Original Sumner lines introduced to the LOP
To the editor: A little more than a century and a half ago, a young American shipmaster ran close-hauled in heavy gales near the end of a voyage from Charleston, S.C., to Greenock, Scotland. He knew he lay dangerously close to the Irish coast, although he was not ebactly sure how close a common enough state of affairs for mariners of that era in a winter sea.
But Capt. Thomas Hubbard Sumner was no common mariner. Harvard educated and a brilliant mathematician, he would discover within the next 24 hours through a combination of intuition and intellect a means of determining his position that would revolutionize the practice of celestial navigation.
Sumner had conned his ship some 700 miles in thick weather without a sun sight. On the morning of Dec. 18, 1837, a break in the clouds enabled him to obtain a single observation. The wind, he recalled, was southeast and boisterous. The rock-ribbed bays east of Dungarvan and Helvick Head a lee shore bore somewhere northwest.
Sumner worked a traditional computation for longitude, which put his ship nine nautical miles east of her dead-reckoning position, 51 degrees, 37' N; 6 41' W. As he was obviously well aware, improvement in chronometer reliability had elevated the so-called time sight to center stage of 19th-century celestial practice. Factoring in measurements of the sun's declination, sextant altitude and the DR latitude, it employed spherical trigonometry to provide time at the ship. A simple comparison with the Greenwich-regulated chronometer gave time difference converted to arc: longitude east or west of the prime meridian.
But Sumner also knew that the time-sight computation had a major flaw. It was only as good as its key ingredient, the latitude. A small error in latitude could mean a huge and potentially fatal error in longitude.
Sumner now had the inspiration that changed irrevocably the way seamen navigate. He reworked the longitude problem two more times, using the same sextant altitude but substituting assumed latitudes 10 and 20 miles farther north. Plotting the three positions, he was startled to find he could join the points in a ruled line a line, incidentally, whose ENE bearing would guide him to a safe landfall.
In the book he wrote describing his discovery, Sumner reasoned that "the observed altitude must have happened at all three points, and ? at the ship, at the same instant of time." From this he concluded that his ship had been located on a vast circle, or arc, of equal altitudes whose distant center was the sun's geographic coordinates declination and hour angle reformulated as latitude and longitude and that any small segment of the circle could for all practical purposes be treated as a straight line. To later generations of navigators the linear projection became known as a Sumner Line. Today, of course, we call it a line of position (LOP), with the intersection of two such lines yielding a positional fix of pinpoint accuracy.
Aside from his momentous feat of navigation, details of Sumner's life are sketchy. What we do know is that he was born in Boston in 1807, took his degree from Harvard in 1826 and shipped immediately for China as an ordinary seaman. He rose quickly to command. His book, A New and Accurate Method of Finding a Ship's Position at Sea, was published to professional acclaim in 1843. Unfortunately, his final years were tragic. Sumner died, insane, in 1876, at the age of 69.
Alan Littell, a long-term contributor to Ocean Navigator, is a self-syndicated travel journalist. He lives in Alfred, N.Y., and Athens, Greece.