their planets, in consequence of the action of two forces-a centripetal force, which is gravitation, and a tangential force originally impressed on them.

The centrifugal force obviously arises from the action of the tangential. It is the antagonist of the centripetal force.

The figure of the curve in which a body revolves is determined by the relative intensities of the centripetal and tangential forces. If the two be equal at all points, the curve will be a circle, and the velocity of the body will be uniform. But if the centrifugal force at different points of the body's orbit be inversely as the square of its distance from the centre of gravity, the curve will be an ellipse, and the velocity of the body variable.

In elliptical motion, which is the motion of planetary bodies, the centre of gravity is in one of the foci of the ellipse. All lines drawn from this point

A

E

D

Fig. 111.

to the circumference are called radii vectores, and the nature of the motion is necessarily such that the radius vector, connecting the revolving body with the centre of gravity, sweeps over equal areas in equal times.

The squares of the velocities are inversely as the distances, and the squares of the times of revolution are to each other as the cubes of the distances. Let A BCDE, Fig. 111, be an elliptical orbit, as, for example, that of a planet, the longest diameter being A B, and the shortest D E. The points, F and G, are the foci of the ellipse, and in one, as F, is placed the centre of gravity, which, in this instance, is the sun. The planet, therefore, when pursuing its orbit, is much nearer to the sun when at A than when at B. The former point is, therefore, called the perihelion, the latter the aphelion, and D and E points of mean distance. The line A B, joining the perihelion and aphelion, is the line of the apsides; it is also the greater or transverse axis of the orbit, and DE is the conjugate, or less axis. A line drawn from the centre of gravity to the points D or E, as F D, is the mean distance, F is the lower focus, G the higher focus, A the lower apsis, B the higher apsis, and F C or G C— that is, the distance of either of the foci from the centre-the eccentricity.

When a body rotates upon an axis, all its parts revolve in equal times. The velocity of each particle increases with its perpendicular distance from the axis, and therefore so also does its centrifugal force. As long as this force is less than the cohesion of the particles, the rotating body can preserve itself; but as soon as the centrifugal force overcomes the cohesive, the parts of the rotating mass fly off in directions which are tangents to their circular motion.

There are many familiar instances which are examples of these principles; the bursting of rapidly rotating masses, the expulsion of water from a mop, the projection of a stone from a sling.

If the parts of a rotating body have freedom of motion among themselves, a change in the figure of that body may ensue by reason of the difference of centrifugal force of the different parts. Thus, in the case of the earth, the figure is not a perfect sphere, but a spheroid; the diameter or axis upon which it revolves, called its polar diameter, is less than its equatorial, it having assumed a flattened shape toward the poles, and a bulging one toward

the equator. At the equator, the centrifugal force of a particle is of its gravity. This diminishes as we approach the poles, where it becomes 0. The tendency to fly from the axis of motion has, therefore, given rise to the force in question.

This may be illustrated by an instrument represented in Fig. 112, which

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Fig. 112.

consists of a set of circular hoops, made of brass or other elastic material. They are fastened upon an axis at the point a, but at the point b can slide up and down the axis. When at rest they are of a circular form. By a multiplying wheel a rapid rotation can be given them, and when this is done they depart from the circular shape and assume an elliptical one, the shorter axis being the axis of rotation.

But if the parts of the rotating body have not perfect freedom of motion among themselves, their centrifugal force gives rise to a pressure upon the axis. If the mass is symmetrical as respects the axis, the resulting pressures compensate each other. But as each one of the rotating particles, by reason of its inertia, has a disposition to continue its motion in the same plane, it is obvious that such a free axis can only be disturbed from its position by the exercise of a force sufficient to overcome that effect. It is this result which is so well illustrated by Bohnenberger's machine, already described.

CHAPTER XXII.

OF ADHESION AND CAPILLARY ATTRACTION.

Adhesion of Solids and Liquids-Law of Wetting-Capillary Attraction -Elevations and Depressions-Relations of the Diameter of TubesMotions by Capillary Attraction-Endosmosis of Liquids and of Gases. To the arm of a balance, b c, Fig 113, let there be attached a flat circular plate of glass, a, and let it be equipoised by the weights in the opposite scale, d; beneath it let there be brought a cup of water, e, and on lowering the glass plate within an inch, or even within the hundredth part of an inch of the water, no attraction is exhibited; but if the glass and the water are brought in contact, then it will require the addition of many weights in the opposite scale to pull them apart.

Fig. 113.

T

If the cup, instead of being filled with water, is filled with quicksilver, alcohol, oil, or any other liquid, or if instead of a plate of glass we use one of wood or metal, the same

effects still ensue. The force which thus maintains the surface in contact is called "Adhesion."

[If we cut a piece of lead into two parts with a clean knife, and afterwards press the newly-divided surfaces together, giving them a twisting motion at the same time, we shall find them adhere firmly. When india-rubber is cut with a clean knife, the fresh-cut surfaces will cohere in a similar manner.] Adhesion does not alone take place between bodies of different forms. Two perfectly flat plates of glass or marble, when pressed together, can only be separated by the exertion of considerable force. In both this and the former case the absolute force required to effect a separation depends on the superficial area of the bodies in contact.

If, on bringing a given solid in contact with a liquid, the force of adhesion is equal to more than half the cohesive force of the liquid particles for one another, the liquid will adhere to the solid, or wet it. Thus, the adhesive force developed when gold is brought in contact with quicksilver is more than half the cohesion of the particles of the quicksilver for each other: the quicksilver, therefore, adheres to or wets the gold.

But if the force of adhesion developed between a solid and liquid is less than half the cohesive force of the particles of the latter, the liquid does not wet the solid. Thus, a piece of glass in contact with quicksilver is not wetted. It is on these principles that Vera's pump acts. It consists of a cord which passes over two wheels, to which a rapid motion can be given. The water adheres to the cord, and is raised by it. See Fig. 73, Chap.

XIII.

If the surface of some water be dusted over with lycopodium seeds, the fingers may be plunged in it without being wetted, the lycopodium preventing any adhesion of the water.

But it is in the phenomena of capillary attraction that we see the effects of adhesion in the most striking manner. These phenomena are exhibited by tubes of small diameter, called capillary tubes, because their bore is as fine as a hair. If such a tube, a, Fig. 114, be immersed in water, the water at once rises in it to a height considerably above its level in the glass cup, b.

Fig. 114.

Or if instead of water we fill the glass cup with quicksilver, and immerse the tube in it, bringing it near the side, so that we can see the metal in the interior of the tube through the glass, it will be found to be depressed beneath its proper level.

These experiments are still more conveniently made by means of tubes bent in the form of a syphon, as represented in Fig. 51, Chapter X. If one of these be partially filled with water, and then with quicksilver, the water will be seen to rise in the narrow tube above its level in the wide tube, and the quicksilver to be depressed.

[Perhaps the most common examples we can furnish of capillary attraction are the following, which we adduce without comment:--1. A lump of sugar placed upon a wet surface becomes very soon saturated throughout. 2. A sponge placed in a saucer of water soon absorbs all the fluid. 3. A piece of blotting-paper applied to some ink upon a sheet of paper. 4. The action of the wicks of candles and lamps, &c.]

When tubes of different diameters are used, the change in the level of the liquid is different. The narrower the tube, the higher water will rise, and the lower will quicksilver be depressed.

When tubes are very wide, or what comes to the same thing, when liquids are contained in bowls or basins, the surface is found not to be uniformly level; but near those points where it approaches the glass, in the case of water it curves upward, and in the case of quicksilver it curves downward, as seen in Fig. 115.

In tubes of the same material dipped in the same liquid, the elevations or depressions are inversely as the diameters of the tubes; the narrower the tube the higher will water rise, and the deeper will quicksilver be depressed.

There is a beautiful experiment which shows the connection between the diameter of the tube and the height to which it will Fig. 115. lift a liquid. Two square pieces of plate glass, A B, C D, Fig. 116, are arranged so that their surfaces form a minute angle. This position may be easily given by fastening them together with a piece of wax or cork, K. When the plates are dipped into a trough of water, EF, G H, the water rises in the space between them to a smaller extent where the plates are far apart, and to a greater where they are closer. The upper edge of the water gives the form of a hyperbola, D I A. The plates may be supposed to represent a series of capillary tubes of diameters continually decreasing; they show that the narrower the intercluded space or bore of such tubes, the higher the liquid will rise.

The figure of the surface which bounds a liquid in a capillary tube is also to be remarked. Whenever a liquid rises in a tube, its bounding surface is concave upward, as seen in Fig. 117, where f g is the tube, and a a the surface. When the liquid neither rises nor sinks, the surface, a a, is plane,

as at de; when the liquid is depressed, the surface, a a, is convex upward, as seen at bc. All these conditions may be exhibited by a glass tube properly prepared. In such a tube, when quite clean, the concavity and elevation of the liquid are seen; if the interior of the tube be slightly greased, the surface of the water in it is plane, and it coincides in position with the level on the exterior. If it be not only greased, but also dusted with lycopodium, the liquid is depressed in it, and has a convex figure.

It may be shown, according to the principles of hydrostatics, that it is the assumption of this curved surface which is the cause of the elevation or depression of liquids in capillary tubes.

Motions often ensue among floating bodies in consequence of capillary attraction. At first sight they might seem to indicate the exertion of direct forces of attraction and repulsion emanating from the bodies themselves; but this in reality is not the case, the motions arising in consequence of a

disturbance of the figure of the surface on which the bodies float. Thus, if we grease two cork balls, A B, and dust them with lycopodium powder, they will, when set upon water, repel the liquid all round, each ball reposing in a hollow space. If brought near to each other, their repulsion exerted on the water at C makes a complete depression, and they fall toward one another as though they were attracting each other. It is, however, the lateral pressure of the water beyond which forces them together.

Again, if one of the balls, E, is greased and dusted with lycopodium, and the other, D, clean, and therefore capable of being moistened, an elevation will exist all round D, and a depression round E. When placed near together the balls appear to repel each other; the action in this case, as in the former, arising from the figure of the surface of the water.

If we take a small bladder, or any other membranous cavity, and having fastened it on a tube open at both ends, A B, Fig. 119, fill the bladder and tube to the height, C, with alcohol, and then immerse the bladder in a large vessel of water, it will soon be seen that the level at C is rising, and at a short time it reaches the top of the tube at B, and overflows. This motion is evidently due to the circumstance that the water percolates through the bladder, and the phenomenon has sometimes been called endosmosis, or inward movement. Examination proves that while the water is thus flowing to the interior, a little of the alcohol is moving in the opposite way; but as the water moves quicker than the alcohol, there is an accumulation in the interior of the bladder, and, consequently, a rise at C.

Fig. 119.

One liquid will thus intrude itself into another with very great force. A bladder filled full of alcohol, and its neck thickly tied, will soon burst open if it be plunged beneath water. Similar phenomena are exhibited by gases. If a jar be filled with carbonic acid gas, and a piece of thin india-rubber tied over it, the carbonic acid escapes into the air through the india-rubber, which becomes deeply depressed, as at A, Fig. 120. But if the jar be filled with air, and be exposed to Fig. 120. an atmosphere of carbonic acid, this gas, passing rapidly through it, accumulates in the interior of the vessel, and gives to the india-rubber a convex or dome-shaped form, as seen at B.

Endosmosis is nothing but a complex case of common capillary attraction. The facts here described were originally discovered by Priestley; but, at a later period, attention was called to them by Dutrochet, who, regarding them as being due to a peculiar physical principle, gave to the movements in question the names of endosmose and exosmose, meaning inward and outward motion. But I have shown that there is no reason to revert to any peculiar physical principle, since the laws of ordinary capillary attraction explain every one of the facts.

The bursting of a bladder, filled with alcohol and sunk under water, gives us some idea of the power with which the latter liquid forces its way into the membranous cavity; and it is surprising with what a degree of energy these movements are often accomplished. An opposing pressure of two or three atmospheres seems to offer no obstacle whatever, and I have seen gases