have a mass ratio of $q=0.6$ and a mass of $1/10$ the initial cloud mass. The second test case was similar, except that the progenitor cloud was centrally-condensed with a 1/r-density distribution and the cloud had a total mass of only 5 times the ‘seed’ binary’s mass. A full discussion of the test cases is given by [@Bate2000].

### Test Case 1

The evolution of the mass ratio, separation and amount of gas in the circumbinary disc are given for the PBE code and for a full SPH calculation in Figure \[bate.testcase1\]. The curves are given as functions of the amount of gas that has fallen on to the binary, $M_{\rm acc}$, relative to the binary’s initial mass. In addition, an MPEG animation of the SPH calculation is included on this CD-ROM as bate2.mpg. The CPU time required to evolve the SPH calculation until the entire cloud falls on to the binary in is prohibitively long, which, after all, is the reason that the PBE code was developed in the first place. It takes $\approx 60$ orbits for the binary to increase its mass by a factor of 6 (i.e. $\approx 60$% of the total cloud was accreted). The SPH 