We are so familiar with this “fibrous” structure of the natural world that it seems almost a matter of course. Mill, for example, assumes it, unconsciously no doubt, through all his exposition of inductive methods: and if he had not assumed it, these methods would have come tumbling about his ears in irreparable ruin. But assuredly neither he nor any other logician has a right to make such an assumption in silence. In spite of many speculative difficulties, there is no principle more vital to knowledge, practical and theoretical, than the principle of “negligibility”; the principle which asserts that sequences can be isolated and repeated, and that vast bodies of contemporaneous facts and happenings may be wholly neglected. It is much more important than the principle of causation, if by causation is meant, not a working, though possibly imperfect, regularity, but the speculative completeness implied by the phrase “universal causation” as commonly interpreted. It may be said, and I think with truth, that these observations scarcely apply to a material world conceived in a purely mechanical fashion. In such a world negligibility is theoretically measurable. The mass of Sirius, without doubt, modifies the weight of the pen with which I am writing. But the effect is demonstrably infinitesimal, and negligibility is not assumed, but proved. Laplace’s calculator, surveying the universe, would have no difficulty either in fixing his attention on particular repetitions which exemplify the “laws of nature,” or in regarding them as integral parts of a single mechanical whole, whose successive phases (if the law of energy dissipation be universal) can never be repeated.