392 
through it,—this will be a tangible 
representative of the axis of apparent 
diurnal rotation of the heavens,—but 
only far enough to let one end just 
projet; this end will represent the 
North Pole (P) of the heavens. Next 
drive three pins up to their heads 
into the orange in positions similar 
to p, 3,a in the figure: the three pin- 
heads will represent the Pole Star (f), 
and the two Pointers (a, 3). Strain 
a fine thread from the pin f round 
the pins 8, a, and pin it down again 
at m,a point in the direction of Ba 
produced. The thread (if properly 
strained) will cling to the orange 
along the Great Circles £6, Bam. 
The construction is now complete. 
Face the north, and hold the 
orange with the projecting end of the 
needle pointing towards the North 
Pole of the heavens (which it repre- 
sents), and turn the orange slowly 
round the needle (held in the hand) 
in the same direction as the stars 
appear to move, 7.é. rising from the 
east or right hand: the set of pin- 
heads representing the Pole Star and 
Pointers will now move in precisely 
the same manner as the apparent 
diurnal motion of the actual Pole 
Star and Pointers, and it will be at 
once recognised that the ‘‘ angle of 
obliquity (p 6 a) of the directive line” 
continues invariable, i.e., that the 
Pointers do always “point” equally 
well to, z.e. with equal deviation from, 
the Pole Star. 
It will also be understood that the 
Great Circle (8am) through the 
Pointers was the line traced out in 
the heavens by the centre of the 
middle hair of the equatorial in the 
first experiment, and that the arc pm 
was the angle obtained as the differ- 
ence of the readings on the hour- 
circle. 
Effects of Aévial Refraction.—The 
effect of the earth’s atmosphere on 
the rays of light by which the stars 
become visible to us is to raise the 
apparent position of all by a small 
amount, so that all appear higher 
than they would if no atmosphere 
existed. The amount of apparent 
increase of altitude depends on the 
actual altitude, and is greatest (about 
thirty-three minutes) for a star in the 
horizon, and rapidly diminishes with 
increase of actual altitude, and van- 
ishes at the zenith. 
Correspondence. 
(July, 
Now as the Pole Star and Pointers 
are generally at very different alti- 
tudes above the horizon, the apparent 
increase of altitude is generally 
different for each of the three, being 
always greatest for the lowest, and 
least for the highest ; moreover this 
apparent increase of altitude changes 
in magnitude slowly from instant to 
instant, the variation being different 
for each of the three, viz., least for 
the Pole Star, which can never be 
more than about 134° above or below 
the pole, and greatest for the further 
Pointer (6), which may be about 32° 
49' above or below the pole. 
The effe@ of this varying increase 
of altitude of the visible positions of 
the three stars (different in amount 
for each star) on the problem in hand 
is a slight change both of position and 
of shape of the spherical triangle 
pm from the normal form (of the 
diagram) which it would have (ex- 
cluding atmospheric effects), and this 
change varies slowly from instant to 
instant. Thus the apparent shape of 
the spherical triangle f6m does 
really vary throughout the night, and 
therefore also the “‘ apparent devia- 
tion” (fm), and also the ‘‘ apparent 
angle of obliquity ” of the Pole Star 
from the Pointers do really vary 
throughout the night. 
This effe@ is, however, zero at the 
North Pole of the earth, for all three 
stars will there be apparently raised 
by a constant small amount (different, 
of course, for each star, but invariable 
for the same star): thus the apparent 
shape of the spherical triangle p B m 
will be (slightly different indeed from 
its true shape, aérial effects excluded, 
but) of invariable form throughout 
the night, so that the “angle of 
obliquity of the diredtive line ” of the 
Pointers is both actually and appa- 
rently invariable at the North Pole of 
the earth. 
The effe& due to refraction will 
increase at first very slowly from the 
North Pole towards the Equator, 
and will be sensibly zero in all high 
northern latitudes, and even in Great 
Britain will be so small as to be in- 
appreciable to the unaided eye. The 
effe& will increase more rapidly 
towards the Equator. The solution 
of the following Problem— 
Problem—“ In what latitude, and at what 
hour does the effe& of aérial refraction cause 
oe 
