He is best known for developing the celestial navigation method known as the Sumner line or circle of equal altitude.
[1]: 96 Shortly after graduating, he married and ran off to New York with a woman with whom he had become entangled but the marriage was short-lived and they were divorced three years later.
[1]: 96 On November 25, 1837, Sumner sailed from Charleston, South Carolina, bound for Greenock, Scotland, and it was during that voyage, while entering Saint George's Channel and the Irish Sea, that he discovered the principle upon which his new method of navigation was based.
His state gradually deteriorated and in 1865 he was committed to the Lunatic Hospital at Taunton, Massachusetts, where he died in 1876 at the age of 69.
On December 17, 1837, as he was nearing the coast of Wales, he was uncertain of his position after several days of cloudy weather and no sights.