History of Boys' experiment, Clarendon Laboratory Archive

## Background to Boys' experiment to determine G

In 1687 Newton published his Pricipia in which he said that one of the consequences of his law of gravitation was that on level ground a plumb bob would hang vertically as it was attracted towards the centre of the Earth. However, if there was a large mass nearby like a mountain, the bob would be pulled slightly off vertical because of the extra attraction towards the mountain. This effect was called the "Attraction of Mountains". In 1772 Nevil Maskelyne the Astronomer Royal, proposed using this Attraction of Mountains both to check Newton's Law of Gravitation and to deduce the mass of the Earth.
Maskelyne's idea was well received by the Royal Society and they commissioned a surveyor called Charles Mason to find a suitable mountain in the Highlands of Scotland. Mason eventually found Schiehallion to the north of Perth which had no other mountains nearby and so seemed ideal. The Royal Society asked Mason to do the experiment but he refused and Maskelyne was not keen to do it either! Eventually, Maskelyne was persuaded to go. His measurements took four months in the summer of 1774 and Maskelyne presented the results to the Royal Society on July 6 1775. The plumb bob had been attracted by the mountain so Newton's law was verified.
Working out the mass of the Earth was more involved and the Society hired the mathematician Charles Hutton to do the sums. Hutton, inventing contour lines along the way, determined that the mean density of the Earth was 4.5g/cm3. The presently accepted value is about 5.5g/cm3 so Hutton's result was within 20%.

### Cavendish's experiment

The Revd. John Michell was the Rector of Thornhill near Dewsbury in Yorkshire having retired at the age of 37 from being a Professor of Geology at Cambridge. Michell devised a very sensitive torsion balance for measuring gravitational attraction. Charles Coulomb had proposed the torsion balance for measuring very small forces in 1784 but Michell claimed that Coulomb had not published his ideas when he devised his balance.
The torsion balance is simple and elegant: a horizontal beam with small lead balls at each end is suspended from its centre by a thin torsion wire. A large lead ball is then placed near each of the small balls in the same horizontal plane such that the gravitational attraction of each of large ball on its small ball tends to twist the torsion wire in the same direction. The gravitational twisting force is balanced by the force produced by twisting the torsion wire.
The angle of twist is measured by the position of a pointer protruding from the end of the beam onto a fixed scale. The large balls are then moved to the other side of the small balls and the change in twist measured.
The force required to twist the wire can be measured by timing free oscillations of the beam about the axis of the torsion wire. Thus, if the masses of the balls and various dimensions of the apparatus are known, the gravitational force and hence G can be deduced. See diagram and calculations (9 KBytes).
Sadly however, Michell died in 1793 before he could use his balance, and the apparatus was given to Henry Cavendish. Cavendish used the balance in 1798 and measured the mean density of the earth at 5.48g/cm3. This implied that G was 6.754x10-11m3s-2kg-1 although Cavendish did not derive it. Cavendish used a pendulum beating seconds to measure time and this removes G from the calculations replacing it with the mass and radius of the Earth. See Philosophical Transactions of the Royal Society, 1798 p469.
Cavendish used 2" lead balls hanging on the end of a 73" beam which was suspended by a 40" long torsion wire of "copper silvered". The large balls were also lead, 12" in diameter. The period of free oscillation of the beam was about 15 minutes.

### Boy's experiment

Almost a hundred years later Charles Vernon Boys who was an Assistant Professor of Physics at the Royal College of Science, South Kensington, London, further developed the Michell balance. Boys had the advantage of being able to use quartz fibre rather than the copper torsion wire used by Cavendish. He calculated the effects of changing the sizes of the various parts of the apparatus and concluded amid some controversy that the apparatus should be much smaller. He built a small apparatus to test these conclusions using a torsion beam only 5mm long. Boys described the apparatus and presented his results at a meeting of the Royal Society on June 20 1889. [Proceedings of the Royal Society, 46 p253.] His results confirmed his ideas. He was able to measure G to about 1 part in 1000.
It proved very difficult to improve this measurement in London because the experiment was sited in an underground tunnel where it was subject to vibration caused by "arts students" walking overhead and "coal deliveries" into an adjacent cellar. Thus when R B Clifton offered Boys space in the cellars of Clarendon Laboratory (12 KB) Boys moved his experiment to Oxford.
Boys built another apparatus to attempt to measure G to 1 part in 10,000. To achieve this accuracy he would need to measure times and some lengths to 1 part in 20,000 with other parameters to 1 part in 10,000. The 2" lead balls and 73" beam used by Cavendish were replaced by 0.2" diameter gold balls hanging from a 1" beam. The balls on opposite sides of the beam were separated vertically by 6" to reduce the effect of attraction from the opposite large ball. The large balls were of lead either 2.25" or 4" in diameter. The period of oscillation of the beam was about 3 minutes. Because the beam was very short, the angle of twist was measured by viewing with a telescope, the reflection of an illuminated scale in a tiny mirror fixed on the beam.
Oxford was much quieter than London, but even so Boys was hampered during the day by "the rattling traffic on the stones in St. Giles, about a quarter of a mile away", and on weekday nights from the railway shunting yards a mile away. The early hours of Sunday morning were the best times to work and he eventually determined the value of G to be 6.658x10-11m3s-2kg-1.
The experiment took four years and when completed Boys wrote [Philosophical Transactions of the Royal Society, 186, 1, (1895)] that he would have liked to do more measurements under wider conditions but "the strain which they entail is too severe, for not only have I had to give up holidays for the last three years, but to leave London on Saturdays and occasionally to sit up all Saturday and Sunday nights at the end of a week's work."
The original apparatus and Boys' notebooks are now in the Science Museum in London. The cellar, now fitted with electric light, is still used by the Department of Earth Sciences whose building replaced the original Clarendon Laboratory just after the Second World War. A slate-topped bench used by Boys is still in use and there is a plaque on the wall commemorating the experiment.

Boys states in his paper that he intended "to leave also permanently in the Museum a series of photographs of the apparatus as it appears in situ when each of the [measuring] operations is being carried out". It seems likely that the photographs in the Clarendon Archive are these photographs. They do not appear in Boys' paper and the Science Museum do not have copies.

You can read more about Boys at the Local Heroes website and at the History of Mathematic archive.