In his recent _Introduction to Mathematics_[7] Dr. Whitehead has pointed out how the "whole life of Nature is dominated by the existence of periodic events." The rotation of the earth produces successive days; the path of the earth round the sun leads to the yearly recurrence of the seasons; the phases of the moon are recurrent, and though artificial light has made these phases pass almost unnoticed to-day, in climates where the skies are clear, human life was largely influenced by moonlight. Even our own bodily life, with its recurrent heart-beats and breathings, is essentially periodic.[8] The presupposition of periodicity is indeed fundamental to our very conception of life, and but for periodicity the very means of measuring time as a quantity would be absent. Periodicity is fundamental to certain departments of mathematics, that is evident; it is perhaps less evident that periodicity is a factor that has gone to the making of ritual, and hence, as we shall see, of art. And yet this is manifestly the case. All primitive calendars are ritual calendars, successions of feast-days, a patchwork of days of different quality and character recurring; pattern at least is based on periodicity. But there is another and perhaps more important way in which periodicity affects and in a sense causes ritual. We have seen already that out of the space between an impulse and a reaction there arises an idea or "presentation." A "presentation" is, indeed, it would seem, in its final analysis, only a delayed, intensified desire--a desire of which the active satisfaction is blocked, and which runs over into a "presentation." An image conceived "presented," what we call an _idea_ is, as it were, an act prefigured. Ritual acts, then, which depend on the periodicity of the seasons are acts necessarily delayed. The thing delayed, expected, waited for, is more and more a source of value, more and more apt to precipitate into what we call an idea, which is in reality but the projected shadow of an unaccomplished action. More beautiful it may be, but comparatively bloodless, yet capable in its turn of acting as an initial motor impulse in the cycle of activity. It will later (p. 70) be seen that these periodic festivals are the stuff of which those faded, unaccomplished actions and desires which we call gods--Attis, Osiris, Dionysos--are made. * * * * *