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ELASTICITY

Railways. Khartum has railway and tele-•graphic communication with Cairo. The ^government owns and operates about 1,500 '-miles of railways in addition to the Sudan ^military line and the suburban road from Cairo ;to Helwan. About 800 miles of light •agricultural railway are in private hands. The government has built a telephone line •from Alexandria to Cairo. There are about 2,500 miles of government-telegraph, 50 *telephone-tcircuits and 350 miles of line. In Dec., 1899, the Sudan was declared open for general traffic. A railway from near Berber to Suakin and Port Sudan was completed in 1905, while other railways are projected. See PYRAMIDS, CAIRO, ALEXANDRIA, SUDAN, GORDON. See Sir Gardner Wilkinson's Manners and Customs of the Ancient Egyptians; A. B. Edwards: A Thousand Mile sup the Nile; S. Lane-Poole : Egypt; and Baedeker's Egypt.

Ehrenbreitstein (d-ren-brit'stin), a town and fortress of Rhenish Prussia. It is situated on the right bank of the Rhine, opposite Coblenz, with which it is connected by a bridge of boats and an iron railroad-viaduct. The fortress is on a high, rocky summit, 387 feet above the river, and is very strong. It was begun in 1672, and was captured by the French in 1799, who blew up the works two years later. It was turned over to Prussia by the Congress of Vienna in 1815, and was soon again fortified. Population of the town 5,299.

Eiffel (i'fet), Qustave, a French engineer, was born in 1832. He engaged in many important works of engineering, as the construction of the bridge over the Douro at Oporto, the design of the great locks intended for the French Panama Canal and the building of the iron framework of Bartholdi's statue of Liberty. But the work with which his name is most prominently associated is the famous Eiffel Tower on the Champ-de-Mars, in Paris, which was completed on March 31, 1889. It comprises three stories, reached by a series of elevators, the platform at the top being 985 feet above the ground. A little less than 7,000 tons of iron were used in build- ' ing it. The cost was about $1,000,000, of which $300,000 were voted by the government, the rest being supplied by M. Eiffel, who expects to recoup himself by the admission-fees during the 20 years for which they are granted to him.

Ein' Feste Burg. Hymn by Martin Luther, first published in 1538. The words are a revision of Psalm 46. Both words and music have been changed for the sake of greater conformity to the spirit of modern ideas. The composers Bach, Mendelssohn, Nicolai, Raff, Wagner and Meyerbeer have all employed this stirring choral in various vocal and instrumental compositions.

Eisenach (ifzen-ak}, a town of Germany, in Saxe- Weimar, on the northwestern edge of the Thuringian forest. The castle of Wartburg stands 600 feet above the town. It was built in 1067, and was the home of St. Elizabeth and also the ten months' asylum ;to which Luther was borne by the elector of Saxony in 1521. It also was the birthplace of Bach, the great composer. The chapel in which Luther preached, with 'the room he occupied and in which he overcame the Evil One by throwing an inkstand at his head, is still pointed out The town has a population of 35,153.

Eland. See ANTELOPE.

E'lastic'ity, a general property of matter, which may be briefly but roughly defined as the resistance which a body offers to a change either of size or of shape. A more accurate definition is the already classical one of Lord Kelvin, which runs as follows: "Elasticity of matter is that property in virtue of which a body requires force to change its bulk or shape, and requires a continued application of the force to maintain the change, and springs back when the force is removed, and, if left at rest without the force, does not remain at rest except in its previous bulk and shape."

When two or more forces are applied to a body in such a way that their resultant is zero, there is no acceleration, and no evidence, therefore, from the motion of the body, that such individual forces are acting. Such forces are said to be in equilibrium. A pair of forces in equilibrium is called a stress. The change in shape or size which results from such a stress is called a strain. And the elasticity of any body is measured by the ratio of the stress to the corresponding strain. Thus:

^^^—Strffi

In nature we meet practically three kinds of stresses. To each of these three stresses corresponds one kind of elasticity, each of which is included, however, in the general definition given above. We proceed to consider these three types of stresses.

I.  ELASTICITY   OF   LENGTH

When a force is applied to a body in such a way as to alter its length, either by compressing it or stretching it, the force is necessarily distributed over the cross-section of the body. The longitudinal stress at any point in a body is defined as the ratio of the force to the area at that point. A longitudinal stress always produces an elongation of the body to which it is applied. The total change in length depends not only upon the stress but upon the original length of the body. Accordingly the longitudinal strain is defined as the ratio of the total elongation to the length. Now the elasticity of length for any material is measured by the ratio of the longitudinal stress to the longitudinal