Navigation, the art or system of rules and practices by means of which vessels are directed in their course upon the water. Prior to the invention of the mariner's compass navigation was limited to enclosed seas like the Mediterranean, to gulfs and archipelagos, and to the coasts. Beyond the sight of land, the mariner had no guide in cloudy nights, and no resource in stormy weather; consequently, the most remote and venturesome expeditions only moved along the shore; and the sea was avoided as much as possible, especially during the winter season, from the middle of November to the middle of March. The discovery of the mariner's compass changed this state of things entirely, by furnishing a never-failing guide, as useful and safe to the navigator in the night as during the day, and in storms as in fair weather. It is uncertain to whom the world is indebted for the first observation of the directing powers of the magnet, and for their application to the purposes of travelling by land and sea (SeeCompass.) The introduction to Church-ills "Collection" contends for the honor of the discovery in behalf of Flavio Gioja of Pasi-tano. near Amalfi, in Campania. The date assigned to Gioja's invention is about the begin-nimj of the 14th century.

There can be" no doubt that to him belongs the merit of having invented something by which its adaptation to nautical purposes was very much promoted; but that it was used at sea before his time appears from various passages in authors of an older date. It was known in China many centuries previous to its introduction into Europe, and was used in the eastern portion of the Mediterranean during the first half of the 13th century. - When ships, carrying with them an unfailing guide to direct their course, began to traverse the great seas in all directions, the cross staff and the astrolabe furnished them with the means of measuring the altitude of the sun and stars, and thus of approximately determining the latitude and time. But the most serious inconvenience arose from the unavoidable use of a plane chart to represent the sphere, the gross distortions and errors of which often misled the mariner, especially in voyages far distant from the equator. Recourse was had to globes to remove this evil, and a famous pair is mentioned which was made in 1592, under the direction of Mr. William Sanderson, a merchant, " commended for his knowledge as well as generosity to ingenious men." On the terrestrial one were described the voyages of Drake, Cavendish, and Frobisher. The plane chart, however, being so much more easy and convenient in practice, kept its place until the invention of the projection of the sphere upon a plane surface by Gerard Mercator, in 15G9. Mercator's projection consists in keeping the meridians parallel, but augmenting the length of the meridians between the parallels of latitude, in receding from the equator, in such a manner that the just proportions of the meridians and parallels of latitude to each other are preserved.

The signal advantage of this projection is, that the directions of the compass, or what in technical language are called the "compass courses," are straight lines. The navigator works most conveniently upon a plane surface, and by means of Mercator's projection he is able to lay down his courses with a parallel rule, the points being taken from a compass drawn on the chart, and the line being one that cuts all the meridians at the same angle, and marks the magnetic bearing of the objects through which it passes. This is called the rhumb line or loxodromic curve, and the definition of it answers for the definition of the compass course. Such is the suitableness of Mercator's projection to the use of the mariner's compass, that the latter now seems to have been an incomplete discovery until the announcement of the former. It is suggested that Mercator arrived at his invention by simply observing on the globe where the meridians were cut at each parallel of latitude by the rhumb lines; and it is admitted that he never laid down, if ho knew it, the mathematical theory on which it rests.

This was first announced by Edward Wright, of Cains college, Cambridge. Shortly after this (1595), the famous navigator Capt. John Davis, who gave his name to the straits which he discovered, published a small treatise called "The Seaman's Secrets," at the end of which he gives a figure of a staff of his contrivance, to make a back observation; "than which instrument," he said, "the seaman shall not find any so good, and in all clymates of so great certaintie." The celebrated Portuguese mathematician Pedro Nunez, or Nonius, had as early as 1537 published his book, which, with additions, was printed 30 years afterward by Basil in Latin, and called De Arte et Ratione Navigandi. In this he introduces, among much of what was then very valuable matter, his method of the division of a quadrant by concentric circles. Davis's back staff maintained the first place until it was superseded by the quadrant. Another important invention is the log, first mentioned by Pigafetta in the early part of the 16th century. About the year 1620 logarithms were introduced into navigation by Edmund Gunter, whose scales are of such general repute; and shortly afterward Richard Norwood published his method of setting down and perfecting a sea reckoning, with the use of a traverse table.

In 1700 Dr. Hal-ley published a general map on which were delineated the lines of equal variation. It was hailed with great applause, as the means of determining the longitude at sea; but this expectation proved futile. But of all the gifts to the navigator, by far the greatest of this time is Hadley's quadrant. It has been superseded by the sextant, which does not differ from it in principle, but is very much more nicely constructed, and more accurate, convenient, and generally useful. (See Quadrant, and Sextant.) For a long time the problem of the longitude engaged the attention of the men of science in Europe, and especially in Great Britain. The British house of commons has at various times offered rewards for the solution of this problem, one of which amounted to £20,000 sterling. Newton's improvement of the theory of the moon led to the construction of Mayer's lunar tables, and to the publication of the "Nautical Almanac and Astronomical Ephemeris," by Dr. Maskelyne, in 1767. The appearance of the latter created a new era in navigation, to which it rendered essential service. The lunar method, as it is called, has since received great additions, corresponding to the advancing state of astronomical knowledge, and the improvements in the instruments of the seaman and the astronomer.

The method by the chronometer owes its highest success to the science and ingenuity of English artists and mechanics of the present generation, and that immediately preceding. (See Clocks and Watches, and Longitude.) in our day the art or science of navigation has not failed to receive valuable accessions; such as Sumner's method for determining the position by lines of bearing or of equal altitudes; Chauvenet's great circle protractor, which furnishes great circle courses immediately by inspection, saving a world of figures, and also solves in the same way the problems of nautical astronomy; precise and trustworthy sailing directions and memoirs, like those of Horsburgh, the Blunts of New York, Findlay, and the invaluable memoirs of Kerhallet; and valuable contributions to our knowledge of the laws of storms by Redfield, Reid, and Piddington, and of the currents and meteorology of the ocean generally by Berghaus, Keith Johnston, and Maury. - AVithout attempting a scientific treatise on navigation, we may give the general reader a simple conception of the manner in which the place of a ship and her direction are ascertained upon the sea, under favorable circumstances.

When the ship has left port, the reckoning is begun by observing the compass bearing and distance of some conspicuous object, as a lighthouse; and from the time of taking this bearing the reckoning is continued by noting down (generally from hour to hour) the courses sailed, which are ascertained by observations of the compass, and the distance on each course, which is ascertained by the log. (Se,e Log.) The reckoning is made up with these data, from the time of any independent determination of the ship's position, by considering the sum of the distances sailed in the N. and S. and E. and W. directions, and reducing the whole to one residual expression of the actual course and distance made good; this is done by means of a traverse table invented for the purpose. The reckoning here described is called dead reckoning, and is susceptible of error from so many disturbing causes, that it can only be depended upon for a short time. The navigator is provided with simple and easy methods of acquiring a knowledge of his position by independent observations of the sun, moon, and stars. We will look only at the first of these luminaries. The elements of position are the latitude and longitude.

The determination of the latitude by the altitude of the sun at noon is readily understood, if it be remembered that if the sun moved always on the equator, the height it reached at noon at any place would depend merely on the distance of that place from the equator; but the sun being removed from the equator more or less, according to the season of the year, the navigator reduces it to that circle by applying the declination, which is the astronomical expression in degrees and minutes for the interval of its separation. For this declination and all his astronomical data, he is indebted to the nautical almanac. The longitude is determined by chronometers. A chronometer is expected to keep the time of a certain place, as Greenwich or Paris; but as all chronometers are subject to a slight rate of loss or gain, this rate, and the error at starting, are applied at the moment of observation, to obtain the correct Greenwich time. The change of a degree in longitude is equivalent to a change of four minutes in time; the business of a navigator then is simply to compare his own time with the standard time, or the time at Greenwich; he obtains his own time through an observation of the sun when its altitude is changing rapidly.

In the case of the determination of the longitude by the lunar method, the clock showing the Greenwich time is in the sky. Such observations are detached and disconnected. The navigator, if set down suddenly in the middle of the ocean, could determine'his position as well as if he had pro-i led there gradually, and known it from day to day. - We have selected single and plain cases only; but navigation, regarded as an art, is a copious and complex system of rules and practices, involving the use of numerous tables. Bowditch's "American Navigator" is a large octavo of nearly 800 pages, containing over 50 tables. Raper'a "British Standard Navigator" (edition of 1849), approved by the admiralty, numbers 900 pages and 74 tables. Navigation, regarded as a science, requires at the very least a knowledge of spherical trigonometry and algebra in the mathematics, and of the apparent motions and phenomena of the principal heavenly bodies in astronomy. In addition to the above named authorities, see Peirce's " Plane and Spherical Trigonometry;"Chauvenet's "Trigonometry " and "Manual of Astronomy;" Francoeur's Astronomie pratique; Boitard and Ansard-Deusy's Navigation pratique; Churchill's "Collection," introductory discourse; Dr. Wilson's "Dissertation," in Robertson's "Elements;" and Humboldt's "Cosmos." (See Ship).