Arithmetic is the 'common logic' of the people, and, as one of the 'three R's,' is enforced in the public elementary schools of this country. The method by which this subject is taught must largely determine its value as an instrument of education, and on the early processes of instruction will depend generally all subsequent development. Unlike some other subjects, arithmetic to be really useful demands a clear conception and a definite understanding of each step before another can be advantageously taken. Hence the first four rules.' But this is a misinterpretation, if subtraction is made to follow addition, and multiplication is then made to precede division. A common mistake has been to take these 'rules' in the order indicated, and even to require the addition of long columns of figures including millions' before proceeding to subtraction. This practice is now discarded by all intelligent teachers of young children, and an appeal to their observation-to their 'intuition by the presentation of objects has happily been substituted. The abacus or ball-frame was long the only 'apparatus' found in our infant schools adapted to this purpose, although, of course, ingenious teachers used laths, pebbles, and other appliances to aid in the correct conception of any given number. Other devices have been recently supplied, each affording some valuable suggestion. The most recent is the special adaptation of the arrangement of the domino 'dots' to the purposes of instruction in number. Farnsworth's Domino Cards give, on a large scale, the familiar double arrangement of numbers up to nine. The groups of dots, always presented in the same order, are themselves the unvarying symbols, and need no immediate translation into‘Arabic numerals.' This great advantage of ready representation in the concrete of all numbers less than ten in every possible combination gives to these fifty-four cards an unspeakable value. Children can learn to add, subtract, multiply and divide with exactness and rapidity, 'up to eighteen,' by the use of single cards; and two or more cards can be employed as effectively for more advanced exercises. On the basis of a knowledge of number thus firmly laid may be erected an enduring superstructure. Our opinion is confirmed by the testimony of H.M. Inspector, John Lomax, Esq., M.A., who records, with satisfaction, that 'remarkable accuracy and quickness in the teaching of numbers has been secured 'in the Infant School at Stockport, where these Cards have been introduced. We confidently commend these Domino Cards.

An Elementary Text-book of Botany. Translated from the German of Dr. K. Prantl. The Translation revised by S. H. Vines, M.A., D.Sc., F.L.S. W. Swan Sonnenschein and, Co., Paternoster Row.

It is a question whether the library of the scientific Englishman is not becoming a little over-burdened with translations from the German. All the world knows that the Germans are facile principes in that immense faculty of taking pains that is one great requisite of genius of a natural science order. Their patient investigations during the last few years in Physiology, Zoology, and Botany have revealed more actual facts as to plants and animals than have been furnished in the same time by any other nation. We owe them a heavy debt of gratitude for the vast store of materials they have accumulated. But we are not sure that in their admiration of German industry

the English scientific folk are not becoming a little slavish. An idea seems to have arisen that translations from the German are the only reliable scientific books, and that any work of purely English origin would not be sufficient for the study of a given subject. And as far as Botany is concerned the leaders in the scientific world seem to encourage this notion. Not one of our foremost English botanists has brought out an original work of any magnitude on the subject during the last twenty years. Professors Thiselton Dyer, and Bennet translate Sachs, Lehrbuch in place of giving us a work from their own pens, and Mr. Bennet further translates Otto Thome's book.

Dr. Vines, in his turn, translates Prantl's work. Professor Bentley's book, in its later editions, deviates but little from the first edition, that was published in 18-. Truly Dr. Maxwell Masters, in his excellent re-editing of 'Henfrey,' gives us all the latest facts and theories. But these are still arranged on the basis of the work of 1857.

The English Botany book is yet to be produced. Before long probably some English scientific man will give us a work in which all the many facts collected by the indefatigable patience of foreign observers and their generalizations will be collected and arranged, in that systematic and tangible manner which would seem to be the special prerogative of our English writers.

In the main the book before us would serve very well for the student who has studied plants practically, and who is not yet sufficiently skilled to comprehend the large work of Sachs. This volume should be taken as the intermediate stage between that practical dissection and description of plants that must be the first step_in Botany, and the reading of the highest treatises. Dr. Prantl deals, after the fashion of modern botanists, largely with the Cryptogamia. The fashion is an excellent one, for larger, more interesting, and more important generalizations are probably to be arrived at by the study of low plants than by the study of the more complex forms. The whole question of the evolution of plants, and of the gradual separation of vegetable living things from animal living things in the course of development, turns on the knowledge of these low forms of plant life. Hence the modern teacher of Botany who does his work well early leads his students to study the Cryptogamia. He will find in this volume a very excellent account of that sub-kingdom, and in addition some useful practical hints

as to the locale and the habitat of the commoner forms of these flowerless plants. Some of these hints, we take it, are from the pen of Dr. Vines, as they have in many cases an English rather than a German significance. With advancing botanical knowledge comes the necessity for the modification of those purely artificial arrangements that we make of plants and animals to aid us in our remembrance of their structure, their functions, and their relations one to another. Our systems of classification need reconstructing, and in this constantly recurring reconstruction we are sometimes likely to forget the immensely important fact that all systems of classification are artificial, and that in Nature there is no such thing as a class, or an order, or a genus. So long, however, as we bear in mind that divisions and subdivisions are of man's making, and are only convenient ways of tabulating, and aids to remembering facts, classification will be of use to us. The system adopted by Professor Prantl differs largely from that hitherto in vogue in England.

The classification of the Cryptogamia is a thoughtful and reasonable one. We regret, however, that one piece of nomenclature introduced by Messrs. Bennet and Murray at the meeting of the British Association in 1886 has not been incorporated here. That is the carefull distinction between the use of the ending 'spore' and the ending 'sperm.'

We should take exception further to the placing o Characeæ as a division of the Algæ. There is in this di vision of plants a marked distinction between axis and appendages that is not presented by any other of the

plants classed under the head of Algæ. If morphological distinctions are of any value in classification, surely so striking a one as this ought to serve to separate Chara and Nitella from all the plants in which there is no distinction between a central stem and the lateral appendages as the branches, leaves, and sexual organs, that are borne by that stem.

Turning to the classification of the Phænogamia, that are an admirable modification which separate the Gymnospermeæ from the Angiospermeæ before making division into Monocotyledones and Dicotyledones. The further subdivision of these two last classes on pages 206-229 presents many points of difference from the system at present used by English botanists, and we are not sure that in all cases the alteration is for the better.

Dr. Vines has given a very useful appendix, by the aid of which the relative positions of the English orders and the divisions of Dr. Prantl can be seen at a glance.

The account of the structure and functions of plants is excellent, though the hypercritical will take exception to the terms used in the titles of the first and second parts. Anatomy, we still think, should be a general name for the whole body of facts that bear upon structure. Its subdivisions are Morphology, the name for facts in relation to organs, and Histology, the name for the facts in relation to tissues. The book under consideration, unfortunately, speaks of the Histology of plants under the name of Anatomy.

We are inclined also to join issue with our authors in their retention of the ugly phrase, 'alternation of generations.' It is so misleading a phrase that we would suggest the use of H. Spencer's 'hetero-genesis' by all biologists, in place of the older and less accurate name.

The student who has carefully studied, by dissection and microscopic investigation, actual plants, and who desires to pursue his botanical studies in company with the best authorities by the aid of the most advanced works, will find Dr. Prantl's book of use as an intermediate stage, at least until our English botanists produce a text-book that is not a translation from a foreign author.

Standards of Teaching of Foreign Codes relating to Elementary Education. By By A. Sonnenschein. London: W. Swan Sonnenschein and Allen.

'Nothing can be more serviceable to the cause of national education than that the English people should be accurately informed as to what our neighbours and competitors are doing.' Thus wrote Mr. Mundella on June 14th, 1881, on receiving proof-sheets of this useful publication. We fear that, with regard to educationists generally, it was published too late to serve its immediate purpose, which had reference to the 'Proposals for the Amendment of the Code,' which were generously submitted to public criticism. But an accurate compilation of this nature, exhibiting the standards of attainments required for school children of a given age in the chief States of Europe can only lose its value by the lapse of time. Fifteen countries are selected, and their regulations as to arithmetic, language, geography, etc., are minutely given. Though these Standards are by no means uniform, there is evidence in almost every case of their having been determined by practical men. An Introduction of fifteen pages contains some sensible strictures on certain points in our English Code, and we endorse nearly all that the author has written on the subject of Intuition '-the German Anschauung,' or 'Teaching by Observation.' We believe, with Mr. Felkin (quoted p. 17) that 'it is the most important of all kinds of instruction,' inasmuch as in the hands of a good teacher 'it forms the child's mind, and develops his powers of observation.' The 'oral lessons,' formerly so prevalent in our public elementary schools, have been almost crowded out by the mechanical drudgery of the 'three R's.' There is, however, some hope of a return to intelligent methods, especially in the work of our infant schools. We are glad to commend to the attention of all patriotic educationists what Mr. Mundella calls an

admirable and valuable work. Mr. Sonnenschein apologises for its incompleteness, but so far as it goes we believe it to be reliable.

A History of Modern Europe, for Schools. By John Lord, LL.D. London: Simpkin and Marshall.

Dr. Lord's History of Europe' has been a school book for about forty years, and its sale has reached fortyseven thousand. This success renders lengthened notice on our part superfluous. Our duty is to intimate the addition of four supplementary chapters, bringing the book nearly to the present date; together with an appendix of questions for examination on each chapter. These supplementary chapters are not unworthy of the book, being written so as to comprise the principal of recent events, and with general fairness in regard to party politics. The questions are less able, being in many particulars too literal and commonplace. A better suggestive question on the miseries of the French retreat from Moscow might have been adopted than 'How many horses died in a week, and what was done with their remains?' Generally speaking, an answer to a question should be found in the text. We look in vain through the paragraph which describes the Great Exhibition (p. 426) for information to answer the question 'What made this (the Exhibition) a great success?' All we can gather from the descriptive paragraph on this point is, It was a great success,' without any hint as to the causes thereof. The author of these supplementary chapters has also mistaken the famous expression in Louis Napoleon's letter to the Empress, in which Prince Imperial is spoken of as having received his 'baptism of blood,' and this is referred to by the question, 'What was the "baptism by fire?" We turn to the text-rather puzzling to find under the general date, 1848 to 1880and find the phrase 'baptism of fire' spoken of as having been used in regard to the trifling affair at Saarbrück, the only gleam of success that shone on the French forces. Questions like the following also occur:-'What is the present condition of the Republic?' (of France). Rather a difficult one, we submit, to be answered by a schoolboy student. What are the great sources of national wealth?' we regard also as much too comprehensive. 'How has Prussia astonished the world?' might be answered in several ways; but 'What about Bismarck?' would puzzle many a politician to answer, and the following question, 'What is his policy?' drive the poor examinee to despair. The author-we still speak of these supplementary chapters-also calls (p. 461) the German Reichstag by the term Reistadt, and spells Gortschikoff with a z-Gortszikoff-both, we fancy, unusual. The author also attributes the rapid recovery of France from the disastrous effects of the German war mainly to the extensive division of the soil among small proprietors. This is very questionable. The recuperative power of France was more plainly attributable to the habits of thrift and prudence on part of the masses of the people, together with their hoarding up savings, in addition to ordinary investments, against a rainy day. The appearance of these savings in buying shares in the Rentes astonished even the great French financiers, and enabled the nation to pay off the immense German indemnity at a very early period, and without any interruption to national industry. The paper and printing of this edition are inferior to the editions issued in Dr. Lord's time. With better examination questions, and the convenience of giving the precise date to each paragraph, this book will hold its own as one of the most useful of modern histories.

Elementary Science Manuals. Botany for Schools and Science Classes. By W. J. Browne, M.A. Lond., Inspector of National Schools. Dublin: Sullivan Brothers. London : Simpkin, Mashall and Co. 1881.

This would be a very useful book to any one who had read a great many others. An advanced student in Botany

would find it of value in placing in very condensed and not altogether unsystematic form a large number of more or less valuable facts. But we cannot think that these books, that always remind us of Liebig's extract of meat, are of use in themselves to beginners. Without much, very much explanation, Mr. Browne's book must be wholly unintelligible to young students. Its most possible use would be as a text-book in the hands of a good teacher, who might well model the course and details of his lessons on the method here adopted.

To get rid of the fault-finding. Is it not to-day a pity in any scientific book, no matter how simple, to use the Fahrenheit scale in preference to the Centigrade? This is done in the volume under discussion (page 14, line 19 from end). The old-fashioned word 'pistil' is retained instead of the more accurate 'gynoecium.' Mr. Browne would probably be the first to admit that this pistil is an exploded one. Cryptograms, again, are not so called because 'their floral organs are hidden ' (p. 17). The name is given to them because their sexual organs are minute and difficult of discovery. And lime is not calcium oxalate, though the student of page 20 would be led to this inference. The more recent and more meaningful terms dorsifixed and basifixed are, we think, better in relation to anthers than adnate and innate (p. 51). And the descriptions of certain plants given at the end of this little volume are far too meagre to be of much use, whilst to give a little pageful of useful products,' 16 all told, is doing either too little or too much.

The book is accurate on the whole, and is evidently written by a man acquainted with the subject. The author has read Sachs. The diagrams are of the good old type. A number of questions are given on the subject-matter of each chapter. But these kinds of questions are Students on the whole, we fear, useless. will not use them, and teachers ought to construct them for themselves.

Light, Heat, and Sound. By Annie Besant.

London: 28, Stonecutter Street, E. C.

This treatise is clear, free from verbosity, and contains a judicious combination of reference to familiar phenomena, scientific explanation and demonstration by arithmetical or other formulæ. To most of the chapters useful examination questions are appended, by which the utility of the book will be greatly increased. We should prefer the illustrative diagrams to be printed with the text, whereby the trouble of turning back to two Photolithographed sheets would be avoided. The student will find modern scientific theories sufficiently alluded to in this manual without being unwisely discussed. As an illustration of this, we may quote the opening sentences on HEAT.Heat, like light, is a mode of motion, and heat and light cannot wholly be separated.' followed by experimental proofs of the statement, and is enough for the student who is not desirous of fully examining the proofs of the Correlation of Forces, nor the resolvability of a group of sciences into the results of Motion. Speaking of the fact of water boiling by less heat under less atmospheric pressure-about one degree for every 300 metres-On high mountains, therefore, cooling becomes a matter of difficulty, as the water passes into steam before it is hot enough to cook meat.' In several passages the authoress honestly refers to the leading authorities-Deschanel on Heat, and Tyndall on Sound, a praiseworthy habit in all scientific manuals.

This is

An Easy System of Calisthenics and Drilling. By Thomas McCarthy. London: Allen and Co.

Physical exercises are now pretty well established in modern education. Their importance is felt in regard to healthy muscular development, which in regard to girls was too often confined to a formal walk and occasional lesson with the wand and rings. What a well-devised

system of drill effects is shown by the conversion of the awkward and half-bent country lout into the smart soldier with his elastic yet firm step and erect bearing. To simplify the course of regimental drill, seems to be a desideratum for boys and girls' schools, and this the book before us carries out. Adequate directions are given in regard to the manner of performing the various movements, together with cautions against faults to be avoided. The drill and marching exercises are supplemented by those with the wand, light dumb-bells, and Indian club. The descriptions, of whose clearness we cannot complain, would be immensely improved by the addition of diagrams or descriptive figures.

A Practical Introduction to Greek Prose Composition. By Thomas Kerchever Arnold, M.A. New edition, edited and revised by Evelyn Abbott, M.A., LL D London: Rivingtons. Two such sponsors for a book as Messrs. Arnold and Abbott must assure the world that their brain-child is everyway commendable. There cannot possibly be a better help to the young Grecian than this easy and exhaustive manual. In a day scarcely yet gone by, Greek grammars were the torment and abhorrence of schoolboys, dog Latin being the medium for explaining those more hieroglyphical secrets of the crabbed Greek, and to thousands beside the present writer,aorists, supines, and verbs in μ were in those years, ay, and still are, baffling and inscrutable mysteries. Now, however, by means of such an introduction as this, with its lucid order and its popular and easy explanations in our familiar Queen's English, the road to Parnassus is strewed rather with flowers than with flints, and all diligent scholars may go on their way rejoicing. Those terrible old grammar: of Eton, Winton, and good King Edward may well be voted obsolete, while such pleasant substitutes as the book here noticed, usurp with all acceptance their ancient places in these fortunate modern times.

Lessons on Form. By Richard P. Wright. London: Longmans, Green and Co.

All geometricians are aware that the title of this book indicates a series of steps in the field that Euclid has developed into the grandest system of mental training yet known. But the term form would not be thus understood by a novice. To beginners, however, in the mathematics of form, such explanatory lessons as Mr. Wright here gives will be most valuable accompaniments to the study of Euclid, side by side with which it should be read. Taken by itself, Mr. Wright's book gives the substance or marrow of many of the results which Euclid develops by a regular series of steps that hang together and sup port one another like links of a chain. Such a rigid logical course Mr. Wright does not attempt, but his lessons are none the less valuable, and will greatly assist the student in rightly appreciating the nature of the geometrical field. As an example of the thoroughness of Mr. Wright's explanations, we may mention the lesson on ANGLES, with the number and character of each according to the points of intersection. A thorough knowledge of this chapter will form an excellent preparation to the study of triangles, with which Euclid begins. Mr. Wright's lesson (Chapter IV.) on TRIANGLES may be read beside the First Book of Euclid with great advan tage, as showing the principal results aimed at, together with various ways of proving several propositions. The importance of Euclid's famous 47th Proposition (Book I.), generally known as the Theorem of Pythagoras, and on which a great deal of Mensuration and the whole superstructure of Trigonometry rests, will be well understood by Mr. Wright's clear and explanatory chapter, the 7th in his book, in which he lucidly shows the leading algebraical formulæ thence derived, together with the rationale for the main processes of Mensuration. Several methods of demonstrating the great theorem are given in addition to that by Euclid. The student will find himself in safe hands in mastering Mr. Wright's pages.

vil Service History of England. By London: A. White and H. A. Dobson. rosby, Lockwood and Co.

is not improperly called a fact-book of history, s indeed crammed with a marvellous number of facts. first half of the book comprises a summary of the dal historical details. The second half is made up of a eries of appendices or special chapters on Constitutional History, Colonial and Indian History, British Biography, Literature, and Inventions and Discoveries. There may be some advantages in treating these latter-mentioned matters separately. We refrain from discussing the general value of these compendiums as short cuts to preparations for examinations. How far even memory is made certain by a firm impression being made by a complete picture instead of by a bare outline will depend very much upon the nature of the examination, as to whether a reasoning or deductive set of questions are set or those merely requiring the recapitulation of facts and dates. For the latter 'cramming' may be sufficient, but history is no more represented thereby than is a human being by a skeleton. The evils, however, belong more to the system than to this book, which is well enough of its class. Scarcely a word is uttered in common with the majority of made-up books on British history. The authors, instead of discarding, keep to the misleading term Anglo-Saxon. The authors sum up Stephen's cha'warlike and cruel.' This phrase is not only badly written, but scarcely accurate. Stephen was more weak and yielding than cruel. He was indeed mild for the age, and his great fault seems to have been that of irresolution. Beckett is mentioned as 'Archdeacon of Canterbury,' which we are willing to regard as a slip for Archbishop. The author falls into the popular, erroneous expression, Joan of Arc, instead of Jeanne Darc. There is no place named Arc near Domremy, Jeanne's birthplace. The necessity for compression leads to a rather The second vague description of the National Debt. part of the book is more satisfactory. The constitutional part is thoroughly well done.

racter as

As India and the Colonies are treated each to an appendix we think such a Supplement is necessary to Ireland, and also to Scotland.

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