Some will probably answer "one," and some "eleven." If so, the step is too long, and may be subdivided thus:
"When it is noon here, is the sun going towards the Mississippi, or has he passed it?"
"Then has noon gone by, at that river, or has it not yet come?"
"Then will it be one hour before, or one hour after noon?"
"Then will it be eleven, or one?"
Such minuteness and simplicity would, in ordinary cases, not be necessary. I go into it here, merely to show, how, by simply subdividing the steps, a subject ordinarily perplexing, may be made plain. The reader will observe that in the above, there are no explanations by the teacher, there are not even leading questions; that is, there are no questions whose form suggests the answers desired. The pupil goes on from step to step, simply because he has but one short step to take at a time.
"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, cannot, 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 distances 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.