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.

(2.) Truths must not only be taught to the pupils, but they must be
_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 c