Never satisfied with the restricted nature eo the solution provided by this "visible pole" formula G bennet went looking for a "general universal formula " derived from the cosine rule which would apply anywhere in the world.. he came up with cos C = (sin dec - sin alt sin lat)/ cos alt cos lat Where C = Azimuth of the body (0dd - 360dd) George Bennett pointed out to me that because the cosine of an angle is ambiguous the solution is C for a morning observation or 360dd - C for an afternoon observation. You must know beforehand. Of course none of these formulae would have been capable of solution in the field in the 19th century that's why they were broken down to logs and haversines as follows: Zn = hav (360DD- Zdd) = log sec L + log sec alt + log cos S + log cos (S-p) Where Z = Azimuth Angle and Zn = Azimuth Regards Kieran Kelly Sydney Australia