FINDING THE LOCUS OF GEOGRAPHICAL POSITION. 241 
The altitude represented as having been measured in the 
foregoing problem is subject, like all other observed altitudes 
that navigators are accustomed to take for the purpose of 
fixing a position, to the uncertainties introduced into instru¬ 
mental measurement by the extraordinary deflection of the 
rays of light coming from the horizon, which frequently oc¬ 
curs in every part of the world to such an extent as to produce 
a displacement of the horizon of large magnitude, extend¬ 
ing to five, ten, and even fifteen minutes of arc; and perhaps 
among the greatest advantages that may be claimed for the 
foregoing method of solution is the facility with which it 
lends itself to a deduction of Wirtz’* locus of geographical 
position by constant difference of altitude, which is found 
by comparing the measured difference of altitude of two 
observed celestial bodies with their difference of altitude as 
deduced by the foregoing method of finding altitude by 
inspection. Such a line of position is free from the usual 
uncertainties in the dip of the horizon caused by abnormal 
refraction, as well as from the additional uncertainties of 
the height of the eye, the index correction of the sextant, 
the want of parallelism in the mirrors, and to the errors of 
defective centering of the sextant. 
A point of this horizon-free line of position, as well as its 
azimuth may be speedily deduced by the method already 
described, as will be seen from the following example: 
At sea, September 26, 1899, in estimated geographical 
position 3° 40' south and 32° 34' west of Greenwich : 
Chronom¬ 
eter. 
Star. 
Measured 
altitude. 
Difference of 
altitude. 
R. A. 
Dec. 
h. m. s. 
18 45 45 
19 7 12 
a Arietis ... 
a Canis Maj. 
38° 5'.0 1 
56 7 .3 f 
A h= -f 17°2'.8 
h. m. a. 
2 1 33 
7 34 4 
+ 22° 59 / .5 
+ 5 29.0 
*Ausdem Archiv der Deutschen Seewarte xxv Jargang, 1902. “Ueber 
eine neue kimmfreie astronomiseke Standlinie,” von Dr. Phil. Carl W. 
Wirtz, Observator der Kaiserlichen Sternwarte in Strassburg. 
35—Bull. Phil. Soc., Wash., Vol. 14. 
