research to apprehend, have originated with what was wholly ignorant of all quantitative relations? Or must not the order of the universe be due to a mind whose thoughts as to these relations are high above even those of the profoundest mathematicians, as are the heavens above the earth? If the universe were created by an intelligence conversant with quantitative truth, it is easy to understand why it should be ruled by definitely quantitative laws; but that there should be such laws in a universe which did not originate in intelligence, is not only inexplicable but inconceivably improbable. There is not merely in that case no discoverable reason why there should be any numerically definite law in nature, but the probability of there being no law or numerical regularity of any kind is exceedingly great, and of there being no law-governed universe incalculably great. Apart from the supposition of a Supreme Intelligence, the chances in favour of disorder against order, of chaos against cosmos, of the numerically indefinite and inconstant against the definite and constant, must be pronounced all but infinite. The belief in a Divine Reason is alone capable of rendering rational the fact that mathematical truths are realised in the material world.[21] [21] See Appendix XIII. The celestial bodies were among the earliest objects of science, and before there was any science they stimulated religious thought and awakened religious feeling. The sun and moon have given rise to so extraordinary a number of myths that some authors have referred to them the whole of heathen mythology. There can be little doubt that the growth of astronomical knowledge contributed greatly to bring about the transition from polytheism to monotheism, and that so soon as the heavens were clearly understood to be subject to law, and the countless bodies which circle in them not to be independent agents but parts or members of a single mechanical or organic system, the triumph of the latter was for ever secured. No science, indeed, has hitherto had so much influence on man's religious beliefs as astronomy, although there may now appear to be indications that chemistry and biology will rival it in this respect in the future. And it has been thus influential chiefly because through its whole history it has been a continuous, conspicuous, and ever-advancing, ever-expanding demonstration of a reign of law on the most magnificent scale,--a demonstration begun when with unassisted vision men first attempted roughly to distribute the stars into groups or constellations, and far from yet ended when the same laws of gravitation, light, heat, and chemical combination which rule on earth have been proved to rule on orbs so distant that their rays do not reach us in a thousand years. The system of which our earth is a member is vast, varied, and orderly, the planets and satellites of which it is composed being so adjusted as regards magnitude and