THIRRING'S solution for a rotating mass shell is frequently used to illustrate the appearance of centrifugal and Coriolis force in general relativity. In the equations of motion of test particles within the shell, terms appear which are of second order in the shell angular velocity, ω. These terms are conventionally identified with “centrifugal force”, yet they do bear the relationship to “Coriolis force” that one would expect from Mach's principle. The resolution of this paradox has an important bearing on the foundations of general relativity because, to resolve it, some authors have taken the extreme position that either general relativity or Mach's principle must be abandoned. In this communication we resolve the paradox without abandoning either.