We use numerical simulations to test the feasibility of the suggestion by Ibata et al. (1994) that the excess population of stars which they discovered in the Sagittarius region may be the disrupted remains of a dwarf spheroidal galaxy. We find that a Fornax-like model for the pre-disruption system can indeed reproduce the data. However, the galaxy must be on a relatively short period orbit with a pericentre of about $10$ kpc and an apocentre of about $52$ kpc, giving a current transverse velocity of $255$ km/s and a period of $\sim 760$ Myr. Furthermore, disruption must have occurred predominantly on the last pericentric passage rather than on the present one. The data are consistent with transverse motion either towards or away from the Galactic Plane. These results depend primarily on the rotation curve of the Galaxy and are insensitive to the mass distribution in its outer halo or to the mass of its disk.

8 pages, uuencoded compressed postscript file (4 figures are included). Submitted to MNRAS.