The thermophoretic force on single microspheres has been measured over a wide range of Knudsen numbers and particle thermal conductivities for solid and liquid spheres in air. The microspheres were dioctyl phthalate (DOF) droplets, metallic nickel, polystyrene latex (PSL), and glass. This covers a thermal conductivity ratio (gas to particle) range of 2 x 10(-4)-0.17. In a companion paper, results are reported for monatomic (helium) and polyatomic gases (carbon dioxide and air) to examine the effects of gas properties. The measurements were accomplished by levitating the particle between heated and cooled plates mounted in a vacuum chamber. Light-scattering phase functions were used to determine the size of all materials except the nickel spheres, and for the highly absorbing metallic spheres the size was obtained by measuring the marginal stability limit of the particle, The apparatus developed for the research and the experimental techniques are discussed, and the experimental results in the Knudsen number range 0.05-20 are compared with previously proposed theories. For particle Knudsen numbers greater than about 10, the effects of the temperature jumps (thermal slip) at the heated and cooled plates become significant. The data in the transition regime overlap Loyalka＇s (1992, J. Aerosol Sci. 23, 291-300) solution of the linearized Boltzmann equation for hard-sphere molecules, and the data in the slip regime agree with Brock＇s (1962, J. Colloid Sci. 17, 768-780) theory. The effects of particle thermal conductivity are shown to be nearly negligible in the Knudsen regime, for the data for particles having greatly different thermal conductivities overlap.