solid the strength is found to depend very much on the secure fixing of the ends. Thus when both ends of the column are flat, the strength is three times as great as when both ends are rounded; and when one end is flat and the other end rounded, the strength is twice as great as when both ends are rounded. It has been long known that when an assigned quantity of material is to be formed into a column of assigned height, more strength is obtained by making the column hollow than by making it solid; and some authorities have stated that the column is strongest when the internal diameter is to the external diameter in the same proportion as 5 is to 11. Examples of the use of hollow rods and columns are frequent in nature; as in the bones of animals, the stiff part of feathers, and the stalks of corn and other plants.

680. Dr Young remarks: "It is obvious that when the bulk of the substance employed becomes very considerable, its weight may bear so great a proportion to its strength as to add materially to the load to be supported. In most cases the weight increases more rapidly than the strength, and causes a practical limitation of the magnitude of our machines and edifices. We see also a similar limit in nature: a tree never grows to the height of 100 yards; an animal is never strong enough to overset a mountain. It has been observed that whales are often larger than any land animals, because their weight is more supported by the pressure of the medium in which they swim." But it is easy to lay too much stress on such remarks, and we may therefore just draw attention to some matters of a contrary tendency. The great tubular bridges across rivers and straits, which the present generation has constructed, would have been considered almost impossible a few years since. A tree has been discovered in California which surpasses Dr Young's limit of 100 yards. The ostrich might have been deemed the largest bird that has existed on the earth if we had not received from New Zealand the bones of an extinct creature of far greater size.

On the subject of this and the preceding Chapter the reader may consult a treatise on The Strength of Materials and Structures by J. Anderson.

T. P.

19

LVII. CAPILLARY PHENOMENA.

681. We have stated that the surface of a liquid in equilibrium is a horizontal plane, and that liquids seek their level: see Arts. 358 and 383: we have now to notice some phenomena which are exceptions to these general laws. They occur when solid bodies are placed in contact with liquids, and are called capillary phenomena because they are best seen in tubes the bore of which is not greater than the diameter of a hair.

682. Let a very fine glass tube open at both ends be plunged vertically in a vessel of water. The water is seen to stand at a higher level in the tube than in the rest of the vessel; and moreover the surface of the water in the tube is not plane but curved, with the concavity upwards. Again, if water be put into a vessel of any size the surface of the water is not horizontal, close to the vessel, but concave upwards, rising above the general level; and the same holds with respect to the water close to a solid which floats on the water. These phenomena are also observed in the case of other liquids which wet the surfaces of vessels or tubes in contact with them. But in the case of liquids which do not wet the surfaces in contact with them, the facts are different. Thus when a fine glass tube, open at both ends, is plunged vertically in a vessel of mercury, the mercury is seen to stand at a lower level in the tube than in the rest of the vessel; and moreover the surface of the mercury in the tube is not plane but curved, with the convexity upwards. Again, the surface of mercury close to any vessel which contains it, or any solid which floats on it, is not horizontal but convex upwards, sinking below the general level. In extremely fine glass tubes the surface of water and of other liquids which wet the glass is a concave hemisphere; and the surface of mercury is a convex hemisphere.

683. Water will in general wet a surface with which it is brought into contact; but it will not do so if the sur

face is oiled or waxed. Thus if the inner surface of a fine glass tube be oiled, the phenomena, when it is plunged vertically in water, are like those which are seen when a tube is plunged in mercury. And the water round a ball of wax floating on it is depressed below the ordinary level and curved with its convexity upwards.

684. Thus the statement made in Art. 383 will require to be a little modified if one of the vertical tubes is very fine. Suppose the left-hand tube very fine, and the righthand tube large; then if the liquid be water it will stand at a higher level in the left-hand tube than in the other, and if the liquid be mercury at a lower level.

685. Capillary elevation depends on the nature of the liquid; the nature of the tube is of scarcely any consequence, provided the precaution is taken of first wetting the tube with the liquid which is to be used in the experiment. In a tube of about 04 of an inch in diameter water will be elevated about 1.2 inches, nitric acid about 9 of an inch, alcohol about 5 of an inch. Capillary depression depends on the nature of the tube as well as on that of the liquid. In a glass tube of '08 of an inch in diameter mercury will be depressed about 15 of an inch in a glass tube of 2 of an inch in diameter mercury will be depressed about 06 of an inch; in a glass tube of 4 of an inch in diameter it will be depressed about '015 of an inch. The mercury in a barometer has its upper surface convex, and it is therefore necessary in reading the barometer always to regard the highest point of the sur face. If however the mercury with which the barometer is filled has been boiled for a long time in contact with the atmosphere, it is found that the surface has undergone some chemical change, and is then a plane at right angles to the axis of the tube.

686. Capillary phenomena depend on the attractions which are exerted between the particles of the liquid itself, and also between the particles of the liquid and those of any solid close to the liquid. So long as the mutual distance of the particles is not extremely small the attraction follows Newton's law; but when the distance is extremely small this does not seem to be the case. The theory of capillary phenomena has been studied by some

great mathematicians, and it is one of the most abstruse in natural philosophy. It follows from these investigations that in the case of tubes not exceeding 1 of an inch in diameter, the amount of elevation or depression is greater in the same proportion as the diameter of the tube is smaller; and this law has been verified by obseryation.

687. Capillary phenomena may be observed not only in tubes but in various cases in which solids and liquids are in contact. Thus, as we have already stated, liquid in a vessel experiences capillary elevation or depression close to the sides of the vessel. Let a flat plate of glass be placed vertically in water; then it will be found that close to the plate the water will rise to the height of about oneseventh of an inch above the general level. Again, let a flat plate of glass be placed vertically in mercury; then it will be found that close to the plate the mercury will sink to the depth of about one seventeenth of an inch below the general level. Take two plates and put them vertically in water; if the plates are parallel, and near together, the water rises between them; and so likewise it does when the two plates instead of being parallel are joined along a common vertical edge, in such a manner as to form a very small angle. It is on the principles of capillary attraction that water ascends in wood, sponge, sugar, blotting-paper, and other porous bodies generally. The same forces which produce these capillary phenomena also determine the form which a drop of water assumes when hanging or falling.

688. The wick of a candle or lamp feeds the flame by capillary attraction. The wick is a bundle of threads the surfaces of which are very nearly in contact; and thus the melted tallow, or the oil, rises between them in the same way as the water between the plates in the experiments of the preceding Article. If a short fine iron tube be inserted in a vessel of oil the oil will rise to the top of the tube by capillary attraction, and may there be lighted. Suppose a bundle of threads, such as form the wick of a lamp, to have one end dipped in a vessel of liquid, and to be passed over the edge of the vessel and allowed to hang down on the outside below the level of the liquid. The liquid rises

from the vessel between the threads by capillary attraction, and then issues from the other end in drops after the manner of liquid issuing from a siphon. Any impurity in the liquid remains in the vessel, and is not transmitted through the bundle of threads: the contrivance is appropriately called the Siphon Filter.

689. Let a fine tube open at both ends be plunged vertically in water, and then carefully withdrawn; a drop of water will hang at the bottom of the tube, and a small column of water will remain in the lower part of the tube: the length of this column will be greater than the height of the column in the tube above the general level of the surrounding water before the tube was withdrawn. Thus it is possible to construct a vessel which shall hold some water though the bottom is full of holes. The bottom may be made of wire gauze, of iron or brass; then the meshes of the wire, being very fine, serve as capillary tubes, so that below each mesh a drop of water may hang, and a little column of water be supported above the drop.

690. There are also other phenomena which seem allied to capillary phenomena and are usually connected with them. Small needles, if slightly greased and placed very carefully on the surface of water, will remain without sinking; and some insects can walk on the surface of water. The needles and the feet of the insects are not wetted by the water; a small depression is formed round them, and they are supported in the same way as bodies would be if they displaced just as much water as would fill these depressions.

691. Let two small balls of wood or pith be placed on the surface of water; each floats with the water close round it raised a little above the general level. Let the balls be so near each other that no portion of water at the general level occurs between the two raised portions: then the two balls attract each other and run together. If instead of the wood or pith balls we put two wax balls, the water close round is depressed a little below the general level; and, as before, the balls attract each other when they are brought very near to each other. But if we put a pith ball on water close to a wax ball they repel each other.