Measuring a potato planet, by Ian Hembrow

Measuring a potato planet, by Ian Hembrow

Research grant recipient Ian Hembrow reports on a fascinating study trip to learn about 18th century surveying methods from SIS’s Nicolàs de Hilster.

At the start of 2022 I was thrilled to receive a grant from the Society to support my project to write a biography of the Swedish scientist Anders Celsius (1701-44). Best known of course for his centigrade temperature scale, Celsius made an array of other discoveries and breakthroughs in a stellar career cut tragically short by his death from tuberculosis aged just forty two.

Figure 1. Measuring one degree of latitude in the Arctic Circle, 1736-37.

In particular, he played a vital role in settling the great scientific debate of his age about the shape of the Earth, taking part in a perilous winter expedition to the Arctic Circle in 1736-37 to measure the exact distance of one degree of latitude (see figure 1). Comparing the results with a parallel expedition to the equator proved Newton’s theory that the planet is an oblate ellipsoid, slightly flattened at its poles by the centripetal force of its spin. The Earth, they showed, is shaped like an orange – roughly 43km broader than it is tall.

Keen to find out how Celsius and his companions made their measurements I reached out to the SIS network for help to understand the methods and equipment they used in the frozen north. Surveyor and collector Nicolàs de Hilster answered my call, inviting me to visit him in the Netherlands to do some hands-on study. It turned out to be an enthralling and memorable trip.

Figure 2: Nicolàs lines up for a viewing of the sun.

When I entered Nicolàs’ home, a short train ride west from Amsterdam, I noticed a laptop with what appeared to be an image of the sun surrounded by tables of flickering data. Some sort of astronomical website I thought. But no, this was actually the live-feed from Nicolàs’s own observatory perched on top of the house! I followed my host up the spiral stairs to discover his amazing creation: a cluster of powerful telescopes mounted within a beautiful wooden dome – all hand-crafted from scratch by Nicolàs (see figure 2). The instruments included a custom-made Galilean-type refractor intentionally made to replicate the imperfections of 17th century lenses.

Nicolàs attached a special filter to one of telescopes and invited me to look directly at the sun. Unsurprisingly, I saw a bright, fiery orange ball. “Now adjust that knob and you’ll be able to see some solar flares,” he advised. And sure enough, as I fine-tuned the focus, little looping swirls appeared around the edge of the image, clearly moving in real time.

“Wow!” I said. “How big are they?” “About five times the size of Earth,” replied Nicolàs. I was stunned and nearly moved to tears by the magnificence of what I was seeing.

The observatory though was simply the tip of a very big iceberg. I went on to admire an astounding collection of surveying instruments and devices – from the simplest sighting sticks to massive, high-specification theodolites, an enormous library and two gorgeous bespoke ‘de Hilster’ sun-dials mounted on the walls outside.

Figure 3: ‘Touring the horizon’ with a modern theodolite.

After a fine lunch kindly prepared and served by Nicolàs’s wife Ria, we loaded up the truck with a collection of sextants and measuring rods and headed out into the polder nearby – flat countryside criss-crossed by drainage ditches giving way to sand dunes up towards the nearby North Sea coast. Ever prepared, Nicolàs had found a spot where we could ‘tour the horizon’, first using a modern ‘total station’ instrument (see figure 3) and then a handheld, brass sextant.

Figure 4: Back to older technology with a sextant.

My heart sank when it was explained to me that geodetic sextants use the 400-point Gradian system, rather than the more familiar (to me at least) 360 degrees of geometry. But I needn’t have worried, because once I’d got the hang of how to use the heavy brass device – merging the direct and mirrored images of adjacent sighting points like church spires and telephone masts – I managed to take and call out full-circle readings from our location (see figure 4). Nicolàs noted down the numbers at each point and then pulled out his phone to check their accuracy against the digital results.

Figure 5: Student and teacher: Ian (L) and Nicolàs (R).

Thanks to the expert tuition and supervision, my readings added up to 399.49 grad – just 0.51 of a grad out. Nicolàs smiled and declared this was “acceptable for a first attempt,” before going on to explain how even a small difference like this soon multiplies up to a huge margin of error when applied over the sorts of distances Celsius had to measure.

Back at the house, Nicolàs then showed me the inherent difficulties of using measuring rods to gauge accurate distances. The 1736-37 expedition members used thirty-foot-long wooden poles laid continuously end-to-end on a frozen river surface. But even on the flat floor of a modern building the kinks and dips of a twelve-foot sectioned rod were obvious to the naked eye. Our planet is of course not entirely smooth, so surveyors have to take account of all the slumps and bumps in their way. “Remember Ian,” said Nicolàs, “the Earth is not a true ellipsoid – it’s a potato!”

The key to surveying accuracy, I learned, is to measure, measure and measure again – using multiple base lines and repeated calculations to obtain the best possible answer. And, Nicolàs reminded me, measuring the linear distance was only the start of the job – Celsius then had to do some complex astronomical sightings to determine their precise latitude.

That will have to wait for another time and visit…

My sincere thanks to Nicolàs and Ria for making me so welcome and treating me to such an extraordinary day.

In early May 2022 Ian is retracing the route of the 1736-37 expedition in Swedish and Finnish Lapland. Watch out for his report of that trip.

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