  We examine the dynamics of two coalescing liquid drops in the `inertial
regime', where the effects of viscosity are negligible and the propagation of
the bridge front connecting the drops can be considered as `local'. The
solution fully computed in the framework of classical fluid-mechanics allows
this regime to be identified and the accuracy of the approximating scaling laws
proposed to describe the propagation of the bridge to be established. It is
shown that the scaling law known for this regime has a very limited region of
accuracy and, as a result, in describing experimental data it has frequently
been applied outside its limits of applicability. The origin of the scaling
law's shortcoming appears to be the fact that it accounts for the capillary
pressure due only to the longitudinal curvature of the free surface as the
driving force for the process. To address this deficiency, the scaling law is
extended to account for both the longitudinal and azimuthal curvatures at the
bridge front which, fortuitously, still results in an explicit analytic
expression for the front's propagation speed. This new expression is then shown
to offer an excellent approximation for both the fully-computed solution and
for experimental data from a range of flow configurations for a remarkably
large proportion of the coalescence process. The derived formula allows one to
predict the speed at which drops coalesce for the duration of the inertial
regime which should be useful for the analysis of experimental data.
