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The structure of a statisiical system of particles satisfying the cosmological postulate is examined from the standpoint of the kinematics developed iii the two previous parts of this paper. It is found to depend on a single arbitrary function x of two variables, in addition to the constant k and the function ~ of one variable, which specify the kinematical background of the idealized space-time. The distribution function x is interpreted as a significant constani of the moUon; and the complete determination of the entire system is discussed on imposing (a), the general relativistic theory of gravi- tation; (b), the extension of the Newtonian theory discussed in Part II; and (c), the kinematical-statistical theory proposed by E. A. Milne. The conclusions, if not actually favorable to the relativistic theory, at least nuffify certain formal objections which have been raised against it
H. P. Robertson (Fri,) studied this question.