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they will frequently coalesce and form but one heap, which
quickly acquires a rounded outline. When in their most per-
fect and final form, they are always round.

54. The moving heaps formed by lycopodium on large
stretched drawing-paper (28), are on so large a scale as to be
very proper for critical examination. The phenomena can be
exhibited also even by dry sand on such a membrane, the sand



1831.] formed on Vibrating Elastic Surfaces. 333

being in large quantity and the vibrations slow. When the
surface is thickly covered by sand from a sieve, and the paper
tapped with the finger, the manner in which the sand draws up
into moving heaps is very beautiful.

55. When a single heap is examined, which is conveniently
done by holding a vibrating tuning-fork in a horizontal posi-
tion, and dropping some lycopodium upon it, it will be seen
that the particles of the heap rise up at the centre, overflow,
fall down upon all sides, and disappear at the bottom, appa-
rently proceeding inwards ; and this evolving and involving
motion continues until the vibrations have become very weak.

56. That the medium in which the experiment is made has
an important influence, is shown by the circumstance of heavy
particles, such as filings, exhibiting all these peculiarities when
they are placed upon surfaces vibrating in water (39) ; the
heaps being even higher at the centre than a heap of equal
diameter formed of light powder in the air. In water, too,
they are formed indifferently upon any part of the plate or
membrane which is in a vibratory state. They do not tend to
the quiescent lines ; but that is merely from the great force of
the currents formed in water as already described (38), and the
power with which they urge obstacles to the place of greatest
vibration.

57. If a glass plate be supported and vibrated (6), its sur-
face having been covered with sand enough to hide the plate,
and water enough to moisten and flow over the sand, the sand
will draw together in heaps, and these will exhibit the peculiar
and characteristic motion of the particles in a very striking
manner.

58. The aggregation and motion of these heaps, either in
air or other fluids, is a very simple consequence of the mecha-
nical impulse communicated to them by the joint action of the
vibrating surface and the surrounding medium. Thus in air,
when in the course of a vibration, the part of a plate under a
heap rises, it communicates a propelling force upwards to that
heap, mingled as it is with air, greater than that communicated
to the surrounding atmosphere, because of the superior spe-
cific gravity of the former ; upon receding from the heap, there-
fore, in performing the other half of its vibration, it forms a
partial vacuum, into which the air, round the heap, enters with



334 On the Grouping of Particles, $c. [1831.

more readiness than the heap itself; and as it enters, carries
in the powder at the bottom edge of the heap with it. This
action is repeated at every vibration, and as they occur in such
rapid succession that the eye cannot distinguish them, the
centre part of the heap is continually progressing upwards ;
and as the powder thus accumulates above, whilst the base is
continually lessened by what is swept in underneath, the parti-
cles necessarily fall over and roll down on every side.

59. Although this statement is made upon the relation of the
heap, as a mass, to the air surrounding it, yet it will be seen at
once that the same relation exists between any two parts of the
heap at different distances from the centre ; for the one nearest
the centre will be propelled upward with the greatest force,
and the other will be in the most favourable state for occupying
the partial vacuum left by the receding plate.

60. This view of the effect will immediately account for all
the appearances ; the circular form, the fusion together of two
or more heaps, their involving motion, and their existence upon
any vibrating part of the plate. The manner in which the
neighbouring particles would be absorbed by the heaps is also
evident; and as to their first formation, the slightest irregula-
rities in the powder or surface would determine a commence-
ment, which would then instantly favour the increase.

61. It is quite true, that if the powder were coherent, that
force alone would tend to produce the same effect, but only in
a very feeble degree. This is sufficiently shown by the expe-
riments made in the exhausted receiver (36). When the baro-
meter of the air-pump was at twenty-eight inches, that in the
air being about 29'2 inches, the heaps, or rather parcels, formed
very beautifully over the whole surface of the membrane ; but
they were very flat and extensive compared with the heaps in
air, and the involving motion was very weak. As the air was
admitted, the vibration being continued, the heaps rose in height,
contracted in diameter, and moved more rapidly. Again, in the
experiments with filings and sand in water, no cohesive action
could assist in producing the effect ; it must have been entirely
due to the manner in which the particles were mechanically
urged in a medium of less density than themselves.

62. The conversion of these round heaps into linear concen-
tric involving parcels, in the experiment already described



1831.] Forms of Vibrating Fluids. 335

(29. 31), when the membrane was covered by a plate of glass,
is a necessary consequence of the arrangements there made,
and tends to show how influential the action of the air or other
including medium is in all the phenomena considered in this
paper. No incompatible principles are assumed in the expli-
cation given of the arrangement of the forces producing the
two classes of effects in question ; and though by variation of
the force of vibration and other circumstances, the one effect
can be made, within certain limits, to pass into the other, no
anomaly or contradiction is thus involved, nor any result pro-
duced, which, as it appears to me, cannot be immediately ac-
counted for by reference to the principles laid down.
Royal Institution, March 21, 1831.



APPENDIX.

On the Forms and States assumed by Fluids in contact with
vibrating Elastic Surfaces.

63. When the upper surface of a plate vibrating so as to
produce sound (2. 6) is covered with a layer of water, the water
usually presents a beautifully crispated appearance in the neigh-
bourhood of the centres of vibration. This appearance has
been observed by Oersted*, Wheatstonef, Weber J, and pro-
bably others. It, like the former phenomena which I have en-
deavoured to explain, has led to false theory, and being either
not understood or misunderstood, has proved an obstacle to
the progress of acoustical philosophy.

64. On completing the preceding investigation, I was led to
believe that the principles assumed would, in conjunction with
the cohesion of fluids, account for these phenomena. Experi-
mental investigation fully confirmed this expectation, but the
results were obtained at too late a period to be presented to
the Royal Society before the close of the Session ; and it is
only because the philosophy and the subject itself is a part of
that received into the Philosophical Transactions in the pre-
ceding paper, that I am allowed, by the President and Council,
the privilege of attaching the present paper in the form of an
Appendix.

* Lieber's Hist, of Natural Phenomena for 1813.

t Annals of Philosophy, N. S. vi. p. 82. J Wellenlehre, p. 4 14.




336 On the Forms and States of Fluids [1831.

65. The general phenomenon now to be considered is easily
produced upon a square plate nipped in the middle, either by
the fingers or the pincers (2. 6), held horizontally, covered with
sufficient water on the upper surface to flow freely from side to
side when inclined, and made to vibrate strongly by a bow applied
to one edge, x , fig. 12, in the usual way. Fig. 12.
Crispations appear on the surface of the water,
first at the centres of vibration, and extend
more or less towards the nodal lines, as the
vibrations are stronger or weaker. The cris-
pation presents the appearance of small co-
noidal elevations of equal lateral extent, usually
arranged rectangularly with extreme regularity ; permanent*
(in appearance), so long as a certain degree of vibration is sus-
tained ; increasing and diminishing in height, with increased
or diminished vibration ; but not affected in their lateral extent
by such variations, though the whole crispated surface is en-
larged or diminished at those times. If the plate be vibrated,
so as to produce a different note, the crispations still appear at
the centre of vibration, but are smaller for a high note, larger
for a low one. The same note produced on different sized
plates, by different modes of vibration, appears to produce
crispations of the same dimension, other circumstances being
the same.

66. These appearances are beautifully seen when ink diluted
with its bulk of water is used on the plate.

67. It was necessary, for examination, both to prolong and
enlarge the effect, and the following were found advantageous
modes of producing it. Plates of crown-glass, from eighteen
to twenty-two inches long, and three or four inches wide, were
supported each by two triangular pieces of wood acting as
bridges (18), and made to vibrate by a small glass rod or tube
resting perpendicularly at the middle, over which the moist
fingers were passed. By sprinkling dry sand on the plates,
and shifting the bridges, the nodal lines were found (usually
about one-fifth of the whole length from each end), and their
places marked by a file or diamond. Then clearing away the
sand, putting water or ink upon the plate, and applying the rod
or fingers, it was easy to produce the crispations and sustain

* Weber's Wellenlehre, p. 414.



1831.] on Vibrating Elastic Surfaces. 337

them undisturbed, and with equal intensity for any length of
time.

68. By making a broad mark, or Fig. 13.
raising a little ledge of bees' wax, or

a mixture of bees' wax and turpentine,

it was easy to confine the pool of water

to the middle part of the plate, fig. 13, where, of course, the

crispations were most powerfully produced. Such a barrier is

often useful to separate the wet and dry parts of the glass,

especially when a violin bow is used as the exciter.

69. In other experiments, deal laths, two, three, or four feet
long, one inch and a half wide, and three-eighths or more of
an inch in thickness, were used instead of the glass plates.
These could be made to vibrate by the fingers and wet rod (67),
and by either shifting the bridges or changing the lath, an
almost unlimited change of isochronous vibrations, from that
producing a high note to those in which not more than five or
six occurred in a second, could be obtained. The crispations
were formed upon a glass plate attached to the middle of the
lath, by two or three little pellets of soft cement*.

70. Obtained in this way the appearances were very beauti-
ful, and the facilities very great. A glass plate, from four to
eight inches square, could be covered uniformly with crispa-
tions of the utmost regularity ; for, by attaching the plate with
a little method, and at points equidistant from the centre of the
bar, it was easy to make every part travel with the same velo-
city, and in that respect differ from and surpass the bar which
sustained it. The conoidal heaps constituting the crispation
could be so enlarged by slowness of vibration, that three or
four occupied a linear inch. The glass plate could be removed,
and another of different form or substance, and with other
fluids, as mercury, &c., substituted in an instant.

71. In using laths, it is necessary to confine the parts bear-
ing upon the bridges, either by slight pressure of the fingers,
or by loops of string, or by weights. The exciting glass rod
need not necessarily rest upon the middle of the bar or plate,
but may be applied with equal effect at some distance from it.
Long laths may be made to subdivide in their mode of vibra-
tion, according as the rod is applied to different places, and the

* Equal parts of yellow wax and turpentine.

z



338 On the Forms and States of Fluids [1831.

pressure given by the exciting moist fingers is varied; with
each change of this kind an immediate change of the crispation
is observed.

72. This form of apparatus was enlarged until a board
eighteen feet long was used, the layer of water being now three-
fourths of an inch in depth and twenty-eight inches by twenty
inches in extent. The sides of the cistern were very much in-
clined, so that the water should gradually diminish in depth,
and thus reflected waves be prevented. The vibrations were
so slow as to be produced by the direct application of the hand,
and the heaps were each from an inch to two inches in extent.
Though of this magnitude, they were identical in their nature
with those forming crispations on so small a scale as to appear
merely like a dullness on the surface of the water.

73. In these experiments the proportion of water requires a
general adjustment, the crispations being produced more readily
and beautifully when there is a certain quantity than when there
is less. For small crispations, the water should flow upon the
surface freely. Large crispations require more water than
small ones. Too much water sometimes interferes with the
beauty of the appearance, but the crispation is not incompatible
with much fluid, for the depth may amount to eight, ten, or
twelve inches (111), and is probably unlimited.

74. These crispations are equally produced upon either the
under or the upper surface of vibrating plates. When the lower
surface is moistened, and the bow applied (65), the drops which
hang down by the force of gravity are rippled ; but being im-
mediately gathered up as described in the former paper (44), a
certain definite layer is produced, which is beautifully rippled
or crispated at the centres of vibration.

75. Most fluids, if not all, may be used to produce these
crispations, but some with particular advantages ; alcohol, oil
of turpentine, white of egg*, ink, and milk produce them.
White of egg, notwithstanding its viscosity, shows them readily
and beautifully. Ink has great advantages, because, from its
colour and opacity, the surface form is seen undisturbed by
any reflexion from the glass beneath ; its appearance in sun-
shine is exceedingly beautiful. When diluted ink is used for
large crispations, upon tin plate or over white paper, or mer-

* Wheatstone.



1831.] on Vibrating Elastic Surfaces. 339

cury, the different degrees of colour or translucency corre-
sponding to different depths of the fluid, give important infor-
mation relative to the true nature of the phenomena (78. 85. 97).
Milk is, for its opacity, of similar advantage, especially when a
light is placed beneath ; and being more viscid than water, is
better for large arrangements (72.98), because it produces less
splashing.

76. Oil does not show small crispations readily (120), and
was supposed to be incapable of forming them, but when
warmed (by which its liquidity is increased) it produces them
freely. Cold oil will also produce large crispations, and for
very large ones would probably be better than water, because
of its cohesion. The difference between oil and white of egg
is remarkable ; for the latter, from common observation, would
appear to be a thicker fluid than oil : but the qualities of cohe-
sion differ in the two, the apparent thickness of white of egg
depending upon an elastic power (probably due to an approach
to structure), which tends to restore its particles to their first
position, and co-existing with great freedom to move through
small spaces, whilst that of oil is due to a real difficulty in re-
moving the particles one by another. It is possible that the
power of assuming, more or less readily, the crispated state,
may be a useful and even important indication of the internal
constitution of different fluids.

77. With mercury the crispations are formed with great
facility, and of extreme beauty, when a piece of amalgamated
tin or copper plate, fixed on a lath (69), is flooded with the
fluid metal, and then vibrated. A film quickly covers the
metal, and then the appearances are not so regular as at first ;
but on removing the film by a piece of paper, their regularity
and beauty are restored. It is more convenient to cover the
mercury with a little very dilute acetic or nitric acid ; for then
the crispations may be produced and maintained for any length
of time with a surface of perfect brilliancy.

78. When a layer of ink was put over the mercury, the acid
of the ink removed all film, and the summits of the metallic
heaps, by diminishing the thickness of the ink over them, be-
came more or less visible, producing the appearance of pearls
of equal size beautifully arranged in a black medium. When
mercury covered with a film of dilute acid was vibrated in the



340 On the Forms and States of Fluids [1831 .

sunshine, and the light reflected from its surface received on a
screen, it formed a very beautiful and regular image ; but the
screen required to be placed very near to the metal, because
of the short focal lengths of the depressions on the mercurial
surface.

79. It is sometimes difficult to arrive by inspection at a
satisfactory conclusion of the forms and arrangements thus
presented, because of multiplied reflexion and the particular
condition of the whole, which will be described hereafter (95).
When observed, well formed with vibrations so slow as to pro-
duce three or four elevations in a linear inch (70), they are seen
to be conoidal heaps rounded above, and apparently passing
into each other below by a curvature in the opposite direction.
When arranged regularly, each is surrounded by eight others ;
so that, a single light being used, nine images may be sent from
each elevation to the eye. These are still further complicated,
when transparent fluids are used, by reflexions from the glass
beneath. The use of ink (75) removes a good deal of the diffi-
culty experienced, and the production of slow, regular, sus-
tained vibrations, more (67. 69).

80. These elevations I will endeavour to distinguish hence-
forth by the term heaps.

81. The crispation on the long plate of glass described (67)
always ultimately assumed a rectangular arrangement, i. e. the
heaps were equidistant, and in rows parallel or at right angles
to each other. The rows usually form angles of 45 to the
sides of the plate at the commencement ; but if the vibration
be continued, the whole system usually wheels round through
45 until the rows coincide with the edges of the plate.

82. The lateral dimension of the heaps remained constant,
notwithstanding considerable variations in the force of vibra-
tion. But it was soon found that variation in the depth of
water affected their number ; that with less water the heaps
were smaller, and with more water larger, though the sound
therefore and the number of vibrations in a given period re-
mained the same. The number of heaps could be reduced to
eight or increased to eleven and a half in the three inches by a
change in no other condition than the depth of fluid.

83. With the above plate (67. 8 1 ) the appearances were usually
in the following order, the pool of water being, quadrangular or



1831.]



on Vibrating Elastic Surfaces.



341



nearly so, and the exciting rod resting in the middle of it.
Ring-like linear heaps concentric to the exciting rod first
form to the number of six or seven ; these may be retained by
a moderated state of vibration, and produce intervals which
measured across the diameter of the rings are to the number
of ten in three inches, with a certain constant depth of water.
15y increasing the force of vibration, the altitude of these ele-
vations increases, but not their lateral dimension; and then linear
heaps form across these circles and the plate, and parallel to
the bridges, having an evident relation to the manner in which
the whole plate vibrates. These, which like all other of these
phenomena are strongest at the part most strongly vibrating,
soon break up the circles, and are themselves broken up, produ-
cing independent heaps, which at first are irregular and change-
able, but soon become uniform and produce the quadrangular
order ; first at angles of 45 to the edges of the plate, but gra-
dually moving round until parallel to them. So the arrange-
ment continues, unless the force be so violent as to break it up
altogether : if the vibratory force be gradually diminished, then
the heaps as gradually fall, but without returning through the
order in which they were produced. The following lines may
serve to indicate the course of the phenomena.

Fig. 14.




When perfectly formed, the heaps are also to the number of
ten in three inches with the same depth of water as that which
produced the rings. The intervals between the rings and the
heaps are the same, other influential circumstances remaining
unaltered.

84. Another form of heaps occasionally occurred, but always
passing ultimately into those described. These heaps were
grouped in an arrangement still very nearly rectangular,
and at angles of 45 to the sides of the plate, but were con-
tracted in one direction, and elongated in the other ; these
directions being parallel to the sides and ends of the plate.



342 On the Forms and States of Fluids [1831.

If the marks in fig. 15 be supposed to represent Fig. 15.

the tops of the heaps, an idea of the whole will ~"_j-_^-_^

be obtained. Three inches along these heaps -

included eight, but across them it included T_~I_~L'

fifteen nearly. These numbers are therefore the Z_~~L.~I_T_~I
relation of length to breadth. But along the I_~H~IL~7V~
lines of the quadrilateral arrangement three ~ ~"
inches included eleven heaps, which, notwithstanding the dif-
ference in form, is the same number that was produced by the
same plate, with the same depths of water, when the heaps were
round ; therefore an equal number of heaps existed in the
same area in both cases ; and the departure from perfect rect-
angular arrangement, and also the ratio of 1 : 2, is probably
due to some slight influence of the sides of the plate.

85. When mercury covered with a film of very dilute nitric
acid is vibrated (77), the rectangular arrangement is constantly
obtained. When vibrated under dilute ink (78), it is still more
beautifully seen and distinguished. The tin plate sustaining
the mercury was square, and when the whole surface was
covered with crispations, the lines of the rectangular arrange-
ment were always at angles of 45 to its edges.

86. When sand is sprinkled uniformly over a plate on which
large water crispations are produced, i. e. four, five or six in
the inch, it gives some very important indications. It imme-
diately becomes arranged under the water, and with a little
method may be made to yield very regular forms,

It is always removed from under the heaps,
passing to the parts between them, and fre-
quently producing therefore the accompanying
form, fig. 16, of great regularity. As the sand
figure remains when the vibration has ceased,
it allows of the determination of position, the
measurement of intervals, &c. very conveniently.

87. Very often the lines of sand are not continuous, but
separated with extreme regularity into portions, as represented
fig. 17. The portions of these lines were sometimes, with
little sand on the plate, very small, fig. 18; and when more
sand was present they were thickened occasionally, fig. 19;
then assuming the appearance of heaps arranged in straight
lines at angles of 45 to the lines regulating the position of the




1831.] on Vibrating Elastic Surfaces. 343

water-heaps which formed them, and just double in number to
the latter. At other times, the sand, instead of being deficient
at the intersecting angle, would accumulate there only, fig. 20 ;
Fig. 17. Fig. 18. Fig. 19.




\ / \ / \



.v



\ / \ / \ / * * <k f \ *

/ \ / \ / \ *%*%#*

N / S / \ / v * * * v <

/ \ / \ X' \ ***<%*>

and at other times would accumulate there principally, but still
show the original form by a few connecting particles, fig. 21.

88. When the heaps were of the form described (84), the
sand was still washed from under them ; it did not however
assume lines parallel to the rectangular arrangement of the
heaps, but was arranged as in fig. 22.

Fig. 20. Fig. 21. Fig. 22.




89. When only the circular linear heaps (83) were produced,



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