If the abbreviated mode of multiplication has been mechanically learned, still more has the abbreviated mode of dividing "over the line." In this, great heaps of figures are carefully piled up together, and a mistake in the construction would cause an error. Take, for example, 7860÷12=655. The work is done thus: write the dividend and the line at the right hand; write the divisor, 12, under 78; ask not how many twelves in 78, but how many ones in seven. Try with seven times; 7x12=84, it does not go; then with 6; it will go; write 6 at the right of the line; six times one from seven leaves one, which write over the seven; then say, twice 6 is 12, from 18 leaves 6, which place over the 8. Now make another divisor by writing 1 under 2, and another 2 next the 2, under 6, and make 66 the next dividend. Then, 1 in 6 5 times; write 5 at the right of the 6 in the quotient; 5 times 1 from 6 leaves 1, which write over the upper 6; then, twice 5 is 10, from 16 leaves 6. Then remove the divisor along again; and say, 1 in 6 5 times, 5 from 6 leaves 1, twice 5 is 10, 10 from 10 leaves nothing; and set the second 5 at the right hand in the quotient. As the numbers are used, they are struck out. There is not the least effort to understand the work. When it is completed it is proved by multiplication; and, if wrong, there is no intelligent endeavor to find the error, but the operation is to be repeated.

[Translated from Raumer's "History of Pedagogy," for the American Journal of Education.]

PHYSICAL EDUCATION includes,

1. Care of the health.

2. Inuring to endurance and want.

3. Training in doing; in bodily activity. Gymnastics.* 4. Training of the senses, especially of the eye and ear.

I. CARE OF THE HEALTH.†

The realists have paid especial attention to the care of the health; such as Montaigne, Bacon, Locke, and Rousseau.

At a later period, Hufeland's "Art of Preserving Life" has had much reputation. Much of what he says relates to people whose nerves are disordered by overexertion, and is useful for the recovery of such.

Care of health includes, first, diet. The most harmful food had become even customary among us, old and young; and it was at a late date that we began to examine the operation even of the most usual articles of diet. The temperance societies, for instance, have come out all at once against brandy, and its numerous family. All such measures have influenced the diet of the young, but have not had a thorough operation on it. Who does not know how many parents now give their young children coffee every day; and how extensively the children drink tea.

Warnings enough can not be given against the frequenting of the stomach-destroying confectionery-shops. Another fact of the same kind is the sight of even boys walking about with tobacco-pipes and cigars in their mouths.§

Clothing.-Rousseau, and the Philanthropinists, his followers, were the first who declared war against unsuitable modes of clothing

* Bacon, in a section on Athletics, says, "Endurance, both of active exertion and of suffering. Constituents of active exertion, strength, and quickness; enduring suffering is either patience under indigence or fortitude in pain." (De Augm. Scient., 4, 2, 113.)

I have already treated of the education of the youngest children.

This evil increases in Berlin, every year. In the time of the Turning societies, therefore, they and the cake-bakers were utterly at variance.

§ And have any good results followed from the efforts of the health-police against the sale of opium-cigars, for instance, which were openly vended at the Frankfort fair? Woe to all people who learn to love that poison!

children.* The Turners introduced an appropriate, convenient, and healthful costume; and endeavored at the same time to oppose the foolish vanity of a change of fashions. I shall say nothing at all of the fashions as prevailing among women. To appear new is always the thing sought after, even if a new monstrosity is the result. The sense of beauty seldom betrays, but yet we have seen the hoop-petticoat and the French rococo style

reappear.

When shall we cease to make children sleep in deep, stupifying feather-beds, and in unventilated chambers?

Early to bed and early to rise, says the old proverb. Excessive mental labor is harmful to all, especially by night, and is utterly destructive to the young, and most of all when drowsiness is kept away by coffee, &c. Such a course results in a truly horrible condition of overstimulation, in which even a healthy person completely loses control over himself.

The body is a temple of the Holy Spirit. How do those desecrate that temple, whose god is their belly! And it is most fearfully defiled and destroyed by the withering secret sins which have made such fearful progress amongst our youth. But our educators do little to avert the evil they rather pour oil upon the fire. When, to the influence of stimulating drinks, excessive eating, hot feather-beds, we add that of provocative dances, plays, and romances, and of those indecent pictures which make such deep impressions on the minds of the young, and destructively stimulate and entice during waking and sleep, who can wonder that such sins gain influence over our youth, and destroy them, soul and body? Do we make serious efforts to prevent these influences? Do we not rather behold them with indifference; arranging the dances ourselves, taking the children to the theaters when Kotzebue's and other loose pieces are acted? Is it not so? And does not all the world cry out, Pietism! if any one says a word against this destruction of souls?

. But the question has been asked, almost despairingly, by many, How are these secret sins to be prevented? First, by not giving them any assistance by making the young more susceptible to them, by rendering them morally and physically weak and corrupt. And, second, by positive discipline and strengthening of the body. The best protection of all, however, is an education in the fear of God; a means which may avail even when the destruction has gained a footing. Those who are corrupted in this way must be managed according to their peculiarities. To shameless cowards the truth should be told, that their habit is suicide; and that, if they go on in See the chapter on him.

it, they have already lived most of their days. The sight of any one who has become idiotic by onanism produces a powerful effect on boys. There are also, however, cases where it is better to encourage, and to give assurances that, upon a cessation of the habit, the body will become strong again, though on that condition only.

Lying goes hand in hand with this devilish secret vice; and bodily and mental filth, and atrophy.

Lorinser's article "On the protection of health in the schools "* directed the eyes of educators to the startling condition of the health of the pupils in our gymnasia. It was asked, What are the universal sources of the destructive physical condition of the schools, that make their pupils die faster than other German youth? Lorinser answered, The evil is based in the number of studies, the hours of instruction, and the home labor.

The number of studies, especially since real studies have made way into the gymnasia, has increased since that time. Still, several Prussian gymnasium programmes indicate that the number of hours of instruction was as great formerly as now; because as much time was devoted to their fewer studies as to our more numerous ones. Thus the reason of the evil should not be found in the number of hours of instruction, unless we answer that the scholars of the present day are less capable of study than they were then. Nor should the number of studies be blamed, without further examination; for fewness of studies has its evils too. Ratich taught "Only one thing at once. Nothing is more injurious to the understanding than to teach many things at the same time; it is like cooking pap, soup, meat, milk, and fish all in the same kettle, at once. But one thing should be taken up in order after another; and only when one has been properly attended to should another be entered upon. A single author should be selected for each language, from whom it should be learned. When he is thoroughly understood, and as it were quite swallowed down, another may be read. Nothing new should be taken up until what went before is understood quite thoroughly, and to entire sufficiency."

On this it has been remarked,

"Is this really according to the 'course of nature?' Would it be natural to eat broth alone, or fish alone, for eight months together, and even longer, as Ratich's pupils studied Terence? Is not a variety of reading matter, as in Jacobs' excellent readers, much more suitable to it? Just as we never eat one thing alone, but bread with meat,

*This appeared, in 1836, in the "Berlin Medical Gazette," (Berliner Medicinisches Zeitung.)

for example, it should be the care of the teacher not to clog his pupils with one thing forever. And, as the skillful host tries to furnish dishes which are suitable to each other, and which by their very connection shall conduce alike to good flavor and good digestion, so should the skillful pedagogue teach the same pupils, during the same term, various things, such as will serve to complete each other, and by whose alternation the pupil shall remain fresh, not satiated, but mentally nourished in a healthy way."

A judicious interchange of studies would be favored even by Lorinser; but an injudicious one-consisting merely in a restless changing from one thing to another, without ever asking whether all these single studies will harmonize together, and become one complete whole in the boy's mind-such an interchange I shall, of course, not need to discuss at all. On that point I agree wholly with Lorinser's complaints.

But the chief reason of the bodily as well as the mental bad condition of the pupils seems to lie less in the multitude than in the illcontrived method of the doing of the school-work. Many things

are forced upon the pupils which they do not like; especially a chilly, abstract method of studying language, and an unnatural, over-stimulated mode of mathematical study and production. Nor is this the case at the gymnasium merely; the evil is still greater in the lower schools. And, on the other hand, the pupils are kept away from what is appropriate for them, and from what they enjoy. Such a perverted method of mental stimulation and over-stimulation must necessarily destroy the body as well as the mind.

The case requires particular attention where each teacher in a school is attentive to his own department only, and makes such requirements upon the scholars as if they were under his instruction only, and had no other work to do. Thus, when the historical teacher requires of them to learn the most trifling things, such as innumerable dates; the geographical teacher, the smallest towns and rivers, the number of inhabitants of unimportant cities; the French teacher, the six first books of "Télémaque;" or the Latin teacher, many pages of the "Loci Memoriales," to be committed to memory; when the mathematical teacher spurs them forward to the integral calculus, &c.; in such a case, the conscientious scholar must indeed succumb to the burden of "home-labor," or must quite give up conscientious work.*

*As an instance of the unreasonable conduct of many department-teachers, it may be mentioned that, in a certain well-known institution, the teacher of mathematics set as much home-work to the scholars to do as all the rest of the teachers together.