HIGH SCHOOL ATTENDANCE AND APPORTIONMENT FOR 1872.-Continued. NOTE. The apportionment for the first half-year, distributed in July, was at the rate of $9 per pupil. Towards the close of the year, a balance remaining in consequence of certain projected new schools not having gone into operation, it was decided to distribute the money, which would otherwise have lapsed on 31st December, before the second half-year's returns had been received. The balance was accordingly apportioned as follows: First, -A grant, at the rate of 75 cents per pupil (average attendance), in the first half-year of 1872, was made; and, secondly, those schools which did not thus obtain an apportionment of at least $200 (half of the legal minimum at the rate of $400), were allowed the difference, so that all should receive at least at the rate of $200 each for the half year. The balance was thus absorbed. Some new schools being now about to go into operation, the rate per pupil, at least for the last half of 1872, had to be placed at $8, the grant being paid out of the vote of the current year. Should the attendance and the number of schools allow of a larger grant for the next half-year, an increased rate will be adopted. a In the column for deductions are entered those amounts by which the grants on the basis of attendance for the second half-year were diminished, in consequence of the sums added to make up the $200 for the first half-year, together with the sum earned by attendance for the second halfyear, exceeding the minimum at the rate of $400. No deduction is made where the attendance, without any added grant, has obtained a grant exceeding the rate of $400 for the year. b Certain of the apportionments for the second half-year were less than $200, those for the first half being in excess; but in all cases the minimum at the rate of $400 for the year was granted to each of those schools. VII. Mathematical .Department. (To the Editor of the Journal of Education.) SIR, I herewith send you for publication in the Journal of Education the solutions of the questions in Natural Philosophy and Algebra, proposed to candidates for First-class Certificates, at the recent examination of Public School Teachers. It will be observed, that, instead of offering any solutions of my own of the questions in Natural Philosophy, I have transmitted, without alteration, the papers of Mr. Somerville, who has answered with substantial accuracy eight out of the nine questions proposed, and would undoubtedly have answered the remaining question also, had he not, in reading the question, inadvertently changed cylinder into cone. What he has written on this, the only problem which he did not succeed in solving, shows that he understood the principle involved; and, as the working of the problem happens to be extremely simple, he may be regarded as having virtually floored the paper. As Mr. Somerville was a pupil in the Normal School, I think it may fairly be inferred, from his admirable performance, that the instruction given in Natural Philosophy in the Normal School is of a very superior order. The greatest number of marks, over the whole field, was obtained by a lady, Miss Anna Living. It is somewhat noteworthy that, in Algebra, among other subjects, she was decidedly ahead of all her competitors. You will find specimens of her work in the paper of solutions herewith transmitted. I send you also, for publication, specimens of her answers to the questions in History and English Literature. They will show intending candidates for First-class certificates what sort of answers the examiners regard with satisfaction, and will, at the same time, convince intelligent persons throughout the Province that the examiners are faithfully observing the instructions they have received from the Council of Public Instruction, to place no candidates in the First-class who have not attained to a high degree of excellence. I have the honour to be, Sir, Toronto, 22nd Jan., 1873. Your obedient servant, x weight of 1 cubic foot of water; but the pressure on the inner surface of the sphere is d3 x weight of a cubic foot of water,.. the pressure on the inner surface is equal to three times the weight of the water. 4th. A uniformly accelerating force is measured by considering how much the velocity is increased in one unit of time. When a body is moving with a velocity which is not uniform, its velocity at any instant is measured by considering how far it would SOLUTIONS OF THE QUESTIONS IN ALGEBRA. 1. The H. C. M., found by the ordinary rule, is x2-x-1. 2. The three values of the cube root of unity are the roots of the equation, x-1=0. But, x3-1= (x-1) (x2 + x + 1) = 0. Therefore, the required roots are found by the solution of the equations, x-1=0, and x2 + x + 1=0. 3. Let the reciprocals of the required numbers be = 10 lbs, acting in the direction of E B. 2 = √5 20 lbs, be And 1+1+x+ + = 14 x 1 1 2 /5 2 5. 5 lbs in the Again, 5√5 resolved along A B is 5 √√5 × direction of E A, and there is also another force of 5 lbs acting along E A.. the whole force acting in the direction E A is 10 lbs;... the four numbers are,, 1, 1. but there is 10 lbs acting along E B .·. these neutralize each other, and the R is along F G at right angles to A B. And the result is = 20 + 10 = 30 lbs. 8th. Since the C. G. of a cone is of its 1r height from the apex, it follows, that if the cone were laid with its axis horizontal, the radius of the base would need to be of the r height. But, if laid on its side, it would not need to be so long since the C. G. is lowered. As the time is up, I have no more time to investigate it. G. A. S. [NOTE.-Mr. Somerville unfortunately mistook the problem, by substituting the word cone for cylinder. Had it not been for this oversight it seems evident that he would have solved the question proposed, as he shows, by what he has written, that he understands the principle involved. G. P. Y.] 9th. Taking the moments around the point A we have 192 × 2 T × 12 = y. 2, and 1 5. The following solution of this question is by Mr. James Ferrie: As the minute and the hour hands are together four times in the course of 12 hours, between 4 and 5 o'clock, the time will be of an hour past 4 o'clock, i.e. 4 h. 21 m. 49 sec. by the watch going too fast. And, as the watch losing time shows 59 minutes 59 seconds, when the other shows 60 minutes 1 second, we find the time on the watch going too slow by the proportions 60 m. 1 sec. 59 m. 59 sec. :: 4 h. 21 m. 49 sec., which gives for answer 4 h. 21 m. 40 14500 39611 sec. 6. When p+q✔-1 is substituted in the given equation, the result is of the formA + B √✔-1=0, A and B being rational. But, in order that this equation may subsist, A and B must each be zero. Now, if p-q✔-1 be substituted in the given equation, the result is A-B-1-0. The roots of the equation, x2 26 2 friction at A. are equal; and for every value of m greater than are imaginary. 52.c -+m=0, remain real, so long 7 -m is positive. When this expression is zero, the roots 26 2 the roots 7), p + q b = C. -b, and a p q=c ··· From which equations, Miss Living finds :- VIII. Educational Intelligence. TRINITY COLLEGE.-The annual convocation of Trinity College Univer In like manner, assuming p and r to be the roots of the equation sity was held in the Hall of the College at the usual time, the Chancellor p+r b = .. p2r + pqr = p2q + pqr . r = 1. of the University, the Hon. J. H. Cameron, Q.C., D.C.L., presiding. The Provost having read prayers, the following degrees were conferred in the usual manner: B. A.-William Cartwright Allen, Rev. Robert Doherty, Frederick M. Morson and Alex. B. Chafee. M.A.-Rev. Wm. Stephen Westney. M.B.-Egerton R. Griffin. M.D.- Joseph Allright, Logan Murray Moore, Charles William Marlatt, Hugh Lang, Samuel Shakespere Stephenson, Geo. Steacy, Jas. McLaren Wallace, Archibald Sinclair Campbell. D.C.-Salter J. Vankoughnet. Admitted to the Divinity Class.-W. C. Allen, A. B. Chafee, J. H. Fletcher, W. E. Grahame, W. M. Tooke and W. Jupp. The Chancellor then presented the following prizes, addressing a few congratulatory remarks to each recipient :-Ogden Pulteney Ford, B.A., the Hamilton Memorial Prize for 1872. Ogden P. Ford, B.A., the Bishop of Toronto's prize for Divinity. John Austin Worrell, the Prince of Wales' prize for 1st class in Classical Honours, 1871. Reginald Gourlay, prize poem for English subjects. W. C. Allen, the Prince of Wales' prize for 1st class in Classical Honours, 1872. W. C. Allen, Classical prize for third year. Chas. John Logan, Classical prize for second year. Clarendon L. Worrell, Mathematical prize for second year. Several students having matriculated, the Chancellor briefly addressed those assembled, expressing the pleasure he felt at seeing so many students matriculating and taking the degree of M.D. ·It showed a clear indication of the good work which was being done by the College. He referred in very appropriate terms to the munificent bequest to the College of 84,000 by the late Mr. T. C. Street, and concluded by expressing a hope that a new Convocation Hall would soon be provided. The Convocation was then adjourned. IX. Departmental Notices. TEACHERS' GOLD MEDAL FOR COMPETITION. As already intimated in this Journal, we desire to state that William McCabe, Esq., LL.B. (a former successful teacher) has intimated to the department his intention to offer a gold medal, to the most successful candidate for a First Class Certificate of the highest grade, at the July examinations of this year. We hope that this generous offer will stimulate a large number of our teachers to endeavour to obtain the very highest place in their profession. NEW SCHOOL MANUAL. In answer to various inquiries on the subject of a new School Manual we would say, that as the School Law will likely be revised and consolidated at the next session of the Legislature Mr. Somerville did not finish the solution, but his equations give in 1874, it is not thought desirable to publish a School x=5, and y=10; hence, the required distance is 30. CONTENTS OF THIS NUMBER. I. SCHOOL LEGISLATION. (2) The Chief Superintendent on Education. (3) Education Returns for the House of Assembly...... II. EDUCATION IN VARIOUS COUNTRIES.-(1) An Act to Compel Children to Attend School in Michigan. (2) Deaf Mute Education. (3) Syllabus of Latin Pronunciation. (4) A Gift to Science. (5) Chat about Work and Study... III. MATHEMATICAL DEPARTMENT AND CORRESPONDENCE......... IV. MONTHLY REPORT ON METEOROLOGY OF THE PROVINCE OF ONTARIO.... V. BIOGRAPHICAL SKETCHES. (1) John Young, Esq. (2) Captain C. Rubidge, R.N. (3) Archdeacon Brough. (4) Mrs. Ruttan. (5) Mr. Samuel Fields. (6) Mr. Bright. (7) The Right Rev. Charles Pettit McIlvaine, D.D...... 33 87 41 43 44 44 VI. PAPERS ON SCIENCE.-(1) The Intellectual enjoyments of Science. (2) Water as Fuel. (3) Different Kinds of Lightning..... VII. MISCELLANEOUS.-(1) The Public School Teacher. (2) God Save the Queen. (3) Names of the United States. (4) Irish University Education 45 Ontario. SCHOOL LEGISLATION. No. 3. The new School Bill which was introduced into the Legislature, by the Hon. Attorney-General Mowat during the recent session of the Legislature, received two formal readings by the House, but was withdrawn on the last day of the Session, in deference to the wishes of several of the members. The first seven sections of the Bill relate to the election every two years of certain members to the Council of Public Instruction and to the periodical appointment of others by the Governor in Council. It was proposed to elect one member by the Public School Inspectors, one by the Head Masters of High Schools, and one by the Head Teachers of the Public Schools, and of the Roman Catholic Separate Schools. Several members of the House of Assembly also wished to give the Wardens of Counties, (as the representatives of the Municipal System of the Province, on which our School System itself is based,) the right to elect one member to the Council. |