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The Length Of HOW DO WE KNOW? THE LENGTH OF ONEBY ANDREW METRE ROBINSON Defining the length of a metre meant a revolution in accurate scientific measurement. From metal bars to spectrums of light to today’s laser-based system, discover how pioneers rewrote the rules HE EARLIEST UNITS for to the mile, a length of 1,760 yards line. So there were 12 lines in an measuring length were based (1,609m). The milliare equalled mille inch, 12 inches (and 36 barleycorns) on the human body – most passuum, a ‘thousand paces’ of a length in a foot, and three feet in a yard. obviously the arm and the taken by a Roman legionary on a long In France, before the 1789 foot – and on seeds and march. This makes a ‘pace’ about Revolution paved the way for the grains. An Ancient Greek 1.6m – clearly an impossible average introduction of the metric system, a relief sculpture dated to about length for walking. The Roman ‘pace’ staggering 250,000 measures were in 450BC, kept at the Ashmolean must therefore refer to the full cycle of use under the guise of some 800 names, Museum in Oxford, shows left-right-left or right-left-right, giving including the aune for length. Since T a male figure with two arms a reasonable single pace of about 0.8m. the time of Charlemagne, eight French stretched out and a foot-shaped In Medieval England, the barleycorn kings – including Louis XIV, the ‘Sun depression above one of the arms. defined the inch, the foot and the yard. King’ – had attempted to lay down the The sculpture may have been set up During the reign of Edward II, in the law regarding standard weights and in a public place as a set of standard 14th Century, the inch was defined as measures. All failed, because uniformity measurements. If its damaged arm ‘three grains of barley, dry and round, did not please the feudal aristocracy, is completed by symmetry, then the placed end to end, lengthwise’. For who habitually manipulated the full arm span, known as the fathom, smaller lengths, the barleycorn was diversity of customary units to the measures 2.08 metres (m); the split into four equal parts, to create the disadvantage of their peasantry. forearm, known as the cubit, 0.52m; Inconsistency particularly and the foot 0.297m. bedevilled the cubit, a unit In the Roman Empire, the approximately equal to the milliare gave its name distance from a man’s This Ancient Greek relief from 450BC shows an early attempt at standardising measurement PHOTO: NPL, ASHMOLEAN MUSEUM OXFORD PHOTO: 92 / FOCUS / AUGUST 2014 How do we know? The Length Bar Interferometer at the National Physical Laboratory uses laser light to define a given length up to a metre > IN A NUTSHELL From early forms of defining length with seeds and parts of the body, to defining a length based on accurate measurements of the size and shape of the Earth, it’s taken hundreds of years for a standard metre to be used throughout the world. AUGUST 2014 / FOCUS / 93 How do we know? elbow joint to the farthest on its walls – that is, the summer modern conversion of 250,000 stadia fingertip of his extended hand, solstice – Eratosthenes, further north would give 39,690km (24,662 miles) or about half a metre. In ancient Egypt, in Alexandria, measured the angle – very close to the current value of the short cubit equalled six palms, created between the obelisk and its Earth’s equatorial circumference, while the royal cubit (used in the shadow. Since Syene and Alexandria 40,075km (24,901 miles). construction of the Pyramids) equalled lay almost on the same meridian of seven palms. The eight different cubits longitude, this angle measured the known in the early civilisations vary in difference in latitude between Syene TRUSTED TRIANGULATION length from Roman 0.444m to and Alexandria. As the Earth’s geography became Palestinian 0.641m. If the Earth were a perfect sphere, clearer through the great sailing Clearly a measurement of length the angle at the Earth’s centre voyages of the 16th Century, so did the defined by a universally agreed subtended by the well and the obelisk accuracy of surveying techniques on standard was needed, especially – by definition the difference in their land. Triangulation was first reported for international trade. The Greek latitudes – had to equal the angle of in a book published in Antwerp mathematician and geographer the shadow, from simple geometry. in 1533. In the 17th Century came Eratosthenes, who became director of (This assumed, reasonably, that the telescopes with cross-hairs for sighting the library at Alexandria in 235BC, was Sun was so far away that all its rays the stations being triangulated. the first to attempt such a definition by were parallel at the Earth.) The angle These were introduced in the 1670s determining the Earth’s circumference was 7.2°. Given the distance by camel in France, the earliest country to using astronomy and geometry. from Alexandria to Syene, known to be attempt an exact survey of itself, under Eratosthenes employed a well in about 5,000 stadia, the circumference the direction of Jean-Dominique far-off Syene (modern Aswan) and a of the Earth (subtending 360°) could Cassini, the first of four generations vertical obelisk in the grounds of the be calculated. Multiply 5,000 by the of Cassini surveyors of France. The Alexandria library. On the day when ratio 360:7.2 and you get 250,000 survey shifted the western coastline the overhead Sun shone directly stadia. The length of the stadium of existing maps about one-and- into the well, casting no shadow is unfortunately disputed, but one a-half degrees of longitude east in THE KEY Isaac Newton’s theory of gravity predicted the true shape of the Earth, and therefore the DISCOVERY varying length of a degree of latitude. It would prove a crucial step in defining the metre Newton found that NEWTON USED THE noted that a pendulum clock the Earth was in fact trigonometrical survey of the carried to the equator should an oblate spheroid Paris meridian in his calculation beat slightly slow, since of the force of gravity. His gravity was weaker there theory led him to predict, in his – which had indeed Principia Mathematica of 1687, been observed when that the Earth could not be a a French savant took perfect sphere. Centrifugal such a clock to the force, caused by axial spinning, Caribbean in 1672. was balanced by gravitational Third, he pointed force. But since the equator out that moved faster than the poles, astronomers the equator must bulge very had observed slightly, while the poles must be Jupiter to be slightly flattened, resulting in an flattened at oblate spheroid like a flattened the poles. tomato. Gravitational attraction Finally, he at the equator must be slightly showed how less than at the poles, since the gravitational gravity weakens with distance pull of the Sun from the centre of the Earth. and the Moon on To prove this, Newton first a bulging equator re-analysed the French survey could account for the data to show that a degree of swivel in the Earth’s latitude appeared to lengthen axis that had been known slightly as one moved north — to be the cause of the an increase to be expected precession of the equinoxes from a bulging equator and since the time of the flattened poles. Second, he ancient astronomers. PHOTO: ALAMY X2, THINKSTOCK X2, AKG IMAGES, NASA IMAGES, AKG X2, THINKSTOCK ALAMY X2, PHOTO: 94 / FOCUS / AUGUST 2014 How do we know? relation to the Paris meridian, and the southern coastline about half a degree of latitude to the north. Brest moved CAST OF From an Ancient Greek to a French emperor, it’s 177km (110 miles), Marseilles 64km CHARACTERS taken an eclectic mix to standardise measurement (40 miles). When in 1682 Louis XIV paid a visit to the Paris Observatory and saw the new map, he exclaimed Eratosthenes to Cassini: “Your journey has cost me (c. 276BC - a major portion of my realm!” c. 195/194BC) was a The French survey data also adjusted Greek mathematician, the shape of the Earth: from the perfect astronomer and sphere imagined by Eratosthenes to a geographer, as well prolate spheroid: that is, a sphere as a poet and music slightly flattened at the equator and theorist, who became slightly bulging at the poles. But Isaac director of the library at Newton, working across the English Alexandria in 235BC. He Channel, disagreed with Cassini (see is principally known for his accurate calculation ‘The Key Discovery’). Newton Isaac Newton of the circumference of calculated an oblate Earth, bulging at (1642-1727), the son the Earth and his map the equator and flattened at the poles. of an English yeoman of the world based on Not until the 1730s-40s, after Newton’s farmer who needs parallels and meridians. death, was the question resolved in no introduction as a Newton’s favour. Two gruelling mathematician and expeditions led by French savants physicist, also studied measured a degree of latitude in alchemy and religion. Lapland, near the pole, and in Peru, at Although he never left the equator. The results were conclusive the shores of England, Pierre François André enough, said the French writer he took a keen interest Méchain (1744-1804), Voltaire – a devotee of Newton – “to in calculating the shape a French astronomer flatten both the poles and the Cassinis”. of the Earth from and hydrographer, he both survey data and surveyed the southern gravitational theory.
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