5X0 The Centre of Gravity of the Earth , [September, 
4. What will be the greatest variation during the year 
between the polar distances of this star ? — The 
greatest length of the arc, within the curve, of a line 
drawn parallel to the direction of the star : this arc 
it will be found is about 40". 
Again corresponding with recorded observations. The 
same test may be applied to the star 51 Cephei, or any other 
star near the pole, and the Nautilus curve will give the same 
exadt results. 
Consequently we have a curve which gives accurately by 
scale the changes which take place in the polar distance of 
any star near the North Pole during each month of the year. 
The same curve shows where the right ascension of any 
star in the Northern Hemisphere will change most during 
the year, and where it will be a constant. In all cases the 
right ascension of a star will be a constant when a line from 
the star to the curve is tangential to the curve, and the 
variation in the right ascension will be greatest when a line 
from the star to the curve cuts the curve at right angles. 
The Nautilus curve which gives these exadt results is the 
curve which would be traced at the pole by the zenith during 
a year, when observations were taken at the instants of time 
indicated by midnight at Greenwich, for each day of the 
year, and due to no other cause than the fact that the centre of 
gravity of the Earth is not coincident with the Earth's centre. 
This curve is at present unknown to astronomers or geome- 
tricians. 
Having demonstrated the curve which applies to north 
stars, I next give the Nautilus curve for the South Pole. If 
the curve for the South Pole reveals equal accuracy, although 
a different curve, it seems difficult to find any more complete 
proof of the truth of the fadts here advanced. 
The Curve traced by the South Pole annually (Diagram 4). 
The annual rotation of the Earth causes the South Pole 
of the Heavens to trace a curve slightly different in form 
from that traced by the North Pole. The centre of the 
circle traced by the South Pole moves 20' '25 annually to- 
wards 12 hours right ascension, whereas the centre of the 
circle traced by the North Pole moves 2o"*25 in the opposite 
diredtion, — that is, towards 24 hours right ascension. 
The curve traced annually by the South Pole is constructed 
as follows ; — 
Draw the line A M 2o"’25 in length ; divide the line into 
12 equal parts. This line represents the course towards 
