ABSTRACT

Let t be a one-dimensional continuous series, s a three-dimensional continuous series, which we will not assume to be Euclidean as yet. If R be a many-one relation whose domain is t and whose converse domain is contained in s, then R defines a motion of a material particle. The indestructibility and ingenerability of matter are expressed in the fact that R has the whole of t for its field. Let us assume further that R defines a continuous function in s.