which compose the atmosphere differ in weight; yet on account of diffusion they are usually uniformly mixed. Water vapor coming from a water surface diffuses very rapidly through the air. It is often the rate of diffusion that determines the rate of evaporation. In the absence of wind, diffusion prevents the air next to the water from becoming so saturated with water vapor that evaporation is stopped. For the same temperature and pressure the average speeds of the molecules of different gases vary inversely as the square root of the density of the gas. Light gases will therefore diffuse much faster than heavier ones. 170. Diffusion through porous walls. When hydrogen and air are separated by an unglazed earthenware wall, the hydrogen diffuses through the small interstices faster than air. This is well shown by the following simple experiment: The open end of a cup of porous earthenware is closed by a stopper through which a glass tube passes. The other end of the tube dips (Fig. 134) into a dish of colored water. A glass beaker is inverted over the porous cup. By the aid of a rubber tube, ordinary illuminating gas, which is largely hydrogen, flows from the gas mains up into the beaker. As this gas is lighter than air, it will stay for a short time in the inverted beaker. Just as soon as the gas is turned on, the pressure inside the porous cup rises, caus FIG. 134 ing the air in the glass tube to bubble out through the water. The cause of this is that gas diffuses in through the walls of the porous cup so much faster than air diffuses out that an increase in pressure is produced in the cup. If the beaker is now removed, the gas in the cup will diffuse out more rapidly than air goes in, and the pressure will fall below ordinary atmospheric pressure. This is shown by the rising of the water in the glass tube. Diffusion through membranes can be used for partially separating mixtures of gases. For example, if hydrogen and oxygen are mixed in a vessel which has a porous wall, the hydrogen will diffuse out faster than the oxygen. In the lungs it is diffusion through the surrounding membranes that carries carbon dioxide out and oxygen in. Metals, when heated, may become so porous that gases will diffuse through them. Reference has already been made in section 165 to the diffusion of water vapor through the soil. In loose soils it seems probable that the water deeper down evaporates, and that this vapor is carried through the loose upper part out into the air. In some cases this is the chief method by which the ground dries out (see also section 276). 171. Osmosis; osmotic pressure. Liquids also diffuse through porous membranes. In 1748 Abbé Nollet filled a bladder with alcohol and immersed it in water. The water diffused through so much faster than the alcohol that the bladder swelled almost to the bursting-point. The simpler facts of diffusion through membranes can be shown by the following experiment: The large end of a thistle tube is covered with a piece of animal membrane, such as the skin of sausage, and the bulb is filled with a sirup. The bulb is then immersed in water, as shown in Fig. 135. The water molecules will pass through the membrane more rapidly than the molecules of the sugar solution, and in half an hour this sirup will rise in the tube a considerable distance above the level of the water. This process is usually called osmosis. FIG. 135 If the outer vessel also contains a sirup, the osmotic action will always tend to cause water to pass into the more concentrated solution. The tendency will be to make the two solutions of equal concentration. Theoretically, at least, the solution will rise in the tube until the hydrostatic pressure is sufficient to stop the water from diffusing through the membrane. The pressure which is just sufficient to stop the action is called the osmotic pressure of that solution. Instead of actually permitting the sirup to keep on rising in the tube until its hydrostatic pressure stops the action, the usual way is to apply sufficient pressure (for example, by a piston in the tube) to stop the osmotic action. Animal membranes are not strong enough to stand the very large pressures which are often necessary to stop the action. With special types of membranes very great pressures have been developed,-pressures of many atmospheres. Osmosis plays a very important part in plant and animal growth. The roots of a plant contain sap, a more concentrated solution than the soil water. The surface of the root acts as the membrane, and water passes into the root. Osmotic action takes place through membranes in the bodies of human beings and animals and forms a very important part in growth and other activities. PROBLEMS 1. Why does a damp cloth absorb water more quickly than a dry one? 2. How high will water rise in a tube which is 2 mm. in diameter? 3. How much will the surface of mercury be depressed in a tube 4 mm. in inside diameter? 4. Mercury is raised by gas pressure 23.2 cm. in a tube 4 mm. in inside diameter. Compute the error produced by capillary action. 5. (a) If the length of the horizontal portion of the wire frame of Fig. 126 is 8.0 cm., with what force will a water film pull downward on it? (b) What will be the force if alcohol is used? 6. If the inside diameter of one tube of Fig. 127 is 1.0 cm. and that of the other is 3 mm., what will be the difference in levels (a) if the tubes contain water? (6) if the tubes contain mercury? CHAPTER XV ELASTICITY Elasticity, 172. Hooke's law, 173. Limit of elasticity, 174. Stress and strain, 175. Young's modulus, 176. Practical use of Young's modulus, 177. Volume elasticity, 178. Modulus of volume elasticity, or bulk modulus, 179. Elasticity of shape, or rigidity modulus, 180. Other cases of elasticity, 181. Ultimate stress or strength, 182. 172. Elasticity. It is often important for one to understand how to compute the amount a wire or rod will stretch, or a beam will bend, under a given load. Not only in the design of large structures, such as bridges or the steel frame of a building, but often in very simple cases it is necessary to compute the extension, bending, or twisting under the maximum load. In this chapter is given an elementary introduction to the fundamental definitions, facts, and laws of the subject of elasticity. 173. Hooke's law. If a vertical wire or small rod is clamped at the upper end, and weights are applied at the bottom, results something like the following are obtained: BRASS WIRE: LENGTH 195 CENTIMETERS, DIAMETER 200 0.034 .029 An inspection of the table given above, which is taken from actual observations, shows that the elongation is closely proportional to the stretching force. This is a case of a general law due to Robert Hooke. In 1676 Hooke published the law as Ut tensio sic vis, which, translated freely, means "The extension is proportional to the force." It should be clearly understood that this law is a summary of the results of experiment. In many cases it is fairly accurate; in many other cases only roughly true, but near enough for most practical purposes. Laws similar to this are approximately true for cases other than stretching; for example, the compression of solids and liquids, the bending of beams and plates, and the twisting of wires and rods. In some treatises Hooke's law is generalized and is said to apply to all these cases, but originally it applied only to stretching. In the chapter entitled "Vibratory Motion" it was stated that in any case where the restoring force was proportional to the displacement the vibrations were of the simple harmonic type. Another way of stating the same thing is: In those vibrations where the displacements obey Hooke's law the motion is simple harmonic motion. This applies to cases where the "damping," or frictional force tending to stop motion, is small. 174. Limit of elasticity. The experimental data given in the last section show that when the load is removed the wire resumes (approximately) its original length. This is usually true if one does not deform the body too far. If a rod or wire is stretched too much, it will not return but takes a "set." The range of perfect elasticity is the range within which the rod or wire resumes its original length when the load is removed. The limit of this range is called the elastic limit. In some materials (for example, lead) the elastic limit is very small; in other cases (for example, harddrawn brass and tempered steel) the range is relatively large. A spring balance is useful because it has a wide range of perfect elasticity. 175. Stress and strain. Consider a vertical wire or a rod which is stretched by a force applied at one end. This force is transmitted over the entire length of the wire, each part being stretched. When one portion of the wire communicates the force to the next, |