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the force was applied could be varied according to circum-

23. When lycopodium or light powders were sprinkled upon
this surface, the rapidity with which they ran to the centre,
the cloud formed there, the involving heaps, and many other
circumstances, could be observed very advantageously.

24?. The currents which I have considered as existing upon
the surface of the plate, membranes, &c. from the quiescent
parts towards the centres or lines of vibration (9), arise neces-
sarily from the mechanical action of that surface upon the air.
As any particular part of the surface moves upwards in the
course of its vibration, it propels the air and communicates a
certain degree of force to it, perpendicular or nearly so to the
vibrating surface ; as it returns, in the course of its vibration,
it recedes from the air so projected, and the latter consequently
tends to return into the partial vacuum thus formed. But as

1831.] On a Peculiar Class of Acoustical Figures.

of two neighbouring portions of air, that over the part of the
plate nearest to the centre of oscillation has had more pro-
jectile force communicated to it than the other, because the
part of the plate urging it was moving with greater velocity,
and through a greater space, so it is in a more unfavourable
condition for its immediate return, and the other, i. e. the
portion next to it towards the quiescent line, presses into its
place. This effect is still further favoured, because the portion
of air thus displaced is urged from similar causes at the same
moment into the place left vacant by the air still nearer the
centre of oscillation ; so that each time the plate recedes from
the air, an advance of the air immediately above it is made
from the quiescent towards the vibrating parts of the plates.

25. It will be evident that this current is highly favourable
for the transference of light powders towards the centre of
vibration. Whilst the air is forced forward, the advance of
the plate against the particles holds them tight; but when
the plate recedes, and the current exists, the particles are at
that moment left unsupported except by the air, and are free
to move with it.

26. The air which is thus thrown forward at and towards
the centre of oscillation, must tend by the forces concerned to
return towards the quiescent lines, forming a current in the
opposite direction to the first and blending more or less with
it. I endeavoured, in various ways, to make the extent of this
system of currents visible. In the experiment already referred
to, where gold-leaf was placed over the centre of oscillation
(16), the upward current at the most powerful part was able
to raise the leaf about one tenth of an inch from the plate.
The higher the sounds with the same plate or membrane, i. e.
the greater the number of vibrations, the less extensive must
be the series of currents ; the slower the vibrations, or the
more extensive the excursion of the parts from increased force
applied, the greater the extent of disturbance. With glass
plates (2. 12) the cloud is higher and larger as the vibrations
are stronger, but still not so extensive as they are upon the
stretched membrane (22), where the cloud may frequently be
seen rising up in the middle and flowing over towards the

27. When the membrane stretched upon the funnel (22) was

324f On a Peculiar Class of Acoustical Figures. [1831.

made to vibrate by the horse-hair proceeding downwards, and
a large glass tube, as a cylindrical lamp-glass, was brought
near to the centre of vibration, no evidence of a current en-
tirely through the lamp-glass could be perceived ; but still the
most striking proofs were obtained of the existence of carrying
currents by the effects upon the light powder, for it flew more
rapidly under the edge, and tended to collect towards the axis
of the tube ; it could even be diverted somewhat from its course
towards the centre of oscillation. A piece of upright paper,
held with its edge equally near, did not produce the same
effect ; but immediately that it was rolled into a tube, it did.
When the glass chimney was suspended very carefully, and at
but a small distance from the membrane, the powder often
collected at the edge, and revolved there ; a complicated action
between the currents and the space under the thickness of the
glass taking place, but still tending to show the influence of
the air in arranging and disposing the powders.

28. A sheet of drawing-paper was stretched tightly over a
frame so as to form a tense elastic surface nearly three feet by
two feet in extent. Upon placing this in a horizontal position,
throwing a spoonful of lycopodium upon it, and striking it
smartly below with the fingers, the phenomena of collection at
the centre of vibration, and of moving heaps, could be obtained
upon a magnificent scale. When the lycopodium was uniformly
spread over the surface, and any part of the paper slightly
tapped by the hand, the lycopodium at any place chosen could
be drawn together merely by holding the lamp-glass over it.
It will be unnecessary to enter into the detail of the various
actions combining to produce these effects; it is sufficiently
evident, from the mode in which they may be varied, that they
depend upon currents of air.

29. A very interesting set of effects occurred when the
stretched parchment upon the funnel (22) was vibrated under
plates ; the horse-hair was directed downwards, and the mem-
brane, after being sprinkled over with light powder, was
covered by a plate of glass resting upon the edge of the
funnel ; upon throwing the membrane into a vibratory state,
the powder collected with much greater rapidity than without
the plate; and instead of forming the semi-globular moving
heaps, it formed linear arrangements, all concentric to the

1831.] On a Peculiar Class of Acoustical Figures. S25

centre of vibration. When the vibrations were strong, these
assumed a revolving motion, rolling towards the centre at the
part in contact with the membrane, and from it at the part
nearest the glass ; thus illustrating in the clearest manner the
double currents caged up between the glass and the mem-
brane. The effect was well shown by carbonate of magnesia.

30. Sometimes, when the plate was held down very close and
tight, and the vibrations were few and large, the powder was
all blown out at the edge ; for then the whole arrangement
acted as a bellows ; and as the entering air travelled with
much less velocity than the expelled air, and as the forces of
the currents are as the squares of the velocity, the issuing air
carried the powder more forcibly than the air which passed in,
and finally threw it out.

31. A thin plate of mica laid loosely upon the vibrating
membrane showed the rotating concentric lines exceedingly

32. From these experiments on plates and surfaces vibrating
in air, it appears that the forms assumed by the determination
of light powders towards the places of most intense vibration,
depend, not upon any secondary mode of division, or upon any
immediate and peculiar action of the plate, but upon the
currents of air necessarily formed over its surface, in conse-
quence of the extra-mechanical action of one part beyond
another. In this point of view the nature of the medium in
which those currents were formed ought to have great influ-
ence over the phenomena ; for the only reason why silica as
sand should pass towards the quiescent lines, whilst the same
silica as fine powder went from them, is, that in its first form
the particles are thrown up so high by the vibrations as to be
above the currents, and that if they were not thus thrown out
of their reach they would be too heavy to be governed by
them ; whilst in the second form they are not thrown out of
the lower current, except near the principal place of oscillation,
and are so light as to be carried by it in whatever direction it
may proceed.

33. In the exhausted receiver of the air-pump, therefore, the
phenomena ought not to occur as in air ; for as the force of
the currents would be there excessively weakened, the light
powders ought to assume the part of heavier grains in the air.

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

Again, in denser media than air, as in water for instance, there
was every reason to expect that the heavier powders, as sand
and filings, would perform the part of light powders in air, and
be carried from the quiescent to the vibrating parts.

34. The experiments in the air-pump receiver were made in
two ways. A round plate of glass was supported on four narrow
cork legs upon a table, and then a thin glass rod with a rounded
end held perpendicularly upon the middle of the glass. By pass-
ing the moistened fingers longitudinally along this rod the plate
was thrown into a vibratory state ; the cork legs were then ad-
justed in the circular nodal line occurring with this mode of vibra-
tion ; and when their places were thus found they were perma-
nently fixed. The plate was then transferred into the receiver of
an air-pump, and the glass rod by which it was to be thrown into
vibration passed through collars in the upper part of the re-
ceiver, the entrance of air there being prevented by abundance
of pomatum. When fine silica was sprinkled upon the plate,
and the plate vibrated by the wet fingers applied to the rod,
the receiver not being exhausted, the fine powder travelled
from the nodal line, part collecting at the centre, and another
part in a circle, between the nodal line and the edge. Both
these situations were places of vibration, and exhibited them-
selves as such by the agitation of the powder. Upon again
sprinkling fine silica uniformly over the plate, exhausting the
receiver to twenty-eight inches, and vibrating the plate, the
silica went from the middle towards the nodal line or place of
rest, performing exactly the part of sand in air. It did not move
at the edges of the plate, and as the apparatus was inconvenient
and broke during the experiment, the following arrangement
was adopted in its place.

35. The mouth of a funnel was covered (22) with a well-
stretched piece of fine parchment, and then fixed on a stand
with the membrane horizontal ; the horse-hair was passed
loosely through a hole in a cork, fixed in a metallic tube on the
top of the air-pump receiver ; the tube above the cork was
filled to the depth of half an inch with pomatum, and another
perforated cork put over that ; a cup was formed on the top
of the second cork, which was filled with water. In this way
the horse-hair passed first through pomatum and then water,
and by giving a little pressure and rotary motion to the upper

1831.] On a Peculiar Class of Acoustical Figures. 327

cork during the time that the horse-hair was used to throw the
membrane into vibration, it was easy to keep the pomatum
below perfectly in contact with the hair, and even to make it
exude upwards into the water above. Thus no possibility of
the entrance of air by and along the horse-hair could exist, and
the tightness of all the other and fixed parts of the apparatus
was ascertained by the ordinary mode of examination. A little
paper shelf was placed in the receiver under the cork to catch
any portion of pomatum that might be forced through by the
pressure, and prevent its falling on to the membrane.

36. This arrangement succeeded : when the receiver was
full of air, the lycopodium gathered at the centre of the mem-
brane with great facility and readiness, exhibiting the cloud,
the currents, and the involving heaps. Upon exhausting the
receiver, until the barometrical gauge was at twenty-eight
inches, the lycopodium, instead of collecting at the centre,
passed across the membrane, towards one side which was a
little lower than the other. It passed by the middle just as it
did over any other part ; and when the force of the vibrations
was much increased, although the powder was more agitated
at the middle than elsewhere, it did not collect there, but went
towards the edges or quiescent parts. Upon allowing air to
enter until the barometer stood at twenty-six inches, and re-
peating the experiments, the effect was nearly the same. When
the vibrations were very strong, there were faint appearances
of a cloud, consisting of the very finest particles, collecting at
the centre of vibration; but no sensible accumulation of the
powder took place. At twenty-four inches of the barometer
the accumulation at the centre began to appear, and there was
a sensible, though very slight effect visible of the return of the
powder from the edges. At twenty-two inches these effects
were stronger ; and when the barometer was at twenty inches,
the currents of air within the receiver had force enough to
cause the collection of the principal part of the lycopodium at
the centre of vibration. Upon again, however, restoring the
exhaustion to twenty-eight inches, all the effects were repro-
duced as at first, and the lycopodium again proceeded to the
lower or the quiescent parts of the membrane. These alternate
effects were obtained several times in succession before the
apparatus was dismounted.

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

37. In this form of experiment there were striking proofs of
the existence of a current upwards from the middle of the mem-
brane when vibrating in air (24), and the extent of the system
of currents (26) was partly indicated. The powder purposely
collected at the middle by vibrations, when the receiver was
full of air, was observed as to the height to which it was forced
upwards by the vibrations ; and then the receiver being ex-
hausted, the height to which the powder was thrown by similar
vibrations was again observed. In the latter cases it was nothing
like so great as in the former, the height not being two-thirds,
and barely one-half, the first height. Had the powder been
thrown up by mere propulsion, it should have risen far higher
in vacuo than in air : but the reverse took place ; and the cause
appears to be, that in air the current had force enough to carry
the fine particles up to a height far beyond what the mere
blow which they received from the vibrating membrane could

38. For the experiments in a denser medium than air, water
was chosen. A circular plate of glass was supported upon four
feet in a horizontal position, surrounded by two or three inches
of water, and thrown into vibration by applying a glass rod
perpendicular to the middle, as in the first experiment in vacuo
(34) ; the feet were shifted until the arrangement gave a clear
sound, and the moistened brass filings sprinkled upon the plate
formed regular lines or figures. These lines were not however
lines of rest, as they would have been in the air, but were the
places of greatest vibration ; as was abundantly evident from
their being distant from that nodal line determined and indicated
by the contact of the feet, and also from the violent agitation
of the filings. In fact, the filings proceeded from the quiescent
to the moving parts, and there were gathered together ; not
only forming the cloud of particles over the places of intense
vibration, but also settling down, when the vibrations were
weaker, into the same involving groups, and in every respect
imitating the action of light powders in air. Sand was affected
exactly in the same manner ; and even grains of platina could
be in this way collected by the currents formed in so dense a
medium as water.

39. The experiments were then made under water with the
membranes stretched over funnels (22) and thrown into vibration

1831.] On a Peculiar Class of Acoustical Figures. 329

by horse-hairs drawn between the fingers. The space beneath
the membrane could be retained, filled with air, whilst the upper
surface was covered two or three inches deep with water ; or
the space below could also be filled with water, or the force
applied to the membrane by the horse-hair could be upwards
or downwards at pleasure. In all these experiments the sand or
filings could be made to pass with the utmost facility to the
most powerfully vibrating part, that being either at the centre
only, or in addition, in circular lines, according to the mode in
which the membrane vibrated. The edge of the funnel was
always a line of rest ; but circular nodal lines were also formed,
which were indicated, not by the accumulation of filings upon
them, but by the tranquil state of those filings which happened
to be there, and also by being between those parts where the
filings, by their accumulation and violent agitation, indicated
the parts in the most powerful vibratory state.

40. Even when by the relaxation of the parchment from
moisture, and the force upwards applied by the horse-hair, the
central part of the membrane was raised the eighth of an inch
or more above the edges, the circle not being four inches in
diameter, still the filings would collect there.

41. When in place of parchment common linen was used, as
becoming tighter rather than looser when wetted, the same
effects were obtained.

42. Both the reasoning adopted and the effects described
were such as to lead to the expectation,'that if the plate vibrating
in air was covered with a layer of liquid instead of sand or ly co-
podium, that liquid ought to be determined from the quiescent
to the vibrating parts and be accumulated there. A square
plate was therefore covered with water, and vibrated as in the
former experiments (2. 6) ; but all endeavours to ascertain
whether accumulation occurred at the centres of oscillation,
either by direct observation, or the reflexion from its surface
of right-lined figures, or by looking through the parts, as
through a lens, at small print and other objects, failed.

43. As, however, when the plate was strongly vibrated, the
well-known and peculiar crispations which form on water at the
centres of vibration, occurred and prevented any possible de-
cision as to accumulation, it was only when these were absent
and the vibration weak, and the accumulation therefore small,

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

that any satisfactory result was to be expected ; but as even
then no appearance was perceived, it was concluded that the force
of gravity combined with the mobility of the fluid was sufficient
to restore the uniform condition of the layer of water after the
bow was withdrawn, and before the eye had time to observe
the convexity expected.

44. To remove in part the effect of gravity, or rather to make
it coincide with, instead of oppose the convexity, the under
surface of the plate was moistened instead of the upper, and by

Fig. 9.

inclining the plate a little, the water made to
hang in drops at a or b or c, fig. 9, at pleasure.
On applying the bow at x , and causing the
plate to vibrate, the drops instantly disappeared,
the water being gathered up and expanded
laterally over the parts of the plate from which
it had flowed. On stopping the vibration, it
again accumulated in hanging drops, whicli instantly disap-
peared as before on causing the plate to vibrate, the force of
gravity being entirely overpowered by the superior forces
excited by the vibrating plate. Still, no visible evidence of
convexity at the centres of vibration were obtained, and the
water appeared rather to be urged from the vibrating parts
than to them.

45. The tenacity of oil led to the expectation that better
results would be obtained with it than with water. A round
plate, held horizontally by the middle (6. 42),
was covered with oil over the upper surface,
so as to be flooded, except at x , fig. 10, and
the bow applied at x as before, to produce
strong vibration. No crispation occurred in
the oil, but it immediately accumulated at a,
b } and c, forming fluid lenses there, rendered
evident by their magnifying power when print was looked at
through them. The accumulations were also visible on putting
a sheet of white paper beneath, in consequence of the colour
of the oil being deeper at the accumulations than elsewhere ;
and they were also rendered beautifully evident by making the
experiment in sunshine, or by putting a candle beneath the
plate, and placing a screen on the opposite side to receive the
images formed at the focal distance.

Fig. 10.

1831.] On a Peculiar Class of Acoustical Figures. 331

46. When the vibration of the plate ceased, the oil gradually
flowed back until of uniform depth. On renewing the vibration,
the accumulations were re-formed, the phenomena of accumula-
tion occurring with as much certainty and beauty as if lyco-
podium powder had been used.

47. To remove every doubt of the fluid passing from the
quiescent to the agitated parts, centres of vibration were used,
nearly surrounded by nodal lines. A square plate, fig. 11,
being held at c, and the bow applied at x , Fig 1 1
gave with sand, nodal lines, resembling those

in the figure. Then clearing off the sand,
putting oil in its place, and producing the same
mode of vibration as before, the oil accumulated
at a and b, forming two heaps or lenses as in
the former experiment (45).

48. The experiment made with water on the under surface
(44) was now repeated with oil, the round plate being used (45).
The hanging drop of oil rose up as the water did before, but
the lateral diffusion was soon limited ; for lenses were formed
at the centres of vibration just as when the oil was upon the
upper surface, and, as far as could be ascertained by general
examination, of the same form and power. On stopping the
vibration, the oil gathered again into hanging drops ; and on
renewing it, it was again disposed in the lens-like accumulations.

49. With white of egg the same observable accumulation at
the centres of vibration could be produced.

50. Hence it is evident that when a surface vibrating normally,
is covered with a layer of liquid, that liquid is determined from
the quiescent to the vibrating parts, producing accumulation
at the latter places ; and that this accumulation is limited, so
that if purposely rendered too great by gravity or other means,
it will quickly be diminished by the vibrations until the depth
of fluid at any one part has a certain and constant relation to
the velocity there and to the depth elsewhere.

51. From the accumulated evidence which these experiments
afford, I think there can remain no doubt of the cause of the
collection of fine powders at the centres or lines of vibration of
plates, membranes, &c. under common circumstances ; and that
no secondary mode of division need be assumed to account for
them. I have been the more desirous of accumulating experi-

332 On the Moving Groups of Particles [1831.

mental evidence, because I have thought on the one hand
that the authority of Savart should not be doubted on slight
grounds ; and on the other, that if by accident it be placed in
the wrong scale, the weight of evidence against it should be
such as fully to establish the truth and prevent a repetition of
the error by others.

52. It must be evident that the phenomena of collection at
the centres or lines of greatest vibration are exhibited in their
purest form at those places which are surrounded by nodal
lines ; and that where the centre or place of vibration is at or
near to an edge, the effects must be very much modified by the
manner in which the air is there agitated. It is this influence,
which, in the square plates (6. 12) and other arrangements,
prevents the clouds being at the very edge of the glass. They
may be well illustrated by vibrating tin plates under water over
a white bottom, and sprinkling dark-coloured sand or filings
upon various parts of the plates.

On the peculiar Arrangement and Motions of the Heaps formed
by Particles lying on vibrating Surfaces.

53. The peculiar manner in which the fine powder upon a
vibrating surface is accumulated into little heaps, either hemi-
spherical or merely rounded, and larger or smaller in size, has
already been described (6. 28), as well also as the singular
motion which they possess, as long as the plate continues in
vibration. These heaps form on any part of the surface which
is in a vibratory state, and not merely under the clouds pro-
duced at the centres of vibration, although the particles of the
clouds always settle into similar heaps. They have a tendency,
as heaps, to proceed to the nodal or quiescent lines, but are
often swept away in powder by the currents already described
(6). When on a place of rest, they do not acquire the invol-
ving motion. When two or more are near together or touch,

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