thorny problems to work out. THINKING BIG AND THINKING SMALL-AN ASIDE ON NUMBERS Some scientists, such as geologists and paleontologists, think of time in terms of thousands and millions of years. In their vernacular a hundred years more or less is insignificant-too small to recognize or to measure. To other scientists, such as engineers who design sophisticated communication systems and navigation systems, one or two seconds' variation in a year is intolerable because it causes them all sorts of problems. They think in terms of thousandths, millionths, and billionths of a second. The numbers they use to express these very small "bits" of time are very large. of a second, for example, is one 1 1,000,000 1 1,000,000,000 microsecond. of a second is one nanosecond. To keep A billionth of a second is an almost inconceivably small bitmany thousands of times smaller than the smallest possible "bit" of length or mass that can be measured. We cannot think concretely about how small a nanosecond is; but to give some idea, the impulses that "trigger" the picture lines on the television screen come, just one at a time, at the rate of 15,750 per second. The whole picture "starts over," traveling left to right, one line at a time, the 525 lines on the picture tube, 30 times a second. At this rate it would take 63,000 nanoseconds just to trace out one line. Millionths and billionths of a second cannot, of course, be measured with a mechanical clock at all. But today's electronic devices can count them accurately and display the count in usable, meaningful terms. Whether one is counting hours or microseconds, the principle is essentially the same. It's simply a matter of dividing units to be counted into identical, manageable groups. And since time moves steadily in a "straight line" and in only one direction, counting the swings or ticks of the timer-the frequency with which they occur —is easier than counting the pellets in a pailful of buckshot, for example. "Bits" of time, whatever their size, follow one another single file, like beads on a string; and whether we're dealing with ten large bits-hours, for example-or 200 billion small bits, such 63 MICRO 525 LINES 30 TIMES/SEC TRACE MOVES BACK TO LEFT EDGE OF SCREEN TO START NEW LINE COUNT as microseconds, all we need to do is to count them as they pass through a "gate," and keep track of the count. The "hour" hand on a clock divides a day evenly into 12 or 24 hours-depending on how the clock face and works are designed. The "minute" hand divides the hour evenly into 60 minutes, and the "second" hand divides the minute evenly into 60 seconds. A "stop watch" has a finer divider-a hand that divides the seconds into tenths of a second. When we have large groups of identical items to count, we often find it faster and more convenient to count by tens, dozens, hundreds, or some other number. Using the same principle, electronic devices can count groups of ticks or oscillations from a frequency source, add them together, and display the results in whatever way one may wish. We may have a device, for example, that counts groups of 9,192,631,770 oscillations of a cesium-beam atomic frequency standard, and sends a special tick each time that number is reached; the result will be very precisely measured onesecond intervals between ticks. Or we may want to use much smaller bits-microseconds, perhaps. So we set our electronic divider to group counts into millionths of a second, and to display them on an oscilloscope. Electronic counters, dividers, and multipliers make it possible for scientists with the necessary equipment to "look at," and to put to hundreds of practical uses, very small bits of time, measured to an accuracy of one or two parts in 1011; this is about 1 second in 3,000 years. Days, years, and centuries are, after all, simply units of accumulated nanoseconds, microseconds, and seconds. The earth swings around the sun, and the moon swings around the earth. The earth "swings" around its own axis. These movements can easily be observed and charted, from almost any spot on earth. The observations were and are useful in keeping track of time, even though early observers did not understand the movements and often were completely wrong about the relationships of heavenly bodies to one another. The "swings" happened with dependable regularity, over countless thousands of years, and therefore enabled observers to predict the seasons, eclipses, and other phenomena with great accuracy, many years in advance. When we observe the earth's swing around its axis, we see only a part of that swing, or an arc, from horizon to horizon, as the sun rises and sets. A big breakthrough in timekeeping came when someone realized that another arc-that of a free-swinging pendulum could be harnessed and adjusted, and its swings counted, to keep track of passing time. The accuracy of the pendulum clock was far superior to any of the many devices that had preceded it-water clocks, hour glasses, candles, and so on. Furthermore, the pendulum made it possible to "chop up" or refine time into much smaller, measurable bits than had ever been possible before; one could measure quite roughly, to be sure-seconds and even parts of seconds, and this was a great advancement. The problem of keeping the pendulum swinging regularly was solved at first by a system of cog wheels and an "escapement" that had the effect of giving the pendulum a slight push with each swing, in much the same way that a child's swing is kept in motion by someone pushing it. A weight on a chain kept the escapement lever pushing the pendulum, as it does today in the cuckoo clocks familiar in many homes. But then someone thought of another way to keep the pendulum swinging-a wound-up spring could supply the needed energy if there were a way to make the "push" from the partially wound spring the same as it was from a tightly wound spring. The "fusee"-a complicated mechanism that was used for only a brief period-was the answer. From this it was just one more step to apply a spring and "balance wheel" system directly to the pinions or cogs that turned the hands of the clock, and to eliminate the pendulum. The "swings" were all inside the clock, and this saved space and made it possible to keep clocks moving even when they were moved around or laid on their side. But some scientists who saw a need for much more precise time measurement than could be achieved by conventional mechanical devices began looking at other things that swing-or vibrate or oscillate things that swing much faster than the human senses can count. The vibrations of a tuning fork, for instance, which, if it swings at 440 cycles per second, is "A" above "Middle C" on our music scale. The tiny tuning fork in an electric wrist watch, kept swinging by electric impulses from a battery, hums along at 360 vibrations or "cycles" per second. As alternating-current electricity became generally available at a reliable 60 swings or cycles per second-or 60 hertz (50 in some areas)—it was fairly simple to gear these swings to the clock face of one of the commonest and most dependable time-pieces we have today. For most day-to-day uses, the inexpensive electric wall or desk clock driven by electricity from the local power line keeps "the time" adequately. But for some users of precise time these common measuring sticks are as clumsy and unsatisfactory as a liter measuring cup would be for a merchant who sells perfume by the dram. These people need something that cuts time up with swings much faster than 60ths or 100ths of a second. The power company itself, to supply electricity at a constant 60 hertz, must be able to measure swings at a much faster rate. Power companies, telephone companies, radio and television broadcasters, and many other users of precise time have long depended on the swings or vibrations of quartz crystal oscillators, activated by an electric current, to divide time intervals into megahertz, or millions of cycles per second. The rate at which the crystal oscillates is determined by the thickness-or thinness-to which it is ground. Typical frequencies are 2.5 or 5 megahertz (MHz)-22 million or 5 million swings per second. Incredible as it may seem, it is quite possible to measure swings even much faster than this. What swings faster? Atoms do. One of the properties of each element in the chemistry Periodic Table of Elements is the set of rates at which its atoms swing or resonate. A hydrogen atom, for example, has one of its resonant frequencies at 1,420,405,752 cycles per second, or hertz. A rubidium atom has one at 6,834,682,608 hertz, and a cesium atom at 9,192,631,770 hertz. These are some of the atoms most commonly used in measuring sticks for precise time-the "atomic clocks" maintained by television network master stations, some scientific laboratories, and others. Primary time standards, such as those maintained by the U.S. Naval Observatory or the National Bureau of Standards, are "atomic clocks." Everything swings, and anything that swings at a constant rate can be used as a standard for measuring time interval. GETTING TIME FROM FREQUENCY The sun as it appears in the sky-or the "apparent sun"— crosses the zenith or highest point in its arc with a "frequency" of once a day, and 36514 times a year. A metronome ticks off evenly spaced intervals of time to help a musician maintain the time or tempo of a composition he is studying. By moving the weight on its pendulum he can slow the metronome's "frequency" or speed it up. Anything that swings evenly can be used to measure time interval simply by counting and keeping track of the number of swings or ticks-provided we know how many swings take place in a recognized unit of time, such as a day, an hour, a minute, or a second. In other words, we can measure time interval if we know the frequency of these swings. A man shut up in a dungeon, where he cannot see the sun, could keep a fairly accurate record of passing time by counting his own heartbeats-if he knew how many times his heart beats in one minute-and if he has nothing to do but count and keep track of the number. 1,000,001 -1,000.002 The term frequency is commonly used to describe swings too fast to be counted by the human ear, and refers to the number of swings or cycles per second-called hertz (Hz), after Heinrich Hertz, who first demonstrated the existence of radio waves. If we can count and keep track of the cycles of our swinging device, we can construct a time interval at least as accurate as the |