The physical universe has, perhaps, no more general characteristic than this,--its laws are mathematical relations. The law of gravitation, which rules all masses of matter, great or small, heavy or light, at all distances, is a definite numerical law. The curves which the heavenly bodies describe under the influence of that law are the ellipse, circle, parabola, and hyperbola--or, in other words, they all belong to the class of curves called conic sections, the properties of which mathematicians had begun to investigate nearly twenty centuries before Newton established that whatever was true of them might be directly transferred to the heavens, since the planets revolve in ellipses, the satellites of Jupiter in circles, and the comets in elliptical, parabolic, and hyperbolic orbits. The law of chemical combination, through which the whole world of matter has been built up out of a few elements, always admits of precise numerical expression. So does the law of the correlation of heat and gravitation. Each colour in the rainbow is due to a certain number of vibrations in a given time; so is each note in the scale of harmony. Each crystal is a geometrical construction. The pistils of flowers, and the feathers in the wings and tails of birds, are all numbered. If nature had not thus been ruled by numerical laws, the mathematical sciences might have existed, but they would have had no other use than to exercise the intellect, whereas they have been the great instruments of physical investigation. They are the creations of a mental power which, while occupied in their origination and elaboration, requires to borrow little, if anything, from matter; and yet, it is only with their help that the constitution of the material universe has been displayed, and its laws have been discovered, with that high measure of success of which physicists are so proud. But they could not have been applied to the universe at all unless its order had been of the exact numerical and geometrical kind which has been indicated; unless masses had attracted each other, and elements combined with each other, in invariable proportions; unless "the waters had been measured as if in the hollow of a hand, the heaven meted out as with a span, the dust of the earth comprehended in a measure, and the mountains weighed in scales and the hills in a balance." Now it is possible to deny that things have been thus weighed, measured, and numbered by a Creative Intelligence, but not that they have been weighed, measured, and numbered. If we are to give any credit to science, there can be no doubt about the weights and measures and numbers. This question, then, is alone left,--Could anything else than intelligence thus weigh, measure, and number? Could mere matter know the abstrusest properties of space and time and number, so as to obey them in the wondrous way it does? Could what has taken so much mathematical knowledge and 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]