508 LITTLEHALES: THE SUMNER LINE 



wich apparent time, will make the local apparent time or hour- 

 angle a multiple of ten minutes, and in a latitude represented 

 by the nearer whole-degree of latitude to the latitude given 

 by the dead reckoning. Accordingly, the longitude of the 

 assumed position would be 34° 08' 46.5" W., or 2M6™ 35.1«<'<= 

 W., which, applied to the Greenwich apparent time, gives the 

 local apparent time 19° BO""; and the latitude of the assumed 

 position should be 42° N. 



From the Azimuth Tables (H. O. Pub. No. 71), for latitude 42° 

 N. and hour-angle 19'' 30-, i.e., L.A.T. ?'■ 30™ A.M., we obtain: 



corresponding to Dec. 19° N., Azimuth N. 90°- 01 E. 

 corresponding to Dec. 20° N., Azimuth N. 89° - 06 E. 



Therefore corresponding to Dec. 19°21'll"N.,AzimuthN.89°42E. 

 The altitude that a celestial body in this declination would 

 have, in this azimuth and hour-angle, to an observer in the as- 

 sumed geographical position in latitude 42° N. and longitude 

 34° 08' 46.5" W. is now calculated from equation 3 as follows: 



t = 19'' 30"^ log sin = 9.96562 

 p = 70° 38' 49" log sin = 9.97474 

 Z = 89° 42' log cosec = 10.00001 



Calculated h = 29° 20' 34" log cos = 9.94037 

 Corrected 

 7Tieasured b = 29 50 05 



A /) = 29' 31" toward 



This intercept of 29|', being laid off from, the assumed geo- 

 graphical position along the bearing, N. 89° 42' E., of the observed 

 celestial body, gives the point through which the line of posi- 

 tion of the observer is to be drawn at right angles to the bearing. 

 Since the corrected measured altitude is higher than the cal- 

 culated altitude, the intercept is, in this case, laid off toward the 

 observed body, and gives a line of position agreeing with that 

 found by drawing a line through the geographical positions de- 

 duced in the solution of this problem under Article 372 of the 

 America?! Practical Navigator. 



It will be useful to point out that, with azimuth tables in 

 which the interval between the hour-angles is only four minutes. 



