Measuring height with a thermometer

Phase diagrams can be plot devices in more than one sense. In the mid-nineteenth century, the British empire was anxious to map the lands north of India. The British and the Russian were engaged in a "Great Game", in which geographical information was but one of the prizes, as each sought to expand their area of control in Asia. Unfortunately for the British, the emperor of China had closed the borders with India to foreigners, under penalty of death. More than one British surveyor perished in attempts to cross the border and map Tibet. Eventually Thomas Montgomerie of the British Survey hit upon recruiting well-educated Indians as clandestine surveyors whose cover identity would be that of itinerant lamas.

The "pundits" were given extensive training over two years and learned to use a sextant, measure altitude by boiling point determination (This is an application of the Clausius-Clapeyron equation: as altitude increases, atmospheric pressure decreases and the boiling point of water decreases in a known relationship) and to walk a measured pace. Pundits counted their paces with the traditional rosary carried by holy men; their rosaries had been altered to contain only 100 beads instead of the usual 108 and a single circuit of the beads was equivalent to a traverse of 5 miles. Observations were recorded on the papers inserted into their prayer wheels.

One of the first pundits was Nain Singh, who at 33 and headmaster of a school in the Himalayas was recruited along with his cousin Mani Singh to survey Tibet. Singh walked thousands of miles in his mapping ventures, and the maps constructed from his survey were the best available until well into the 20th century. On his third and last survey journey, Singh traveled more than eight months from Leh to Lhasa to map the trade route. His measurement of the altitude of Lhasa using measurements of the boiling point of water were accurate to within a hundred meters. Singh retired after this journey to train other pundits. He was well recognized for his feats by many geographical societies and the government of India in his later years. If this all sounds vaguely familiar, it may be because Rudyard Kipling drew heavily on the events around the "Great Game" in his novel, Kim.