EXPERIMENTS of seemingly endless variety can be performed with water. Some of them, such as the fountain constructed by Hero of Alexandria in 150 B.C. to demonstrate that water can rise above its own level, are little more than illusions. Others dramatize the remarkable properties of water; an example is Lord Kelvin's electrostatic generator in which drops of falling water develop potentials of thousands of volts. Still others are based on the peculiar behavior of water. An experiment of this kind has been devised by Gerard Schol, a physics teacher of Drachten in the Netherlands. Schol's experiment involves the commonly observed but long neglected phenomenon that drops of water can exist as independent floating objects on the surface of clean water. Schol writes:

"I was rowing a boat about two years ago and happened to hold the oars still for a few seconds. A stream of water that ran from one oar struck the surface at a point from which scores of droplets darted in a radial pattern. They resembled glittering gems and remained on the surface for as long as 15 seconds before vanishing.

"I had seen floating drops on previous occasions on pools and surf and even while pouring a drink. They can easily be mistaken for bubbles. Close examination discloses obvious differences, however, particularly when there is a bit of wind. The drops race across the surface in response to even a gentle breeze because they make almost frictionless contact with the supporting water, whereas bubbles are anchored to the water by surface tension.

"Moreover, in contrast to bubbles, the drops are massive and their higher index of refraction causes them to glitter characteristically, particularly when they are viewed in sunlight at about the angle at which rainbows are observed. Finally, the weight of the drops pushes shallow depressions into the supporting surface of the water. A depression can be seen easily by examining a floating drop that stands still or a photograph of a moving drop. All floating drops have the form of oblate spheroids. To distinguish floating drops from ordinary drops I call the floaters water globules.

"Water globules can be made readily. Punch a hole about two millimeters in diameter in the bottom of a tin can. Fill the can with water, hold it about a meter above any still body of water and let the contents drain through the hole. A great many drops will spatter radially away from the point where the stream hits the surface. If the surface is clean, water globules will form among the drops that spatter. If the surface is dirty, globules may not form immediately, but a few will appear within seconds and the number will increase as the jet sweeps the surface clean.

"The globules will form in a range of sizes from less than a millimeter in diameter to as much as five millimeters. They are easily seen in light from any direction but particularly when they are lighted from the rear by sunlight. Many globules remain afloat for 15 seconds and then merge with the surface water.

"Some globules disappear sooner, in two or three steps, shrinking to half their diameter every five seconds or so. In my opinion this effect occurs when the drops encounter particles of dirt that protrude from the surface of the water. A particle of dirt pierces the thin layer of molecules constituting the 'skin' of the globule. The interior of the water globule is under considerable pressure, which is maintained by surface tension. Hence when the globule is pierced, water rushes out along the path created by the dirt particle. The escaping jet creates a force of reaction identical with that of a rocket, which lifts the shrinking globule above the surface. The jet necks down after the shrunken globule pulls away from the particle of dirt. The small remaining globule subsequently exists for a time as an independent entity.

Having done a number of experiments with the tin can, I devised an apparatus for launching a continuous stream of water globules indoors [see illustration, right]. The launcher consists of a small nozzle that directs a jet of water upward at an angle of approximately 45 degrees. The diameter of the nozzle and the velocity of the jet are adjusted so that the stream breaks into drops just before it reaches the top of its parabolic trajectory.

"Immediately after the trajectory bends downward the drops land on the surface of water in a plastic tray of the kind used in photographic darkrooms. The angle at which the drops strike the surface amounts to only a few minutes of arc. The plastic tray is filled to the brim. Indeed, the water rises above the edges as a meniscus that extends around the four sides of the tray. After the apparatus has operated until all dust is carried from the surface the efficiency of globule production approaches 100 percent. Substantially all drops from the jet coast across the surface to the opposite end of the tray. They are easily photographed.

"Overflow from the tray drains into a catch basin from which it is pumped to an elevated reservoir of constant head. The apparatus also contains a source of high voltage. A source of monochromatic light is provided for investigating the nature of the globules.

"The nozzles were made of soft glass tubing seven millimeters in diameter. The middle of a 15-centimeter length of the tubing was rotated in a gas flame until a zone approximately 15 millimeters long became plastic. The tube was then removed from the flame and the ends were promptly drawn apart to form a constriction about three millimeters in outside diameter. One side of the constriction was scratched lightly with the corner of a sharp file at the narrowest point, and then the ends of the tubing were pulled (without bending) until the glass broke squarely at the scratch.

"The angle of the nozzle must be adjustable with respect to the horizontal and vertical planes. I clamp the nozzle to the vertical rod of an apparatus stand that has a base with three feet in the form of two knurled screws at one end and, at the middle of the opposite end, a metal projection of fixed length. The clamp that attaches the nozzle to the vertical rod can be turned in any direction, moved to any height and locked to the rod with a thumbscrew.

"The tray on which the drops are launched rests on an elevated platform of plastic eight millimeters thick, 15 centimeters wide and 20 centimeters long [see illustration at right]. The platform has three legs that can be adjusted to alter the height of the tray and to level the tray. The adjustable tray support is made by drilling and threading holes at the two corners of one side of the platform and making a similar hole at the center of the opposite side. Three supporting legs of the plastic rod were threaded to mate with the holes in the platform. (Prethreaded iron rod, which is available from hardware stores in the U.S. as stud-bolt stock, would also be suitable for the legs.)

"The platform stands in a catch basin that is 40 centimeters long, 30 centimeters wide and six centimeters deep. This container can be a baking pan made of sheet metal or plastic. It receives the overflow from the tray. Water is raised from the catch basin to the elevated reservoir by a small centrifugal pump of the kind normally used for circulating water in aquariums.

"Surplus water from the reservoir returns to the catch basin through a hose that connects to an overflow port near-the top of the reservoir. The overflow scheme maintains a constant head of pressure in the reservoir. The reservoir is a tin can with a capacity of approximately three liters. The velocity of water in the hose that interconnects the reservoir and the nozzle is controlled by a pinch clamp of the Hoffman type that has an adjustment screw.

"The production of water globules is critically dependent on three adjustments. The tray must be level and filled to the point at which the surface of the water becomes convex, that is, until a meniscus forms completely around the brim of the tray. The nozzle must project upward a jet that breaks into drops before the parabolic trajectory reaches its maximum height. The path of the impinging drops must meet the surface of the water in the tray at an angle of not more than 15 minutes of arc. Before carrying out an experiment I rinse the apparatus with several changes of tap water. After being refilled the system will run unattended for a number of hours.

"My experiments were designed to probe two questions. What mechanism accounts for the existence of water globules? What are the properties of the globules and how can they be influenced?

"Quite early in my investigation I discovered more or less by accident that the globules are sensitive to an electric field. While the apparatus was running I happened to pick up a piece of plastic tubing (polyvinyl chloride) about 40 centimeters long and to rub it with a piece of wool. The friction dislodged electrons from the wool and deposited them on the plastic. The rod emitted a faint crackling sound, which indicated that negative discharges in excess of 10,000 volts were occurring. I was standing next to the tray across which the globules were coasting. The globules vanished whenever I brought the rod near the tray. What would be the effect of a comparable positive charge? A glass rod rubbed with silk acquires positive charge. I tried it. The globules vanished as they did under a negative charge.

"These experiments convinced me that water globules owe their existence at least in part to electrical forces. It is well known that although the water molecule is electrically neutral, it forms an electric dipole. The two hydrogen atoms are bonded to the single oxygen atom at an angle of approximately 105 degrees. The asymmetry causes a negative charge to appear on the oxygen side of the molecule and a positive charge to appear on the hydrogen side. The molecule is free to rotate into alignment with an external electric field.

"Moreover, the interaction between neighboring molecules, which are kept in a state of perpetual motion by thermal energy, is such that molecules at the surface of the liquid spend most of their time with the oxygen atoms turned away from the body of the liquid. Hence the surface of water, either in a container or in the form of a drop, is negatively polarized. It is my opinion that when a drop from a nozzle approaches the surface of water in the tray at a small angle, and hence at sufficiently low vertical velocity, a force of repulsion exists between the two negatively polarized surfaces and is strong enough to support the weight of the globule. The distance between the polarized surfaces is very small and so maximizes the repulsive force. (An experiment I shall describe below discloses that the separation between the globule and the surface is less than the wavelength of yellow light.) An external electric field of sufficient strength should alter the orientation of the water molecules, causing the molecules to rotate so that the hydrogen atoms point toward the surface, which should then become positively polarized. Such reversals of polarization of the molecules should cause the globules to merge with water in the tray.

"To test this assumption I applied an electric field of adjustable and known potential between an electrode and the surface of the water in the tray. The electrode was an aluminum strip 10 centimeters long, 1.5 centimeters wide and approximately one millimeter thick. The strip was supported at a right angle to the stream of globules one centimeter above the center of the tray by an insulator, which was a rod made of polyvinyl chloride. The electrode was connected through a resistor of 50,000 ohms to a direct-current power supply that was adjustable from 0 to 1,000 volts. The resistor's role was to limit the current to a safe value if the electrode accidentally made contact with a grounded conductor. A voltmeter measured the potential on the electrode. The circuit was completed by hanging a wire connected to the grounded side of the power supply in the water at one corner of the tray.

"All globules directly below the electrode disappear at a characteristic voltage, which varies with the composition of the water. In distilled water the globules merge at a potential of about 450 volts, which is equivalent to an electric-field strength on the order of 45 volts per millimeter. An exact value cannot be given because the behavior of the globules is influenced by several variables, including their mass.

"In distilled water a gradient of 45 volts per millimeter causes 99 percent of the globules below the electrode to disappear. The remaining globules are the largest ones. All globules merge with the tray water when the potential is increased to 550 volts, which is equivalent to a field strength of 55 volts per millimeter.

"The addition of table salt to the water greatly increases the potential required to stop the globules. The same effect is observed when liquid detergent is added to the water. The addition of liquid detergent also causes larger globules to form, perhaps because the extraordinarily long molecules of the detergent form a highly polarized surface layer on the water. It seems reasonable to suppose that the resulting electrical force at the surface is stronger than that of distilled water. If this is the case, a proportionately stronger electric field would be required to make the globules disappear.

"Interesting phenomena can be observed by putting nozzles at each end of the tray to launch drops on a collision course, particularly if detergent is added to the water. Globules that collide elastically bounce apart, often vibrating so violently that they break into clusters of small globules suggestive of what happens when atomic particles collide. Other colliding globules merge to form large globules. Multiple encounters frequently result in globules that grow in diameter to more than three centimeters. The weight of the globules depresses the surface of the supporting water in the immediate vicinity. Relatively large flattened globules almost sink below the surface.

"Part of the light that enters the space between the bottom of a globule and the surface of the supporting water in the tray follows the curvature of the drop by multiple reflection and emerges on the other side. I suspect that this effect may account in part for the glittering ring that appears to surround globules that are lighted from the rear. To estimate the thickness of the film of air that separates the globules from the tray water I examined the globules from the top with monochromatic light from a sodium lamp. Newton's rings appear in each globule. Such rings form a pattern of concentric dark and light bands or fringes that arises from the optical interference of light waves reflected through the globule from the supporting surface and from the lower surface of the globule. The central fringe of the pattern appears as a black disk, which indicates that the space between the two surfaces is less than a wavelength of yellow light and not more than a fraction of a micron.

"I have found no published explanations of water globules, although the fact that drops of water can float temporarily on larger bodies of water is mentioned in a few references. I hope that my investigations will encourage others to tinker with the globules. Experiments performed with alcohol and nonpolarized liquids of low viscosity should be interesting. I also hope that those who undertake these or any related projects will let me have a report of their results. My address is: Gerard Schol, Sint Jansberg 63, Drachten, The Netherlands."

A PAIR of sine waves that vary with respect to axes at right angles can combine to generate a family of curves known as Lissajous figures. The figures can take the form of a straight line, a pattern of complex elliptical forms or a circle, depending on the relative amplitude, period and phase of the sine waves. The patterns are named for the 19th-century French physicist Jules Antoine Lissajous, who investigated them both experimentally and mathematically.

To generate the figures Lissajous cemented a small mirror to one tine each of two tuning forks mounted at a right angle. A beam of light that was reflected sequentially by the mirrors came to a focus as a small spot on a distant screen. The mirror attached to one vibrating fork caused the spot to oscillate in the vertical plane. The mirror of the second fork simultaneously contributed to the beam a horizontal component of vibration. Persistence of vision caused observers to perceive the path of the rapidly moving spot as a geometric figure.

Lissajous could alter the frequency, amplitude and phase of the tuning forks by adding weights to the tines and altering the force with which he set the forks into vibration. He could thus generate all possible forms of the figures. As he reported, waves of the same frequency, which are either in phase or exactly 180 degrees out of phase, generate straight lines. Sine waves of equal amplitude that are 90 degrees out of phase generate a circle. Waves of unequal frequency generate complex patterns, but distinct and easily recognized patterns appear when the frequencies differ in the ratio of whole numbers. For example, the frequency ratio of 1:2 generates a pattern in the form of the numeral 8, which has two loops. A ratio of 1:3 generates a comparable figure of three loops, and so on. The figures are therefore useful for measuring the phase and frequency relations of sine waves. Such measurements of alternating electric currents are made routinely by observing Lissajous figures with cathode ray oscilloscopes.

A much simpler and more inexpensive apparatus for investigating the figures is submitted by Philippe Lebrun of the School of Mines in Paris (École des Mines de Paris, 60 Boulevard St. Michel, 75 Paris 6e, France). "My apparatus," he writes, "consists of a pendulum-made by suspending a tin can filled with lead balls by a slender nylon string about two meters long [see illustration on page 107]. To the bottom of the can I attached a miniature incandescent lamp. The lamp is energized through a pair of thin flexible wires twisted around the string. These leads connect to the output of a small transformer that provides appropriate voltage for the lamp.

"The path of the swinging pendulum can be recorded photographically in a dark room by putting an appropriately focused camera on its back 50 centmeters directly under the pendulum bob. A pattern of ellipses appears on the film when the pendulum is free to swing in all directions, as in the case of a Foucault pendulum. Normally I work with color film. Various figures generated by altering the amplitude of the pendulum can be recorded in the form of multiple time exposures by using lamp bulbs of distinctive color for each exposure of the series.

"Interesting Lissajous figures can be generated by increasing the frequency at which the pendulum beats in one azimuth. This is accomplished by passing the string between a closely spaced pair of smooth horizontal rods rigidly mounted about 50 centimeters below the point where the string is suspended. The ratio between the two periods at which the pendulum beats can be altered by raising or lowering the horizontal rods."

Lebrun's apparatus works nicely and is easy to set up. On the other hand, it is relatively bulky. The pendulum must be suspended in a room with a ceiling height of at least 25 meters to provide adequate range for the camera. Roger Hayward, who illustrates these columns, submits a design for an apparatus that is more compact, although it is more difficult to construct. It employs two pendulums. They cause two mirrors to vibrate at right angles as in the case of Lissajous's apparatus. The details of the construction are depicted by the accompanying illustrations.

Bibliography

HARMONIC CURVES. William F. Rigge. The Creighton University, 1926.

WATER. Arthur M. Buswell and Worth H. Rodebush in Scientific American, Vol. 194, No. 4, pages 76-89; April, 1956.

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