the story of the thirteen duels which John Bolyai accepted, fought, and won successively with the mere interlude of a violin-solo. On the other hand, although neither our use nor our understanding of logarithms is helped by the knowledge that Napier conceived the idea of them before exponents were used, and developed them wholly from geometrical and fluxional considerations, yet as an indication of the way in which science has grown up, nothing could be more instructive.

On the first of these points Professor Cajori lays some stress, not omitting to emphasise also the importance of the history of mathematics as a repository of the errors of the past, which if known can be avoided.

Professor Cajori's book is, as he calls it, a brief general history of mathematics. One must not expect to find in it a new treatment nor the embodiment of new views regarding the theory or the mode of development of knowledge. He relies, on this score, and especially in the earlier parts of the work, on the books and opinions of other investigators rather than on the subject-matter itself, and in some instances is uncritical on the philosophical side of the questions. For example, on that old crux, Why the Greeks made no progress in Mechanics, Physics, etc., he cites Whewell's theory that it was due to their not having "distinct and appropriate ideas"; which, since that is the very problem, is not calculated to throw much light on the ancient stagnancy in science. Perhaps, also, more references to the literature which contests the philosophical foundations of the Gauss and Riemann mathematical metaphysics might be given, for nothing, perhaps, needs more the curb of philosophical criticism than just this branch of speculation. But a small book cannot be an encyclopædia of the formal sciences, and our remarks, far from aspersing the character and merit of Professor Cajori's work, will go merely to show its scope and purpose. Its style is vivid and terse, and in mechanical execution and arrangement of matter the book attains a high standard. Undoubtedly, as a manual and handy book of reference it will fulfil an important office. More especially is this true of the chapter entitled "Recent Times," where, in contradistinction to the early history, much valuable information has been brought together which could hardly be found elsewhere in so compact a form, if at all, in any one book. This is its really valuable feature. It remains to be added, and as forcibly as possibly, that for a book designed to be acceptable to teachers and students" the price is much too high, and that apparently without justification. T. J. MCCORMACK.

PSYCHOLOGY FOR TEACHERS. By C. Lloyd Morgan, Principal of University Col lege, Bristol. London: Edward Arnold. Pages, 251. Price, 3s. 6d. net. The greater part of the fundamental doctrines of this latest book of Professor Morgan's are contained in his Introduction to Comparative Psychology, reviewed by us in the last Monist; and all the excellent qualities of lucidity and animation which marked that work are again displayed here. The book is designed for teachers and aims to show, by a running exposition of the salient points of psychology, how the practical problems of education can be elucidated and furthered by attention to the

results of scientific analysis. The charm of the book lies in the fluency and vivacity of the author's style, as in the breadth and naturalness of his interests. What is offered us are not vague generalisations, but doctrines and facts which appeal to our familiar and best experience. The ten chapters which constitute the book are entitled as follows: States of Consciousness, Association, Experience, Perception, Analysis and Generalisation, Description and Explanation, Mental Development, Language and Thought, Literature, Character and Conduct. Skilful is Professor Morgan's use in these expositions of the idea of a "focus" and "margin" of consciousness, and of the idea of a "mental background." The chapter on literature is admirable, and itself a striking witness of that union of scientific grasp with literary appreciation which the author commends. This book is by long odds the best popular work for persons beginning the subject of pedagogy which we know of, and one which certainly no practical teacher can afford to leave unread. It constituted originally a course of lectures delivered in Edinburgh in connexion with the Summer School of Art and Science, and it should also be mentioned perhaps that Dr. J. G. Fitch, late one of Her Majesty's Chief Inspectors of Training Colleges, has supplied to the book a commendatory preface. T. J. MCC.

LECTURES ON HUMAN AND ANIMAL PSYCHOLOGY. By Wilhelm Wundt. Translated from the Second German Edition by J. E. Creighton and E. B. Titchener. London Swan Sonnenschein & Co. New York: Macmillan & Co. 1894. Pages, 454.

Price, $4.00.

The work from which this translation has been made is the revised and enlarged edition (1892) of Wundt's early popular lectures on psychology, published when the science was merely a “programme for the future" (1862) and necessarily in a very incomplete condition. The present volume, which is substantially a new and modern work, will serve a good purpose in instruction, as an intermediate reading between the first elements and the more technical treatises The translators, who are two assistant professors in the University of Cornell, have acquitted themselves creditably of their arduous task, and it is to be hoped that their success and experience will encourage them to undertake the translation of Wundt's larger work— than which they could render the world no greater service. A superficial glance shows a few oversights in the book. The velocity of light is given (p. 92) as "42, 100 miles" in a second, where German miles not English miles are meant. Also (p. 93) the ambiguous term "billions" might have been replaced by "millions of millions," or by figures. On p. 1 and elsewhere natural philosophy," which in English commonly means physics," and not "' philosophy of nature" in the German sense, hardly gives the right contrast to "natural science." As regards the typography, it was certainly ill-advised to retain the cuts with the German colordesignations, when they might have been replaced at a very small cost.

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should also have had an index.

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The work

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STUDIES FROM THE YALE PSYCHOLOGICAL LABORATORY. Edited by Edward W. Scripture, Ph. D., Instructor in Experimental Psychology, Yale University. New Haven, Conn. Pages, 124. Price, $1.00.

The "studies" of this little volume constitute the second year's work of the Yale Psychological Laboratory. They are chiefly by Mr. Scripture, the contents being as follows: On mean values for direct measurements, by E. W. Scripture; Researches on the mental and physical development of school-children, by J. Allen Gilbert; Remarks on Dr. Gilbert's article, by E. W. Scripture; Experiments on the highest audible tone, by E. W. Scripture and H. F. Smith; On the education of muscular control and power, by E. W. Scripture, T. L. Smith, and E. M. Brown; A psychological method of determining the blind-spot, by E. W. Scripture; Tests of mental ability as exhibited in fencing, by E. W. Scripture. Mr. Scripture's discussion of errors in measurement leaves nothing to be desired in point of mathematical ornamentation. He has submitted his conclusions to three mathematicians, each of whom dissents at some point from his deductions. He says, however, that any value this article may have is due to their patient labor with one who is not a mathematician but who is obliged to use mathematical means to solve practical "problems." Dr. Gilbert's researches on the development of school children present some interesting results, as do also "Tests of mental ability as exhibited in fencing." Mr. Scripture finds "that fencing does not develop mental quickness "more than scientific pursuits, but it does develop to a high degree the rapidity of "executing movements."

SUBSTANCE AND ITS ATTRIBUTES.

Ltd. 1895. Pages, 197.

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London Kegan Paul, Trench, Trübner, & Co.,

The task which the author of this anonymous work has assailed is by no means a puny one, although he has attempted it within a relatively modest compass. He has eviscerated," he claims, the inherent attributes of primitive and essential substance, contending, properly enough, and not advancing the idea for the first time in the history of philosophy, that substance without attributes is a contradiction in terms. He has defined," after his manner, the expressions "spirit" and "matter," tracing their consanguinity and connexion to what he takes to be their obvious natural source. He has also pointed out the "precise source and foundation of physical forces," and that, also, after a manner of his own. He has manifested" the basis of life, "fairly analysed and formally promulged" the great law of causality, and discovered nothing less than a definite foundation for the ego or soul of man as essentially a spirit-entity. He has given "a fresh representation of the Absolute," which bears its epitheton ornans well, propounded a scheme of psychology, which he recommends for "its simplicity and harmony with facts," and, finally, he tells us it will be a sufficient reward and a cause of much rejoicing to him if he shall have contributed in the least by his book to throw down and destroy "one of the most complicated and most mischievous structures ever built up by the

'perverted ingenuity of man-the a priori schemes of Kantian and Hegelian tran"scendentalism," which he characterises as a terrible incubus that has too long enthralled philosophy. Add to this a batch of theological conceptions, which receive putative explanation here, and we shall have approximately the contents of this work. It is a mechanical ontology which has issued from the insight lately offered by science, that most physical phenomena can be represented as modifications of a hypothetical substance called the ether. The ether is the "Universal Sub"stance which exists as an ens by itself, which is the absolute basis of all beinghood, which is uncreated, infinite, eternal, without parts, all-pervading, unseen, that "cannot be displaced, and withal impersonal." As this ether can be anything and everything, the development of a full-fledged ontology from it and a consequent solution of all possible problems offers no material difficulties. But more significant than being just one of the thousand fanciful and possible developments of this insight, it is not. T. J. MCC.

MENTAL DEVELOPMENT IN THE CHILD AND THE RACE. Methods and Processes By James Mark Baldwin, M. A., Ph. D., Stuart Professor of Psychology in Princeton University. With Seventeen Figures and Ten Tables. New York and London: Macmillan & Co. 1895. Pages, 496. Price, $2.60. "Every philosopher who becomes a father," said Max Müller once, "imagines himself de ipso facto in possession of the secrets of the origin of language and mind"—or, at least something to that effect. Professor Baldwin justly repudiates this disparaging insinuation, and with commendable heroism and an indomitable zeal for the truth accepts the derogatory epithet of 'nursery psychologist" as a badge of honorable service and merit. None the less, Professor Baldwin is perfectly aware of the enormous difficulties and dangers which attend the investigations of this subject, which may be safely said to be still in its infancy. In fact, it is difficult to escape noticing here and there, a tinge of scepticism and despondency in the author's voice, as he lingers before that 'dark backward and abysm' of the early human mind—especially when he is confronted with the appalling diminutiveness of his predecessors' results. If such expressions escape him, however, they have purely a regulative function, and far from despairing of ultimate partial success-for otherwise he would not have written the book-Professor Baldwin is sanguine that rich and valuable results will be obtained, in fact has obtained them. When well into his own work, a cheerful optimism and confidence inspires him.

Professor Baldwin has opened up a new line of inquiry, and pursued it under a new method" the dynamogenic method," which we shall speak of later. First as to the origin and contents of the book. Professor Baldwin began his work with simple observations on infants, which he published off and on in the scientific periodicals. On coming to the subject of child's imitations, however, especially in relation to volition, he was so deeply impressed with the genetic function of imitation as to feel compelled to entertain a widened view of the subject and to work out a theory of

mental development in the child on a new and considerably modified plan. That plan involved the consideration of a doctrine of the race-development of consciousness-the great problem of the evolution of mind. The first chapters, I-VI, are devoted to the statement of the genetic problem, with reports of the facts of infant life and the methods of investigating them, and also to what he calls the mere "teasing out" of the strings of law on which the facts are beaded-principles of suggestion, habit, accommodation, etc. Here the central problem of motor adaptation is considered. "Chapter V. gives a detailed analysis of one voluntary function, Handwriting. Then follows the theory of Adaptation, stated in general terms in Chapters VII. and VIII.; and afterwards comes a genetic view in detail (Chaps. IX. to XVI.) of the progress of mental development in its great stages, Memory, Association, Attention, Thought, Self-consciousness, Volition. So the whole is a whole, the theory resting upon an induction of facts (put before it) and supported by the deduction of facts (put after)." Professor Baldwin emphasises the bearing which his results will have on education and more especially on social or collective psychology, where the genetic theory will find "both its root and its ripe fruitage." He proposes, however, to take up this aspect in another work which shall bear the sub-title Interpretations: Educational, Social, and Ethical, in contrast to Methods and Processes, by which the present volume is described.

We may stop to note the author's philosophical position, which falls, he says, under the very indefinite category of "ethical or spiritual idealism." For example, concerning the explanation of consciousness or reason by evolution, the author takes the stand, now quite common among philosophers, "that the natural history "question is not the same as the question of the essence or nature or explanation "of mind. Philosophy has its problem just the same, however consciousness arose, "and no amount of evolution theory can settle the problem set by philosophy." In fact, Professor Baldwin has serious doubts regarding the personal qualifications and even the good intentions of the biologists. "One almost despairs of them!" he says. And, again, regarding their puffed-up disinclination (for their hearts have been made fat and their ears heavy by the fulsome praises of the age), regarding their puffed-up disinclination to listen to the plaintive note of one who but tries to interpret the wail of the human babe "-he slyly remarks: "But I am not prepared to dispute the point [the possibility of their listening] with any of my readers who find such an expectation quite too optimistic," All in all, the poor biologist comes in for some pretty hard hitting.

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Respecting the advantages which Professor Baldwin cites as belonging to this subject in the first place, infant psychology meets the urgent needs of mental analysis, in fact, is the only means of testing the truth of our mental analyses; we find in the child the elements of mind in the simplest human form. Again the phenomena of the infant consciousness are simple as opposed to reflective, and there is also a corresponding simplicity on the organic side. Lastly, in the list of advantages, a more direct application of the experimental method is possible in observing young