1875. 
a third when an apparently 
straight line joining them 
passes through the third, if 
produced.” 
Now this definition is only tolerably 
good for very small portions of the 
celestial sphere: apparently straight 
lines cannot be drawn at all over any 
considerable portion of the sphere. 
The only real analogue to straight 
lines in plane is that of GREAT 
CircLEs on the sphere, which are 
really the shortest lines which can be 
drawn between two points: small 
portions of Great Circles do really 
seem apparently straight: no other 
lines on the sphere can possibly be 
apparently straight, but are both 
actually and apparently curved, and 
in general twisted. The proper defi- 
nition of ‘*‘ pointing”? as applied to 
stars is therefore— 
Definition.—* Two stars are said 
to ‘point’ at a third, when 
a Great Circle through them 
passes through the third if 
produced.” * 
Apply this to the case of the 
Pointers and Pole Star. Their rela- 
tive positions are plotted to scale in 
Fig. 1 from data taken from the 
“‘ Nautical Almanac.” In the figure P 
is the north pole of the heavens, p is 
the Pole Star, a and @ are the two 
Pointers (a and 6 Urse Majoris). 
The lines Pf, PG, Pa, Ba, Bp— 
straight lines in the diagram—repre- 
sent the Great Circles in the heavens 
joining the points named: thus the 
(straight) line 6 a represents the Great 
Circle in the heavens, which is the 
true “ directive line ’’ of the Pointers, 
and along which, therefore, they must 
be said to ‘‘ point.” It will be ob- 
served that the Pointers (a, 3) do not 
lie on the same Great Circle through 
P (the Great Circles Pa, P§, include, 
in fa&, an angle cf about 30') and 
therefore do not ‘ point”’ to the pole 
(P); the Great Circle arc fm, drawn 
perpendicular to Bam, is “ deviation” 
of the “ directive line’? Bam of the 
Pointers from the Pole Star (f), and 
subtends at the further Pointer the 
angle pBa, which is what has been 
styled above the ‘‘ angle of obliquity 
of the directive line” of the Pointers 
from the Pole Star. 
Imagine this figure traced in visible 
glittering lines in the heavens at any 
instant: it will seem to swing round 
Correspondence. 
389 
the celestial pole (P)—in consequence 
of the earth’s rotation—as a whole, 
i.€., preserving an invariable figure 
(barring aérial effects of refraction), 
so that the “angle of obliquity” 
fGBa will remain constant. It follows, 
therefore, that — excepting aérial 
effe&s—the Pointers do at all times 
of the same night, and at all places, 
‘* point ” equally well to—(deviate by 
a constant quantity from)—the Pole 
Star. 
It is easy to verify the above by a 
simple experiment :— 
Experiment.—Take an orange (or a 
worsted ball) to represent the celes- 
tial sphere: drive a knitting needle 
