WAUKEGAN
2058
WAVE-MOTION
health was permanently injured by over-study when a young man. In 1712 a visit to Sir Thomas Abney, a London alderman, led to making his home with this friend for the remainder of his life. He wrote a number of theological works, a treatise on Logic and a volume on The Improvement of the Mind, which has been much used as a textbook. His reputation, however, is due to his hymns, of which he published three volumes. A large number of his hymns and psalms are retained in church collections, many of them our best-known hymns, as Before Jehovah's Awful Throne; O God, Our Help in Ages Past; Joy to the World, the Lord has Come; and Come, Holy Spirit, Heavenly Dove. His beautiful cradle-hymn, Hush, My Dear, Lie Still and Slumber, perhaps is the best known of his children's songs. He died on Nov. 25, ^1748. Consult Hood's Life and Julian's Dictionary of Hymnology.
Wauke'gan, 111., county-seat of Lake County, on Lake Michigan, is 35 miles north of Chicago. It is built on a bluff on the shore. On account of its mineral springs and pleasant situation, it is quite a popular summer-resort. There are several important industries, among them a sugar-refinery, wire-mills, brass-works, scale-works, sash and door, organ-stop, envelope and wire-fence factories, a planing-mill, a malt-house and brewery, a coal-dock and a salt-dock. At Noith Chicago, a village a few miles south on an electric railway, are large zinc-works, a foundry, a hardware-factory, a brass-factory, and here the government has a naval training-school. North Chicago has a population of 2,000; Waukegan of 16,069.
Waukesha (wa'ke-sha'}, Wis., county-seat of Waukesha County, *a city of Wisconsin, 17 miles west of Milwaukee. Is one of the most popular health-resorts in the country. It Is served by three railroads, has electric communication with Milwaukee and other cities, and contains large malleable iron and steel works. There are ten mineral springs, the Bethesda being the largest and the first discovered, in 1868. The water is shipped to all parts of the world, the works covering 20 acres. There are a very large hotel and fine bathing-houses, with beautiful parks and drives. Population 8,740,
Wau'sau, Wis., a city on the Wisconsin River, the capital of Marathon County, central Wisconsin. It is on the Chicago, Milwaukee and St. Paul and the Chicago and Northwestern railroads, and is 180 miles northwest of Milwaukee. It lies in a heavily timbered pine-belt, and its industries, consequently, are chiefly mills for dressing lumber and the manufacture of furniture, sashes, doors and blinds, together with planing-mills. It also has machine-shops, foundries, tanneries and cigar factories, besides mining and granite-quarry-
ing. The city is growing rapidly, is being connected with adjacent towns by electric street railway, is in the center of a fine dairying country. Marathon County is said to have the finest herd of Guernsey cattle in the world. Population 16,560.
Wave=Mo'tion, a state of disturbance being propagated from one part of a medium to another. A body is said to be disturbed when it is thrown out of equilibrium. Thus a stone dropped into quiet water produces a disturbance which at a later instant may reach a point several yards away. And since a body is in equilibrium only when its potential energy is a minimum, a disturbance implies the addition of energy to the system. Indeed, wave-motion might be defined as one of the two principal methods for distributing energy, the other being currents.
In any consideration of wave-motion, it is quite important to distinguish carefully between the motion of the wave and the motion of the particles of the medium through which the wave is traveling. Waves are roughly divided into two classes according to the motion of the particles. If these motions occur in the same direction in which the wave is traveling, the wave is said to be a longitudinal one; but if the particles are displaced in a plane which is perpendicular to the direction of propagation, the wave is said to be transversal. If the period of vibration of one of the disturbed particles of the medium is T, and the length of the wave be A,, then the speed of the wa ~~* V is given by the following equation:
y-JL
v ~ T
This is a perfectly general expression, true for all kinds of waves whatsoever.
Following is an outline of some of the more important types of waves met with in nature:
Water-Waves. These are the ordinary waves encountered at sea and at the seashore. They really are due to gravitation, which tends to pull down the crest and elevate the trough of a disturbance as if the surface of the water were elastic. They are more properly called surface waves.
The motion of the small particles which make up the water must be carefully distinguished from the motion of the waves. The motion of the particles in surface waves is in a circle, which gives to the outline of the wave a form very approximately that of a trochoid. The speed with which water waves travel depends very greatly upon the depth of the water.
If the depth of the water is greater than half
/pr
a wave-length, the speed of a wave is ^/ —,
where g is the acceleration of gravity and X is the length of the wave. The longer the wave, therefore, the faster it travels. But in the case of shallow water the speed of the wave is
