and repair. Moreover, these laws cannot be stated in quantitative terms. No one can tell, in general, how long it takes fully to energize a mind at a given time, or how far removed the fatigue point is from the initial point of greatest energy. Very much depends upon age, discipline, physical health, the character of the stimulus, and other circumstances. As a rule, the periods lengthen as the individual passes from childhood to youth and from youth to manhood. That is, a man's mental force is less quickly aroused and mobilized than a child's, and it tends to persist much longer.

3. From the laws of congruence and energy we derive some important rules of teaching. While these are applicable to all grades of teaching, they are particularly important in relation to primary teaching. The principal of these rules may be formulated as follows:

(a) Sufficient time must be allowed the pupil for him to collect his energies, to mobilize his forces. Slow and halting recitations tend to dullness of mind, while rapid recitations develop either confusion or shallowness. There must be a certain singleness or isolation of the fact or idea. "The child must be accustomed to give one impression time to take root," says Radestock,* "and not follow it immediately by a corresponding action, that it may not pass away with that action into air." The same writer quotes the following from Lazarus with approval: "Deep thinking requires time; it is therefore a great pedagogical mistake if teachers, as is now generally done, urge their pupils to answer rapidly, and praise those who immediately have an answer ready. This causes everything to be lowered to a mere effort of mechanical memory. The pupil should be given time for individual contemplation, for deep and energetic thought labor." This does not imply that lessons are not to be well prepared and subjects well thought out beforehand. When the fullest preparation has been made, there is still opportunity for energetic thought at the time of the recitation.

(b) The pupil should be held to the same subject as long as the mental current flows with full volume. To no new subject can all the energy that has been aroused by any activity be transferred, and to some subjects none whatever. Unnecessary changes from subject to subject, or from lesson to lesson, involve the dissipitation and consequent loss of both time and power, the amount of which will depend in great part upon the relative congruity or incongruity of the different subjects or activities. More power can be transferred from Latin to Greek than from French to German. This is Dr. Bain's physiological explanation of the rule laid down: "We know well enough

that the nervous currents, when strongly aroused in any direction,

tend to persist for some time. In the act of learning, this persistence will count in stamping a new impression; while part of the effect of a lesson must be lost in hurrying without a moment's break to something new, even although the change is of the nature of relief."

(c) Advantage should be taken of favoring times to do, or to secure the doing of, certain kinds of work. The more difficult subjects should be pursued by a pupil or student when both body and mind are fresh and vigorous. It is the flood-tide, not the ebb-tide, that brings the great ships up to the dock.

(d) Before the pupil reaches the fatigue point, the teacher should permit him either to take up another subject or to drop study for the time altogether. Persistent application on a stream of falling energy involves waste of time and power, and may lead to serious results. To some extent, no doubt, the needed relief can be had through a change of method.

(e) Whether the pupil should take up a new study, or drop all study for the time, depends upon the kind of fatigue that has supervened. Diminished power for one activity is not diminished power for all activities. Thus, a pupil who has studied arithmetic or algebra as long as it is profitable to-day, will take up geography or history with interest, and vice versa. To a degree studies are like gases; they are vacuums one to another. As a jar that is already filled with hydrogen gas will still hold as much carbolic acid gas as a jar of the same size that is empty, so a pupil that is satisfied for the present with mathematics will pursue literature with interest and profit.

(f) The school course of study should be made up with constant reference to the psychic laws that have been laid down. Into the question how far psychology and how far environment should control the educational ideal, we need not enter. No one denies that psychology must largely influence the choice of studies, and almost wholly control their co-ordination.

(g) The working program of the school, in particular, should be made up with reference to the same principles.

(h) The principle of congruence and its limitations have important applications to elective studies in colleges and universities. In filling out election blanks, it is believed students who are left wholly to themselves often choose studies that make strange bedfellows. Nor is this surprising; the criteria that should govern the choice are very subtle and intricate. This topic will come before us again.

The arguments on which the three last rules rest are practically the same. They involve the important subject of concentration. Congruent studies re-enforce one another with respect to both content and mental aptitude. One subject involves other subjects. The physicist must be a mathematician, the Latin scholar must know

something of Greek, the historian must be acquainted with politics and political economy. For a time depth and breadth vary directly; after that indirectly. But in the absolute sense a specialist is an impossibility. An astronomer cannot study the moon by itself, or a physiologist the eye. No one object or subject can be understood when taken alone: it is related to other objects, it is a part of the universe. Still, to be effective the mind must be grooved, and this involves the repetition of the same act and of similar acts. Once more, if the practical requirements of the school compel a study to be discontinued before the fatigue point is reached, thus departing from the ideal, then some related subject may be taken up, because more of the power that has been accumulated can be transferred to a related than to an unrelated subject. And still the distance of the fatiguepoint must be considered.

4. But congruence alone must not dictate the course of study, the daily school program, or the student's elections. Fortunately, there may be power for one subject when there is none for another subject. We have spoken of the mind under the similitude of a stream or current. The fact is, however, that the mind is less like a river from which you may take water for any purpose, than it is like a bank where the total amount of money that is on deposit is divided among many different accounts, and is subject to check by as many different persons. This is due to specialization of powers-to the difference between specific and generic force. The one-study college is, therefore, just as unphilosophical as those schools that break the work hours up into small crumbs of time. Thus the fundamental laws of mental energy, or of interest if you will, impose a veto upon an exaggerated form of concentration.

It is further to be observed that concentration is a relative term, at best. No wise teacher proposes to limit the pupil to a single study or class of exercises. To do so would in reality involve the dogma of formal discipline in its extreme form. Another remark is, that concentration in the primary school may be overdone as easily as specialization in the higher school. It has been shown time and again that the child may be over-taught certain subjects. His impressible mind may be so deeply and narrowly grooved that it can never be broadly cultivated. It become indurated, as it were. result may be due in part to the intensity of the activity, but it is more due to its persistence. As the mind matures, there is less and less need of caution on this point. The pupil gets farther and farther away from the mechanical elements of knowledge, becomes more and more occupied with the higher logical elements, and so is less responsive to narrowing influences. While the child's activities must be duly limited, his full development still calls for a profusion of educational material.

At this point some very practical questions confront the teacher and superintendent. How long should a pupil be kept at work on the same subject? How much work should he do in one school-day? How frequently should he change from one subject to another? How many studies should he have? No man can answer these questions in formulæ; the teacher or superintendent must answer them as they arise, and to do so he will find his best observation and judgment seriously taxed. It may well be doubted whether, measurably, the common schools are not now sacrificing the best results to swollen programs and short exercises. The question is one that the superintendent should study with a transcript of the facts that have been stated in one hand, and his course of study and time-table in the other. There is no reasonable doubt that much evil in the school that is now charged to the account of overwork should rather be charged to work done in the wrong way.

5. The psychic facts to which the names of congruence and energy have been given demand fuller investigation than they have hitherto received. It is well known that the school programs, both in respect to the co-ordination of subjects and the length of exercises, commonly rest upon a rude empirical basis. The factors that control those who make them appear to be the necessities of the school, real or supposed, tradition, and individual experience. This empiricism is not surpris ing, considering the meager attention that psychologists and pedagogists have given to the principles that underlie good school programs. Very little attention has been given to the time elements involved in psychic energy as applied to school exercises. When three heavy subjects appear upon the program for the day-subjects demanding the fixation of the attention-you will not indeed commonly find them all crowded into the same session; but that is about as far as the attempt to accommodate the work to the pupil's ability in this regard has been carried. Such delicate questions as these occur: How much time elapses between the application of different stimuli to the child mind at different ages and the development of maximum psychic power? How long is the interval between such maximum and the fatigue point? In respect to the swelling of the mental current to its full volume, and in respect to its persistence, how much depends upon the pupil's age? How much upon the peculiar stimuli at different ages? And how much upon the teacher's skill? It is easy to translate these questions into the practical interests of the school. They cannot be answered without much careful observation and collaboration of facts. The whole subject should enlist the serious attention of students of child study, both under its physiological and psychological aspects, and it is earnestly recommended to their attention.

6. The correlation of the teacher and the text-book, if one be used, demands something more than passing attention. Dr. Bain has said that undoubtedly the best of all ways to learn anything is to have a competent teacher "dole out a fixed quantity of matter every day, just sufficient to be taken in and no more; the pupils to apply themselves to the matter so imparted, and to nothing else." The singleness of aim is favorable, he urges, to the greatest rapidity of acquirement; defects should be left out of account until one thread of ideas is firmly set in the mind. Still he admits that not unfrequently, and not improperly, the teacher has a text-book to aid him in his work. * "To make this a help and not a hindrance demands the greatest delicacy, since the pupil must be kept in one single line of thought, and never be required to comprehend upon the same point conflicting or varying statements. Even the footnotes may have to be disregarded in the first instance, since they act like a second author, and so keep up an irritating friction."

Nothing else is so essential to successful elementary teaching as unity or congruence of subject-matter. Dr. Bain does not exaggerate the value of the "one thread of ideas," or the "one single line of thought." His scruple about footnotes even is often justified. These more definite rules will determine the teacher's general relations to the text-book.

(a) If the book is the main source of instruction, the teacher should teach the book; that is, the matter of the book. If footnotes tend to confuse, what shall be said of the teacher who takes an independent line from the beginning? No wise teacher certainly would be so absurd as to give a pupil who is just beginning a new subject two textbooks. A good Sunday-school teacher, dealing with the life of Jesus in a primary class, would not try to follow all the Gospels, or even two of them, at the same time; rather than do that, it would be better to select his material here and there and to blend them in a new gospel of his own. The teacher may teach something more or something less than the book teaches on a single point, but nothing different or contradictory.

(b) The teacher should also follow the methods of presentation that the book employs. Nothing could be more absurd than for a teacher who has assigned to a class a book lesson that is presented inductively, to go ahead and teach it deductively.

(c) The teacher should study to make the first presentation of a lesson successful. If two or more presentations are required, besides the loss of time, the mind is left in a littered-up condition that is confusing. This is the reason why it is often more difficult to teach a

"Practical Essays," pp. 218, 219.