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108 CKITICAL NOTICES: can at least take care that none escape our notice nor fail of proper record. Of course if means could be devised for making the phe- nomena more experimental, the rate of progress might be greatly accelerated. But even so in view of the resistance which the violent prejudices of the extremists on both sides will continue to offer to a scientific revision of their beliefs, in view of the emotional perturbation which the investigation of such delicate matters seems so often to involve, it would require a sanguine man to expect any settlement of the subject in the next fifty years. F. C. S. SCHILLER. A Treatise on Universal Algebra with Applications. Vol. I. By ALFRED NORTH WHITEHEAD, M.A., Fellow and Lecturer of Trinity College, Cambridge. Cambridge : University Press, 1898. Pp. 586. IN consenting to review this important volume for the readers of MIND I fear I have undertaken a task for which I am but indiffer- ently qualified. My belief, before I received the book, was that it was almost wholly devoted to a discussion of the general principles of symbolic reasoning, with occasional appeals to mathematics and geometrical diagrams by way of illustrations. But this is not the case. Only a comparatively small portion of the work is devoted to what may fairly be called the general principles of symbolic reasoning ; the rest is taken up with ap- plications of these principles, as the author understands them, to the elucidation of Grassmann's Calculus of Extension. Now, of the latter work I know nothing except what I have been able to learn from Mr. Whitehead's presentation of it, and from a few references to it by other writers. So far as I can judge from these data, Mr. Whitehead has rendered great service to science by reducing to a comparatively simple and workable form a method of research which, as originally presented by its inventor, was, from all accounts, extremely obscure and difficult to apply. In forming an opinion on the first portion of Mr. Whitehead's work (especially book ii., which treats of Symbolic Logic) I feel myself on surer and more familiar ground. Yet even here I find myself somewhat in a difficulty. Mr. Whitehead and I regard the subject of Symbolic Logic from different standpoints ; and this fact renders it no easy matter for me to do full justice to his work. Alone, or nearly so, among logicians, I have always held the opinion, and my recent studies have confirmed it, that the simplest and the most effective system of Symbolic Logic is that whose elementary constituent symbols denote not classes, not properties, not numbers, ratios, regions, or magnitudes, not things