586 On Certain Errors in Lunar Observations. [October, 
but this curve is on the sphere a straight line, and if we 
represented these four points on the sphere they would be 
shown as in the diagram below. . 
The angular distance zy calculated on the sphere, plu 
the angular distance y x calculated on the sphere, will be 
greater than the arc of the Equinoctial z #. 
Angular distances therefore measured with the sextant on 
the sphere of the heavens do not, in all cases, correspond 
to the angular distances calculated on the sphe ^» 
distances are obtained by the polar distances and difference 
in right ascension of two bodies. 
The true angular distance of the Moon from a , 
given in the “Nautical Almanac,” is calculated from the 
Polar distance of these two bodies, and their difference in 
right ascension. The measurements taken with the sextant, 
however, measures as we may term it between 
two objects, and in some instances will give a less distance 
than that obtained by calculation. 
Any person may test this problem by aid of a pan . of 
compasses and a common globe, in the following manner .- 
Suppose you wished to travel from lat. 51 , long, o , to lat. 
5I Take S a pair of compasses and measure along a parallel of 
latitude, on the Globe, a distance of 3° of 
Double this distance, and the point will be reached w 11c 
has a longitude of 6o° on the same parallel. Then measure 
the same half distances north of the middle distance, an 
with the compasses we shall reach a point west of 60 longi- 
tude, and on the same parallel. It is in fad the old 
story of great circle-sailing repeated. 
When we measure angles with the sextant between two 
obieCts, we make the objeCt we look at through the horizon 
glass the pole of our sphere, and a straight line from this 
pole to the second objeCt is the angular distance measuied. 
