Ex-meridian is a celestial navigation method of calculating an observer's position on Earth.
The navigator measures the altitude of the Sun as close to noon as possible and then calculates where the position line lies.
This method uses an assumed longitude and calculates the latitude that a position line crosses it.
The assumed longitude is usually obtained from the DR or Dead Reckoning position run up from a morning sight taken at around 9.00 am.
This is worked out by applying the distance from that position either by log or by the estimated speed over time with the course steered.
A sight is taken, that is the distance above the horizon of a heavenly object, in this case nearly always the sun, is measured with a sextant and the exact time noted in UTC.
The assumed longitude is now added or subtracted to the Greenwich Hour Angle of the object to obtain the local hour angle, that is the difference in longitude between the DR position and the geographical position of the object.
With this information it is possible using the haversine formula to calculate the latitude where the position line crosses the assumed longitude.
The Ex-Meridian method of calculating sights is at its most accurate when the azimuth of the object is near to south or north.
The tables are a quick and easy way to correct the altitude when the object is fairly low in the sky and the observer has only missed noon by a few minutes but if noon has been missed by more than that or the sun is high in the sky it is better to work out a sight by the intercept method.