5. HYDROGRAPHY 



197 



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 neces- 

 sary that the amount 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 un- 

 weighted observations the probable position 

 should be equidistant from the lines of posi- 

 tion 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 posi- 

 tion, and in a series of more than three or 

 four sights a combination of these is pref- 

 erable. 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. 75). In practice, it is not necessary to 

 move the lines of position. The probable 

 position may be found with the use of di- 

 viders, 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 ob- 

 served. In a triangle of error formed by 

 three lines of position the three bisectrices 

 will intersect at a point, as in B, Figure 75. 

 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 75. 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 75. 



When more than four stars are observed 



Figure 75. — Probable position of ship from stellar 

 observations. 



in one series, the lines of position in the 

 same general direction should be combined 

 to reduce the data to not more than four 

 lines of position. Assuming all observations 

 to be of equal weight, the lines of position 

 from two stars in the same general direc- 

 tion 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. 

 75). 



When the sun is visible, observations 

 should be made on it at least five times a 

 day. The first and last observations should 

 be taken when the altitude of the sun is 

 between 12" and 25" ; the noon sight should 

 be taken at local apparent noon, and the 

 other two approximately halfway between 

 the noon sight and the early morning and 

 late afternoon sights. The meridian altitude 

 sight should be taken independently by two 

 or more observers. Individual sun sights 

 should not be run up in the final plot, but 

 shall be used as separate lines of position at 

 the times of observation to which the line 

 as a whole is adjusted. 



