The fourth dimension

vi PREFACE

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.

My thanks are due to the friends who have assisted me in designing and preparing the modifications of my previous models, and in no small degree to the publisher of this volume, Mr. Sonnenschein, to whose unique appreciation of the line of thought of this, as of my former essays, their publication is owing. By the provision of a coloured plate, in addition to the other illustrations, he has added greatly to the convenience of the reader.

C. Howarp Huyton.