|MadSci Network: Science History|
There are many ways, of widely varying accuracy, that the height of a mountain may be measured. How was it actually done in the late 1700s and early 1800s? On a quick web search, I encountered this article about Mt Everest. Amongst the other information, there is information about early estimates of its height. Among the items carried by early explorers was the marine sextant. This was mainly used to accurately measure the elevation of the sun, which is an essential part of knowing one's position on the face of the Earth (Yes, the 18th century GPS!). But it could also be used to sight on the top of a mountain, and accurately determine its angle of elevation. Now if you know the angle of elevation of the top of a mountain, and if you know how far way from it you are, you can determine its height. The basic formula is very simple trigonometry: h = x tan a. There is a correction for the curvature of the Earth that makes the trig a bit more complicated, and another correction for optical refraction that makes it a lot more complicated, and somewhat imprecise. But the biggest problem was usually that the explorers would usually take a sighting on the top of a mountain from the ocean, and they did not really know exactly how far away the top of the mountain was. That did not stop them from making their best guess! It is possible to do a little better in the following way: you take an elevation, and you know that h = x tan a. But you do not know x, the distance you are from the peak. So you move 10 km closer -- which you can measure accurately -- and measure a new elevation. You then have h = x tan a1 = (x-10) tan a2 and you have two simple equations in two unknowns, h and x, which you can solve. Once again, there are awkward curvature and refraction corrections. Other ways of estimating the height of a peak include: (1) changes in vegetation and the position of the snow line. (2) fall off in barometer pressure with altitude. (3) distance of the visible horizon from the peak. (4) experience of the time and effort required to do the ascent. All were used to a greater or lesser extent by the early explorers and mapmakers, usually for confirmation of a sextant method, which was regarded as the most accurate. Finally, it should be mentioned that, even as long ago as that, there were some quite heroic efforts with surveyor's chain and theodolite, where mountain heights were determined by direct measurement.
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