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defiles, mountains, and every remarkable object, feature, and property of the country’. Additionally, Mackenzie collected information on climate and soils, plants, minerals,peoples and antiquities. The last was his speciality. In the course of the Mysore Survey and other travels, he amassed the largest ever collection of Oriental manuscripts, coins, inscriptions and records. Congesting the archives of both India and Britain, the Mackenzie Collection was still being catalogued a hundred years later.
    Under the circumstances, Lambton’s big idea to launch yet a third survey looked like a case of overkill; and with Mackenzie’s efforts promising to make Mysore the best-mapped tract in India, Lambton anticipated official resistance. But as Arthur Wellesley now appreciated, his subordinate was proposing not a map, more a measurement, an exercise not just in geography but in geodesy.
    Geodesy is the study of the earth’s shape, and it now appeared that while holed up through a dozen long Canadian winters Lambton had made it his speciality. Studying voraciously, reading and digesting all the leading scientific publications, he had taken a particular interest in the work of William Roy, founder of the British Ordnance Survey, and of Roy’s even more distinguished mentors in France.
    Surveying of a basic nature had been among Lambton’s early responsibilities in Canada. Some old maps of New Brunswick actually show a ‘Lambton’s Mountain’. It is not very high and the name, unlike Everest’s, would not stick. Instead it became ‘Big Bald Mountain’ – which was more or less what Lambton would also become. But such surveying, although based on the simple logic of triangulation, was child’s play compared to what the Cassini family in France and William Roy in Scotland and England had been attempting.
    Triangulation, together with all its equations and theorems (like that of Pythagoras), is strictly two-dimensional. It assumes that all measurements are being conducted on a plane, or level surface, be it a coastal delta or a sheet of paper. In practice, of course, all terrain includes hills and depressions. But these too can be trigonometrically deduced by considering the surfaceof the earth in cross-section and composing what are in effect vertical triangles. The angle of elevation between the horizontal and a sight-line to any elevated point can then be measured and, given the distance of the elevated point, its height may be calculated in much the same way as with the angles on a horizontal plane. Thus would all mountain heights be deduced, including eventually those of the Himalayas. Adding a third dimension was not in theory a problem.
    However, a far greater complication arose from the fact that the earth, as well as being uneven, is round. This means that the angles of any triangle on its horizontal but rounded surface do not, as on a level plane, add up to 180 degrees. Instead they are slightly opened by the curvature and so come to something slightly more than 180 degrees. This difference is known as the spherical excess, and it has to be deducted from the angles measured before any conclusions can be drawn from them.
    For a local survey of a few hundred square miles the discrepancies which were found to result from spherical excess scarcely mattered. They could anyway be approximately allocated throughout the measurement after careful observation of the actual latitude and longitude at the extremities of the survey. This was how Mackenzie operated. But such rough-and-ready reckoning was quite unsatisfactory for a survey of several thousand square miles (since any error would be rapidly compounded); and it was anathema to a survey with any pretensions to great accuracy.
    The simplest solution, as proposed by geographers of the ancient world, was to work out a radius and circumference for the earth and deduce from them a standard correction for spherical excess which might then be applied throughout any