Maxwell's manuscripts held at Cambridge University Library contain several items of interest from a control or stability point of view. The extracts reproduced in Part III consist mainly of a draft of the second half of Maxwell's essay on the stability of the motion of Saturn's rings. Here Maxwell investigates the stability of a fluid ring rotating round a centre of attraction. Two related letters written by Maxwell are also reproduced. Maxwell's claim to the effect that a ring of equally spaced satellites, with equal sufficiently small masses, represents a stable configuration, is shown to be erroneous.