The mountain that weighed the Earth

> The Schiehallion experiment wasn’t the state of the art for long. A more precise result was achieved in 1798 by Henry Cavendish, who was on the committee for the Schiehallion experiment. Cavendish’s experiment measured the gravity of large lead spheres using an extremely precise torsion pendulum, and cut the error from 20% down to 1.2%.

Cavendish was a peculiar fellow.

> At his death, Cavendish was the largest depositor in the Bank of England. He was a shy man who was uncomfortable in society and avoided it when he could. He could speak to only one person at a time, and only if the person were known to him and male. He conversed little, always dressed in an old-fashioned suit, and developed no known deep personal attachments outside his family. Cavendish was taciturn and solitary and regarded by many as eccentric. He communicated with his female servants only by notes. By one account, Cavendish had a back staircase added to his house to avoid encountering his housekeeper, because he was especially shy of women.

https://en.wikipedia.org/wiki/Henry_Cavendish

Interesting...

A few years later, the gravitational deflection of the Himalayas on a plumb line by Airy proved less than expected, which suggested that mountains have 'roots' that extend below them, displacing more dense rock--like icebergs more or less.

I used the gravitational force of the Longmenshan range to calculate the perturbations in the elastic stress field of the Earth's crust in Sichuan province, China, to estimate the tectonic forces in the region, which caused the 2008 Wenchuan earthquake: https://agupubs.onlinelibrary.wiley.com/doi/full/10.1002/201...

> Primary sources:

> Maskelyne’s notes: https://doi.org/10.1098/rstl.1775.0050

> Hutton’s notes: https://doi.org/10.1098/rstl.1778.0034

> Cavendish’s notes on his own experiment: https://doi.org/10.1098/rstl.1798.0022

I got to reproduce Cavendish’s experiment when I was a student. Love that we can easily read the primary source today, archived and indexed by DOI.

I remember reading about this in Mason & Dixon. Mason, who worked at the Royal Observatory, was the one who identified this mountain as the best place for the experiment (and was asked to help with it but declined).

IIRC, it was partly the Mason Dixon line that inspired this experiment. They noticed syatematic errors in the line because their plumb bobs were deflected by gravitational pull from local terrain. At the time they speculated it was because of the Alleghenies, though it was probably more localized variations in gravity.

The precision they achieved with 18th century tools is remarkable. Measuring 0.0032 degrees of deflection without modern instruments, then getting within 20% of the correct answer.

I love stories where the constraint forces creative problem-solving. They couldn't measure gravity directly, so they found a mountain-sized workaround.

It's interesting that a device based on specifically constructed weights, at a scale to fit in a lab bench experiment (or at least a room) were capable of providing this much accuracy compared to a field experiment which used significantly larger masses, but was probably subject to many many more distorting qualities and estimation/rounding errors.

I can imagine that given enough motivation to chase down accuracy, they could have re-scaled the lead weight experiment to fit larger spaces, larger pendulums, assuming they could control for drafts, pigeons living in St Pauls Cathedral...

How far does it deflect the Sun?

can GPS sats figure out the mass of the earth by being able to detect its gravitational distortion on their orbit?

or maybe that upcoming space laser interferometer (LISA) since it has to figure precisely how all mass is affecting its position?

I love the history of figuring the circumference of the earth, imagine getting it right within 2% in 240 BC

(then Columbus effing it up by 25%)

https://en.wikipedia.org/wiki/Earth%27s_circumference#Histor...