We present new intermediate-resolution spectra (lambda/Delta lambda = 3300) of fourteen early-type halo stars near the O VI resonance doublet at 1031.93 and 1037.62 Angstrom These spectra were obtained with the Berkeley extreme and far-ultraviolet (EUV/FUV) spectrometer in the ORFEUS telescope aboard the space platform ASTRO-SPAS during the mission of space shuttle Discovery down in 1993 September. Most of the targets are at high \b\, at a mean distance of about 2.8 kpc, providing an opportunity to study conditions in a region of the Galaxy comparatively unexplored by Copernicus (see work of Jenkins). The ORFEUS halo stars confirm the surprising paucity of O VI in the halo reported by Hurwitz et al. for two extragalactic sight lines through the southern Galactic hemisphere. We find an O VI scale height significantly lower than those reported for other highly ionized species; h(0) is between about 80 pc and 600 pc if the midplane density n(0) is between 1.5 and 5 x 10(-8) cm(-3). Only upper limits on N V exist for our sight lines; the O VI/N V ratio is constrained to lie above similar to 3. The O VI/C IV ratio is about 1-3. There is an inconsistency between the mean abundance of coronal gas in the halo derived from our O VI data and the much greater abundance derived from N V (reported by Sembach & Savage) and the O VI/N V ratio of similar to 15 observed in the disk and predicted by various models. We identify a foreground contribution from the radio loop I/soft X-ray enhancement along many of the high-b sight lines studied in N V as the most likely cause of the discrepancy. Unless the O VI/N V ratio in the halo falls well below its expected value, the projected column of coronal gas varies by a factor of similar to 100 among high-b sight lines. Insofar as it is sensible to discuss ''typical'' values under these circumstances, we arrive at projected columns of 8 x 10(13) cm(-2) for O VI and 5 x 10(12) cm(-2) for N V. For comparison with models or other observations that are inherently exclusive of low \z\ coronal gas, smaller columns should be adopted. The Galactic fountain model of Benjamin & Shapiro provides a self-consistent framework for interpretation of our observational results and various studies of C IV. The data are consistent with a flow velocity of similar to 15 km s(-1), isochoric cooling, a mass flux of similar to 3 M(.) yr(-1) per side, a density of similar to 10(-2) cm(-3), and a cooling length of a few hundred pc. There is weak evidence for an excess of O VI along sight lines characterized by foreground absorption from intermediate negative velocity (INV) gas detected primarily in low-ionization species. The tentative O VI excess is about 4-8 x 10(13) cm(-2) and may be produced in interfaces between the cool INV gas and a hot, low-density medium. We constrain the product of the midplane pressure and filling factor in the hot phase of the interstellar medium; at log T = 6.0, P/k x f(h) is probably <4000-12,000 cm(-3) K assuming isothermal gas, collisional ionization equilibrium, and solar abundances.
