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 as the new-born infant whose food is rationally regulated, is silent and tranquil during the two hours of digestion and assimilation, and cries out the moment the hour for a fresh meal has struck, so do these children "ask for help," ask for "new materials," new "forms of work," as soon as they have accomplished their mysterious phenomena of internal maturation, and ask for them _determinately_, indicating _their most immediate need_, just as one in physical want would be able to state distinctly whether he were hungry, thirsty, or sleepy. A child, in like manner, asks for reading, or grammatical exercises, or means for observing Nature. His sensibility manifests itself in a lucid and intense desire, to which the teacher has only to respond.