Seconds pendulum

Abstract: This paper is part of a larger work on the history, philosophy and utilisation of pendulum motion studies (Matthews 2000). The paper deals with the fate of Christiaan Huygens 1673 proposal to use the length of a seconds pendulum (effectively one metre) as a universal, natural and objective standard of length. This is something which, if it had been adopted, would have been of inestimable scientific, commercial and cultural benefit. Why it was not originally adopted in the late seventeenth century, and why it was again rejected in the late eighteenth century (1795) when the Revolutionary Assembly in France adopted the metric system with the metre being defined as one ten-millionth of the quarter meridan distance – raise interesting questions about the methodology and politics of science. Given that pendulum motion is a standard component of all science courses throughout the world, and given that most science education reforms, including the US National Science Education Standards and recent Australian state reforms, require that something of the ‘big picture’ of science be conveyed to students (the relationship of science to culture, commerce, history and philosophy) – it is suggested that these educational goals can be advanced by teaching about the fate of Huygens' proposal.

Abstract: The pendulum played a major role in the seventeenth-century Scientific Revolution. Galileo used the ‘marvellous properties’ of the pendulum to demonstrate his ‘conservation’ laws, to legitimise his recourse to mathematical proofs in physics (natural philosophy), and he recognised that its isochronous properties provided the basis of reliable timekeeping. Christiaan Huygens patented a pendulum clock in 1657, and he proposed the seconds pendulum as an international standard of length. Newton, in his Principia, used this value to establish that acceleration due to gravity on the surface of the earth was the same type of acceleration as the moon’s centripetal acceleration towards the earth. The importance of the pendulum in science and philosophy was exceeded only by its importance to commerce, navigation, exploration and colonisation as an accurate measure of the passage of time was crucial for the determination of longitude at sea.

Abstract: Early modern scholars and statesmen were acutely aware of the need for improved standards of measurement, albeit for differing reasons. The variety of man-made units across territories and histories was, by the seventeenth century, already a sceptical commonplace, and was understood in terms of the mutability of human institutions. The late seventeenth century saw many scholars advance possible candidates for a universal standard. The most promising of these was the use of a seconds pendulum as a standard for length, a project which was actively pursued by the French Academie Royale des Sciences in the 1670s and 1680s, and remained a goal cherished by savants through the eighteenth century. This paper’s first section places the Academie’s early metrological projects in the context of the scholarly community’s ideal of a universal measurement standard, which was often expressed in ways combining political, theological, and humanistic concerns. Melchisedech Thevenot’s ludic proposal that honeycombs might be a length standard is explored as one example. The second section examines the Academie’s attempts to test the seconds pendulum as a universal length standard, by taking the missions to Uraniborg (1671) and to London (1679) as case studies in the practice of metrological work.

Abstract: The decrement of a pendulum falls slowly with the amplitude: hence the need for determinations based on small changes of angle. The resulting errors of observation lead to erratic values but not to systematic error. The result of measurements with a seconds pendulum enclosed in a case is shown by a smoothed curve, the departure from observed times being expressed by smoothing fractions, and a smoothing figure is a measure of this departure for the whole or part of the experiment. From the decrement the rate of loss of energy is calculated. This 7 kg. pendulum with amplitude 53' dissipates a Board of Trade Unit (which serves a 70 W. lamp for 14 hours) in rather over 100,000 years. Experiments with different pendulums are described by which the component losses due to suspension, rod, and bob are found. Suspension springs made from thin strip clamped in chaps dissipate large and variable amounts of energy compared with springs made from thick strip ground thin in the middle. The variable losses are associated with variable rates of the pendulum. The cylindrical case adds considerably to the air resistance. The measured loss due to a gravity impulse lever is little in excess of the computed loss from collision with the pendulum: for a seconds pendulum 1/2000 part of the free pendulum loss.