96— current definitions of,98-100— denied legitimate anchorage,265— determined by consciousness,145— does not explain spiritualism,155— evolution of the fourth,44— fourth, direction of,134— as "jack of all trades,"156— impossible to actualize,124— key, to non-Euclidean geometry,90— movement of a plane into,147-8— no motion of material masses into,125— nota priori,116— proof of the existence of the fourth,136Dimensionality, and the intellect,200— as dependent upon the will of the investigator,95Dimensionality, conception of, purely conventional,92— logical difficulties which beset,97— of perceptual space,72— — space, the four,142-3Dimensions, four, no basis in consciousness for,172— piled upon one another,300— vanity, the, of segmenting space into many,299Direction as dimension,99Disappointment with the sensible world,120-1Discoveries, metageometrical, as excrescences of mental unfoldment,131— never the result of methodic reflection,29-30Disorder, the edict of, and space,230Disorderliness, the fringe of,277Dispossessal of the intellect by the intuition,195Dissimilarities, besetment of,291Distinctions, between conceptual and perceptual space, fundamental,73-5Diversity, a result of the fragmentative tendency of life,6— as transfinite quantity,42Divinity, prize of, won by the intellect,43Duadic phase of evolution,210-1Duodim, defined,6;128,129,134,177— consciousness,163Duopyknon,212,213— the meaning of,6Duopyknosis,208-10,218— as a stage in the evolution of space,6Duration and space,224— eternal,234Dynamic appearance, space as,104,107Dynamism, of the intellect, functional,303EEarth, the nebulous youth of,335— a new,358East effloresces as West,306Ego, the,270— and percepts,244— as sovereign,244— Thinker's dependence upon,245— — treatment of,246Egopsyche,265— as an agency of self-consciousness,258— defined,7Egos, compared to choppy sea,256-7Egypt, birth-place of geometry,44Eisenlohr,44Elaborative period of the non-Euclidean geometry,66-70— — of mental development,31-32Element of evolution, basal,259Elements of the non-Euclidean geometry,79-80Elephant and blind men,257Ellis, Wilmot E., on ether as four-dimensional,157-9Embrace of direct cognition,205Engenderment of space,260Ensoulment of the world-plasm,329Entities, hyperspace, and the phenomenal world,128-130Enumeration, reformation of the system of,38Enveilment of consciousness,273-4Environment, artificial and natural,162Epiphysis, the,345Equidistantial, described by hyperspatial perpendicular,80Essence, elemental, as world-plasm,329Ether as possessing fourth dimensional characteristics,157Ethics recast in a new mold,358Euclid,46,70,83,263— and the parallel-postulate,45— never-dying elements of,53Evidences, mathematical, exemplifies intellectual evolution, x— the vanity of fragmentary,204Evolution, a continuous process,327— and the norms of reality,175— basal element of,259— commencement of,232-3— intellectual, forward movement of,184— kosmic, vicissitudes of,215— laws of, govern mind,28— mental, results of,122— of faculties, synchronous with evolution of matter,332— — material characteristics of the earth,335— — organs, time required for,188— preparation of the field of,218Exaltation of matter into spirit,329Examples of new perceptive evidences,341-3Existence on a higher plane, states of,162Experience, corroborative testimony of, denied hyperspace,263— prior, and conception,25Experiences, spatial, systematization of,78Extension, space as an unbounded,61Extra-spatiality, degraded into spatiality,261Extravaganza, mathematical, and the fourth dimension,156Eyes, as Roentgen rays,353FFact-mass,289Factors of conscious determinations,162— four, of the criterion of truth,324-5Facts as facets of truth,284— attempts to reform,304— logic as symbolism of,287— — the modeler of,288Faculties, dual derivation of,162— evolution of, synchronous with evolution of material qualities,332,ff— extended,239— foreshadowed by the hyperdimensional,131— higher, man must win his way to,357— new faculties evidenced by four-space,24-29— rudimentary nature of,341,ff— the source of,349Faculty and the intellect,247,ff— as transmissible character,251— determined by function,336— greatly extended,117— higher than the intellect,126— I-making, self-consciousness as,243— intuitive,185— of perception in higher worlds,353— — awareness, the awakening of,89-91— overshadowed by the intellect,188— of perception in higher worlds,353— rudimentary condition of,192,ffFaculty, outcropping of,249-51Failure of efforts to justify the objective existence of four-space,125-6Failures at solving the parallel-postulate, outcome of,48,83Faith, dispossessed by knowledge,358Fay, mathetic,160Fechner,39Finity and unboundedness of space,76Flammarion, Camille,341-2,344Flexity, as property of hyperspace,63Flexure, space as a,305Fluxional, between sense objects and ideal representations,122-3Fluxion, psychic, as difference between memory image and object,7-8;122Focus of consciousness,163,290— — the intellect,310Fohat, and the creation of morphons,219— as creative energy,213— Creator,8Fohatic energy,226Form, as vehicle of life,330— definition of,8— driven back over the path of its genesis,327— pure, cannot exist in nature,294— the idealty of,110— the universe not a pure,108Formative period of mental development,31— — of non-Euclidean geometry,55Formula, eight different alcohols from one,155Four-dimensionality, justification of,176Four-space, a curiosity of analytics,40— and Riemann,27— as a divertisement,175— consciousness does not act in the,172— existence of, denied,171-2— movement of matter in,157— reality of, glibly proclaimed,154— the,8,240— — denizens of,353— — domain of,154— — study of,124— use of analogies to popularize,128Fourth dimension, analogical reasoning of,177-9— as a transcendental problem,140— — an attitude of the intellect,200— electric current as a component in,153— imaginability of,106-7— Simon Newcomb on,125Fragmentariness of the intellectual method,164Fragmentary view of the universe,260Fragmentation, tendency to,296— harks back to cell-division,301Freedom, a new,338— determined by absence of bonds,280— mathematical,60— mental,66-7— now dawning for the mind,32— of consciousness ingenus homo,332— regal freedom of the mind,118— three degrees of,125— unrealizable, for the Thinker,255Fringe, chaogenetic,308,309— of disorderliness,257— — kathekosity,229Frischauf,66Full, the universe as a,310Function determines faculty,336Functions back of latent faculties, indefinite,343— cellular and histologic,253Functioning, instinctive, of the intellect,289Fundamentals, totality of, kosmic,265GGamut of realism,169Gauge, awareness as a,161-202Gauss, Charles Frederick,8-9,56-8,59,174— — — as formulator of the non-Euclidean geometry,57Geminos of Rhodes,45,52Generability, as property of space,62— of hyperspace, Keyser on,144— — space by lines,143Generation, the, of the hypercube,134— of the hypertetrahedron,135-6Genesis, of space,211,227,ff— — the earth, its nebulous youth,335— — — form,327— — — sensible world,167Genus homo, freedom of consciousness in,332Geometricity,266Geometries, non-Euclidean, based upon a negation of the latent geometrism,262-3— three possible,54Geometrism, engenderment of,262— established by life,264— kosmic geometrism, establishment of,231— latent,257— native geometrism of space,262— rediscovered by the intellect,9-10Geometrism, the basis of,237,261Geometry, anti-Euclidean,69— and the study of magnitudes in space,203— artificial,262-4— a two-fold,59— breakdown of,266— determinative period of the non-Euclidean,61-4— diverse systems of,323— Euclid's Elements of,53-4— formal bulwarks of,77-9—Imaginary Geometry, The,60— natural geometry,261— Plato and the divine geometry,193— possible systems of,174— radical essence of pure,85Geometry, non-Euclidean, at variance with the parallel-postulate,83-5— — based upon a misconception,91— — determined by qualitative differences,140— — elaborative period of,66-70— — first published treatise on,60— — formative period of,55— — the final issue of,88-9— — growth and development of,92— — invalidation of,174— — key to,90— Lambert's Non-Euclidean geometry,note,51— — popularization of,66-7— — Schweikart's treatise on,59— — self-consistence of,57— — some elements of,79-80— — superperceptual knowledge of,72Geometry, non-Legendrean,70— symbolic, and commensurable quality,145Gerling, as correspondent of Gauss,58Germ-plasm, continuity of,260Giantism,347Glimpse, a, of the reality of space,314Glorification of the flesh,227Groups, transformation, discovery of,30Guide-posts to a new domain,273,277Gulf, interposed between manifestation and non-manifestation,206HHalley, memoir of, mastered by La Grange,50Halstead, G. B.,note,49,66;note,79Heindel, Max,note,353Helmholtz,39,66Hewer, the, of the concrete, the intellect as,295Hinton, C. H.,154— on the fourth dimension,153History, the, of mind, three great epochs of,31-32Homogeneity, the, of realism,165Hoüel, J.,60,66Hudson,344Humanity and the exalting power of life,331,ffHypercube, boundaries of, and mirrors,136-9— the generation of,134,145Hyperdimensional, as a prophecy of new faculties,131Hyperspace,175— a monument to the intellect,356— and the involved procedure of arriving at a recognition of its relations,73— and the passage thither,293,ffHyperspace as a figurative mountain-peak,200— — — movement,44-68— — an all-powerful something,160— — — idealized construction,10— — evidence of new faculties,24— —ignes fatuii,154— — illusion,202— a symbol of higher consciousness,180-4— concept of, as an evolutionary quantity,44-5— confounded with real space,91— creation of,335— denied the corroborative testimony of experience,263— direction of, baffling to mathematicians,146— discovery of, a sign of mental evolution,180— domain of, a fairy-land,239— magnitudes of, the non-sensuous,72— mysterious hiding place in,129— the logical difficulties of,139-141— the six pillars of,62-3Hyperspatiality as the toys of childhood,241Hypertetrahedron, the,135Hypertrophy of the pituitary body,347Hypervolume, the,134Hypothesis, a superfoetated,141— four-space, utility of,129;154Hypotheses, admissibility of,118— incompatibility of the non-Euclidean,67;71— Riemannian,80— solution of, Bolyai,31Hyslop, James H., on the logical difficulties of hyperspace,139-141IIcosahedron, examination of the,285Ideal, and the real, kosmic chasm between,107— perceptual value of,275,ffIdeas and words as symbols,126-7— Malebranche on,222— realism of,24-35— the symbolism of,205Identification of consciousness with being,205-6— with the objects of study,189-90Identity of things-in-themselves,