Getting the measure of a turbulent triangle

Triangulation was a technique used for more than 200 years to measure the size and shape of the earth and map its surface, but it has now been replaced by satellite positioning systems. Nearly all the familiar triangulation pillars placed on the tops of hills by the Ordnance Survey of Great Britain have been sold. In other countries they have become national monuments. Stations in the 19th-century Struve arc of triangulation, which runs along a meridian passing through ten countries from the Arctic Ocean to the Danube delta, are being prepared for designation as a World Heritage Site.

Triangulation generally demanded painstaking manipulation and accurate reading of precise mechanical and optical instruments in conditions that were usually uncomfortable and sometimes life-threatening.

For these reasons, it appealed to young men trained in science and mathematics who wanted an adventurous setting within which to use their knowledge and skills.

Ken Alder's book is about the definition of the metre during the turbulence of the French revolution in the last decade of the 18th century. Reformers decided that weights and measures, redefined in terms of natural phenomena and made practicable by logical metric and decimal systems, would bring equality and rationality into civic life. The men who made measurements in those times led dangerous lives. Antoine Lavoisier, the greatest chemist of his age and man-about-town, was imprisoned after his rooms were searched for papers and apparatus relating to weights and measures. He was later guillotined for his tax-collecting activities for the king.

The Marquis de Condorcet, like Lavoisier an official of the Academy of Sciences and an enthusiast for bringing into civic affairs the order and freedom from tyranny that he saw in nature, committed suicide to avoid execution.

The Legislative Assembly shone its light of reason on the chaos of French weights and measures and decided that the metre should be defined as one ten-millionth of the distance from the North Pole to the Equator. To this end the astronomer-surveyors Jean-Baptiste-Joseph Delambre and Pierre-François-André Méchain, members of the Academy of Sciences, were given the task of measuring by triangulation the distance along the meridian from sea-level at Dunkirk southwards through Paris to sea-level at Barcelona. The decision that such a short arc would make an appropriate foundation for defining a universal standard of length owes more to nationalism than rationalism.

Work began in 1792, Delambre observing the northern half of the arc, Méchain the southern. They expected to meet in the middle within a year or two, but political events in Paris and their repercussions in the towns and villages along the arc prevented them from finishing until seven years later, when a metre-long platinum bar was deposited in the French National Archives.

Alder's narrative of the surveyors' progress and how it was affected by bloody revolution is well researched, allowing the distinct characters of the two men to be clearly seen. Méchain suffered a near-fatal injury and imprisonment when working on the arc in Spain. His fear of failure and anxiety over his attempt to cover up an error brought a tragic end to his life. On the other hand, the suave Delambre ended his career comfortably dispensing patronage as permanent secretary of the Academy of Sciences.

Alder writes about technical matters with a clarity that the general reader should understand. He is particularly good on the different sorts of measurement error and the procedures adopted by Delambre and Mechain to reduce their effects on angles measured with Jean Charles Borda's cercle répétiteur.

Regrettably, Alder makes a few gauche technical statements. Saying that the positioning accuracy of Borda's instrument of "one second of a degree" is "comparable to today's global positioning systems" implies the latter are no more accurate than triangulation, which is untrue. Using "geodeser" for "geodesist" is perverse when the latter has been in common usage throughout the English-speaking world for more than a century. Having pointed out that the great number of observations in triangulation led Adrien-Marie Legendre and Carl Friedrich Gauss to develop statistical methods for finding most probable values from many measurements, he misses a chance to use his research into contemporary documents to present a few statistics about the accuracy of the arc that would make interesting comparisons with similar statistics for other arcs, most of which were measured using horizontal circles of theodolites. Such shortcomings, however, are compensated by Alder's vivid setting of the work within revolutionary France.

Triangulation, like satellite positioning, was a political matter.

Michael Cooper is emeritus professor of engineering surveying, City University, London.