  In this paper we compare the dimensional method with the Lie groups tactic in
order to show the limitations and advantages of each technique. For this
purpose we study in detail a perfect fluid cosmological model with time-varying
"constants" by using dimensional analysis and the symmetry method. We revise
our previous conclusion about the variation of the fine structure constant
finding for example that in the radiation predominance era if $\alpha$ varies
is only due to the variation of $e^{2}\epsilon_{0}^{-1}$ since $c\hbar=const$
in this era.
