GENERAL ISTavIGATION. 19 



using the approximate position : The sine of the correction equals 

 the product of the sine of half the difference of longitude by the sine 

 of the middle latitude. It is applied on the equatorial side of the 

 observed bearing, and its effect is always to increase the latitude of 

 the observer. 



Soundings taken at random are of little value in fixing or check- 

 ing position, and may at times be misleading. In thick weather, 

 when near or closing the land, soundings should be taken continu- 

 ously and at regular intervals, and, with the character of the bottom, 

 systematically recorded. By laying the soundings on tracing paper, 

 according to the scale of the chart, along a line representing the track 

 of the ship, and then moving the paper over the chart parallel with 

 the course until the observed soundings agree with those of the chart, 

 the ship's position will in general be quite well determined. This 

 plan was suggested by Lord Kelvin, whose admirable sounding ma- 

 chine renders the operation of sounding possible in quite deep water 

 without slowing down the ship and consequent loss of time. 



Dumb compass. — All ships should be supplied with the means of 

 taking accurate bearings both by day and by night. The standard 

 compass is not always conveniently placed for the purpose; in such 

 case some species of alidade or dumb compass is of great importance. 

 The utility of such an instrument in ascertaining the change of bear- 

 ing of an approaching ship's light should not be forgotten. 



Sumner's method. — Among astronomical methods of fixing a 

 ship's position the great utility of Sumner's method should be well 

 understood, and this method should be in constant use. The Sumner 

 line — that is, the line drawn through the two positions obtained by 

 working the chronometer observation for longitude with two assumed 

 latitudes, or by drawing through the position obtained with one lati- 

 tude a line at right angles to the bearing of the body as obtained from 

 the azimuth tables — gives at times invaluable information, as the ship 

 must be somewhere on that line provided the chronometer is correct. 

 If directed toward the coast, it marks the bearing of a definite point; 

 if parallel with the coast the distance of the latter is shown. Thus 

 the direction of the line may often be usefully taken as a course. A 

 sounding at the same time with the observation may often give an 

 approximate position on the line. A very accurate position can be 

 obtained by observing two or more stars at morning or evening twi- 

 light, at which time the horizon is well defined. The Sumner lines 

 thus obtained will, if the bearings of the stars differ three points or 

 more, give an excellent result. A star or planet at twilight and the 

 sun afterwards or before may be combined ; also two observations of 

 the sun with sufficient interval to admit of a considerable change of 

 bearing. In these cases one of the lines must be moved for the run 



