Should the star bear east of the meridian, the local sidereal time may be found by subtracting the (easterly) hour angle from the star’s right ascension or adding them as above and subtracting 24 hours. Reference to the Time Diagram, Fig. 3, will make these points clear also.
It is customary to add up the familiar logs of time sight—sec. lat., cosec. p. d., cos ½ sum, sin, remainder—divide by 2 and seek the H. A. (hour angle) in the A.M. or P.M. column of Table 44, Bowditch, using the log as a sin; but a more expeditious way is to use the sum of the logs as the log haversine in Table 45 and pick out the hour angle directly.
CHAPTER IX
Sumner Method
Every mariner who has reached a position in the profession where he is intrusted with the responsibilities of navigating a vessel is under obligation to the late Capt. Thomas H. Sumner, of Boston. This shipmaster discovered and developed the principle of the so-called Sumner or Position Lines, a principle which has proved of inestimable value and which, with its subsequent improvements, has well-nigh revolutionized the methods of navigation.
The discovery was purely accidental and for that reason is interesting. Here, in Capt. Sumner’s own words, is how it occurred: “Having sailed from Charleston, S. C., 25th November, 1837, bound for Greenock, a series of heavy gales from the westward promised a quick passage. After passing the Azores, the wind prevailed from the southward, with thick weather, after passing longitude 21° W., no observation was had until near the land, but soundings were had not far, as was supposed, from the edge of the bank. The weather was now more boisterous, and very thick, and the wind still southerly.
“Arriving about midnight, 17th December, within 40´ by dead reckoning, of Tuskar light, the wind hauled S.E. (true), making the Irish coast a lee shore. The ship was then kept close to the wind and several tacks made to preserve her position as nearly as possible until daylight, when, nothing being in sight, she was kept on E.N.E. under short sail, with heavy gales. At about 10 A.M. an altitude of the sun was observed, and chronometer time noted; but having run so far without any observation, it was evident that the latitude by dead reckoning was liable to error and could not be entirely relied upon.
“However, the longitude by chronometer was determined, using the uncertain D. R. latitude, and the ship’s position fixed in accordance. A second latitude was then assumed 10´ to the north of the last and working with this latitude a second position of the ship was obtained and again a third position by means of a third latitude still 10´ further north.
“On picking off these three positions on the chart it was discovered that the three points were all disposed in a straight line lying E.N.E. and W.S.W., and that when this line was produced on the first-named direction it also passed through the Smalls Light. The conclusion arrived at was that the observed altitude must have happened at all three points, at the Smalls Light, and at the ship at the same instant of time. The deduction followed that, though the absolute position of the ship was doubtful, yet the true bearing of the Smalls Light was certain, provided the chronometer was correct. The ship was therefore kept on her course, E.N.E. and in less than an hour the Smalls Light was made bearing E. by N. ½N. and close aboard. The latitude by D. R. turned out to be 8´ in error.”
If the captain had worked more time sights using different latitudes, he would have added new positions on the line to which he refers, each placed upon it according to the latitude used. Had he cared to pursue his experiments farther, and used latitudes very wide of his dead reckoning position, he would have discovered that the resulting positions instead of lying in a straight line, were in a curve and an arc of a circle.