Hinton - The Fourth Dimension.pdf

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230 THE FOURTH DIMENSION If we suppose the ether to be filled with vortices in the shape of four-dimensional spheres rotating with the A motion, the B motion would correspond to electricity in the one-fluid theory. There would thus be a possibility of electricity existing in two forms, statically, by itself, and combined with the universal motion, in the form of a current. To arrive at a definite conclusion it will be necessary to investigate the resultant pressures which accompany the collocation of solid vortices with surface ones. To recapitulate: The movements and mechanics of four-dimensional space are definite and intelligible. A vortex with a surface as its axis affords a geometric image of a closed circuit, and there are rotations which by their polarity afford a possible definition of statical electricity.
APPENDIX I THE MODELS IN Chapter XI. a description has been given which will enable any one to make a set of models illustrative of the tesseract and its properties. The set here supposed to be employed consists of:— 1. Three sets of twenty-seven cubes each. 2. Twenty-seven slabs. 3. Twelve cubes with points, lines, faces, distinguished by colours, which will be called the catalogue cubes. The preparation of the twelve catalogue cubes involves the expenditure of a considerable amount of time. It is advantageous to use them, but they can be replaced by the drawing of the views of the tesseract or by a reference to figs. 103, 104, 105, 106 of the text. The slabs are coloured like the twenty-seven cubes of the first cubic block in fig. 101, the one with red, white, yellow axes. The colours of the three sets of twenty-seven cubes are those of the cubes shown in fig. 101. The slabs are used to form the representation of a cube in a plane, and can well be dispensed with by any one who is accustomed to deal with solid figures. But the whole theory depends on a careful observation of how the cube would be represented by these slabs. In the first step, that of forming a clear idea how a 231
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THE FOURTH DIMENSION
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THE FOURTH DIMENSION BY C. HOWARD H
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PREFACE I HAVE endeavoured to prese
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CONTENTS CHAP. PAGE. I. FOUR-DIMENS
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THE FOURTH DIMENSION ————
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FOUR-DIMENSIONAL SPACE 3 existence
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FOUR-DIMENSIONAL SPACE 5 Bringing i
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THE ANALOGY OF A PLANE WORLD 7 him.
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THE ANALOGY OF A PLANE WORLD 9 to a
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THE ANALOGY OF A PLANE WORLD 11 Aga
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THE ANALOGY OF A PLANE WORLD 13 sec
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CHAPTER III THE SIGNIFICANCE OF A F
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SIGNIFICANCE OF A FOUR-DIMENSIONAL
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CHAPTER IV THE FIRST CHAPTER IN THE
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THE FIRST CHAPTER IN THE HISTORY OF
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CHAPTER V THE SECOND CHAPTER IN THE
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SECOND CHAPTER IN THE HISTORY OF FO
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CHAPTER VI THE HIGHER WORLD IT is i
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THE HIGHER WORLD 63 dimensions. His
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THE HIGHER WORLD 65 If now he turns
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THE HIGHER WORLD 67 to him that, by
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THE HIGHER WORLD 69 simply the plan
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THE HIGHER WORLD 71 turn these rods
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THE HIGHER WORLD 73 revolution, the
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THE HIGHER WORLD 75 the mode of act
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THE EVIDENCES FOR A FOURTH DIMENSIO
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CHAPTER VIII THE USE OF FOUR DIMENS
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5 THE USE OF FOUR DIMENSIONS IN THO
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THE USE OF FOUR DIMENSIONS IN THOUG
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CHAPTER IX APPLICATION TO KANT’S
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APPLICATION TO KANT’S THEORY OF E
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3 APPLICATION TO KANT’S THEORY OF
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A FOUR-DIMENSIONAL FIGURE 123 The r
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A FOUR-DIMENSIONAL FIGURE 125 new d
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A FOUR-DIMENSIONAL FIGURE 127 pick
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A FOUR-DIMENSIONAL FIGURE 129 Now s
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A FOUR-DIMENSIONAL FIGURE 131 of me
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A FOUR-DIMENSIONAL FIGURE 133 note
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A FOUR-DIMENSIONAL FIGURE 135 These
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NOMENCLATURE AND ANALOGIES 137 to a
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NOMENCLATURE AND ANALOGIES 139 null
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NOMENCLATURE AND ANALOGIES 141 laye
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NOMENCLATURE AND ANALOGIES 143 a li
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NOMENCLATURE AND ANALOGIES 145 oppo
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NOMENCLATURE AND ANALOGIES 147 the
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NOMENCLATURE AND ANALOGIES 149 dime
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NOMENCLATURE AND ANALOGIES 151 larg
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NOMENCLATURE AND ANALOGIES 153 axes
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NOMENCLATURE AND ANALOGIES 155 lie
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CHAPTER XII THE SIMPLEST FOUR-DIMEN
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THE SIMPLEST FOUR-DIMENSIONAL SOLID
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Purple Red THE SIMPLEST FOUR-DIMENS
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Light blue Gren Light purple THE SI
Page 189 and 190: REMARKS ON THE FIGURES 179 ochre cu
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Page 213 and 214: CHAPTER XIV * A RECAPITULATION AND
Page 215 and 216: RECAPITULATION AND EXTENSION 205 ou
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Page 257 and 258: APPENDIX I: THE MODELS 247 sponding
Page 259 and 260: APPENDIX II: A LANGUAGE OF SPACE 24
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