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ELATERS

594

ELDER

strain. And hence for this ratio, which is generally known as Young's modulus, we have

__      ,   nr   i i        Longitudinal stress Young's Modulus=Longitudinal gtrain

If a force F, applied to a wire of cross-section a and length L, produces an elongation e, then

(7)

Young's Modulus:

FL

e a

(f)

This is the equation employed by engineers in computing the proper cross-section of the ties in a bridge.

II. ELASTICITY  OF   VOLUME

Let us denote the volume of a body by V. Imagine the volume to be subjected to pressure, so that it is diminished by an amount v. The ratio of the diminution to the total volume is called the voluminal strain. Suppose further that this change of volume has been produced by applying a force F to a surface of area a; as, for instance, when air is compressed in an ordinary bicycle-pump. The ratio of the total force to the area over which it is applied is the voluminal stress; and is what we call pressure. In accordance with our general equation, the elasticity of volume for any material is measured by the ratio of the voluminal stress to the voluminal strain. This ratio is generally known as the bulk modulus, and is commonly denoted by k.

•rt 11 **   'i  i          7       Voluminal stress

Bulk Modulus = k = -^—.-.-—=——r-

volurmnal strain

(7) G)

F V

a v

The reciprocal of the bulk modulus is what is known as the compressibility of a substance.

III. ELASTICITY  OF   SHAPE

When a rod or shaft is twisted, the two surfaces which face one another at any cross-section of it are displaced one over another in exactly the same way (though not to the same extent) in which they would be if cut in two by a pair of shears. Such a strain is called a shearing strain, and the stress (force per unit area) is called a shearing stress. The ratio of the shearing stress to the shearing strain is called the rigidity modulus.

T,. .,.,       , ,        Shearing stress

Rigidity modulus=5r=-7——

J                  Shearing strain

The rigidity modulus of any material measures its ability to resist a shear, and hence its fitness for mill-shafting, for propeller-shafts of steamships, etc. A quantitative discussion of rigidity would be too long for our limited space, but may be

found in any good treatise on strength of material. Elasticity of shape^ is employed as a criterion by which to divide all bodies into two fundamental groups: solids and fluids. Solids are denned as those bodies which exhibit both elasticity of shape and elasticity of size. Fluids are bodies which possess elasticity of size but do not possess elasticity of shape. Bodies which exhibit no elasticity are called rigid. They do not exist in nature; but there are many bodies which we may, without error, treat as rigid. See Watson's Physics or Min-chin's Statics for an excellent account of this subject. HENRY CREW.

El'aters (in plants). Peculiar cells which develop among the spores in the spore-cases of many liverworts, as Mar-chantia. They are long, slender and spirally thickened, and by their jerking movements help to scatter the spores. See HEPATIC^.

Elba. See NAPOLEON.

Elbe, a large river of northern Europe, takes its rise from the flowing together of many small streams which have their origin on the southern side of the Giants' Mountains on the northern border of Bohemia. Its total length is about 725 miles, and it is navigable for 525 miles, but for sea-vessels only up to Hamburg (84 miles). Of its many tributaries the most important are the Moldau, Eger, Mulde, Saale and Havel, and in connection with these is a fine system of canals. The general direction of the river is northwestward, and it empties into the North Sea at Cuxhaven, where its mouth is ten miles wide. Within the mouth, which really is an arm of the sea, the tide rises about ten feet. The numerous islands between Hamburg and Har-burg divide the river into several branches, and between Hamburg and the sea the sandbanks and shoals leave only a very narrow channel. The navigation was formerly hindered by all sorts of tolls, but these were all abolished in 1870.

Elberfeld (Wbfr-fZlf), one of the^manufacturing capitals of Germany, is situated 16 miles from Dlisseldorf, on a small stream flowing into the Rhine. The town is famous for its dyeing, bleaching and calico-printing establishments; also for large manufactures of cotton, silks, tapes, ribbons, thread, lace, buttons, fancy woolen goods, etc. Its Turkey-red dye works are especially noted. There also are manufactures of machinery, iron and steel wares, pianofortes, paper and carpets, besides large breweries. For miles around an immense number of weavers labor for the Elberfeld factories. Population, 170 118

El'der. A species of Sambucus, a genus belonging to the honeysuckle family. 1 hey are shrubby plants with pinnately compound leaves and numerous small white flowers in flat clusters, followed by the.