The Orion Nebula is pivotal in establishing the "dY/dZ relation," which describes both the enrichment of helium as stars produce heavy elements and, from an extrapolation to a condition of no enrichment, the primordial helium abundance. With the goal of redetermining the helium abundance of the Orion Nebula, we have obtained new long-slit spectrophotometric observations. These observations confirm previously noted trends that the density, level of ionization, and emission measure decrease with the distance from the Trapezium. The reddening, measured from ratios of Paschen to Balmer lines, must arise mostly in a neutral sheet in front of the H II region. Most of the hydrogen line emission originates in the ionized flow from the interface between the H II region and the molecular cloud. The observations show that the level of ionization of the gas does not change dramatically across our sampled region; in particular, the ionic abundance ratio He+/H+ is nearly constant, with He+/H+ = 0.088 +/- 0.006. In the bright innermost region the errors are largely dominated by systematic errors due to uncertainties in the reddening curve for Orion grains and deviations from case B emissivity; statistical errors dominate the error budget in the fainter, outer regions. Photoionization models are computed to determine the correction for the unobserved presence of neutral helium in regions where hydrogen is ionized. We also derive abundances for the heavy elements by comparison with the photoionization model calculations. Emergent continua from newly recomputed Kurucz LTE stellar atmospheres are used as input to the models. The calculations also include a number of important effects of grains on the ionization and thermal structure of the nebula; heating and cooling of the gas by photoemission-recombination from charged grains are found to be substantial. These models reproduce quite well the observed emission-like spectrum, as well as the mid-infrared continuum from the Trapezium region, and show that the correction for neutral helium is small. Our final helium abundance, He/H = 0.088 +/- 0.006, is lower than the commonly quoted value because the correction for neutral helium is much smaller than that used in previous work. By comparing our Orion results with solar, stellar, and nebular measurements of helium and heavy-element enrichments, and with the theoretical Y(p) from primordial nucleosynthesis, we find that all of the data are consistent with a single line in the Y-Z plane. This is a provocative result for studies of galactic and primordial nucleosynthesis.
