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# Marcq Saint-Hilaire method

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A method of sight reduction proposed by Captain (later Admiral) Marcq de Blond de Saint-Hilaire in an influential paper entitled ‘Calcul du point observé’ published in 1875 in the French Revue maritime et coloniale. The process described became known to the French as the méthode du point rapproché and, some years later, to the British navigation establishment as the intercept method, on which nearly all sight reduction methods one way or another are still based. The concept of the astronomical position line, a section of a circle of equal altitude small enough to be treated as a straight line, was due to Captain Sumner and is now known as the Sumner position line. Saint-Hilaire's contribution, some 70 years later, was not so much a new mathematical process as a fresh approach to the whole subject. This saw zenith distance as the same thing as geographical distance, so that a sextant observation of a celestial body in fact measures the distance from the body's geographical position in nautical miles. The concepts are straightforward. For every heavenly body at a given instant there is a spot on the earth's surface, its geographical position, where it is at the zenith. For anywhere else the body's observed altitude subtracted from 90° gives its zenith distance which determines a circle of equal altitude, with its centre at the geographical position of the body, somewhere along which the observer's position must lie.

The navigator is only interested in a small segment of this circle near his estimated position, which may without significant distortion be plotted as a straight line, the position line. The intercept is the difference between the calculated and the measured zenith distances and is plotted on the chart towards or away from the position from which the sight has been worked according to whether the observed or calculated altitude is the greater. From that point the position line is drawn at right angles.

Mike Richey

A Marcq Saint-Hilaire plot. The two position lines (in bold) are plotted at right angles to the azimuths at a distance from the D.R. corresponding to the length of the intercepts. The plot here is drawn in a notebook where one line space equals a mile. The only instrument required is a protractor

Subjects: Maritime History.

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