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This book probably suffers to some extent from the fact that it was prepared as a doctorate thesis, for the method of exposition sometimes suggests that Dr. Varendonck was working under the recommendation which the reviewer remembers to have had impressed upon him when he entered for his first examination: 'Assume that the examiners know nothing'. Excellent as this precept may perhaps be for a candidate dealing with (possibly ignorant or prejudiced, but presumably patient) examiners, it is less applicable to an author's dealings with his other readers, for whom the perusal of his book should, we may suppose, be a pleasure and not merely an official duty; as regards whom it may (except in the case of elementary text books) legitimately be assumed that they already know something on the subject of the book; and who (unlike examiners or reviewers) are at liberty to put down the book, should they find it too long-winded for their taste. In the present case the reader will probably feel that the original thesis might very well have been condensed and abbreviated before its presentation to the general public and that the main points which Dr. Varendonck wishes to bring forward would have stood out much more clearly, if their presentation had been less encumbered by long elaboration and illustration of a good many fairly obvious and well known matters. At any rate it may be safely said that the reading of the book would have been made considerably easier, and probably also more profitable, by a judicious arrangement of sub-headings (in the text, not merely in the list of contents) within the five chapters of which the volume is composed, averaging as these do forty closely printed pages apiece.
Having said this much in deprecation of the manner in which the book is written, it is only fair to add that the matter it contains is often of considerable interest. Dr. Varendonck starts with a consideration of what he calls 'Duplicative Memory' (i. e. simple redintegration) a