# NavList:

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

**Magnetic Variation - Lewis and Clark**

**From:**Kieran Kelly

**Date:**2004 Feb 17, 07:22 +1100

I sent the post below recently as a way of showing people how land explorers calculated compass variation in the days before modern maps. I was intrigued about the Gregory method shown below and went hunting for the maths. Surprisingly I found the answer in a Bowditch of 1977 Vol 1 as follows: 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) I am not a mathematician but it appears he was trying to solve for Z - the Azimuth Angle - and compare it to the compass to get the difference between true and magnetic north. In this case Gregory was using the south visible pole so substituted 360dd in his formula for 180dd. Note that this is not a universal formula because it relies on the restricted navigational triangle based on the visible celestial pole. This is how it was done in Australia. How did Lewis and Clark calculate Mag Variation in the United States? Kieran Kelly ---------------------------------------------------------------------------- ------ >Kieran stated he has a way to find local variation using " a >sextant, compass and amplitude". How can this be done? Am I missing something >or are my thoughts to confined i.e.. ship board application only? The Australian explorer Augustus Gregory used several techniques for finding variation (i.e. difference between true and magnetic north. I will quote one here using an early morning sun altitude. This is verbatim from the field books: 28 AUGUST 1856 at Camp LVII Alt sun symbol 7dd 30' az N 279dd 30' e mag Polar Distance 99dd 30' Lat 18dd 00' sec .021794 Alt 7dd 30' sec .003731 2)125dd 00' 1/2 sum 62dd 30' cos 9.664406 diff 37dd 00' cos 9.902349 77dd 25' log sin sq 9.592280 360 282dd 35' 279dd 30' 3dd 05' var E So there you have it. Mag var with a compass, sextant and log tables. In this case he did not use amplitude tables. Also because he is on land with no ship nearby, deviation is presumed to be zero (I think). This was only one technique he used and is based using haversines for a solution of the celestial triangle originating at his visible pole i.e. the south pole. I can post some of his other techniques if you are interested.. Regards Kieran Kelly Sydney Australia