512 HUGH MACCOLL : though not equally, perhaps, or at all, on all the substances of other worlds beyond our ken ; so that, in comparison with some constant standard unit lying hidden in some infinitely distant sphere, the dimensions of everything in our visible universe of the sun, of the moon, of the earth, of its mountains, oceans, seas and rivers, of the houses upon its surface, and of the inhabitants who live in them, our own selves included, may be rapidly diminishing, 1 and in nearly the same relative proportions, so that the actual size of each one of us to-day may, in comparison with this constant unit, be only the hundredth or the millionth part of what he or she was yesterday. Personally I believe the actual variation to be much less serious ; but this is an opinion for which, as for other cherished convictions, I can find no logical foundation. 12. Let us now examine the meanings of the words finite, infinite and infinitesimal in reference to time. Here too we have the actual and the ideal, and, as in the case of space, the ideal is easier to deal with than the actual. Actual time is measured by clocks and watches, and the correctness of these is tested by observations of the motions, or apparent motions, of the sun, moon and stars ; but the respective motions of these, when mutually compared, are not uniform ; so we take the apparent motion of one of them, the sun, and dividing its cycle into a certain number of equal parts, we take one of these as our constant unit of reference. For all practical purposes this answers all our needs ; but what of the assumptions on which this theory of time is founded ? How do we know that these solar cycles are even approxi- mately equal '? How do we know that, in comparison with some other unit of time, depending, say, upon the more uniform motion of some other heavenly body, far away in space beyond our power ever to discover, the motions of all the heavenly bodies, of our clocks, of our watches, of every- thing we know, including our very thoughts and sensations, may not be rapidly increasing in velocity, and in nearly the same relative proportions, so that, when measured by this standard unit, our years, days, hours, minutes and seconds, and, consequently, the duration of our lives may be infinites- imal in comparison with the years, days, hours, etc., and the duration of the lives of our fathers or grandfathers ? The paradox arising from the possible variation of our standard and unit of space has thus its counterpart in the paradox 1 Of course it is equally possible that the variation may be in the oppo- site direction.
