# NavList:

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

**Re: Meridional Distances**

**From:**Sam Chan

**Date:**2002 Sep 17, 21:51 -0700

The formula in Bowditch uses a series expansion. A closed form derived in Williams is M(psi) = a * Ln (Tan(pi/4 +abs(psi)/2)) - (a e)/2*Ln{(1+e*sin(abs(psi)))/(1-e*sin(abs(psi)))} where psi is the Geodetic Latitude a is the length of the semi-major axis e is eccentricity. For those who really want to know, the equation for the Meridional Distance (Distance along the arc of a meridian on the surface of an ellipsoid) as given by Williams is: L(psi) = integral from 0 to psi of (a[1-e^2])/sqrt([1-e^2 sin^2(psi)]^3) d(psi) No closed form solution to this integral can be had so a numerical solution must be used. Sam Chan ----- Original Message ----- From: "Chuck Taylor"To: Sent: Tuesday, September 17, 2002 9:20 AM Subject: Re: Meridional Distances > > > > Although I have tables accurate to 2 decimal places for the Meridional > > Parts, the Meridional Distances come only in whole degrees, so need to > > be interpelated for in-between values. > > Peter, > > Bowditch has tables of Meridional Parts to quite a number of decimal places. > The method for computing distances using Meridional Parts is called "Mercator > Sailing" and is also described in Bowditch. > > The introduction to the tables in Bowditch gives a formula for computing > Meridional Parts. I have programmed this into a calculator. One could also > program it into a spreadsheet. If memory serves me correctly (I'm away from my > home library) there is a typo in the formula in Bowditch 95, but Bowditch 80/84 > Volume 2 has it right. > > Best regards, > > Chuck Taylor > Everett, WA, USA