Page 247 hydrogkaphy 3387 



Repeated observations will disclose that each observer has a figure of error of 

 characteristic shape and size, which is usually longer in one direction than in the other. 

 This characteristic figure of error, once it has been determined for an observer, may be 

 apphed to one or two lines of position to derive a more probable position than would 

 be otherwise possible (see A and B, fig. 59) . 



Not all of the observations in any one series are of equal weight. They should be 

 weighted according to the rates given as described in 3384E, and these weights taken 

 into consideration in determining the most probable position. The treatment of 

 weighted observations on stars in the same general direction is comparatively easy 

 when they are combined by bisectrices to form one line of position. 



The use to be made of weighted observations in opposite directions is a matter of 

 considerable judgment. If the observation on a north star is "excellent" and that on a 

 south star is "poor," it is not necessarily a foregone conclusion that the most probable 

 position is close to the line of position derived from the observation on the north star. 

 In using weighted observations on stars in opposite directions, the characteristic figure 

 of error of the observer must be taken into consideration. If the average size of this 

 figure is 1 mUe between the north and south lines of position, this same approximate 

 distance should be expected whether the observations are of equal or unequal weight. 



(See (7 and A %• 59.) 



The weights of the difl^erent observations may be indicated on the plot by using 

 a different colored ink for lines of position of different weights, or by writing the actual 

 weight alongside each line of position. 



A. SELECTION OF STARS 



To compensate for certain errors and to obtain maximum accuracy, the celestial 

 bodies to be observed should be selected so that the lines of position wUl plot in a sym- 

 metrical quadrilateral. For best results the celestial bodies should be of about the 

 same magnitude, differ by about 90° in azimuth, and be at approximately the same 

 altitude. Theoretically, four stars should be selected approximately at the four inter- 

 cardinal points, for their lines of position will plot in a rectangle and their altitudes will 

 change at approximately the same rate. Such selection is seldom made in practice 

 because most observers want to use Polaris as one of the stars and the others are 

 selected with reference to it, with the result that the sides of the figure formed by the 

 plotted lines of position are roughly north-south and east-west. 



It is important that stars of approximately equal magnitude be selected in order to 

 equalize as nearly as practicable the observing conditions on all observations of a series. 

 If a bright star is observed in a series with several famter stars, the observations on the 

 former may be more accurate but the result will be an unequal distribution of error 

 when the mean position is determined (see 3384E). For the same reason neither a 

 moon sight nor a sun sight should be combined with star sights; an additional reason 

 is a different refraction if the altitude of the sun or moon is higher than that of the 

 stars. An additional error may be introduced in the case of the sun by the use of a 

 colored shade glass. 



The altitudes of the observed bodies must be kept within certain definite limits. 

 Bodies at comparatively high altitudes are undesirable because of the diSiculty of 

 measuring the altitude in a truly vertical plane. Bodies at comparatively low altitudes 

 are usually invisible when the horizon is bright enough for best observations and low 

 altitude observations are subject to greater errors of refraction. The best results are 

 usually obtained from observations on bodies at altitudes between 15° and 20°, but 



