  We show that the scattering amplitude of four open string scalars or tachyons
on the world-volume of a D$_p$-brane in the bosonic string theory can be
written in a universal form. The difference between this amplitude and the
corresponding amplitude in the superstring theory is in an extra tachyonic
pole. We show that in an $\alpha'$ expansion and for slowly varying fields, the
amplitude is consistent with the tachyonic DBI action in which the even part of
the tachyon potential is $V(T)=e^{-(\sqrt{\pi} T/\alpha)^2}$ with $\alpha=1$
for bosonic theory and $\alpha=\sqrt{2}$ for superstring theory.
