We report and interpret HST /Space Telescope Imaging Spectrograph ( STIS ) long-slit observations of the optical and ultraviolet ( UV ) ( 1150 - 10270 Å ) emission-line spectra of the rapidly brightening Spot 1 on the equatorial ring of SN 1987A between 1997 September and 1999 October ( days 3869 – 4606 after outburst ) . The emission is caused by radiative shocks created where the supernova blast wave strikes dense gas protruding inward from the equatorial ring . We measure and tabulate line identifications , fluxes and , in some cases , line widths and shifts . We compute flux correction factors to account for substantial interstellar line absorption of several emission lines . Nebular analysis shows that optical emission lines come from a region of cool ( T _ { e } \approx 10 ^ { 4 } \mbox { K } ) and dense ( n _ { e } \approx 10 ^ { 6 } \mbox { cm } ^ { -3 } ) gas in the compressed photoionized layer behind the radiative shock . The observed line widths indicate that only shocks with shock velocities V _ { s } < 250 ~ { } km~ { } s ^ { -1 } have become radiative , while line ratios indicate that much of the emission must have come from yet slower ( V _ { s } \mathrel { < \kern - 10.0 pt \lower 3.87 pt \hbox { $ \sim$ } } 135 ~ { } km~ { } s ^ { -1 } ) shocks . Such slow shocks can be present only if the protrusion has atomic density n \mathrel { > \kern - 10.0 pt \lower 3.87 pt \hbox { $ \sim$ } } 3 \times 10 ^ { 4 } \mbox { cm } ^ { -3 } , somewhat higher than that of the circumstellar ring . We are able to fit the UV fluxes with an idealized radiative shock model consisting of two shocks ( V _ { s } = 135 and 250 ~ { } km~ { } s ^ { -1 } ) . The observed UV flux increase with time can be explained by the increase in shock surface areas as the blast wave overtakes more of the protrusion . The observed flux ratios of optical to highly-ionized UV lines are greater by a factor of \sim 2 - 3 than predictions from the radiative shock models and we discuss the possible causes . We also present models for the observed { H } \alpha line widths and profiles , which suggests that a chaotic flow exists in the photoionized regions of these shocks . We discuss what can be learned with future observations of all the spots present on the equatorial ring .