A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
From: Kent Nordström
Date: 2009 Mar 1, 11:53 +0100
Referring to  from Frank Reed,  from Wolgang Köberer and  from George Huxtable. Thanks for providing your views on the possible limitations in distance when using the Dunthorne formula. And thanks to Wolgang, who translated the text from the German manual much better than I did. I am not aware what Wolgang will do ref to Georges question so I provide the formulas without any intention to interfer in Wolgangs effort.
The formula no.18 in the German manual, page 386:
cos D = cos Δ + cos m * cos s * ( cos D cos Δ )
cos m * cos s
(Formel von Dunthorne)
In the above formula:
D = true distance
Δ = H h, true values of altitudes
m, s = H, h
m, s = H, h, apparent values of altitudes
D = apparent distance
Δ = H h, apparent values
These designations have been taken from another issue of the German manual, I dont know which because I just have copies of some pages from these manuals.
The formula no.20
cos D = cos Δ - 2 * cos m * cos s * sin ½ ( D + Δ ) * sin ½ ( cos D Δ )
cos m * cos s
That is, the formula no.20 is the same as no.18 but put into another form.
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