448 The Centre of Gravity of the Earth . [August, 
the sum of the declinations of these two stars between 
January and June of the same year. 
Again, take the two stars a OCtantis and S Ursae Majoris, 
and compare the sum of the declinations of these two stars 
on March 30th and September 30th, 1880, and these will be 
found as follows : — 
< 7 OCtantis 
... 89° 
16' 
I2"7 
S., March 30, 
8 Ursae Majoris 
... 86° 
36' 
iE'7 
N., „ 
Sum 
- 17 5° 
52' 
24"*4 
cr OCtantis 
... 89° 
16' 
4 7"* 1 
Sept. 30. 
8 Ursae Majoris 
... 86° 
36' 
5 I#/ 7 
Sum 
- 175 0 
53' 
3 8"-8 
52' 
24"’4 
Difference... 
. . . 
1' 
I 4*4 : 
= 74"*4- 
It thus appears that those differences actually occur in ob- 
servations which must occur in consequence of the centre of 
gravity of the Earth not coinciding with the Earth’s centre, 
causing 'a divergence in the zenith of certain localities, in 
consequence of the plumb-line being directed to the centre 
of gravity of the sphere, and not the true centre. 
An examination of the Diagrams 1 and 2 will show that 
the great difference between the observed zenith distances of 
stars will occur at or near the pole, and when stars can be 
seen both above and below the pole. If a star can be seen 
only above the pole, the changes in zenith distance or 
declination, due to the position of the centre of gravity of 
the Earth, will be but slight. For example, supposing an 
observer at Q, Diagram 1, the zenith of this observer would 
be found by the production of the line joining G and Q, but 
a star near the zenith of Q could only be seen when the 
centre of gravity (g) occupied the same, or nearly the same, 
position that is shown in Diagram 1. Consequently the 
observed change in zenith distance of a star near the 
Equator, due to the position of the centre of gravity of the 
Earth, will be very slight, whereas the change in zenith dis- 
tance of a star near the poles will be very great, as shown 
by Diagrams 1 and 2. Hence the greatest changes found 
annually in the declination of stars will be in circumpolar 
stars. 
If the axis of diurnal rotation of the Earth were always 
parallel to itself, the zenith of an observer at the poles would 
