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

**Ex-meridian sights**

**From:**Russell Sher

**Date:**2001 Feb 12, 6:51 AM

I have a question about the tables used to correct ex-meridian sights: In bowditch (1995) tables 24 and 25 are used for ex-meridian altitudes (previous editions used tables 29 and 30 I believe). Table 24 gives the amount by which the altitude of a body changes per minute of time either side of meridian transit. This change (called the factor 'a' and is in seconds of altitude) is then entered into table 25 to give the actual corection for the altitude. This next table is based on the formula: Correction = a X t X t/60 (in words: 'a' multiplied by 't' squared then divided by 60). Where 'a' is extracted from table 24 and 't' is the difference in time between the observation and meridian passage The divide by 60 is just for the seconds/minute relationship since 'a' is in seconds and 't' is in minutes. My question is: Why is t squared ?? why is the formula not simply: Correction = a X t/60 ?? (since 'a' is said to be the change per minute; see below...) regards Russell Extract from Bowditch describing table 24, from which the 'a' factor is extracted... Table 24. Altitude Factors - In one minute of time from meridian transit the altitude of a celestial body changes by the amount shown in this table if the altitude is between 6� and 86�, the latitude is not more than 60�, and the declination is not more than 63�. The values taken from this table are used to enter table 25 for solving reduction to the meridian (ex-meridian) problems. The table was computed using the formula: a = 1.9635" cos L cos d csc( L ~ d )