  Field emission data are often represented on a Fowler--Nordheim plot but a
new empirical equation has been recently proposed to better analyze
experiments. Such an equation is based on approximations of the Murphy and Good
model and predicts that a constant parameter $\kappa$, depending only on the
work function of the emitter, can be extracted from the data. We compared this
empirical equation with simulations of the Murphy and Good model in order to
determine the range of validity of the approximations and the robustness of the
relationship between $\kappa$ and the work function. We found that $\kappa$ is
constant only over a limited range of electric fields and so depends
significantly on the field enhancement factor. This result calls into question
the usefulness of the new empirical equation.
