HOW DO WE KNOW? HOW TO MEASURE LONGITUDE BY ANDREW ROBINSON Before we were able to plot our position at sea, thousands of sailors lost their lives; the genius of one British clock-maker changed all that and won the prestigious Longitude Prize in the process ESPITE THE PATRIOTIC degree of longitude west of Ushant. and practicality of proposed methods, claim in ‘Rule, Britannia!’, the Four ships were smashed and 1,647 which consisted of scientists, naval anthem composed in 1740, sailors drowned; only 26 survived. officers and government officials. Britain was actually far from As a result of the 1707 catastrophe, They included the president of the ‘ruling the waves’ in the mid- the British Parliament passed the Royal Society (Sir Isaac Newton), 18th Century. As the Royal Longitude Act in 1714. This stipulated the first lord of the Admiralty, the Navy was only too painfully enormous cash prizes for anyone speaker of the House of Commons, aware, neither British sailors – British or otherwise – who could the first commissioner of the Navy nor the seamen of any rival invent a method of measuring and professors of mathematics at D nation, such as France or longitude that would be effective Oxford and Cambridge. Imaginatively, Spain, had a reliable way to determine at sea. The top prize, £20,000, was Parliament also empowered the their position in the open ocean. offered for a method accurate to half committee to offer financial grants This was especially true during foul a degree of longitude. Furthermore, to develop promising proposals. weather, when it was impossible to the act established a Board of observe the positions of the Sun, Moon Longitude to adjudicate the validity and stars. Navigation and landfall GREEK GENIUS remained always a precarious affair. The concept of longitude, and of In 1741, a British naval squadron course latitude, dates back to ancient lost its way – along with several ships Greek mathematicians and astronomers and more than half of its crew – off the who accepted that Earth was essentially western tip of South America because a sphere. Earth’s circumference was its estimate of its longitude was some measured with considerable accuracy Y 200 miles in error. Much closer to by Eratosthenes in the third century M home, in 1707 a British fleet returning BC, but without specifying any from France became lost in fog terrestrial lines of latitude and near the western end of the English longitude. These were invented in the Channel. Its commander, misjudging 2nd Century BC by Hipparchus, who his position as west of the island of also compiled the first known star AN ART LIBRARY, ALA LIBRARY, AN ART Ushant (at the furthest tip of the catalogue, with about 850 stars EM Brittany peninsula), sailed north and measured in terms of celestial latitude ran his warships into the rocks of the Hipparchus came up with a framework of lines of and longitude. Hipparchus’s Scilly Isles, which are located a whole latitude and longitude on the celestial sphere framework strongly influenced PHOTO: BRIDG PHOTO: 92 / FOCUS / SUMMER 2014 How do we know? HMS Endeavour was captained by James Cook; on a later expedition on the HMS Resolution, a Harrison chronometer helped him navigate > IN A NUTSHELL Finding out how to measure longitude was crucial to being able to navigate at sea. Following the launch of the Longitude Prize to Accompanies the 50th anniversary incentivise someone to come up of Horizon and the launch of with a method, one Yorkshire-based Longitude Prize 2014 clockmaker took up the challenge… www.longitudeprize.org SUMMER 2014 / FOCUS / 93 How do we know? Ptolemy, the father figure of between A and B as the crow flies New York, and Honolulu time two cartography, in the second (the hypotenuse of the triangle). Both hours behind San Francisco. The 360 century AD. Ptolemy measured his were imprecise, because of uncertainty degrees of longitude are encompassed terrestrial longitudes in degrees about the size and shape of the Earth. during the 24 hours of the Earth’s eastwards from a prime meridian Even assuming the Earth to be a complete rotation, which means that running through the Fortunate Isles perfect sphere, no one knew its exact for every one-degree change in longitude (Canaries), and his latitudes in degrees circumference, or the length of a degree the local time changes by four minutes. north and south of the equator. of latitude or longitude on the ground. Thus the local time on the opposite To determine the longitudes of A possible method for measuring side of the globe (180 degrees different places on his map of the known world, longitude, understood by the ancient in longitude) differs by 4 x 180 = 720 Ptolemy used Pythagoras’s theorem of Greeks, involved the equation of minutes, or 12 hours, as we should right-angled triangles to calculate the longitude with time. As the Earth expect. If navigators were to compare difference in longitude between places rotates on its axis, the time of sunrise their local time, as measured from the A and B. The trouble was that the two gets later the further west you are from celestial clock by detailed astronomical ‘known’ sides of each of Ptolemy’s a given longitude. For this reason, New observations, with the time measured triangles were the distance along a York time is today set five hours behind in London at the time of their parallel of latitude between the latitudes Greenwich time in London, San observations, they would be able to of A and B, and the actual distance Francisco time three hours behind compute their longitude. THE KEY John Harrison invented an ingenious device for compensating for the effects DISCOVERY of temperature in a chronometer. It enabled longitude to be deduced from time Harrison’s H-3 timekeeper TEMPERATURE VARIATIONS reduce a mechanical clock’s accuracy through thermal contraction and expansion of its pendulum or balance spring. John CTION Harrison produced an initial solution E to this problem in the 1720s, while OLL C making grandfather clocks. His RT A Wheel balance pendulum comprised rods of steel E NC and brass (which di!er in their E F coe"cients of expansion) parallel DE to each other but of di!ering length. They were connected in a Frame containing TRY OF TRY bimetallic S so-called ‘gridiron’, such that the pendulum remained the same strip that /MINI compensates length no matter its temperature. for temperature Cleverer still was Harrison’s changes MUSEUM invention in his H-3 chronometer ME (pictured), some time before 1749, of the ‘bimetallic strip’ — a device ARITI M nowadays familiar from mechanical central-heating thermostats. He riveted together a thin steel strip and a thin brass strip of the same Wheel balance length. When the temperature NWICH/NATIONAL NWICH/NATIONAL increased, the brass expanded EE GR more than the steel and curved the strip in one direction. When the temperature fell, the brass USEUMS contracted more than the steel and curved the strip in the opposite direction. Two small ‘curb pins’, attached to the free end of the Y X4, ROYAL M ROYAL Y X4, M bimetallic strip and embracing the outer turn of the balance spring, reduced the spring’s length TOCK, ALA S slightly with temperature rise, or increased it with temperature John Harrison’s ingenious H-3 fall, compensating for its thermal chronometer, which was the first expansion or contraction. to introduce the bimetallic strip HOTO: THINK HOTO: P 94 / FOCUS / SUMMER 2014 How do we know? The method appears very neat but, when it was proposed by astronomer Gemma Frisius in 1530, it suffered CAST OF Figuring out how to measure position on the from a fatal flaw. At this time, no CHARACTERS planet has taken centuries of scientific endeavour suitable clocks of remotely sufficient accuracy existed. During the 17th Century, the measurement of time Galileo Galilei (1564- improved with the invention of the 1642), a founder of pendulum-regulated clock by Christiaan modern science, Huygens in 1656, followed by his was a pioneer of the patenting of the spiral balance spring refracting telescope. in 1675 – an idea that had earlier In 1610, he squinted occurred to Robert Hooke – which through it at Jupiter’s was soon incorporated into clocks. But four moons, and sea trials of a pendulum clock built for began to record tables Huygens in the 1660s showed it to be showing the times unreliable when a ship swayed, while of their appearance and disappearance Hooke’s balance-spring clock was never Christiaan Huygens around Jupiter. Galileo tested at sea. Moreover, both designs (1629-95), a suggested his tables be suffered from the effects of temperature Dutch physicist, used by navigators as a variation, which caused pendulums mathematician and celestial time check to and springs to expand with an increase astronomer with many calculate their longitude. in temperature, and vice versa. achievements, he is perhaps best known for his invention of the JUPITER TIMEPIECE pendulum-regulated A second possible method for clock in 1656. He John Harrison measuring longitude was entirely believed it suitable (1693-1776) was an astronomical, employing careful for determining English carpenter- observation of heavenly bodies. In longitude at sea. turned-clockmaker. Italy, Galileo Galilei, pioneer of the Atlantic trials were Inspired by the prize refracting telescope, made an exciting initially encouraging, money o!ered in the proposal in 1612. For a year Galileo but soon it was clear 1714 Longitude Act, had recorded through his telescope that pendulums only he completed his first the movements of Jupiter’s moons and worked properly under marine chronometer, concluded that the moons’ eclipses conditions of flat calm.