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and algebra. At my request Dr. Wright has consented to add trigonometry as a subject of instruction to the higher classes. The practical uses of arithmetic are too obvious to require exposition. It is used in the home as well as in the office in every enumeration, measure- ment, financial calculation, or manipulation of statistics. Arithmetical operations are neces-
sary for every other branch of mathematics not purely geometrical. Just as figures can b used to represent lines and areas. so lines and Breas can represent figures. The problems connected with lines and areas are those dealt with by plane geometry or Euclid, as the subject is often termed in our schools from the ancient Alexandrian who ingeniously and logically put together a number of those problems. The combination of arithmetic and geometry is the science of mensuration, an entirely practical science for obtaining in arithmetical terms areas of plane figures and contents, weights and values of solids. It is by mensuration that the merchant and the customs officer ascertain the contents of a cask, the surveyor the area of a field, and the
engineer the weight of any part of his structure. The practical uses of algebra, in which figures, lines, a reas, and contents are represented by alphabetical symbols, are, except for furnishing methods for multiplication of higher branches of mathematics, a little less obvious than the
uses of arithmetic and mensuration, and the science is more open to the danger of its pro- cesses being carried out without a full know- ledge of their meaning. It is certainly not often that the problems of daily life can ba solved by equations, simple or quadratic, though the equations have their purposes to which I shall presently refer. Familiarity with
harmonical, progressions-arithmetical,
and geomet ical-produc-s neatness of arrangement often of practical utility. I have myself on various occasions had to remodel scales of salaries, allow ances, rewards etc., to a logical system with a first term and a common difference. Trigonometry is in some sense a continuation of mensuration, bringing in calculations based on angles between straight lines in the case of plane and between circular areas in the case of spherical trigonome- try. No man can become a surveyor and engineer or a navigator without a knowledge of the solation of triangles, that is the calculation of measurements from measured sides and angles, which requires the power of being able to solve algebraic equations and use logarithms. Though the theory of Ingar- ithms is difficult their use is simple and mechanical and by rubstituting processes of addition and subtraction for the more lengthy ones of multiplication and division enormously simplifies complicated calculations. This is one instance in which the work of advanced mathe maticians is used to facilitate the practical employment of mathematics by those who have only studied the elements, and if we were to go and consider the higher branches of the subject we should find many other instances in which the formale derived from difficult processes are made available for the daily use of the engineer, the shipbuilder, the navigator and others in similar walks of life who make use
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of the results obtained by mathematicians without knowing it. Of these higher branches as they are now taught in this to College, it would be superfluons now speak, except to say that the few of you boys who may be tempted by mathematical aptitude to go beyond your school course, will find the subject more and more fascinating with each advance in it. This fascination is nearly a defect in the study, which developing as it does the reasoning power to the highest extent is beld by some to be inimical to the cultivation of the imagination. This reminds me of a story which I am tempted to tell, though it will probably be more interesting to the masters and other gentlemen here present than to the ladies and the scholars. A Cambridge under- graduate who was an enthusiast for literature, with much difficulty persuaded a mathematical friend to read 'Paradise Lost.' When the book was returned, he expected the friend to be as enthusiastic as himself. But the latter said he There was could find very little in the work. one neat thing. The dimensions of Satan were given, and the time he took to fall from Heaven' to Hell. It was thus possible to calculate the distance between the Celestial and Infernal
CHINA OVERLAND TRADE REPORT.
65
of the first year of tenure if the holder's report is not deemed satisfactory.
My reason for this innovation is to offer an inducement to boys to continue their educa'ion into Standards VI. and VII.
After reading his annual report, Mr. WILLIAMS, addressing His Excellency, said:
Th scholars in these schools are classified as
regions by a simple substitution in the formula, equals ft. Before I close my remarks wish to emphasise the use of mathematics other than its immediate practical application. It is recognised to be the study which more than any other develops what I have elsewhere called the male element of the mind-the reasoning power. I wish also to add a word of practical advice to the boys and a suggestion to the Head Master in an ordinary Elementary English School A blunder in a mathematical operation absolute from Standard I. upwards to Standard VII. ly vitiating, as it must do, the result obtained Formerly no instruction was given in the by a correct process, is the worst of faults, and
District Schools above Standard V. During is generally avoidable by checking. A mere
the past year a Standard VI., and Standard going over a calculation a second time is not
VII. were formed, but the resu'ts have not always or even generally the best way of check; been satisfactory. Boys left as soon as they ing. Sometimes this can be done by reversing could get a situation, thus preventing con- the process and generally by an op-ration
tinuity of work. As the great majority of mental arithmetic. I suggest to the Head
of boys leave school on passing Standard V.. Master that when he finds a boy habitually
(and some of them before that) to take blundering in his calculations he should make him show at the foot of each solution the method P positions as junior clerks with our local he has adopted to roughly check it. Tu conclu-firms at salaries ranging from $15 to 830 I made a point of inquiring personally how these and siou. I would explain that I have chosen to give to this College, as the most important many such boys were getting on, and I had con- versation with employers representing two educational establishment in this Colony, the shipping firms, one wholesale firm, two large prize for mathematics, because the mathematical
retail firms, and three engineering firms, and I prize was the one which, when I was at the
should like to give you their testimony, as to Royal Military Academy, I was most desirous
solue extent it reflects on the practical
of value
our educational system. Of of winning, and the urticle I have selected as a
course there prize. is the nearest approach I could find here
are exceptions, and we are to that which was presented to me for mathe- pleased to hear of certain boys making headway, matios twenty-five years ago, and which is now on my offic+ tabl. I propose to give a similar prize for the same subject to this College every year while I remain at Hongkong. (Applause). The HEAD MASTER thanked His Excellency for the kind remarks in his address, and trusted that the boys, after the encouragement give them, would show satisfactory resul's in this subject at the annual examination next year.
The proceedings concluded with three cheers for the King, His Excellency, the visitors and the Head Master.
ANGLO-CHINESE DISTRICT GOVERNMENT SCHOOLS,
SPEECH DAY.
H.E. the Governor on the 26th inst. distributed prizes to prize winners of the Wantsai, Yaumati, and Seiyingpun Government Schools at the Wantsai School.
Mr. W. H. WILLIAMS, late Head Master of the Sanyangyun School, read the annual report, from which the following extracts are made
The results in arithmetic generally are satis factory, and as a result of experiments I have made with Standards V., VI, and VII., as well as with Chinese masters, I am convinced that the Chinese boys have a marked ability for
In view of the impor mathematical studies. tance of this subject, from both a practical and purely educational point of view, I would like to recommend that Practical Mathematics be provided for Standards V., VI., and VII., follow ing a graded three years' course and including the elements of Practical Geometry, Trigonometry,
To
Mensuration, and Graphical Calculations. accomplish something in this direction I do not think the Saturday morning Geography class for Anglo-Chinese teachers could do better than continue their meetings again this year and go through a course of Practical Mathe-
matics. I have tried one or two of the masters, and I can confidently say they would take it up eagerly and turn it to the very best use in
their own schools, and in twelve months' time they should get through a good deal of useful work.
SCHOLARSHIPS.
It has been the rule to grant a number of free internal scholarships open to boys in each class. I now recommend
(I) Abolition of these scholarships. As a reward for diligence the top boy in each class now receives a class prize for general proficiency
(II) That four scholarships be awarded an- nually open for competition t› boys who have passed through Standards Ỷ., and tenable for two years.
The scholarships to be granted annually com- mencing. March 1st, 1905, granting free admis- sion to school during the tenure of the scholarship. The Headmaster to have the right | to withhold or transfer a scholarship at the end
but let us examine the case of the average boy leaving school. This is a summary of their evidence. "The boys you sent us from your Anglo-Chinese Schools are all right when it comes to copying letters in a legible hand, and they take things down from dictation fairly well, but they show little or no resource, are lacking in general intelligence, and do not make that progress and show that interest in their work which an employer looks for, while their ignorance of practical mathematica is astonish- ing." They gave me illustrations of this, and I tried to atone for it by saying that there was the probability of the employer and his European subordinates expecting too much from junior clerks, but this was met by the employers giving me living instances of boys who after two or three years in the business were not capable of taking charge of a desk, of writing in good business style to a foreign firm, or of dealing intelligently with quotations and
estimates from Chinese firms here and inland because they lacked knowledge concerning the commodities or were unable to apply what knowledge they had. Only the other day I dis- covered the senior clerk of our own depart- ment using a most primitive method to convert £30sterling into dollars at 1s. 11d., and using up a whole sheet of foolscap paper, pretending to check it by going over the same figures again. Now this may seem a harsh criticism, but un fortunately the main points are true, and it
tion to ask the reason and where possible is for those of us who are interested in Educa supply the remedy: Much of the blame (if I may use the word) attaches to the scholars them- gelves who are tempted by the offer of a fifteen dollar billet when they have only a superficial education in English and in western
The Government provides the school, the knowledge, and even in their own language. It is for the apparatus, the teachers. Chinese boy therefore to look further ahead. He need not be afraid that he is losing oppor tunity when he refuses the first which comes his way. An employer, whether he be a business man or a Government official, is only too glad
and ready to engage a competent servant, and I have told the boys that they are badly paid
because they are not worth more, and that a little knowledge is a dangerous thing.
The annual report of the Wantasi school was then read by Mr. YOUNG HEE, the Head Master. Among other things it stated:
At the beginning of the year under review After there were 104 pupils on the register. the usual New Year vacation, work was re- commenced on the 2nd March, when 13 boys from the vernacular school and 48 new boys were enrolled. During the remainder of the year 13 more new pupils were admitted, making together 74 new boys enrolled throughout the year.
The total number of scholars at this
school during the year was 178. During the year, the school was open on 198 days, and the average daily attendance was 114.67, which is
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