Intercept method

The Intercept Method or Marc St. Hilaire Method

The intercept method, or Marc St Hilaire method, is used to for comparing the true zenith distance and calculated zenith distance of a heavenly object to find the intercept (position) on a position line. The line obtained is actually part of a small circle, as opposed to great circle, where any observer can stand and the heavenly object would have the same altitude in the sky. When plotting the small segment of this circle on a chart it is drawn as a straight line, the resulting tiny errors are too small to be significent.

An assumed position is used, this is usually a DR or Dead Reckoning position. This is worked out by applying the distance from the last known 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 is measured with a sextant and the time taken. The sextant angle obtained is corrected for dip (the error caused by the observers height above the sea) and refraction to obtain the true altitude of the object above the horizon. This is then subtracted from 90° to obtain the angular distance from the position directly above, the zenith. This is the True Zenith Distance of that object at that time. The true zenith distance of the object is also the distance on the earth's surface from the observer to where that object is overhead, the geographical position of the object.

Looking in the Nautical Almanac the declination (the celestial latitude), and the hour angle (the celestial longitude) are obtained of the heavenly object for the time that the sight was taken. Using this information it is now possible to calculate the zenith distance of that object from the observers DR position. This is the Calculated Zenith Distance.

If the observer is on the position circle which passes through his DR position, or actually at his DR position, the calculated and true zenith distances will be the same. If the calculated zenith distance is larger than the true zenith distance, then the DR position is further away from the geographical position of the object than the true position and vice versa.

To draw the position line on a chart the bearing from the heavenly object must either be calculated or have been observed. The bearing is the radius of the small circle and this crosses the circumference at 90°. Draw a line from the DR position either towards, if the calculated zenith distance is greater than the true zenith distance, or away from the observed object, if the calculated zenith distance is less than the true zenith distance, along the bearing. Put a mark on the chart (the intercept)and then draw a line at right angles (90°) to the bearing through this point. The observer's position is somewhere along this line.

To obtain a fix (a position) this line must be crossed with another position line either from another sight or from elsewhere e.g. a bearing of a point of land or crossing a depth contour such as the 200 metre depth line on a chart.

Until the age of satelite navigation ships took sights at dawn, noon and dusk. The morning sights were taken before sunrise during twilight when the horizon was visible but before the stars disappeared due to daylight. At dusk sights were taken after sunset but before the horizon disapeared due to darkness. Three or more stars can be observed when taking sights at dawn and dusk and crossed to give a position accurate to within a mile under favourable conditions.

The noon sight is a running fix. A sight of the sun is taken around 9 am ship's time and the position line is run up to noon. At noon a meridianal altitude is taken which obtains the latitude which is crossed with the run up earlier sight and a noon position obtained. As the noon sight is a running fix it is not as accurate as the star sights taken at dawn and dusk.