A variety of CCD astrometric data was used to predict the location of the path for the occultation of the star we have denoted "Tr176" by Triton, which occurred on 1997 July 18, and was visible from locations in northern Australia and southern North America. A network of fixed and portable telescopes equipped with high-speed photometric equipment was set up to observe the event, with the following observational goals: (i) mapping the central flash (to establish the global shape of Triton's atmosphere at about 20-km altitude by modeling the detailed shape of the central flash), (ii) obtaining one or more light curves of high signal-to-noise ratio from a large telescope (to accurately determine the thermal structure of Triton's atmosphere), and (iii) obtaining light curves distributed across Triton's disk (to probe the thermal structure of Triton's atmosphere above different areas and to establish the shape of the atmosphereat about 100-km altitude by modeling the half-light surface). Although the large, fixed telescopes proved to be outside of the occultation shadow and observations with some of the portable telescopes were foiled by clouds, light curves were successfully recorded from Brownsville, Texas, and Chillagoe, Queensland. These were combined with data from another group to determine the radius and shape of the half-light surface in Triton's atmosphere and the equivalent-isothermal temperatures at the sub-occultation latitudes on Triton. A circular solution for the half-light surface (projected into Triton's shadow) yielded a radius of 1439+/-10 km. However, the data are indicative of a global shape more complex than a sphere. Such a figure is most likely caused by strong winds. Light-curve models corresponding to the best fitting circular and elliptical atmospheres were fit to the data. The mean pressure at 1400-km radius (48-km altitude) derived from all of the data was 2.23+/-0.28 microbar for the circular model and 2.45+/-0.32 microbar for the elliptical model. These values suggest a global pressure increase at this level since a previous Triton occultation in 1995 August. The mean equivalent-isothermal temperature at 1400 km was 43.6+/-3.7 K for the circular model and 42.0+/-3.6 K for the elliptical model. Within their (sometimes large) uncertainties, the equivalent-isothermal temperatures agree for all Triton latitudes probed.
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