NATURE 



337 



THURSDAY, AUC.UST 13, iJ 



TABLES FOR NAVIGATORS. 

 Asimuih Tables for lite Hit^her Dcdinalions {limits of 

 declination 24' to 30", both inclusive) between the 

 parallels of latitude d' and 60', 7cilh Examples in the 

 use of the Tables in English and French. By H. B. 

 Goodwin, Naval Instructor, Royal Navy. Pp. xii + 

 74. (London : Longmans; Green, and Co., 1896.) 



A LEADING feature of present-day methods of 

 navigation is the use of tables. There is scarcely 

 any method in use in navigation for which one, and 

 probably many, tables, of more or less practical utility, 

 are not provided ; and it would almost appear in some 

 cases as though new methods had been proposed because 

 tables could be prepared to use in connection with them, 

 rather than because they were of real practical use. 

 Some tables, such as those for " reduction to the 

 meridian," may almost be regarded as lu.xuries, as they 

 really save but little time and labour ; though, on account 

 of the easy adaptation of the formuke to different forms 

 of tabular computation, the number of them is large. 

 On the other hand, there are tables which are really 

 indispensable. 



Of this latter class azimuth tables are a prominent 

 type. 



The object of the first of these azimuth tables, by 

 Burdwood, published about a quarter of a century ago, 

 was, to judge from the preface, merely to facilitate the 

 calculation of compass error. Its publication, however, 

 and that of its e.\tension by Davis, may be said to have 

 effected a revolution in the art of navigation, as Sumner's 

 method, now so extensively used, was thereby rendered 

 practically useful. 



This method, of which the principle had been before 

 recognised, was proposed by Captain Thomas Sumner, 

 of Boston, in the year 1837. It enabled the navigator to 

 determine both his latitude and longitude at any time, 

 instead of being restricted to observations of the heavenly 

 bodies, when near the prime vertical, for longitude ; and 

 when on or near the meridian, for latitude ; observations 

 for determining the latitude, in other cases, depending on 

 a long process known as the " double altitude." 



The principle of this method, as to which Lord Kelvin 

 has remarked that every other method of navigation 

 might be abolished so long as it was retained, is, that 

 when the altitude of a heavenly body is observed, the 

 observer must be situated somewhere on that small circle 

 on the earth's surface which has the heavenly body as its 

 pole. .-Xnother obsen-ation of the same body, when its 

 azimuth has sufficiently changed, or of another body, at 

 the same time, with an azimuth differing considerably 

 from that of the first, places the observer, similarly, on 

 another small circle. His actual position must therefore 

 be at one of the two points of intersection of these circles ; 

 and, as these points are usually a long distance apart, his 

 position, known appro.ximately, will decide the question. 



These circles, when transferred to a Mercator's chart, 



form regular curves, and the chords joining any two 



points on these curves within a few miles of each other, 



or the tangents to the curves through any points on them, 



NO. 1398, VOL. 54] 



such chords or tangents practically coinciding with the 

 arcs, are called " lines of position." The intersection of 

 two such " lines of position '' fixes the position of the ship 

 on the chart. 



For the chord method the calculation of four longitudes 

 would be necessary, i.e. two longitudes obtained from 

 each of the altitudes with two assumed latitudes in the 

 neighbourhood of the latitude by account ; or else two 

 longitudes and two latitudes when the heavenly body was 

 near the meridian at the second observation. For the 

 tangent method would be required two longitudes, or a 

 longitude and a latitude, and two azimuths, as from the 

 conditions of the problem, the tangent "line of position" 

 must be at right angles to the heavenly body's azimuth. 



Thus Sumner's method, though useful, was long and 

 tedious. Captain Sumner himself remarking that the 

 calculations would be much shortened and simplified it 

 some ready means could be found of obtaining the 

 azimuth of the body observed. This ready means is 

 provided by Burdwood and Davis' tables. The longitude 

 is calculated with the latitude by account ; the azimuth 

 taken from the tables, and the " position line " drawn 

 through the position obtained. A second line is similarly 

 drawn, the latitude being calculated, by reduction to the 

 meridian, with the longitude by account, when the body 

 observed is near the meridian, and the intersection of 

 these two lines fixes the position of the ship. 



Thus the cumbrous chord method is done away 

 with, the tangent method is shortened and simplified. 

 " Summer," therefore, almost deserves the character 

 given to it by Lord Kelvin, especially as it is veiy usefu 

 in high latitudes, in the winter months, during which the 

 sun, when it does appear, is never very near the prime 

 vertical, and the longitude obtained from observation of 

 it is not so trustworthy. 



Burdwood and Davis' azimuth tables give the true 

 bearing or azimuth of any heavenly body whose declina- 

 tion lies between o^ and 23" north or south, for limits of 

 latitude 0° to 60^ north or south, for every four 

 minutes of apparent time (in the case of the sun) or of 

 hour angle (in the case of any other body). They are, 

 therefore, most useful for obtaining the azimuth of any 

 such body for compass error or line of position. 



But the great increase in the speed of modern steam- 

 ships necessitates more frequent observations in order to 

 obtain the position of the ship. The correct position at 

 noon each day was almost all that was required in the 

 days of sailing ships and ships of low steam power. 

 But now that ships may run 200 miles between noon and 

 sunset on a summer's day, and considerably more between 

 sunset and sunrise on a winter's night, it is necessary to 

 know the position as often as possible, and strict orders 

 are issued to the officer of the watch in Atlantic liners 

 to omit no observation by which the ship's position may 

 be determined. 



Hence observations of the moon, the planets, and the 

 stars are becoming of more frequent occurrence. One 

 great advantage of observations of the moon is that it is 

 frequently to be seen after sunrise or before sunset, and 

 the position can be, therefore, readily fixed by simul- 

 taneous observations of the sun and moon (Sumner). 

 Observations of the planets and stars can be made with 

 very great accuracy in the twilight, and afford most satis- 



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