page_title: Kater's pendulum
section_title: Repsold–Bessel pendulum
hierarchical_section_title: Kater's pendulum / History / Repsold–Bessel pendulum
caption_attribution_description: English: Drawing of Repsold pendulum, a freeswinging reversible pendulum developed in 1869 by German instrument maker Adolf Repsold for use as a precision gravimeter in geophysical serveys. 56.0 cm long between the interchangeable knife blade suspension points, it had a period of 3/4 second. Although symmetrical in form, one of the weights on the end was lighter than the other. It was swung from one built in knife edge pivot and the period timed, then turned upside down and swung from the other pivot and timed. From the two periods and the distance between the knife blades, the gravity could be calculated. Alterations to image: none.
context_page_description: A Kater's pendulum is a reversible free swinging pendulum invented by British physicist and army captain Henry Kater in 1817 for use as a gravimeter instrument to measure the local acceleration of gravity. Its advantage is that, unlike previous pendulum gravimeters, the pendulum's centre of gravity and center of oscillation do not have to be determined, allowing a greater accuracy. For about a century, until the 1930s, Kater's pendulum and its various refinements remained the standard method for measuring the strength of the Earth's gravity during geodetic surveys. It is now used only for demonstrating pendulum principles.
context_section_description: Repeatedly timing each period of a Kater pendulum, and adjusting the weights until they were equal, was time-consuming and error-prone. Friedrich Bessel showed in 1826 that this was unnecessary. As long as the periods measured from each pivot, T₁ and T₂, are close in value, the period T of the equivalent simple pendulum can be calculated from them:
  Here  and  are the distances of the two pivots from the pendulum's center of gravity.   The distance between the pivots, ,  can be measured with great accuracy.    and , and thus their difference ,  cannot be measured with comparable accuracy.  They are found by balancing the pendulum on a knife edge to find its center of gravity, and measuring the distances of each of the pivots from the center of gravity. However, because  is so much smaller than , the second term on the right in the above equation is small compared to the first, so  doesn't have to be determined with high accuracy, and the balancing procedure described above is sufficient to give accurate results.
  Therefore, the pendulum doesn't have to be adjustable at all, it can simply be a rod with two pivots. As long as each pivot is close to the center of oscillation of the other, so the two periods are close, the period T of the equivalent simple pendulum can be calculated with equation (2), and the gravity can be calculated from T and L with (1).
  In addition, Bessel showed that if the pendulum was made with a symmetrical shape, but internally weighted on one end, the error caused by effects of air resistance would cancel out. Also, another error caused by the finite diameter of the pivot knife edges could be made to cancel out by interchanging the knife edges.
  Bessel didn't construct such a pendulum, but in 1864 Adolf Repsold, under contract to the Swiss Geodetic Commission, developed a symmetric pendulum 56 cm long with interchangeable pivot blades, with a period of about ¾ second. The Repsold pendulum was used extensively by the Swiss and Russian Geodetic agencies, and in the Survey of India. Other widely used pendulums of this design were made by Charles Peirce and C. Defforges.
caption: Repsold pendulum.
exif: {}