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 the form of which 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 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.