1881.] and its Effect on Astronomical Observations . 445 
the angle cpg, which angle is the divergence produced on 
the plumb-line at the pole p, in consequence of the centre 
of gravity of the Earth not coinciding with the Earth’s 
centre. In like manner, at the opposite pole w, a star r 
would be assigned a polar and zenith distance, s w r', which 
polar distance would be too great by the amount of the angle 
cwg, which angle is the amount of divergence of the 
plumb-line, at the pole w, due to the centre of gravity of the 
Earth not being coincident with the Earth’s centre. The 
declination, consequently, of the two stars T and r, derived 
from these observed zenith distances, would be too small by 
the amount of the angles cpg, cwg. 
I will now suppose that an interval of six months elapsed, 
and the two stars, T and R, were again observed when the 
Earth had moved round 180 0 of its orbit ; half a rotation of 
the earth having occurred in addition to the rotations due to 
six months. 
The centre of gravity (g) of the Earth would, in conse- 
quence of half a rotation of the Earth, be located on the 
opposite side of the axis to that on which it was located six 
months previously ; consequently the zenith at the Poles 
would be directed towards a point in the Heavens different 
from that point towards which it was directed six mo nths 
previously. 
The following diagram (2) will demonstrate this fadt. 
As before, the points p and w represent the North and 
South Poles ; ecq the Equator ; c the centre of the Earth ; 
G the centre of gravity; pt the direction of the North 
Star; wr the direction of the South Star. A line from g 
through p will give, if produced, the direction p n for the 
zenith of p ; and a line from G through w will give, if pro- 
duced, the direction w s for the zenith of w. Consequently 
the observed zenith distance of the star T will be less from 
this observation than it was six months previously by twice 
the angle gpc; and the zenith distance of the star r, ob- 
served from w, will be also less than it was on the previous 
occasion by twice the angle G w c. But zenith distances at 
the pole are also polar distances, and consequently the 
assigned polar distances of the stars T and r would be less 
by twice the angle gpc when observed at the two intervals. 
If these two stars, having say eighteen hours’ right ascen- 
sion, the one a North Polar star, the other a South Polar 
star, — were observed at 6 a.m. in March, and again at 6 p.m. 
in September, the assigned polar distances of these stars 
would be found to differ considerably at the two dates, and 
consequently the sum of their declinations would be found 
