problem is impossible. You cannot draw any such line in space as we understand it." If our visitor conceived of the fourth dimension, he would reply to us as we replied to the "flat-land" people: "The problem is absurd and impossible if you confine your line to space as you understand it. But for me there is a fourth dimension in space. Draw your line through that dimension and the problem will be solved. This is perfectly simple to me; it is impossible to you solely because your conceptions do not admit of more than three dimensions."

Supposing the inhabitants of "flat-land" to be intellectual beings as we are, it would be interesting to them to be told what dwellers of space in three dimensions could do. Let us pursue the analogy by showing what dwellers in four dimensions might do. Place a dweller of "flat-land" inside a circle drawn on his plane, and ask him to step outside of it without breaking through it. He would go all around, and finding every inch of it closed, he would say it was impossible from the very nature of the conditions. "But," we would reply," that is because of your limited conceptions. We can step over it."

"Step over it!" he would exclaim. "I do not know what that means. I can pass around anything if there is a way open, but I cannot imagine what you mean by stepping over it."

But we should simply step over the line and reappear on the other side. So, if we confined a being able to move in a fourth dimension in the walls of a dungeon of which the sides, the floor, and the ceiling were all impenetrable, he would step outside of it without touching any part of the building, just as easily as we could step over a circle drawn on the plane without touching it. To do this he would only have to make a little excursion in the fourth dimension.

-Harper's Magazine, 104: 249.

106. Assignments on Connecting New Ideas with Old.

A. Explain to a pupil in the first year of the high school the meaning of one of the following terms. Try to connect the strange idea with ideas that are familiar to him. Make an effort to put yourself in his place, for in this way you can more readily think of the things he knows about and will be interested in. Beware of using terms that he will not understand.

(1) Wireless telegraphy. (2) A trust. (3) Hypnotism. (4) The New England town-meeting. (5) Reciprocity. (6) The canals of Mars. (7) The solar spectrum. (8) The referendum. (9) The shorter catechism. (10) The facial angle. (11) Graft. nopoly. (13) Monoplane. (14) Political Insurgency. bezzlement. (16) Kleptomania. (17) Volt. (18) Ohm. (20) F.O.B.

(12) Mo(15) Em

(19) H.P.

B. A boy ten years old wishes to know why it is that a spoon when it is put in a glass of water looks as if it were bent or broken. Explain the phenomenon to him in simple terms.

C. Explain to a younger person what you think Emerson meant when he said, "Good manners are made up of petty sacrifices." Use familiar examples.

D. Suppose that a laboring man who has had but little education has brought to you the following lines of poetry for explanation. He has found them in Shakespeare's Julius Cæsar, which he is now, with interest but with difficulty, reading for the first time. What will you say to him? Remember that many things with which you are well acquainted will be to him very new and strange.

Between the acting of a dreadful thing
And the first motion, all the interim is
Like a phantasma, or a hideous dream:
The genius and the mortal instruments
Are then in council; and the state of man,
Like to a little kingdom, suffers then
The nature of an insurrection.

-Act II, Sc. 1.

O conspiracy,

Sham'st thou to show thy dangerous brow by night,
When evils are most free? O, then, by day

Where wilt thou find a cavern dark.enough

To mask thy monstrous visage? Seek none, conspiracy;
Hide it in smiles and affability;

For if thou path, thy native semblance on.
Not Erebus itself were dim enough

To hide thee from prevention.

-Act II, Sc. 1.

The posture of your blows are yet unknown;
But for your words, they rob the Hybla bees,
And leave them honeyless.

Logical Definition.

-Act V, Sc. 1.

107. Another method of connecting the new idea with old ideas is by the process known as definition. To define an idea is to put it in its appropriate place among the classes of things with which we are familiar. This we can do most easily by the following method: (1) we mention some large class with which the reader is already acquainted; then (2) by naming some prominent characteristic of the thing to be defined, we show where, in that large class, it properly belongs. Thus if our purpose is to define the idea hypnotism, we may begin by saying that it is a kind of sleep (sleep being a large class with which we are already familiar), and complete the definition by adding that it is induced by motions of the hand or other suggestions of the operator (this being the essential characteristic which distinguishes this kind from other kinds of sleep). Hypnotism is thus placed definitely among the classes of things with which we are familiar.

The large class is termed the genus. characteristic is termed the differentia.

The distinguishing It is generally best

to choose as small a genus as can be used conveniently. To define a gnat as an animal is hardly to define at all; the class is too large. It is better to classify it as an insect, and still better as a fly. So in defining a Pastoral we may say that it is a piece of literature treating of rural life. Here the genus, "piece of literature," is a very large class including both prose and poetry. The definition will be more accurate as well as more helpful if we say that a Pastoral is a narrative or slightly narrative poem. And it will be still further improved if we add the differentia, as above, treating of rural life. The following is a convenient method of displaying and separating the parts of a logical definition :

As we meet definitions in our text-books, in the dictionaries, and in general reading, we do not always find the parts in the logical order shown above. Thus if we read, "Politics treats of the principles governing the conduct of state affairs; it is a branch of civics," we see that here the differentia comes before the genus, and that the normal order would be, "Politics is that branch of civics, which treats of the principles governing the conduct of state affairs."

Often, too, a definition is incomplete. The genus may be missing as in this, "A pastoral treats of rural life;' or the differentia may be missing as in this, "A monitor is a sort of battleship." Sometimes, for a given purpose, an incomplete definition like those just quoted will serve well enough; but especially in the class room, incomplete definition is a widespread fault which every student should try to overcome in his own practice.

A synonym is useful in definition when it is a more familiar word than the word to be defined. Often, however, even in dictionaries, a synonym that is even less familiar than the word it purports to explain will be given. A person who doesn't know what a "tariff" is will probably not be enlightened if told that it is an "impost" or a "duty." If I do not know what "buncombe" means, I probably do not know what "flapdoodle" means, either.

A definition should not employ in the genus or differentia any part or derivative of the word to be defined. It is of no value to be told that "an inheritance is that which is inherited," or that "gerrymandering is the process of applying the gerrymander."

In all sorts of exposition, but in definition especially, it