that whenever the forces that produce distortions in any body are within the elastic limit, the distortions produced are directly proportional to the forces that produce them.

The loads suspended from vertical rods of the same material and form, when the elastic limit is reached, are directly proportional to the sizes of the rods, as determined by measuring the areas of their cross sections. Hence the elastic limit of a substance, for elasticity of traction, is usually expressed in pounds per square inch, or kilograms per square centimeter, of cross section.

18. Elastic Fatigue. When a force that does not exceed the elastic limit is applied to a solid for a long time, the change of form may slowly continue; and when the force is removed, the body may not return exactly to its original form. This result is due to elastic fatigue and indicates a permanent change in the relative positions of the molecules of the body.

19. Measurement of Elasticity. — If a load of 4200 lb. is suspended from a copper rod 100 in. long and 1 sq. in. in cross section, the rod will be stretched slightly until it is 100.02 inches long. The external force (weight of the load) tending to produce elongation will then be exactly counterbalanced by the elastic force produced in the rod and tending to restore its original size and shape; and the load will remain at rest. The external force and the equal restoring force, in any case of elasticity, are each called a stress; the change of size or shape in the body is called a strain. So long as the elastic limit is not exceeded, the elasticity of any body is measured by the ratio of stress to strain; that is,

Elasticity =

Stress
Strain

Force applied

(1)

Change produced

In accordance with this expression the elastic limit may be defined as the maximum force that can be applied to a body without producing a permanent change in its volume or form. It is commonly said that rubber is very elastic, because it can be stretched to two or three times its length without exceeding its elastic limit; that is, it has a wide range of perfect elasticity. But as measured in physics, substances like copper, steel, marble, and ivory are far more highly elastic

than rubber, because a much greater force is required to produce a given change in them.

In the measurement of elasticity many devices are used. One for testing the torsion, or twist, of a rod is shown in Fig. 3. This

FIG. 3

consists of some form

of stable clamp to which one end of the rod is fastened. The other end of the rod is clamped in the axis of a wheel to the rim of which the twist is applied by weights. The reading pointer may be fastened to the rod at any distance from the fixed clamp and on making the experiment the relation between the weights used (stress) and the twist (strain) produced is determined. The following results of an experiment will serve as an example of the method.

The rod was of cypress, 1 cm. square and 100 cm. long. An examination of the curve (Fig. 4) shows that the twist was proportional to the pull up to 1100 g. Beyond that

pull it was not. That is, the limit of elasticity was reached at that point.

Demonstration.

Make a paste by rubbing some lampblack into kerosene, and put a thin coating upon a flat slab of iron or stone. Place a large marble upon the slab. Notice how small a part of the marble touches the slab. Drop the marble from a height of

6 or 8 ft., and notice both the height to which it rebounds and the increased size of the contact between the marble and the slab. Repeat with a steel ball such as would be used in ball bearings, and with a small rubber ball.

20. Cohesion and Adhesion. Cohesion is the mutual attraction that particles of the same kind have for each other at molecular distances. It is measured by the force required to pull a body apart.

If the attraction is between particles of different kinds, it is called adhesion. Both of these attractions are molecular; there is no essential difference between them, and no need of two names. Cohesion is very great in solids, and serves to give them form and strength. In liquids cohesion is not strong enough to determine the form, except in very small quantities, when they take the form of drops. In gases cohesion is very slight. In many cases adhesion is greater than cohesion, as in the case of two boards glued together, or two pieces of china cemented to each other; if they are again broken, the break will be more likely to take place in the board or china than in the joint. Finely divided matter is often made into a solid body by compression, as in the making of emery wheels. If a piece of rubber gum is cut with a knife, the two pieces may be made to cohere perfectly by pressure.

FIG. 5

Demonstration. - Press together two pieces of plate glass as in Fig. 5, and see whether both can be lifted by raising the upper piece by the corner. Put two or three drops of water between the plates, and they will cling together more firmly. Why?

II. SPECIFIC PROPERTIES

21. Tenacity. When a body resists forces that tend to pull it apart, the substance of which it is composed is said to be tenacious. Tenacity is a direct result of cohesion, a tenacious substance being one that has great cohesion. The tenacity of a substance is measured by the breaking weight per unit area of cross section.

The tenacity, or tensile strength, of steel is of great importance on account of the extensive use of this material in building operations. There are many grades of steel, but

most of them have a tensile strength between 60,000 and 100,000 pounds per square inch.

Demonstration. - To determine the breaking weight of No. 24 copper wire, make a loop in one end and suspend it from a hook overhead. Fasten a pail to the other

end so that it will be three or four inches above a table. Place known weights in the pail until the wire begins to stretch, then slowly pour in sand until the wire breaks.

By measuring the diameter of the wire and taking the weight of the total load, the tensile strength can be computed, by dividing the breaking weight by the area of cross section.1 (For example, if a wire

in. in diameter is broken by a load of 104 lb., the tensile strength is equal to 3.1416

104÷

32 x 32

=33,898 lb. per square inch.)

In bodies of the same material, tenacity varies with the form of the body. When the areas of cross section are equal, a tube has greater

FIG. 6

tenacity than a solid cylinder of the same material, and a wire with circular cross section has greater tenacity than one with a square cross section.

Tenacity diminishes with the length of time the load is carried, so that a wire may finally break with a load that it would carry safely at first. Tenacity also diminishes. as the temperature increases, on account of the increased rate of molecular vibration.

1 The area of a circular cross section is equal to 3.1416 times the square of half the diameter.