def _smooth_the_residuals(self):
        """
        Apply the MID_SPAN to the residuals of the primary smooths.

        "For stability reasons, it turns out to be a little better to smooth
        |r_{i}(J)| against xi" - [1]
        """
        for primary_smooth in self._primary_smooths:
            smooth = smoother.perform_smooth(self.x,
                                             primary_smooth.cross_validated_residual,
                                             MID_SPAN)
            self._residual_smooths.append(smooth.smooth_result)
Apply the MID_SPAN to the residuals of the primary smooths.

        "For stability reasons, it turns out to be a little better to smooth
        |r_{i}(J)| against xi" - [1]