High signal-to-noise ratio optical spectrophotometry of a sample of field subluminous B stars drawn largely from the Palomar Green ultraviolet-excess survey is analyzed with a new grid of model atmospheres and synthetic spectra. The stellar effective temperatures, surface gravities, and photospheric helium abundances are determined simultaneously from a detailed analysis of hydrogen and helium absorption line profiles. The derived temperatures and gravities place the subluminous B stars in the theoroetical Hertzsprung-Russell (H-R) diagram along and bounded below by theoretical sequences of the zero-age extended horizontal branch, lending strong support to the hypothesis that these stars are composed of helium-burning cores of approximately 0.5 solar mass overlain by very thin layers of hydrogen (approximately less than 0.02 solar mass). Various scenarios for their past evolutionary history are examined in the context of their probable future evolution into white dwarfs of lower than average mass.