is required in the course and distance run between the times of observation.
This method of finding both latitude and longitude at the same time is commonly known as “Sumner’s” method from the publicity given to it in 1847 by the publication of an excellent pamphlet on the subject by a master of that name in the American mercantile marine, although in a modified form it was practised at a much earlier date in the British navy under the name of “cross bearings of the sun.” Prior to the publication of azimuth tables in 1866 the calculation was more lengthy and troublesome, the work being practically doubled.
We have taken an illustration from observations of the sun, but the method is obviously applicable to all heavenly bodies provided they are so situated that the arcs drawn will intersect at a good angle; this in twilight or at night-time is readily done by selecting two heavenly bodies whose bearings differ considerably, and in such cases the small complication of allowing for the run of the ship is often obviated by making the observations simultaneously. The armillary sphere or star globe is useful in selecting objects suitably situated.
The principle of Sumner’s method has of recent years received a very important and valuable development under the name of the “new navigation.” In this method, originally proposed by Marc St Hilaire, a comparison is made between the altitude of a heavenly body as actually observed and that calculated from the supposed position of the ship. For instance, the position of an observer at the instant of observing a (true) altitude of the sun of 40° 10′ must be somewhere on a portion of the circumference of a circle (usually of such size that the portion considered may be represented on a chart by a straight line) having its centre in latitude equal to the sun’s declination, and in longitude equal to the Greenwich apparent time at the instant, the radius of such a circle being equal to the sun’s zenith distance of 49° 50′. If at the same time the true altitude of the sun is from the estimated position of the ship calculated to be 40° 5′, it is evident that the greater observed altitude must be owing to the ship being nearer to the centre of the circle than was supposed, and a line of position drawn through the estimated position at right angles to the bearing of the sun must be transferred parallel to itself through a distance of 5′ towards the direction of the sun’s bearing. The second line of position, obtained when the sun’s bearing has altered some 25°, is dealt with in a similar way, and the intersection of' the two lines so obtained gives the position of the ship at the time of second observation. This mode of procedure enables all observations, whether near or far from the meridian, to be similarly dealt with; in all cases the altitude the heavenly body should have is computed and compared with what it actually has. The practice of problems such as the foregoing is greatly facilitated by the extended means of finding at any moment the azimuth or true bearing of a heavenly body. When the azimuth was only required for the determination of compass error, the valuable tables from which the computed results could be obtained by inspection were limited to those cases of most practical importance, but from the ingenious and simple graphical form known as Weir’s azimuth diagram azimuths of all heavenly bodies, whose declinations extend from 60° N. to 60° S., can be obtained during the whole time they are above the horizon, thus greatly facilitating the laying down lines of position.
A careful record of everything pertaining to the navigation of the ship, with the results of all observations and calculated positions, is kept in the ship’s log, an official book of great importance, a rough original of which is kept on deck with entries made in it of all such events at the time of their occurrence. A copy of the headings of a page of this as transferred into the official log is here given:
| Hour. | Knots | Tenths of Knots. |
Course. | Wind. | Weather. | Deviation. | Barometer. | Thermometer | Temperature of Sea. |
Remarks. | |
| Direction. | Force. | ||||||||||
The course entered here is that which would be indicated by the “standard” compass, of the ship (placed in the most favourable magnetic position on board); that actually steered by is the one most conveniently seen by the helmsman. Comparisons between the latter and the “standard” are frequently made, their indications generally varying somewhat owing to the difference of deviation in different positions on the ship. The compass card is usually graduated into points and degrees, but the course is always estimated in degrees. The speed is ascertained from the indication of the patent log, the hand log being generally only used as a rough check on this. Wind direction and force are the result of estimation; as the speed and course of the ship so greatly affect the apparent direction and velocity no practical anemometer for use on board ship exists. Wind force is estimated in terms of what is known as the “Beaufort” scale, based on the supposed amount of sail a vessel could carry at the time. The height of the mercurial barometer is carefully read at the end of each watch, as also is the thermometer; the more sensitive aneroid barometer is kept in a very accessible position and, more frequently referred to by the officer of the watch. When navigating in localities and during seasons at which circular storms or hurricanes may be expected (as known from the Barometer Manual) the barometer is anxiously and frequently watched, and at all times its indication is compared with that normally experienced in the locality traversed as shown on the barometer charts, due allowance being made in the tropics for the ordinary daily movement. All observations relating to ocean meteorology are of great service in the compilation and improvement of wind and current charts, and in many ships more extensive meteorological journals are voluntarily kept on forms supplied by the Meteorological Office. A knowledge of the temperature of the surface of the sea is often of great practical use in navigation as giving warning of change in direction of the surface ocean current, especially in localities where there exist near to each other warm and cold currents setting in different directions, as, for instance, near the edge of the Gulf Stream. As an indication of the vicinity of ice such observations are usually much less trustworthy. On the completion of the calculations giving the ship’s position at noon each day the results are tabulated in the ship’s log on the following form:
| Course made good. | Distance. | Latitude. | Longitude. | Variation Allowed. | True Bearings and Distance. | |
| Current. | Made Good. | Through the water. | D.R. Obs. | D.R. Obs. | ||
The course and distance made good each day are calculated by trigonometry between the best determined positions at two successive noons, such positions in fine weather being always those determined astronomically, and the current being considered the difference in the positions at noon as determined astronomically and as calculated by dead reckoning since the previous noon; such differences, however, obviously include the errors of all kinds. The latitude and longitude found by dead reckoning are entered under that heading (D.R.). The astronomical positions of latitude and longitude (entered as “obs” or “by observation”) are very seldom both determined at noon, but are carried up or back to that instant by calculation from the intervening dead reckoning. The variation allowed is taken from the published variation chart, on which the latest results of such observations are embodied at intervals of about ten years with the annual changes (as far as known) in different localities, thus enabling the navigator to obtain its value at intermediate dates. Finally the course and distance are calculated from the position of the ship at noon to either the port of destination or some prominent position or danger near to which the vessel must pass. This is entered under the heading “true bearings and distance.”
Authorities.—The following list of some writers of navigation whose works have not been already mentioned may be found useful to refer to: Thomas Addison, Arithmetical Navigation (1625)—he was the first to apply logarithms; Antonio de Najera (Lisbon, 1628) follows Nuñez and Cespedes, but corrects the declination of sun and stars; Sir R. Dudley, L’arcano del mare (1630–1646, 2nd ed., Florence, 1661)—too ponderous for the use of seamen; Sir Jonas Moore (1681)—one of the best books of the period; William Jones (1702)—a useful compendium containing trigonometry applied to the various sailings, the use of the log, and tables of logarithms; Pierre Jean Bouguer, Traité complet de la navigation (folio, 1698)—good but too large; Manuel Pimental, L’Arte de navegar (Lisbon, 1712); Pierre Bouguer, jun., Nouveau traité de navigation (1753)—without tables, published at the request of the minister of marine, improved and shortened in 1769 under the superintendence of the astronomer Lacaille; Nathaniel Colson, The Mariner’s New Calendar (1735)—a good book; Seller, Practical Navigation—a book very popular in its time (there was an edition as late as 1739); Samuel Dunn published good star charts and tables of latitude and longitude (1737), and framed concise rules for many problems on navigation (published by the board of longitude); John H. Moore, The Practical Navigator and Seaman’s New Daily Assistant (1772)—very popular, and generally used in the British navy—the 18th and 19th editions (1810,1814) were improved by J. Dessiou; W. Wilson (Edinburgh, 1773)—a treatise of good repute at the time; Samuel Dunn, New Epitome of Practical Navigation, or Guide to the Indian Seas (1777)—for the longitude he depends chiefly on a variation chart from observations by East Indiamen, and he still makes no mention of the Nautical Almanac or of parallel rulers; Samuel Dunn (probably a son of the last named, 1781) is the last writer who gives instructions for the use of the astrolabe: he also wrote on “lunars” (1783, 1793), a name which was generally adopted about this time, and published an excellent traverse table (1785), and Daily Uses of the Nautical Sciences, (1790); Horsburgh, Directory for East India Voyages (1805); A. Mackay, The Complete Navigator (about 1791); 2nd ed. 1810)—there is no instruction for finding longitude by the chronometer. Kelly, Spherical Trigonometry and Nautical Astronomy (1796, 4th ed., 1813)—clear and simple; N. Bowditch, Practical Navigator (1800)—passed through many editions and is now (in a revised form) the official text-book of the United States navy; J. W. Norie, Epitome of Navigation (1803, 21st ed. 1878)—still a favourite in the mercantile marine from its simplicity, and because navigation can be learned from it without a teacher; T. Kerigan, The Young Navigator’s Guide to Nautical Astronomy (1821); Inman, Epitome
of Navigation (1821)—with an excellent volume of tables, formerly