Page:1902 Encyclopædia Britannica - Volume 27 - CHI-ELD.pdf/789

EKATERINOSLAY—ELASTIC SYSTEMS 733 river carries ice in spring and winter, all communication with Totma. It has steam flour-mills, and carries with the lower Amur is practically interrupted there. junction on a brisk trade in exporting corn. Population, 9776. It is the centre of government for the Amur Cossacks* _ The famous Ananiinslciy Moghilnik (burial-place) is on the Population, about 2000. right bank of the Kama, 3 miles from above the town. It was discovered in 1858, was excavated by Alabin, Lerch, and NevoEkateri noslav, a province of South Russia, struyeff, in charge of the Archaeological Commission, and has since having Poltava and KharkofF on the N"., the Don province supplied extremely valuable collections of archaeological objects on the^E., the Sea of Azov and Taurida on the S., and belonging to the Stone, Bronze, and Iron Ages. It represented a mound, about 500 feet in circumference, adorned with decorKherson on the W. Area, 24,478 square miles. Its surface first ated stones (which have disappeared), and contained an inner is undulating prairie gently sloping south and north, with a wall, 65 feet in circumference, made of uncemented stone flags. few hills reaching 1320 ft. in the north-east, where a gentle Nearly 50 skeletons were discovered in it, mostly laid upon burned swelling (the Don Hills) compels the Don to make a great logs, surrounded - with pots filled with partially burned bones. A variety of bronze decorations and glazed clay pearls were curve eastwards. Another row of hills, to which the east- great strewn round the skeletons. The knives, daggers, and arrowward bend of the Dnieper is due, rises in the west. These points are of slate, bronze, and iron, the two last being very rough hills have a crystalline core (granites, syenites, and diorites), imitations of stone implements. On one of the funeral flags the while the surface strata are Carboniferous, Permian, image of a man, without moustaches or beard, dressed in a costume helmet recalling those of the Circassians, was discovered. The Cretaceous, and Tertiary. The province is rich in and exact period of these funeral mounds is not known. minerals, especially in anthracite and coal, iron ores, and rock-salt. Granite, limestone, grindstone, slate, as also Elastic Systems. —In the article Elasticity graphite, manganese, and mercury, are found. It is (Ency. Brit. vol. vii.) there is an outline of the general watered by the Dnieper, the Don, and their tributaries, mathematical theory of Elasticity, and an account of the and several affluents of the Sea of Azov. The soil is results obtained by applying it to the solution of the very a very fertile black earth, but the crops have occa- important problem of the torsion of prisms. The present sionally to suffer from droughts—the average yearly article is meant to supplement the former one by giving rainfall being only 15 inches. Forests are scarce. Popu- an account of some of the results that have been arrived lation (1860), 1,138,750; (1897), 2,112,651—chiefly Little at in the application of the theory to other problems. Russians, partly Great Russians, and some Greeks. The 1. Flexure of a Beam.—The simple theory of the bendland is owned as follows : the peasants hold in communal ing of a beam by applied couples has been explained in ownership 37 per cent., and in private ownership 4 per the original article, §§ 57-62, If M is the couple, the cent.; nobility, 31 per cent.; German colonists, 9*5 per central line of the beam is bent into a circle of radius cent.; Greeks, 7 per cent.; the remainder being owned by EI/M, where E is the Young’s modulus of the material, and I is the moment of inertia of the cross-section about various persons and companies. Wheat is grown extensively with the aid of modern machinery, the axis through its centroid at right angles to the plane and the average crops are 7,580,000 quarters of various cereals, of flexure. This plane is supposed to contain one prin577,000 quarters of potatoes, and about 1000 cwt. of tobacco. cipal axis of inertia of each cross-section,1 and the locus of Vines have been grown lately. There were in 1895, 295,670 horses, the perpendicular principal axes after flexure is a surface 653,770 horned cattle, and 2,174,350 sheep—nearly 6700 tons of raw wool being obtained every year. Mining attains every year cutting the plane more and more importance, the returns in South Russia (Ekater- of flexure at right inoslav and Don) being, in 1896, coal from 83 mines, 2,926,000 angles and known tons (12,000 workers) ; iron ore from 19 mines, 1,208,000 tons ; manganese ore (4 mines), 45,550 tons ; iron (all in Ekaterinoslav), as the “ neutral 608,600 tons ; steel, 51,100 tons ; rails, 246,000 tons ; iron goods, surface”; the 50,000 tons. Besides, mercury, ore, and fireclay are extracted. traces of this surNearly 40,000 persons find occupation in factories, of which the iron face are dotted in works and the 34 agricultural machinery works are the most import- Fig. 1. The quanant, while in the district of Mariupol the making of agricultural implements and machinery has undergone a very great extension tity El is known as a domestic industry in the villages. Grain is exported to a as the “ flexural very large extent (about 950,000 tons, and 520,000 tons in transit), rigidity.” The vid the Dnieper, the Sebastopol railway, and the port of Mariupol. applied couple M is balanced at any section by a couple Nearly 4000 boats and 1000 rafts are loaded and unloaded every year, carrying over 2,000,000 tons of goods (value 13,000,000 arising from the stress exerted across the section. Suproubles), and giving occupation to 27,000 men. The port of posing, to fix ideas, that the curve into which the central Mariupol is visited every year by about 80 steamers and 40 sail- line is bent is concave downwards, the stress at any ing vessels engaged in foreign trade, and 1600 vessels engaged in point above (below) the neutral surface is simple longicoasting. The government is better provided with schools, gymnasia, professional and primary, than many other governments tudinal tension (pressure) of amount per unit area equal of Russia. The chief towns of its 8 districts are : Ekaterinoslav to the product of M/I and the distance of the point (121,216 inhabitants), Alexandrovsk (16,393), Bakhmut (19,416), from the neutral surface. The corresponding strain Mariupol (31,772), Novomoskovsk (12,862), Pavlograd (17,188), consists of extension (contraction) of the longitudinal Slavyanoserbsk (3120), and Verkhnednyeprovsk (11,607). fibres above (below) the neutral surface accompanied (p. A. K.) by lateral contraction (extension) of the perpendicular Ekaterinoslav, capital of the above province, on fibres, and the effect of the lateral strain is seen in the the right bank of the Dnieper, 607 miles by rail south- change of shape of the section producing the anticlastic south-west of Moscow. It is a rapidly growing town, well curvature of the beam (cf. Elasticity, Ency. Brit. provided with schools, including a number of professional vol. vii. p. 809). The extension (contraction) of a ones, and is an important depot for timber shipped down longitudinal fibre distant y above (below) the neutral the Dnieper, as also for grain. Its iron works, steam flour- surface is My/El, and the lateral contraction (extension) mills, and agricultural machinery works give occupation is <rMy/EI, where o- is the “Poisson’s ratio” of the to 5000 workers. Considerable trade is carried on in material (a fraction nearly equal to J for most hard cattle, grain, and raw wool. Population (1861), 18,881, solids). The displacements produced are—(1) a deflexion without suburbs; (1897), 121,216. of the central line by which the centroid of each cross1 Elabuga, a district town of Russia, government and 'When this is the case the beam is said to be bent in a “ principal 279 miles south-east of Vyatka, on Kama river, near its plane.”