On the Mutual Binding of Floating Corpuscles and on Their Shunning




(1)
Mathematics in Naples, Naples, Italy

 


 Deceased



Almost 32 years ago, I wanted to find out whether iron wires floating on water placed at different inclinations in relation to the Meridian would retain their position, and return to the same situation and direction in which they had been set, as William Gilbert says. While I was observing attentively, an amazing spectacle was offered to me, which had not been noticed hitherto: some extremities of the floating bodies rushed to each other to unite closely while others separated as occurs for a magnet and iron. Thus, stimulated by this novelty, I tried again using other corpuscles, straws, leaves of trees, and countless other bodies. I wished very much to understand the cause of this effect. After countless experiments, I noticed that these opposite operations resulted from the edges of water round adjacent floating bodies, some raised, some depressed. I took two copper sheets, thinner than paper, V and X (Table 8.​1, Fig. 10). At their centres C and L, I applied two straws CD and LM which I welded with wax perpendicularly to the planes of the sheets. I then set the sheets horizontally on the water of a vessel FRSO. When the floating sheets were depressed below the surface of the water, they were surrounded by water edges EA, GB and IN, KO. Then I made two wooden chips Y and Z both of an equal thickness of about half a finger breadth (Table 8.​1, Fig. 11). I also adapted to them perpendicular straws. When they were set on water, sloping wedges EA, GB formed round their circumference, above the surface FHO of the water. After this preparation, I dextrously pushed with my fingers the top D of a straw to move the small sheet V towards X, while retaining this firmly before it came into contact with the other sheet V. The distance between the sheets was less than one finger breadth. Then, firstly, I saw that the two sheets V and X spontaneously moved towards each other. Although retained by the small effort of a finger and prevented from reaching each other, afterwards they joined quickly, not less than previously. In the process of their union, the water edge GHN by which the sheets were separated previously levelled off completely. I then turned to the wooden chips Y and Z which were equally immobile and inert when distant from each other by more than a finger breadth. Drawn closer, the chips suddenly moved towards each other to join. This process was different from the previous one in that the two raised wedges GB and IM, not only did not level off nor did they move down to the surface of the subjacent water but, on the contrary, the intermediate space and the cavity BHI were filled completely up to the top BI. Finally, I joined the copper sheet V with the chip Z (Table 8.​1, Fig. 12) and I saw that, whenever I drew them closer at a distance of less than one finger breadth, not only they did not unite but, on the contrary, they rapidly moved away from each other and separated as if they abhorred their mutual view and vicinity. Experience thus shows that drawing closer and joining of sheets occur only when the water edges are similar, i.e. when both are raised above or when both are depressed below the surface of the water. When they are different, one being depressed below and the other raised above the surface of the water, separation and escape of the chips occur. In all these operations it was found that, if one of the sheets is retained fixed and immobile, or rather if it is in the orifice of a vessel, the other sheet free and not retained either joins or avoids the contact with the former which is immobile. Since both float freely over the fluid, the movement is common to both bodies. There is a difference, however: the smaller and less ponderous body joins or escapes the other more quickly while the displacement of the larger sheet is slower and more nonchalant. Such is the true and accurate story of this surprising effect. Thus, I do not wonder that the true cause of this effect was not proposed since the history of this operation was not obvious and was not noticed perfectly. It could be observed clearly and evidently only by way of the mentioned small sheets which I devised.

I reported this experiment to friends many of whom are still alive, in Sicily as well as in Rome; afterwards, in 1655, to the Serene Grand Duke Ferdinand of Florence, to Prince Cosme of Tuscany and the best patron of the arts, and to the very wise Leopold, Cardinal Medici, who kindly wrote in his recent letter that he remembered well my demonstration and the explanation which I presented at this time. Later, after the institution of the Accademia del Cimento, I publicly showed this experiment to its very learned members and to countless famous gentlemen of different nations to whom the spectacle of the best experiments of this Academy was offered, under the chairmanship of the Serene Cardinal.

Beside these novelties, I observed another one resulting from a very different cause. For its understanding one must review at first the fairly common effect of two perfectly flat and smooth small sheets of glass which are joined closely together and hold with such pertinacity that, if the upper one is raised horizontally, the contiguous lower sheet follows and is pulled and sustained hanging as if it were glued and bound to the upper one. If the upper glass sheet is a little inclined to the horizon, the lower one suddenly glides towards the sloping part of the upper plane without parting from the upper sheet. Always adhering to the upper sheet, it descends impelled by the natural instinct by which heavy bodies attempt more and more at reaching the centre of the earth the way they can, i.e. through an inclined path since the direct and perpendicular path is impeded.


Proposition CLXXXIX


If two mobile droplets of water come into contact laterally, they do not remain immobile but move sideways until their tops are on the same vertical lines.

Of two droplets of water ABC, one is hanging from a horizontal sheet AC, suspended by a thread DE and the other FGH is raised on the wooden chip LM floating on the water RS (Table 8.​1, Fig. 13). If the top B of the upper droplet touches the top G of the lower one, their horizontal and parallel surfaces G and B correspond to each other. There is no reason for the droplets and, consequently, the chips to move sideways since none of them has any horizontal motive force. If indeed they moved horizontally, they would not come closer to the centre of the earth more than previously and it is not in the habit of nature to operate in vain.

Then there is lateral contact between the droplets. The left side AB of the upper hanging droplet touches the right side GH of the lower droplet. Contact thus is achieved. There is congruence of the surfaces not at one point as the bulging and convex configuration would require but over a fairly considerable area such as IK. Here adherence and congruence occur between the two parts of water with as much pertinacity as when the two glass sheets presented above were joined together. The drops of water can uneasily be torn apart from each other but one side can move over the other very easily, as required by the fluidity of water. Consequently, since the droplets achieve a contact IK oblique and sloping towards the centre of the earth, the lower heavy droplet FGH must necessarily exert its innate downwards force the way it can. Therefore, it always falls and flows downwards but keeps adhering to the upper droplet until it arrives at the lowest point of the slope AB. This droplet cannot flow and fall downwards unless its top G moves closer towards the top B. This drawing closer cannot occur unless the subjacent floating sheet LM moves sideways towards S and the upper sheet AC moves somewhat towards R. Consequently, the two sheets must necessarily move sideways and come closer to each other. They then remain immobile and do not proceed further exactly when the sloping obliquity is finished, i.e. precisely when the top of the lower droplet reaches and adheres to the lower end of the upper droplet B. Then the two tops level off somewhat and are made horizontal and parallel. This occurs by way of an union of a noticeable surface of each droplet. This is followed by the effect of immobility mentioned above.

I now pass to other more difficult experiments the presentation of which must be preceded by some lemmata taken either from hydrostatics or from mechanics.


Proposition CXC


A soft or fluid body immersed into another fluid body, not only is expressed upwards by the latter, but its parts are also constricted from the sides.

According to the corollary of Prop. 10, the nature of the consistency of a fluid is such that, of its lower parts evenly arranged, i.e. interconnected horizontally, those which are more compressed impel upwards and raise the other parts adjacent to themselves if these are less compressed. But, as Archimedes says, the impetus and impulse of the compressing fluid must occur vertically. This is of course very true whenever a consistent and hard prism floats in water. But if, in a vessel BCEI full of water (Table 8.​1, Fig. 14), there is in the space AIFG, not a wooden prism, but another soft body or a yielding fluid of a lesser specific weight than that of the adjacent water, not only the surface FG of the fluid IG is impelled vertically upwards towards IA, but, moreover, the side AG is propelled and squeezed towards IF so that at the same time the fluid IG with a lesser specific weight rises vertically towards IA and also moves sideways from AG towards IF. From this it is deduced that water or any fluid BG with a higher specific weight than that of the body IG, not only exerts a force by compressing vertically, but also exerts a force sideways, not in a horizontal direction BA and HG, but obliquely BK and LG. This, I think, must replace the assumption of Archimedes since naturally all heavy bodies try to fall towards the centre of the earth, in whatever way they can achieve this, not only vertically but also obliquely.

This being established, if in the same vessel with water in the space ABHG one assumes an adjacent prism AGFI full of air or of any other fluid of lesser specific weight than water, the water partition AG will in no way remain standing at the same place but will fall and flow from the top A towards the bottom F. The opposite could never occur, i.e. the water partition AG remaining standing, water would descend below the surface GH and then, in a vertical movement of reaction, would propel the lower surface FG of water perpendicularly upwards towards IA. Of course this would occur if, between water and air, there was a wooden partition which would prevent the water from flowing into the cavity AF. But, without any interposed partition, water must necessarily flow down obliquely to fill the aerial cavity AF. This is confirmed by an obvious experiment. A parallelepiped-shaped leather purse is maintained vertically and opened above like a well. Its four angles are held open by the fingers or by rods. The purse full of air is immersed into water. You will see that not only the bottom but also the four sides of the purse bulge towards the central axis of the well. If the fingers or the rods are retrieved together and no longer exert any force, not only the bottom of the well rises but also the sides constrict and move towards each other. This is an obvious indication that the water, not only exerts a force perpendicularly upwards by expelling the air, but also attempts at moving obliquely sideways by squeezing the walls of the leather well. From this it can be inferred that, if the walls of this well are more flexible and yielding, and thin more and more until becoming indivisible as is the partition separating water from air, then the same occurs, i.e. water flows down obliquely into the aerial cavity AF.

Then, if, instead of air, the cavity AIFG is filled with another fluid with a lesser specific weight than that of the water BG, for example if it is filled with oil, unquestionably the same occurs, i.e. not only the base FG is raised vertically upwards but also the partition AG, the limit between fresh water and oil, is impelled transversely towards IF.


Proposition CXCI


If a part of water compresses an underlying fluid with a greater moment than another adjacent part, the latter will be impelled in a transverse movement by the former, carrying with it the corpuscles floating on it.

The fluid contained in the space AF must not always be rarer and more stretchable than the fluid AH (Table 8.​1, Fig. 15). If it is a mass of water of the same consistency, such as BG, but if the weight or the moment of the fluid BG is greater than the gravity of the other fluid AF, the surface AG (which separates the fluids) will also be impelled transversely towards IF. This can be confirmed by the following experiment. The water ABHG is tainted with Indian ink or any other coloured liquid, whereas the adjacent water AF remains transparent. A wooden prism X is then superimposed which compresses the surface of the water AB. While the wooden prism descends, the subjacent water is compressed by its weight and thus the blackened water is impelled not only below the surface GH but, penetrating the partition AG transversely, it is carried through and mixed with the limpid water AGFI. Thus, although both waters have the same consistency and the same rarity, the limit between them can be pushed sideways by the excess of weight of the superimposed prism X. This is confirmed by the following. The lower layer GH of water does not compress the imaginary balance FH by its consistency or hardness but by its weight or moment. Therefore, the gravity of the water is increased by the weight X as if the fluid BG were quicksilver. In either instance thus, the partition or limit AG between the fluids would be impelled towards IF.

If a straw or any wooden corpuscle Z having a greater moment is floating above point A of the water GB which has a greater moment, it must necessarily be displaced somewhat sideways from A towards I also by the subjacent water since the water BG cannot be moved sideways towards IF without carrying with it its surface AB and thus cannot be transported towards I without bringing with it the incumbent and floating corpuscle Z.

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Oct 7, 2016 | Posted by in GENERAL | Comments Off on On the Mutual Binding of Floating Corpuscles and on Their Shunning

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