  We consider long-slit emission-line spectra of galactic nuclei when the slit
is wider than the instrumental PSF, and the target has large velocity
gradients. The finite width of the slit generates complex distributions of
brightness at a given spatial point in the measured spectrum, which can be
misinterpreted as coming from additional physically distinct nuclear
components. We illustrate this phenomenon for the case of a thin disc in
circular motion around a nuclear black hole (BH). We develop a new method for
estimating the mass of the BH that exploits a feature in the spectrum at the
outer edge of the BH's sphere of influence, and therefore gives higher
sensitivity to BH detection than traditional methods. Moreover, with this
method we can determine the black hole mass and the inclination of the
surrounding disc separately, whereas the traditional approach to black-hole
estimation requires two long-slit spectra to be taken. We show that with a
given spectrograph, the detectability of a BH depends on the sense of rotation
of the nuclear disc. We apply our method to estimate the BH mass in M84 from a
publicly available spectrum, and recover a value 4 times lower than that
published previously from the same data.
