... Judged by their instrumental profiles, spectrometers fall into two basic classes---Lorentzian and Gaussian---with many other line profile functions (sinc functions, Voigt functions, Airy functions, etc.) falling into one of these two categories in some limit. We demonstrate that the Rayleigh, Sparrow, and Houston resolution criteria are of limited use compared to the ``equivalent width'' of the line profile. ... Rayleigh criterion. ... All of these functions have continuous higher derivatives. ...