The Great Arc (4 page)

The other survey was a more formal affair, similar to surveys already undertaken in Bengal. It was equipped with theodolites for triangulation, with plane-tables for plotting the topographic detail, and with wheeled perambulators and steel chains for ground measurement. Colonel Colin Mackenzie, who conducted it, was another noted mathematician who had originally forsaken his home in the Hebridean Isle of Lewis to visit India in order to study the Hindu system of logarithms. His Mysore Survey was a model of accuracy and the maps which it yielded faithfully delineated the frontiers of the state as well as indicating ‘the position of every town, fort, village … all the rivers and their courses, the roads, the lakes, tanks [reservoirs], 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 surface
of 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 triangulation. But here arose another and still greater problem. The earth, although round, had been found to be not perfectly round. Astronomers and surveyors in the seventeenth century had reluctantly come to accept that it was not a true sphere
but an ellipsoid or spheroid, a ‘sort-of sphere’. Exactly what sort of sphere, what shape of spheroid, was long a matter of dispute. Was it flatter at the sides, like an upright egg, or at the top, like a grapefruit? And how much flatter?

Happily, by Lambton’s day the question of the egg versus the grapefruit had been resolved. In the 1730s two expeditions had been sent out from France, one to the equator in what is now Ecuador and the other to the Arctic Circle in Lapland. Each was to obtain the length of a degree of latitude by triangulating north and south from a carefully measured base-line so as to cover a short arc of about two hundred miles. Then, by plotting the exact positions of the arc’s extremities by astronomical observations, it should be possible to obtain a value for one degree of latitude. Not without difficulty and delay – the equatorial expedition was gone for over nine years – this was done and the results compared. The length of a degree in Ecuador turned out to be over a kilometre shorter than that in Lapland, in fact just under 110 kilometres compared with just over 111. The parallels of latitude were thus closer together round the middle of the earth and further apart at its poles. The earth’s surface must therefore be more curved at the equator and must be flatter at the poles. The grapefruit had won. The earth was shown to be what is called an ‘oblate’ spheroid.

There remained the question of just how much flatter the poles were, or of how oblate the spheroid was; and of whether this distortion was of a regular or consistent form. This was the challenge embraced by the French savants and by William Roy in the late eighteenth century. Instruments were becoming much more sophisticated and expectations of accuracy correspondingly higher. The pioneering series of triangles earlier measured down through France was extended south into Spain and the Balearic Islands and then north to link across the English Channel with Roy’s triangles as they were extended up the spine of Britain. The resultant arc was much the longest
yet measured and, despite a number of unexplained inconsistencies, provided a dependable basis for assessing the earth’s curvature in northern latitudes, and so the spherical excess.

Lambton was now proposing to do the same thing in tropical latitudes, roughly midway between the equator and northern Europe. But like his counterparts in Europe, he played down the element of scientific research when promoting his scheme and stressed the practical value that would arise from ‘ascertaining the correct positions of the principal geographical points [within Mysore] upon correct mathematical principles’. The precise width of the Indian peninsula would also be established, a point of some interest since it was now British, and his series of triangles might later be ‘continued to an almost unlimited extent in every other direction’. Local surveys, like Mackenzie’s, would be greatly accelerated if, instead of having to measure their own base-lines, they could simply adopt a side from one of Lambton’s triangles. And into his framework of ‘principal geographic points’ existing surveys could be slotted and their often doubtful orientation in terms of latitude and longitude corrected. Like an architect, he would in effect be creating spaces which, indisputably sound in structure, true in form and correct in position, might be filled and furnished as others saw fit.

He could, however, scarcely forbear to mention that his programme would also fulfil another ‘desideratum’, one ‘still more sublime’ as he put it: namely to ‘determine by actual measurement the magnitude and figure of the earth’. Precise knowledge of the length of a degree in the tropics would not be without practical value, especially to navigators whose charts would be greatly improved thereby. But Lambton was not thinking of sailors. As he tried to explain in long and convoluted sentences, his measurements aimed at ‘an object of the utmost importance in the higher branches of mechanics and physical astronomy’. For besides the question of the curvature of the earth, doubts had surfaced about its composition and,
in particular, the effect this might be having on plumb lines. Plumb lines indicated the vertical, just as spirit levels did the horizontal, from which angles of elevation were measured both in astronomy (when observing for latitude and longitude) and in terrestrial surveying (when measuring heights). But inconsistencies noted in the measurement of the European arc had suggested that plumb lines did not always point to the exact centre of the earth. They sometimes seemed to be deflected, perhaps by the ‘attraction’ of nearby hills. If the vertical was variable – as indeed it is – it was vital to know why, where, and by how much. New meridional measurements in hitherto unmeasured latitudes might, hoped Lambton, provide the answers.

Whether, reading all this, anyone in India had the faintest idea what Lambton was on about must be doubtful. But Arthur Wellesley warmly commended his friend’s scientific distinction, Mackenzie strongly urged the idea of a survey which would surely verify his own, and Governor-General Richard Wellesley was not averse to a scheme which, while illustrating his recent conquests, might promote the need for more. The beauty of map-making as an instrument of policy was already well understood; it would play no small part in later developments.

In early 1800, therefore, the third Mysore Survey was approved, if not fully understood, and Lambton immediately began experimenting with instruments and likely triangles. For what was described as ‘a trigonometrical survey of the peninsula’ it was essential first to establish a working value for the length of a degree of latitude in mid-peninsula. Like those expeditions to Lapland and Ecuador, Lambton would therefore begin in earnest by planning a short arc in the vicinity of Madras. It was not, though, until April 1802 that he began to lay out the first base-line which would also serve as the sheet-anchor of the Great Trigonometrical Survey of India.

The delay was caused by the difficulty of obtaining suitable
instruments. Fortuitously a steel measuring chain of the most superior manufacture had been found in Calcutta. Along with a large Zenith Sector (for astronomical observation) and other items, the chain had originally been intended for the Emperor of China. But as was invariably the case, the Macartney Mission of 1793 had received an imperial brush-off and Dr Dinwiddie, who was to have demonstrated to His Celestial Highness the celestial uses of British-made instruments, had found himself obliged to accept the self-same instruments in payment for his services.

Subsequently landing in Calcutta, Dinwiddie had made a handsome living from performing astronomical demonstrations. But he now graciously agreed to sell his props for science, and the chain in particular would serve Lambton well. Comprised of forty bars of blistered steel, each two and a half feet long and linked to the next with a finely wrought brass hinge, the whole thing folded up into the compartments of a hefty teak chest for carriage. Thus packed it weighed about a hundredweight. Both chain and chest are still preserved as precious relics in the Dehra Dun offices of the Survey of India.

A suitable theodolite for the crucial measurement of the angles of Lambton’s primary triangles was more of a problem. A theodolite is basically a very superior telescope mounted in an elaborate structure so that it pivots both vertically about an upright ring or ‘circle’, thus enabling its angle of elevation to be read off the circle’s calibration, and horizontally round a larger horizontal circle so that angles in a plane can be read in the same way. Plummets, spirit levels and adjustment screws are incorporated for the alignment and levelling of the instrument, and micrometers and microscopes for reading the calibration. Additionally, the whole thing has to be rock stable and its engineering, optics and calibration of the highest precision. In fact there were probably only two or three instruments in the world sufficiently sophisticated and dependable
to have served Lambton’s purpose. Luckily he had discovered one, almost identical to that used by William Roy, which had just been built by William Cary, a noted English manufacturer. But it had to be shipped from England, a considerable risk in itself for an instrument weighing half a ton and about the size of a small tractor. And unfortunately the ship chosen was unaccountably overdue.

It had still not arrived when Lambton marked out and cleared his Madras base-line. The site chosen was a stretch of level ground between St Thomas’s Mount, a prominent upthrust of rock where the ‘doubting’ apostle was supposed to have once lived in a cave, and another hill seven and a half miles to the south. Situated on the south-east edge of the modern city, the Mount has since been overtaken by development, but the other end of the base-line is still predominantly farmland and scrub as in Lambton’s day. Having cleared and levelled the ground and aligned the chosen extremities, Lambton commenced measurement with Dinwiddie’s hundred-foot chain.

By now he had received from England a second chain, but this was reserved as a standard against which Dinwiddie’s was frequently checked for any stretching from wear or expansion. Expansion and contraction due to temperature change was a major problem. William Roy of the Ordnance Survey, while measuring his first base-line on Hounslow Heath (now largely occupied by Heathrow Airport), had discarded both wooden rods and steel chains before opting for specially made glass tubes. Lambton in India had no such handy alternative; he had to make the best of the chains. When in use, the chain was drawn out to its full hundred feet and then supported and tensioned inside five wooden coffers, each twenty feet long, which slotted cleverly onto tripods fitted with elevating screws for levelling. Each coffer he now equipped with a thermometer which had to be read and recorded at the time of each measurement. By comparison with the other chain, which was kept in
a cool vault, a scale of adjustment was worked out for the heat-induced expansion.