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pression for – 1, which is 3 — 4 ; or to another unreduced expression, as 2—3, which is absurd. And to say that +1=-1, is the same as to say that taking 2 from 3 is the same as taking 3 from 2.
Again, if the same quantities be added at different times, the results will be the same or equal ; and, conversely, if different quantities be added, the results will be different or unequal; and if the results are unequal, it follows that the quantities that were added were unequal. Then taking the quantity 2, to that add 1, and the result will be 3 ; to it add -1, and the result will be 1. This last result is less by 2 than the first; consequently, the numbers added are unequal. But 2= 2, therefore +1 is greater by 2 than --1, because the result is greater by 2. I have heretofore confined the illustrations to definite, known quantities. I will give one more demonstration by using indefinite known quantities, which will prove the proposition true for any value of the minus quantity. Now, suppose we admit for the time that 0 <- a, and that -a <-(a + m); then, if we add a + m to both members of the first inequality, 0 <- a, we shall have a +m <m; which is absurd. Adding the same to the inequality, -a- (a -+ m), we shall have m < 0; which is absurd. On the contrary, if we take the inequalities 0->--a and -a>-(a + m), which we have shown to be true with definite, known numbers, and to them add the same quantities, a + m, we shall have atm> m and m>0; which is true.
Knowing that this view of the question gives us a key to many of the intricate operations in the science of algebra, I submit the question to teachers, Would it not facilitate the progress of our pupils in this interesting study, to explain, early in their course, the nature of the minus quantity ?-Mass. Teacher.
SELF-INTEREST.-He who makes an idol of his interest, will often make a martyr of his integrity.
A little roguish fellow sits,
Abrimming o'er with fun,
Like beams of genial sun.
His sparkling eyes with jetty shade,
Are peering all around,
A playmate may be found.
His mind is not on book or task,
But wanders far away,
For active, out-door play.
He feels like bird imprisoned, caged,
A captive in free land ;
The tricks in thraldom planned
And near me sits another youth
With pale and thoughtful face, And in his mien is dignity
Blent with a softer grace.
In earnest attitude he sits,
With head inclined o'er book, And closely scans the learned page
With sweetly studious look.
Ho is e'en now in heart a man,
In honor tried and true,
Which angel eyes might view.
O, who can tell whence this great change,
Or so unlike they are ? 'Tis He alone who doth affix
The magnitude of star.
'T is He who makes the lowly flower
Beneath the regal bloom ; While, tho' unseen, it fills the air
With rich and sweet perfume. Mass Teacher. MUSINGS ON THE TRIENNIAL.
BY PROF. E. D. SANBORN.
To H. E. SAWYER, Esq.—My good Friend and former Pupil: The triennial Catalogue of Dartmouth College is before us. It stands between the dead and the living, a record of the past, a prophecy of the future. It reveals the march of intellect and leaves the highway of life strewn with dead. As in the progress of a conquering army many a strong man bites the dust, while the victors pass on; so, too, in the peaceful walks of literary life, we often leave our prostrate brethren behind us; and of many a youthful student it may be said:
“ He the young and strong who cherished
with the march of life.” Dartmouth College has been in existence ninety-two years. More than three thousand students have received the honors of graduation. Almost one half of the whole number are dead; only eighteen hundred and fifty-five survive. Of these more than two thirds have been my own pupils I am beginning to feel that my pupils may say
“What knowest thou that we know not also ?” I have repeated myself so often, that I almost fear to open my mouth in their presence lest some one should say, “I have heard that before ;” and proceed to recite to his next neighbor, sotto voce, the anecdote or apothegm which will be hung as a pendant to my discourse. The success of his pupils is the teacher's highest reward ; and for myself in looking over an assembly, at Commencement, who have mostly sat together before me in the recitation room, some of whom are already silvered with age, and many are conspicuous for their honors, I can say as Pyrrhus used to say to his Epirotes, “ Ye are my wings.” I would not wish to be classed with those teachers who ar. rogate all the glory their scholars win, to themselves, men who know everything, teach everything, and, like the Bourborns, never forget and never learn anything, men who inspire “ like Apollo and govern like Jove." So Phønix in the Iliad, boasted that his tutorship made the god-like Achilles. He says:
“Great as thou art, my lessons made thee brave,
A child I took thee but a hero gave." This class of teachers have been hardly beset by satirists from the days of Juvenal to those of Dickens. Horace smarted under the rod of Orbilius as Irving did under that of the pedagogue who was the prototype of Ichabod Crane. But this class of officials are more exposed to public scandal than most others, because they are never secluded. There is many a professional man who affects to be a village oracle, of whom it may be said
“ And still they gazed and still the wonder grew,
That one small head should carry all he knew.” But the powers of such great men are only tasked on great occasions. They appear like frogs after a shower. Professional life everywhere has a tendency to crystalize into forms, modes and rules. Exclusive devotion to a single pursuit narrows the mind, clips the wings of fancy, dries up
the sources of invention and makes a man a mere bundle of technicalities. He can talk only on one theme; on that he is always fluent, always tiresome. Teachers are not peculiar in this respect; they are only more exposed. Like Spartans they bear the lash, because they have been trained for that very purpose. Juvenal compared the Roman teacher worn out with the constant repetition of the same thoughts, to "a hashed cabbage,” which was neither savory nor nutritious. But all teachers are not men of routine any more than all statesmen are men of " red tape," or all lawyers of the firm of “ Fog & Dodson," who so sorely tried the equanimity of the Court in that famous breach of promise case, Bardel vs. Pickwick. Some teachers are progressive; they move with the age ; study its wants, learn its history and promote its welfare. Others commence life with a small capital of cheap wares
and never replenish their stock: thus at the end of forty years, they possess less intellectual wealth than when they began life. So a naturalist may study the rocky tablets of our earth's history till he is himself petrified and has no more mental succulence than a fossil trilobite; or he may be so devoted to the flora of our country as “ to peep and botanize upon his mother's grave," and dry his gathered leaves and flowers in huge herbariums till they turn the tables upon him, and dry up all the juices of his soul, and leave it as parched and withered as the last leaf of Autumn that clings with dying fingers to the stock that bore it. So a physician may study the human frame with such exclusive zeal as to lose all consciousness of its outward integuments and make his lectures mere anatomical preparations ; so that when we listen we mentally exclaim, “Can these dry bones live ?! I have heard of an eminent mathematician, who, after reading Paradise Lost, asked triumphantly “What does it prove ?" The disciples of Themis, too, sometimes become prosy, dull, formal and repetitious, " for that Old Time, the defendant, doth with force and arms," invade their premises and “steal, take and carry away " the glory of their youth and the vigor of their manhood, and leave them only“ wise saws and modern instanres." Teachers, then, are not the only lag. gards in the race of life, though like the wheel-horses ofa coach, they are often lashed for others' delinquencies. An old divine once divided men into two great classes, to wit: those who had attentively read his book and those who had not. I rather choose to describe teachers as the prophet did the figs which he saw in vision, “ the good, very good, the evil, very evil."
Socrates was a type of the “ very good.” He never grew old in feeling and sentiment. His great heart was always warm. He always loved the society of youth. One day he met a youthful and beautiful stranger, and struck with his intelligent and sweet expression of face, he placed his staff across the way and arrested him. A