cavendish                package:Rlab                R Documentation

_C_a_v_e_n_d_i_s_h'_s _1_7_9_8 _d_e_t_e_r_m_i_n_a_t_i_o_n_s _o_f _t_h_e _d_e_n_s_i_t_y _o_f _t_h_e _e_a_r_t_h

_D_e_s_c_r_i_p_t_i_o_n:

     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.

_F_o_r_m_a_t:

     A numeric vector with 29 values.

_E_x_a_m_p_l_e_s:

     plot(cavendish)

