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Education and christian love

Work together, hand in hand;
And Truth, its mighty impress

Has stamped on youth's fair brow.
Oh! when, in all the ages past,

Did Hope stand forth as now!

And as the morn advances

And the day begins to rise,
While the song of the Present's triumph

Echoes, singing to the skies,
As teachers we stand not idle;

For beyond the failures of Time,
Upheld by Faith's inspiration,

Have we gained a height sublime.
And on that height now standing,

Pledge we life-work as our bond;
And placing our hand in the Infinite's,

Catch a glimpse of life beyond,
Which no mortal pen can describe,

No human lips e'er portray;
For now are the glimmers of dawn,-

But then the fullness of day.
And now, a true band of teachers,

We turn to the light of our homes,
To figlit against Giant Ignorance

As nerved for the conflict he comes.
May our hearts for each other, aglow,

Be filled with sympathy true,
First kindled on Heaven's pure altar,

Then sent by angels to you.
For the blessings of the All-Father,

For the glory vouchsafed to-day,
For the shining hopes of the future,

We are grateful; and we pray
When our teaching here is ended,

When the silver cord is riven,
We may meet the great, great Teacher

In the school-room vast of Heaven.

BETTER make penitents by gentleness, than hypocrites by severity. -St. Francis de Sales.

The master of superstition is the people, in all superstition wise men follow fools.-Bacon.

EVERY SYSTEM of discipline should accomplish completely the object it aims at.

A TIMELY SUGGESTION.—[We are always glad of a few words like those below:]

Teachers who are called to labor where the use of the Bible is prohibited, may yet teach its holy precepts by a well-ordered life and a godly conversation. Although there may be no visible altar of

praye in that school—the pupils never hear a verse of scripture read or repeated there—yet he, in whose heart dwells the love Jesus, may carry the sacred word with him—the Holy Spirit ever hovering near. Indeed, he who is thus fettered by human power may have his strength in God increased. Let him seek for such a holy consecration of his time and talents as shall tell for the good of all and for the glory of our Father in heaven. If he be a faithful teacher and one who is determined to serve God in “sincerity and truth,” he will not lack occasions to show his reverence for his Maker and his faith in divine revelation.H. S. Z., Douglas Center, Wis.

A Hint.–Friend, do you know that you mean to be honest? Do you love your neighbor as yourself? Are you kind to the poor? Do you love your enemies? Have you charity for the erring? Are you careful to speak evil of no one, and not to convey reproach by word, look or act secretly against any? Then please to watch for the smile of our Heavenly Father-for he seeketh such to bestow upon them his favor.

Watch every circumstance-sun-beams and clouds, whether in the physical or the moral world; not because of your well-doing, but because of the obedience which can be secured only through His son, JESUS CHRIST—Ib.

ROLL OF HONOR.—If scholars know that those who are perfect in attendance, in deportment, and in scholarship, are to have their names put on the Roll of Honor and sent to the County Superintendent, and the best of these be published, they will be apt to try to do well in these things, especially if encouraged by the teacher. This is not a sort of competition in which only a few can win. In this there is room for all, and nothing would please me more than to see every scholar perfect in everything.

One caution is necessary. Use this Roll of Honor to aid in the discipline of your school ; but do not carry on your school for the sake of the Roll of Honor. Try to have a good school independently of that, and use that only as an additional aid to your already good discipline.

Treat the scholars fairly and justly. Do not give too long lessons, but require them to be really perfect in what they do have. It is not best to give lessons which require study out of school hours. Six hours of real study are enough for an adult, much more for a child. In regard to tardiness, time-pieces will vary. You must arrange that by keeping to some fixed standard of time, to which the the scholars will soon learn to adjust themselves. Give them a little latitude for a day or two, at first. In regard to deportment, you should not allow any sort of communication, unless by your express permission, and then only in rare cases.

Wilful disorder of any sort is bad deportment. So is impertinence to the teacher or refusal to obey any reasonable order.

In reporting, state the exact truth. If there are excuses to be made for some who almost deserved to go upon the Roll of Honor, but were prevented by circumstances beyond their control, state the facts in a letter to me, but do not put them on the Roll of Honor.–From a Circular by A. O. WRIGHT, Supt. of Juneau county.

Our School Houses.—While there is a goodly number of excellent school houses in the county, there are not a few that deserve summary condemnation; and I am sorry to say, such are not unfrequently found in districts in which the dwelling houses and barns show unmistakably the ability of the citizens to have a better state of things. A large majority of our school houses are without serviceable blackboards, and destitute of outline maps, and many of them seem never to have been painted inside or outside, or whitewashed, since they were built; thus making them so cheerless and uninviting, so inimical to the health both of the bodies and souls of the scholars, that it is astonishing that men, having the common sense that we credit ourselves with, should tolerate it. Probably if mothers, as well as fathers, had a right to take a part in our school meetings, these matters would be otherwise. It is certainly not asking too much of a district to provide as comfortable a room for their children to pursue their education in, as the sitting room of the average house in the district; and that the machinery for carrying on the school should be in some decent proportion to the machinery used on our fams. An original outlay of $20, and $5 annually thereafter, would be sufficient. I shall say nothing of the out-houses, but ask you to go through your respective towns and look at them, and then think of your sons and daughters.-From the Report of A. F. NORTH, Superintendent of Waukesha County, to the Board of Supervisors, 1872.

INFINITY IN MATHEMATICS.

BY A. P. MORGAN, MILWAUKEE.

In the discussion of the subject of infinity in all our text-books on algebra, and in other mathematical works, there seems to me a radical error. It consists in the representation of infinitely small quantity by 0. But O means nothing. It signifies the absence of quantity. Its meaning is just as definite and exact as 4 or 17, or any other number whatever. It cannot possibly represent quantity, let it be ever so small.

In physics, whether the ultimate atoms be susceptible of division or not, their aggregate, in any substance, makes up the entire mass. is impossible for them to become so small as to be nothing, or even to be considered as nothing. This results from the indestructibility of matter.

Take a line, an inch in length for instance. Let it be bisected; let the halves be bisected, and so on continuing the bisection of the parts indefinitely until the length of each becomes less than any finite quantity, or in the language of the books, less than any assignable quantity. The parts are then infinitely small, but is their length 0? If so, their sum is 0. It is impossible that the sum of any number of nothings should be something. But their sum is not 0. Their sum is the length of the given line.

The infinite in quantity appears in the consideration of two kinds of series, viz:

1. In series which arise by addition or subtraction.
2. In series which arise by multiplication or division.

All series of the first kind pass through all values from nothing, to quantity infinitely great, in two directions. Their limit in one direction is + co, and in the other Between the two lie all finite values, both positive and negative. These series all pass through 0, in going from one limit to the other. The meaning of all such series is to be interpreted according to their application.

For example, the series o ....8, 6, 4, 2, 0, -2-4-6, etc., begins with + , passes through 0, on to

In a straight line infinite in length, let any point be taken from which to estimate distance. This point will be represented by 0. Distances to the right may be represented by all positive numbers, from 0 to + co, and distances to the left will be represented by all negative numbers from 0 to In series of the second kind, the ultimate limits are quantity infin

1-VOL. III, No. 1.

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a

itely great and quantity infinitely small. Beginning with infinity, there is a constant decrease through all finite values down to unity, and onward to quantity infinitely small. O does not appear in series of this kind. How shall we represent quantity infinitely small? A single example will make this plain. In the series, o ....

...16, 8, 4, 2, 1, 1, 1, 1, te, etc., each term to the right of unity is found by dividing 1 by each term to the left. Hence,

Quantity infinitely small must be represented by a

Let us discuss the value of the fraction , under all suppositions that may be made, as to the value of a and b.

1. When a and b are both finite quantities, the value of the fraction is finite.

2. When the value of a or b, or of both is nothing: When a=0, becomes =0. When b=0, there is no operation and no result. This is the case also when a=0, and b=0.

3. When the value of a or b, or of both, is infinitely great: When a= 0, 7 becomes = When b= 0, me becomes = When a=co, and b= 0, the fraction becomes, or indeterminate.

4. When the value of a or b, or of both, is infinitely small: When a=2becomes .= When b= becomes a: 1 = 0. When a=., and b= becomes, 1+1=, or, indeterminate.

is the symbol of quantity infinitely great. h, is the symbol of quantity infinitely small.

*, is the symbol of indetermination. Let , %, and %, stand for just exactly what they express. ©, means that finite quantity is not divided by anything. 5, means that infinite quantity is not divided by anything. ,, indicates no quantity, no operation, and no result.

The doctrine of infinity, here set forth, is nothing new. I have seen it advocated in at least one mathematical work in this country, and it is prevalent in Europe. It is in strict accordance with modern philosophy. But I have nowhere seen any suggestion of a change of symbols in accordance with the fact. It seems to me the change here suggested will render operations involving infinity, much more definite as well as simple.

BATTLE HYMN OF 1873.
Hark! what ringing notes are these,
Borne upon the morning breeze?
They are coming from afar,
Trumpeting the sound of war;
And “ To arms! to arms!” they cry;

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