Experiment 4

The plumb line should point directly towards the Earth's center. In other words, it must be perfectly vertical - unless there's a massive object nearby. A heavy object close to the plumb bob will attract it and cause deviation from true vertical alignment.

The challenge here is that increasing the mass of the plumb bob does not significantly affect its deflection because both gravitational attraction between the bob and the massive object as well as the attraction with Earth increase proportionally. Only an extremely large object can have a measurable effect on the plumb line’s orientation. Additionally, the distance between objects plays a crucial role in determining gravitational force, but in this experiment, the initial separation between the plumb bob and the massive object cannot be reduced further, nor can the gap between the plumb bob and Earth be meaningfully increased.

Despite these complexities, in 1774, Nevil Maskelyne, Charles Hutton, and Reuben Burrow successfully measured deviations in plumb lines at the northern and southern sides of Schiehallion mountain by observing zenith distances of stars through observatories built there. Zenith refers to the sky point indicated by the plumb line, while zenithal star distance measures how far a star lies relative to this zenith point, expressed in degrees. Their combined result showed a total deviation of just 11.6 arcseconds, implying each plumb line deviated about 5.8 arcseconds from perfect verticality.

Nowadays, repeating such experiments has become much easier.

A - Observer One.
B - Observer Two.
C - Mountain.
D - Star.
N - North direction.
S - South direction.
E - East direction.
W - West direction.

With tools like Google and Wikipedia, finding suitable observation sites is straightforward. Using software like Stellarium helps select appropriate stars and optimal times for measurements. Modern GPS navigation systems ensure easy access to measurement locations and provide precise timing needed during experiments. Equipment necessary for accurate readings, including models like Leica Nova TS60, Trimble S9 HP, and Sokkia FX-201, are readily available. All that's left after setup is performing simple calculations. If done correctly, you'll confirm gravity's influence once again.

Example

Observer One conducted measurements at coordinates 56°40'21.5"N 4°06'00.4"W. Observer Two worked from 56°39'39.5"N 4°06'00.4"W. For Observer One, the zenithal distance was recorded as 47°40'03". Observer Two noted a value of 47°40'57". This translates into a 42-arcsecond spatial separation between observers and a difference of 54 arcseconds in their respective zenithal measurements. Therefore, the overall plumb line deviation sums up to 12 arcseconds, indicating approximately 6 arcseconds per plumb line.

Verifying accuracy of these results involves measuring zenithal distances for eastern and western stars from those same points. Given instrumentation errors, consistent values across stars should emerge if measurements were correct.

Wikipedia
Schiehallion experiment
Zenith
Minute and second of arc

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