book may be used to advantage. If one takes a book, opens the same—the eyes to be kept closed in the mean time and then casts a rapid glance at a part of the page and tries to estimate how many lines are visible, this way of doing, if often repeated and always tried on different pages, will soon conduce to great accuracy in estimating. A small child is not able to estimate even three lines correctly, though looking at them for fully a second.
As the mind develops, it acquires a more simple and rapid process of counting. Something that at first had to be undertaken slowly and with care, perhaps in separate stages, may later on be accomplished much more quickly and without requiring any special effort, or calling for any great amount of attention, in fact almost "mechanically."
One is fully conscious of every perfectly new impression received by the brain; hence the fascination of a novel idea. The more the charm of novelty fades with the recurrence of the same sensation, the less will consciousness be called into play.
Counting from one upward, by constant repetition, finally comes to be done unconsciously, even as the quick movement of the fingers in practicing on the piano gradually becomes almost automatic, though at first this, too, required great care and attention. In all similar cases consciousness is no longer called into play.
An impression that seemed most startling when first received may, if too often repeated, grow to be trivial. The simple work of counting finally comes to be an unconscious action of the nerve-fibers and cells of the brain.
On newly built roads, the trains are run but slowly; the longer such roads have been used, the more rapidly are trains run on them, and stops at way-stations are no longer needed; it is even thus with the trains of thought in the human brain.
And on this rests the practical importance of rapid counting. Whoever can, unconsciously but correctly, count up to twenty or even only up to twelve, has a great advantage over others who can not, without error, distinguish six from seven in this manner. For such a one can turn his consciousness to other matters and greatly increase his knowledge, where another would make but slow progress.
Those movements in man, which take place through some impression received from without and not aided by any conscious act of the brain (as, for instance, the contracting of the pupil when a bright light strikes the eye), are termed reflex actions.
In part these are brought about by arbitrary but oft-repeated motions, inasmuch as such will gradually take place more rapidly and without premeditation.
In this way, through practice, counting from one to five is done unconsciously, and somewhat resembles a reflex action.
If many such simple mental acts (by the repetition of which noth-
