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.


Photo Source

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.


Photo Source:

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.


theodolite-used in trigonometric survey

Photo Source:

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.

Calcutta baseline-survey of India

Photo Source:

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.

Heading west to Bangalore:

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.

hills for mapping -survey of India

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.

Adventure at Doorgs/hills:

When they reached Narnicul Doorg some 100 miles from Madras, they were not allowed to survey-the reason the local chief believed it as his territory and not some English officer. The next doorg they were not let due to privacy reasons. The local chief assumed that they would be able to site his home, his settlement and as a telescope was going to make things larger, also thought it would a great trouble as women could be seen more clearly. Not only this the locals could not believe that they were mapping the terrain with machines and chains. They were more familiar with pen and paper for tracing out landscape and if nothing else works to ask directions to the place.

Thus the entourage always had a military escort to defend against sudden uprisings,attack from locals not to mention robbers who assumed that the brass instruments were gold and would rob them from the team.Finally in 1804 the triangles arrived to Bangalore from Madras. While Lambton went further west, his assistant John Warren carried out the second base line measurement at Bangalore. This took a further 49 days and voila the first and second base line only differed by 3.7 inches. Talk about perfection!

One of the revised base points in bangalore baseline during trigonometric survey
One of the revised base points

Lambton went across Karnataka and in to Western Ghats and down towards Mangalore and Malabar coast. The arrival of Monsoons hindered him from continuing his work at Malabar coast and he returned back to Bangalore in 1805. With Bangalore as the base triangles were extended north towards Hyderabad and south towards Kanyakumari. More baselines were formed at Coimbatore, Kanyakumari, Tirunelveli … But disaster stuck at Tanjore. When the Theodolite was being dragged up to one of the temple towers- [lack of hills and doorgs meant surveyors had to use temple towers] it slipped and fell .

Lambton took full responsibility of this accident, retired to his tent with the machine and painstakingly repaired  the damage piece by piece. Such was his passion and dedication. For his work he was offered the honorary fellowship from Royal society of London. He had already been working on the survey for more than 16 years and he needed a assistant to shoulder the responsibilities. Thus in 1818 George Everest joined him.  And what he did is topic of another post.

For more information about Trigonometrical survey here is a worthwhile book at Amazon.


Leave a Reply

Your email address will not be published. Required fields are marked *