NAVIGATION 181 to make a back observation; "than which in- strument," he said, " the seaman shall not find any so good, and in all clymates of so great certaintie." The celebrated Portuguese math- ematician 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 Eatione Namgandi. 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 Davis's back staff main- tained the first place until it was superseded by the quadrant. Another important invention is the log, first mentioned by Pigafetta in the ear- ly part of the 16th century. About the year 1620 logarithms were introduced into naviga- tion by Edmund Gunter, whose scales are of such general repute; and shortly afterward Richard Norwood published his method of set- ting 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 ex- pectation 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 It has been superseded by the sextant, which does not differ from it in principle, but is very much more nicely con- structed, and more accurate, convenient, and generally useful. (See QUADRANT, and SEX- TANT.) For a long time the problem of the longitude engaged the attention of the men of science in Europe, and especially in Great Brit- ain. The British house of commons has at va- rious 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 ser- vice. The lunar method, as it is called, has since received great additions, corresponding to the advancing state of astronomical knowl- edge, and the improvements in the instruments of the seaman and the astronomer. The meth- od by the chronometer owes its highest suc- cess to the science and ingenuity of English artists and mechanics of the present genera- tion, 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 Suinner's method for determining the posi- tion by lines of bearing or of equal altitudes ; Chauvenet's great circle protractor, which fur- nishes great circle courses immediately by in- spection, saving a world of figures, and also solves in the same way the problems of nautical astronomy ; precise and trustworthy sailing di- rections and memoirs, like those of Horsburgh, the Blunts of New York, Findlay, and the in- valuable 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. Without attempting a scientific trea- tise 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 cir- cumstances. When the ship has left port, the reckoning is begun by observing the compass bearing and distance of some conspicuous ob- ject, 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. (See LOG.) The reckoning is made up with these data, from the time of any independent determination of the ship's position, by con- sidering the sum of the distances sailed in the N. and S. and E. and W. directions, and re- ducing the whole to one residual expression of the actual course and distance made good ; this is done by means of a traverse table in- vented for the purpose. The reckoning here described is called dead reckoning, and is sus- ceptible 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 knowl- edge of his position by independent observa- tions of the sun, moon, and stars. We will look only at the first of these luminaries. The elements of position are the latitude and lon- gitude. The determination of the latitude by the altitude of the sun at noon is readily "un- derstood, 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 min- utes 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 start- ing, 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 busi- ness 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 al- titude is changing rapidly. In the case of the
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