ion we gave the water been enough
thus to break, to soften, and to melt the stick?

Fourth, we draw off the water and see the stick straighten itself as
fast as the water is lowered. Is not this more than enough to
illustrate the fact and to find out the refraction? It is not then
true that the eye deceives us, since by its aid alone we can correct
the mistakes we ascribe to it.

Suppose the child so dull as not to understand the result of these
experiments. Then we must call touch to the aid of sight. Instead of
taking the stick out of the water, leave it there, and let him pass his
hand from one end of it to the other. He will feel no angle; the
stick, therefore, is not broken.

You will tell me that these are not only judgments but formal
reasonings. True; but do you not see that, as soon as the mind has
attained to ideas, all judgment is reasoning? The consciousness of any
sensation is a proposition, a judgment. As soon, therefore, as we
compare one sensation with another, we reason. The art of judging and
the art of reasoning are precisely the same.

If, from the lesson of this stick, Emile does not understand the idea
of refraction, he will never understand it at all. He shall never
dissect insects, or count the spots on the sun; he shall not even know
what a microscope or a telescope is.

Your learned pupils will laugh at his ignorance, and will not be very
far wrong. For before he uses these instruments, I intend he shall
invent them; and you may well suppose that this will not be soon done.

This shall be the spirit of all my methods of teaching during this
period. If the child rolls a bullet between two crossed fingers, I
will not let him look at it till he is otherwise convinced that there
is only one bullet there.

Result. The Pupil at the Age of Fifteen.

I think these explanations will suffice to mark distinctly the advance
my pupil's mind has hitherto made, and the route by which he has
advanced. You are probably alarmed at the number of subjects I have
brought to his notice. You are afraid I will overwhelm his mind with
all this knowledge. But I teach him rather not to know them than to
know them. I am showing him a path to knowledge not indeed difficult,
but without limit, slowly measured, long, or rather endless, and
tedious to follow. I am showing him how to take the first steps, so
that he may know its beginning, but allow him to go no farther.

Obliged to learn by his