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Length is the most necessary measurement in everyday life, and units of length in many countries still reflect humanity's first elementary methods.

The inch is a thumb. The foot speaks for itself. The yard relates closely to a human pace, but also derives from two cubits (the measure of the forearm). The mile is in origin the Roman mille passus - a 'thousand paces', approximating to a mile because the Romans define a pace as two steps, bringing the walker back to the same foot. With measurements such as these, it is easy to explain how far away the next village is and to work out whether an object will get through a doorway.

For the complex measuring problems of civilization - surveying land to register property rights, or selling a commodity by length - a more precise unit is required.

The solution is a rod or bar, of an exact length, kept in a central public place. From this 'standard' other identical rods can be copied and distributed through the community. In Egypt and Mesopotamia these standards are kept in temples. The basic unit of length in both civilizations is the cubit, based on a forearm measured from elbow to tip of middle finger. When a length such as this is standardized, it is usually the king's dimension which is first taken as the norm.


For measurements of weight, the human body provides no such easy approximations as for length. But nature steps in. Grains of wheat are reasonably standard in size. Weight can be expressed with some degree of accuracy in terms of a number of grains - a measure still used by jewellers.

As with measurements of length, a lump of metal can be kept in the temples as an official standard for a given number of grains. Copies of this can be cast and weighed in the balance for perfect accuracy. But it is easier to deceive a customer about weight, and metal can all too easily be removed to distort the scales. An inspectorate of weights and measures is from the start a practical necessity, and has remained so.


Among the requirements of traders or tax collectors, a reliable standard of volume is the hardest to achieve. Nature provides some very rough averages, such as goatskins. Baskets, sacks or pottery jars can be made to approximately consistent sizes, sufficient perhaps for many everyday transactions.

But where the exact amount of any commodity needs to be known, weight is the measure more likely to be relied upon than volume.


Time, a central theme in modern life, has for most of human history been thought of in very imprecise terms.

The day and the week are easily recognized and recorded - though an accurate calendar for the year is hard to achieve. The forenoon is easily distinguishable from the afternoon, provided the sun is shining, and the position of the sun in the landscape can reveal roughly how much of the day has passed. By contrast the smaller parcels of time - hours, minutes and seconds - have until recent centuries been both unmeasurable and unneeded.

Sundial and water clock: from the 2nd millennium BC

The movement of the sun through the sky makes possible a simple estimate of time, from the length and position of a shadow cast by a vertical stick. (It also makes possible more elaborate calculations, as in the attempt of Erathosthenes to measure the world - see Erathosthenes and the camels). If marks are made where the sun's shadow falls, the time of day can be recorded in a consistent manner.

The result is the sundial. An Egyptian example survives from about 800 BC, but the principle is certainly familiar to astronomers very much earlier. However it is difficult to measure time precisely on a sundial, because the sun's path throug the sky changes with the seasons. Early attempts at precision in time-keeping rely on a different principle.

The water clock, known from a Greek word as the clepsydra, attempts to measure time by the amount of water which drips from a tank. This would be a reliable form of clock if the flow of water could be perfectly controlled. In practice it cannot. The clepsydra has an honourable history from perhaps 1400 BC in Egypt, through Greece and Rome and the Arab civlizations and China, and even up to the 16th century in Europe. But it is more of a toy than a timepiece.

The hourglass, using sand on the same principle, has an even longer career. It is a standard feature on 18th-century pulpits in Britain, ensuring a sermon of sufficient length. In a reduced form it can still be found timing an egg.

Hero's dioptra: 1st century AD

One of the surviving books of Hero of Alexandria, entitled On the Dioptra, describes a sophisticated technique which he has developed for the surveying of land. Plotting the relative position of features in a landscape, essential for any accurate map, is a more complex task than simply measuring distances.

It is necessary to discover accurate angles in both the horizontal and vertical planes. To make this possible a surveying instrument must somehow maintain both planes consistently in different places, so as to take readings of the deviation in each plane between one location and another.

This is what Hero achieves with the instrument mentioned in his title, the dioptra - meaning, approximately, the 'spyhole' through which the surveyor looks when pinpointing the target in order to read the angles.

Hero adapts, for this new and dificult task, an instrument long used by Greek astronomers (such as Hipparchus) for measuring the angle of stars in the sky. It is evident from his description that the dioptra differs from the modern theodolite in only two important respects. It lacks the added convenience of two inventions not available to Hero - the compass and the telescope.

The hour: 14th century

Until the arrival of clockwork, in the 14th century AD, an hour is a variable concept. It is a practical division of the day into 12 segments (12 being the most convenient number for dividing into fractions, since it is divisible by 2, 3 and 4). For the same reason 60, divisble by 2, 3, 4 and 5, has been a larger framework of measurement ever since Babylonian times.

The traditional concept of the hour, as one twelfth of the time between dawn and dusk, is useful in terms of everyday timekeeping. Approximate appointments are easily made, at times which are easily sensed. Noon is always the sixth hour. Half way through the afternoon is the ninth hour - famous to Christians as the time of the death of Jesus on the Cross.

The trouble with the traditional hour is that it differs in length from day to day. And a daytime hour is different from one in the night (also divided into twelve equal hours). A clock cannot reflect this variation, but it can offer something more useful. It can provide every day something which occurs naturally only twice a year, at the spring and autumn equinox, when the 12 hours of day and the 12 hours of night are the same length.

In the 14th century, coinciding with the first practical clocks, the meaning of an hour gradually changes. It becomes a specific amount of time, one twenty-fourth of a full solar cycle from dawn to dawn. And the day is now thought of as 24 hours, though it still features on clock faces as two twelves.

Minutes and seconds: 14th - 16th century

Even the first clocks can measure periods less than an hour, but soon striking the quarter-hours seems insufficient. With the arrival of dials for the faces of clocks, in the 14th century, something like a minute is required. The Middle Ages, by a tortuous route from Babylon, inherit a scale of scientific measurement based on 60. In medieval Latin the unit of one sixtieth is pars minuta prima ('first very small part'), and a sixtieth of that is pars minute secunda ('second very small part'). Thus, on a principle 3000 years old, minutes and seconds find their way into time.

Minutes are mentioned from the 14th century, but clocks are not precise enough for anyone to bother about seconds until two centuries later.

Barometer and atmospheric pressure: 1643-1646

Like many significant discoveries, the principle of the barometer is observed by accident. Evangelista Torricelli, assistant to Galileo at the end of his life, is interested in why it is more difficult to pump water from a well in which the water lies far below ground level. He suspects that the reason may be the weight of the extra column of air above the water, and he devises a way of testing this theory.

He fills a glass tube with mercury. Submerging it in a bath of mercury, and raising the sealed end to a vertical position, he finds that the mercury slips a little way down the tube. He reasons that the weight of air on the mercury in the bath is supporting the weight of the column of mercury in the tube.

If this is true, then the space in the glass tube above the mercury column must be a vacuum. This plunges him into instant controversy with traditionalists, wedded to the ancient theory - going as far back as Aristotle - that 'nature abhors a vacuum'. But it also encourages von Guericke, in the next decade, to develop the vacuum pump.

The concept of variable atmospheric pressure occurs to Torricelli when he notices, in 1643, that the height of his column of mercury sometimes varies slightly from its normal level, which is 760 mm above the mercury level in the bath. Observation suggests that these variations relate closely to changes in the weather. The barometer is born.

With the concept thus established that air has weight, Torricelli is able to predict that there must be less atmospheric pressure at higher altitudes. It is not hard to imagine an experiment which would test this, but the fame for proving the point in 1646 attaches to Blaise Pascal - though it is not even he who carries out the research.

Having a weak constitution, Pascal persuades his more robust brother-in-law to carry a barometer to different levels of the 4000-foot Puy de Dôme, near Clermont, and to take readings. The brother-in-law descends from the mountain with the welcome news that the readings were indeed different. Atmospheric pressure varies with altitude.

Mercury thermometer:1714-1742

Gabriel Daniel Fahrenheit, a German glass-blower and instrument-maker working in Holland, is interested in improving the design of thermometer which has been in use for half a century. Known as the Florentine thermometer, because developed in the 1650s in Florence's Accademia del Cimento, this pioneering instrument depends on the expansion and contraction of alcohol within a glass tube.

Alcohol expands rapidly with a rise in temperature, but not at an entirely regular speed of expansion. This makes accurate readings difficult, as also does the sheer technical problem of blowing glass tubes with very narrow and entirely consistent bores.

By 1714 Fahrenheit has made great progress on the technical front, creating two separate alcohol thermometers which agree precisely in their reading of temperature. In that year he hears of the researches of a French physicist, Guillaume Amontons, into the thermal properties of mercury.

Mercury expands less than alcohol (about seven times less for the same rise in temperature), but it does so in a more regular manner. Fahrenheit sees the advantage of this regularity, and he has the glass-making skills to accomodate the smaller rate of expansion. He constructs the first mercury thermometer, of a kind which subsequently becomes standard.

There remains the problem of how to calibrate the thermometer to show degrees of temperature. The only practical method is to choose two temperatures which can be independently established, mark them on the thermometer and divide the intervening length of tube into a number of equal degrees.

In 1701 Newton has proposed the freezing point of water for the bottom of the scale and the temperature of the human body for the top end. Fahrenheit, accustomed to Holland's cold winters, wants to include temperatures below the freezing point of water. He therefore accepts blood temperature for the top of his scale but adopts the freezing point of salt water for the lower extreme.

Measurement is conventionally done in multiples of 2, 3 and 4, so Fahrenheit splits his scale into 12 sections, each of them divided into 8 equal parts. This gives him a total of 96 degrees, zero being the freezing point of brine and 96° (in his somewhat inaccurate reading) the average temperature of human blood. With his thermometer calibrated on these two points, Fahrenheit can take a reading for the freezing point (32°) and boiling point (212°) of water.

A more logical Swede, Anders Celsius, proposes in 1742 an early example of decimilization. His centigrade scale takes the freezing and boiling temperatures of water as 0° and 100°. In English-speaking countries this less complicated system takes more than two centuries to prevail.

Chronometer: 1714-1766

Two centuries of ocean travel, since the first European voyages of discovery, have made it increasingly important for ships' captains - whether on naval or merchant business - to be able to calculate their position accurately in any of the world's seas. With the help of the simple and ancient astrolabe, the stars will reveal latitude. But on a revolving planet, longitude is harder. You need to know what time it is, before you can discover what place it is.

The importance of this is made evident when the British government, in 1714, sets up a Board of Longitude and offers a massive 20,000 prize to any inventor who can produce a clock capable of keeping accurate time at sea.

The terms are demanding. To win the prize a chronometer (a solemnly scientific term for a clock, first used in a document of this year) must be sufficiently accurate to calculate longitude within thirty nautical miles at the end of a journey to the West Indies. This means that in rough seas, damp salty conditions and sudden changes of temperature the instrument must lose or gain not more than three seconds a day - a level of accuracy unmatched at this time by the best clocks in the calmest London drawing rooms.

The challenge appeals to John Harrison, at the time of the announcement a 21-year-old Lincolnshire carpenter with an interest in clocks. It is nearly sixty years before he wins the money. Luckily he lives long enough to collect it.

By 1735 Harrison has built the first chronometer which he believes approaches the necessary standard. Over the next quarter-century he replaces it with three improved models before formally undergoing the government's test. His innovations include bearings which reduce friction, weighted balances interconnected by coiled springs to minimize the effects of movement, and the use of two metals in the balance spring to cope with expansion and contraction caused by changes of temperature.

Harrison's first 'sea clock', in 1735, weighs 72 pounds and is 3 feet in all dimensions. His fourth, in 1759, is more like a watch - circular and 5 inches in diameter. It is this machine which undergoes the sea trials.

Harrison is now sixty-seven, so his son takes the chronometer on its test journey to Jamaica in 1761. It is five seconds slow at the end of the voyage. The government argues that this may be a fluke and offers Harrison only 2500. After further trials, and the successful building of a Harrison chronometer by another craftsman (at the huge cost of 450), the inventor is finally paid the full prize money in 1773.

He has proved in 1761 what is possible, but his chronometer is an elaborate and expensive way of achieving the purpose. It is in France, where a large prize is also on offer from the Académie des Sciences, that the practical chronometer of the future is developed.

The French trial, open to all comers, takes place in 1766 on a voyage from Le Havre in a specially commissioned yacht, the Aurore. The only chronometer ready for the test is designed by Pierre Le Roy. At the end of forty-six days, his machine is accurate to within eight seconds.

Le Roy's timepiece is larger than Harrison's final model, but it is very much easier to construct. It provides the pattern of the future. With further modifications from various sources over the next two decades, the marine chronometer in its lasting form emerges before the end of the 18th century. Using it in combination with the sextant, explorers travelling the world's oceans can now bring back accurate information of immense value to the makers of maps and charts.

Sextant: 1731-1757

The 18th-century search for a way of discovering longitude is accompanied by refinements in the ancient method of establishing latitude. This has been possible since the 2nd century BC by means of the astrolabe. From the beginning of the European voyages in the 15th century practical improvements have been made to the astrolabe - mainly by providing more convenient calibrated arcs on which the user can read the number of degrees of the sun or a star above the horizon.

The size of these arcs is defined in relation to the full circle. A quadrant (a quarter of the circle) shows 90°, a sextant 60° and an octant 45°.

The use of such arcs in conjunction with the traditional astrolabe is evident from a text of 1555 about voyaging to the West Indies. The author talks of 'quadrant and astrolabe, instruments of astronomy'.

The important development during the 18th century is the application of optical devices (mirrors and lenses) to the task of working out angles above the horizon. Slightly differing solutions, by instrument makers in Europe and America, compete during the early decades of the century. The one which prevails - largely because it is more convenient at sea - is designed as an octant in 1731 by John Hadley, an established English maker of reflecting telescopes.

Hadley's instrument, like others designed by his contemporary rivals, uses mirrors to bring any two points into alignment in the observer's sight-line. For the navigator these two points will usually be the sun and the horizon. To read the angle of the sun, the observer looks through the octant's eyepiece at the horizon and then turns an adjusting knob until the reflected orb of the sun (through a darkened glass) is brought down to the same level.

The double reflection means that the actual angle of the sun above the horizon is twice that on the octant's arc of 45%. So Hadley's instrument can read angles up to 90%.

In 1734 Hadley adds an improvement which becomes standard, installing a spirit level so that the horizontal can be found even if the horizon is not visible. In 1757, after Hadley's death, a naval captain proposes that the arc in the instrument be extended from 45° to 60°, making possible a reading up to 120°.

With this Hadley's octant becomes a sextant, and the instrument in use ever since finds its essential form.

This History is as yet incomplete.