pabilities, it is equally true that without great change and improvement, many a farmer will be unable to meet his liabilities, or be obliged to struggle on with embarrassments that might be avoided.

I close this letter with the remark that the recent act of Congress, making a conditional grant to each of the States for the general purpose here advocated, invests the subject with an increased interest and opens a door to the realization of an extended plan of Agricultural improvement. Doubting not, Sir, that you will earnestly press this whole subject upon the attention of the next Legislature, I add no more.

CIVIS.

TWO SORTS OF TEACHERS.

In going into schools, as I sometimes do, I notice two sorts of teachers, the fussy and the quiet. No doubt other classifications may be made, but as to their general method of getting along, they may be classed as above. First as to action -deportment: Your fussy teacher-the term may not be elegant but it is aptis always in motion. He walks up and down everywhere and nowhere; if he sits, it is now on a chair, now on a bench; his feet first upon the floor, then upon his desk; he has now this object in his hand now that; he begins one thing, then stops and begins another, thus precious time is lost in indecision and confusion. Next in language—he talks incesantly, and often in a tone that reminds you more of a cracked clarionet than a human voice; and in a key that makes you think of a young parot at the top of the room. Then he pours out words at random, twice as fast as his ideas come; he asks a question four or five different ways in a breath; when answered, he answers it over again, in as many different ways. If he undertakes to explain anything, his sentences overlap, like shingles on a roof; that is, he constantly begins back and says every thing wholly or partly over again. In government and discipline he is equally capricious and undetermined. It a child leans one degree out of perpendicular, he is as much disturbed as if his lesson is entirely wanting. He has fifty frivolous rules, and changes them a dozen times in a term. He loses his temper twenty times a day, and at night is in a state of complete mental fret and haggardness.

Your quiet teacher, on the other hand, "takes things easy." I do not mean that he is lazy, though he may be so, but he does not make a fuss He is not in all parts of the school-room at once; though if need be, he can change his position with all needful celerity. But he does every thing quietly. His motions are gentle and dignified, and no more than are needed; he does not waste his energy, and so is always fresh. In speech he says what he has to say and is done with it. If he asks a question, it is intelligible the first time; and when he gives an explanation, his words are well chosen, and he does not repeat it in a dozen different forms, till no one knows what he means. In the management of his charge

he acts upon the principle that children already know, for the most part, what they ought and what they ought not to do, and he does not therefore lay down a multitude of rules which merely tempt to infractions. He seeks rather to infuse and awaken a general spirit of order and obedience and self-respect. If a slight disturbance occurs, he does not make five times as much noise in noticing it—a glance of the eye is usually a sufficient reminder or rebuke. His temper is seldom ruffled and never beyond his control. His pupils appreciate his kindness and firmness, and dread nothing so much as his disapprobation.

I have of course drawn portraits that represent somewhat extreme opposites, but it will be found that most teachers incline very much to the one or the other of these types; and one of the most important facts connected with the matter is, that teachers impart themselves, in no small degree, to their pupils. One of the most thorough-going, laborious teachers I ever knew, was so excessively nervous and irritable, that some of his pupils seemed always to go home with a swarm of bees about their ears. Less marked but most desirable and most lasting, is the influence of a teacher of the opposite class. I happened to know a community in which three teachers of that description successively labored, and with the most happy results. I am quite certain that they have each left an impress of a most salutary nature, upon the minds and characters of their pupils, and one that will never be effaced. SCRUTATOR.

MATHEMATICAL DEPARTMENT.

Solution of Problem 46.-Let x y and z represent the sides of the triangle and denote by a b and c respectively the perpendiculars let fall from the angles opposite these sides. Put x+y+2=2S. Then ax=by =cz=2√s(s—x)(s—y)(8—2) (1) From (1) we find y =

8=12 (1++)

ах

Τ

ах

2= and

с

=m, then S=mx. This

Assume 1
3(1

α

a

응)(m-응)

value of S placed in (1) gives ax=2x2/ m m (m—1) (m— 2 ) (m— 2 )

Having found the value of x we can readily determine the values of y

and 2.

Cottage Grove.

L. CAMPBELL.

Note. Mr. Samuel Clegg's solution of problem 46 is wholly incorrect. This you will readily see by examination, (see No. 2, Vol. 7). L. C.

Problem 55.-A farmer has a triangular field, which he wishes to divide into two equal parts by a fence; find the points in the sides of the field from which he must draw the line for his fence to be the least pos sible expense to him. L. CAMPBELL.

Problem 56.-The centers of two given spheres are at the extremities of the major axis of a given ellipse. Find a point in the circumference of the ellipse from which the greatest portion of spherical surface is visible. L. CAMPBELL.

TO REDUCE RODS TO FEET. - Rule: Annex two ciphers to the number of rods given, subtract the number of rods, and divide by 6. The quotient will be the exact No. of feet. Required an explanation

H. B. The difference between any two numbers, consisting of the same digits, is always divisible by 9. Required an explanation. H B.

SUBTRACTION.

In the last number of the Journal, I notice a few remarks about subtraction, and as I had the usual amount of trouble in understanding the "borrowing" and "paying" under certain circumstances, when I was a school boy, and since as a teacher I have seen how easily the difficulty may be overcome, perhaps it would not be amiss to state the method I have adopted. I will illustrate by an example :

2021
1354
667

In the above example we cannot ta e 4 units from 1 unit, therefore we will add 10 units to the minuend, (by adding to the unit's figure,) making 11. Now, 4 from 11 leaves 7. But since the minuend is increased by 10, the answer will be too large, unless the subtrahend be increased in a like manner. We therefore add one unit of the second order, (which is equal to the 10 units added to the minuend,) to the sub. 1 and 5 are 6. Here we meet with the same difficulty as before; we cannot take 6 from 2. We now increase the minuend, by 10 units of the second order, and afterward increase the subtrahend by the addition of an equal unit, viz.: 1 unit of the third order, for the same reason as before given.

This explanation you will at once perceive, is simple, and easily under. stood; while the old method of borrowing 10 from Mr. 2, and then squaring accounts by paying 1 to Mr. 5, (that is the explanat on I received when a boy) or taking 1 of the next higher denomination and re

ducing it and adding to the lower and then considering the figure from which we borrowed, one less, or what amounts to the same thing in the answer, considering the next figure of the subtrahend one larger, particularly if the figure of the higher order in the minuend be a cipher, is, or at least with me was, a matter which I found considerable difficulty in understanding perfectly.

I think no teacher will regret a trial of the method above illustrated.
KENOSHA.
H. B.

ACCURACY IN ARITHMETIC.

No person, who is willing to allow an error to pass undetected, can be a good arithmetician. Accuracy, absolute accuracy, should be aimed at in every operation; and no labor is too great which is necessary to secure it. Not only should the results be accurate, but the comp ter should know for himself that they are so. If he has any doubt concerning a result, he should examine each and every step of his work. One problem thus solved and proved by a learner is of more real value to him than ten solved by him and proved by another, or tested by comparison with a printed answer.

An intelligent and highly accomplished accountant, who has charge of the books of a large manufacturing establishment employing three hun. dred men, once spent nearly a week in examining his accounts, to discover the cause of an error of a few cents; and, said he, "I never spent the same amount of time more profitably." Another gentleman, bearing also a high reputation and receiving a good salary as an accountant, spent, to use his own language, the "greater part of four days in searching out the cause of an error of ten cents." Both these gentlemen say, that if they should adopt any other principle than that of ubsolule accuracy, they could not retain their situations. Every accountant, business man, and practical man bears similar testimony, and confirms these views. Indeed, most of them say that the knowledge of arithmetic acquired in the school-room has been of little practical value to them, because they did not learn to be accurate and rapid in performing their work, and to know for themselves that they had been accurate.

Rapidity in the performance of numerical operations is scarcely of secondary importance to accuracy and certainty. The most accurate computers are usually the most rapid in their work.-Dana P. Colburn.

THE moral education of a child at home should be well completed, before it is sent to school.

EDITORIAL MISCELLANY.

INSTITUTES-WHAT WE NEED.

The New Law, in requiring the County Superintendents, (many of whom have not had wide experience as teachers,) to hold Institutes, but failing to make any provision for their assistance in so doing, or for securing the attendance of those for whose benefit the Institutes are held, reminds one of the famous ordinances of the Common Council of Boston, in days of yore, which required colored per sons, from whom some mischief was apprehended, to carry a lantern when appearing in the streets at night, but which omitted to require that a candle be placed therein; and after supplying that omission, still neglected to mention that it must be lighted. We do not doubt that many of the superintendents can do good service in the work of an Institute, nor that they may be able to command some valuable local assistance, without making compensation for it. Still it is no disparagement to either our superintendents or teachers to say, that it is vastly easier to judge of a person's qualifications, by an examination, than to elucidate successfully, in Institute exercises, the points in which ordinary teachers are most deficient, or to find a pretty good teacher for the school-room, than for the Institute platform.

Since the withdrawal of Mr. Allen from his labors for the most part, under the Board of Normal Regents, and his entrance into a local school, we know of no person in the State, competent to the work and disengaged, whose services can be commanded for holding Institutes. The recent very acceptable labors of Prof. Sill in several of our Institutes lead us to remark that in Michigan, he and the other members of the Faculty of the State Normal School, together with Mr. Gregory, the State Superintendent, have in time past acted to some extent as an Itinerant Normal Faculty, holding Institutes in various parts of the State, to the great advantage doubtless of the teachers in attendance, especially such as had not attended the Normal School.

We have no Normal School Faculty to call upon, because we have as yet unfortunately no State Normal School; but if a moderate appropriation were placed at the disposal of the State Superintendent, a very good faculty might be organized at least for a spring and fall campaign of Institutes. Mr. Pickard is himself one of the very best men we know of in an Institute, whenever his time is at his disposal in that way; Mr. Allen, whenever he can leave his school, is a host, and there are other excellent teachers, who are showing good adaptation for Institute work. It seems to us that hereafter, Institutes of longer duration, in fewer localities, and where most needed, would be much more profitable than a continuance of the prevalent type of four days sessions. The propriety of this is shown by the success of such Institutes recently held. We do hope the Leg islature may be induced to extend the aid required, in some way.