eader 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 b