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of the lead upon which it rests should be clean.

The peculiar effects exhibited in these experiments depend
upon the occurrence of isochronous vibrations performed by
the rocker. When by loading the rocker these are rendered
slow, they become visible ; but when they occur with sufficient
rapidity, they produce the necessary result, a musical note, of
higher or lower pitch, as the vibrations or tappings are more
or less numerous. It often happens that other and extraneous
sounds, as those due to the ringing of the metal, the vibration
of the table, or subdivisions of the whole vibrating system,
mingle with the true sound produced by the blows of the
rocker ; these were referred to and illustrated, and a method
shown of easily distinguishing the latter from the former. It
consisted in pressing perpendicularly with a small stick or
pointed metal rod on the back of the rocker, exactly over the
groove, so as to make the vibrations quicker, but not to disturb
their regularity; the true sound of the beats of the rocker
immediately rises in pitch, and may be sometimes made to pass
through an octave or more at pleasure, falling again as the
pressure is removed.

As the sound is evidently due to the rapid blows of the rocker,
the only difficulty was to discover the true cause of the sustaining
power by which the rocker was continued in motion, whilst any
considerable difference of temperature existed between it and
the block of lead beneath ; this Mr. Faraday referred to the
ultimate expansion and contraction, as Professor Leslie and
Mr. Trevelyan have done generally ; but he gave a minute
account of the manner in which, according to his views, such
expansion and contraction could produce the effect. When
the heated rocker is reposing upon a horizontal ridge of lead,
it touches at two points, which are heated and expanded, and
form, as it were, two hills ; when one side of the rocker is raised,
the point relieved from its contact is instantly cooled by the



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

neighbouring portions of lead, the expansion ceases, and the
hill falls. When the rocker, therefore, is left free, the raised
side descends through a greater space than that through which
it was lifted, and also to a lower level than the other side ; in
consequence of which a momentum is given to it, which carries
its centre of gravity beyond the point to which it would pass
if there had been no alteration in the heights of the sustaining
points. It is this additional force which acts as a maintaining
power ; and recurs twice in each vibration, i. e. once on each
side. The force is gained by the whole rocker being lifted
bodily by the point on which it is for the time supported, and
comes into play by the side of the rocker which is descending,
having a greater space to fall through than that which is passed
over by the mere force of its momentum during its previous
rise. A curious consequence of this action is, that the force
which really lifts the rocker is on one side of the centre of
gravity, whilst the rising side of the rocker itself is on the other.
This, however, is not the only maintaining cause or mecha-
nical force generated by the alternate expansion and contraction
of the lead. If the vertical direction of the forces be put out
of consideration for a time, and the two points of support be
examined, it will be found that whilst the rocker is quiescent,
both points (with their neighbouring parts) being heated, will
expand and compress the lateral portions of the lead, until the
tension of the latter is equal to their own. When one side of
the rocker is raised, the point that it rested upon is instantly
cooled, and therefore contracts ; but as the neighbouring parts
retain their tension, they move towards the contracting part,
the other point of support moving with the rest. When the
rocker returns in its oscillation, it reheats and re-expands the
first point of support, whilst the second, now out of contact, is
cooled and contracted, and the first point, therefore, moves
towards the second. A necessary consequence of this mutual
relation of the points is, that the one under process of heating
is always moving towards the other which is under process of
cooling, and, consequently, towards a perpendicular from the
centre of gravity ; but as it is at the same time the supporting
point to the rocker, that supporting point is, by irresistible
impulse, carried in a direction under and towards the line
passing from the centre of gravity towards the earth, at the



314 On a Peculiar Class of Acoustical Figures. [1831.

same instant that the centre of gravity of the rocker is, by the
momentum of the latter, moving in the opposite direction:
hence a very simple maintaining power, sufficient, whenever
the rocker continues to vibrate, to compensate for the loss of
force in each half of the vibration which would occur if the
rocker and lead were of the same temperature. Mr. Faraday
illustrated the sustaining force of the lateral motion of the points
of support, by placing a rocker on a piece of lead, and the latter
on a board. A pair of sugar-tongs was held tightly by the
bend against the edge of the board, so that the line from the
tongs towards the rocker was perpendicular to the axis of the
latter. On making the limbs of the sugar-tongs vibrate in the
manner of a tuning-fork, they communicated longitudinal vibra-
tions of equal duration and number to the board, and through
it to the lead and points supporting the rocker ; which latter
itself immediately acquired vibratory motion isochronous with
the vibrations of the tongs, and by successive blows upon the
lead produced sound ; upon removing the rocker, and repeating
the other parts of the experiment, no sound was produced.

Experiments with other metals were then made. A piece of
curved silver plate being heated and placed on an iron triblet,
rocked and sang in the manner of the others ; this is an effect
which working silversmiths have long known. The superiority
of lead, as the cold metal, was referred to its great expansive
force by heat, combined with its deficient conducting power,
which is not a fifth of that of copper, silver, or gold ; so that
the heat accumulates much more at the point of contact in it,
than it could do in the latter metals.

Mr. Trevelyan's paper had been read to the Royal Society
of Edinburgh, but is not yet published. Mr. Faraday stated
that Mr. Trevelyan had very liberally allowed him the use of
a written copy.

On a Peculiar Class of Acoustical Figures ; and on certain
Forms assumed by groups of particles upon vibrating elastic
Surfaces*. [Read May 1% 183L]

1. THE beautiful series of forms assumed by sand, filings, or
other grains, when lying upon vibrating plates, discovered and

* Philosophical Transactions, 1831, p. 2,99.



1831.] On a Pectdiar Class of Acoustical Figures. 315

developed by Chladni, are so striking as to be recalled to the
minds of those who have seen them by the slightest reference.
They indicate the quiescent parts of the plates, and visibly
figure out what are called the nodal lines.

2. Afterwards M. Chladni observed that shavings from the
hairs of the exciting violin bow did not proceed to the nodal
lines, but were gathered together on those parts of the plate
the most violently agitated, i. e. at the centres of oscillation.
Thus when a square plate of glass held horizontally was
nipped above and below at the centre, and made to vibrate by
the application of a violin bow to the middle of one edge, so
as to produce the lowest possible sound, sand sprinkled on the
plate assumed the form of a diagonal cross; but the light
shavings were gathered together at those parts towards the
middle of the four portions where the vibrations were most
powerful and the excursions of the plate greatest.

3. Many other substances exhibited the same appearance.
Lycopodium, which was used as a light powder by Oersted,
produced the effect very well. These motions of lycopodium
are entirely distinct from those of the same substance upon
plates or rods in which longitudinal vibrations are excited.

4. In August 1827, M. Savart read a paper to the Royal
Academy of Sciences*, in which he deduced certain important
conclusions respecting the subdivision of vibrating sonorous
bodies from the forms thus assumed by light powders. The
arrangement of the sand into lines in Chladni's experiments
shows a division of the sounding plate into parts, all of which
vibrate isochronously, and produce the same tone. This is
the principal mode of division. The fine powder which can
rest at the places where the sand rests, and also accumulate at
other places, traces a more complicated figure than the sand
alone, but which is so connected with the first, that, as M.
Savart states, " the first being given, the other may be anti-
cipated with certainty ; from which it results that every time
a body emits sounds, not only is it the seat of many modes of
division which are superposed, but amongst all these modes
there are always two which are more distinctly established than
all the rest. My object in this memoir is to put this fact beyond
a doubt, and to study the laws to which they appear subject."

* Annales de Chiinie, xxxvi. p. 187.



316 On a Peculiar Class of Acoustical Figures. [1831.

5. M. Savart then proceeds to establish a secondary mode
of division in circular, rectangular, triangular and other plates ;
and in rods, rings, and membranes. This secondary mode is
pointed out by the figures delineated by the lycopodium or
other light powder ; and as far as I can perceive, its existence
is assumed, or rather proved, exclusively from these forms.
Hence much of the importance which I attach to the present
paper. A secondary mode of division, so subordinate to the
principal as to be always superposed by it, might have great
influence in reasonings upon other points in the philosophy of
vibrating plates ; to prove its existence therefore is an important
matter. But its existence being assumed and supported by
such high authority as the name of Savart, to prove its non-
existence, supposing it without foundation, is of equal con-
sequence.

6. The essential appearances, as far as I have observed
them, are as follows: Let the plate before mentioned (2),
which may be three or four inches square, be nipped and
held in a horizontal position by a pair of pincers of
the proper form, and terminated, at the part touching the
glass, by two pieces of cork ; let lycopodium powder be
sprinkled over the plate, and a violin bow be drawn down-
wards against the middle of one edge so as to produce a clear
full tone. Immediately the powder on those four parts of the
plate towards the four edges will be agitated, whilst that
towards the two diagonal cross lines will remain nearly or
quite at rest. On repeating the application of the bow several
times, a little of the loose powder, especially that in small
masses, will collect upon the diagonal lines, and thus, showing
one of the figures which Chladni discovered, will also show
the principal mode of division of the plate. Most of the
powder which remains upon the plate will, however, be col-
lected in four parcels ; one placed near to each edge of the
plate, and evidently towards the place of greatest agitation.
Whilst the plate is vibrating (and consequently sounding)
strongly, these parcels will each form a rather diffuse cloud,
moving rapidly within itself; but as the vibration diminishes,
these clouds will first contract considerably in bulk, and then
settle down into four groups, each consisting of one, two, or
more hemispherical parcels (53), which are in an extraordinary



1831.] On a Peculiar Class of Acoustical Figures. 317

condition ; for the powder of each parcel continues to rise up
at the centre and flow down on every side to the bottom,
where it enters the mass to ascend at the centre again, until
the plate has nearly ceased to vibrate. If the plate be made
to vibrate strongly, these parcels are immediately broken up,
being thrown into the air, and form clouds, which settle down
as before ; but if the plate be made to vibrate in a smaller
degree, by a more moderate application of the bow, the little
hemispherical parcels are thrown into commotion without being
sensibly separated from the plate and often slowly travel to-
wards the quiescent lines. When one or more of them have
thus receded from the place over which the clouds are always
formed, and a powerful application of the bow is made, suf-
ficient to raise the clouds, it will be seen that these heaps
rapidly diminish, the particles of which they are composed
being swept away from them, and passing back in a current
over the glass to the clouds under formation, which ultimately
settles as before into the same four groups of heaps. These
effects may be repeated any number of times, and it is evident
that the four parts into which the plate may be considered as
divided by the diagonal lines are repetitions of one effect.

7. The form of the little heaps, and the involved motion
they acquire, are no part of the phenomena under considera-
tion at present. They depend upon the adhesion of the par-
ticles to each other and to the plate, combined with the action
of the air or surrounding medium, and will be resumed here-
after (53). The point in question is the manner in which fine
particles do not merely remain at the centres of oscillation, or
places of greatest agitation, but are actually driven towards
them, and that with so much the more force as the vibrations
are more powerful.

8. That the agitated substance should be in very fine
powder, or very light, appears to be the only condition ne-
cessary for success ; fine scrapings from a common quill, even
when the eighth of an inch in length or more, will show the
effect. Chemically pure and finely divided silica rivals lyco-
podium in the beauty of its arrangement at the vibrating parts
of the plate, although the same substance in sand or heavy
particles proceeds to the lines of rest. Peroxide of tin, red
lead, vermilion, sulphate of baryta, and other heavy powders



318 On a Peculiar Class of Acoustical Figures. [1831.

when highly attenuated, collect also at the vibrating parts.
Hence it is evident that the nature of the powder has nothing
to do with its collection at the centres of agitation, provided it
be dry and fine.

9. The cause of these effects appeared to me, from the first,
to exist in the medium within which the vibrating plate and
powder were placed, and every experiment which I have made,
together with all those in M. Savart's paper, either strongly
confirm, or agree with this view. When a plate is made to
vibrate (2), currents (24) are established in the air lying upon
the surface of the plate, which pass from the quiescent lines
towards the centres or lines of vibration, that is, towards those
parts of the plates where the excursions are greatest, and then
proceeding outwards from the plate to a greater or smaller di-
stance, return towards the quiescent lines. The rapidity of
these currents, the distance to which they rise from the plate
at the centre of oscillation, or any other part, the blending of
the progressing and returning air, their power of carrying light
or heavy particles, and with more or less rapidity or force, are
dependent upon the intensity or force of the vibrations, the
medium in which the vibrating plate is placed, the vicinity of
the centre of vibration to the limit or edge of the plate, and
other circumstances, which a simple experiment or two will im-
mediately show, must exert much influence on the phenomena.

10. So strong and powerful are these currents, that when
the vibrations were energetic, the plate might be inclined
5, 6, or 8 to the horizon, and yet the gathering clouds retain
their places. As the vibrations diminished in force, the little
heaps formed from the cloud descended the hill; but on
strengthening the vibrations they melted away, the particles
ascending the inclined plane on those sides proceeding up-
wards, and passing again to the cloud. This took place when
neither sand nor filings could rest on the quiescent or nodal
lines. Nothing could remain upon the plate except those
particles which were so fine as to be governed by the currents,
which (if they exist at all) it is evident would exist in whatever
situation the plate was placed.

11. M. Savart seems to consider that the reason why the
powder gathers together at the centres of oscillation is, " that
the amplitude of the oscillations being very great, the middle



1831.] On a Peculiar Class of Acoustical Figures. 319

of each of those centres (of vibration) is the only place where
the plate remains nearly plane and horizontal, and where, con-
sequently, the powder may reunite ; whilst the surface being
inclined to the right or left of this point, the parcels of powder
cannot stop there." But the inclination thus purposely given
to the plate, was very many times that which any part acquires
by vibration in a horizontal position, and consequently proves
that the horizontality of any part of the plate is not the cause
of the powder collecting there, although it may be favourable
to its remaining there when collected.

12. Guided by the idea of what ought to happen, supposing
the cause now assigned were the true one, the following amongst
many other experiments were made. A piece of card about an
inch long and a quarter of an inch wide was fixed by a little
soft cement on the face of the plate near one edge, the plate
held as before at the middle, lycopodium or fine silica strewed
upon it, and the bow applied at the middle of another edge ;



Fig. 1.




the powder immediately advanced close to the
card, and the place of the cloud was much
nearer to the edge than before. Fig. 1 repre-
sents the arrangement; the diagonal lines being
those which sand would have formed, the line at
the top a representing the place of the card,
and the x to the right place where the bow was
applied. On applying a second piece of card,
as at 6, the powder seemed indifferent to it or nearly so, and
ultimately collected as in the first figure: c represents the
place of the cloud when no card is present.

13. Pieces of card were then fixed on the
glass in the three angular forms represented
in fig. 2 ; upon vibrating the plate, the fine
powder always went into the angle, notwith-
standing its difference of position in the three
experiments, but perfectly in accordance with
the idea of currents intercepted more or less
by the card. When two pieces of card were fixed on the
plate, as in fig. 3 a, the powder proceeded into the angle, but
not to the edge of the glass, remaining about ^th of an inch
from it ; but on closing up that opening, as at b, the powder
went quite up into the corner.



Fig. 2.





320 On a Peculiar Class of Acoustical Figures. [1831.

14. Upon fixing two pieces of card on the plate as at
c, fig. 3, the powder between them collected in the middle
very nearly as if no card had been present ; Fi g- 3.

but that on the outside of the cards gathered
close up against them, being able to proceed
so far in its way to the middle, but no further.

15. In all these experiments the sound was
very little lowered, the form of the cross
was not changed, and the light powders col-
lected on the other three portions of the plate, exactly as if no
card walls had been applied on the fourth ; so that no reason
appears for supposing that the mode in which the plate
vibrated was altered, but the powders seem to have been
carried forward by currents which could be opposed or di-
rected at pleasure by the card stops.

16. A piece of gold-leaf being laid upon the plate, so that it
did not overlap the edge, fig. 4, the current Fig 4

of air towards the centre of vibration was

beautifully shown ; for, by its force, the air

crept in under the gold-leaf on all sides, and

raised it up into the form of a blister ; that

part of the gold-leaf corresponding to the

centre of the locality of the cloud, when light

powder was used, being frequently a sixteenth or twelfth of

an inch from the glass. Lycopodium or other fine powder,

sprinkled round the edge of the gold-leaf, was carried in by

the entering air, and accumulated underneath.

17. When silica was placed on the edge of
another glass plate, or upon a book, or block
of wood, and the edge of the vibrating plate
brought as nearly as possible to the edge of
the former, fig. 5, part of the silica was al-
ways driven on to the vibrating plate, and
collected in the usual place ; as if in the
midst of all the agitation of the air in the
neighbourhood of the two edges, there was
still a current towards the centre of vibration, even from bodies
not themselves vibrating.

18. When a long glass plate^is supported by bridges or
strings at the two nodal lines represented in fig. 6, and made




Fig 5.




1831.1 On a Peculiar Class of Acoustical Figures. 321

to vibrate, the lycopodium collects in three divisions ; that
between the nodal lines does not proceed at once into a line
equidistant from the nodal lines and parallel to them, but
advances from the edges of the plate towards the middle by
paths, which are a little curved and Fig 6

oblique to the edges where they occur

near the nodal lines, but are almost

,. i i i_ j *!,

perpendicular to it elsewhere, and the

powder gradually forms a line along the middle of the plate ;
it is only by continuing the experiment for some time that it
gathers up into a heap or cloud equidistant from the nodal
lines. But upon fixing card walls upon Fi ^

this plate, as in fig. 7, the course of the
powder within the cards was directly
parallel to them and to the edge, instead
of being perpendicular, and also directly towards the centre
of oscillation. To prove that it was not as a weight that
the card acted, but as an obstacle to the currents of air
formed, it was not moved from its place, but bent flat down
outwards, and then the fine powder resumed the courses it
took upon the plate when without the cards. Upon raising
the cards the first effect was reproduced.

19. The lycopodium sprinkled over the extremities of such a
plate proceeds towards places equidistant from the sides and
near the ends, as at a, fig. 8 ; but Fig. 8.

on cementing a piece of paper to the

OX VI

edge, so as to form a wall about one

quarter or one third of an inch high,

b, the powder immediately moved up to it, and retained this

new place. In a longer narrow plate, similarly arranged, the

powder could be made to pass to either edge, or to the

middle, according as paper interceptors to the currents of air

were applied.

20. Plates of tin, four or five inches long, and from an inch
to two inches wide, fixed firmly at one end in a horizontal
position, and vibrated by applying the fingers, show the pro-
gress of the air and the light powders well. The vibrations
are of comparatively enormous extent, and the appearances
are consequently more instructive.

21. If a tuning-fork be vibrated, then held horizontally



322 On a Peculiar Class of Acoustical Figures. [1831.

with the broad surface of one leg uppermost, and a little lyco-
podium be sprinkled upon it, the collection of the powder in a
cloud along the middle, and the formation of the involving
heaps also in a line along the middle of the vibrating steel bar,
may be beautifully observed. But if a piece of paper be
attached by wax to the side of the limb, so as to form a fence
projecting above it, as in the former experiments (19), then
the powder will take up its place close to the paper ; and if
pieces of paper be attached on different parts of the same leg,
the powder will go to the different sides, in the different parts,
at the same time.

22. The effects upder consideration are exceedingly well
shown and illustrated by membranes. A piece of parchment
was stretched and tightly tied, whilst moist, over the aperture
of a funnel five or six inches in diameter ; a small hole was
made in the middle, and a horse-hair passed through it, but with
a knot at the extremity that it might thereby be retained. Upon
fixing the funnel in an upright position, and after applying a
little powdered resin to the thumbs and fore-fingers, drawing
them upward over the horse-hair, the membrane was thrown
into vibration with more or less force at pleasure. By sup-
porting the funnel on a ring, passing the horse-hair in the op-
posite direction through the hole in the membrane, and
drawing the fingers over it downwards, the direction in which



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