The idle ramblings of a Jack of some trades, Master of none

Oct 2, 2007

The Great Arc

What is involved in a successful geodesy? Lots of stargazing over a long time is only one possible beginning. But what if a terrestrial survey is required? John Keay describes the whats, hows, and whos, in his excellent The Great Arc: The Dramatic Tale of How India Was Mapped and Everest Was Named.

We should know some trigonometry. Measure a baseline accurately and determine the angles made at each end of the line to a suitable point in the distance. This gives us a triangle, each of whose sides can become baselines for further triangles, and so on, till we envelop our area with them. Over flat areas, we can use large triangles. Where the terrain is irregular, the triangles need to shrink. Mathematically, the task is simple. In practice, the complications are staggering.

Planar trigonometry that we study in school will not work. The earth is not flat, contrary to Friedman's wild exclamations. It is a sphere: angles in a triangle do not add up to 180o. An adjustment called the spherical excess needs to be applied to get the computation correct. But wait - the earth is not a perfect sphere either. It is oblate, a sort of squashed sphere. We need to model its curvature precisely before we can measure baselines.

Okay, let's say we've got the adjustment factors we need. How do we measure a baseline accurately? Why, we use a rigid measuring rod of known dimensions. But rigid materials will expand in the heat: depending on the temperature, it will be longer or shorter than its proclaimed length. We need to measure the coefficient of expansion for the material accurately. But what if the thermometer has measurement errors?

Assume now that we've sorted out these issues and we are ready to start taking angles. From one end of the baseline (accurately measured), I use a theodolite to shoot the angle to the tip of a rod you have plunged into the ground or hill or elevated building about twenty miles away. You need to make sure that the rod is absolutely vertical, so you use a plumb-line, which is supposed to point to the centre of the planet, the true vertical. But you realise that the plumb-line is deflected owing to the gravitational pull of nearby mountains. More corrections ensue.

I am now concerned that the line-of-sight between my theodolite and your rod is not rectilinear. Atmospheric refraction bends the light and I can see over the horizon to a greater distance than anticipated. Or it starts to rain and I can't see you at all. Or a dust haze distorts my view. Or natives, scandalised by your ungodly presence on a sacred mount, have slaughtered you and destroyed your post.

At this point, I am ready to give up on the survey. And yet, intrepid Victorians such as William Lambton and George Everest continued this effort decade after decade. They did not stop for war, death, rain, disease, callous administrators, suspicious Indians or budget-cutting Imperials. The Great Survey of India, from Madras all across the peninsula and up to the Himalayas is a monumental effort, superb in its success and glorious in its conceit and scope. It ranks in achievement with other grandiose plans of Victorian megalomania such as the laying of telegraph cable across the Atlantic Ocean or the construction of the London Underground. A shame indeed that Lambton is forgotten today, his grave ignored and his passing unmourned, and while Everest's name lives on, mispronounced1 in the highest peak on Earth, his story too has been consigned to the trash-heap of history.

1. George Everest pronounced his surname to rhyme with leave rest
2. The Ordnance Survey's efforts in England.


Bente Lilja Bye said...

Did you know that the European Struve Arc href="" -the equivalent to the Great Asian Arc - is the first natural science site on the UNESCO list of world heritage?

Fëanor said...

@Lilja: Thanks for the comment, and no: I was unaware of the European Arc. I see that you run the Geodetic Journey? Looks interesting!

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