Page 245 hydrography 3387 



For accurate deterininations, observations taken by different observers, by different 

 sextants, or at different times of the day, should never be combined to determine a 

 probable position. 



When morning and evening star sights are taken from a vessel underway, the 

 various sights of each observer must be run up or run back by dead reckoning to a 

 selected central position. 



Each observer's sights shoidd be plotted on a separate sheet and a ship's position 

 derived therefrom. Ordinary cross-section paper may be used for this purpose but 

 polar coordinate paper is preferable. An arbitrary scale may be adopted which should 

 be noted on each sheet used. A large enough scale should be chosen so that 1 nautical 

 mile will be represented on the paper by at least 1 inch. In addition to the line of 

 position, the dead-reckoning position for which the sights were computed, the run-up 

 or run-back of each sight and the derived ship's position shoidd be clearly indicated. 

 The rough copies on which the lines of position were originally plotted shall be trans- 

 mitted to the Washington Office ; smooth copies are not necessary. The dead-reckoning 

 position, the adopted position of the ship, and the lines of position after being run up 

 or run back should be inked. The name of each star observed and its direction should 

 be indicated alongside each line of position. The observed lines of position and the 

 distance and direction each was run up should be left in pencil. 



Due to the inherent inaccuracy of astronomic sights, the lines of position corrected 

 for the run of the ship between sights will practically never intersect at a point. Three 

 lines of position will form a triangle of error. The probable position of the ship derived 

 from a series of morning or evening star sights is based on the assumption that there is 

 some type of error common to all the sights, approximately equal in amount and in 

 the same direction with reference to the stars observed. It is not especially necessary 

 that the amoimt of this error be small, but for best results it must be symmetrical. In 

 determining the most probable position of the ship the directions of the observed bodies 

 must always be considered. For unweighted observations the probable position should 

 be equidistant from the lines of position and should lie either toward or away from 

 each star of the series; never away from some and toward others. 



There are two general methods which may be used to find the most probable position, and in a 

 series of more than three or four sights a combination of these is preferable. The first method is to 

 move all of the lines of position either away from or toward the objects observed by an equal distance 

 to bring them as nearly as possible to a common intersection (see A and C in fig. 58). In practice, 

 it is not necessary to move the lines of position. The probable position may be found with the use 

 of dividers, merely visualizing the transfer of the lines of position, but in this operation one must be 

 certain to adopt a position which is on the correct side of each line of position considered; that is, 

 it must be either toward or away from each star of the series. 



The second method is to draw bisectrices between intersecting lines of position. Each bisectrix 

 must be drawn so that it is either toward or away from the two objects observed. In a triangle of 

 error formed by three lines of position the three bisectrices will intersect at a point, as in B, figure 58. 

 For four lines of position from stars in four directions two bisectrices should be drawn, each between 

 two opposite lines of position, as in D, figure 58. Where two opposite lines of position are from stars 

 in the same direction, a mean line should first be drawn between them and this mean line and the 

 other two lines treated as three lines and the. bisectrices drawn as in B, figure 58. 



When more than foin- stars are observed in one series, the lines of position in the 

 same general direction shoidd be combined to I'educe the data to not more than foiu- 

 lines of position. Assuming" all observations to be of eciual weight, ihc lin.'s of position 

 from two stars in the same general direction should be combined by drawing the 

 bisectrix between them. From the figure of error thus formed the most probable 

 position is determined as described above. (See E, fig. 58.) 



