  We study the coalescence of two drops of an ideal fluid driven by surface
tension. The velocity of approach is taken to be zero and the dynamical effect
of the outer fluid (usually air) is neglected. Our approximation is expected to
be valid on scales larger than $\ell_{\nu} = \rho\nu^2/\sigma$, which is $10
nm$ for water. Using a high-precision boundary integral method, we show that
the walls of the thin retracting sheet of air between the drops reconnect in
finite time to form a toroidal enclosure. After the initial reconnection,
retraction starts again, leading to a rapid sequence of enclosures. Averaging
over the discrete events, we find the minimum radius of the liquid bridge
connecting the two drops to scale like $r_b \propto t^{1/2}$.
