Experimentally measured growth rates of the positional instability of vertically elongated plasmas in Doublet III are compared with those obtained from a numerical code based on linear perturbation theory. The relevant elements of the circumstances of the experiment have been included in the code. The perturbations of plasma currents and currents in the wall of the vacuum vessel as well as in the coils surrounding the plasma are included in the model. The modelling of the complicated external circuitry of the coils is based on a simple assumption which was supported by observation. Comparison of the measured growth rates with those calculated suggests that the essential phenomena are adequately described by the model.