be mentioned before a class; because, as a matter of fact, no instance of any such event is on record.
Let us now pass to the subject of Arithmetic. Instead of fictitious lines, we have here to deal with fictitious statements, i.e., with tatements which, if treated as truths, are false, but which, when clearly understood to be mere convenient fictions, do actually convey truth. Such a statement, for instance, is, " Twelve pence equal one shilling." No one is ever really deceived by this particular statement; but that is because all are familiar with the actual coinage, and know that, as a matter of objective fact, "a shilling" is not identical with "twelve pennies" (in the sense in which "a dozen apples" is identical with "twelve apples"). But a similar statement, made about unfamiliar objects, or about abstractions, might be misleading, unless the teacher took care to prevent misconceptions. And even in the case of our familiar coinage, it is essential to good mental discipline that the pupils should occasionally be made to define carefully the sense of the word "equal," in the sentence "twelve pence equal one shilling," and have their attention directed to the fact that, if accepted as true, it becomes false; that it contains and conveys truth only while clearly understood to be a fictitious but well-arranged convention. If the teacher forgets to do this, he ought to be grateful to any one who reminds him of his omission.
Now let us suppose that, in our imaginary College, the pupils are unacquainted with the actual coinage, and the teacher not sufficiently awake to the meta-physical necessity for defining, for them, words the real meaning of which is present to his own mind. He simply
