# Sumner Method

## Sumner method

[′səm·nər ‚meth·əd]
The establishing of a line of position from the observation of the altitude of a celestial body by assuming two latitudes (or longitudes) and calculating the longitudes (or latitudes) through which the line of position passes; the line of position is the straight line connecting these two points (extended if necessary).

## Sumner Method

a method of determining the geographic latitude and longitude of an observer’s position from the measured altitudes of celestial bodies through the establishment of celestial lines of position. The method is named after the American sailor T. Sumner, who in 1843 proposed using straight lines of equal altitude on a marine chart to determine position. Such lines are often called Sumner lines.

The position of a ship or airplane can be determined from observations of the altitudes of two or more stars by constructing circles of equal altitude. Such a circle is the locus of the points on the earth’s surface at which the altitude of the celestial body at the given moment is equal to the observed altitude (seePRACTICAL ASTRONOMY). One of the points of intersection of the circles on the globe is the sought-for position. It is not difficult to select the necessary point because the approximate place of observation is usually known. In the Sumner method, the short arc of the circle of equal altitude close to the position of the ship is replaced by the straight line of equal altitude tangent to the circle. This straight line is sometimes called a celestial line of position. On a marine chart in the Mercator projection, which preserves the magnitudes of angles, the line is perpendicular to the direction to the celestial body.

Various methods have been proposed for computing the quantities involved in the establishment of celestial lines of position. Important contributions were made, for example, by Sumner and, in 1849, by the Russian sailor M. A. Akimov. The method used today was set forth by the French sailor M. Saint-Hilaire in 1875; it is equally convenient for celestial bodies at any azimuth (seeNAUTICAL ASTRONOMY). The sought-for position is determined by the intersection of two position lines (to provide a check, additional position lines may also be used).

### REFERENCES

Sumner, T. Novyi i lochnyi sposob opredeliat’ mesto sudna v more po proektsii na merkatorskoi karte. St. Petersburg, 1863. (Translated from English.)
Belobrov, A. P. Morekhodnaia astronomiia. Leningrad, 1954.
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