events , , , ... which may be regarded as "aspects" of the proton, and are related to each other more or less in the way in which the appearances of the proton from different places would be related if the electron could see. Similarly let us assume a series of events , , , ... compresent with but not with each other, analogous to what would be appearances of the electron to the proton if the proton could see. And let us further suppose that, after a certain set[Pg 348] of such events, an exactly similar set recurs, or a very approximately similar set. This supposition provides us with the material required for a periodic relative motion. We shall say, therefore, not that perspectives differ because spatial relations change, but that change in spatial relations consists of systematic alteration in perspectives. Such a view is feasible, but it makes similarity and difference of quality essential. It ceases to be fantastic if we drop the analogy with vision except as regards purely formal characteristics. Let us now set forth the analysis of a periodic process suggested by the above, bringing it into relation with the construction of points in Chapter XXVIII. Let us assume, to begin with, that the process is discrete; this hypothesis can be dropped later, but simplifies the initial statement. Suppose, for the sake of illustration, that there are ten qualities, , , ... , and that there exist events which are subject to the following conditions: (1) , a, , ... have the quality : , , ... have the quality etc. (2) Each of the 's is compresent with its immediate neighbour to left and right, but with none of the other 's; (3) If , any point of space-time of which but not is a member has a time-like interval from any point of which but not is a member. In that case, the series of 's constitutes a periodic process, having ten 's in each period. The last digit in the suffix of an indicates the quality of the —i.e. if the last digit is , the quality is —while the remaining digits indicate the number of the period. If all the 's are events in the history of one piece of matter, that piece of matter is undergoing the periodic process. If there is a correlative series of 's in another piece of matter,[Pg 349] the two periodic processes together make up one relative motion of a periodic character, such as the revolution of an electron about a proton. Generalizing the above, while still assuming that the process is discrete, suppose we have qualities , ... , and a set of events where, as before, the last suffix indicates the quality, i.e. has the quality (). Suppose, also, that each is compresent with of its predecessors and of its successors, where ; but that no is compresent with any except these. The remaining assumptions are to be as before. Then again we obtain a rhythm which may be regarded as an analysis of periodic processes in physics.