16. In dividing or classifying, two Rules must be observed, one of which refers to the Number and the other to the Arrangement of the Parts.

FIRST RULE OF DIVISION OR CLASSIFICATION.

The NUMBER of classes must be the same as the number of Real or Conventional differences in the basis, upon which the division or classification is made. This also determines the Kinds.

Thus, in classifying words according to the number of syllables in each, we may look at the syllables as one or more. This gives us two Classes; Monosyllables and Polysyllables. Or we may view them as having one, two, three, &c., syllables. This gives monosyllables, dissyllables, trisyllables, tetrasyllables, &c., to as many kinds as we have different numbers of syllables in our words.

It is unphilosophical to mix these two classifications, as is done when we call words "of four or more syllables, Polysyllables."

SECOND RULE OF DIVISION OR CLASSIFICATION.

The Divisions or Classes must be so arranged, that the First division may be explained without using any of the others; and the Second, without using any but the First. In short, arrange the classes so that each may be explained without using any of those, which have not been explained already.

17. It is always best to teach the parts or classes in that order, in which we have named them.

18. Useless kinds or classes should never be made. As the kinds of fractions called Compound and Complex, also Articles, and Adjectives Pronouns. Such divisions embarrass and confuse the learner without having the leas possible scientific or practical use,

19. The Rules are directions for using the Principles in the arts or in practice. Hence, a PRINCIPLE in science is a RULE in art.

In classifying substances with reference to the taste, we put all the sour or acid substances into the same class, because they agree in taste.

This class is a result-first, of a process of abstraction, by which we view a property or quality, called sour or acid, a part from the other properties of the objects and also from the objects themselves; second, of a process of classification, by which we group or arrange together all the objects, in which we perceive the property, called sour or acid.

Having formed a class, we next proceed to examine it in order to find some fact, which is true of every member in the class. This is called Generalization, because the fact or truth, which we find, must be true of every individual in the class. Suppose that, in examining a class of acids, we find, that each one will change the blue color, derived from vegetables, to a red; we might then state this fact as generally true of acids, and this General Truth is called a Principle. Now, since this Principle belongs to that kind, which we call Chemical, we call the Statement of the fact, that, Acids change vegetable blue to red, a Principle in the science of Chemistry.

If we wish to change this Principle in the Science to a Rule in the Art of Chemistry, we state the Fact in the form of a Direction, which is called a Rule; thus, "To change a vegetable blue to red, apply an acid."

1. (Principle.) The value of a fraction depends on the ratio of the denominator and the numerator.

2. (Rule.) To multiply the value of a fraction, multiply the numerator or divide the denominator.

3. (Principle.) "Ice, taken in moderate quantity, is a tonic, and serves to keep the system in such a healthy condition, that food gives it more strength;" therefore, (Rule)

"Every humane man and every farmer should have an icehouse."

4. (Principle.) "Clean books look much the best," therefore, (Rule) "We should not let our books be torn, nor allow the leaves to be turned down at the edge."

Not only should pupils be required to give clear and in telligible rules for such operations as they perform, but great pains should be taken to know, that they understand the principles, upon which the rules are founded.

FIFTH EXERCISE. (See page 557.)

1. Should a young colt be required to work enough daily to pay for his keeping? How else can he repay it?

2. What do we expect of stalks before they begin to bear grain?

3. How ought we to regard the growth or development of the mind? 4. Does a child learn that falling causes pain by being told that it will, or by falling?

5. Name the mental processes as they first appear in infants.

6. What does Synthetic mean? — Analytic? What is the Synthetic Course? - the Analytic?

7. How do the Synthetic and Analytic Courses compare with each other? For what is each to be used?

8. Is house-building an Analytic or a Synthetic process ?-pulling a house down?

9. Of what does the Secondary or Higher Course consist?

10. If you show something to a person, who does not understand English, and at the same time speak an English word, what will he think the word means?

How would you tell a person the meaning of the word, stone, if the person did not understand English? -hat?-eye? - book?

11. How do infants learn the meanings of words?

12. Could you tell the meaning of an English word, without showing the thing, which it named, to one who understands English?

13. Suppose I say that the Rhinconella resembles the Rhinconeta, would it give you an idea of the former?

14. Criticise the following Definitions.

a. Addition is the aggregation of the individualities composing an entirety.

b. Addition is addition.

c. Addition is making several numbers into a single number.

d. All horses are quadrupeds.

e. All quadrupeds are horses.

f. "Subtraction is taking a less number from a greater."

g. All kinds of apples are fruit.

h. All kinds of fruit are apples.

16. When objects are divided into large, middling-sized, and small, what is the basis of classification?- torrid, temperate, and frigid? -long, short? — high, low?

17. Of what kind is the difference between and 12? and 7? Which would you prefer, to be the President of the United States or to be the Chief Executive officer of the United States?

18. Give the Rules of Classification.

If we have four natural differences in a basis, how many classes must we have?

Suppose on the same basis we agree to have but three classes, are our differences natural or conventional? Why?

19. If we have arranged the parts of a subject in six cases, may we use case fifth to help explain case third? Why? Case first, to explain case second? Why?

20. In what order should we name the parts of a subject? — study or teach the parts?

!

GENERAL REMARKS.

If we divide or classify mankind according to development, we have three kinds or classes.

First. Those, who have hands;-who can work and only know how to work according to the orders of others.

This kind are mere machines. They are valuable only because they can work when and as another bids them. If you cut off their hands they are utterly spoiled and worthless. A brute, in the same predicament, would still have some value; these have none. Machine men.

The Second kind are those, who have hands and heads; or those, who can work, and know why they work, and how to work.

This kind are superior to machines, and to brutes, and also to the first kind. They can labor, they have the practical skill; they know why they labor and how to labor. They understand the science of that, wherein they toil. But even these come short of manhood. They fail in the great end of human existence. They are simply motor-machine

men.

The Third kind are those, who have hands, heads, and hearts; who can work, and know why they work, and how to work; who will and do work "for pulling down" whatever is evil and wrong, and "for building up" whatever is good and desirable for the human race.

These, really, are human beings. They toil-the hand is trained. They know why and how-the head does its part. They seek to promote the welfare of their fellow-men. The heart is interested and is right. They are men“Living souls."

If we would be like them, our knowledge should be thoroughly useful or practical, thoroughly scientific, thoroughly social or benevolent, and thoroughly moral or pious.

Now, the great medium or means, through which knowl