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would be vertical, and enlarges in appearance the horizontal dimensions of the object. %. order entirely to avoid this illusion, we must use a vessel of plane smooth sides, formed of plates of glass set in a metal frame, (§ S.) We then have, in a complete manner, the curious spectacle of a considerable mass of liquid presenting the form of a perfect sphere, and imitating, in some measure, a planet suspended in space. Instead, also, of the above vessel, a glass balloon may be used, which is more simple and less expensive. In this case, indeed, the mass of oil only appears in its real figure when it occupies the centre of the balloon; but the apparent distortion is small, as long as the sphere is not moved considerably from this centre. A vessel of this kind is very convenient for most of the experiments which I shall describe in this part of the memoir; but it would not serve for those which I shall have to make known subsequently. 6. Now, having obtained, by means of the process above detailed, a fine sphere of oil well suspended, and presenting, I will suppose, a diameter of six to seven centimetres, we shall observe the following circumstances, which it is important to notice before we proceed further: In the first place, the equilibrium, previously well established, is soon disturbed of itself. At the end of a few minutes we see the sphere quit its place, and rise with extreme slowness towards the upper part of the ambient liquid. If a little alcohol be then added to restore the equilibrium, on treating the mixture by the process of $ 4, this equilibrium is again broken in the same manner at the end of a certain time. In fine, it is only by continuing for some days to maintain it by the successive addition of small quantities of alcohol that we come to obtain a permanent equilibrium, which is then no further disturbed, except by an accidental cause, of which we shall speak in the following paragraph. If the temperature does not fall below 18° centigr., the above phenomena are the only ones observed; but sometimes, if the temperature remains below that limit, and always, if it is below 15°, another effect is manifested, namely, a diminution in the transparency of the oil. These phenomena are owing to a gradual chemical action which takes place between the oil and the alcoholic mixture. The first of these would be very inconvenient in most of the experiments; but, happily, it may be obviated. This can evidently be effected by employing the two liquids only when they have already exerted upon one another all the action of which they are capable. The oil and the alcoholic mixture which I used are now inert with regard to one another, because, having been employed a great number of times, they have had time to exercise the whole of their mutual action. Besides, it is easy, in a short time, to bring the two liquids to that state of relative neutrality, by agitating them together in order to divide the oil, and thus to accelerate the action, then separating them by a suitable process. This operation requires some precautions, which we shall examine in § 24, in order not to interrupt the course of the memoir by details which are not now indispensable. In all that follows we shall always suppose that two liquids thus prepared are employed. 7. Another cause disturbs the equilibrium between the sphere of oil and the ambient liquid. This is the variations of temperature, which alter the equality of the two densities; and the degree of sensibility of such a system in this respect would hardly be conceived. For example, when the vessel is carried into a room a little warmer or colder than that in which it had been before, the sphere soon falls in the first case and rises in the second. On the mere application of the hands to the outside of the vessel, it will be seen, after a few seconds, that the sphere begins to fall. We must be continually on our guard against these effects of temperature; otherwise, they disturb the experiments. The following is a recent instance

which occurred to me. The oil and the alcoholic liquor were enclosed in different flasks, and the latter contained a very slight excess of alcohol. Having, by chance, carried these two flasks into a room warmer than that in which they had been, I first introduced into the mixture a certain quantity of oil, which, by reason of the slight excess of alcohol, descended slowly to the bottom of the flask. A short time afterwards I poured in another quantity of oil, and I was surprised to see this, on the contrary, rise towards the upper part of the mixture. The reason of the singular difference was this: the alcoholic mixture inclosed in one of the flasks was very considerable in quantity relatively to the oil which the other contained. Now, at the first moment the liquids, not having sensibly changed their temperature, maintained between them tho same relation of density ; but after a short time the oil, by reason of its small volume, having become warmer than the alcoholic mixture, had thus become relatively lighter. The warmth of the hand which held the flask in pouring out the oil must have also contributed to the effect in question.

8. Now let us suppose a fine sphere of oil in permanent equilibrium in the surrounding liquid, and let us endeavor to submit it to other forces than its own attractions.

The first idea which presents itself is to try the action of centrifugal force. For this purpose it is necessary to impress on the sphere of oil a movement of rotation around one of its diameters, and which is effected by introducing into this sphere a small metallic disc, which is made to turn upon itself by means of an axis which traverses it perpendicularly. This disc carries the oil with it by its adherence, and the whole mass of this liquid takes a movement of rotation.

Before explaining the effects which result from this movement, I shall describe in detail the apparatus I have employed—an apparatus by the aid of which all the experiments succeeded perfectly and with ihe greatest facility. It is represented in fig. 1.

Fig. 1.

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The vessel is with plane sides, formed of rectangular plates of glass set in an iron frame; the sides are each 25 centimetres bread and 20 ligh. The small disc and its axis are also of iron, a metal whose prolonged contact with oil does not stain it as copper does. The diameter of the disc is about 35 millimetres, and the axis is formed of an iron wire about 1} millimetre thick. This

axis is fixed by its lower end into a hole pierced in the middle of the plate of glass which forms the bottom of the vessel. This hole is closed below by a small plate of iron cemented to the glass. The upper end of the axis is screwed to a larger wire, which forms the prolongation of it, and which, held with a moderate degree of friction, [a frottement dour, in a piece of which I shall speak hereafter, receives at its other extremity the handle by means of which the disc is turned. When the whole system is in place the disc ought to be half way up the vessel. The square plate of glass which closes the vessel above is pieced with two openings, each furnished with an iron neck, which is closed with a stopper of the same metal. One of these openings is in the middle of the plate, and its diameter is 55 millimetres. It is through the stopper which closes it that the rod passes, d frotrement dour, which receives on the one side the axis of the disc, and on the other the handle. (See figure 2.) The other

Fig. 2.

opening is smaller, and is placed near one of the angles of the plate. It serves for introducing into the vessel either the metallic wire, by the aid of which we unite the partial masses of oil, or additional portions of alcohol, or of mixture at another degree, (§ 9,) &c., when these operations are to be performed without removing the disc from its place. Lastly, this same plate is cemented into an iron frame, which is turned up all round, so as to fit upon a vessel as a lid upon a box. The upper edges of the vessel have been ground with emery all together, after their being placed in the frame, so that the upper plate of glass fits exactly upon them; and by rubbing these edges and the metallic stoppers with a little oil, the vessel, when the plate and stoppers have been placed, may be considered as perfectly closed and keeping the mixture without evaporation of alcohol. In my apparatus the plates of glass are fixed to the metallic framing by a resinous cement, and this is slightly attacked by the alcoholic mixture. It would perhaps be better to use some glazier's putty; for the alcoholic mixture, being prepared so as not to act any more upon the oil, (§§ 6 and 24.) this latter cement would probably not suffer any alteration. However, the resinous mastic resists to such a degree, that I have been able to leave the alcoholic liquor, without inconvenience, in the vessel for whole months. The apparatus which I have just described is the best suited for obtaining, in all their beauty, the phenomena, which are the objects of these experiments; but, as I have said above, a hollow sphere of glass of pretty large dimensions might be used with less cost, and without too much disadvantage, at least for the experiments treated of in this part of the memoir. This ought to be furnished with two tubular openings, one of which would serve for introducing the system of the disc, and the other would effect the same object as the second opening of which we have spoken above. I shall, however, in what follows, suppose all along that the plane-sided vessel above described is the one employed.

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9. The apparatus being properly arranged, the next thing is to operate so as to cause a sphere of oil to surround the disc in such manner that their two centres are sensibly coincident. To attain this point, let us first endeavor, before introducing the disc into the vessel, to bring the centre of the sphere to remain at the height at which that of the disc should be. It would be extremely difficult to accomplish this by suspending a sphere in a homogeneous alcoholic mixture, as we have hitherto supposed; for then there is no reason why the sphere should not stand higher or lower; and, if even by chance it were placed exactly at the desired height, the movements which would be produced on introducing the disc would very probably change this height. It is, therefore, necessary to employ a more sure process, and the following succeeded perfectly. We begin by causing the alcoholic mixture to contain a small excess of alcohol. Then, the vessel being furnished with its lid, and the stopper which closes the central opening being lifted up, the mixture is introduced by this opening in such quantity that the vessel be not completely filled. A certain quantity of a mixture, less charged with alcohol, and marking only 16° on the areometer of Beaumé, is then cautiously added. This, from its excess of density, falls to the bottom of the vessel, where it spreads itself in a horizontal layer. The oil is then introduced, which, by reason of the small excess of alcohol contained in the upper mixture, descends through the latter till it rests upon the denser layer of the lower mixture, either in a single mass or in several partial masses (§ 4.) This being so, we unite, if the case requires it, the i. spheres into a single one; then we stir the liquor cautiously with a glass rod, so as to mix imperfectly the layer at the bottom with the higher layers, but without dividing the mass of oil, and the system is then left to rest. It will be seen that there must hence result in the alcoholic liquor a state of density increasing from the upper layers of less density to the lower of greater density than that of the oil; and that, in consequence, the mass of oil will necessarily remain in stable equilibrium with respect to the vertical direction, in a certain layer whose mean density is equal to its own. Now, in performing the operation with the neces. sary precautions—that is to say by stirring the liquid only a very little, then leaving it to rest to observe the effect which results, again stirring it and leaving it to rest, and so on; lastly adding, if necessary, a small portion of mixture at 16°, or of pure alcohol, according to circumstances, we easily succeed in causing the mass of oil to remain exactly at the desired height, and, as we have seen, without tendency to a change of position in the vertical direction." In geometrical strictness, truly, this mass of oil cannot then be any longer perfectly spherical; it must be flattened a little in the vertical direction; but, if we have operated so that the increase of the densities is very feeble at the height at which the oil stands—and we easily obtain that result by suitable trials—the flattening in question is completely insensible to the eye, and the mass appears exactly spherical.

For the experiments which we have to describe, the most convenient diameter to give to the sphere of oil is about 6 centimetres. We easily accomplish this by first forming a less sphere, and adding successively fresh portions of oil, which we unite with the first.

The next thing is to place the disc. This being attached by its axis to the rod which passes through the metallic stopper, (§ 8,) we begin by oiling it as well as the axis, then introduce it slowly into the alcoholic liquid, and cause it to penetrate by its edge into the sphere of oil. As the disc has previously been oiled, the sphere envelopes it without difficulty, and, what is remarkable,

"The different liquid layers thus superposed tend of themselves, it is true, to mix; but, as they are placed in the order of their densities, this spontaneous mixture proceeds only with extreme slowness, and it requires a great many days for the liquor to become homogeneous. No inconvenience therefore results from this for the experiments

gradually of itself assumes such a position that the axis of the disc traverses it diametrically. This effect is evidently owing to the attractive action of this axis, or rather of the coating of oil with which it has been moistened—an action which tends to operate in a symmetrical manner all around it, and thus brings the entire sphere of oil into a position symmetrical with respect to this same axis. Now it will be seen that the centre of the sphere tending, on the one hand, to remain at the height of that of the disc, on account of the superposition of the alcoholic layers of unequal density, and, on the other hand, to place itself in the axis of the disc, on account of the symmetry of the attractive actions exerted by the latter upon the oil, the centre of the sphere and that of the disc will coincide, and will thus remain in a fixed position. Only the sphere will then be slightly elongated in the vertical direction by the attraction of the axis of the disc; but this elongation is very trifling if the sphere present, as we have supposed, a diameter of 6 centimetres. 10. The sphere of oil being thus suitably placed, we slowly turn the handle. We then presently see the sphere flatten at its poles and swell out at its equator, and we thus realize on a small scale an effect which is admitted to have taken place in the planets. However, although the results may be of the same nature in the case of the great planetary masses and in that of our little masses of oil, I must not omit to remark here that there is an essential difference between the forces which are in play in the two cases. In the first, the force which tends to give to the great planetary mass a spherical figure, and against which the centrifugal force acts, is universal attraction; in the second, the force which acts the same part with regard to the small mass of oil, is molecular attraction, which is subject to different laws. But as, on either hand, the aggregate of the actions reduces itself to a contest between centrifugal force and another force tending to preserve the spherical form of the liquid mass, it appears that the results must be analogous, if not identical, with respect to the figure which that mass assumes.

[This, we do not think, is quite correct. The forces which produce the equilibrium of the ring are as follows: First. The centrifugal force which tends to throw the atoms from the centre of motion. Second. The force developed by the external and internal horizontal curvatures, the direction of which is towards the centre. Third. The force developed by the external and internal vertical curvatures, one of which acts towards the centre, and the other from the centre. The roundness of the ring is caused by the combined action of the external and internal curvatures, which, under no circumstances of velocity of rotation, would produce a flattened ring—J. H.]

In order to observe, in all its beauty, the phenomenon on which we are engaged, the handle must, at first, be turned with very little velocity—a turn in five or six seconds. The effects are even then very decided. If we afterwards apply a somewhat greater velocity—for example, a turn in four seconds— the flattening at the axis, and the swelling at the cquator, are seen to be more considerable, and they are further augmented by increasing the velocity of the handle to one turn in three seconds. Before proceeding further we may remark that, in these experiments, the handle must not be turned too long, for the mass of oil which, in the first moments, presents exactly a figure of revolution, eventually loses this form. At each fresh trial, therefore, the system must be left to repose. The oil then resumes its spherical form, and slowly, of itself, replaces itself in the proper position. The change of form which supervenes when too many turns are given to the disc occasions results of a particular kind, and which are not without interest. I shall speak of them by-and-by, (§ 22.)

11. Now, if instead of moving the handle slowly a considerable velocity is given to it, as two or three turns in a second, new, and very curious, phe

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