“Can it be noon, then,” continues the teacher, “here and at a place fifteen degrees west of us at the same time?”

“Can it be noon here and at a place ten miles west of us at the same time?”

It is unnecessary to continue the illustration, for it will be very evident to every reader that, by going forward in this way, the whole subject may be laid out before the pupils so that they shall perfectly understand it.  They can, by a series of questions like the above, be led to see, by their own reasoning, that time, as denoted by the clock, must differ in every two places not upon the same meridian, and that the difference must be exactly proportional to the difference of longitude.  So that a watch which is right in one place can not, strictly speaking, be right in any other place east or west of the first; and that, if the time of day at two places can be compared, either by taking a chronometer from one to another, or by observing some celestial phenomenon, like the eclipses of Jupiter’s satellites, and ascertaining precisely the time of their occurrence, according to the reckoning at both, the distance east or west by degrees may be determined.  The reader will observe, too, that the method by which this explanation is made is strictly in accordance with the principle I am illustrating, which is by simply dividing the process into short steps. There is no ingenious reasoning on the part of the teacher, no happy illustrations, no apparatus, no diagrams.  It is a pure process of mathematical reasoning, made clear and easy by simple analysis.

In applying this method, however, the teacher should be very careful not to subdivide too much.  It is best that the pupils should walk as fast as they can.  The object of the teacher should be to smooth the path not much more than barely enough to enable the pupil to go on.  He should not endeavor to make it very easy.

(2.) Truths must not only be taught to the pupils, but they must fixed, and made familiar. This is a point which seems to be very generally overlooked.

“Can you say the Multiplication Table?” said a teacher to a boy who was standing before him in his class.

“Yes, sir.”

“Well, I should like to have you say the line beginning nine times one.”

The boy repeated it slowly, but correctly.

“Now I should like to have you try again, and I will, at the same time, say another line, to see if I can put you out.”

The boy looked surprised.  The idea of his teacher’s trying to perplex and embarrass him was entirely new.

“You must not be afraid,” said the teacher.  “You will undoubtedly not succeed in getting through, but you will not be to blame for the failure.  I only try it as a sort of intellectual experiment.”

The boy accordingly began again, but was soon completely confused by the teacher’s accompaniment.  He stopped in the middle of his line, saying,