"Recently, while washing the dishes," he writes, "I lifted a water glass upside down from the pan and noticed that a film of soapy water had formed across the mouth of the glass. As I watched the film some water from my wet hand run down the side of the glass and onto the film, distorting it into a funnel-like shape. When I shook the glass, several droplets that hung from the film went into orbit, much like the movement of the planets around the sun. The orbits were somewhat erratic and did not last very long because I could not hold the film level or keep it still. As soon as the dishes were finished I made a rigid support for the film.

"My first attempt was a crude ring, made from the wire of a coat hanger clamped in a vise. To form the film I lifted a pan of soapy water under the ring so that the wire was submerged and then I lowered the pan gently. I put water droplets on the film with a medicine dropper. A drop launched near the edge would spiral toward the center and finally come to rest. I could control the shape of the spiral by moving the dropper tangentially when releasing the drop. I could easily simulate the orbit of a single body, as conventionally demonstrated by gravitational models that consist of a suitably curved surface of plastic or stretched rubber on which a rolling sphere represents the orbiting body [see "The Amateur Scientist," SCIENTIFIC AMERICAN, October, 1958]. With a little practice I soon learned how to simulate a number of other gravitational effects, including the orbits of several bodies about each other, tidal effects, the formation of stars and the reentry of a missile or a satellite into the earth's atmosphere. All are demonstrations that cannot be made with the solid models.

"To measure these phenomena I made another apparatus that consisted of a ring assembly to hold the film, a stand, a pan of soap solution and some leveling wedges [see top illustration]. With this apparatus I measured the static properties of the film, such as its shape, rate of evaporation and surface tension.

"For the ring I used about B0 centimeters of three-millimeter copper-coated steel welding rod bent into circular form 20 centimeters in diameter. The ring should be reasonably circular, but it does not have to be perfect. (A substitute material for the ring, if one is desired, should be nonporous and at least three millimeters thick, otherwise it will not hold a film long enough for experiments.)

"The ends of the wire ring were soldered together in the form of a butt joint. A supporting crossarm was made from a 30-centimeter piece of the same kind of rod. This stiffened the ring and also served as a base line for measuring the shape of the fi]m. The ends of the crossarm were bent down. It right angles to make brackets about three centimeters long and were soldered to the ring. This arrangement provided a convenient space between the crossarm and the fi]m. The ends of the crossarm were attached to the ring at points remote from the butt joint so that the joint would not be damaged by the heat of subsequent soldering. Half of the crossarm was calibrated for length by a series of file notches at one-centimeter intervals from the center of the ring [see above].

"To attach the ring and crossarm to the stand I soldered two 25-centimeter rods vertically to the unmarked side of the crossarm, one at the edge and the other about two centimeters from the center point. The ring assembly was painted black and the file marks white. The vertical rods were pushed into close-fitting holes drilled in a wooden stand shaped like a C:. The stand rested on three wedges. The pan of soap solution was placed on the base.

"My soap solution consisted of one part of Liquid Lux detergent and 19 parts of tap water. Other detergents tended to produce a viscous area in the center of the films that impeded the free travel of the droplets. The pan was placed about 20 centimeters below the ring and the solution was some three centimeters deep.

"To make a film the pan is gent]y raised until the ring is immersed, then slowly lowered until the film separates from the solution. I found that if the crossarm was immersed in the solution, a second film would form that distorted the main film. When the crossarm is not immersed, the single film will last about three minutes in still air.

"As an initial experiment I timed the average life of a film with a stopwatch. The film bends downward slightly under its own weight, causing the liquid to flow toward the center. After about one minute enough liquid has drained so that the edges of the film take on the characteristic interference colors of a soap bubble. During the second minute the edges turn black and the coloring extends almost to the middle of the film. 13y the end of the third minute the color has reached the center. The film is easily broken at this stage and is almost useless for experimentation. Films usually break; during the fourth minute.

"To measure evaporation from the film I made a distortion gauge: a small copper wire coated with black enamel that was scratched at one-millimeter intervals. One end was wrapped around the crossarm near the center so that the remainder extended down into the film. The point at which the film made contact with the wire was recorded at 10 second intervals until the film broke. The evaporation rate appeared to be constant, as I expected, because the area of the film remains constant during its lifetime.

"I found the shape of the film by sliding the measuring wire along the crossarm and observing the point of intersection between the film and the wire at one-centimeter distances. The unloaded film appeared to be roughly spherical. Determination of its true shape would require a more precise, method of measurement.

"To find the approximate shape of the film when it was loaded by a droplet I first centered the droplet in the ring by adjusting the wedges to level the stand and then measured the film shape as before. A graph of these measurements resembled the inverse-square, funnel-shaped curve used in the solid simulators. Attempts to measure shape 11 when the film was loaded with two drops failed. One drop or the other would fall off, so I settled for synthetic loading. I achieved that by attaching to the crossarm a small ring of the same wire used for the distortion gauge. The ring could be placed in contact with the top side of the film at any desired position on the vertical axis and would thus distort the film any desired amount.

"The weight of a droplet was measured by determining the number of drops required to make a gram of liquid. The medicine dropper I used released drops of about .024 gram. I measured the surface tension of the soap h solution by using a balanced rod and finding the force required to lift it clear of the solution. The method indicated a surface tension of .03 gram per centimeter, about half that of pure water.

"After making these static measurements I began experimenting with the orbits of drops and with tidal effects. To investigate the velocity of the drops I needed an accelerator for shooting drops onto the film at controlled speed and direction. My first two attempts to make an accelerator-one with a pendulum and one with a film placed at an angle to the main film-were unsatisfactory.

"The final model consists of a pipette that injects a drop into a jet of air that acts as the accelerator. It works beautifully. The air jet is formed by a glass nozzle that makes approximately a right angle with the glass tubing from which it was formed. The diameter of the nozzle is about three millimeters. An adjustable rubber sleeve near the opening of the nozzle helps to preserve the streamline flow of the jet. A rubber tube connects the nozzle to a glass Y joint. A clothespin on the rubber tube serves as a pinch clamp for regulating the flow of air. From one arm of the joint a rubber tube is connected to a mouthpiece; the tube from the other goes to a water manometer. Oscillations of the water column in the manometer are suppressed by a check valve. The valve consists of the neck of a toy balloon and a paper clip. One end of the rubber tube is slipped over the open arm of the manometer and the free end of the tube is weighted by the paper clip.

"When the clothespin and the rubber sleeve of the nozzle are properly adjusted, droplets released by the pipette can be accelerated smoothly. A needle valve-at the top of the pipette controls the rate at which drops are released [see illustration below].

"To calibrate the accelerator I placed the nozzle 19.6 centimeters above the soap solution. That is the distance at which drops require .2 second to fall to the pan. The horizontal distance traveled by the drop at various pressures, as indicated by the manometer, was then measured. By multiplying the horizontal distance by 5 I found the velocity of the drops in centimeters per second. Velocity was then plotted against the manometer pressure. By referring to the graph I could launch a drop onto the film at any desired velocity.

"Having calibrated the apparatus, I observed the orbit of a drop around a stationary body by launching a drop around the distorting ring. After several elliptical orbits the drop spiraled in to collide with the ring, simulating the orbital decay of a satellite around a massive body.

"My second experiment was to observe the orbital decay of two drops of equal mass. First I put one drop in the center of the film and then launched the other around it. In this case I found that I could shoot the drop more easily by hand than with the accelerator. The orbiting drop first spirals toward the stationary drop. As the spiral decreases the center drop begins to spiral outward until both drops orbit around a common center, separated by some three centimeters. When drag decelerates the system until the objects are spaced about one centimeter apart, both drops become radially elongated, simulating tidal action. The model is imperfect in one major respect: the velocity of the bodies decreases as they spiral inward instead of increasing as in the case of celestial objects. When the tidal bulges finally make contact, the more massive drop of two that are unequal in size usually absorbs the smaller one. By coloring one drop with ink and waiting until both drops coalesce one can see that the central body spins violently on its axis. This phenomenon suggests the conservation of angular momentum. The entire sequence normally takes six or seven seconds. The use of an immiscible fluid such as cooking oil for the drops reduces friction and provides a longer show, but the tides and the capture of the drops are not as easily seen. When I used composite drops of both oil and water, the tides would simulate those of the earth (the oil) and the oceans (the water). To photograph the bodies in the various stages of orbital decay the drops were colored with ink and flash exposures were made against a white background.

"I found that I could provide a droplet with an 'atmosphere' by tapping the main ring with my finger until the droplet broke into several small parts. At one stage, before the fluid coalesces, the surrounding area contains some of the drop's liquid, simulating the atmosphere. A small drop, when added to the film as a satellite, orbits normally until it hits the atmosphere. It then falls directly toward the center drop, as observed in the case of a reentering missile. Even some curls of turbulence are evident.

"Another interesting phenomenon is the simulation of the formation of a star or a planet. This is demonstrated by spraying fine droplets of solution onto a fresh film with a toothbrush and letting them coalesce into a drop; the spray represents the interstellar gas cloud and the drop the star.

"The apparatus can doubtless be modified for demonstrating still other interesting effects. For example, a curved universe could be simulated by using a saddle-shaped ring for negative curvature or by deflecting the film by an upward current of air to form a positive curvature. Another possibility is to show the effects of gravity on light by vibrating the film and allowing the waves to travel through the droplets. I have not had time so far to explore fully all the potentialities of the model. The experiments that have been made, however, certainly support an observation once made by the British physicist C. V. Boys: 'There is more in a common soap bubble than those who have only played with them generally imagine.'"

While experimenting with Leyden jars in 1777 the German physicist Georg Christoph Lichtenberg observed that an electric discharge between a pointed electrode and a conductive plate covered with fine powder would scatter the powder into strange and beautiful patterns that differed characteristically, depending on the polarity of the point and the conductive plate. The patterns subsequently became known as Lichtenberg figures. Elric W. Saaski of Iron River, Wis., has built a modern apparatus for investigating the figures and recording them by color photography. The apparatus shows the phenomenon in greater detail than Lichtenberg's.

"My apparatus," writes Saaski, "resembles the Klydonograph more than it does the arrangement used by Lichtenberg. Essentially the Klydonograph consists of a photographic emulsion sandwiched between two electrodes: a small brass disk that rests on a somewhat larger one. The small disk is connected to the power line; the larger one, to the ground. I substituted a water surface for Lichtenberg's powder and for the photographic emulsion of the Klydonograph. The fluidity of the medium and its ability to hold ions in solution are convenient for controlled experimentation. When I made the accompanying photographs, I connected one side of the capacitor to a metal pan 12 centimeters in diameter; the pan contained water to a depth of one centimeter. Then I moved a pointed discharge electrode, which was connected to the other terminal of the capacitor, toward the water until a spark jumped, discharging the capacitor and creating the Lichtenberg figure on the surface.

"To produce the direct-current surges for my experiments I used a power supply that consisted of a transformer, a rectifier and a capacitor. The high potential is derived from a 9,000-volt, center-tapped neon-sign transformer that supplies a constant current of 18 milliamperes. This output is converted to direct current by a pair of 1B3 GT high-voltage diodes in a full-wave rectifier circuit. The rectifier was built on a plastic sheet six inches wide and eight inches long, supported on six half-inch porcelain legs. The full-wave circuit was of conventional design, with the current for the filaments supplied by a "flyback" transformer I had rebuilt to function as a step-down transformer on 110 volts a.c. The rectifier does not have to be this elaborate, however. One 1B3 GT tube can be used in a halfwave circuit, with the current supplied by a common 'D' cell if necessary [see illustration below]. The maximum output of the full-wave rectifier is 40 milliamperes at 6,300 volts (peak voltage). I was somewhat apprehensive about the ability of the 1B3 GT tubes to take the current surges as the capacitor was charged because the tubes are designed for a maximum load of one milliampere, but my fears proved groundless.

"The rectified current is stored in a capacitor, the modern counterpart of Lichtenberg's Leyden jar. In principle a capacitor is merely two conducting plates separated by some type of insulator. When the two plates are connected to a source of direct current, an excess of electrons accumulates on one plate, with a corresponding deficiency on the other. The charging voltage must not exceed the dielectric strength of the insulating material between the conductors or the insulator will be punctured.

"When the charged capacitor is disconnected from the source of current and a circuit is completed from one plate to the other, electrons flow until the difference in potential is equalized. By stacking a number of insulated plates and connecting alternate plates it is possible to increase the capacity of the unit to store energy. Capacitors of the size needed for this experiment are priced at $100 and up, depending on the construction. I made one for less than $10. The unit consists of 30 five-inch-square sheets of aluminum foil sandwiched between 79 six-inch-square sheets of Mylar plastic film .003 inch thick. Mylar film has a breakdown strength of approximately 4,000 volts per thousandth of an inch thickness. Unfortunately the dielectric strength of substances does not increase in direct proportion to thickness. My capacitor operates at six kilovolts. For safety's sake I use Mylar film .003 inch thick, rated at 12 kilovolts breakdown. Polyethylene plastic can also be employed. The rated breakdown voltage of this material, however, is only one kilovolt per thousandth of an inch thickness. Both plastics can be ordered through most hardware stores and mail-order houses in the forms used for protecting machinery from the weather.

"Since aluminum generally cannot be bonded to other metals, I found it best to cut each capacitor plate and its external lead from a single piece of foil. Plates cut five inches square with a lead one inch wide and five inches long utilize the 12-inch width of a roll of aluminum foil without waste. Alternatively plates can be cut 10 inches on a side with a lead two inches wide. This saves time and yields a more efficient capacitor because the leakage of charge from the larger plate is 50 percent less than for an equal area consisting of smaller plates.

"The size of the available container must also be considered when one is choosing the dimensions of the plates. My assembly was potted in a sheetmetal box six and a half inches wide, two inches deep and eight inches high. It is lined with plastic sheeting. The negative plates are clamped to the metal box; the positive series, to an insulated terminal on top. After the assembly was completed the container was filled with transformer oil, an insulating fluid bought from our local power company. Mineral oil or any nonreactive liquid can be used, but transformer oil is effective and cheap. Although a capacitor will work in air, the intense electric field between the plates produces ozone. Gradually the ozone weakens the dielectric, causing the material to rupture.

"The capacitance of the unit, approximately .44 microfarad, was determined by the formula C = 2.24 x 10^-7 KA/d(n - 1), where C is the capacitance in microfarads, K is the dielectric constant, A is the area of one side of one plate in square inches, d is the thickness of one dielectric sheet in inches and n is the number of plates. The dielectric constant of polyethylene is 2.4, that of Mylar about 3.

"The energy capacity of the unit, 8.8 joules, was found by the formula J = CE²/2, where the energy capacity in joules equals one-half the product of the capacitance in microfarads and the charging potential in kilovolts squared. One joule is equivalent to one watt-second, or 1/746 horsepower.

"To record the discharges, a 35-millimeter camera equipped with a closeup lens was placed on a platform 12 1/2 inches above the pan. The room was totally darkened. The camera shutter was opened. The capacitor was then discharged. The Lichtenberg figures literally take their own picture without need for elaborate shutter synchronization. The correct opening of the camera diaphragm was determined by trial.

"The flash is readily seen in the darkened room; serpentine arms extend from a white core as a dull reddish flame that dwindles off into tapering fingers of light blue. Positive and negative discharges are easily distinguished. The former is larger and more detailed than the relatively small and thick-limbed negative discharge. The positive discharge has been likened to the drainage basin of a mountain valley.

"Occasionally the spark jumps to the side of the pan. This effect has been ascribed to anomalies in the distribution of ions at the surface of the water and to the position of the discharge electrode. The spark appears to be a branch of the Lichtenberg figure, one that usurps the available energy, thus preventing the growth of the complete figure. The process by which the branch becomes the main current-carrier is not evident in ordinary photographs because the brilliance of the discharge obliterates the previous activity. Analysis of this phenomenon by high-speed photography would be an extremely interesting but rather elaborate project. I have, however, investigated one peculiarity of these discharges without extensive equipment. The distance a spark travels across water can be increased sharply by adding ions to the water in the form of a salt. A limit is reached when the concentration approaches approximately 150 ions per million water molecules. The maximum discharge distance is about 11 times greater than that of air and three times greater than that of distilled water. At a concentration of only 60 ions per million water molecules the discharge distance is still 90 percent of the maximum distance. Below this concentration it drops rapidly."

Bibliography

THE LIGHTNING BOOK. Peter E. Viemeister. Doubleday & Company, Inc., 1961.

SOAP-BUBBLES. C. V. BOYS. Dover Publications, Inc., 1959.

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