# A peek in to the trigonometric survey

## Surveyor’s wheel for mapping:

Ever seen a surveyor’s wheel or a perambulator? No? Then here is a modern picture. What it does is measures the distance. The wheels turn and the turn is measured w.r.t to a reference point. In older days this tool was used to map terrain and was extensively used during 1799-1800 to may Mysore. The surveyor was none other than Colonel Colin Mackenzie, a renowned mathematician who was marking towns, forts, rivers, roads and hills with the help of this and few other tools like theodolites and steel chains as well. There was nothing wrong in his approach but there were quite a few limitations.

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All was fine if the wheels were used over plain surfaces, but give them a rough terrain, forests  or slippery surfaces -then wheels bounce,slip and lo accuracy would be gone to the winds. So a surveyor could have to use alternative means for lost distances, obstacles on the way – a tape perhaps and resort to estimates as well.

Some of these could be circumvented by adopting a method called Triangulation.

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## Triangulation for mapping:

A length AB is measured on ground. Then with the help of Theodolite angles are measured from both A as well as B. Theodolite is a kind of telescope that could measure both angles of elevation and planes. Then with the help of trigonometry the length of other two sides can be determined mathematically- given one side and two angles. These lengths in turn formed the base of other triangles and could be extended in any direction for mapping the terrain. Off course it wasn’t just this. There were other calculations too that entered. For example one had to take in to account the spherical access. This was due to the fact that angles of a triangle do not necessarily add up to 180 degrees-reason earth was known to be uneven, an oblate spheroid, flatter at the poles.

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## The adventures of William Lambton:

This method was greatly used in an expedition called ‘The Great Arc’ or the Great Trigonometrical survey started by British surveyor William Lambton. He wanted to map the width of Indian Peninsula by such series of triangles starting first with the Mysore survey. Thus the trails of Lambton and his team in South Indian terrain began.And it all started with the establishing of first base line in Madras.

### Dealing with Tools:

First the Theodolite. It weighed half a ton and had to be shipped from England. The ship was intercepted by the French at Mauritius, unpacked to check its contents. When they discovered its purpose it was repacked and shipped safely to India. Next it was a steel chain needed to measure the baseline. A 100 foot steel chain that had forty bars of corrugated steel was linked with other by brass hinges. Though it could be neatly packed and folded it needed a teak chest that was clearly heavy not something that could be transported easily.

### Setting up chains:

Lambton had to make do with this. The site for base line measurement was St Thomas Mount and a hill 7.5 miles to South. Lambton cleared the site, laid the steel chain supported by 20 ft coffers that had a thermometer fitted in it to measure the chain’s expansion due to heat. The base line’s chain length was compared with a similar chain that was kept in a cool vault. And expansion and contraction were duly accounted for in the calculations.

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The whole measurement took nearly two months or rather 57 days- moving chains, lifting coffers and tripods by men, the 7.5 miles took 400 individual measurements by chain. Add in Madras heat and summer, checking and rechecking of chains and thermometers you will realize the dedication of the men and Lambton in doing this exercise without complaints. With the help of Theodolite, angles were measured and after surveying the coast for nearly a year he headed west.

When you come towards Bangalore , you cannot miss the steep hills with its gigantic rocks,sparse vegetation and sometimes a lone watch tower, fort at the top.

Though all these served as strategic locations for battles, it now served a more important purpose – sites for mapping. It could work out as points for triangulation. There were plain landscape below the hills, no obstacles and it could be perfect for mapping. But no things, never went as per plan for Lambton and his team.