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A seismograph in one city can record an earthquake on another continent. That was not possible until instruments became sensitive enough to slow, small ground motions and until stations shared their readings. John Milne worked on both. This post covers what the records say about him, how his horizontal pendulum worked in his own words, a worked example of the physics, and what you can learn from his approach.
Who was John Milne?
The Who Was Who entry gives his dates as 30 December 1850 to 31 July 1913 and describes him as a mining engineer and seismologist. The title page of his book Seismology calls him the late Professor of Mining, Geology and Seismology in the Imperial College of Engineering, Tokyo. Its introduction is signed from Shide, near Newport, on the Isle of Wight, in June 1898.
His obituary in Nature says he found seismology "in its embryo stage", with instruments "of the most unsatisfactory type", and lived to see well-equipped observatories all over the globe. It notes that he died before reaching sixty-three and that his earthquake studies spanned thirty-five years.
What is a horizontal pendulum?
In Seismology, Milne describes it in its simplest form as "a horizontal bar pivoted at one end on a vertical axis, round which it is free to rotate". If the axis is exactly vertical, gravity gives no restoring force at all. So the axis is tilted forward very slightly. Milne explains that this gives the arm a feeble stability and a slow period, and that the sensitivity increases with the period, which grows as the axis approaches the vertical.
He also records that he was not the first to build one. He names M. Perrot in 1862, Professor F. Zollner in 1869, and later W. S. Chaplin, Thomas Gray and J. A. Ewing, and he credits Ewing with introducing the principle into seismometry.
What did Milne's own instrument look like?
Milne describes booms of aluminium tube or lacquered bamboo, from 2 ft 6 in to 5 ft 6 in long, pivoting on a quartz cap resting on a steel point and held up by a thin brass wire. At the outer end was a plate with a slit. It moved over a second slit, at right angles, in a closed box, so only a point of light from a small kerosene flame reached a photographic film on a drum turned by clockwork. Once an hour the minute hand of a watch briefly blocked the light, marking the time.
He gives a figure for its sensitivity: with a period of fifty-five seconds, a 1 mm deflection at the outer end was equivalent to a tilt of 0.08 seconds of arc.
Worked example: why does tilting the axis help?
For a horizontal pendulum whose axis is tilted by a small angle i from the vertical, only the component g sin i provides the restoring pull. So its period is T = 2π√(l ÷ (g sin i)), compared with T = 2π√(l ÷ g) for an ordinary pendulum. The length below is a sample value.
Step 1: an ordinary pendulum. With l = 1.0 m and g = 9.8 m/s², T = 2π√(1.0 ÷ 9.8) ≈ 2.0 s.
Step 2: what tilt gives Milne's 55 s? Rearranging, sin i = 4π²l ÷ (gT²) = 39.48 × 1.0 ÷ (9.8 × 3025) = 39.48 ÷ 29,645 ≈ 0.00133. So i ≈ 0.00133 rad ≈ 0.076°, or about 4.6 minutes of arc. A tiny tilt turns a 2-second pendulum into a 55-second one.
Step 3: how small is 0.08 seconds of arc? One radian is 206,265 seconds of arc, so 0.08″ = 0.08 ÷ 206,265 ≈ 3.9 × 10^-7 rad. That is like raising one end of a beam about 2.6 km long by 1 mm (1 mm ÷ 3.9 × 10^-7 ≈ 2,600 m).
A long period means the pendulum responds to slow ground motions, which is why Milne found that long booms recorded "earthquakes originating at a great distance" clearly. For the pendulum formula itself, see our guide to the simple pendulum experiment.
How did his stations work together?
In the 1908 preface to Seismology, Milne wrote that the British Association then had the co-operation of "forty-five widely separated stations, each furnished with similar instruments". The International Seismological Centre lists him as the publisher of the Shide Circular Reports on Earthquakes from 1900 to 1912. It says he recognised the need for international exchange of readings, and that his work led to the International Seismological Summary, set up just after the First World War. Today's ISC continues that work.
What mistakes do students make with seismographs?
Thinking the pen moves with the ground. The heavy part tends to stay put while the frame moves; the record is the relative motion.
Using g instead of g sin i. For a tilted-axis pendulum, the restoring pull is much weaker, so the period is much longer.
Confusing seismograph with seismoscope. A seismoscope shows that shaking happened; a seismograph records it against time. Our post on Zhang Heng's seismoscope covers the earlier instrument.
What can a student learn from Milne?
He improved an existing idea instead of waiting for a new one, gave clear numbers for what his instrument could detect, and saw that data becomes far more useful when many people collect it the same way. Milne himself thanked a long list of colleagues and wrote that the results "illustrate the value of co-operation among scientific workers".
If pendulum and oscillation problems are where you lose marks, the Fermi Problem Library has a step-by-step solver that explains the reasoning, so you can see where g sin i enters.
Try it now: find the period of Milne's sample pendulum if the tilt is doubled.
