a rule given for clearing the distance, called Dunthorne's improved method, is remarkably short. Maskelyne's rule for finding the latitudes by two altitudes and the elapsed time is also good. The third edition of the Tables was issued in 1802.

attempt to give lunar distances. In the English Nautical | especially is an improvement on those by Lyons and Dunthorne, and Almanac for 1767 we find everything necessary to render it worthy of confidence, and to satisfy every requirement at sea. The great achievement was that of giving the distance from the moon's centre to the sun, when suitable, and to about seven fixed stars, every three hours. The mariner has only to find the apparent time at ship, and clear his own measured lunar distance from the effects of parallax and refraction (for which at the end of the book are given the methods of Lyons and Dunthorne), and then by simple proportions, or proportional logarithms, find the time at Greenwich. The calculations respecting the sun and moon were made from Mayer's last manuscript tables under the inspection of Maskelyne, and were so continued till 1804.2 The calculations respecting the planets are from Halley's tables, and those of Jupiter's satellites from tables made by Wargentin and published by Lalande in 1759 (except those for the fourth satellite). The original Nautical Almanac contained all the principal points of information which the seaman required, but the great value of such an authentic publication to the whole astronomical world led soon to a considerable increase to its contents. As much of this was unnecessary for the ordinary requirements of navigation, since 1903 it has been issued in twographer of the Admiralty. This post has since been occupied by a forms, the larger for observatory purposes, the smaller for the class for whom it was originally intended.

Various useful rules and tables were appended to early volumes of the Almanac. Thus that for 1771 contains a method and table for determining the latitude by two altitudes and the elapsed time (first published by Cornelius Downes of Amsterdam in 1740). At the end of the Almanac for 1772 Maskelyne and Whichell gave three special tables for clearing the lunar distance; still their rule is neither short nor easily remembered. An improvement of Dunthorne's solution is also given. In the edition for 1773 a new table for equations of equal altitude was given by W. Wales. In those for 1797 and 1800 tables were added by John Brinkley for rendering The plan of the Nautical Almanac was soon imitated by other nations. In France the Académie Royale de Marine had all the lunar distances translated from the British Nautical Almanac for 1773 and following years, retaining Greenwich time for the three-hourly distances. The tables were considered excellent, and national pride was satisfied by their having been formed on the plan proposed by Lacaille. They did not imitate the mode given for clearing the lunar distance, considering their own better. Though the Spaniards were leaders in the art of navigation during the 16th and 17th centuries, it was not till November 4, 1791, that their first nautical almanac was printed at Madrid, having been previously calculated at Cadiz for the year 1792. They acknowledge borrowing from the English and French. The excellent Berlin Astronomisches Jahrbuch began to appear in 1776, the American Ephemeris in 1849. These two ephemerides and the French Connaissance des temps are independent and valuable works.

the calculations for double altitudes easier.

A book of Tables Requisite to be Used with the Nautical Ephemeris was published by Maskelyne at the same time as the first Almanac. and ten thousand copies were quickly sold. A second edition, prepared by Wales, appeared in 1781, an octavo of 237 pages, in the preface of which it is stated that it contains everything necessary for computing the latitude and longitude by observation. There are in all twenty-three tables, the traverse table and table of meridional parts alone being deficient as compared with modern works of the kind; dead-reckoning Maskelyne did not touch. He gave practical methods for working several problems; that for computing the lunar

1 The French nautical almanac or Connaissance des temps appeared under letters patent from the king, dated 24th March 1679seventeen years before the first issue. The following is a literal translation of its advertisement: "This little book is a collection of holy days and festivals in each month. The rising and setting of the moon when it is visible, and of the sun every day. The aspects of the planets as with respect to each other, the moon and the fixed stars. The lunations and eclipses. The difference of longitude between the meridian of Paris and the principal towns in France. The time of the sun's entrance into the twelve signs of the zodiac. The true place of the planets every fifth day, and of the moon every day of the year, in longitude and latitude. The moon's meridian

the time of high water, as well as for the use on passage, for finding by moonlight." A table of refraction. The equation of time [this table is strangely arranged, as though the clock were to be reset on the first of every month, and the explanation speaks of the premier mobile']. The time of twilight at Paris. The sun's right ascension to hours and minutes. The sun's declination at noon each day to seconds. The whole accompanied by necessary instructions."

2 Mayer's tables were printed at London under Maskelyne's superintendence in 1770.

The publication of the Requisite Tables'met a great want, and the existence of such accurate and conveniently-arranged mathematical general use of many refinements which had been previously neglected. tables for the special purposes of nautical calculations led to the more They formed the original of many subsequent and greatly extended collections, of which those by J. W. Norie are the more generally used in modern times in the mercantile marine, and the very accurate and comprehensive tables by James Inman (originally published in 1823) are constantly used in the British navy. Until the middle of the 17th century mariners generally employed small collections of Dutch charts, known as waggoners from Waghenair, the name of a celebrated Dutch hydrographer in 1584. 1671 appeared the English Pilot by John Sellers, who is styled the Hydrographer Royal." It forms a collection of rude sketches of the coasts of England, the North Sea, France and Spain, with safling directions, and on its appearance the importation of Dutch charts was prohibited. Private enterprise, for many years after that, supplied both the British navy and the British mercantile marine powerful patronage of the East India Company, whose hydrographer with constantly improving charts, especially latterly, under the (Alexander Dalrymple), in 1795, was selected as the first hydrosuccession of distinguished naval officers under whom have grown up a large school of able nautical surveyors, the results of whose labours are now published in the well-known Admiralty charts. Prior to the issue of charts by the Admiralty, the instructions to masters of vessels in the British navy enjoined them to " provide such charts and instruments as they considered necessary for the safe navigation of the ship," while on the completion of a voyage of discovery it was customary for the results to be published for the Admiralty by private firms.

The establishment of the Admiralty Hydrographic Office in tion. On the 12th of August of that year an order in council 1795 marked a great step in the advancement of the art of navigaplaced all such nautical documents as were then in the possession of the Admiralty in charge of Dalrymple, whose catalogue, compiled for the use of the East India Company in 1786, contained 347 charts between England, the Cape, India and China; thus the germ of the present hydrographic department was established. The expense was then limited to £650 a year. The first official catalogue of Admiralty charts was issued in 1830, the total number being then 962.

After the close of the long devastating war in 1815 both trade and science revived, and several governments besides that of Great Britain saw the necessity of surveying the coasts in various parts of the globe; the greater portion of the work fell to the English hydrographical department, which took under its charge nearly every place where the inhabitants were not able to do it for themselves. Since that time its career of usefulness has steadily developed, and it not merely undertakes the constant improvement of the charts of the whole world, but periodically issues for the use of the seafaring community a vast amount of most accurate and practical nautical information on the various closely allied subjects of navigation, tides, compass adjustment and ocean meteorology.

A knowledge of the times and heights of high and low water and the directions of the tidal streams due to those phenomena are in many parts of the world (and especially round our own coasts) of vital importance to navigation. The theory of the tides was first laid down by Newton and Laplace, and in Phil. Trans., 1683, there is an account of Flamsteed's tide table for London Bridge, which gave the times of each high tide on every day in the year. For a long subsequent period empirical tide tables for a few places in England were published by private individuals, but in 1832 the researches of Dr W. Whewell and Sir J. W. Lubbock enabled official tide tables to be issued by the Admiralty. These have steadily advanced in detail and accuracy, being now in many cases based on continuous tidal observations for a whole lunar period of 18 years, and represent the practical epitome of our knowledge of the tides and tidal currents of the whole world. The formulae and tables on which these predictions are based are given in the introduction to each annual volume (see TIDE).

MODERN NAVIGATION

Having thus sketched the progress of the art of navigation from an early period to the present time, we will now describe the modern methods by which it is brought into practical use,

referring our readers for more technical information to the professional text-books enumerated at the end of this article. The great development in both size and speed of modern ships enormously increases the responsibilities of those who command and navigate them, and has led to a careful examination of the existing modes of determining a ship's position at all times by day or night, both when in sight of land and on the open ocean. An examination of the present text-books on the subject of navigation shows how problems and methods which were formerly considered chiefly as theoretical exercises have now, from the altered conditions of the navigation of very fast ships, become methods of frequent practice, while corresponding improvements have been made in the instruments, such as compasses, charts and chronometers, by the aid of which more satisfactory results are now attained. Much has also been done to advance the study of this and its numerous allied subjects by the development of the Royal Naval College at Greenwich and the United Service Institution; also by the establishment of shipmasters' societies (of which the well-known society in London is typical), where during the year valuable papers are read and useful discussions take place among those actually carrying out the practice of navigation.

In planning out in advance a long ocean voyage the experienced navigator would first, by laying down the track from port to port on a great circle chart, ascertain the shortest route between them, remembering that the greatest saving in distance over other routes is when the ports are far apart in longitude and both in high latitudes of the same name. On examining such a track in conjunction with the wind and current charts it will be seen what modifications the intervention of land, unfavourable currents or winds, ice or unduly high latitude render necessary, and such modified route would be finally adopted subject to possible change as the voyage progressed. The judgment formed on the best route to follow would also be largely influenced by the remarks in the volumes of Sailing directions or " Pilots " relating to the region about to be traversed, while among the many excellent modern publications of the Hydrographic Office of the Admiralty perhaps the Ocean Passage Book is one of the most generally useful, since, when used in combination with the admirable charts of suggested full-powered and auxiliary tracks, it very greatly assists all navigators in planning out a successful voyage. Finally the intended route would be transferred from the great circle chart to one on Mercator's projection, which is the more convenient for purposes of navigation since in constructing the former for the sake of simplicity a projection of the coast's surface is adopted on which great circles are correctly shown as straight lines (gnomonic), while for practical purposes in navigation such a representation on which a ship's track when steering a continuous course (technically termed a rhumb line) is truly shown as a straight line (Mercator) is the most convenient, although in high latitudes giving a very distorted representation of the surface depicted. It is well to remember that on great circle charts rhumb lines become curves and great circles straight lines, and, vice versa, on Mercator charts, the rhumb line on each projection being that nearer to the equator, all meridians and the equator on both projections are shown as straight lines.

collision between outward and homeward bound ships, has been
successfully carried out in the North Atlantic.
The leading
transatlantic steamship companies now agree to follow great
circle routes from the Irish coast to points on the Banks of
Newfoundland, which vary somewhat in position with the
season of the year, but are published in advance. These " lanes "
being avoided by sailing vessels, risks of collision are materially
lessened.

Having thus planned the most desirable general track to pursue, three methods are employed to ascertain the position of the ship at any time during such voyage: these are (1) projecting the track on charts; (2) simple trigonometrical calculations where the data are the course steered and distance run; and (3) astronomical observations, which form an entirely independent method.

Of these the first is the least trustworthy, owing to the usual difficulties attending accurate graphic methods and the small scales on which ocean charts are necessarily drawn. When near the land the larger scale coast charts are used, and in the approaches to harbours still larger scale plans give increasing accuracy to this record of a ship's position. Index charts of all parts of the world are provided, by referring to which the navigator ascertains which chart or plan to employ, always preferably using that on the largest scale.

On leaving harbour, and while near the coast, the position is not found by calculation but by frequently observing (when a variety of objects is in sight) (1) simultaneous sextant angles between suitably situated objects subsequently laid down on the chart by a station pointer; (2) simultaneous compass bearings of two or more objects (technically known as cross bearings); or (3) a combination of both methods by employing one bearing and one angle. All such methods are capable of considerable accuracy if the observations are made simultaneously. Should only a small number of objects, or sometimes only one, be visible (às frequently occurs at night) other and rougher methods are practised, depending upon the change of bearing of an object while a certain distance in a certain direction is traversed by the ship, such knowledge being based in many cases on an estimate of the action of the tide. When a ship is steaming at the rate of 20 knots the navigator remembers that a mile is passed over in three minutes, and that if in sight of land and fixing positions by objects on shore, it is essential to adopt, some rapid method; otherwise when laid down on the chart the position shows where the ship was, and not where she is. This difficulty has led to the more general use of methods of obtaining positions by angles instead of bearings, and laying then down on the chart by the aid of the station pointer. Many advantages accrue from this, as the observer is not restricted in position on board, as is the case when using the compass, and especially if a double sextant (having two index glasses and one horizon glass) is employed two angles can be measured simultaneously, the result on the chart being very rapidly arrived at. An ingenious combination of sextant and station pointer in one has been proposed, and most simply carried out by attaching vertical sights to the legs of a station pointer, which is put on a suitable horizontal stand, and the legs moved until the sights are in line with the objects observed. To assist the navigator in the choice of suitable objects between which to measure the angles, a very useful pamphlet is issued by the Admiralty, from the diagrams in which it can be seen at a glance which combination of objects in sight gives the most favourable result, always remembering as a broad principle that nearer objects are more suitable than distant ones, and that the accuracy of position determined depends on the relative distances of the objects as well as on the magnitude of the angles between them. In these circumstances, which render these rougher methods those only available, and especially in hazy weather in many A method of drawing approximate great circles directly known localities (such as the English Channel), a continuous on Mercator charts was proposed by Airy in 1858, and is some- line of deep sea soundings at fairly even distances apart affords times very useful. The excellent idea, originally suggested an additional verification of position, remembering that only by M. F. Maury, of establishing steam "lanes" in localities an occasional sounding might prove very misleading. where there is much ocean traffic, so as to minimize the risks of. The chronicle of progress in the art of navigation would be very

Ships rarely steer on great circles, which would generally theoretically involve continually altering course, but a series of chords of such circles are described of lengths such as involve a practical change of course of one or two degrees on the completion of each.

Great circle charts are very useful for drawing what is known as a composite track where if the great circle route would lead into too high a latitude the shortest route to and from the highest desirable parallel is readily laid down, the intervening track being pursued on that parallel.

"

incomplete without reference to the extended use of Lord | tions of moon, stars and planets, the navigator in most parts` Kelvin's sounding machines, either in the original form, where of the world need seldom proceed far without the means of the increased pressure at different depths is recorded by dis- astronomically rectifying his position either in latitude, longitude coloration of chemical tubes, or in the later form known as the or both at the same time. depth recorder," where similar results are obtained by the automatic record of the position of a piston forced upwards in a tube by this increased pressure. Very satisfactory results can be obtained at speeds of 15 or 16 knots, enabling that great safeguard of navigation in many places, viz. a continuous line of soundings, to be accurately and rapidly obtained. In connexion with this should be mentioned a most ingenious invention known as the "submarine sentry," which on being set for any desired depth and towed overboard remains at that depth whatever the speed of the ship may be. On striking bottom it at once floats to the surface and rings a warning bell. Such an instrument is of obvious value in ships where, owing to the small number of available men, it is difficult to maintain a continuous line of soundings. To avoid an unnecessarily wide détour in rounding points and shoals, extensive use is now made of both horizontal and vertical danger angles; the former is the angle on the arc of a horizontal circle passing through a point at the required distance from the danger, and through two previously selected, easily recognized, fixed objects. Should circumstances enable the selection to be made of an angle of about 90°, the ship by continually measuring the angle may be steered on the arc of such a circle with great precision, and may even be safely taken through a channel between two dangers. The vertical danger angle enables similar results to be attained by measuring the vertical angle subtended by a known height; but except where the selected object is one whose height is well determined, such as a lighthouse, this method is not so trustworthy as the former.

Before losing sight of land the latitude and longitude of the last well-determined position found by the methods referred to is taken from the coast chart, transferred to the ocean or small scale chart, and considered to be the "departure" or starting-point of the ocean voyage, and from that point the course and distance run by the ship is laid down, being rectified on every occasion when the position is more accurately determined by astronomical means. To obviate the inevitable inaccuracies attending this graphic method and as a corroboration of the ship's position, the changes of latitude and longitude involved in each alteration of course are daily calculated by plane trigonometry, such calculations being materially abbreviated by the use of the Traverse Table, which is a tabulated expression of the solutions of right-angled plane triangles.

The foregoing modes of keeping account of a ship's position are technically known as dead reckoning." The general introduction of compasses with short needles and slow periods of vibration has done very much towards improving the accuracy with which a ship's "dead reckoning." is kept.. The original model of these was that patented by Lord Kelvin in 1876, and since adopted in the British navy as the standard. In this instrument we have a compass specially designed to enable the principles of compensation or correction proposed by Sir G. B. Airy in 1837 to be accurately carried out, while its slow period of swing renders it in all circumstances extremely steady.

The record of distance run is always obtained from the patent log, usually in the form of the Cherub or Taffrail log introduced in 1878. The common or hand log has ceased to be regarded as anything but the very roughest of guides, and the patent log in its original form, in which it recorded the revolutions of a small screw towed by the ship, does not give satisfactory results at great speeds, nor can anything more favourable be said of those forms where pressure on known arcas is employed. The revolutions of the engines, with due allowance made for the condition of the ship's bottom, afford now perhaps the best means of estimating speed (see LOG).

Astronomical observations afford the most accurate means of ascertaining positions at sea, other methods (dead reckoning) being only relied upon when the weather does not admit of the practice of these, though by utilizing twilight and night observa

The practical problems involved are precisely those employed at astronomical observatories, but it is not possible to attain similar accuracy of results, for though the sextant (the instrument always employed at sea in making such observations) is capable of marvellous accuracy, yet, as practically all such observations depend directly upon altitudes measured above the sea horizon, the uncertainty and variability of the true position of this, due to the changing effects of refraction, much affect observations made at any one time. This error in practice is greatly reduced by methods of combining several observations made at different times and using their mean or average result. A notable feature of the progress of the art of modern navigation is the greatly increased practice of star navigation, and many of the supposed difficulties of night observations are found to be removed by experience. Determinations of positions at sea by twilight observations, when the brighter stars become visible while the horizon is still well defined, are probably the most accurate means we possess; and the careful navigator, by combining for latitude stars passing north and south of the zenith, and for longitude those near the prime vertical both east and west, can generally depend upon a good result, especially if suitable stars can be found for each pair at about the same altitudes. For these purposes the armillary sphere is extremely useful: this is a small celestial globe on which are depicted the principal stars visible to the naked eye. On elevating the pole to the approximate latitude of the observer, and turning the sphere until the sidereal time is under the fixed meridian, a correct representation of the heavens at the time of observation is obtained; the stars are then easily identified by their bearings and altitudes. This valuable instrument is not merely useful when at twilight, only a few of the brighter stars being visible, the constellations to which they belong are difficult of recognition, but it enables arrangement to be made in advance for such observations as are desired to be taken during the night. By marking in pencil on the globe the positions of the planets in right ascension and declination, the same sphere is also available for their identification. The heavenly bodies commonly observed at sea are: The Sun, Moon, Venus, Mars, Jupiter, Saturn, the Pole star, and the larger (or first magnitude) fixed stars, the positions of all of which in the heavens are given in the Nautical Almanac for fixed epochs at Greenwich, with the requisite data for computing their positions at all other times in all other places.

The chief astronomical observations made at sea are those for ascertaining (1) latitude, (2) time and thence longitude, (3) error of compass, and (4) latitude and longitude simultaneously.

To ascertain latitude by itself altitudes of heavenly bodies are measured above the horizon when they are on or near the meridian and therefore exactly or nearly north or south of the observer; in the case of the sun, of course, this means at or near noon, and in the case of other bodies such local times are previously accurately ascertained by a simple calculation made from the Nautical Almanac or more roughly found from an armillary sphere. The principle involved is the simple one that by subtracting the observed altitude when on the meridian from 90° the distance of the zenith or point overhead north or south of the heavenly body is found; then by combining with this the distance, obtained from the Nautical Almanac, of the body considered north or south of the celestial equator at the same instant, it is found how far the zenith is north or south of the celestial equator, and this is exactly the same as the latitude of the observer since the celestial equator is merely the imaginary extension of that of the earth. Such observations are not necessarily restricted to that which can be taken at the instant when the body observed is on the meridian (meridian altitude); equally accurate and multiplied observations can be made on either or both sides of the meridian if the body is somewhat near it (ex-meridian and circum-meridian altitudes), and a simple calculation or reference to a specially constructed table or graphic curve gives the required result.

Errors arising from uncertainty as to the true position of the horizon are with twilight and night observations largely counteracted by taking the means of results obtained from observations made of heavenly bodies crossing the meridian both north and south of the observer, taken as nearly at the same time as convenient. In northern latitudes the pole star is so near to the pole that