June 24, 1915] 
NATURE 
403 

ranges which have recently been. opened; it has 
appeared to me to be worth while to attempt to 
explain some of these difhculties, in order that those 
which are avoidable may be eliminated. 
An experimental arrangement which can be used 
to illustrate the essential difficulties to be met with 
in aiming with the rifle, is represented in perspective 
in Fig. 1. A is a rough model of the eye. It com- 
prises a tube about 13 in. in diameter and 3 in. long, 
closed in front with a lens L of about 3 in. focal 
length; into the back of this tube fits another tube, 
which carries a screen of ground glass S. B is a 
sheet of cardboard, with a notch in the upper edge, 
to represent the rear-sight of the rifle. C is a piece 
of card cut to a point, to represent the fore-sight of 
the rifle. D is a circular opaque disc which, for 
convenience, may be attached to the glass of a window 
of the room in which the experiment is conducted; 
this disc represents the ‘“‘bull’s-eye” of the target. 
By sliding the screen S in or out, either B, C, or D 
may be focussed; but all cannot be focussed at the 
same time. If, however, the lens is covered with 
a piece of card provided with a circular aperture of 
about 4 in. diameter, A, B, and C can all be focussed 
simultaneously ; and the screen S can be moved in or 
out through some distance without impairing the 
clearness of the image on the ground glass. The 
brightness of the image is, however, much diminished. 
This illustrates the advantage and disadvantage due 
to the use of ‘‘pin-hole” spectacles. If the card is 
arranged so that its circular aperture lies over the 


Fic. 1. 
middle of the lens, and the images of B, C, and D 
are formed at the middle of the ground glass screen, 
the position of the image of either B, C, or D is 
identical with-that of the corresponding image pro- 
duced, with the card removed, by adjusting the posi- 
tion of the ground glass screen; but if the aperture 
of the card is displaced towards the edge of the 
lens L, the various images are displaced both 
relatively and absolutely. 
Further, let the perforated card be removed, and 
let the screen S be adjusted so that the ‘‘ bull’s-eye”’ is 
focussed; then on covering the lens from below by a 
piece of unperforated card, it will be seen that as the 
card rises, the image of the ‘‘bull’s-eye”’ sinks, while 
the images of the sights rise. A similar effect can be 
observed with regard to the eye. If the model eye A 
is removed, and replaced by the eye of the observer 
adjusted so that B, C, and D are in alignment, while 
D is focussed, it will be found that if the pupil of the 
eye is gradually covered from below by a piece of card 
the “bull’s eye’’ appears to rise above the sights.! 
To understand this result, it must be remembered that 
the image produced on the retina is inverted, and that 
an absolute depression of the image is interpreted as 
an apparent rise of the object viewed. The apparent 
motion referred to is very marked when the light is 
dim and the pupil is expanded; it can only be noticed 
with some difficulty in bright daylight. 
1 See ‘Spherical “Aberration of the Eve,” by E. Edser (Nature, 
April 16, 1903). Also “ Light for Students,’’ by E. Edser (Macmillan and 
Co.), p. r65. 
NO. 2382. VOL. 95] 

| much smaller, and may even disappear. 
Returning to the arrangement represented in Fig. 1, 
it will be found that when the ‘** bull’s-eye’’ is focussed 
by the unstopped lens L, raising the card B causes the 
image D to sink. Similarly, in a dim light, on bring- 
ing the rifle into position so that the rear-sight inter- 
cepts light from the lower part of the pupil, the * bull’s- 
eye’’ appears to rise. In a great number of cases, 
when the fore-sight is brought too high so as partially 
to cover the “‘bull’s-eye,’ the latter appears to 
swell at its upper left-hand edge (at about ‘ half-past 
ten’), and sometimes this swelling develops into a 
second ‘ bull’s-eye’’ detached from the first one. 
The following important phenomena can also be 
noticed :— 
(1) On focussing the bull’s-eye with the lens L un- 
stopped, the image of the fore-sight C is surrounded 
by a narrow penumbra; a similar but wider penumbra 
borders the image of the rear-sight B. If the lens is 
now stopped down, the circular aperture of the card 
being over the middle of the lens, the images of B 
and C become sharp, and it will be noticed that the 
images of the edges of the sights now have the.same 
positions as the edges of the corresponding penumbras 
produced by the unstopped lens. Thus it appears that 
in aiming with the rifle, when the bull’s-eye is 
focussed, the top of the narrow penumbra surrounding 
the fore-sight should be brought level with the top of 
the wider penumbra bounding the shoulders of the V 
or U rear-sight. I have found that this procedure 
leads to consistent and good shooting, A peculiarity 
of the penumbra surrounding the ocular image of the 
fore-sight will be mentioned later. 
(2) On focussing the fore-sight B with the lens L 
unstopped, the image of the bull’s-eye D becomes 
The image 
of the rear-sight is slightly improved. Similarly, when 
aiming with the rifle, the image of the bull’s-eye is 
diminished in size when the fore-sight is focussed by 
the eye. 
(3) On focussing the rear-sight B with the lens L 
unstopped, the bull’s-eye D disappears, and the fore- 
sight B becomes smaller and less distinct. 
Now young people can alter the focus of their eyes 
without effort; they see the bull’s-eye, the fore-sight, 
| and the rear-sight in rapid succession, so that some- 
times they appear to see all three at the same time. 
In this case sighting is easy. But with advancing age 
comes the necessity for effort in focussing the eye to 
different distances, even if this capacity is not lost 
altogether. For myself, I can read print (even small 
print) at ten inches from my eye, but a perceptible 
effort is required to alter the focus of my eyes; and 
from the result of my own experience, together with 
that of several men in a condition similar to my own, 
I strongly advise that the bull’s-eye only should be 
focussed, the tip of the fore-sight being brought just 
| below the bottom of the bull’s-eye and level with the 
top of the penumbra which bounds the shoulders of the 
rear-sight. 
A peculiarity of the image of the fore-sight, when 
the bull’s-eye is focussed by the eye in a dim light, 
must now be mentioned. At first sight the appearance 
presented is that of three images? standing side by 
side, the central image being the darkest. On careful 
scrutiny, however, two overlapping images only are 
seen, the portion common to both being darker and 
giving the appearance of a third image (Fig. 2, A). 
No such appearance can be obtained with the model 
represented in Fig. 1; we must therefore seek for its 
explanation in some defect peculiar to the eye. With a 
little care a somewhat similar double image can be 
seen even in fairly bright daylight. Let the pointed 
tip of a lead pencil be placed (for steadiness) upright 
against the glass of a window, and then, with one eye 
°* These appear to be the three images mentioned ly Mr. Trotter. 
