# NavList:

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

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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

```
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