Mathematical...... 26 On Teachers' Salaries, 37 On Temperance.. 37 ..70, 71 Kindergartens,.. .38, 131 Kingston Collegiate Institute.... 58 L Legislative Public School Appor. tionment, 1872.. 65 Libraries, Free Public, in Ontario.... 17 Lindsay Separate School, 15 LITERATURE AND READING : Pa pers on. 24 Home, Sweet Home.. 25 The Price of Poems... 25 English Synonyms.. 25 About Canadian Newspapers, 25 London-its Educational Institutions.. 110 Loretto Abbey-Lord Dufferin's Visit to. 155 P Opinions of Great Men on the MISCELLANEOUS CORRESPON Adequate School Accommo- 13 dation.... 41 A Tribute to the Queen..... 13 New method of finding Sun's School premises and AccommoQueen Victoria and Her distance from Earth 5 dation... 14 6 School House Ventilation Without Drought.. 41 Canada's subscription to Chica Morse, S. F. B.... 108 Compulsory Sale of School go sufferers 14 10 Sites... 65 SCHOOL Grant, 1872. in schools.. 70, 71 Houses, prizes for plans, ... 96, 98 Murchison, Sir R... 99 12 Houses, Ventilation. Meetings, Annual.. 177 Four pictures 45 98 Rules for guidance of life... 45 Law Decisions.... 35 College President to young Normal School for Ontario...81, 148 Trustee qualifications... 180 men. 45 Nova Scotia University EducaSmokers... SCIENTIFIC SUBJECTS : Papers on 45 tion...... 10 Characteristics of Courtesy... 45 Social Science in St. Paul's The old Professor 74 Cathedral... 41 The Governor General's estiOntario Law Course Classic Verse and Natural 73 Science.. 43 The Magic Needle. Beautiful Chemical Experi- ment. 42 Wonders of Science. Usefulness of a piece of Com- mon Mirror.... 42 Curiosities of Animal Life,.. 42 43 43 Conversation at home 109 25 Siberian Delusion Dispelled, 43 Effect of good reading 109 Open the door for the children, 31 Smith, Goldwin, ou Educational Four Pictures 56 The veritable "Uncle Tom"... 109 The old Professor 74 St. Michael's College, Lord Death of a Scholar...... 110 Rain in Summer 154 London, its educational institu Rest 108 Sunday Schools in Canada, Adtions 110 110 dresses to Lord Dufferin..... 157 138 Sunday Schools in Canada, On 167 127 138 Superannuation Fund, 6, 16, 79, 115 Monosyllabic poem.. 138 T 138 Provincial First-class Certifi. cates ..47, 96 | TEACHERS' Association, South Words of wise men 138 Hastings.. ..15, 46, 174 Literary men hold out well 138 Q 15 True and false manners. 113 138 QUEEN, H. M. THE. A tribute Of Ontario. Retired from the profession... 181 14 Telegraph Wires... 43 What makes the man 139 At home 109 Township Boards as opposed to To interest boys in farming... 139 At the paper mill.. 126 161 School Sections.. 15 Lord Dufferin's Visit to.. 150 R 43 127 Toronto..... .105, 175 Unconscious brain work 141 England.. 47 Visit of Lord Dufferin to To. The Number 7....... 141 Roman Catholic Separate ronto f... 148 Preparing skeleton leaves 142 School Apportionment, 1872 65 Upper Canada College, Visit of The leaves of Autumn 143 Ryerson's, Dr. Lessons in Lord Dufferin to.... 151 8 92 174 A word to boys.. 173 7 Wykeham Hall, or Bishop Read an hour a day 173 Strachan's School.. 128 Archbishop Sumner on Obsta Lord Dufferin's Visit to......... 153 Y SITES. 186 Inadequate provision tor Young, Dr. on Recent ExaminaWhy timber is painted... 186 School Accommodation....... 40 tion.. 1 86 13 M McCabe, Mr. Gold Medal Offerad by... 115 McGill College, 62, 80, 174 Macdonald, Hon. J. S. Manning, Archbishop, on Education,.. 10 Mathematical Departm't,89,102, 172 MATHEMATICAL AND SOIENCE 136 The Natural Sciences School, 136 The Study of Nature as á Means of Intellectual Development.... 136 Remarkable Facts in Nature, 136 Weather Indications... 136 Injury to Physical Health in Schools,.... 136 137 Meteorology in Canada. 172 METEOROLOGICAL REPORTS MONTHLY, 4, 30, 44, 63, 69, 95, 111, 124, 134, 159,... 171 Observations.. 5 MISCELLANEOUS : A Sabbath in the Country..... 12 137 4 6 15 CONTENTS OF THIS NUMBER. students—and none of them obtained 40 per cent. of the THE RECENT EXAMMATION OF TEACHERS I. MONTILY REPORT ON METEOROLOGY OF THE PROVINCE OF ONTARIO.(2) Me 1 marks assigned to the Algebra paper ; 18 out of the 21 fell teorological Observations II. MISCELLANEOUS CORRESPONDENCE OF THE JOURNAL.-(1) New Method of finding below 30 per cent., 13 out of the 21 were under 20 per cent., the Distance of the Sun from the Earth. (2) Diophantine Problem. (3) Correspondence. (4) Superannuated Teachers' Fund.. and 7 out of the 21 were under 10 per cent. It may perhaps III. PAPERS ON EDUCATION IN ONTARIO, &c. (1) working of the New Law and be said that this extraordinary record proves the paper to have Regulations. (2) Governor Howlaud's Speech. (3) Compulsory Education. (4) Public School Library, Liberality. (6) The First Sabbach School in Canada. (6) Provincial Sabbath Schools. (7) Dr. Ryerson's First been too difficult ; but I deny that this is the case. I appeal Lessons in Christian Morals. (8) The Clergy in the Schools IV. MISCELLANEOUS EDUCATIONAL INFORMATION.-(i) Valuable Art Collection for to the notes below, as proving that the questions, though they Montreal (2) Dalhousie College, Halifax. (3) Nova Scotia University 9 Algebraists, are really simple to those who have an intelligent V. BIOGRAPHICAL SKETCHES.-(1) Hon. Judge Aylwin. (2) Peter O'Reilly, Esq. (3) Mrs. Davis. (4.) Capt. John Dench. (5) Recent Canadian Death. (6.) apprehension of the elementary principles of the science. Sír Roderick I. Murchison.. 11 VI. MISCELLANEO'S. - (1) Sabbath in the Country. (2) Sunday in the Wilderness. In Natural Philosophy one gentleman answered with sul (3) Opinions of Great Men on the Sabbath. (4) Stand up for your Sun- 12 VII. EDUCATIONAL INTELLIGENCE ... pression, all the questions proposed, except one where he was VIII. DEPARTMENTAL NOTICES 16 partially wrong. A considerable number of other gentlemen IX. ADVERTISEMENTS 18 made a creditable appearance in this branch ; but I am obliged THE RECENT EXAMINATION OF TEACHERS. to say that the papers of the ladies in Natural Philosophy were, for the most part, like their papers in Algebra, a signal To the Editor of the Journal of Education. failure. Ten ladies, out of twenty-one who competed, failed SIR,—The answers given to the first-class papers in Algebra to get more marks than were assigned to the correct answer of and Natural Philosophy, at the recent examination for teachers' a single question. certificates, are such as to call, in my opinion, for some remark. Here, again, it would be ridiculous to say that the paper is I have added to this letter a few notes, in which I show how too difficult for first-class teachers. The solutions, given in the to solve all the questions proposed, except one or two, which notes appended, will show that the paper is really a very easy are of a very simple character. one—that is, to a person who knows anything of the principles The answers to the questions in Algebra are, on the whole, of Natural Philosophy, and has not merely got up some rules a signal failure. I do not think that any person, who is com- by rote. But as it is not unlikely that the cry of difficulty petent to pronounce a judgment, will say that the Algebra may be raised, I will state two facts which should be conclusive. paper is too difficult. With the exception of the last problem The first question on the paper asks how the velocity of a —which was not taken into account in fixing the total value of moving particle is estimated, when the velocity is not uniform. the paper, but was introduced for an important purpose, Only one lady out of twenty-one answers this clearly and mentioned below—it contains nothing which does not lie correctly; two others give ambiguous answers ; the rest give directly in the line of familiar Algebraical principles, or which no answer, or an answer which is decidedly erroneous. This a candidate for a first-class certificate ought not to be able to fact, of course, means that 20, or at least 18, out of the solve off-hand. The notes which I have appended will show 21 female candidates for first-class certificates, are ignorant of how easy the questions are to a moderately qualified student; the science of Dynamics. Again, the fourth question asks :yet not one of the candidates who presented themselves at the what power will sustain a weight of 40 lbs. in a system of two recent examination for first-class certificates is entitled to 60 moveable pullies, where each pully hangs by a separate string, per cent. of the total marks ; and the great majority of them the weight of the pullies (each of which weighs 2 lbs.) being fall very far below that point. taken into account ? Inability to answer this question means I regret to say that the ladies have been particularly unsuc- ignorance of the elementary principles of Statics ; and yet the cessful in this department. There were 21 female candidates question was answered by only four ladies out of twenty for first-class certificates-20 of them being Normal School one. 2m m +1 2 + 2m m +1 + m+1 3 6 m 24, yzv 64, y 24, ryz I have sometimes doubted whether it is desirable to make the with in their text-books, but had never understood. As the quesstudy of Algebra and Natural Philosophy, any more than that of tion is book-work, I need not give the solution here. Geometry, compulsory on female teachers. I do not question the ,7. Only one of the papers which I have examined, that of Mr. ability of ladies to learn these branches ; but ought they to be re- W. G. Carson, contains a correct solution of the seventh question. quired, in the present state of female education throughout the The following is Mr. Carson's solution, E is the middle point of Province, to do so? Would it not be better to grant first-class AC, and D of BC : certificates to female teachers, if they had the necessary attainments in other branches, and in the event of their passing a suc = P's time from A to E. cessful examination in Algebra and Geometry, and Natural Philosophy, to add this to their certificate as a circumstance which would P's time from E to D. enhance the value of the certificate? One advantage of such an hrs. arrangement would be that those ladies who wished to study Natural Philosophy, might be required to prepare themselves for doing so time Q travels to D. by a previous course of Geometry as well as of Algebra ; and the master, whose duty it is to teach Natural Philosophy in the Normal 17 School, would be delivered from the hard and (in some respects) im time of Q from D to C. practicable task of giving instruction in this science to a class, one 3 half of the members of which have no acquaintance with the elements of Geometry. I have no desire to make rash changes. I P's time from D to B. only throw out an idea which has frequently occurred to me, and 2 (m + 1) which the recent examination has forcibly revived. The Principal and masters of the Normal School have become 2 m m + 1 satisfied that new arrangements are necessary to render that Institution thoroughly efficient; and, acting on their representation, 2 (m + 1) 3 the Chief Superintendent and the Council of Public Instruction have framed regulations as to the entrance examination to the 1 Normal School, and the curriculum to be pursued, which I have 2 (m + 1) 3 (m + 1) no doubt will have a very beneficial effect. 3 mx = mx + x + 2 mx - m? m I am, sir, x = m (m + 1). Your obedient servant, 8. As Mr. Carson's papers are open before me, I may give his GEORGE PAXTON YOUNG, solution of the eighth question also. He takes o, x, y and - as the Toronto, 13th Jan., 1872. Chairman of ('entral ('ommittee. numbers sought. vxy = 1, xyz 8, yxv = ALCEBRA.-First Class. 27, vxz = 64 (czy:) % = 14824, VXYZ 24 1. The first question in the Algebra Paper, though simple and VRY 1. even elementary in its character, was correctly answered by a com 24. paratively small number of the candidates. The expressions, whose VXYZ 27, x product is to be found, may be written in the forms, VXYZ 24, vxz = (? - * - 1) V-1-(x2 + 2x - 1), vryz 8, v = 3. (2o – 2 – 1) N-1 + (x2 + 2x – 1). 9. The following solution of the ninth question is from the papers of Mr. Derness. Every number, or any number n, when divided The product of these is, (t? – X – 1)2 – (x2 + 2x – 1)?: Expand by ? will give a quotient without a remainder, or with either l or and arrange according to the powers of x, and the required result 2 as remainder. is obtained. n = 3 2. Very few of the candidates answered the second question in 9 the Algebra Paper. I am at a loss to understand what puzzled or 39 + 1 them. Divide every term by xn. Then or 3 q + 2. :. Ist. -- no < 99 2:M-n (a2 – 62) – 4 a b 2 , 2nd. no 9q2 + 69 + 1 3rd. --n? a quadratic which can be solved by the ordinary rules. 9q2 + 129 + 4. 3. Most of the candidates solved the equation in the third ques. Evidently the first is divisible by 3. In the 2nd the first two terms tion, finding x = But not many succeeded perfectly in showing are divisible by 3; therefore if we add 2 to the third term, it that this value of x, when substituted in the given eqnation, satis- renders it divisible. In like manner it may be shown that the fies the equation. In fact, the substitution gives us third is divisible by adding 2 to 4, equal to 6 (which] is divisible - 1= 2. 10. The tenth question has not been solved by any of the candiNow has two values, + and - 3; and Vi has two valnes, dates whose papers I have yet examined. Where is the difficulty ? 1. We require to take the former value of the first Let 24 = rate required, and y the distance between A and B. Then expression along with the latter value of the second, thus : 1 1 39 2x + 4 2x 4 60, 4. The fourth question was correctly answered by the majority 1 1 8 of the candidates. and ข 5. The fifth should have presented no difficulty to a candidate 3x + 4 3x 4 3х) 60. for a first-class certificate ; but, out of thirty-eight papers which I Eleminate y, and the result is a pure quadratic, giving 2x = 6. have examined, only one, that of Mr. J. Derness, contains a per 11. The eleventh question, as being somewhat peculiar, I did not fectly correct answer. Let r be the common root. Then take into account in fixing the total value of the paper; so that its 202 + pr + 3 = 0 presence in the paper could be an injury to no candidate, though po? + (p-10)r - 7 = 0. it might be of service to some. It has not been solved by any of the candidates whose papers I have yet examined. I gave it for ..10r + 10 = () and -1. the purpose of exemplifying a method which is of the greatest use in Algebra. It is easily seen that the law, which has to be estabHence, from the first of the given equations p = 4. Divide lished, holds for a certain number of terms. For instance, it is 22 + 4x + 3 by 2 + 1, and we get 2 + 3. Therefore the second true when the series consists of only one term, or when it consists root of the first equation is – 3. The second root of the second of two terms; for 12 = 13, and, (1 + 2)2 13 + 23. Now, equation is found in the same way. when a law has been ascertained to hold good for a certain number 6. A considerable number of the answers to the sixth question of terms, how do we proceed to show that it holds universally? In were unsatisfactory. Many of them gave me the impression that this way : assume that it has been found to hold for (n - 1) terms. the candidates were trying to remember something they had met Then prove that it holds also when n terms are taken, If this can + ns. be done, it must hold whatever number of terms be taken. In the (Mr. Hands, in this last line, has written A - B for B-A, manicase before us, assuming the law to hold for (1 - 1) terms, let festly by oversight. Other gentlemen have given the numerical 1 + 2 + + (n - 1) value of the result, obtained by putting 32 for g, namely, 2 11: S, One gentleman, Mr. Derness, correctly remarks that this problem contains the principle of Attwood's machine.] (1 + 2 + + n)2 = (s + n) = + 2 ns + no. n (n - 1) But, by hypothesis, so = S. Also, s = Therefore 2 To the Editor of the Journal of Education. (1 + 2 + + n) S + na (n 1) + n° S + n) SIR, -The prepared answers of the following questions in the : 19 + 23 + recent examination papers on Arithmetic were wrong : Divide £4,762 15s. 91d. by 300. Ans.-£15 178. 62000. (QuesNATURAL PHILOSOPHY.-First Class. tion 1, III. Class). A coal dealer bought 784,000 lbs. of coal at 1. I ask particular attention to the first question, because a large $4.50 per ton (2,340 lbs.), and sold 527,500 lbs. at $5.50 per short number of the papers which I have read---not less than fifty per ton (2,000 lbs.), and the balance at $4.20 per short ton. Find his cont.-exhibit the most indistinct and erroneous ideas in regard whole gain ? Ans.-$412.324. A circular fish pond of 90 feet even to so elementary and fundamental a matter as the mode of radius is surrounded by a walk 25 feet wide. Find area of the estimating the velocity of a moving particle, whose velocity is not walk? Here the radii are 90 and 115, then sum of radii multiuniform. The following answer, by Mr. John F. Maclaren, is cor- plied by their difference 5,125, which multiplied by 3.1416 gives rect : "The velocity of a moving point, when the velocity is not the required area. (Question 12, II Class). The above questions aniform, is estimated by finding the space through which the point are so very simple that the errors in the given answers would be would move in a certain unit of time, were it to keep the same detected at once, and I am safe in saying that the candidates would velocity throughout that unit of time, which it had at the beginning suffer no injustice, because, if a candidate's answer does not agree of it." with the given answer (even if correct), the Examiner is bound to 2. The second question presents no difficulty. read the proffered solution, and to allow for accuracy of reasoning 3. Very few correct answers have been given to the third ques- whilst deducting for inaccuracy of result. No one correctly tion; and none are as simple as they might have been. Let Å be solved the following question, No. 4, I. Class :--City of Toronto 6 the highest point to which the first particle rises, and P the point per cent. Debentures, having six years to run, are offered for sale. where, in its descent, it meets the second particle ascending. Then, What price shall I pay in order to realize 10 per cent on my inas the one particle is a second ahead of the other, a second is occu- vestment? Now the amount of $100 for 6 years at 6 per cent is pied with rising from P to H, and again falling from A to P. But 100 (1.06)", which must equal the amount at 10 per cent. for 6 the times of rising and falling are equal ; therefore, it takes half a years, of the price paid-hence, for every $100, I should pay second to fall from H to P, and therefore HP= 4 feet. But the 1:06 0 Х height of H above the ground is 1600 feet. Hence P is 1596 feet above the ground. Only two or three candidates (students of the Normal School, I 4. The fourth question is easy book-work. believe), solved the following question (6th, Class I.) :-A man 6. Almost all the gentlemen, whose papers I have read, have bought a farm for $5,000, and agreed to pay principal and interest answered the fifth question correctly; but it has been answered by (6 per cent.) in four equal annual payments. Find the annual only three ladies out of twenty. This, as I have observed above, payınent? Most of the candidates that attempted the solution of is a significant fact. The problem is of the simplest character. this question, found the amount, at compound interest, of $5,700, Can any one, who understands the elements of Statics, fail to per- and divided that amount by four for the annual payment, thus ceive that the weight being !40 lbs., and the pully to which it is proceeding on the false principle that an annual payment of $100 attached weighing 2 lbs., the tension of the string passing round 6 per cent. interest) will amount to $400 in 4 years. They should that pully must be or 21 ? In like manner the tension of the have found what annual payment continued 4 years will give the string passing round the the second pully must be one-half o amount of $5,000 for 4 years. I need hardly say that compound (21 + 2), that is, it must be 114. interest is the only correct principle to employ in the solution of 6. The following is the answer given to the sixth question by Mr. the last two questions. J. G. Hands. The 6th question in 1st Class Book-keeping paper, the solution Weight of flask = y of which has been declared " impossible,” is as follows :Weight of air = y-* What is meant by averaging an account? What is the balance Weight of water in vacuo = weight of Alask and water, minus weight of the following account, and when is it due ? of flask, plus weight of air displaced JOHN SMITH. 1871. 1871. Cr. .: Specific gravity of air March 1.. To Sundries... $436 00 March 25...By draft at 60 weight of water April 12... “ Goods 548 00 days $400 00 The question was correctly answered by almost all the other gentle- July 16... 312 00 April 6......By draft at 30 men, whose papers I have read, and by four ladies out of twenty. Sept. 14... " 536 00 days 650 00 7. The seventh and eighth questions are book-work. June 20.....By cash. 200 00 8. The ninth question is solved with substantial accuracy by Aug. 3.. 84 00 several gentlemen, though all the solutions which I have read con Solution of the above by Mr. McColl. tain defects of expression. From CA cut off CF = A E. Join BF, DF. Thon BEDF is a parallelogram. The resultant of the Averaging an account is finding at what time several debts due forces EB and ED is EF. We have, then, acting on the particle at different dates might be paid without loss to either party, or at at E, the following forces : what time an account would properly begin to draw interest. In the direction EA, a force represented by EC. The balance of the account is $1,832--$1,334 $498. AssumIn the direction EC, -.-a force represented by EA, together ing March 1st as date of reference we have :with a force (the resultant of EB and ED) represented Dr. Cr. by EF. $436 x $400 x 87 34800 But EA and EF, which are equal to CF and EF, are equal to EC. 548 x 42 23016 650 X 69 44850 Therefore the particle at E is kept at rest. 312 x 137 42744 200 X 111 22200 9. The following solution of the tenth question is from the papers 536 x 189 * 105592 84 x 155 13020 of Mr. J. G. Hands : The weight upon which the force of gravity acts is only 2 lbs.; 171352 114870 10lbs. of B being counterbalanced by A. But the weight to be set 114870 Balance.... June 22nd, 1871, when the balance should be paid. that is i th of the velocity produced by gravity upon a particle Mr. J.G. Hands gave the same solution, and Mr. J. Derness moving freely. and Miss Meehan, taking September 14th as date of reference, General formula -.. obtained the same result. These four were Normal School A-B students, J, A. McLELLAN, 66 0 (Days of A+B |