NUMBER OF CERTIFICATES

Awarded by the Council of Public Instruction, and by the County and City Boards of Examiners, at the July Examinations, 1874.

Now, we cannot but think that in our seats of learning all over substantial happiness; and as citizens and members of society, their the continent, this study of the Indian languages and dialects has duties toward each other and to the State.

been shamefully neglected. The number of Indian scholars which Now, taking into consideration that the majority of our pupils they have produced, taken collectively, is wofully small. We have must in life gain a livelihood by physical labor, would it not be never heard of a Professor of the native languages or of any one of well to teach them physiology as well as the science of grammer, or them. And yet, philologically, they possess a peculiar importance. of quantity? Would it not be as important for them to acquire a They hold the key to the secret of the peopling of a great continent. knowledge of some of the principal facts relating to food and sleep, They may point to Phoenicia, to Carthage, to Spain, or they may and physical exertion and rest, as to acquire a knowledge of the point across the Pacific on the other hand, to Japan or Cathay, or facts of physical geography or the processes of algebraic demonstra they may lead us by Behring's Straits-to the ancient home where tion.

kindred lips spoke cognate words centuries before Columbus. The: Is it more important to know the rules of speech or the laws of diversity which exists among the Indian languages makes the study numbers than to know the laws of digestion, respiration, nervous more interesting, and greatly enlarges the scope of its usefulness. and muscular action? laws to which we are directly subject every Some of them, spoken three hundred years ago, are now spoken no moment of our lives, the ignorance, neglect and violation of which more; but in such cases, much has been preserved in the writings is so plainly evident in the American physique, and which causes of early travellers and missionaries to compensate for the loss.-apprehensions for its future? Montreal Gazette.

2. PHONETIC SPELLING.

It would not be as much of a wonder, if physiology were made one of the regular and universal branches to be taught in our common schools, as it is that it is not. At any rate, it is a matter of wonder that a practical knowledge of even the principal facts of physiology In a recent address before the American Philological Association should be so rare among our people. It would certainly be better in Hartford, on Tuesday, Prof. Francis A. March favored phonetic to tell a class of pupils that a fit of sleeplessness is often caused by spelling. "It is no use," he said, "to try to characterize with bathing, or severe and protracted mental or physical exertion after fitting epithets and adequate terms of objurgation the monstrous a hearty supper, as it arrests the digestion, and why it arrests it, spelling of the English language. The time lost by it is a large and how indigestion acts on sleep, rather than to be taught in after part of the whole school time of the mass of men, and with a large life by the local paper that to cure a fit of sleeplessness we must majority of those who are said to read, and who can read if you give run up and down stairs several times. them time, it is a fatal bar through life to that easy and intelligent Physiology is surely of as much importancce to our common reading which every voter, every human being ought to have at school pupils as any of the other empirical branches of study. command. Count the hours which each man wastes in learning to Especially since the capacity and opportunities of so many of our read at school, the hours that he wastes through life from the hind- pupils is limited, it is expedient that those branches of study should rance to easy reading, the hours wasted at school in learning to spell, be selected which will be of the most direct use and benefit in after the hours spent through life in keeping up and perfecting this life.

knowledge of spelling, in consulting dictionaries--a work that never This subject the relative importance of the various branches ends-the hours that we spend in writing silent letters; and mul- taught in our common schools-is a matter for grave consideration, tiply this time by the number of persons who speak English, and and a candid discussion of it would lead to a great improvement in we shall have a total of millions of years wasted by each generation. our educational results.-Laborer, in Pennsylvania School Journal. The cost of printing the silent letters of the English language is to be counted by millions of dollars for each generation. Who has not heard the groans of Germans or Frenchmen trying to learn how our words sound, or read the petitions of the Japanese?"

3. PHYSIOLOGY IN THE SCHOOLS.

II. Mathematical Department.

EXAMINATION FOR FIRST CLASS CERTIFICATES,
JULY, 1874.

Solution of Questions in Algebra and Natural Philosophy.
ALGEBRA.

&c.

[The author. in sending us this article has the following in a private note which we think it well to print herewith. "It is no wonder that the public press is continually complaining that our young men are crowding into the professions and clerkships, trying to make their living with their brains, 1 (a) Put y=v x. Substitute in the given equations; eliminate ¿, while our manufactories and other industries suffer for the want of hands -good laborers. As the mental faculties are the only ones they have been taught to use, it is no wonder they shrink from manual employment when their physical powers never have been properly trained or developed, and when physical labor is a sort of motor nerve,' excruciating instead of a comparatively easy and pleasant muscular exertion."- ED.]

The assertion of Herbert Spencer, that reason by extinguishing other superstitions finally becomes itself the object of superstition; that in minds freed by its help from unwarrantable belief, it becomes that to which an unwarrantable amount of belief is given, seems to derive some force from the present phase of education in our country. Eloquence exhausts itself upon the glorious attributes of the human intellect. The mind in our present plan of education would seem to be the only part of the human being worthy of development, of culture, or of being understood. And all that is or can be said of the sublime attributes of the mind, is undoubtedly true, still it is not the part of a rational nature to contemn the casket which contains this great treasure even though this casket 2. were in itself worthless. It would yet be of the highest value for 3. the offices it performs; much more when it is itself a piece of rare workmanship curiously and wonderfully wrought.

Of the great importance of the offices it performs and the relations it bears to that divine attribute, the mind, any one must be convinced by reflecting for a moment upon the single fact, that a glass of liquor taken into the stomach is capable of throwing the mind into a chaos of disorder and darkness.

Though the spirit is the noblest part of man, still, its existence and continuance here on earth for God's own wise and good reas ons, is only possible through the medium of the physical organism and in subjection to physical and material laws, the operation of which it is eminently fitting and proper that we should seek to know and understand as far as our finite powers will permit.

4.

I conceive the proper object of our common schools to be, not 5. merely the attainment of a certain degree of proficiency in "mental gymnastics," but the training and preparation of our children for their career in life as individuals in the pursuit of their true and

(b) The given equation may be treated as a quadratic, in which √(2x2-3x-1) is the unknown quantity. For, putting this expression equal to y, the equation becomes

y=3y2-2.

Hence y may be found, and therefore x.

(c) Take the cube of both sides, and simplify. Then
18 3

(x2 — a2) =-a

2

Therefore x is equal to zero. [It may be useful for a student to substitute zero for x in the given equation, and to consider whether this value of x does, in point of fact, satisfy the equation.]

Apply the ordinary rule.

Suppose that, before the accident, the watch is gaining a seconds
in the hour. Then when it indicates 6 o'clock P.M., the true
6Xx3600
3600+x*

time is
it indicates midnight is

Similarly, the additional time taken before
6×3600
Therefore the number of
3600-x

hours which elapse from the time when the watch indicates

noon till the time when it indicates midnight is Therefore, by the question,

12

{

36002

12

12×36002 36002-**

3600-x2 } = 12 +36002 — 1· · x=1.

Eliminate, from the given equations.
Let the roots be p and q. Then

p+q= −m.

p2+q2 = m2 -8.
p3+9=12m-m3.

Therefore m (m3 – 12m)=(m2 −8)2. Therefore, &c.

6. The first part of the question is book-work.
With regard to the second part, let the series be,
1, x, x2, &c.

Then 8 -1=10x-10. Therefore, &c.

[Among the real solutions of the equation 28--110r4-10, are x=1 and x = -1. Are these values, or is either of them, admissible?]

7. Let 10x be the number of men, and 5x the number of boys em-
ployed at first. The work done by these men and boys is
equivalent to that of 12x men. The withdrawal of 10 men and
10 boys leaves an efficient force equivalent to that of 12-14
men; but if, on the withdrawal of the 10 men and 10 boys,
each of the remaining boys had done a man's work, there
would have been left an efficient force equivalent to that of
15-20 men. Now, by the question, the work which 122 men
could perform in a certain time (say t days), is done by 12x-
14 men in t+7 days, and by 15-20 men in t+17 days.
Therefore 12xt = (12x − 14) (t+7)=(15x – 20) (t+17).
Therefore x=4; and 10x=40; 5x=20.

8. Book-work.

NATURAL PHILOSOPHY.

Professor Phin has devised a substitute for spongy platinum in the experiments with hydrogen gas that is well worth the attention of chemical teachers. Make a cylinder of pumice stone of an 1. In this question, by a clerical error, the force acting at B in inch in diameter. With a fine saw cut it into discs about one the direction B D is made 10lbs. instead of 20, which was the num-twentieth of an inch thick. Soak these for some time in a strong ber intended to be written by the examiner who prepared the paper. solution of bichloride of plantium in alcohol, and then as long in an Assuming the force acting in the direction B D to be 20lbs, the alcoholic solution of sal-ammoniac. After being once thorsolution is as follows:-Taking the resolved parts of the forces, first oughly ignited, these discs will inflame a jet of hydrogen, and be in a vertical, and then in a horizontal direction, we obtain the found much more useful, and far more convenient and economical equations, that the brittle form commonly purchased of apparatus dealers.

m=20+20+5=45.
n=5√3.

These values provide that no motion of the rod can take place either in a vertical or in a horizontal direction. Take now the moments round A, and we have (denoting C B by 2c) as their algebraical sum,

20×3c-mx4c+20×6c;

which (since m = 45) is zero. Therefore no rotation can take place, and the beam is absolutely at rest. (Candidates were not allowed to suffer by the error above referred to.)

III. Papers on Practical Education.

1. SIGNALING CLASSES.

Much diversity of custom prevails among teachers with respect to means and methods of signaling the movements of classes. Many teachers use the bell, giving a stroke for attention, one for rising, and another for moving in a certain order. Some teachers signal 2. Most of the candidates, who solve this question, proceed by by successive snaps of the finger, or by raising in succession one, resolving the forces vertically and horizontally. This easily leads two, and three fingers; one advantage of this means is that it is to the desired result. One gentleman supplies an elegant variation always at hand. This is perhaps its chief, if not its only, recommendain the proof. He observes that the force which acts in a direction tion. Again, some teachers move their classes by the simple tap of parallel to the plane, being equal to that whose direction is parallel a pencil upon the desk, others by counting one, two, three, etc., or to the base of the plane, the resultant of these two must bisect the by giving the orders attention, rise, pass. angle between their directions; and must, therefore, make equal If a bell is used, it should be with the least sound audible. Anyangles with the direction of the weight, and with the direction of thing like a loud stroke or jingling of the bell should be avoided. the force of reaction; Therefore (he concludes) the reaction is equal Nothing is more inspiring of disorder, confusion, and noise in a to the weight. school than a loud and careless use of the bell. On the other hand

The

3. The solution of this question by Mr. Fletcher is rather elegant. no inarticulate sound is more conducive of quietness and good Representing the weight of the square by x, he says: "Since the order than the almost inaudible tap of the teacher's pencil. On C. G. of the square is at its centre, x must act at that point, which general principles, however, where signals are given by the teacher, is in the diagonal A C. The question then simply amounts to find- we prefer vocal ones to those given by any other means. ing the C. G. of three weights, x, q, and x+34; for the direction teacher's voice is the natural medium of communication with his of the string must pass through that point.’ Mr. Fletcher has no pupils, and is no less available as a means of indicating the order difficulty in showing that the centre of gravity of the three weights of their movements than of directing the course of their general Its sound is the only proper sovereign one of the place. in question is at the middle point of the line drawn from A to the conduct. centre of the square. Whatever means of signaling a teacher may employ, the system of signals should be as simple as possible consistent with a proper

4. Let the particles come into collision in t seconds after the degree of order in the movements of pupils. Some teachers give

first has left A.

Then,

384-32t-32 (t−2)

...t=7.

But A B=16 (t − 2)2+384t — 16t2

... A B=2304.

5. If h be the perpendicular let fall from C on A B. Then,

Time of falling down C B from rest=z√ (3)

gh.

too many signals, having one for attention, another for taking up books, another for turning toward the aisles, another for rising, another for dressing the line, another for moving to recitation seats, and another for sitting. To thus grind up the aggregate of the movements of a class, and then shake a tea-bell at each one of the microscopic particles, is not order, but rather a most ridiculous affectation of it.

Without almost constant care on the part of the teacher, the pupils become careless in observing the separate signals. At the signal for rising some will be gathering up their books; others, again, will be moving to the recitation. This evil, like all others, can be corrected only by attending to it--by having but few signals and requiring prompt and exact observance of each. Again, teachers are liable to fall into the habit of giving the different signals too rapidly. This invariably causes the pupils to anticipate the signals, to make the movement before the particular signal for it has been given. The teacher is often thus led to hurry up the [The above is Mr. Fletcher's proof, with some details omitted.] signals in order to get them all in, if possible, before the pupils

But time of falling down C A from rest =X

gh

... (z — x)2=yz.

have executed all the changes. Where a great many different culture or useful knowledge. It was little else than copying, and motions are required to be gone through with, each having its par- very blindly and mechanically, at that, without any knowledge of ticular signal, the teacher will usually be able to give all the signals its principles, and rarely enabling those who pursued it to make it by the time the class, doing its best, will have completed its share a useful art. It is now taught differently, and largely for a different of the performance. We have seen it tried, and the feat success purpose. Its simplest elements and principles are brought within fully accomplished. The effect is very amusing. Those who do the comprehension of children and youth, as easily as are those of not dare to venture upon such an undertaking should have but few arithmetic; and it is found that practice in drawing gives facility separate signals for any general movement, should give them slowly and accuracy in execution as readily and surely as in penmanship by some appropriate and natural rather than artificial means, and or in the mechanic arts. Its object is not, as now taught so generally, should insist upon each signal being promptly and properly re- to make artists of those who learn it, although it is serviceable for sponded to by each and every pupil to whom the signals are that, as to make artisans, and to enable all persons who may have addressed.--The School.

2. SPARE THE ROD."

I

arts.

occasion for it, to embody the conceptions of the mind in beautiful and useful forms. Hence, drawing, and especially industrial drawing, has of late been rapidly introduced into the public as well as the technical schools of our cities and large towns. The bearing In the course of a sermon of an eminent Divine, he said: Many of this subject upon the productiveness of a people, and upon their persons object to a physical punishment for children, but they ability to compete successfully in the markets of the world, is of might as well revile God for making the child suffer pain when it vast importance in this age of activity in the useful and ornamental stumbles on a stone. Punishment is needed sometimes, and where It is doubtful if any branch of education is to-day receiving it is needed use it, and where it is not needed do not use it. It is more attention in this commonwealth, than industrial drawing; and purely a matter of practical skill and wisdom. Use just so much the same is true in all the progressive and productive countries of as is necessary to accomplish your end-so much and no more. Europe. Indeed, it is now regarded as the principal key to success have no doubt that a man, say with great experience in the rearing in manufactures, in respect to superiority in design and finish. Prof. Ware, of the Massachusetts Institute of Technology, says: of children, might stop and reason with the child, and so dispense with the rod, but I should like to know what a woman who has to At the Universal exhibition of 1851, England found herself, by work for a living, who has fourteen children, I should like to know general consent, almost at the bottom of the list, among all the what she is going to do about it. You that have amplitude countries of the world, in respect to her art manufactures. Only of means can stop and blow the bubbles of society, but for othersthe United States, among the great nations stood below her. don't be afraid to do what God does; all creation is whipped first result of this discovery was the establishment of schools of art Men say by Him, and you need not be afraid to use the switch. At the Paris Exhibition of 1867, England every large town. that it awakens more bad passions than it cures. Well, that stood among the foremost, and in some branches of manufacture is because you don't whip hard enough. All slight pinces, all slapping of the ears are abominations. You must aim to establish a counter-irritation and have it so. Those, then, must be the points

in

The

distanced the most artistic nations. It was the schools of art, and
the great collection of works of industrial art at the South Kensing-
still held her place at the foot of the column."
ton Museum, that accomplished this result. The United States

-inside and outside at the same time, thoroughness in whipping or nothing, that is the rule. Our government in the family destroys instruction, says: "In some countries, as in Wurtemburg and The report of the French Imperial Commissioner upon technica self-government. People marvel why children turn out badly for whom so much Bavaria, (Nuremberg,) drawing is the special object of the schools; has been done. Suppose your child has never been allowed to walk; and the impulse it has given to all the industries requiring that art suppose the servant was obliged to carry him in her arms or wheel is sufficiently striking, and so generally recognized as to render him in a carriage all the time, and he never be allowed to set his evident the usefulness and necessity of this branch of instruction. foot upon the ground till he was twenty-one, and then people marvel A glance at the immense variety of children's toys with which that he cannot walk when so much has been done to spare his legs Nuremberg supplies the whole world, will suffice to show the proup to this time! So some people are so anxious for the salvation gress due to this diffusion of the art of drawing. The very smallest of the souls of their children that they damn them; they won't let figures, whether men or animals, are all produced with almost the child go out in the street because there are bad boys there. artistic forms; and yet all these articles are made in the cottages of You think for them; you lay down your life for the boy; and you the whole population, from children of tender age, as soon as they can the mountainous districts of the country. They find employment for never teach him a just discrimation between right and wrong; you never let him make blunders, which is the best thing in the world handle a knife, to their parents; and this home manufacture, which for a child to do. You insist on it that the child shall be stuffed does not interfere with field work, contributes greatly to the prowith knowledge; you bother him in every way, and then, at last, sperity of a country naturally poor and sterile." It has recently been when he gets out into life he had learned nothing. The family is said, by one who ought to know whereof he asserts, that some of the a school in which the children are to practice continuously. You great failures which have recently occured among manufacturers are can teach the child to use its own judgment, but if you have nothing largely or wholly due to the fact that the companies have been but your own imperious will, and say nobody can have any rights obliged, of late, to sell their goods below cost because of inferiority in your family, the law is yourself all the time" the children must but of superior design, find no difficulty in disposing of all the in design. Other companies manufacturing the same kind of goods, do as I say or I will cut their heads off." Your will is so strong that, like a sparrow beating up against a tornado, the child's will goods they can produce, and at a large profit. is swept down before it, and consequently when he gets away from home, comes down to New York, perhaps, his first expression is, "Thank God, now I will see life." And the worst of this is, to him this life is the common sewer; he is but the natural result of bad government. And you say, Good gracious, if there ever was a boy that had good government my boy had!" but he had not, for you never allowed him to exercise the first principle of

self-conservation.

3. FREE-HAND DRAWING.

A writer in a recent educational journal, in answer to the question why there is such an interest in art education, says: "It is because the great industrial exhibitions of the world, from the first one at London in 1851, to the last at Vienna, show, beyond a scintilla of doubt, that such an education is a leading factor of national prosperity. Because a large class of American manufacturers have discovered that under the leveling influence of steam transportation and telegraphy, they must be completely driven from even the home market, unless they can carry to that market in the future more beautiful products than hitherto. Indeed, nothing is so salable as beauty. Because American artisans are learning the more artistic the work they can do, the better the wages they can

The following from the late report of Mr. A. P. Stone, Superin- command; that, in truth, there is hardly any limit to such increase. tendent of Schools, Springfield Mass., is equally well adapted to Because they further find, in all varieties of building construction,

our Schools:

Hitherto, drawing has been taught and practiced to some extent that a knowledge only sufficient to enable them to interpret the in a portion of the schools, but not, I think, as a universally recog-working-drawing placed in their hands, (and nearly everything is nized and required exercise in the programme of school work for all now made from a drawing,) will add one-third to their daily wages." the schools. Sufficient progress has been made to convince those

who need convincing, of the desirableness of incorporating it more SAYS Thackeray somewhere: "Our education makes of us the fully into the regular duties of every pupil, from the Primary grades most eminently selfish men in the world. We fight for ourselves, to the High School. Within the memory of the present genera- we push for ourselves, we yawn for ourselves, we light our pipes tion, public sentiment has undergone a great change in regard to and say we won't go out, we prefer ourselves and our ease; and the drawing. As too often taught, or rather practised, in our schools, greatest good that comes to man from woman's society is that he not many years since, it was looked upon as an accomplishment in has to think of somebody to whom he is bound to be constantly name rather than in reality, and as adding little or nothing to one's attentive and respectful."

BAROMETER AT TEMPERATURE OF 32° FAHRENHEIT

Approximation. dOn Lake Simcoe.

о