1874.] The Pole Star and the Pointers. 289 
in twelve hours of these three stars, and due merely to the 
rotation of the earth on its axis. 
W N Erepresents, as before, the horizon; the curved line 
PE a portion of the great circle, at right angles to the equi- 
noctial, and cutting the east point on the horizon. P repre- 
sents the pole of the heavens, and p w the remaining portion 
of the great circle that is above the horizon. 
Mivthe arc’ of the circle PE we represent: two stars; 
aand gp. A straight line joining these two stars, and pro- 
duced in the direction of the pole, would reach a point L. 
We will suppose a star situated at L on the meridian, and 
above the pole. 
Under the conditions given above the stars 8 and a point 
with great exactitude towards L, because an apparently 
straight line joining 6 and a, and produced, would pass 
through L. 
FIG. 3. 
w N E 
In consequence of the rotation of the earth on its axis 
the star at L and above the pole would in twelve hours be 
carried round the true pole, P, and would trace a semicircle, 
and reach the point L’ below the pole, the arc PL being equal 
to PL’. Due to the same cause the stars a and 6 would 
appear to trace semicircles round Pp, and would occupy, in 
twelve hours from the time at which they were at a and £, 
the positions shown by a’ and P’. 
A line joining a’ and g’, and produced towards the pole, 
would now reach the point L, as before, but the star which 
was at L is now at L’, below the pole. Consequently the 
two stars «’ and 6’ do not now point towards the same star 
at which they pointed when they were in the positions shown 
by « and p. 
In order to illustrate the problem we have selected three 
stars in such a relative position as to show the effects in a 
prominent manner, and it happens that the actual position 
of the pole star and the pointers is not so very different from 
that of the three stars given above. We will now map out, 
