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be viewed, not through the upper wheel, but directly upon the
lower ; their explanation has in part been given, and will be
sufficiently evident.

The form which the appearance occasionally assumes when
a carriage wheel is revolving before upright bars, is exceedingly
well shown by the little machine described (fig. 4), when mounted
with a single wheel carrying several equal radii at equal di-
stances. The bars of the grate should be equidistant, the in-
tervals between them being about that between the extremities
of two contiguous spokes of the wheel. The varied appear-
ances produced by varying the motion of the wheel and grate,
both in direction and velocity, will be better understood from a
few easy experiments than from any description.

The lines which thus occur may any one of them be imitated
by the two cardboard bars held and moved in the hand ; the
whole system may then be obtained at once if one of the inde-
pendent wheels (fig. 1) be revolved by the pin between the
fingers, and a single pasteboard bar (of equal width with the
radii) passed once, not too rapidly, before it ; by returning the
bar the lines are seen a second time. Should the eye not
readily catch the appearance, a black instead of a white single
bar may be used, or a shadow be thrown by an opake bar from
a candle, or the sun, upon the revolving wheel ; and then, to
extend and follow out the forms, the bar should be moved
to and fro slowly before the revolving wheel, to the extent of
one half or the whole length of a radius, when it will imme-
diately be seen that all the lines produced, even when a grate
is used, are merely the courses of so many points of intersection
between the radii of the wheel and the bars passing before or
behind it.

A variation in the mode of observing many of these curious
spectra, but which still further supports the explication given,
is to cast the shadows of the revolving wheels, either by sun
or candlelight, upon a screen, and observe their appearance.
The way in which the cogs or radii of the wheels shut out more
or less of a background from the eye, as already described,
will enable them, to an equal degree, to intercept light, which



1831.] On a Peculiar Class of Optical Deceptions. 303

would otherwise fall upon a screen. When the two equal cog-
wheels are revolved so as to have the shadows cast upon a
white screen, that shadow exhibits all the appearances and
variations observed when the eye is looking by the wheels in
shade at a white background. The shadow is light where the
wheels appear dark, for there the light has passed by the cogs ;
and dark where the wheels appear light, for there the cogs have
intercepted most of the rays. The screen should be near to
the wheels, that the shadow may be sharp ; and it is convenient
to have one wheel of rather smaller radius than the other, or
else to place them obliquely to the sun for the purpose of dis-
tinguishing the shadow of each wheel, and showing how beau-
tifully the spectrum breaks out where they superpose. When
the spoke-wheels are revolved they also cast a shadow, pre-
senting either the appearance of fixed or moving radii according
to the circumstances already described. When the two small
spoke-wheels upon one pin are revolved in an oblique direction,
their shadow exhibits very beautifully the lines often seen in
the wheels of carriages.

During these experiments the attention cannot but be drawn
to the observation of the figures produced by the shadow of
one wheel upon the face of the other. These are frequently
very beautiful, and combining as they often do with the designs
produced, as already described, are occasionally more striking
than any of the appearances yet spoken of. Mr. Wheats tone
is, however, engaged in an inquiry of a much more general and
important kind, which includes these effects, and which, I trust,
he will soon give to the public.

Several of the effects with wheels already described, and
some new ones, may be obtained with great simplicity, by means
of reflexion, in a very striking manner. If a white cardboard
wheel, with equal radii, be fixed upon a pin, and rotated be-
tween the fingers before a glass, so that the wheel and its re-
flected image may visually superpose in part, the fixed lines
will be seen, like those of fig. 2, passing in curves between the
axis of the wheel and the reflected image. If the person gra-
dually recede from the glass, but still look through the wheel
in his hand at the reflected image, i. e. still retain them super-
posed, which is best done by bringing the revolving wheel close
to the eye, he will see the lines or radii of the reflected image



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

gradually become straight, and when from three feet to any
greater distance from the glass, will see the spectrum of the
reflected image, having as many dark radii upon it as there are
radii in the wheel he is revolving. Whatever the velocity, or
however irregular the motion of the wheel, these lines are per-
fectly stationary. The explanation of the change of form and
ultimate appearance of the whole, and of the number and fixed
position of the lines, will be so evident when the experiment is
made, in conjunction with what has been said, as to require no
further statement here.

A very striking deception may be obtained in this way, by
revolving a single cog-wheel (fig. 6) between the fingers before
the glass, when from twelve to fifteen or eighteen feet from it.
It is easy to revolve the wheel before the face so that the eyes
may see the glass through or between the cogs, and then the
reflected image appears as if it were the image of a cog-wheel,
having the same number of cogs, but perfectly still, and every
cog distinct ; instead of being the image of one in such rapid
motion, that by direct vision the cogs cannot be distinguished
from each other, or their existence ascertained. The effect is
very striking at night if a candle be placed just before the
face, and near to it, but shaded by the wheel ; in the reflexion
the wheel is then well illuminated, and the reflected face or
shadow forms a good background against which to observe
the effect.

I have, perhaps, already rendered this paper longer than
necessary ; but the singularity of the appearances, and the faci-
lity with which they may be observed, have induced me to
suppose that many persons would like to repeat the experi-
ments, and must be my excuse for some further variations in
the mode of experimenting.

A disc of cardboard, about two inches and a half in diameter,
was cut into a wheel like fig. 16; another disc, rather larger,
was cut into a similar wheel, and then the radii of one were
twisted obliquely like the wings of a ventilator, and the radii
of the other similarly set, but in the opposite direction : a small
hole being made in the centre of each, a large pin was passed
through that of the smaller wheel, and then a small piece of
cork passed on to the pin to hold the wheel near the head, but
free to turn ; two or three beads were then added, the second



1831.] On a Peculiar Class of Optical Deceptions. 305

wheel put on, and then a second piece of cork ; the end of the
pin was then stuck into a quill or a pencil, and thus was formed
an apparatus very like a child's windmill, except that it had
two sets of vanes, each revolving in opposite directions. On
walking across a room towards a window, or a candle, with
this little toy in the hand, or blowing at it slightly from the
mouth, the lines were beautifully seen, being either stationary
or moving, according to the relative velocity of the two wheels.
This could be altered at pleasure by inclining the vanes more
or less, or by blowing towards the centre of the wheels, or
towards the edges when the larger hind wheel received more
propulsive force.

Spinners or whirligigs formed of discs of cardboard stuck
upon pins, and upon which radii, either straight or curved, or
other forms, had been drawn in bold lines with black ink, when
spun upon a sheet of paper, and then looked at through the
moving fingers or through equidistant bars of pasteboard moved
before them, show a great many of the effects.

Finally, a couple of open radial wheels (fig. 1) upon pins or
wires, if revolved between the fingers in different positions and
directions, show a great many of these effects extremely well.
Their shadows may be thrown upon each other, or upon the
wall ; one may be held near the eye, when it acts like a grate
with parallel bars ; and if one side of each wheel is black whilst
the other is white, still greater variety may be obtained. They
will be quite sufficient, when employed in a few experiments,
to make anything in this description clear, which I may have
left obscure.

The curious appearance exhibited by the wheel animalcule
has such a resemblance to some of those described in this paper,
that they inevitably associate in the mind of a person who has
witnessed both effects. This little insect has been well described
by Mr. Baker* and others, and can only be viewed distinctly
under a high magnifying power ; it then presents an elongated
sack-like form (fig. 17), either attached by the posterior part
to the side of the vessel containing the water in which it exists,
or else floating in the fluid. When the effect in question is
observable, there is seen the appearance of two wheels, one on

* Baker on the Microscope, vol. ii. p. 266; see slso Leeuwenhoek, Phil.
Trans., Nos. 283, 295, 337 ; and Adams on the Microscope, p. 548.

X



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

each side of the head ; they seem formed of deep teeth or short
radii, perhaps fourteen or fifteen in number ; the form of these
teeth is not sharp or well defined, but hazy at the edges ; the
interval between them is perhaps rather more than the width
of the teeth ; the teeth are not distinctly set on to a nave or
axis, but appear sometimes even to melt away or attenuate
at the part towards the centre, and sometimes appear as inde-
pendent portions, i. e. as much separated from the centre
part or supposed place of attachment as from the neighbouring
teeth.

These parts are never seen as wheels, except in motion ; the
animal is sometimes seen without them, the parts which produce
the appearance being then either retracted and drawn inwards,
or disposed in other forms, for the animal is of a very change-
able nature. The motion of the wheels is continuous, as if
they were spinning constantly in one direction upon their axis ;
the velocity is such as to carry the teeth rapidly before the eye,
but is not enough to confound the impression of one tooth
with that of its neighbours, and therefore they may be distinctly
seen. Both wheels move usually in the same direction ; and
when the head of the animal is towards the observer, the
direction is generally the same as that of the hands of a clock.
Baker states, however, that he has seen them move in opposite
directions, and also has seen the motion first discontinued, and
then reversed, in the same wheel. The velocity is not always
the same, but varies with the efforts of the animal to catch its
food. Whatever the mechanism of the parts, the result is, that
currents are established in the water towards the head of the
animal, which currents pass off outward from the edges of the
apparent wheels ; and little particles floating in the water may
be seen to pass towards the head, and be suddenly thrown off
at the edges of the wheels with considerable force.

So striking are the appearances of these animalcula, that
men of much practice in microscopical observation are at this
day convinced they do possess wheels, which actually revolve
continuously in one direction. The struggle in Mr. Baker's
mind between the evidence of his senses and his judgment,
illustrates this point in so lively a manner, that I may be excused
quoting his account of it : " As I call these parts wheels, I also
term the motion of them a rotation, because it has exactly the



1831.] On a Peculiar Class of Optical Deceptions. 307

appearance of being such. But some gentlemen have imagined
there may be a deception in the case, and that they do not
really turn round, though indeed they seem to do so. The
doubt of these gentlemen arises from the difficulty they find in
conceiving how or in what manner a wheel or any other form,
as part of a living animal, can possibly turn upon an axis sup-
posed to be another part of the same living animal, since the
wheel must be a part absolutely distinct and separate from the
axis whereon it turns ; and then say they, how can this living
wheel be nourished, as there cannot be any vessels of communi-
cation between that and the part it goes round upon, and which
it must be separate and distinct from ? To this I can only
answer, that place the object in whatever light or manner you
please, when the wheels are fully protruded they never fail to
show all the visible marks imaginable of a regular turning
round ; which I think no less difficult to account for, if they do
not really do so. Nay, in some positions you may, with your
eye, follow the same cogs or teeth whilst they seem to make a
complete revolution ; for the other parts of the insect being very
transparent, they are easily distinguished through it. As for
the machinery, I shall only say, that no true judgment can be
formed of the structure and parts of minute insects by imaginary
comparisons between them and larger animals, to which they
bear not the least similitude. However, as a man can move his
arms or his legs circularly as long and as often as he pleases by
the articulation of a ball and socket, may there not possibly be
some sort of articulation in this creature whereby its wheels or
funnels are enabled to turn themselves quite round ?

" It is certain all appearances are so much on this side of the
question, that I never met with any who did not, on seeing it,
call it a rotation ; though, from a difficulty concerning how it
can be effected, some have imagined they might be deceived.
M. Leeuwenhoek also declared them to be wheels that turn
round (vide Phil. Trans., No. 295). But I shall contend with
nobody about this matter : it is very easy for me, I know, to be
mistaken, and so far possible for others to be so too, that 1 am
persuaded some have mistaken the animal itself, which perhaps
they never saw ; whilst, instead thereof, they have been exa-
mining one or other of the several water-animalcules that are
furnished with an apparatus commonly called wheels, though



On a Peculiar Class of Optical Deceptions. [1831.

they turn not round, but excite a current by the mere vibration
offibrillae about their edges."

Notwithstanding the evidence adduced by Mr. Baker, which,
as I have said, is admitted by some at the present day, it must
be evident, from a consideration of the nature of muscular force,
and the condition of continuity under which all animals exist,
that the rotation cannot really occur. The appearances are
altogether so like some of those exhibited in the experiments
already described, that I feel no doubt the wheels must be con-
sidered not as having any real existence, but merely as spectra,
produced by parts too minute, or else having too great a velocity
when in use by the animal to be themselves recognized. It is
not meant that they are produced by toothed or radiated wheels;
for that supposition would take for granted what has already
been considered as impossible continual revolution of one part
of an animal whilst another part is fixed ; but arrangements
may be conceived, which are perfectly consistent with the usual
animal organization, and yet competent to produce all the effects
and appearances observed. Thus, if that part of the head of
the animal were surrounded by fibrillae, endowed each with
muscular power, and projecting on all sides, so as to form a kind
of wheel ; and if these fibrils were successively moved in a
tangental direction rapidly the one way, and more slowly back
again, it is evident that currents would be formed in the fluid,
of the kind apparently required to bring food to the mouth of
the animal ; and it is also evident, that if the fibrils, either alone
or grouped many together, had any power of affecting the sight,
so as to be visible, they would be less visible at the part through
which they were rapidly moving, than that through which they
were slowly returning ; and at that place, therefore, an interval
would appear, which would seem to travel round the wheel, in
consequence of the successive action of the fibrils. But if,
instead of the whole group of fibrils acting in succession as
one series, they were to be divided by the will or powers of
the animal into fifteen or sixteen groups, the action being in
every other respect the same, then there would be the appear-
ance of fifteen or sixteen dark spaces, and as many light ones
disposed as a wheel ; and these would continue to travel round
in one direction, so long as the animal continued the alternate
action of the fibrils. This may be illustrated by supposing



1831.] On a Peculiar Class of Optical Deceptions. 303

fig. 14 to represent a fixed circular brush, with long hairs, and
the little dots to be the sections of so many wires, forming the
arms of a frame which, when turned round, shall carry the
hairs of the brush forward a little, and then, letting them go,
allow them to return quickly to their first position. If this
frame be turned continually round, it would cause the brush,
when looked at from a distance, to appear as a revolving toothed
wheel, although in reality it had no circular motion. Now,
what is performed here by the wire- arms at the outer extremity
of the hairs, and the natural elasticity of the latter, may, in the
wheel animalcula, be effected at the roots of the fibrillse by
muscular power ; and in this or some similar way the animal
may have the power of urging the current necessary to supply
food, and, at the same time, producing the spectrum of a con-
tinually revolving wheel, or even the more complicated forms
discovered by Leeuwenhoek (fig. 15), without requiring any
powers beyond those which are within the understood laws of
Nature, and known to exist in the animal structure *.
Royal Institution, Dec. 10, 1830.

[In Mr. Whitock's carpet and fringe-manufactory at Edin-
burgh, they were covering a cord with silk. The cord was of
two strands, differently coloured, slightly twisted, and was
turning rapidly round on its axis. In many places it looked
like a party-coloured cord perfectly still. This was from the
continual recurrence of portions different from their neighbours,
in the same place ; they were not visible all the way round, but
only above or below, or in some particular part of their revolu-
tion. July 1833. M. F.]



ADDITIONAL NoTEf.

In consequence of the necessity I was under of sending the
paper (page 291) referred to in the above* Proceedings ' to press
by a certain time, I was unable to pursue many of the beautiful
combinations of form, colour, and appearance to which the
experiments led, especially as they promised only amusement,
and little more of instruction than the paper itself contained ;

* See in relation to this subject, Homer, on the Dsedaleum, Phil. Mag.
1843, iv. 36.

t Quarterly Journal of Science, 1831, vol. i. 334.



310 On a Peculiar Class of Optical Deceptions. [1881.

but one or two varieties in the appearances, which have occurred
to me since, are so striking, that I am glad of the opportunity
of noticing them briefly in the same Number with the paper.
At page 304 I have described the singular appearance pro-
duced when the reflected image of a revolving cog-wheel, held
before a glass, is observed through the cog-wheel itself. If,
in such a wheel, a little nearer the centre, a series of regular
apertures be cut, so as to represent cogs and their intervals,
but the number different by 1.2.3, or any small quantity, from
the number of the cogs, then, upon making the experiment as
before, that series of cogs in the revolving wheel through which
the eye looks will appear to stand still, but the other series
will travel in the spectrum : upon changing the eye to the other
series of apertures, then the quiescent part of the spectrum
will move, and the moving part become quiescent. If two or
three series more of such apertures be cut in the wheel, con-
centric one to another, but the number of intervals varying in
each, then a great variety of changes are produced, as the eye
looks through one part or another of the wheel. The series of
cogs in the spectrum move with different velocities, or in oppo-
site directions, changing with the slightest motion of the eye.
Two or three persons looking through different parts of the
wheel see appearances entirely different ; yet all these decep-
tive appearances result from a single reflexion of a single wheel,
moving in a constant direction and with uniform velocity.

By the application of colours and coloured foils, very curious
effects occur, which are endless in their variety. As an illus-
tration, let a wheel with a single series of cogs at the edge, and
with intervals equal to the cogs, have a circle of colour applied
between the cogs and the centre of the wheel ; let the part below
the cogs be green, and the part below the spaces red; the
coloured circle will consist of green and red alternately. If
this wheel be revolved before the glass, the green and red
mingle, and the reflexion observed in the ordinary way will
exhibit one uniform colour ; but if the reflexion be observed
from between or behind the cogs, the green and red imme-
diately separate, and besides having the appearance of fixed
cogs, there is also the appearance of fixed unmingled colours.
If the interval be equal to only half a cog, and three colours be
applied, the three colours may, after being mingled by rotation,



1 83 1 .] On Sounds from heated Metals. 3 1 1

be again developed, and it is easy in this way to separate many
colours from each other. The experiment in illustration of
Newton's theory of colour, by painting the head of a top and
spinning it, is well known ; by the means just described the
experiment can be still further extended, and the colours sepa-
rated one from another, even while the whole system remains
in motion.

The combination of other forms than wheels by the apparatus
described, page 294, produces very beautiful effects. The
application of colours here also is so evident as to need no
illustration. The variation of the proportion of the interval to
the remaining pasteboard causes many curious appearances,
especially when the shadows produced in sunlight are observed.

Since the printing of the paper, a friend has referred me to
the article ' Animalcula ' in Brewster's Encyclopaedia, where
an opinion on the appearance of these creatures is given, nearly
the same as that I have ventured. Speaking of the opinions of
those who suppose them to be true revolutions^ it is said, " Yet
notwithstanding our respect for the skill and talents of such
renowned naturalists, we cannot deny that we think the pro-
duction of the vortex is more probably effected by the simple
motion of the fibrilla that it may ensue from their rapidly
bending in regular or alternate succession, or by some analogous
means."



Trevelyan's Experiments on the Production of Sound during
the Conduction of Heat*.

[Read Friday evening, April 29, 1831.]

MR. TREVELYAN had remarked that when a heated poker was
laid down upon a table, so that the knob rested upon it, whilst
the hot part was supported by an interposed block of cold lead,
regular musical notes were frequently produced. By extend-
ing the experiments, he found that a better form than that of
a poker might be used for the hot metal: a piece of brass
about four inches long, one inch and a quarter broad, and half
an inch thick, should have a groove of one-eighth of an inch in
width, formed down the middle of one of the broad faces, and
then that face bevelled from the edges of the groove on each

* Quarterly Journal of Science, 1831, ii. 119.



312 On Sounds from heated Metals. [1831.

side. Beingnow placed with the groove down ward a upon a table,
and shaken, it rocks to and fro, and is in right condition for the
experiment. It is convenient to fasten a brass wire, terminated
byaknob, to one end of this rocker, so as to act as a prolongation
of an axis : it renders the whole arrangement steady and regular
in action. When this piece of metal is used instead of the
poker, musical sounds are almost always produced. The surface



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