A Centre Of Gravity: How Londoners Measured The Renowned Force

Laurence Scales
By Laurence Scales Last edited 46 months ago
A Centre Of Gravity: How Londoners Measured The Renowned Force

The spacecraft Rosetta — which is expected to land a probe on a comet today — will be reliant on Newton's law of gravity for the success of its flight. But to put the famous equation to use and compute the path of planets, the career of comets and ultimately the rendezvous with comet 67P, a missing number was needed: the pull of the earth. Starting in 1774, four Londoners embarked on the quest to measure it.

The problem was measuring a weakling force (even something the size of the earth cannot permanently anchor your rear to your sofa). To do it involved gauging the density of the planet or — put crudely — weighing the world. It was nearly 50 years after Newton’s death in 1727 that the first of several painstaking attempts was made.

Maskelyne

It was decided to use a mountain to provide a convenient source of gravitational attraction pulling sideways. In 1774, as the mountain would not come to him, Greenwich astronomer Nevil Maskelyne went to a Scottish peak called Schiehallion to take readings.

Nevil Maskelyne

Maskelyne took hundreds of readings of a plumb line over several weeks on windswept slopes, using the stars as a fixed reference. (They may appear fixed but of course the earth spins and wobbles on its axis, compounding the complexity.) He was implausibly trying to measure the angle of dangle, drawn towards the mountain by the order of 0.01 of a degree.

He fed his Scottish measurements into a computer at the Military Academy in Woolwich. The computer’s name was Professor Charles Hutton. Being human, he not only provided the answer, but also revealed his not unexpected finding that the calculations were "long and tedious". However, after all those careful readings, a bald assumption was made about the density of the mountain. Yet, the experiment was a start. It suggested that the earth was not hollow, and the final calculation only differed from modern measurements by about 20%.

Cavendish

Georgian pin-up Professor Sir Humphry Davy, looking askance at his nerdy Royal Society colleague Henry Cavendish, remarked that he still wore "the clothes of our grandfathers". In fact, so shy was Cavendish that if he went out for a beer with the others from the Royal Society he was unlikely to speak or — if addressed — might even run away. He worked on so many things and so reclusively that some of his discoveries only emerged long after his death. Cavendish Road off Clapham Common is the only reminder that one of England’s greatest minds once weighed the earth nearby, at his home, in 1798.

The Cavendish Experiment

His method was simple: to compare the attraction of lead balls with that of the earth. He acquired the method and equipment from John Michell who died before he could use it. (It was Michell who first saw the possibility of a black hole, in 1783.) A balancing beam with a small ball on each end was hung from a fixture. A large lead ball, 1ft in diameter, was placed at each end beside the hanging balls, so that they would cause the beam, by their own gravitational attraction, to twist infinitesimally towards them. The set-up was so delicate that Cavendish had to take readings of the angle of twist remotely using a telescope, and in fact the beam never stopped oscillating. He came within about 1% of the modern value.

Baily

Francis Baily is a name relatively unknown, despite being a founder of both the Royal Astronomical and Royal Geographical Societies. He explored frozen North America before returning to the daredevil business of stockbroking and life assurance. His name only surfaces occasionally in Baily’s beads, the gem-like glints of sunlight left momentarily round the edge of the moon when it fully eclipses the sun, which he witnessed in Scotland. Baily retired and repeated Cavendish’s experiment in 1841, but tried to improve the accuracy.

Baily also had his apparatus at home, 37 Tavistock Place (since demolished), where he lived with his sister. He had an observatory with thick walls and double glazing covered with brown paper to exclude any warming shafts of sunlight. Baily spent three years on it, with lead balls this time gilded to reflect heat and so eliminate convection currents which might disturb the apparatus. The gilding was only added after 18 months of observation and 1,000 readings were discarded. He used various materials for his small balls including platinum, ivory and glass. In the midst of it all Baily was run over in Covent Garden. "I met with a dreadful accident… that nearly deprived me of existence… and seven weeks elapsed before I could again venture to resume the observations."

Boys

CV Boys, an exceptional experimenter, was also a perpetual prankster and liked to try and drop enormous smoke rings over pedestrians in Victoria Street from his window.

CV Boys

In 1895 he finalised his attempt to improve on previous results.  He set up equipment at Kensington’s Royal College of Science (a building now part of the V&A), picking less cumbersome balls in seeking a more accurate result.

Another innovation was a finer thread on which to hang his beam. He melted quartz, dipped an arrow into it and then fired it off. This produced a strong fibre 0.0001in diameter. But London was now teeming. Bad vibes (from the underground or traffic) affected the experiment. He abandoned London for Oxford and, even there, had to limit his measurements to the quiet of a Sunday night.

Measuring gravity remains a challenge. Modern methods still involve twists, dangles and balls, but laser interferometry has replaced the telescope and eyeball.

How did they do?

Density of the earth (compared to that of water)

Newton’s estimate, between 5 and 6 times.
Maskelyne 4.5
Cavendish 5.448
Baily 5.675
Boys 5.527
Present Day 5.515

The earth, by the way, has a mass of approximately 5,972,190,000,000,000,000,000,000 kg.

By Laurence Scales

Last Updated 12 November 2014