584 On Certain Errors in Lunar Observations. [October, 
because with B as a centre, and radius B A, the arc would 
pass on the B side of C. , 
Every surveyor who has used the sextant knows that it 
he measures a series of angles round the horizon, and adds 
together these angles, their sum will amount to more than 
360° if the various objects are not on the same level, as 
shown by C and B. This is due to the faCt.that CBis the 
hypothenuse of a right-angled triangle, the right angle being 
at A. Consequently B C measured with the sextant is greater 
than C A measured with the sextant. _ 
Suppose we keep the three points C A B in exactly the 
same relative position as regards each other, but take the 
points A and B as each 30° above the horizon, whilst C is a 
few degrees vertically above A, and A and C both on the 
meridian. We have the same apparent conditions as befoie . 
CAB appears as a right angle, and the side C B represents 
the hypothenuse. Consequently, if we measure BC with 
the sextant, we should find this arc greater than A B ; the 
fadt of having elevated this triangle above the horizon, 
causing apparently no difference in the angular distance as 
measured with the sextant. 
Now let us examine the contradiction which exists. Sup- 
pose A and B each 30° above the horizon, whilst C is on the 
meridian and a few degrees above A. The points C and B 
may, under these conditions, be both on the Equinoctial, 
whilst A is a point on the sphere, on the same meridian asC, 
and is south of the Equinoctial. It follows therefore that, 
calculated on the sphere of the heavens, the angle at C is 
the right angle, whilst the angle at A is less than a right 
angle. Consequently B A is the hypothenuse of the right- 
angled spherical triangle A C B, and not B A. 
By looking through the objeft-glass of the b 
sextant at B, we make B the pole of our sphere ; 
and the straight line joining B and A, as mea- 
sured with the sextant, is measured in the same 
manner as we should measure on a meridian, as 
shown below. Suppose B A a portion of the 
meridian, and B the pole, BAC a right. angle; 
the angular distance B C, measured with the 
sextant, would be greater than B A, and if we 
turned this triangle down so that B A coincided 
with the horizon, or so that B A was parallel 
to the horizon, the conditions as regards mea- 
surements with the sextant would not be 
altered. c ~x 
