NavList:

I first became interested in meridional parts back in the 1970s. I purchased a copy of the 1964 Admiralty Manual of Navigation volume II and read that meridional parts (MP) were calculated by an integral. Fast forward to today and I now follow the Australia/NZ to Santiago air route. As it is nearly east-west it is probably not the best of routes to study mercator sailing but never the less a study of it has proved interesting. I discovered that the anti-Gudermannian function is the meridional part for a sphere. I also realised that when looking at a meridional parts table it is important to know whether the table was computed for the sphere or a spheroid. Here are some comments. I will use 10° as the latitude.

Meridional parts are used to construct Mercator charts and to calculate Mercator sailings. They deal with distance on the chart, NOT distance on the earth. Probably of no practical use in this era of electronic computers?

• 1599 Wright. MP for the sphere.
• Norie 1836 Table III for the sphere.
• In 1909 the Smithsonian published a document called the Table of Hyperbolic Functions. Table VII is called the Anti-Gudermannian and is meridional parts for a sphere. For 10° the mp is 603.7.
• In 1906 Raper's tables included mp for the sphere and a table called "Reduction of Latitude.". For the sphere mp = 603. The reduction for a compression of 1/293 was 4' so the mp for the spheroid was 599.
• Norie 1918. MP = 603.7 so is for the sphere. I cannot find a table giving reductions to the spheroid.
• Inman 1932 MPs for sphere with a table for converting to the spheroid.
• 1938 Hughes Table for Air and Sea Navigation Clarke 1880 Spheroid.
• Norie 1943. Two tables, One for the sphere and one for the spheroid.
• Burton 1947 Spheroid
• Norie 1952. Two tables. One for the sphere and one for the spheroid.
• Bowditch 1958. MP for spheroid and conversion table (international, clarke 880 and sphere).
• Norie 1963. MP for the spheroid.
• Bowditch 1995 Spheroid.
• Norie 1981. Spheroid

David C