Geographic Positions at Sea 231 



If the two-star observations are not simultaneous, the first observation is usually 

 referred to the second by applying a correction to altitude of the first. This correction, 

 expressed in minutes of arc, is equal to the number of nautical miles run, multiplied by 

 the cosine of the angle between the ship's course and the direction of the first star. This 

 correction is negligible in the spechnen on the preceding page. 



The adopted results derived from the observations of the two observers are latitude 

 39° 47' 8 N and longitude, 39° 48(8 W, which axe entered on the dead-reckoning sheet 

 (Form 42). The positions depending on the dead reckoning alone may then be adjusted 

 for the day, as has been described. The final values are used to the nearest mmute. 



It is reaUzed that the discrepancies between the dead-reckoned and the astronomic 

 positions may be owing to causes that do not operate uniformly over the time during which 

 the errors are distributed, and that the discrepancies are also partly because of observa- 

 tional errors. But in the absence of information to the contrary, the assumptions of 

 observational errors and of uniform changes are the only ones admissible. The specimens 

 have been selected at random and represent usual conditions. Larger discrepancies are 

 often found which are ascribed, m most cases, to the effects of ocean currents. 



AcCtTRACY OF POSITIONS AT SeA. 



The remarks on this matter m connection with the Galilee work (see page 59) apply 

 likewise to the Carnegie work. With sUght modifications, they are repeated here. 



Accuracy of geographic positions is dependent on so many factors that it is quite 

 impossible to define it by exact figures based on any one investigation of numerical results. 

 The first consideration would naturally be the magnitude of the probable error of the 

 measured altitudes, and if the observation were a meridional one, this probable error would 

 be the probable error of the resultant latitude at the mstant of observation. But as it 

 rarely happens that this instant corresponds to the time of a magnetic observation, the 

 observed latitude must be altered by a quantity which depends upon the run of the ship 

 between observed latitude and the place of the magnetic observations. 



The error in run may be controlled by the astronomic observations immediately pre- 

 ceding and following the magnetic observations. This procedure is, in fact, the method 

 employed in the ocean work. But in attemptmg to assign Umits of accuracy we are agam 

 confronted with the error in this control which depends upon the stabiUty of the speed and 

 direction of the ocean currents, the constancy of the leeway, steermg, and error of the log. 

 Agam, if the observed Sun or star be east or west of the meridian, there is an additional 

 uncertainty introduced by the unknown error in the assumed chronometer rate. This 

 error, however, is very small in the case of our work, since it is controlled by tune comparisons 

 at every port available for the purpose, and is distributed back when appreciable. An 

 investigation of some of the determinations of ship's position by simultaneous observations 

 on three stars mdicates that, if the Sun or star be favorably situated and the weather and 

 sea conditions are fair, the average error to be expected in the determination of geographic 

 position is less than 2 miles. The error in the control of the "error of run " is usually insig- 

 nificant if the controlUng astronomic observations are not more than 6 hours apart. This 

 has usually been the case in our observations, except in high latitudes, where fog and clouds 

 prevail. Of course, there are exceptional times when no astronomic observations are 

 possible for several days. The geographic positions for the results of magnetic incUna- 

 tion and intensity are then more or less uncertain. In the case of results of magnetic 

 decUnation, however, the Sun or star that serves for the magnetic observations usually 

 permits of at least a fairly good determination of position. 



