“_Those in search of mental gymnastics will find abundance of exercise in Mr. C. H. Hinton’s_ Fourth Dimension.”—WESTMINSTER REVIEW. FIRST EDITION, _April 1904_; SECOND EDITION, _May 1906_. Views of the Tessaract. No. 1. No. 2. No. 3. No. 4. No. 5. No. 6. No. 7. No. 8. No. 9. No. 10. No. 11. No. 12. THE FOURTH DIMENSION BY C. HOWARD HINTON, M.A. AUTHOR OF “SCIENTIFIC ROMANCES” “A NEW ERA OF THOUGHT,” ETC., ETC. [Illustration: Colophon] LONDON SWAN SONNENSCHEIN & CO., LIMITED 25 HIGH STREET, BLOOMSBURY 1906 PRINTED BY HAZELL, WATSON AND VINEY, LD., LONDON AND AYLESBURY. PREFACE I have endeavoured to present the subject of the higher dimensionality of space in a clear manner, devoid of mathematical subtleties and technicalities. In order to engage the interest of the reader, I have in the earlier chapters dwelt on the perspective the hypothesis of a fourth dimension opens, and have treated of the many connections there are between this hypothesis and the ordinary topics of our thoughts. A lack of mathematical knowledge will prove of no disadvantage to the reader, for I have used no mathematical processes of reasoning. I have taken the view that the space which we ordinarily think of, the space of real things (which I would call permeable matter), is different from the space treated of by mathematics. Mathematics will tell us a great deal about space, just as the atomic theory will tell us a great deal about the chemical combinations of bodies. But after all, a theory is not precisely equivalent to the subject with regard to which it is held. There is an opening, therefore, from the side of our ordinary space perceptions for a simple, altogether rational, mechanical, and observational way of treating this subject of higher space, and of this opportunity I have availed myself. The details introduced in the earlier chapters, especially in Chapters VIII., IX., X., may perhaps be found wearisome. They are of no essential importance in the main line of argument, and if left till Chapters XI. and XII. have been read, will be found to afford interesting and obvious illustrations of the properties discussed in the later chapters.