Comparatives with Balloons

Comparatives often feature objects that were well known to their readers to give a sense of scale. This is especially true of mountains comparatives. Showing a large man-made object on the comparative serves as an intermediary between the human scale and the geologic scale. Pyramids, monuments, and cathedrals often play this role.

The Great Pyramids and Paris as shown on Thomson & Lizars' A Comparative View.
The Great Pyramids and Paris as shown on Thomson & Lizars’ A Comparative View.

Where structures aid readers in understanding how large something is, they do not tell the reader what it’s like to be at that altitude. Cities of various elevations are also commonplace on mountains comparatives, giving the reader points of reference–understanding the climate, vegetation, animal husbandry, etc. at an altitude is achieved by studying one of the case cities.

That said, the natural features can reciprocally serve as points of reference for human accomplishments. Nowhere is this more apparent that in depictions of high altitude balloon flights.

Gay-Lussac's 1804 balloon flight as shown on Thomson and Lizars' A Comparative View.
Gay-Lussac’s 1804 balloon flight as shown on Thomson and Lizars’ A Comparative View. Own work.

In 1804, Frenchman Gay-Lussac flew a hydrogen balloon to 23,000 feet setting a record that would stand for nearly 50 years. This is no small accomplishment as the first balloon flight had been only 20 or so years before. To show humans aloft, above the birds, would drive home the capabilities of technology. In reviewing the comparatives in David Rumsey’s collection, 16 show balloon flights. While all are spectacular, a couple stand out.

Smith’s 1816 Comparative View of the Heights of the Principal Mountains of the World is the oldest comparative among the holdings and shows Gay-Lussac in his balloon about to break through the border of the image. Its appearance on such an early comparative tells us that the cartographer intended for the concept of the comparative to be reciprocal. The comparative writ large was both to inform the reader about nature’s massive scale, but also to emphasize that having entered the age of science, man could literally soar above it. If the first appearance of a balloon flight were on a later comparative, say of the mid 19th century, we would be forced rather to conclude that it had simply been added to distinguish one cartographer’s product, rather than being able to conclude something fundamental about comparatives.

We continue to see Gay-Lussac’s balloon on comparatives through the first half of the 1800s. By 1851 the Industrial Revolution was in full swing and it was time for the Great Exhibition in London, a World’s Fair to highlight, among other things, technology. For this, the publisher Tallis prepared a book of engravings, mostly maps, that included truly stunning comparatives for both hemispheres. Not wanting to fall short on depictions of achievements, Tallis included Green’s 1840 record setting flight, showing it centered over Dhawalagiri (now Dhaulagiri) in Nepal. It is noteworthy that while his comparative is up to date vis-a-vis Green’s balloon flight, he neglected to show Kangchenjunga, even taller, surveyed in 1838. Perhaps he didn’t have access to that information. Perhaps he elected not to show it so that Green in his balloon would appear on top of the world, sure to delight the exhibit goers.

Tallis' gorgeous 1851 comparative view of waterfalls, islands, lakes, mountains, and rivers of the Eastern Hemisphere. (Photo credit: Ruderman).
Tallis’ gorgeous 1851 comparative view of waterfalls, islands, lakes, mountains, and rivers of the Eastern Hemisphere. Note Green’s & Gay-Lussac’s balloon flights over the mountains. (Photo credit: Ruderman).

The last example I will mention is an enigma. While the examined comparatives so Gay-Lussac’s balloon reaching differing altitudes, most if they specify, either 22,900 feet or 23,100 feet which brackets the 23,018 feet computed from the French accounts of 7,016 m, Weiland’s comparative isn’t even close. He pegs the altitude attained at 21,386 ft. Adding to the mystery, where this comparative has grouped the peaks by continent, he chose to show the balloon over Quito, Ecuador, nowhere near Paris. What could this discrepancy be attributed to? It hardly seems likely that he made a conversion error from meters to feet; as a cartographer he would no doubt be adept at this. As other cartographers of the day accurately stated Gay-Lussac’s altitude, and 16 years had elapsed, it further is difficult to believe that the correct information was not available. We can turn attention to whether this is due to any differing definitions of foot; he stated other heights in feet that approximate modern measurements, but are not exact.

Weiland's comparative. Note Gay-Lussac's balloon on the far left of the upper panel (shown as though it was flown over South America).
Weiland’s comparative. Note Gay-Lussac’s balloon on the far left of the upper panel (shown as though it was flown over South America).

There may be some traction here, as the German states used differing definitions of the foot. This can be tested by plotting the heights reported on Weiland’s view against those used on another, and Thomson’s 1817 is an ideal benchmark. If the plotted points form a cloud, then the difference between the measurements shown on the charts cannot be attributed to some difference in the definition of foot. On the other hand, if the points form a line we can infer that there is a difference in factors is at work. A selection of points in common to both comparatives was plotted and the relationship qualified. They fell nicely on a line.

Plot of the Heights shown by Thomson & Weiland.
Plot of the Heights shown by Thomson & Weiland.

Hard to believe this could be the result of chance; the relationship has incredibly strong statistical significance at less than one in a trillion. (Statistical significance is a measure of how confident one can be that the finding isn’t due to chance; less than a 1 in 20 likelihood of a chance occurrence is the gold standard in scientific research.) Moreover, the slope of the line explains 99.9% of Weiland’s number. The slope of the line is 0.924, meaning that Weiland’s foot was slightly different than that used by the other cartographers. This equates roughly to the foot used in Geneva at the time, 325 mm. It is interesting and surprising, however, that he would use the Geneva for as Weimar, the place of publication, was using its own foot, 282 mm.

© Peter Roehrich, 2015

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