specific angular momentum relative to that of the binary. Thus, if a massive circumbinary disc is formed, the PBE code is expected to over-estimate the binary’s separation, under-estimate the mass in the circumbinary disc, and slightly under-estimate the mass-ratio of the binary.

The evolution of the mass ratio, separation and amount of gas in the circumbinary disc are given for test case 2 in Figure \[bate.testcase2\]. An MPEG animation of the SPH calculation is included on this CD-ROM as bate3.mpg. To avoid the problems that occurred due to the large shear viscosity in the SPH calculation for test case 1, the SPH calculation here uses a formulation with less shear viscosity (see [@Bate2000]). As with test case 1, due to the computational cost, the SPH calculations were stopped before all of the gas had fallen on to the binary. The SPH calculation took $\approx 4$ months on a 300 MHz Sun Ultra workstation (using a binary tree, not a GRAPE board). During the evolution, the binary performed $\approx 40$ orbits and $\approx 60$% of the total mass was accreted by the binary or settled into a circumbinary disc.

The agreement for the evolution of the mass ratio is even better 