A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
From: John D. Howard
Date: 2019 Dec 21, 10:19 -0800
Just to make sure we are both talking about apples and not apples and oranges I assume you are using the plotting sheet to plot lines of position using the Saint-Hilaire intercept method.
In your example, there will not be ANY error in the LOPs or fix if you used a sheet 35 D north or 53 D north. Because you draw LOPs using azimuth and miles then as long as you use the latitude scale for miles it makes no difference what scale you use for longitude.
Draw two LOPs and where they cross is your fix. If the fix is, say, 7 miles north of your AP and 10 miles west that fix will be the same no matter what you used for longitude. The only error will be if you use the plotting sheet to take out your longitude. The latitude will be the same, ie. 7 miles north means add 7 minutes latitude to your AP.
The longitude scale needs to be at the correct scale in relation to latitude for this one use but is easy to check. One minute of longitude is equal to one mile times the cosine of the latitude. In my example 1 minute longitude equal cosine(53) or .6018 miles. So 10 miles west is 10/.6018 minutes longitude or 16.6 minutes west. If you use cos(53.5) then it is 16.8 minutes west.
The latitude will be the same.
Hope this helps.