cavendish: Cavendish's 1798 determinations of the density of the earth
In Rlab: Functions and Datasets Required for ST370 Class

cavendish

R Documentation

Cavendish's 1798 determinations of the density of the earth

Description

Newton's law of gravitation states that the forces of attraction (f) between two particles of matter is given by the formula f=mm'/(r**2), where m and m' are their respective masses, r the distance between their centers of gravity, and G is the gravitational constant, independent of the kind of matter or intervening medium. From the late eighteenth through nineteenth centuries, a large number of experiments were performed in order to determine G. These experiments were usually designed to determine the earth's attraction of masses and described as experiments to determine the mean density of the earth: if the earth is supposed spherical with radius R and g is the acceleration toward the earth due to gravity, then Newton's law becomes dG=3g/(4(pi)R), where d is the mean density (g/ccm) of the earth. Since g and R could be supposed known, determination of d could be viewed as equivalent to determination of G.

Of all these early experiments, that of Cavendish, performed in 1798 using a torsion balance devised by Michell, is generally considered the best. The completeness of his description of his experiments and the excellence of his methods are often described as an ideal example of scientific experimentation. Cavendish concluded his memoir by presenting 29 determinations of the mean density of the earth. After the 6th of these determinations, Cavendish changed his experimental apparatus by replacing a suspension wire by one that was stiffer. Another interesting feature of the data is that Cavendish calculated the sample mean incorrectly: somehow he used 5.88 instead of 4.88 for the 3rd value. This was first noticed by Baily in 1843 but overlooked by Laplace's analysis of the data in 1820. The "true value" of d is 5.517 (1977 Encyclopedia Britannica).

The data and above description were taken from Stigler (1977, The Annals of Statistics, p. 1055-1098) who obtained it from The Laws of Gravitation edited by A. S. Mackenzie.