 # NavList:

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

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Re: FW: Mag. Variation
From: Herbert Prinz
Date: 2004 Feb 24, 15:54 -0500

```George Huxtable wrote:

> hav (180-Z) = sec h sec L cos S cos (S - p)
>
> I have quite a collection of navigational texts, but in none of them can I
> find any referece to that same expression for azimuth. Although Bowditch is
> usually rather good at explaining or deriving the expressions he uses, in
> this case he doesn't seem to do so (or I can't find it).

It's always the same boring old trick:

2 cos((a+b)/2)*cos((a-b)/2) = cos(a) + cos(b)

and

hav(a) = (1-cos(x))/2

as the name suggests. So, from

[1 - cos(180-z)] * cos(h) * cos(L)  =  2 * cos((h+L+p)/2) * cos((h+L-p)/2)

we get

[1+ cos(z)] * cos(h) * cos(L)  =  cos(h+L) + cos(p)  =  cos(h)*cos(L) -
sin(h)sin(L) + cos(p)

Eliminate bracket, move terms around and obtain the plain cosine formula for the
PZX triangle:

sin(h)*sin(L) + cos(h)*cos(L)* cos(z) = cos(p)

Best regards

Herbert Prinz

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