1885.] On Certain Errors in Lunar Observations. 
Make & = £ (D + M + S). 
Cos b + cos (6 = D) ; 
Cos m cos s 
1 
Sin a— — ~ — j— ; — — 
Cos f |w+s) 
Sin£;v = Cos£ |w + s| cos a. 
x = true lunar distance. 
M cos S [ 2 
583 
We have now gone as far as what we may term the con- 
ventional Lunar, and yet there is an error which becomes 
apparent, when the most accurate instruments and observers 
have been employed. I will now point out where this 
error is. 
The lunar distances given in the “ Nautical Almanac ” are 
calculated from the Right Ascension and Declination of the 
Moon and Star into each three hours of Greenwich mean time. 
These distances are the actual true distances of these bodies 
measured on the sphere of the heavens. The declination 
of either body enables the polar distances to be obtained, 
and the difference of right ascension gives the angle at the 
Pole. Consequently, with two sides and the included angle, 
the third side can be calculated. The error therefore is not 
to be found in this department, but in one of a far more 
delicate kind. In order to point out where the error exists, 
I must refer to the sextant itself. 
When measuring angles between any two bodies with the 
sextant, the body which is looked at through the objeCt-glass 
of the sextant becomes for the time being the pole of a 
sphere. If I set my sextant to any given angle, say 25 0 , and 
diredt my sight through the objeCt-glass to any particular 
star, I shall, as I turn my sextant round, cause each objeCt 
25 0 from this star to successively come in contaCt with the 
star, and all lines drawn from these objects to the star will 
be straight lines. 
c 
A 
B 
If I take two points on the horizon as follows, viz. A and 
B, 25 0 apart, and a third point (C) a few degrees vertically 
above A, the angular distance, B C, measured with the 
sextant will be greater than B A measured with the sextant, 
