Wave-Line. See WAVES.

Wa'vellite, an interesting mineral species, a hydric alumina-phosphate, named after its discoverer, Dr. Wavell, who first recognized it in Devonshire, England, at the beginning of this century. It occurs near Bellows Falls, N. H., at the Washington Mine, Davidson co., N. C., and in York and Chester cos., Pa. It is found usually in radiated spheroidal masses; of white or light colors; translucent; harder than calcite, approaching fluor; crystalsystem, right-rhombic. Dana assigns to it the formula 019 P4A16-12H2O. The density of the Devonshire mineral,

=

W. GIBBS. according to Haidinger, is 2.337. Städeler, however, analyzed a Hungarian variety, which gave D. 2.356 and composition 019P4Al6.11H20. Wavellite is one of the phosphates, having so small a molecular volume that the writer argues from this the existence of a type of orthophosphates with an enormously-condensed phosphorusmolecule. (See VOLUMES, MOLECULAR.) Wavellite does not, however, present such convincing evidence of this as several other species, such as pseudomalachite, plumbogummite, hitchcockite, the vivianites, the turquoises, and HENRY WURTZ. others.

Wave Offering is the name of a peculiar rite belonging to the old dispensation, and noticed in Ex. xxxix. 2427; Lev. vii. 30; viii. 27; Num. vi. 20, and other places. It was a peace offering. While the sin offering merely removed defilement, and the burnt offering gave the victim --which was wholly consumed-entirely over to God, the peace offering, whose purpose was to establish a relation between God and man, was participated in by the latter. That part of the victim which was eaten by the priests, the shoulder, was said to be heaved, and that which was eaten by the worshippers, the breast, was said to be waved. Waverley Novels. See ScoTT (Sir WALTER). Wa'verly, Morgan co., Ill. (see map of Illinois, ref. 7-C, for location of county), on Jacksonville South-eastern and Wabash St. Louis and Pacific R. Rs., 30 miles S. W. of Springfield. P. in 1880, 1124.

Waverly, city and R. R. centre, cap. of Bremer co., Ia. (see map of Iowa, ref. 3-I, for location of county). P. in 1870, 2291; in 1880, 2345; in 1885, 2443.

Waverly, R. R. centre, Tioga co., N. Y. (see map of New York, ref. 6-F, for location of county), on Erie R. R., 256 miles W. of New York City, contains a union high school, an opera-house, and several manufacturing establishments. Large quantities of butter and grain are marketed here. P. in 1870, 2239; in 1880, 2767.

Waverly, R. R. junction, cap. of Pike co., O. (see map of Ohio, ref. 7-E, for location of county), 29 miles N. of Portsmouth, which is on Ohio River, was laid out in 1829, and contains a large union school-house, saw, planing, and flouring mills, furniture factories, tannery, etc. Principal business, farming and stock-raising. P. in 1870, 1202; in 1880, 1539.

Waverly, on R. R., cap. of Humphreys co., Tenn. (see map of Tennessee, ref. 6-D, for location of county). P. in 1870, 207; in 1880, 510.

It

Waves. Water is distinguished from solid bodies by its mobility-that is, by the freedom with which its elementary particles move with reference to one another. results from this mobility that a disturbance communicated to particles of water at any point becomes the occasion of disturbance to contiguous particles, and through these to particles more remote, propagating itself in this manner to great distances in the form of oscillatory movements called cares.

The physical characters of waves are familiar to all. A stone dropped into standing water is followed by a series of circular ridges, spreading till they reach the shore or become so indistinct as to escape observation. We never remain long near any extended body of water without observing its surface ruffled by a series of ridges and furrows

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in rapid motion, usually toward the shore. Upon the great ocean the phenomenon presents itself on a grander scale. The crests of the waves attain at times a height of 30 feet, and thus move with the velocity of a railroad passenger train. During our first sea-voyage, upon observing such liquid hills approaching the vessel with such a velocity, it is difficult to divest ourselves of the impression that the latter is in danger of being shattered to fragments. Yet it receives but a moderate shock, and is lifted with a movement which, to the voyager who is accustomed to it, is not even unpleasant. Were the mass of water moving with the velocity of the wave, the effect upon vessels would be disastrous, as is readily seen in the rapidity with which a stranded vessel is broken up when exposed to the full force of the waves. The character of the wave is here so changed by the shelving ground that the water has a rapid moveIn a body of water the movement of any particle is controlled by the proximity of other particles. No particle can move without occasioning a movement of other particles, and it can only move in such a manner as is consistent with the movement of the entire mass. This condition determines the path in which each particle moves. It moves in a closed orbit around its position of rest, returning to the same position at regular intervals. Of this fact we may satisfy ourselves by observation. If we note the effect of waves upon a small body floating in the water, we shall see that the latter is not carried along by the wave. On the contrary, its position is but slightly altered. When the crest of the wave passes the body, it moves a short distance in the direction of the wave-motion; when it is in the hollow of the wave, it moves slightly in the opposite direction. If we observe a float which gradually sinks in the water, we shall find that these movements are not confined to the surface, but extend as deep as our observation reaches. The particles of water move forward rising and sinking, and return sinking and rising, describing a closed orbit; but whether this orbit is circular or elliptical cannot be learned by observation. Mathematicians who have investigated this subject find that in water of very great depth the orbit of each elementary particle is an exact circle whose centre is in the position occupied by the particle when at rest. These circular orbits are greatest at the surface of the water, being there equal in diameter to the height of the wave. They diminish rapidly farther down, so that when the water at the surface has a movement of 20 feet, causing waves 20 feet high from trough to erest, it has at a depth of 50 feet a movement of only 7 feet, and at a depth of 200 feet a movement of not more than 4 inches. The figure below shows how the circular movements of the different particles of water conspire to produce the undulations of the surface which we call waves. A B is the surface

B

of the water when at rest. The circles are the orbits of the particles at the surface, which are supposed to be in motion in a direction opposite that of the hands of a clock. The particle h', whose position of rest is h, is at the highest point of its orbit; the next particle to the right, k', whose position of rest is k, is slightly past the summit of its orbit, and farther to the right each particle is in a little more advance 1 position than the one preceding. The particle a', whose position of rest is a, is at the lowest point of its orbit. The surface of the water at the instant under consideration is represented by the curved line C D, h' being the highest point or crest of the wave, a' the lowest point or trough of the wave. The motion continuing, the crest advances toward the left, and when the particle h' has reached the lowest point of its orbit, that point becomes the trough of the wave, and a', having then reached the highest point of its orbit, is the crest of the succeeding wave. The horizontal distance between the crests of two consecutive waves is called the length of the wave. If we consider the particles of water which, when at rest, lie all in the same vertical line, constituting a vertical filament of water, these all arrive, during wave-motion, at the summits of their orbits at the same instant. The orbits diminish in diameter downward, so that at a depth of a few hundred feet the movement practically ceases. The lower part of the filament remains immovable, and its upper part bends like a stalk of wheat in a field under the action of the wind. When the crest of the wave coincides with the filament, the latter is erect and elongated. It then bends in the direction of the wave's motion, and returns to its erect position when the trough of the wave passes. It is then

shortened and thickened. It then bends in the direction opposite to that of the wave's motion, and so on.

The form of the wave is cycloidal, but it is not the common cycloid, which is a curve traced by a point on the circumference of a circle rolling upon a straight line. Were this the case, the height of the wave would bear the same proportion to its length that the diameter of a circle bears to its circumference; whereas there is not necessarily any definite relation between the height and length of the wave. In the same system of waves we always find the same relation between the height and the length. But a slight change in the direction or intensity of the wind gives rise to a different system in which a different relation exists. Different systems of waves often occur at the same time. It is a matter of common observation at the seashore that at intervals a wave occurs much higher than the preceding. This arises from the coincidence of two waves belonging to different systems. To the same cause is due the “seas which break over the decks of vessels, carrying away everything not securely fastened.

The velocity of a wave depends upon its length. To find this velocity when the length is known, we first find the radius of a circle whose circumference is the length of the wave. Designate this radius by r, the velocity is the same that a heavy body would acquire in falling freely through a height equal to one-half r. To find the radius of the orbit of a particle at a given depth below the surface, divide the given depth by r, and find the number of which this quotient is the natural logarithm. Divide r by this number, and the quotient will be the radius sought. Waves in deep water usually arise from the action of the

wind, and their motion when unobstructed is in the same direction as the wind to which they owe their origin. How powerfully the wind acts in acceleration of the molecular movements to which waves are due will appear upon a little reflection. The elevated part of the wave is fully exposed to the action of the wind, and here the particles of water are moving in the same direction as the wind. The trough of the wave, in which the particles are moving in the opposite direction, is mainly screened from the action of the wind by the neighboring crest. When the wind begins to blow while the water is smooth, it might appear difficult to understand how it can originate waves, since the wind would seem to exert a uniform pressure upon all parts of the surface. The wind, however, never acts with a perfectly uniform and steady pressure. There is always enough of inequality to cause a ruffling of the surface, and the minute waves, once formed so as to present a surface to the direct action of the wind, are rapidly increased in magnitude. They continue to increase until they have attained a velocity nearly equal to that of the wind.

The tendency of waves is to form in long lines at right angles to the direction of the wind. This tendency is the more marked in proportion as the expanse of water is unlimited and the wind unvarying in force and direction. We rarely, however, have an opportunity to observe the phenomenon of waves in its entire simplicity. Under the most favorable circumstances the eye can follow the wave longitudinally but a very short distance. Neither, if we fix our eye upon the crest of a wave and endeavor to follow its movement, can we trace it to any great distance before it disappears and a new wave arises. The more common case is a system of waves caused by a local wind, crossed in different directions by other systems originating in distant parts of the ocean, and by waves reflected from the shore, the whole often forming a tumultuous commotion of waters, in which scarcely any law of movement can be recognized. This shows that different simple movements of the elementary particles may coincide and superpose themselves upon one another in all conceivable ways.

The preceding refers to waves in deep water-that is, water so deep that the bottom exerts no influence upon the movements of the elementary particles. These move in precisely the same manner as though the depth were infinite. Hence, the preceding is called, for distinction, the theory of waves in water of infinite depth. In water of moderate depth the proximity of the bottom exerts an influence the more marked in proportion as the depth is less. Where the depth is considerable, this influence manifests itself in a slight horizontal movement of the water at the bottom. As the depth diminishes, this horizontal movement increases, until finally, at slight depths, the particles have the same horizontal movement at the bottom as at the surface, while the vertical movement is greatest at the surface and diminishes to nothing at the bottom. The particles thus move in orbits which are often nearly circular at the surface, and become more and more flattened toward the bottom, where they are simply straight horizontal lines. The movements of the elementary particles in shallow water were very attentively studied by Hayen. He used for this purpose a trough about 4 inches in width and height and 12 feet long. He inserted glass plates in the sides to enable him to observe the movements of small visible particles suspended in the water. The waves were created by the movement of a metallic plate nearly equal in size to the cross-section of the trough, placed at one end of the latter and moved by clockwork. It was adjusted so that the movement of the top could be greater than that of the bottom in any desired proportion, from the case in which the bottom was stationary to that in which it had the same movement as the top. He found that whatever movement was communicated to the water, no difference was discernible between the horizontal movements of the particles at the top and those at the bottom at a distance of 4 feet from the plate. The most important difference between waves in infinite depth and those in finite depth is, that in the former the velocity with which the wave travels appears to have no relation to the depth, depending solely upon the magnitude of the wave; whereas in the latter the velocity depends upon the depth, being, according to the most trustworthy observations, equal to that velocity which a heavy body acquires by falling freely a height equal to half the depth, measured from the top of the wave.

J. Scott Russell, an English marine engineer, made very extended and valuable researches upon the subject of waves. These researches were undertaken at the instance of the British Association for the Advancement of Science, and the results are detailed in a provisional report made to the Association in 1837, and published in its Transactions for 1837, and a more complete report in 1844. The following is given as summary of results in the report of 1837: (1) The existence of a great primary wave of fluid, differing

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in its origin, its phenomena, and its laws from the undulatory and oscillatory waves which alone had been investigated previous to the researches of Mr. Russell, has been confirmed and established. (2) The velocity of this wave in channels of uniform depth is independent of the breadth of the fluid, and equal to the velocity acquired by a heavy body falling freely by gravity through a height equal to half the depth of the fluid, reckoned from the top of the wave to the bottom of the channel. (3) The velocity of this primary wave is not affected by the velocity of impulse with which the wave has been originally generated; neither does its form or velocity appear to be derived in any way from the form of the generating body. (4) This wave has been found to differ from every other species of wave in the motion which is given to the individual particles of fluid through which the wave is propagated. By the transit of the wave the particles of the fluid are raised from their places, transferred forward in the direction of the motion of the wave, and permanently deposited at rest in a new place at a considerable distance from their original position. There is no retrogradation, no oscillation; the motion is all in the same direction, and the extent of the transference is equal throughout the whole depth. Hence, this wave may be descriptively designated the great primary wave of translation. The motion of translation commences when the anterior surface of the wave is vertically over a given series of particles; it increases in velocity until the crest of the wave has come to be vertically above them; and from this moment the motion of translation is retarded, and the particles are left in a condition of perfect rest at the instant when the posterior surface of the wave has terminated its transit through the vertical plane in which they lie. This phenomenon has been verified up to depths of five feet. (5) The elementary form of the wave is cycloidal; when the height of the wave is small in proportion to its length, the curve is the prolate cycloid; and as the height of the wave increases, the form approaches that of the common cycloid, becoming more and more cusped until at last it becomes exactly that of the common cycloid with a cusped summit; and if by any means the height be increased beyond this, the curve becomes the curtate cycloid, the summit assumes a form of unstable equilibrium, the summit totters, and, falling over on one side, forms a crested wave or breaking surge. (6) A wave is possible in forms of channel where the depth is not uniform throughout the whole breadth. The full consideration of this subject is reserved for the next report. It appears, however, that when the difference between the depth of the sides is considerable, one part of the wave will continue during the whole period of propagation in the act of breaking, so as to show that in these circumstances a continuous wave is impossible. In other cases the ridge of the wave rises so much higher on the shallower part of the fluid as to produce a given velocity without exceeding the limits of equilibrium; and in these cases the wave becomes possible, and the velocity appears to coincide closely with that which we obtain by supposing the wave resolved into vertical elements, each having the velocity due to the depth, and then integrating. . . . In the sloping or triangular channel the velocity is that due to one-third of the greatest depth. In a parabolic channel the velocity is that due to three-eighths or three-tenths of the greatest depth, according as the channel is convex or concave. (7) The height of a wave may be indefinitely increased by propagation into a channel which becomes narrower in the form of a wedge, the increased height being nearly in the inverse ratio of the square root of the breadth. (8) If waves be propagated in a channel whose depth diminishes uniformly, the waves will break when their height above the surface of the level fluid becomes equal to the depth at the bottom below the surface. (9) The great waves of translation are reflected from surfaces at right angles to the direction of their motion, without suffering any change but that of direction. (10) The great primary waves of translation cross each other without change of any kind, in the same manner as the small oscillations produced on the surface of a pool by a falling stone. (11) The wares of the sea are not of the first order; they belong to the second or oscillatory order of waves. They are partial displacements at the surface, which do not extend to considerable depths, and are therefore totally different in character from the great waves of translation, in which the motion of displacement of the particles is uniform to the greatest depth. The displacement of the particles of the fluid in the waves of the sea is greatest at the surface, and diminishes rapidly downward. There are generally on the surface of the sea sev eral co-existent classes of oscillations of varying direction and magnitude, which by their union give the surface an appearance of irregularity which does not exist in nature. (12) When waves of the sea approach a shore or come into shallow water, they become waves of translation, and, obey