that the wonders and subtleties of possible existence surpass all that our mental powers allow us clearly to perceive. The study of abstract logical and mathematical forms has seemed to convince me that even space itself is no requisite condition of conceivable existence. Everything, we are told by materialists, must be here or there, nearer or further, before or after. I deny thisand point to logical relations as my proof. There formerly seemed to me to be something highly mysterious in the denominators of the binomial expansion (vol. i. p. 216) which are reproduced in that strange natural constant e, or and in many results of mathematical analysis. I now perceive, as already partially explained (vol. i. pp. 40-42, 180, 181, 443, 444), that they arise out of the fact that the relations of space do not apply to the logical conditions which govern the numbers of combinations as contrasted to those of permutations. So far am I from accepting Kant's doctrine that space is a necessary form of thought, that I regard it as an accident, and an impediment to pure logical reasoning. Material existences must exist in space no doubt, but intellectual existences may be neither in space nor out of space; they may have no relation to space at all, just as space itself has no relation to time. For all that I can see, then, there may be intellectual existences to which both time and space are nullities. Now among the most unquestionable rules of Scientific Method is that first law that whatever phenomenon is, is. We must ignore no existence whatever; we may variously interpret or explain its meaning and origin, but if a phenomenon does exist it demands some kind of explanation. If then there is to be a competition for scientific recog nition, the world without us must yield to the undoubted existence of the spirit within. Our own hopes and wishes and determinations are the most undoubted phenomena within the sphere of consciousness. If men do act, feel, and live as if they were not merely the brief products of a casual conjunction of atoms, but the instruments of a farreaching purpose, are we to record all other phenomena and pass over these? We investigate the instincts of the ant and the bee and the beaver, and discover that they are led by an inscrutable agency to work towards a distant purpose. Let us be faithful to our scientific method, and investigate also those instincts of the human mind, by which man is led to work as if the approval of a Higher Being were the aim of life. THE END. INDEX. ABACUS, the logical, i. 119; Briggs', Academie del Cimento, ii. 36, 42, 46. Airy, Sir George Biddel, ii. 171, 174, Alphabet, permutations of, i. 196, 203. Analogy, ii. 244, 283; in sign of equality, i. 18; use of, ii. 140; use in discovery, Antecedent defined, i. 258. Apparent equality, i, 319; sequence of Approximation, principles of, ii. 92; to Aqueous vapour, ii. 126. 82. Arago, photometer, i. 335; rotating disc, Archimedes, de arena numero, i. 222; Aristotle, dictum, i. 26; overlooked Arithmetic, reasoning in, i. 188; of ap- Atmospheric tides, ii. 192. Atoms, ii. 10; size of, i. 222; weights Augustin, on time, i. 359. Average, i. 417; divergence from, 213; B. Babbage, Charles, ii. 455; calculating Bacon, Francis, biliteral cipher, i. 220; Bacon, Roger, on rainbow, ii. 159, 247. E energy, ii. 83, 431. sense of, ii. 117; detection quantity, ii. 108. ive propositions, i. 100, 101. 2. 19. lar theory, ii. 150, 173, 304. Roger, means, i. 416; method mechanical, ii. 318. on, i. 170; ii. 416. allography, i. 153; ii. 162, 184, 1, 319, 359, 398, 450. als, pseudomorphic, ii. 324. es, nature of, ii. 99; discovery of, 15. ier, i. 355; ii. 31. nite, ii. 261. cloid, ii. 291. D. Alembert, probability, i. 244, 245; alton, laws of, ii. 82, 91, 274, 329. Decandolle's system, ii. 387. De Morgan, sign of equality, i. 18; Density, unity of, i. 371; of earth, ii. 207; negative, 304. Depth of oceans, i. 347. Descartes, ii. 135, 290. Diamond, ii. 159, 261. Difference, law of, i. 6, 87, 95; sign of, Differential calculus, ii. 99; thermo- Diffraction of light, ii. 27. Discoveries, accidental, ii. 162; pre- Disjunctive terms, i. 79; conjunction, Donkin, i. 226, 227, 243, 248. Draper's law, ii. 257. E. Eclipses, i. 343; ii. 322. Electricity, ii. 163, 187, 237, 264; unit Electro-magnetism, ii. 164. Elements, classification of, ii. 347, 349, Ellicott, on Clocks, ii. 70. ii. 14. Empirical knowledge, ii. 132, 157, 158; Encke, Comet, i. 363; ii. 212; law of error, i. 445; mean, 449; resisting Energy, unit of, i. 376; conservation Equality, i. 56, 183; sign of, 18; Error, function, i. 382; avoidance of, |