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tion, they presented the appearance of a wheel with immove-
uble radii.

When the two wheels of a gig or carriage in motion are
looked at from an oblique position, so that the line of sight
crosses the axle, the space through which the wheels overlap
appears to be divided into a number of fixed curved lines,
passing from the axle of one wheel to the axle of the other, in
general form and arrangement resembling the lines described by
iron filings between the opposite poles of a magnet. The effect
may be obtained at pleasure by cutting two equal wheels out
of white cardboard (Plate III. fig. 1), each having from twelve
to twenty or thirty radii, sticking them on a large needle two
or three inches apart, revolving them between the fingers, and
looking at them in the right direction against a dark or black
ground ; the greater the velocity of the wheels the more perfect
will be the appearance (fig, 2).

When the dark-coloured wheel of a carriage is moving on a
good light-coloured road, so that the sun shines almost directly
on its broadside, and the wheel and its shadow are looked at
obliquely, so that the one overlaps the other in part, then, in
the overlapping part, luminous or light lines will be perceived
curved more or less, and conjoining the axle and its shadow,
if the wheel and shadow are superposed sufficiently; or, tending
to do so, if they are superposed only in part : the more rapid
the motion the more perfect is the appearance. The effect
may be easily observed by making a pasteboard wheel like one
of those just described, blackening it, sticking it on a pin, and
revolving it in the sunshine, or in candlelight, before a sheet
of white paper (fig. 3). If the wheel be converted into a
tetotum or top, by having a pin thrust through its centre, and
spun upon a sheet of white paper, the effect produced by the
wheel and its shadow will be obtained with facility, and in form
will resemble fig. 2. In all these cases no rims are required ;
the spokes or radii produce the effect.

If a carriage wheel running rapidly before upright bars, as
a palisade or railing, be observed, the attention being fixed
upon the wheel, peculiar stationary lines will appear: those
perpendicular to the nave or axis will be straight, but the
others curved ; and the curve will be greatest in those which



1831.] On a Peculiar Class of Optical Deceptions. 293

are furthest from the upper straight line. These curves are
the same in form as those already described and explained by
Dr. Roget*, and the appearance itself is produced in a similar
manner ; but the phenomena are distinct and the causes dif-
ferent. The effect at present referred to is best observed
when the velocities are great, whereas that explained by Dr.
Roget takes place only when the velocities are moderate. It
is probable that some of the appearances briefly mentioned by
an anonymous writer in the ' Quarterly Journal of Science,'
First Series, vol. x. p. 282, and already referred to by Dr.
Roget, were of the kind now to be explained ; for though the
description is not accurate either for the effects which form
the object of this paper, or that explained by Dr. Roget,
and is, indeed, inconsistent with the observation or explanation
of any of the phenomena, it probably had its origin in the
occurrence of some of both kinds under the eyes of the writer.
The effect is easily obtained by revolving a white pasteboard
wheel before a black or dark ground, and then, whilst re-
garding the wheel fixedly, traversing the space before it with
a grate also cut out of white pasteboard. By altering the
position of the grate and direction of its motion, it will be seen
that the straight lines in the wheel are always parallel to the
bars of the grate, and that the convexity of the curved lines is
always towards that side of the grate where its motion coin-
cides in direction with the motion of the radii of the wheel.
By varying the velocity of the wheel and grate, the curves
change in their appearance, and the whole or any part of the
system, as described and figured by Dr. Roget, may be ob-
tained at pleasure.

I have had a very simple apparatus constructed, by which
these and many other analogous appearances can be shown in
great perfection and variety. One board was fixed upright
upon the middle of another, serving as a base ; the upright
board was cut into the shape represented in fig. 4 ; the middle,
and the two extreme projections, forming points of support,
were supplied with little caps cut out of copper-plate and bent
into shape (fig. 5), so that, when in their places, they offer
four bearings for the support of two axes, one on each side the
middle. The axes are small pieces of steel wire tapered at the
* Philosophieal Transactions, 1825, p. 131.



294 On a Peculiar Class of Optical Deceptions. [1831.

extremities ; each has upon it a little roller or disc of soft
wood, which, though it can be moved by force from one part
of the axis to another, still has friction sufficient to carry the
latter with it when turned round. These axes are made to
revolve in the following manner: A circular copper plate
about 4 inches in diameter has three pulleys of different
diameter fixed upon its upper surface, whilst its lower surface
is covered with a piece of fine sand-paper attached by cement.
A hole is made through the centre of the plate and pulleys,
and guarded by brass tube, so fitted as to move steadily but
freely upon an upright steel pin fixed in the middle of the
centre wooden support ; hence when the plate is in its place,
it rests upon the two rollers belonging to the horizontal axes,
whilst it is rendered steady by the upright pin. It can easily
be turned round in a horizontal plane, and it then causes the
two axes with their rollers to revolve in opposite directions,
and the velocities of these can be made either equal to each
other, or to differ in almost any ratio by shifting the rollers
upon the horizontal axes nearer to, or further from the centre
of the stand.

To produce motions of the axes in the same direction, an
aperture was cut in the lower part of the upright board ; a
roller, turned for it, which loosely fitted within the aperture ;
and a steel pin or rod passed as an axis through the roller.
The roller hangs in its place by endless lines made of thread,
passing under it, and over little pulleys fixed on the horizontal
axes ; when, therefore, it is turned by the projecting pin, it
causes the revolution of the axes. The variation in velocities
is obtained by having the roller of different diameters in dif-
ferent parts, and by having pulleys of different dimensions.
This description will be easily understood by reference to the
figures.

This apparatus had to carry wheels either with cogs or
spokes ; which was contrived in the following manner : The
wheels were cut out of cardboard, were about 7 inches in
diameter, and were formed with cogs or spokes at pleasure.
A piece of cork, being the end of a phial cork, about the tenth
of an inch in thickness, was then fastened by a little soft cement
to the middle of the wheel, and a needle run through both,
and then withdrawn, These wheels could at any time be put



1831.] On a Peculiar Class of Optical Deceptions. 295

upon the axes, and, being held sufficiently firm by the friction
of the cork, turned with them. By these arrangements the
axes could be changed, or the wheels shifted, or the velocities
altered without the least delay.

The beauty of many of the effects obtained by this apparatus
has induced me to describe it more particularly than I other-
wise should have done. The appearance which I first had
shown to me by Mr. Maltby was exhibited very perfectly ; two
equal cog-wheels (fig. 6) were mounted, so as to have equal
opposite velocities ; when put into motion, which was easily
done by the thumb and finger applied to the upper pulley of
the horizontal copper plate, they presented each the appear-
ance of a uniform tint at the part corresponding to the series
of cogs or teeth, provided that the eye was so placed as to see
the whole of both wheels ; but when a position was taken up
so that the wheels were visually superposed, then, in place of
a uniform tint, the appearance of teeth or cogs was seen
misty but perfectly stationary, whatever the degree of velocity
given to the wheel. By cutting the cogs or teeth in the wheel
nearest to the eye, deeper (fig. 7), the eye could be brought
into the prolongation of the axes of the wheels, and then the
spectral cog-wheel appeared perfect (fig. 8). The number of
intervals thus occurring was exactly double the number of
teeth in either wheel : thus a wheel with twelve teeth produced
twenty-four black, and twenty-four white alternations. When
one wheel was made to move a little faster than the other, by
shifting the wooden roller on its axis, then the spectrum
travelled in the direction of that wheel having the greatest
velocity ; and with more rapidity the greater the difference
between the velocities of the two wheels. When the wheels
were looked at so that they visually superposed each other in
part, the effect took place only in those parts : and it was
striking and extraordinary to observe two uniform tints
mingling, and instantly breaking out into the alternations of
light and shade which I have described. There are many
variations in the curvature and other appearances obtained by
altering the position of the eye, which will be at once under-
stood when observed, and which for brevity's sake I refrain
from describing.

Wheels were then fixed on the machine, consisting of radii



296 On a Peculiar Class of Optical Deceptions. [1831.

or spokes, each having twelve, equal in length and width
(fig. 1). When revolved alone, each wheel gave, with a
certain velocity, a perfectly regular tint ; but when visually
superposed, there appeared a fixed wheel, having twenty-four
spokes, equal in dimensions to the original spokes. Variations
of the position of the eye, or of the relative velocity of the two
wheels, caused alterations similar to those I have referred to
with the cog-wheels.

In observing these effects, either the wheels should be black
or in shade, whilst the part beyond is illuminated ; or else the
wheels should be white and enlightened, whilst the part beyond
is in deep shade. The cog-wheels present nearly a similar
appearance in both cases, though in reality the parts of the
spectrum which appear darkest by the one method are lightest
by the other. The spoke-wheels give a spectrum having white
radii in the first method and dark radii in the second. Placing
the wheels between the eye and the clouds, or a white wall, or
a lunar lamp, answers well for the first method ; and for the
second, merely reversing the position and allowing the light to
shine on the parts of the wheel towards the eye, whilst the
background is black, or in obscurity, is all that is required.
Strictly, the phenomena should be viewed with one eye only,
but it is not often that vision with two eyes disturbs the effects
to any extent.

The cause of these appearances, when pointed out, is
sufficiently obvious, and immediately indicates many other
effects of a similar kind, and equally striking, which are
dependent upon it. The eye has the power, as is well known,
of retaining visual impressions for a sensible period of time ;
and in this way, recurring actions, made sufficiently near to
each other, are perceptibly connected, and made to appear as
a continued impression. The luminous circle visible when a
lighted coal or taper is whirled round the beautiful appear-
ances of the kaleidophone the uniform tint spread by the
revolution of one of the spoke- or cog-wheels already described
are a few of the many effects of this kind which are well
known.

But during such impressions, the eye, although to the mind
occupied by an object, is still open, for a large proportion of
time, to receive impressions from other sources ; for the original



CHEMISTRY AND PHYSICS.




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1831.] On a Peculiar Class of Optical Deceptions.

object looked at is not in the way to act as a screen, and shut
out all else from sight; the result is, that two or more objects
may seem to exist before the eye at once, being visually super-
posed. The schoolboy experiment of seeing both sides of a
whirling halfpenny at the same moment, the appearances pro-
duced by the thaumatrope, and the transparency of the re-
volving cog- or spoke-wheels referred to, in consequence of
which other objects are seen through the shaded parts, are
all effects of this kind ; two or more distinct impressions, or sets
of impressions, being made upon the eye, but appearing to the
perception as one.

So it is in the appearances particularly referred to in this
paper : they are the natural result of two or more impressions
upon the eye, really, but not sensibly, distinct from each other.
If, whilst the eye is stationary, a series of cogs like those repre-
sented by the continuous outline (fig. 9) pass rapidly before it,
they produce a uniform tint to the eye : and for the purpose of
following out the description, let it be supposed the cogs are in
shade between the eye and a white background ; the tint is
then a hazy, semitransparent grey. If another series of cogs,
represented by the dotted outline, and close to the first, so as
to give no sensible angular difference in the dimensions of the
cogs, pass with equal velocity in the same direction, it will pro-
duce its corresponding tint. If the two sets of cogs be visually
superposed in part, as in the figure, there will be no alteration
in the uniformity of the tint. If the cogs of one set be more
or less to the right or left of the other, then the superposed
part will approach more or less to the tint of the shaded and
uncut part of the cardboard wheel, and be less transparent.
But if, instead of the motion being equal, the velocities are un-
equal, then total changes of the appearance supervene ; the
spectrum (if I may so call it) of the superposed parts becomes
alternately light and dark, and the alternations take place more
or less rapidly as the velocities of the two sets of cogs differ
more or less from each other.

When the cogs move in opposite directions, the uniform tint
which each alone can produce is soon broken up in the super-
posed parts into lighter and darker portions, and when the
velocities of both are equal, the spectrum is resolved into a
certain number of light and dark alternations, which are per-



298 On a Peculiar Class of Optical Deceptions. [1831.

fectly fixed (fig. 10), and which, to the mind, offer a singular
contrast to the rapidly moving state of the wheels, and to the
variations which their velocity may undergo without altering
the visible result.

This effect, strange as it at first appears, will be easily under-
stood by reference to fig. 9. Suppose the eye directed to the
part I beyond the cogs, and the sets of cogs to be moving with
equal velocities in the opposite directions, indicated by the
arrow heads : the part I will be eclipsed by the cogs a and b
simultaneously, and for exactly the same time, for they begin to
cover it and they leave it together ; / therefore is alternately
open to and shut from the eye for equal times ; for what these
cogs have done, will be performed by all the other cogs in turn,
and the cogs are equal in area to the spaces between : half the
light, therefore, from that part of the background comes to
the eye, and produces a corresponding impression. But with
respect to the point d, although the cog b is just leaving it ex-
posed, the cog a is just beginning to eclipse it ; and by the time
the latter has passed over, the edge of the cog e will be upon
the spot, and that cog will therefore hide it until f comes up;
so that in fact the point d is always hidden, no light comes from
that part of the background, and it consequently appears dark
V is circumstanced just as / was, for the cogs a and e cover
it simultaneously, and so do all the other cogs in pairs ; it is
therefore a light space in the spectrum : d 1 is a repetition in
everything of d, and is a dark space. The parts intermediate
between the maxima of light and darkness will, by examination,
be found to be eclipsed for intermediate periods, and to appear
more or less dark in consequence, so that the appearance of the
spectrum belonging to the visually superposed parts of the two
sets of cogs is as in fig. 10.

In the case of equal wheels with radii, the fixed spectrum
produced when the wheels superpose each other has twice the
number of radii of either wheel, that being of course the num-
ber of times which the radii coincide with each other in one
revolution. Fig. 11 represents the fixed spectrum produced
by two equal wheels of eight radii each. When the radii or
spokes are narrow, the difference in the intensity of tint be-
tween the middle and the edges of each image of a spoke is so
slight as to be scarcely perceptible. But as this circumstance



1831.] On a Peculiar Class of Optical Deceptions. 299

and many others will explain themselves immediately they are
experimentally observed, it is unnecessary to dwell minutely
upon them here.

A very simple experiment will render the whole of these
effects perfectly intelligible. If a little rod of white cardboard
5 or 6 inches long, and one-thirtieth of an inch wide, be
moved to and fro from right to left before the eye, an obscure
or black background being beyond, it will spread a tint, as it
were, over the space through which it moves (fig. 12). A simi-
lar rod held and moved in the other hand will produce the same
effect ; but if these be visually superposed, i. e. if one be moved
to and fro behind the other, also moving, then in the quadran-
gular space included within the intersection of the two tints
will be seen a black line sometimes straight, and connecting the
opposite angles of the quadrangle ; at other times oval or round,
or even square, according to the motions given to the two card-
board rods (fig. 13).

This appearance is visible even when the rods are several
inches or a foot apart from each other, provided they are visu-
ally superposed. It is produced exactly as in the former case,
and the black line is in fact the path of the intersecting point of
the moving rods. As their motions vary, so does the course
of this point change, and wherever it occurs, there is less
eclipse of the black ground beyond than in the other parts, and
consequently less light from that spot to the eye than from the
other portions of the compound spectrum produced by the
moving rods.

In this experiment the eye should be fixed, and the part
looked at should be between the planes in which the rods are
moved. The variation produced by using black rods, and
looking at a white ground, will suggest itself. Those who find
it difficult to observe the effect at first, will instantly be able to
do so if the rod nearest the eye is black, or held so as to throw
a deep shade : the line is then much more distinct ; but the
explanation is not quite the same, though nearly so it will
suggest itself. Two bright pins or needles produce the effect
very well in diffuse daylight ; and the line produced by the
shadow of one on the other, and that belonging to the intersec-
tion, are easily distinguished and separated.

If, whilst a single bar is moved in one hand, several bars or



300 On a Peculiar Class of Optical Deceptions. [1831.

a grate is moved in the other, then spectral lines, equal to the
number of bars in the grate, are produced. If one grate is
moved before another, then the lines are proportionably nume-
rous ; or if the distances are equal, and the velocity the same,
so that many spectral lines may coincide in one, that one is so
much the more strongly marked. If the bars used be serpen-
tine or curved, the lines produced may be either straight or
curved at pleasure, according as the positions and motions are
arranged, so as to make the intersecting point travel in a straight,
or a curved, or in any other line.

The cause of the curious appearance produced, when spoke-
or cog-wheels revolve before each other, already described,
will now be easily understood; the spokes and cogs of the
wheels produce precisely the same effect as the bars held in the
hand, and the fixedness of the position of the spectrum depends-
upon the recurrence of the intersecting or hiding positions,
exactly in the same place with equal wheels, provided the
opposite motions of each be of equal velocity, and the eye be
fixed.

When wheels were used in the little machine described
(fig. 4<), having equal but oblique teeth, and the obliquity in
the same direction, the spectrum was also marked obliquely ;
but when the obliquity was in opposite directions, the spectrum
was marked as with straight teeth.

When equal wheels were revolved with opposite motions, one
rather faster than the other, the spectrum travelled slowly in the
direction of the fastest wheel ; when the difference in velocity
between the two wheels was made greater, the spectrum
travelled faster. These effects are the necessary consequence
of the transference of the intersecting points already described,
in the direction of the motion of the fastest wheel.

When one wheel contained more cogs than the other, as, for
instance, twenty-four and twenty-two, then with equal motions
the spectrum was clear and distinct, but travelled in the direc-
tion of the wheel having the greatest number of teeth. When
the other wheel was made to move so much faster as to bring
an equal number of cogs before the eye, or rather any one part
of the eye, in the same time as the other, the spectrum became
stationary again. The explanations of these variations will
suggest themselves immediately the effects are witnessed.



1831.] On a Peculiar Class of Optical Deceptions. 301

When the motion of the wheels upon the machine is in the
same direction, the velocities equal, and the eye placed in the
prolongation of the axis of the wheels, no particular effect takes
place. If it so happens that the cogs of one coincide with those
of the other, the uniform tint belonging to one wheel only is
produced. If they project by the side of each other, it is as if
the cogs were larger, and the tint is therefore stronger. But
when the velocities vary, the appearances are very curious ; the
spectrum then becomes altogether alternately light and dark,
and the alternations succeed each other more fapidly as the
velocities differ more from each other.

When wheels with radii are put upon the machine, it is easy
to observe, in perfection, the optical appearance already referred
to, as exhibited by carriage wheels, &c. (fig. 2). They should
be looked at obliquely, so as to be visually superposed only in
part ; and provided the wheels are alike, and both revolving in
the same direction with equal velocity, they immediately assume
the form described, passing in curves from the axis of one wheel
to the axis of the other, and much resembling in disposition
the curves formed by iron filings between two opposite poles
of a magnet.

If the wheels revolve in opposite directions, then the spectral
lines, originating at each axis as a pole, have another disposi-
tion, and instead of running the one set into the other, are dis-
posed generally like the filings about two similar magnetic poles,
as if a repulsion existed : not that the curves or the cause are
the same, but the appearances are similar. A very little atten-
tion will show that all these lines are the necessary consequence
of the travelling of successive intersecting points ; and any one
of them may be followed out by experimenting with the two
pasteboard rods already described, these being moved in the
hand as if each were the spoke of a wheel.

All these effects may be simply exhibited by cutting out two
equal pasteboard wheels without rims, passing a pin as an axis
through each, spinning one upon a mahogany or dark table,
and then spinning the other between the fingers over it, so that
the two may be visually superposed. If the appearances are
observed by a lamp or candle, the wheels should be so held to
the light that the shadow of the tipper may not fall upon the
lower, otherwise the effects are complicated by similar sets of



302 On a Peculiar Class of Optical Deceptions. [1831.

lines which appear upon the lower wheel, and are produced by
the shadow of the upper. These are the same in form and dis-
position as the former, and are even more distinct ; they should



Online LibraryMichael FaradayExperimental researches in chemistry and physics → online text (page 29 of 49)