the
repetition of the act--to the progress of the child. What interests
the child is the sensation, not only of placing the objects but of
acquiring a new power of perception, enabling him to recognize the
difference of dimension in the cylinders, a difference which he did
not at first notice. The _problem_ presents itself solely in
connection with the _error_, it does not accompany the normal process
of development. An interest stimulated merely by _curiosity_, by a
"problem," would not be that formative interest which wells up from
the needs of life itself, and therefore directs the building up of the
spiritual personality. If it were only the problem which should lead
the soul to find itself, order might be dissipated by it, as by any
other external cause which tends to _seduce_ life into false paths. I
lay, perhaps, excessive stress upon this point, in answer to very
important objections and observations that have been made to me.

Indeed in the second series of objects designed to educate the eye to
appreciate dimensions, the control of error is not mechanical, but
psychological; the child himself, whose eye has been educated to
recognize differences of dimension, will see the error, provided the
objects be of a certain size and attractively colored. It is for this
reason that the next objects contain, so to say, the control of error
in their own size and in their bright colors. A control of error of a
totally different kind, and of a much higher order, is that offered by
the material of the arithmetical frame, in which the control will
consist in the comparison of the child's own work with that of a
model, a comparison which denotes a remarkably intelligent effort of
will on the part of the child, and places him thenceforth in the true
conditions of conscious auto-education. But, however slight the
control of error may be, and in spite of the fact that this diverges
more and more from an external mechanism, to rely upon the internal
activities which are gradually developing, it always depends, like all
the qualities of the objects, upon the fundamental reaction of the
child, who accords it prolonged attention, and repeats the exercises.

On the other hand, the experimental criterion is different, in
determining the _quantity of the objects_. When the instruments have
been constructed with great precision, they provoke a spontaneous
exercise so coordinated and so harmonious with the facts of internal
development,