136 ANNUAL REPORT SMITHSONIAN INSTITUTION, 1918. 



ship's time and the corresponding Greenwich time recorded by the 

 ship's chronometers. This longitude is carried forward to the fol- 

 lowing noon by dead reckoning. The latitude at noon is determined 

 by measuring the altitude of the sun on or very near the meridian. 

 Another time sight may be made before sunset. Or if stars are 

 used at twilight one is observed east or west for longitude and an- 

 other north or south for latitude. A longitude by dead reckoning 

 ma}' be used first to derive the latitude and then with the observed 

 latitude the longitude may be obtained, though in unfavorable cases 

 more trials may be necessary. 



The newer methods, which are rapidly superseding other modes 

 of ascertaining a ship's position, are based upon the use of the Sum- 

 ner line of position. In these methods each sextant altitude of a 

 heavenly body is used to determine all it ever can actually give, 

 a line on the sea on which the ship must be situated. Such a line, 

 though in practice nearly always sensibly straight, is in reality an 

 arc of a small circle on the earth's surface having its center im- 

 mediately under the celestial object observed with a radius equal to 

 the zenith distance of that object. The Sumner line may be defined 

 by two points, in which case two longitudes or two latitudes are as- 

 sumed or based upon dead reckoning and the other coordinate com- 

 puted from the celestial observation. Or the line may be defined 

 by one point derived in this or a similar way from the celestial ob- 

 servation, together with the direction of the line, wdiich will be at 

 right angles to the direction of the body observed at the time of 

 the observation. If the Sumner point, thus used in defining the 

 Sumner line, is to be adopted as a point of departure, it is important 

 that it should be a probable position, taking advantage of the evi- 

 dence furnished by dead reckoning. In the Marc St. Hilaire method, 

 which is generally preferred, this point is the intersection of the 

 Sumner line with the vertical plane of the celestial object observed, 

 assuming for the observer the position obtained by dead reckoning. 

 Or, in other words, it is the point of the Sumner line nearest to the 

 dead reckoning position. 



Some help toward an understanding of Sumner's method will be 

 found in an account of its discovery. Sumner sailed from Charles- 

 ton, South Carolina, in November, 1837, bound for Greenock, Eng- 

 land. After passing longitude 21° W, about 800 miles west of Lon- 

 don, no observations could be made until soundings had indicated 

 that the ship was near land. About midnight of December 17, dead 

 reckoning indicated that the ship was within 40 miles of Tuskar 

 light off the Irish coast opposite Wales, and the ship stood off the 

 supposed shore to await developments. About 10 o'clock the next 

 morning an altitude of the sun was observed and the chronometer 

 time noted, but, having run so far by dead reckoning, it was plain 



