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nature as those which we have considered throughout the preceding details, towards the interior of the liquid to which they belong, and these pressures must consequently also impart a figure of equilibrium to the surface in intaglio; so that if the immersed mass of itself had no tendency to assume any one figure rather than another, the surrounding liquid would give it a determinate one, by compelling it to mould itself in the above hollow figure. This is why a bubble of air in a liquid assumes the globular form, solely in consequence of the pressures ...of by the liquid upon it. Now let us suppose that the immersed mass has assumed that figure which it would acquire in vacuo if really deprived of gravity; the analytical condition of paragraph 5 would then be satisfied as regards this mass. Now at each point of the common surface of the two media, the radii of curvature p and p" have the same absolute values, both in the case of the immersed mass and of the hollow figure of the surrounding liquid, except that their signs are contrary, according as they are considered as referring to one or the other of the two liquids. To pass from one of the two figures to the other, we need therefore only change the signs p and p', or, what comes to the same thing, change the sign of the constant C. Changing the sign does not destroy the condition of equilibrium; and consequently, if the immersed mass is in equilibrium as regards its own molecular attractions, the same will hold good in the case of the hollow figure of the surrounding liquid. The pressures of the latter liquid cannot, therefore, by themselves produce any modification in the figure of equilibrium of the immersed mass. Let us now introduce the second kind of molecular actions, i.e., the mutual attraction of the two liquids, and see what will be its effects. Let us imagine, for an instant, that the immersed mass, or, for the sake of fixing the ideas, the mass of oil in our experiments is replaced by the same kind of liquid as that which surrounds it, i. e., by the alcoholic mixture. In other words, supposing the vessel to contain only the alcoholic mixture and the solid system, let us limit, in the imagination, a portion within the liquid of the same figure and dimensions, and situated in the same manner as the preceding mass of oil. It is then clear that the molecules of the mass near its surface being, like those of the interior, completely surrounded by the same kind of liquid beyond their sphere of activity, these molecules will no longer exert any pressure upon the mass; consequently, the pressures which would exist if this mass could be isolated must be considered as destroyed by the attractions emanating from the surrounding liquid. The latter forces are, therefore, all equal and opposite to the pressures in question. Now, as these are all equal to each other in accordance with the figure which we have attributed to the imaginary surface of the mass, the attractions emanating from the surrounding liquid will also all be equal to each other. If we now replace the mass of oil, the attractions emanating

from the surrounding liquid may certainly alter in absolute value, but it is evi- .

dent that they will retain their directions, and that they will remain equal to each other. We therefore see that they will only diminish, by the same quantity, all the pressures exerted by the mass of oil upon itself; consequently, as all the differences remain equal to each other, the condition of equilibrium will still be satisfied as regards that mass. It is evident that the same mode of reasoning may be applied to the pressures exerted by the surrounding liquid upon itself—pressures which will retain their directions, all of which will only be diminished to the same extent by the attractions emanating from the oil, so that the condition of equilibrium will still be satisfied as regards the hollow figure of the surrounding liquid. Thus the whole of the molecular actions due to the presence of the surrounding liquid will not tend in any way to modify the figure of equilibrium of the immersed mass, which figure will, consequently, be identically the same as if that mass were really void of gravity and were placed in vacuo. We can, therefore, leave the surrounding liquid completely

out of the question, its sole function being to neutralize the action of gravity upon the mass forming the object of the experiments. 9. We shall now pass to the experimental part. And first, to avoid useless repetition, we shall say a few words relative to the apparatus to be used. As the liquid always consists of a mass of oil immersed in an alcoholic mixture of the same density as itself, our solid systems will all consist of iron, and this for the following reasons: In ordinary circumstances oil contracts, I believe, perfect adhesion with all solids; but this is not exactly the case when the same oil is plunged into a mixture of water and alcohol; for then, in the case of certain solids, as, e.g., glass, the phenomena of adhesion sometimes undergo modifications which give rise to trouble in the experiments. We shall meet with an instance of this in the subsequent parts of this memoir. Now, the metals do not present this inconvenience; moreover, the form which we have given to most of our solid systems would render their construction of any other substance besides a metal difficult. Now, among metals we prefer iron, not copper, because oil removes nothing from iron, whilst by prolonged contact with copper it slightly attacks it, acquires a green color, and increases in density, which is a great inconvenience.* When we wish to use one of these solid systems of iron, before introducing it into the vessel, it must be completely moistened with oil; and for this purpose it is not sufficient simply to immerse it in this liquid, but it must be carefully rubbed with the finger. The presence of this coating facilitates the adherence of the liquid mass. We shall continue to make use of the vessel with plane walls, described in the preceding memoir, § 8;f a common-shaped bottle, and the flask previously mentioned (§§ 5 and S) in the same memoir, are not well adapted, because they do not exhibit the true figure of the mass. When the solid system is composed of a single piece, it is supported by a vertical iron wire, which is screwed to the lower end of the axis traversing the metallic stopper; but for certain experiments the solid system is formed of two isolated parts, and then only one of them is attached to the axis, as I have stated; the other is supported by small feet which rest upon the bottom of the vessel. It need not be mentioned that those liquids only which are prepared in such a manner as to be incapable of exerting any chemical action upon each other can be employed, (§§ 6 and 24 of the preceding memoir.) In addition to the little funnel for introducing the mass of oil into the vessel, the iron wire which serves for uniting the isolated spheres, &c., of which I have spoken in the preceding memoir, the experiments require some other accessory instruments, as, in the first place, a small glass syringe, the point of which is elongated and slightly bent. It is used as a sucking-pump, to remove, for instance, a portion of the oil composing the liquid mass, when it is required to diminish the volume of the latter, or to withdraw the entire mass of oil from the vessel, an operation which is sometimes required, &c. In the second place, two wooden spatulas, one being slightly bent, the other straight, covered with fine linen or cotton stuff. When these spatulas are introduced into the vessel, and the cloth with which they are furnished is thoroughly impregnated with the alcoholic liquid, the mass of oil does not adhere to them. Hence, by means of one or the other of these spatulas, the mass can be moved in the surrounding liquid, and conducted to the place which it is required to occupy in the interior | the vessel without any of it remaining upon the spatula. This is the purpose for which these instruments are intended. After they have been used, care must always be taken to agitate them in pure alcohol before allowing them to dry. If this precaution be omitted, the alcoholic mixture with which they are impregnated, on evaporating, would leave the small quantity of oil which it held in solution upon their surface; and when the same instruments are used again, the mass of oil would adhere to it. In the third place, an iron spatula, the uses of which we shall point out in the proper place. Lastly, as it is necessary, in all the experiments which we shall relate, that the alcoholic liquid should be homogeneous, the process indicated in the preceding memoir ($25) cannot be used to prevent the mass of oil from becoming occasionally adherent to the bottom of the vessel; but the same result is obtained by covering the bottom with a square piece of linen.

* In a letter which Dr. Faraday did me the honor of sending to me, regarding the preceding memoir, he informed me that, when about to repeat my experiments before a numerous audience, wishing to produce a still greater difference in the aspect of the two liquids, he dissolved intentionally a little oxide of copper in the oil, so as to render the latter of a green color. The compound having thus been made beforehand, and rendered perfectly homogeneous, and the alcoholic mixture having been regulated according to the density of the modified oil, the presence of the copper in solution could not produce any inconvenience; but in this case also the solid systems should unquestionably be made of iron.

t In making the experiments to the present memoir, I found that it was requisite slightly to modify the apparatus in question. The second perforation in the plate forming the lid of the vessel should be but little smaller than the central aperture; its neck should be less elevated; and, lastly, it should be placed near the other; if left as previously described and figured, the employment of the accessory instruments which we shall describe would be impossible. Moreover, the neck of the central aperture should be furnished with a slight rim, so that it may be easily taken hold of when we wish to remove the lid, as, e.g., when it is required to attach a solid system which is too large to pass through this same aperture to the axis which traverses the stopper. Lastly, the vessel should be furnished with a stop cock at its lower part, so that it may be easily emptied.

New erperiments in support of the theoretical principles brought forward in the preceding obserrations. Figures of equilibrium terminated by surfaces of spherical curvature. New principle relating to layers of liquids.

10. The facts which we shall first describe may be considered as constituting the experimental demonstration of the principle of the superficial layer, (§ 6, bis.) Let us imagine any solid system to be immersed in the liquid mass, and let us give to this mass such a volume that it may constitute a sphere which completely envelops the solid system without the latter reaching the surface at any point. Then, if the above principle be true, the presence of the solid system will exert no influence upon the figure of equilibrium, because, under these circumstances, the superficial layer, from which the configuring actions emanate, remains perfectly free; whilst if these actions emanated from all points of the mass, any unsymmetrical modification occurring in the internal parts of the latter would necessarily produce one in the external form. This is confirmed by experiment. The condition of a solid system completely enveloped by the mass of oil would be somewhat difficult to realize; but it must be remembered that, in the experiments relating to the preceding memoir, the system of the disk, by means of which the mass was made to revolve, was very nearly in this condition, because it did not reach the external surface of the mass excepting at the two very small spaces which gave passage to its axis. But we |. saw (§ 9 of the preceding memoir) that when the mass was at rest, its sphericity was only very slightly altered by the presence of this system. The theoretical condition may be more nearly approached by taking a very fine metallic wire for the axis of this same system; in this case the alteration in form is quite imperceptible. The axis being supposed to be vertical, the disk may, moreover, be placed so that its centre coincides with that of the mass of oil, or is situated above or below the latter without producing any difference. I shall relate another fact of an analogous nature. In the course of the experiments, it sometimes happens that portions of the alcoholic liquid become imprisoned in the interior of the mass of oil, forming so many isolated spheres. Now, however these spheres may be situated in the interior of the mass, not the least alteration is produced in the figure of the latter.

11. Again, let us cause some kind of solid system to penetrate the liquid mass; but now let the mass be of too small a volume to be capable of completely enveloping this system. The latter will then necessarily reach the superficial layer; and, if the principle in question be true, the figure of the liquid mass will be modified, or, in other words, will cease to remain spherical. This does really occur, as we might have expected; the liquid mass becomes extended at those portions of the solid system which project externally from its surface; it finally either occupies the whole of these portions, or only a part of their extent, according to the form and the dimensions of the solid system, and thus assumes a new figure of equilibrium. We shall meet with examples of this hereafter, (S$ 14, 15, 17.)

12. Instead of causing the solid system to penetrate the interior of the liquid mass, let it simply be placed in contact with the external surface of the latter. An action being then established at a point of the superficial layer, equilibrium must be destroyed, and the figure of the liquid mass ought again to be modified. This really occurs; the mass becomes extended upon the surface presented to it, and consequently acquires a different shape. This result might also have been anticipated from what occurs under ordinary circumstances, when a drop of water is placed upon a previously moistened solid surface. One might be induced to believe that, as regards the actual result, this case is referable to that of the preceding paragraph or that in paragraph 10; for it appears that the liquid mass, becoming extended upon the solid system so as to obtain the new figure of equilibrium, should ultimately occupy or envelop this system in the same manner as if the latter had been made to penetrate its interior directly. Under certain circumstances this must occur; but the experiments which are about to be related will show that under other circumstances the result is totally different.

13. Let us take for the solid system a thin circular plate, * attached by its centre to the iron wire which supports it, (Fig. 1,) and let us produce the

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adhesion of its lower surface to the upper part of the mass of oil.f Directly contact is completely established, the oil extends rapidly over the surface pre

* The diameter of that which I have used is 4 centimetres. I mention this diameter for the sake of being definite. It is evident that in our experiments the dimensions of the apparatus are competely arbitrary, except that if these dimensions exceed certain limits, the operations will become embarrassing in consequence of the large quantities of liquid which would be required.

t In order that this operation may be effected with facility, the sphere of oil must first remain in the surrounding liquid beneath the central aperturo in the lid ; the plate being then introduced into ibe vessel, we have merely to lower it by means of the axis traversing the stopper to bring it towards the liquid mass. If the latter does not occupy the position in question, it must be previously placed there by means of u spatuln covered with linen, (09.) It must bo remarked here, that true contact between the plate and the sphere of oil does not

certain resistance has to be overcome, analogous to that treated of in the note to paragraph 4 of the preceding memoir; but to overcome this, the liquid sphero need only bo gently moved by means of the plate. The slight resulting pressure sovn causes the rupture of the obstacle and the production of adhesion.

ensue imm

sented to it; but, what is remarkable, although the precaution has been taken of rubbing the whole of the system, ($ 9,) that is, the two faces of the plate as well as its rim, with oil, the oil terminates abruptly at this rim without passing to the other side of the plate, and thus presents a sudden interruption in the curvature of its surface. In the case in question, the new figure acquired by the mass is a portion of a sphere. This portion will be as much larger in proportion to the complete sphere as the volume of oil is greater; but the curvature will always terminate abruptly at the margin of the plate. (See Fig. 2, which represents a section of the solid system and the adherent mass in the case of three different volumes of the latter.)

The cause of this singular interruption of continuity is readily understood. The rim of the plate reaching to the superficial layer, it is natural that something peculiar should occur along this margin, and that the continuity of form should cease at that point where a foreign attractive action is exerted without transition on the superficial layer.

14. Let us again make use of the above plate; but instead of presenting one of its faces to the exterior of the sphere of oil, let us insert the pla:e edgewise into the interior of this sphere.* The liquid will necessarily extend over both faces of the solid; and if the diameter of the primitive sphere were less than that of the plate, the oil will be seen to form two spherical segments upon the two faces in question, the curvatures of which will still terminate abruptly at the margin of the plate. These two segments may be either equal or unequal, according as the edge of the plate has been introduced into the liquid sphere in such a manner that the plane of the plate passes through the centre of the sphere or not. The upper segment will be slightly deformed by the action of the suspending wire; but this effect will be less sensible in proportion to the thinness of the wire in question. Fig. 3 represents the result of the experiment with two unequal segments. The discontinuity of the curvatures is a very general fact, which we shall frequently find to recur in the course of our experiments; it will hereafter lead us to very important consequences. Fig. 3. Fig. 4.

Fig. 5.

Fig. 6.

15. I have repeated the same experiment, substituting a plate of an elliptic form for the circular plate. In this, as in the preceding case, the oil extends over both faces of the solid, so as entirely to cover them; and, if the volume of

* This operation is performed as follows: The stopper to which the system of the plate is Attached is kept at some distance above the neck of the central aperture, in such a manner, bowever, that the latter is immersed to a sufficient depth in the alcoholic mixture. The plate can then be moved with tolerable freedom, and it is conducted towards the liquid mass For this purpose the latter ought previously to occupy a suitable position. Immediately the liquid muss is cut, the plate is kept still until the action is terminated, after which the stopper is carefully placed in the neck. A process the reverse to the preceding may also be made use of. The liquid mass is first made to occupy a position near the second aperture, and a sufficient distance from the axis which passes through the centre of the central aperture; then, having fixed the solid system firmly in the position which it is to occupy, move the liquid mass towards it, and when this has been cut, allow the action to continue aninterruptedly. These processes are also employed in other experiments, and it is enough to have pointed them out once. In some cases the second is the only practicable one. This may be casily decided upon in making the experiments.

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