1875.) 
Tnost variation in the ‘deviation’ of the 
‘directive line’ of the Pointers from the 
Pole Star (apparent positions only con- 
sidered), and what will that maximum varia- 
tion be?” 
would be a matter of considerable 
mathematical, or rather numerical, 
complexity, and is hardly worth the 
reat labour it would probably involve. 
t seems, however, frobadle that this 
maximum would occur at or near the 
Equator; and it is possible that it 
might be large enough to be appre- 
ciable by the unaided eye. 
Explanation of Cause of Optical 
Illusion.—\t having been shown that 
the principal part of the apparent 
change during the same night of the 
“anole of obliquity of the dire@ive 
line” of the Pointers is only an 
apparent change, having no existence 
in fact, and which can therefore only 
be regarded as an OPTICAL ILLUSION, 
it remains to endeavour to give some 
explanation of the cause of so extra- 
ordinary an illusion. 
It has been explained that the true 
meaning of the phrase ‘two stars 
point at a third” is that the Great 
Circle through the two stars passes— 
if produced—through the third. Un- 
less, therefore, the eye can properly 
trace out and produce a Great Circle 
in the heavens, the mind cannot 
fairly judge of the manner in which 
two stars ‘‘ point ’’—whether well or 
ill—at a third. 
The illusion appears to depend 
entirely on the fa& that the tracing 
of Great Circles in the heavens is an 
unfamiliar matter. This may readily 
be tested by trial. Let anyone 
endeavour to trace Great Circles in 
the heavens between pairs of stars 
not very far apart, and produce them 
as far as possible in both directions, 
and then compare them with the 
Great Circles obtained by straining a 
fine string through the same pairs of 
stars on a celestial globe; he will be 
astonished at the discrepancy when 
the Great Circles are not vertical or 
nearly so. Let it be remembered 
that every such Great Circle ought to 
cut the horizon in two points dia- 
metrically opposite. There will be 
found no difficulty in tracing out 
vertical or nearly vertical Great 
Circles tolerably corre&ly ; but when- 
ever the true Great Circle would be 
considerably inclined to a _ vertical 
circle, it will be found that—if the 
VOL. V. (N.S.) 
Correspondence. 391 
stars be not very far apart—the Great 
Circle as traced by the unaided eye 
will not cut the horizon in two points 
diametrically opposite, nay—if the 
obliquity be very great—-will not cut 
the horizon at all! 
The eye seems to be influenced in 
some way by an impression of the 
position of the horizon; so that if 
pairs of stars be selected at the same 
er nearly the same altitude, the im- 
pulse to draw a horizontal circle— 
which is, of course, a small circle of 
the sphere—through them will be 
found almost irresistible ! 
Anyone who tries this experiment 
fairly a few times will soon be con- 
vinced that the apparent change of 
“ deviation ” of the “ directive line ” 
of the Pointers from the Pole Star 
exists only in imagination, and is a 
remarkable instance of optical illu- 
sion. 
The cause of the great influence of 
the horizon on the attempt to trace 
oblique Great Circles in the heavens 
is probably that all our associations 
of practical life are with figures 
drawn on the earth, i.e. on a hori- 
zontal plane, and that the recollection 
in the mind of these, the familiar 
work, insensibly influences the eye 
in endeavouring to do the unfamiliar 
work in the heavens. 
An Article has been published in 
the ‘‘ Quarterly Journal of Science,” 
No. xliv., for October, 1874, with title 
““On the Curved Appearance of 
Comets’ Tails,” by the author* of the 
Article on the Pole Star and Pointers 
in No. xliii. of that Journal. 
The Author endeavours to explain 
that the “curved appearance” of the 
tail is commonly only an appearance 
due to the position of the tail in the 
sky, and changing in curvature from 
hour to hour in consequence of the 
change of apparent position due to 
the earth’s rotation. The Author’s 
argument is virtually simply a reitera- 
tion of the argument in his Article on 
the Pole Star and Pointers in No. 
xliii. of the “Quarterly Journal of 
Science.” Anyone who has_ unders 
stood the explanation advanced in 
the present Article of the difficulty 
experienced by the eye in tracing 
Great Circles in the heavens will see 
that any supposed change of curvature 
* Lieut.-Col. Drayson, R.A., F.R.A.S. 
3) D 
