The Great Arc Read online

  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. L
uckily 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.

  But April and May are hot months in Tamil Nadu. The temperature seesawed between 80 and 120 degrees Fahrenheit. Although Lambton says nothing of the inconvenience of working in such heat, he was worried sick by the variations. After endless experiments he came to the conclusion that a one-degree change of temperature made a difference of 0.00742 of an inch in the hundred-foot length of the chain. But were the locally purchased thermometers sufficiently accurate? And might the temperature not have changed in the interval between marking the measurement and reading the thermometer? Lambton was deeply concerned; measurements and readings were to be taken only at dawn or in the early afternoon when the temperature was as near stable as it got; the thermometers were checked and rechecked, both chains measured and remeasured against a standard bar. Nothing gives a better idea of his passion for shaving tolerances to an infinitesimal minimum than this pursuit of a variable amounting to just seven thousandths of an inch.

  To complete the full seven and a half miles of the base-line required four hundred individual measurements with the chain. For each of these measurements the coffers and tripods as well as the chain itself had to be moved forward. It was a slow business even after Lambton’s men had been drilled to do it by numbers. The whole measurement took fifty-seven days, and that did not include the time needed for the construction of end-markers. These were meant to be permanent and so had to combine the durability of a blockhouse with the hairline precision required for registering in the ground the actual mark over which the theodolite would be aligned for triangulation.

  And still the all-important theodolite had not arrived. In fact report now had it that the ship in which it was stowed had been captured by the French. This turned out to be true. The ship had been conducted into Port Louis in Mauritius and the great theodolite had there been landed and unpacked. Happily the French authorities, when they realised what it was, rose nobly to the occasion. Repacked and unharmed, it was gallantly forwarded to India and arrived in September ‘along with a complimentary letter to the government of Madras’.

  Lambton could at last begin his triangulation. In late September he took angles from his base-line to pre-selected points to the south and west. The short southern series of triangles down the coast was to determine the length of a degree; it took about a year. Then in October 1804 he turned his back on the coast. Heading west and inland, he would carry his triangles right across the peninsula and then begin the north – south series known as the Great Arc.

  Over the next twenty years sightings of Lambton in Madras would be of rare occurrence. As in Canada, he seemed again to have disappeared into a continental void; perhaps after six years on the public stage, he was happy enough to slip back into the wings of obscurity. But the government insisted on progress reports and the scientific world awaited his findings. Lambton’s personal papers would disappear with him. Until the young Everest joined him in late 1818 there are few firsthand accounts of his conduct or his establishment. But his reports found their way into the Survey’s files and his scholarly monographs into learned journals. Additionally one of his assistants would pen some recollections; and there is the unexpected evidence of two Lambton children, both born while he was working on the Great Arc. As he later admitted, the years spent in India pursuing his obsession would be the happiest of his life.

  THREE

  Tall Tales from the Hills

  When measuring a base-line it was important to discover, as well as its precise length, its height above sea-level. Other heights ascertained in the course of triangulation could then be expressed in terms of this universal standard rather than in terms of individual base-lines. To establish what would in effect be the vertical base of his whole survey Lambton had therefore chosen a site for his base-line which was only three or four miles from the Madras coast and looked, given the lie of the land, to be only a few feet above it. But working out exactly how many was still a matter of some delicacy.

  First, on the sands to the south of Madras’ famous Marina Beach, the highest tides had been carefully observed and their maximum reach marked with a flagpole. (In 1802 ‘sea-level’ was construed as high water, although later in the century a mean between high tide and low tide would be adopted as the standard and all altitudes adjusted accordingly.) From this flagpole on the beach the horizontal distance to the grandstand of the Madras racecourse, still today hard by St Thomas’s Mount, was carefully measured by chain; it came to 19,208 feet. Next, from the railings at the top of the grandstand the angle of depression to the flag on the beach was observed by theodolite. Then the process was reversed with the angle of elevation from the beach to the stand being observed.

  The repetition was necessary because Lambton was keen to measure the effect of a phenomenon known as refraction, whereby sight-lines become vertically distorted, or bowed, by the earth’s atmosphere. Here was another of those subtle variables which bedevilled geodetic surveying. In particular, refraction would play havoc with long-range observations to distant mountain peaks, although, as George Everest would discover, it also had its advantages.

  Having deduced a factor for this refraction, Lambton adjusted his measured angles accordingly. Now, conceiving the sight-line between the flagpole on the beach and the grandstand of the racecourse as the hypotenuse of a rectangular triangle (the right angle being deep beneath the grandstand where a vertical from its railings would intersect with a horizontal from the beach), Lambton had measurements for two of the angles and for one side (the 19,208 feet). Elementary geometry then revealed the length of the other two sides, one of which was the desired elevation of the grandstand above sea-level.

  It was important to factor in the height of the flagpole, since its flag, not its base at ground-level, had been observed from the grandstand. Likewise the height of the theodolite’s telescope above the ground. And finally, to get the height of the base-line, it was still necessary to deduct the height of the grandstand above it.

  This last was done by measuring the stand itself and then ‘levelling down’ towards the base-line, a comparatively simple process in which the incline was broken into ‘steps’ whose fall was
measured by calibrated staves between which horizontal sightings were taken with a telescope equipped with a spirit level. The base-line itself was not perfectly level and had also involved some of this ‘stepping’. So had the original estimate for the distance from the flagpole to the grandstand. All having finally been ‘conducted with as much correctness as the nature of any mechanical process will admit of … I may venture,’ wrote Lambton, ‘to consider it as as perfect a thing of the kind as has yet been executed.’ He then proudly announced that ‘we have 15.753 feet for the perpendicular height of the south extremity of the [base-]line above the level of the sea.’

  Not much attention was paid to this calculation at the time. It had taken several days and much careful planning, but a rise of fifteen feet was no great revelation, and the account of its measurement was buried deep in more technical data about the base-line itself. This in turn was buried deep in a large leather-bound volume whose 1805 publication happened to coincide with news of rather more dramatic elevations elsewhere.

  Twelve hundred miles away, beyond the northern borders of British Bengal, a surveyor named Charles Crawford had entered the Kingdom of Nepal in the heart of the Himalayas just as Lambton was laying out his base-line. From around Kathmandu Crawford had got a good look at the Himalayas and, according to an 1805 report of his journey, he had become ‘convinced that these mountains are of vast height’.

  … bearings were taken of every remarkable peak of the snowy range, which could be seen from more than one station; and consequently the distances of those peaks from the places of observation were … determined by the intersection of the bearings and by calculation. Colonel Crawford also took altitudes from which the height of the mountains might be computed and which gave, after due allowance for refraction, the elevation of conspicuous peaks.