Revisiting Riccioli’s free-fall calculations
DOI: 10.1063/PT.3.1896
Christopher Graney provides a fascinating description of Giovanni Battista Riccioli’s meticulous 17th-century experiments on free fall (Physics Today, September 2012, page 36
As Christiaan Huygens reported in his classic 1673 Horologium Oscillatorium, published 22 years after Riccioli’s Almagestum, the period of a pendulum of length l is T = 2π√
Plotting Riccioli’s data in that way reveals an accurate straight line from which one can deduce the pendulum length. The answer—with a generous error estimate—is l = 1.00 ± 0.05 Roman inches. As Graney notes, Riccioli himself reported the length to the center of the pendulum bob to be 1.15 inches. The 15% discrepancy—less than 4 mm—is plausibly excusable, though one might infer that Riccioli supposed his measurement was accurate to at least 0.05 inches (about 1 mm).
Unfortunately, the discrepancy is in the wrong direction to be attributed either to the distinction between the center of mass and the center of oscillation of a compound pendulum or to the fact, known to Riccioli, that large-amplitude pendulum swings are not quite isochronous. Nevertheless, the discrepancy is intrinsic to Riccioli’s presented data and is not dependent on the disputed length of the Roman foot. One can only presume it reflects on the difficulty of subdividing a Roman foot into such fine equispaced divisions.
More about the Authors
Patrick Warren. (patrick.warren@unilever.com) Unilever R&D Port Sunlight, Bebington, UK.