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The luminous blue variable, $\eta$ Carinae displays a strongly bipolar circumstellar nebula resulting from a violent and massive stellar outburst in the early 1800's. Recently, Davidson et al. (1994) have used the Hubble Space Telescope Faint Object Spectrograph and have isolated the stellar spectrum between 2500 \AA\ and 5500 \AA. Assuming spherical symmetry Davidson et al. derive a mass-loss of order $10^{-3} \, \rm{M_\odot/yr}$ for the stellar wind from the H$\beta$ wind emission line. Since this mass-loss rate exceeds the single scattering limit by an order of magnitude, and since the nebula is bipolar, we have investigated the effects of stellar rotation on the wind. The Wind-Compressed Disk model (WCD; Bjorkman and Cassinelli 1993 and Cassinelli, Ignace, and Bjorkman 1994) has been used to estimate the wind density in radius and latitude. Subsequently, wind emission lines were calculated using the SEI2D line transfer method (Bjorkman et al. 1994). We find that an equatorial disk can form if the stellar rotation speed is of order 100 km $\rm{s}^{-1}$. If a disk forms, the mass-loss rate as deduced from wind emission lines can be reduced significantly below the mass-loss derived assuming spherical symmetry.
