We have adapted the single-ion Vi¿as and Scudder (1986) solution to the Rankine-Hugoniot problem to a multiple-ion solution. Using this technique, we can calculate a shock normal direction, shock speed, best estimate of the upstream and downstream magnetic field and plasma asymptotic states, and &thgr;Bn, the angle between the shock normal and the upstream magnetic field. We test the multi-ion solution with a theoretical case but are restricted to a perpendicular shock in order to close the multi-ion Rankine-Hugoniot equations. For this test case both single-ion and multi-ion solutions are equally valid. We examine parameter regimes to look for differences between single-ion and multi-ion solutions of the R-H equations, and we find that the largest differences occur for quasi-parallel shocks, small values of solar wind speed, large values of heavy ion density, and very strong and very weak shocks. For both the inbound and outbound crossing of comet Halley we have a slow solar wind speed, small values of water group ions and fairly weak shocks. We examine both the quasi-perpendicular inbound crossing and the quasi-parallel outbound crossing at comet Halley. For the inbound crossing we have good resolution data and make an accurate determination. However, it is likely that the shock normal determination was influenced by the interplanetary disturbances flowing from the Sun that permeate the inbound crossing region and that force the normal to an antisunward direction. For the outbound case the FIS experiment is not providing data because it was damaged by cometary dust soon after closest approach. However, the results are more definitive: all of the normals are within 31¿ of each other, which makes the analysis essentially independent of interval. In both cases there are differences between the single- and multi-ion solutions with the multi-ion solution being the more reliable. ¿ American Geophysical Union 1994