# NavList:

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

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Re: Manual calculation of compass variation
From: Herbert Prinz
Date: 2004 Oct 15, 21:35 -0400

```Lisa Fiene wrote:

> Can someone explain to me how James Cook did the following:
>
> "Found the Variation of the Compass by the Even'g and Morning Amplitudes
> and by 2 Azths to be West 20? 59'"
>
> I've just been reading through some of his log entries, and don't really
> understand this one.
>
> Now we know by the compass roses on our charts what the relevant compass
> variation is, so have never really thought of how this is actually
> calculated.

Lisa,

There are two issues here that must be distinguished.

1. What Cook did.

You find compass variation empirically by establishing true north and
comparing it with magnetic north (as per your compass, accounting for
deviation). The difference between the two is variation. One common method
was to measure the azimuth of the sun at rising or setting with a pelorus.
The difference between this azimuth and the prime vertical (i.e. azimuth =
90) is called the amplitude. Tables of amplitudes were commonly provided in
nautical handbooks. You find an example in Bowditch 1981, Table 28. Today
you would compute the azimuth of the sun at rising just like any other
azimuth for the intercept method. If you use HO 229 it's a little tricky,
because they are designed to find z from LHA, not from Hc. So you have to
use them in reverse.

2. What the government does when printing compass roses.

After having obtained many individual observations such as Cook's, in many
places all over the world and over a long time (because variation is
changing with time), scientists made a mathematical model of the geomagnetic
field (using spherical harmonics) which allows us to predict variation for a
given lat, lon and year. This process is not unlike tide prediction, where
observations are made in certain key locations and by analysing the
oscillations one can interpolate for places in-between and extrapolate for
times in the future.

The geomagnetic model is not manageable without electronics and its
discussion is therefore outside the realm of this list. It is implementedin
the firmware of every GPS receiver. Programs for pocket calculators and PC
are available.

Herbert Prinz

```
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