Instruments composed of arrangements of linear accelerometers are used to determine motion variables. With nine accelerometers, the angular rate of the instrument can be resolved algebraically rather than by the solution of a system of nonlinear differential equations. The algebraic equations consist of three quadratic forms in the angular rate and, in general, lead to multiple solutions. The number and distribution of the multiple roots have been analyzed. Examples illustrate the application of the analyses, for batch and real-time processing. Suitable algorithms have been developed and are detailed. Subjects for further study have been indicated.