"patience" and "perseverance" then manifest
themselves, together with those of vivacity, activity, and joy,
characteristic of the spirit when the internal energies have found
their _keyboard_, the gymnasium in which they exercise themselves
freely and tranquilly.

And the spirit, organized in this manner under the guidance of an
order which corresponds to its natural order, becomes _fortified_,
grows _vigorously_, and manifests itself in the _equilibrium_, the
_serenity_, the self-control which produce the wonderful _discipline_
characteristic of the behavior of our children.

The external material, then, should present itself to the psychical
requirements of the child as a staircase which helps him to ascend,
step by step, and on the steps of this staircase there will of
necessity be disposed the means of _culture_, and of the higher
_formation_. Therefore the psychical exercises require new material,
and this, if it is to fulfil its purpose, must contain new and more
complex forms of objects capable of fixing the attention, of making
the intelligence ripen in the continual exercise of its own energies,
and of producing those phenomena of persistence in application and of
patience to which will be added elasticity, psychical equilibrium, and
the capacity for abstraction and spontaneous creation. Thus, in the
subsequent development of the children, we see them applying
themselves to those exercises of the memory which seem to us most
arid, because a desire has been born in them, not only to retain the
images they encounter in the world, but also to "acquire knowledge
rapidly" by a determined effort. An example of this is seen in the
surprising yet common phenomenon of committing the multiplication
table to memory, whereas the memorizing of poems and prose extracts,
although this is sometimes a passion, causes us no surprise.

Very interesting again, is the _detachment_ the child shows at a
certain point from the aids to arithmetical calculation; at a certain
stage of maturity he desires to "reason in the abstract" and make
"abstract calculations with numbers," as if obeying an internal
impulse which seeks to liberate the soul from every material bond and
at the same time to effect an economy of time. Hereupon we see
children of eight years old become eager and precocious calculators.

Children thus launched upon the enterprises of self-education acquire
a remarkable "sensibility" as to their own internal needs. Just