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THURSDAY, DECEMBER I, 1904.

wisdom, benevolence, and courage were preeminent. Wisdom meant intellectuality rather than mere know

ledge. Benevolence resulted in social relationships, so DAI NIPPON.

that beggars are practically unknown, whilst State Dai Nippon, the Britain of the East, a Study in aid for the poor is seldom sought. Courage

Vational Evolution. By Henry Dyer, D.Sc., &c. embodied the idea that it is better to die for one's Pp. xvi + 450. (London : Blackie and Son, Ltd., country rather than yield. Commerce had always 1904.)

been looked down upon as a low pursuit. A nation THE He story of how Japan jumped from what she saturated with such ethical teachings was naturally

was to what she now is will always form one of proud of her autonomy, and sought to escape from the most remarkable episodes in the history of material occidental restrictions. The escape she chose was by civilisation. Not only is it this, but it is also a remark- an education in western utilitarian knowledge, wisely able illustration of the results that can be achieved by backed by an army and a navy. occidental education fostered by and implanted on a

In 1868, when the present Emperor ascended the system of oriental ethics.

throne, he took an oath embodying five principles, the This story, under the title of “ Dai Nippon," or

objects of which were to act as beacons in the ocean * Great Japan," is told by Dr. Henry Dyer, who for

of international struggles of the world. In the fourth about ten years was principal of the College of of these we read that “all purposeless principles and Engineering in Tokyo. From it we learn that Japan useless customs were to be discarded, whilst the has taken from Europe and America every concrete fifth directs that “knowledge and learning shall be aid to progress on which she could lay her hands, and sought after throughout the whole world, in order that in return for this she now offers a code of morals. the status of the Empire of Japan may be raised ever When we realise that it is Japanese ethics which are higher and higher.” When this announcement was at the base of Japanese character, and that these ethics made the education of Japan chiefly consisted in led to the desire to acquire European knowledge, they memorising Chinese classics and characters, learning commend themselves for close consideration.

to reckon on the abacus, and studying history and We may give water to a horse, but to make him edicts. Knowledge relating to science and its applidrink is another matter. In a similar manner we may

cations was almost non-existent, and we can well cover a country with schools, but to induce people imagine the doubts of those who were entrusted with who have neither the ability nor desire to learn to take

the administration of the imperial command as to the advantage of such schools is a formidable task. The courses they should follow. In 1871 a department of Japanese had ability in a marked degree. Their extra- education was created, and with it schools of various ordinary power of memorising, which the few Euro-grades were established throughout the country. The peans who have noticed the same have only regarded children of the lower classes, including females, were as an abnormal curiosity, may possibly be the resultant admitted, while the schedules of study of preexisting of committing to heart the sayings of eastern sages

schools were re-modelled. At the present time it may and endless idiographs. A philosophy which had sunk be said that Japan bristles with schools, and that there into the hearts of the people while many Europeans is not an ignorant family in the country. still revelled in a feral state no doubt played its part in

A child, possibly commencing at a kindergarten, is the suggestion that it was advisable to fall in line with admitted to a common school at the age of six. After western progress. The main lever, however, which four years he passes to a higher grade school, where forced Japan from its insular Utopia into the never- there is also a four years' term. Above this there is a #nding struggle amongst the comity of nations was middle school with a five years' term. Graduates the feeling that national and personal honour had been from this school can by competitive examination pass affronted. A civil war was ended, the Tokugawa to one of six higher middle schools, above which stand party had been defeated, and the feudal barons had two imperial universities, in connection with which been united under the Emperor who still reigns. there are colleges of literature, science, medicine, Internal dissensions had ceased, but western demands engineering, law, and agriculture. The number of had settled like a cloud upon the nation. Treaties had elementary schools is 27,109. Usually no fees are been made with thirteen States, each of which had its charged, but in special cases the local governor may courts of justice; Japan was powerless to fix its tariffs ; allow charges varying between 2}d. and 3d. per Yokohama was policed by a British regiment, and month. legations kept their guards. In these and other direc- In the training of children moral education takes tions Japan felt that, notwithstanding she possessed precedence of instruction in facts of practical use in a culture about which the man in the street is yet pro- daily life. Bodily development is not neglected, but loundly ignorant, she was humiliated and looked down good manners and etiquette rank higher than minds upon as an inferior. Buddhism and Shintoism had re- stored with information. sulted in an extraordinary patriotism and loyalty, while In the secondary schools, although mathematics, the " Bushido" of the Samurai" gave a system of natural history, physics, chemistry, and other subjects moral principles " which entered more deeply into the are taught, we again find-and find in institutions of national life of Japan than do those of the religion we all grades--that “morals ” (without religious dogma) profess into Western civilisation."

head the list. It is clear that the Japanese want good Among these ethical teachings those bearing upon citizens, citizens who recognise the symbol of authority rather than practical demonstrations of the same. In courtesy and politeness have attracted the attention of Japan a crowd will halt before a straw rope on which all travellers, they are scrupulously clean and see a futters a tiny paper notice. In Europe police and bath-tub every day, to show anger is to put yourself truncheons might be required. The good manners of on a level with a dog, and should two persons have the East are hardly So 'superficial as' popularly an altercation, for one to dub the other as a

* shaba imagined. They are the outcome of their philosophy fusagi” or an impeder of the world's progress" emphasised by special training, the end of 'which is would be an epithet not to be forgiven. The courage “to eultivate your mind that even when you are quietly of her soldiers needs no comment, while the endurance seated not the roughest ruffian can dare make an attack of a "jinricksha” man, who for a week can pull a on your person."

heavy European with his baggage 40 or 50 miles per The higher secondary schools are preparatory to the day, is, from an occidental point of view, quite universities, the objects of which are to teach “such | phenomenal. arts and sciences as are required for purposes of the The Japanese are temperate, frugal, modest, and State." To each is attached a university hall, which happy, while the world knows that they possess is established for purposes of original research. In artistic instincts. In many directions a Japanese is the six colleges forming the university the professors distinctly superior to the European. The nation has a and assistants number 245, and the students 3121. soul, and if we reflect on the components which make The entrance fee is 2 yen, and the annual tuition fee up that soul-the soul of Ruskin—it seems that in is 25 yen (i yen=25.). For those who cannot proceed certain directions European countries might be beneto the universities, industrial, agricultural, commercial, fited if only they were able to raise themselves to the and other technical schools have been established. In level of Dai Nippon. Although by the opening of the 1902 there were 845 such schools, attended by 55,596 country much has been gained, there are many signs scholars. The expenditure on these in 1902 was indicating that the blessings have not been unalloyed. 2,739,297 yen, of which 285,253 yen was State aid.

Commerce, competition, and the accumulation of The total annual expenditure by the Government in wealth have been accompanied by increasing poverty, connection with the educational department is roughly whilst those whose vocations have been at the open six million yen (600,000l.).

ports have acquired the manners of those with whom In addition to the schools mentioned, Japan has its

they came in contact. So far is this marked that a naval, military, art, 'and music schools. Over and

Japanese who has been a servant in a European house above these, again, we find educations in departments

may be handicapped in obtaining similar employment of life which in Europe have received but little atten

amongst his own people. To say the least, he has tion. Chess,' or rather go,” clubs are common

become too brusque. Side issues of this nature may throughout the country, and for proficiency in the game

cause a nation to regard with regret the disappearance certificates are awarded. Certificates can also be of old conditions, but, taking all in all, Japan has obtained in the art of flower arrangement, an art which gained more than she has lost. She is no longer a has its terminology and canons, but which in Europe

pupil, but a teacher. finds its perfection in studied negligence."

In connection with education, a point which Dr. Dyer has not emphasised, but which is in strict accord

SYLVESTER'S MATHEMATICAL PAPERS. ance with the imperial edict of 1868, is that the Government keeps up a stream of its best educated

The Collected Mathematical Papers of James Joseph men flowing round the world, each being a specialist,

Sylvester. Vol. i., 1837–1853. Pp. xii +650. visiting countries and institutions with the object of

(Cambridge: University Press, 1904.) Price 185. gathering together what is valuable in his own voca- net. tion. Originally it was the Japanese student who was He appearance of this volume is very welcome for sent abroad; now it is the professional man. You may not know it, but often he may be able to give published in a variety of journals, and generally conmore information than he receives. Generally speak- tained a considerable number of misprints; they will ing, in Dr. Dyer's words, the Japanese Government now be available in an attractive form, with their finds that money spent on education is a good national accidental blemishes removed by a very careful and investment.

competent editor. The work of preparing these papers The chapters devoted to industrial development, the for the press must be troublesome and tedious, and army and navy, commerce, politics, and other subjects the thanks of mathematicians are due to Dr. Baker are as interesting and full of information as those for having undertaken it. Special attention should be bearing upon education.

directed to the note at the end of the volume on With regard to the future of Japan, Dr. Dyer tells Sylvester's theorems about determinants, some of us that his ideas are decidedly optimistic, and he which require correction. believes “that in material, intellectual and moral in- The papers here published range in date from 1837 fluence Japán will fully justify her claim to be called to 1853. The first three relate to mathematical the Britain of the East." So far as the concrete physics; but Sylvester soon followed his natural bent, adjuncts of civilisation are concerned, Japan might be and all the rest of this volume is pure analysis, mostly pleased could she be on the same platform as her ally, algebra. Historically, the most notable results are but it is doubtful if she aspires to much more. Her those on elimination, canonical forms, and the theory 46 millions of people have smiling faces, their ! associated with Sturm's method of locating the real

on

roots of equations. Moreover, there is the paper on parts of the subject may be. Quite apart from other the contacts of lines and surfaces of the second order, reasons, the study of pure mathematics may be dewhere the invariant factors of a matrix are recognised, fended, like that of music or chess or painting, from and the system of two quaternary quadratics is con- the merely æsthetical side, and this Sylvester does in sidered in detail with reference to the simplest simul- terms both vigorous and quaint. For example : taneous roduction of the forms.

“ The fortunate proclaimer of a new outlying planet Appreciations of Sylvester's character and of the has been justly rewarded by the offer of a baronetcy value of his mathematical work have been written by and a national pension, which the writer of this wishes able hands, and it is i unnecessary to enlarge upon him long life and health to enjoy. In the meanwhile, them here. His egotism was obvious and often what has been done in honour of the discoverer of a.. amusing, but never offensive; his enthusiasm was re- new and inexhaustible region of exquisite analysis ? " freshing, and though his temper was touchy, he was the latter reference being to Cayley's discovery of the very generous and kind. As a master of formal calculus of invariants. Fortunately, Cayley was saved analysis he has few equals; the birth of the calculus in another way from the cares of money-making, and of invariants occurred just at the right time to attract he lived long enough to realise to the full his great his attention, and his contributions to this subject alone reputation among those who would appreciate his are enough to make him famous. He had the instincts work. Sylvester in his early life suffered unjustly from of an architect, and it is well, on the whole, that he the current prejudice against his race; so far as it was did not always trouble to clear away the chips. The possible this was afterwards atoned for, and it is to casual remarks scattered about his papers and the be hoped that no bitter feeling was left behind.

G. B. M. fragmentary nature of some of them, help to make the reading of them very stimulating; he takes us into his confidence, shows us how his ideas arose, and gives MENTAL AND SOCIAL MEASUREMENTS. us hints of unexplored regions. He was eminently An Introduction to the Theory of Mental and Social original, and spent little time in studying the works

Measurements. By Edward L. Thorndike, Proof his contemporaries; thus he did not even realise

fessor of Psychology in Teachers' College, Columbia that his theory of reciprocants had been more than

University. Pp. xii +212. (New York : The anticipated by others, especially by Lie. But any mis

Science Press, 1904.) Price 1.50 dollars net., understanding arising from this source must have been long since dissipated, and his place among the great AM

MERICAN colleges seem more awake than our

own to the fact that the newer methods of mathematicians of his time is quite secure.

statistics have made it possible to deal with facts with Sylvester's occasional notes the theory of numbers and his lectures on partitions

which they are directly concerned, and to discuss them suggest

with far more completeness than was practicable a few problems to those who are interested in arithmetic.

years ago. They are making in consequence large The present volume, for instance, contains three notes on cubic Diophantine equations, a subject not yet ex

collections of anthropometric data to serve as tests of

health and development, and for comparisons, between hausted, though Sylvester's own theory of resideration throws much light upon it. The late Henry Smith colleges. Again, there are more teachers in America once referred to this problem as being one which might the above methods have far wider applicability, extend

than in this country who, appreciating the fact that be hopefully attacked with the engines of modern analysis; perhaps the appearance of this edition of

the range of their measurements to psychophysical Sylvester's works may lead to the discovery of a com

subjects. They are also eager to deal with purely plete theory.

psychical matters that elude direct measurement but A good example of Sylvester's power of illuminating their proper class places, or to utilise a third and still

admit of being arranged by mutual comparison into and drawing general conclusions from the simplest mathematical problem is the note (p. 392) on

more general method, which deals with such objects

as can be sorted into a few distinct classes without reelementary geometrical theorem for which no direct proof had been discovered. He observes that the gard to their internal arrangement. The author is proof may be made to depend on showing that a certain fully justified in saying that analytical equation has no real root, and suggests that

“ The obscurest and most complex traits, such as in all such cases where the analytical proof consists legal ability, inventiveness, can be made material for

morality, enthusiasm, eminence, efficiency, courage, in demonstrating the non-existence of roots, the ordinary statistical procedure, the one condition being geometrical proof must necessarily be indirect, while that the general form of distribution of the trait in in other cases the reductio ad absurdum may be con- question shall be approximately known.” venient, but is not necessary. This observation re- In these circumstances a system

of elaborate minds us at once of Gauss's discussion of the division measurements has come into vogue in many American of the circle, and if Sylvester's conjecture is true it colleges. Whether the authorities have always planned gives another case of the curious points of contact their measurements wisely, and whether they discuss that exist between analysis and geometry.

them adequately and accurately, will not be considered It is not to be expected, or even desired, that many here. The volume is written to direct and to warn, should share Sylvester's keen delight in the beauty of in doing which it reveals some grave blunderings. formal analysis; but it is a mistake to discourage Unfortunately, it is composed chiefly for those persons those who are inclined to enjoy it, however unpractical | who are ignorant of even simple mathematics. The

an

author is fully conscious of the serious embarrassments pretation of results is a branch of statistics that has of the position he has chosen, but bravely attempts the hitherto received less attention than it deserves. It well-nigh impossible task of overcoming them. Thusis no doubt a great thing to be able to describe groups he says :

and to determine correlations between them with preIf this book were written by a mathematician for cision, but this is not all that is wanted. It is another the mathematically minded, it would not need to be and even more important achievement to dissect and one fifth as long. If read by such a one it may well analyse results and to discover the dominant causes seem intolerably clumsy and inelegant.

that produced them, but the art of doing this seems Whether he succeeds under these difficulties in as yet inadequately developed and to offer a promising giving easily intelligible explanations may well be field for research.

F. G. doubted; indeed, his language, though frequently lucid, is often quite the reverse. Still, if the volume were

OUR BOOK SHELF. used as a text-book in the hands of an enthusiastic and

Ву capable teacher good results might follow, but it re- Practical Chemistry, a Second Year Course.

G. H. Martin, M.A. (N.D.). Pp. 41. (Bradford : quires an optimistic disposition to believe that it would

G. H. Martin, The Grammar School.) Price is. prove more than superficially instructive, if it were

Mr. Martin has arranged in an unpretentious form a intelligible at all, to the mass of ordinary and un- most excellent syllabus of experiments and examples assisted readers. The author might, however, claim suitable for boys beginning the study of chemistry. a higher rank for it than he has done on the ground It is satisfactory to find that, in a school of such that it' teems with instructive illustrations by which high standing as the Bradford Grammar School, the everyone may profit, and that it presents familiar ideas

science master has seen the wisdom of devoting a from slightly new points of view, much to the

whole year (it is to be hoped it will be extended to a

second year) to teaching the simple facts which underadvantage of even well instructed readers.,

lie important principles without recourse to tests and There is no science more handicapped by cumbrous tables. and repellent terminology than that of the higher One suggestion may be offered. If the book is to statistics. Its ideas are

not always intrinsically have a wide circulation, which it certainly deserves, difficult to grasp, but the phrases by which they are and perhaps to illustrate the results by actual exexpressed are both ugly and unexpressive. The writer amples, possibly in a companion volume. believes that a student, however mathematically minded Boys cannot be expected to work out details of he may be, would save himself time and annoyance if apparatus in the short time allotted to science during he prefaced his earliest studies by a few hours of what school hours if substantial progress is to be made. No might be called kindergarten exercises with beans, doubt the author has his apparatus set up and gives

an appropriate demonstration to the class, but this will acorns, or the like. . By the process of sorting them

not help those teachers who wish to profit by the book into arrays and picking out the medians, quartiles, unless their technical difficulties are solved for them. &c., then by measuring them individually and extract

J. B. C. ing from the measures the remaining statistical con

Retouching By Arthur Whiting. Pp. xvi +91. stants, he would soon obtain a serviceable familiarity

(London : Dawbarn and Ward, Ltd., 1904.) Price with the more elementary technical terms and the ideas

IS. net. they represent. It would be easy to devise a suitable it very often happens that photographic negatives course that would prove a welcome help to students require a certain amount of careful manipulation who are enthusiastic about measurements, and it is owing to defects caused by photographic methods, to be hoped that the next writer on popular statistics scratches, &c. It is also desired sometimes to eliminate will elaborate one.

small defects due to slight movement of the object, or The author gives a large number of frequency desired end. The author has endeavoured in these

to alter or improve portions of the picture to attain a polygons, derived from a wide variety of data, which few pages to place before the reader the different are of interest. It is to be wished that attempts were methods and devices that are in use to cope success. more frequently made to reduce the variously shaped fully with the various defects that may be encountered. polygons obtained by experience into a few classified In the first instance the tools required are described, types, to append to each type the names of the objects is then shown how, in the case of portraits, to preserve

and the special objects of each explained. The reader that had been found to conform to it, and to analyse the likeness but yet to eliminate the blemishes caused the causes of its shape in each instance. It is difficult by optical or chemical or other action; he is here introto doubt that by so doing some desirable help would duced in a few words to the elements of facial anatomy. be given to the interpretation of any new polygon. The author has considered it necessary to insert It is perfectly true that almost any curve or polygon fessionals, in which the main principle to be kept in

a special chapter on retouching portraits of promay be built up in various ways by different types of view is to produce a beautiful face. To attain such curve or polygons appropriately superposed, but ex- an ideal, mouths are reduced, jaws cut down, ears perience alone will tell whether there is not a much knifed, eyes enlarged, and various other surgical greater probability of such and such a type being due operations performed. Working up draperies, retouchto such and such combinations rather than to others. I ing landscapes, preparing prints for the press, and Through these means many hypothetical sources of how to make a portable retouching desk, form other

The book should serve as an origin might be found so rare as to be hardly worth admirable guide to amateurs, and will be found useful considering, and so the field of probable interpretations to those who go more especially into this class of work. would be narrowed. Speaking generally, the inter- | Numerous illustrations accompany the text.

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