the teacher "to teach diligently and faithfully all the branches required to be taught in the School, * * according to the provisions of this Act."

Knowing that third-class teachers are not competent to teach "all the branches required to be taught in the School," the Council of Public Instruction has prescribed that in every School in which two or more teachers are employed, one of them "shall be designated and known as the master, and the others as first, second, assistant," etc. The regulations also give the master power, "to prescribe (with the assent of the Trustees) the duties of the several teachers in the School," but makes him responsible for the control and management of the classes under their charge." The regula

tions further prescribe the specific duties of assistant teachers, and certainly a great shame to the managers of the school, whose declare that in every school, where the number of pupils on the roll exceeds fifty, an assistant teacher shall be employed. Overlooking the words of the Statute and the general regulations, Trustees, in some cases, object to the Programme as beyond the capacity of third-class teachers, and argue that as the subjects prescribed for the examination of third-class teachers are much below those required by law to be taught in the Public Schools, it is both anomalous and unjust to require their third-class teacher to teach them. They say. We are authorized to employ third-class teachers for our School, and yet you require these teachers to teach subjects with which they are wholly unacquainted, and in which they themselves are not required to pass an examination."

We have already answered these objections, and have shown that, according to the letter of the Statute, Trustees are required to employ more than one teacher in every School. We have also shown that the regulations provide for the employment of a master and an assistant or assistants, and prescribe a programme of studies which this master and his assistant shall teach, in order to afford to every child in a Section an education suitable, &c., in the various branches of instruction prescribed by the Statute.

neglect of adequate accommodation or adequate teaching must
cause indifference and neglect in the attendance of pupils. I find
by the returns that your school-house is 48 by 30 in the clear in
the inside-affording sufficient space for all the children of school
age in your section, if properly arranged, and for two teachers, if
divided into two rooms, as so large a school-house ought to be.
"I can find no reasons in your letter that would justify me in
not insisting upon the execution of the law in your section as in
other sections much less favourably situated and much less wealthy
than yours. You and your trustee colleagues are certainly bound
by law, as well as by a consideration of the interests of the children
under your official charge, to employ a second or assistant teacher.
I observe that you speak of the average attendance of pupils; but
that is not the law which speaks not of the average attendance, but
of the number of pupils in a school;' and this is determined,
not by the average attendance, but by the number of pupils on the
school register. It is possible that trustees, from mercenary or
other unworthy considerations, may keep the average attendance of
pupils low by not providing adequate teaching or school accommo-
dation for a large number; but the number of children whose
names are on the School Register show the number of children
whose parents wish to have them taught in the school, and for
whose teaching and accommodation the trustees are bound to pro-
vide, under pecuniary penalties equal to the amount of the school
money lost to their section by their neglect, besides being liable to
prosecution for damages by any parent whose children or child is
not provided with the legally required means of school teaching
and school accommodation.

To admit these objections as valid would be to declare that no child shall receive an education beyond that which a third-class teacher may be able to give! This would, indeed, be an absurdity, as well as a gross injustice to the pupils in our Schools. This, also, as we have shown, was neither the intention of the Legislature, nor the spirit or provisions of the law and regulations which were framed to give effect to that intention. In nearly every school there are advanced pupils (or would soon be, if proper teachers were employed). According to the theory advanced by some trustees, these pupils "Experience shows that trustees in rural sections who provide must remain satisfied with the meagre education which third-class proper teachers and proper accommodations will secure an average teachers can give them, and be denied that better education which attendance of nearly, and in some instances quite three-fourths of the law secures to them, and for which their parents pay rates. the children of school age in their division. Trustees who neglect Third-class teachers may be competent to teach the first and second their duty, not only violate the law and the public trust committed and possibly the third classes in a school, but they are not qualified, to them, and incur a pecuniary penalty, but they do a great and and should not be employed to teach the fourth, fifth, and sixth irreparable wrong to the rising generation, whose interests they classes. They can, therefore, only be useful as assistant teachers. have been elected to protect and promote, and for the sacrifice of Formerly (under the School Law of 1850) County Boards of which no money can ever compensate." Examiners were required, in the issue of third-class certificates, to limit them to a particular School Section (on the application of Trustees), where the pupils were quite young, or were not far advanced. Under the present law, this restriction was removed; but in its place other provisions were introduced, which were designed to give greater facilities for the more thorough instruction of all the pupils of a School Section in the various subjects of a good English education, which the Legislature itself had declared to be

necessary.

I. Papers on the Teachers' Examinations.

1. PUBLIC SCHOOL TEACHERS' EXAMINATIONS. There is undoubtedly an impression to some extent prevalent among the public that the examination of Public School Teachers under the new regulations is unnecessarily strict and severe, and much displeasure is expressed by some good people, that so very small a proportion of the numerous candidates who flock to the half yearly examination succeed in obtaining certificates.

It would certainly be a singular anomaly for the Legislature, on the one hand, to determine that certain higher subjects of instruction be introduced into our Public Schools, and then declare that incompetent persons should be legally qualified to teach them. The law and regulations must be taken as a whole, and their symmetry doubtedly a subject of just regret that our young people are not and completeness must not be destroyed by giving a forced con- better instructed, and this regret is fully shared by the members of struction to one part alone.

The following article will give additional information on this subject:

ADEQUATE ACCOMMODATION AND ASSISTANT
TEACHERS.

In reply to a communication from a Trustee, on these subjects,
the Chief Superintendent has sent the following reply :—
"The second section of the School Act of 1871 provides that
"Each school corporation shall provide adequate accommodation for
all children of school age in their school division or municipality.'
The seventeenth section of the Consolidated School Act authorise
'the trustees of each school section to see that the school under their
charge is conducted according to the authorised regulations.' The
seventh of the authorised regulations says: When the pupils in a
school amount to more than fifty, and less than one hundred, the
trustees must employ an additional teacher as an assistant.'

"Such are the provisions of the law, which it is my duty to see executed by all parties concerned. It is thus seen that the trustees of your school section are required to provide adequate school accommodation, not for the number that may be in the school for the time being, but for all the children of school age in your section. The law makes the school free to all; requires the attendance of all, at least, one-third of the year; assumes that all may be present at one time, at least, a part of the year.

the Board.

It is un

In the County of Oxford the number of applicants for secondclass certificates was six; only five, however, put in an appearance. One of these retired at the close of the first day, finding he was not equal to the exercises required in Arithmetic, and all the remainder at the close of the third day followed his example. To one of these, however, a third-class certificate was granted.

In the third class there were fifty-six applicants, of whom seven failed to appear, The total aggregate number of marks possible in this class was 1,185. Of these 50 per cent., or 593 marks, were required to pass, and thirteen obtained the required number.

The highest number of marks obtained by any of the failing candidates was 582-six ranged below that number down to 550-eight below the latter number down to 500-three from that down to 450 eight between 450 and 400-nine between the last number and 300-and one as low as 184.

It has been stated, in explanation of this not very reputable state of things, that many young persons present themselves for Examination without any expectation of passing, but come up, so to speak, to get their measure taken, that they may know what their intel lectual standing is. This may display a very laudable ambition on the part of the applicants, but it is a practice that ought not to be encouraged, and it might be well for the Board to adopt some sort of test by which all would be excluded except such as really intend to enter the profession.

It is very much to be regretted, that most of those candidates "In examining the returns, I find that the number of children who fail at a given Examination, and afterwards renew the attempt. reported of school age in your section in 1872 was 129, with 112 not only fail again, and in some cases repeatedly, but, what is worse, names on the school register the first half of the present year, although many of them do not appear to have made any material advanceaverage attendance is only little more than half that number-ment in the interval.

... 7th term

Such, however, it is shown by the records of the Board, is not the case. Of the forty-eight candidates at the late meeting, 24 had pre- The two real values of rare and viously applied fled, only two finally obtaining certificates. Of the remaining twenty-two, eight had twice before failed; two, three times; and one, on that occasion, suffered a fifth defeat.

; and the series are,

1, &c.

8, 4, 2,
8, 4, 2,

--

1, &c.

The following instances will show that some of the candidates, The remainder of the question is simple. though threatened with the mortification of successive defeats, are unable du ing 6, 12 or even 24 months, to make any solid advance8. Because m+n-1 is a root of the equation x3 + qx + ment in those very subjects in which their deficiencies had beforero, m · n √ 1 is also a root of that equation. Therefore, been demonstrated. One candidate who competed in four successive Examinations obtained the following marks in arithmetic, at xs+qx+r is divisible by x2 2mx+ m2 + 2 without remainthose several Examinations respectively; the highest number der. Let the quotient be x 8. Then the expressions, sible being 200; viz.: 28, 75, 45 and 52. x3 + qx + r,

pos

The same; spelling, 50 being the maximum, 40, 10, 30 and 15 respectively.

Another in the three successive Examinations in Geography, 150 are identical. Therefore, being the maximum; 65, 78 and 49 respectively.

Surely the public will suffer no loss by the elimination of this sort

of material from the teaching class.

"From such apostles," exclaimed the indignant Cowper, after describing an unworthy class of clergymen :

"From such apostles, O ye mitred hands, preserve the flock, and lay not careless hands on empty skulls, which cannot teach and will not learn."-Woodstock Times.

Toronto, 15th September, 1873.

To the Editor of the Jon nal of Education: SIR,-I send herewith for publication in the Journal of Educa-senting any special difficulty, I gave it as a test question, in view tion some notes which I think may be of interest to teachers.

.(1)

15
8

3. Assume x + y + z = t (m + n + r)..............

..x + 2y + 32 = & x + 3y+ 4% Subtract (1) from (2). Subtract (2) from (3).

· (m + 3n + 4r).
Then y + 2z t (n + 2r).
Then y + 2 = = t (n + r).
tr, and

.2=

2

t.

=

1 lb. on the sq. in.

But pressure of external air = 15 lbs. to sq. in.

.. Elastic pressure of air inside receiver of elastic pressure of external air. [A considerable number of the candidates offered no solution of this very simple question; and a considerable number of others gave a partially erroneous solution.-G. P. Y.]

2. Mr Cochrane's solution.-Let FEH, KEG be drawn parallel to A D, A B, respectively. (The point K is in A D, H in DC, G in CB, and Fin BA.-G. P.Y.) Then, because E A represents the first force in magnitude, its components will be represented in magnitude and direction by EK, EF. Similarly the components of 2 E B are represented in direction by E F and E G, and in magnitude by 2 EF and 2G. The components of 3 EC are represented in magnitude by 3 E G and 3 E H; the components of 4 ED by 4 E H and 4 E K. Hence the particle E is kept at rest by a force of 3 EF in the direction EF

But the forces 5 E G and 5 E K are opposite in direction; .. they must equilibrate each other; .. 5 EG 5 EK. EGEK; which proves first. And the forces 3 FF and 7 E H are opposite in direction.. they must equilibrate each other.

.. 3 EF 7 EH or EF; EH=7:3, which proves second. [Mr. Cochrane's was the only perfectly satisfactory solution of this easy question in the Resolution of Forces.-G.P.Y.]

3. Let B D be the perpendicular let fall from B on A C. The candidates, who solved this question, reasoned in the following manner: Let P, acting in direction BA, or W in BC, be counterbalanced by Q acting in direction B D. Then,

Q:P BD: BA

and W: QB C: B D. Therefore, &c.

4. Let P move up A B from A to B, while W moves down BC from B to E; BE being equal to B A. Draw BD and E F perp. to 4 C; and let E G, parallel to CA, meet BD in G. Then, by the principle of virtual velocities,

PXDB= WXG B.

.. P: W = BG: BDBE: BC= BA: BC. But this is the relation which was found, in the previous question, to subsist between P and W.

[This is not very well put. Mr. Davison should have said that the reaction of plane, the tension of string, and weight of body, are proportional to BD, DM, M B, the sides, taken in order, of the triangle BD M, whose sides are in the direction of the forces.-G. P. Y.] Now, since M B is parallel to the direction of gravity and is 34 feet in length, and since gravity [the weight of the body.-G. P. Y.]=34, therefore each foot of the side corresponds to 1 lb. Therefore, since D M is 20 ft. in length, the tension of the

9. Solution of Mr. John L. Davison.-(Mr. Davison draws AP and B G perpendicular to D C.)

Let R force acting along D A.
R1
B C.

5. (a). "The magnitude of forces is measured by their effects, and the effect of forces which we consider in Dynamics is velocity... Accelerating Force is measured by the velocity which, in a given time, it would add to the motion of a body... .If the velocity added be equal in equal times, the force is said to be uniform or constant." [The above sentences, which I quoted once before from a work on Dynamics by Dr. Whewell, I quote again, because, string 20 lbs. though I have endeavoured, year after year, to get candidates for first-class certificates to apprehend the fundamentally important conceptions of acceleration and uniformly accelerating force, the recent examination shows that very general confusion of mind on the subject still prevails. One candidate says: "A uniformly accelerating force is one in which the acceleration is changed for every [Mr. Davison resolves the forces vertically, and in a direction at unit of time which the body moves." The writer would have been right angles to the vertical; and then takes the moments about 4. nearer the mark if he had said "is not changed." Another candi- This gives him the following equations, x being the distance between date says: "A uniformly accelerating force is a force that will move the central point of the rod and the point of suspension of the a particle through equal spaces in equal times." In this case I weight.-G. P. Y.] should say that there is no acceleration. Does the force of gravity at the earth's surface move a particle through equal spaces in equal times? Another candidate says: "A uniformly accelerating force is that which is acted on uniformly acted on (sic) by the force of gravity." Another: "A uniformly accelerating force is a force whose increment of increase is the same in equal times." A considerable number of other such answers have been given. Surely, teachers who desire to obtain first-class certificates may be reasonably expected to master a conception which is by no means abstruse, [From these equations he obtains x = = 4. Therefore, &c.—G. P. Y.] and without an accurate apprehension of which the whole science of Dynamics must be a mystery to them.-G. P. Y.]

5. (b) and (c). [These have not been satisfactorily answered by any of the candidates. I leave them as exercises for students. I believe that a student will derive benefit from a thorough examination of them. The only remark which I will make is, that the force to whose action, in conjunction with that of gravity acting vertically, the motion of the body along A B is due, is the reaction of the plane.-G. P. Y.]

6. As the uniformly accelerating force of gravity generates a velocity of 32 feet in the second, it will be 10 seconds before the velocity of 320 feet in the second is destroyed; and therefore when the particle shot upwards from A reaches its highest point, its elevation will be 1,600 feet. In 2 seconds more it has fallen 64 feet; hence, if D be the point where it is at the end of the 12th second, AD=1,536 ft. But CD, the space down which the force of gravity has drawn the projectile from B in 12 seconds, is 16 X 144. Therefore,

x= 16 √255.

4 R

+

12 R1
13

112

3 R

5 R1

Thus the

Elsewhere our readers will find a report of the proceedings of the Teachers' Institute held in the Central School during Friday and Saturday last. Those who had the good fortune to be present can testify to the practical and excellent character of the work accomplished, and be done ere our educational system shall have attained its full they will probably conclude therefrom that something more must growth and maturity. What that something is, must be, indeed, School at Ottawa will probably be open for the reception of stuhas been long, evident to all intelligent educators. The Normal dents in a year's time, and two additional ones will likely follow, one at Kingston and the other at some point in the west. whole Province will be amply supplied with Normal School privileges. As adjuncts to these Schools for the training of Teachers it is considered that Teachers' Institutes are necessary, and, judging from the success of that held here last week, we should be disposed to regard them as an essential part of the system. Their advantages have been recognized by the Legislatures of several of the neighbouring States. Appropriations for them have been made, and the result, so far, has been pronounced satisfactory. In the State of Michigan, $5,000 is annually allowed for Institute expenses; in Maine, $4,000; in California, $100 for each County Institute of from three to five days' length; in Pennsylvania the amount varies from $60 to $200 for each County Institute according to the attendance; in Iowa, $50 is allowed for each, and in Indiana the same amount.

In the School Act passed here early in the year 1850, an appropriation was made "for the encouragement of Teachers' Institutes," and in that year Messrs. Robertson and Hind, then masters of the Normal School, held Institutes in each County of the Province.

8. Solution of Mr. John L. Davison. -(D E is drawn parallel to Last year the Local Legislature made a similar appropriation, but A B.) Since A B=39, and B C=26 ... A C=✔✅(2197).

And, by sim. triangles,

√2197:26:26: DC... DC= √208.

Again, by sim. triangles,

√2197 /208 208: CE.. CE 8. [The value of CE is correctly found; but there is a mistake-a simple oversight, I presume-in the statement of the proportion. The second term should be 26 instead of 208.—G. P. Y.]

And.. D M=20. [This is rather curt; though, of course, when D C and CE are known, E D is known; and, when E M and FD are known, MD is known.--G. P. Y.]

At pre

the money has not yet been touched. Assuming, then, that some-
time during 1874 we shall have two Normal Schools in operation,
one in Toronto and one at Ottawa, with possibly the Kingston esta-
blishment in course of erection, and Institutes at different points
as adjuncts to them, the question of efficient management and su
sent the prisons of the Province and the Deaf and Dumb Institute
pervision immediately presents itself for consideration.
at Belleville, and the Institution for the Blind in this town, are sub-
jected to periodical inspection by a competent officer who is
responsible to the Local Government. An officer with similar pow-
ers and suitable qualifications will, we may premise, be needed for
the proposed Institutes and Normal Schools. For the proper dis