but neither illustrations nor demonstrations | full consciousness of duty nobly done. The should be memorized, although great care should be taken to secure a good style of expression, modeled on that of the text. To this first recitation on a new subject all the class should give the strictest attention; and every point in it should be brought out, at least once in the hearing of every pupil. In the course of subsequent recitations in the same general subject, individuals will be questioned on the principles thus developed. For example, what algebra is will have been brought clearly to view in this first recitation; but when a pupil has stated and solved some problem, and has given his explanation of the solution from the blackboard, the teacher may ask: Why do you say you have solved this problem by algebra? The answer will be: Because I have used the equation as an instrument with which to effect the solution. Can you solve this problem without the use of an equation? What do you call such a solution? What is algebra? Again, suppose the solution has involved the reduction of such an equation as 2.c—4—§ (3.x—1)+}(x+1). Of course, in the first place the pupil will solve the example and give a good logical account of the solution; but the teacher will make it the occasion for reviewing certain definitions and principles with this particular student, in such a practical connection. Thus he will ask: What is your first equation? What is your last? [x=2.] Do you look upon these as one and the same equation, or as different equations? In how many different forms have you written your given equation? What general term do you apply to these processes of changing the form of an equation? What is transformation? Similarly, every principle and definition will be reviewed again and again in such practical connections. But the great, and almost universal, evil in our methods of conducting recitations is the habit of allowing mere statements of processes to pass for expositions of principles, as given by the pupil from the blackboard in explanation of his work. The writer's observation satisfies him that this most pernicious practice is, as he has said, almost universal Let us illustrate the common practice, and then point out the better way. The pupil has placed the following work upon the board:

7x-28x+14=238

7x2-28x-224

x2-4x=32

x2-4x+4=36
x-2=+6

x=26-8, and —4. He is then called upon to explain his work. Something like the following is what we hear in the majority of our best schools:

"Given 7x2-28x+14=238, to find the value of x.

"Transposing, I have 7x2-28x-224. "Dividing by 7, x2-4x-32.

"Completing the square, x2-4x+4=36. "Extracting the square root, x-2— ±6. "Transposing, x=2+6=8, and -4.

fact is, all that he has said is useless, nay, worse than useless. He has simply intimated what processes he has performed. That he could solve the problem was sufficiently apparent from his work. There was no need that he should tell us what he had done, when he had performed the work before our eyes. What is wanted is a clear and orderly exposition of the reason why he takes every step. This involves two points, since he is to show (1) that the step taken tends to the desired end, that is, the freeing of the unknown quantity from its connections with known quantities so as finally to make it stand alone as one member of the equation; and (2) that the step does not destroy the equation.* Something like the following should be the style of explanation: "Given 7x2-28x+14=238, to find the value of x. In order to do this, I wish so to transform the equation that, in the end, x shall stand alone, constituting one member of the equation, while a known quantity constitutes the other member. Hence I transpose the known quantity 14 to the second member. This I do by subtracting 14 from each member, which may be done without destroying the equation (or the equality of the members), since, if the same quantity be subtracted from equals, the remainders are equal. I thus obtain 7x-28x-224. I now observe that the first term of the first member contains the square of x, while the second contains the first power. I wish to obtain an equation which shall contain only the first power of . In order to do this. I make the first term a perfect power by dividing each member of the equation by 7, which does not destroy the equality, since equals divided by equals give equal quotients, and I have x2-4x=32. Now, observing that x2-4x constitutes the first two terms of the square of a binomial of which the square of half the coefficient of x, or 4, is the third term, I add 4 to this member to make it a complete square. and also add 4 to the second member to preserve the equality of the members, and have x2-4x+4=36. Extracting the square root of x2-4x+4, I have x-2, an expression which contains only the first power of x; but to preserve the equality, I also extract the square root of the second member, obtaining x-2=+6. Finally, transposing -2 to the second member by adding 2 to each member, which does not destroy the equation, I have x=8, and -4." If it is desired to abbreviate the explanation, it is far better to make it simply an outline of the reasons than a mere statement of the process. In this case, an outline of the reasons may be given thus: The object is to disengage from its connections with other quantities so that it shall stand alone, constituting one member while the other member is a known quantity. The first process is based upon the principle that equals subtracted from equals leave equal remainders; the second, upon the

"Destroy the value of the equation", is an absurd expression which we frequently hear. An equation is not a quantity, and hence has no value. The equality

And the pupil turns to his instructor in the of the members is meant.

final condition in the Latin language. Thus, I the name of each, so as to associate arbitrarily and J, and U and V, instead of being merely the form with the name; or, in simultaneous graphic variations, were changed so as to represent class instruction, to exhibit the letters on sepadifferent sounds, during the 16th and 17th cent-rate cards, and teach their names by simple repetiuries. W was added previously, in the middle tion. This process must, of course, be not only ages. The twenty-six letters of our alphabet have long and tedious, but exceedingly dry and uninterbeen thus classified with regard to their history: esting to a child, since it affords no incentive to (1) B, D, H, K, L, M, N, P, Q, R, S, T, letters mental activity,- no food for intelligence. By from the Phoenicians; (2) A, E, I, O, Z, origin- a careful selection and discrimination, however, ally Phoenician, but changed by the Greeks; in presenting the letters to the attention of the (3) U (same as V), X, invented by the Greeks; child, its intelligence may be addressed in teach(4) C, F, Phoenician letters with changed value; ing the alphabet by this method. The simple (5) G, of Latin invention; (6) Y, introduced forms, such as I, O, X, S, will be remembered into Latin from the Greek, with changed form; much more readily than the others; and these (7) J, V, graphic Latin forms raised to inde- being learned, the remainder may be taught by pendent letters; (8) W, a recent addition, formed showing the analogy or similarity of their forms by doubling U (or V), whence its name. with the others. Thus O becomes C when a portion of it is erased; one half of it with I, used as a bar, forms D; two smaller D's form B; and so on. This method is very simple, and may be made quite interesting by means of the blackboard.

The imperfections of the English alphabet are manifold: (1) Different consonants are used to represent the same sound; as c (soft) and s, g (soft) and j, c (hard) and k, q and k, and ks. (2) Different sounds are expressed by the same letter; as c in cat and cell, g in get and gin, s in sit and as, f in if and of, etc. (3) The vowels are constantly interchanged, as is illustrated in the following table of the vowel elements of the language and their literal representations, the diacritical marks used being those of Webster's Dictionary.

Long.

as in ape, they

Short.

as in end

hat ask

"her, sir, myrrh

"do, rule, too

** urn

"use

ice, my

oi oy " ou ow

"oil, boy
"out, owl

The letters which closely resemble cach other in form, such as A and V, M and N, E and F, and C and G, among capitals, and b and d, c and e, p and q, and ǹ and u, among small letters, should be presented together, so that their minute differences may be discerned. When the blackboard is used (as it should always be in teaching classes), the letters may be constructed before the pupils, so that they may perceive the elements of which they are composed. Thus the children will at once notice that b, d, p, q, are composed of the same elements, differently combined, straight stroke, or stem, and a small curve. "wolf, put, book an appropriate drill, the peculiar forms, with the name of each, will then be soon impressed upon the pupils' minds; and, besides that, their sense of analogy, one of the most active principles of a child's mind, will be addressed, and this will render the instruction lively and interesting. In carrying out this plan, the teacher may use the blackboard, and as a review, or for practice, require the children to copy, and afterwards draw, from memory, on the slate, the letters taught. Cards may also be used, a separate one being employed for each letter. With a suitable frame in which to set them, these may be used with good advantage, the teacher making, and the children also being required to make, various combinations of the letters so as to form short and familiar words. A horizontal wooden bar with a handle, and a groove on the upper edge in which to insert the cards, forms a very useful piece of apparatus for this purpose. LetterBlocks may also be used in a similar manner by both teacher and pupils. These blocks are sometimes cut into sections so as to divide the letter into several parts, and the pupil is required to adjust the parts so as to form the letter. This method affords both instruction and amusement to young children, and at the same time, gives play to their natural impulse to activity. These various methods will be combined and others devised by every ingenious teacher. In some schools a piece of apparatus, called the reading

From this table it will be seen that the letter a is used to represent seven different sounds; e, five sounds; o, sic sounds, etc. (See PHONETICS.) The names given to the letters are not in conformity with a uniform principle of designation. Thus, the names of b, c, d, g, p, t, v, and z are be, ce, de, ge, etc.; while the names of f, l, m, n, s, and are ef, el, em, en, etc.; and the names of j, k, are ja, ka. The heterogeneity of these names and of their construction will be obvious. It is important that the teacher should take cognizance of these incongruities in giving elementary instruction, as they dictate special methods of presentation. (See ALPHABET METHOD.)

ALPHABET METHOD, or A-B-C Method. This has reference to the first steps in teaching children to read. According to this method, the pupil must learn the names of all the letters of the alphabet, either from an A-B-Cbook, from cards, or from the blackboard; that is, he must be taught to recognize the various forms of the letters, and to associate with them their respective names. The method of doing this, once very general, was to supply the pupils with books, and then, calling up each one singly, to point to the letters, one after the other, and to pronounce

frame, is used. This is constructed like a blackboard with horizontal grooves, in which the letters can be placed so as to slide along to any required position. By the use of assorted letters, the teacher can construct any word or sentence, building it up letter by letter, as types are set. Many interesting exercises in reading and spelling may be given by means of such an apparatus, the children being required to construct words and sentences themselves, as well as to read those formed by the teacher. The A B C Method of teaching the elements of reading has now, quite generally, been superseded by the Word Method. See CURRIE, Erly and Infant School Education, and Principles and Practice of Common School Education; WICKERSHAM, Methods of Instruction. (See WORD METHOD.)

ALUMNEUM, or Alumnat (Lat., from alere, to feed, to nourish), the name given in Germany to an institution of learning which affords to its pupils board, lodging, and instruction. The first institutions of this kind arose in the middle ages in connection with the convents. Among the most celebrated are those founded by Maurice of Saxony, in the 16th century, at Pforta, Meissen, and Grimma. When the pupils were received and instructed gratuitously, they were | expected to perform various services for the school and church, such as singing in the choir. The pupils of these schools were called alumni. (See ALUMNUS.)

ALUMNUS, pl. Alumni (Lat., from alere, to feed, to nourish) originally the name of a student who was supported and educated at the expense of a learned institution (see ALUMNEUM), now generally applied to a graduate of a college or similar institution. The graduates of higher seminaries or colleges for females are sometimes called alumnæ.

ago from funds contributed for the purpose by W. F. Stearns, son of the president. This institution occupies twelve public buildings, besides the president's house, including an edifice for scientific instruction, and the college church. There are also a gallery of art, a cabinet of natural history, containing about 100,000 specimens, and an astronomical observatory. The department for physical training is very efficient. It comprises an extensive and well appointed gymnasium; and, at a certain hour, each class is required to attend, and engage in exercise under the direction of the professor, who is a thoroughly qualified physician. The faculty includes twentythree instructors, and there are several endowed professorships. The number of students in 1874 was about 340. The college library contains more than 30,000 volumes; and those of the societies, about 10,000. There is a scientific as well as a classical course; also a post graduate course, established in 1874, in history and political science, with especial reference to a “ science of statesmanship;" while any graduate may arrange to pursue a course of study in any department additional to the college course. The tuition fee is $90 per annum.

ANALYSIS, Grammatical, or Sentential.-By the analysis of a sentence is meant a decomposition of it into its logical elements. Every sentence must either be a single proposition, or be composed of propositions more or less intimately related; and every proposition must contain a subject and a predicate, the former expressing that of which we speak, and the latter, what we say of it. The entire or logical subject must contain a noun or pronoun, either alone or with related words called modifiers or adjuncts, or it may be a phrase or a clause. The entire or logical predicate, in the same manner, AMHERST COLLEGE, at Amherst, Mass., must consist of a verb with or without adjuncts. is one of the chief seats of learning in the These constitute all the parts, and all the relations, United States. It was founded in 1821 by the involved in the construction of a sentence. A few Orthodox Congregationalists, especially for the words, such as interjections, may be used indeeducation of young men for the ministry; but pendently of them. Grammar has been defined its charter was not obtained till 1825. Its first as the "art of speaking and writing correctly," president was the Rev. Zephaniah S. Moore, who or as the "practical science which teaches the in 1823 was succeeded by the Rev. Heman right use of language"; and for general purHumphrey, to whose strenuous and prudent poses this account is, perhaps, sufficiently exefforts the college owed much of its success. He plicit. It does not, however, truly distinguish continued in office till 1845, when he was suc-grammar from the other arts concerned in teachceeded by the Rev. Edward Hitchcock; and, on the resignation of the latter, in 1854, the present incumbent, the Rev. William A. Stearns, D.D., was elected. This institution has been the recipient of very large donations from private persons, and appropriations from the State amounting to upward of $50,000. The college funds amount in the aggregate to more than $650,000. Its charity fund for the gratuitous education of clergymen amounts to about $70,000; and its fund for free scholarships is at least $100,000. The names of the principal donors to the institution are Dr. William J. Walker, to the extent of $240,000; Samuel A. Hitchcock, $175,000; Samuel Williston, $150,000; and a college church was erected a short time

ing the "right use of language," and hence does not correctly point out its peculiar province. From a want of precision in defining the limitations of any art or science, there must necessarily follow a corresponding inaccuracy and looseness in its treatment; since, before we can reason properly as to the best methods of attaining any object, we must clearly conceive what that object is, and carefully distinguish it from all others.

The special province of grammar does not extend beyond the construction of sentences; but it is quite obvious that to use language correctly, those principles and rules must be understood which underlie the proper method of combining sentences so that they may constitute elegant and logical discourse. A person may be sufficiently

familiar with grammatical rules to construct sen- | laid for the intelligent study of all other gramtences with perfect correctness, but may so ar- matical terms and distinctions; and this being range them as to express only nonsense; and the foundation, should, of course, be the first such a person could scarcely be considered as understanding the "right use of language." The sentence being the peculiar province of grammar, it follows that the only subjects of investigation embraced within it are words, their orthography, inflectional forms, and pronunciation, and their arrangement in sentences. All grammatical definitions and rules are founded upon the relations of the parts of a sentence to each other; and, therefore, these relations should be first taught. It is with reference to these relations, that words are classified into parts of speech, or, as they might properly be called, parts of the sentence. To define or explain these parts of speech before giving any definition of a sentence, is, therefore, clearly illogical; yet this has been the method of many grammarians, words being explained and parsed as if they had only individual properties. It is in this that the distinction between parsing and grammatical analysis consists. Both are, in fact, only different kinds of analysis, and are based on precisely the same relations, those in which the words stand to each other as parts of a sentence.

Parsing, as uniformly employed by grammarians, is a minute examination of the individual words of a sentence, with the view to determine whether the rules of grammar, proper to the particular language in which the sentence is written, have been observed or violated. Analysis, on the other hand, deals with the relations upon which those rules are based, and which are common to all languages. Thus, in parsing, the pupil is obliged to scrutinize all the inflectional forms in which the words composing the sentence are used; and, in order to determine whether they are proper or not, must not only know the rules of syntax, but the relations of the words to each other, so as to be able to apply those rules. The relations are invariable in all languages, but the rules which refer to the inflections are founded on particular usage, and hence are in no two languages exactly alike. On this account, since the general logically precedes the special, the treatment of sentential analysis should precede any exercises in parsing. Otherwise, how, for example, could a pupil be required to distinguish the cases of nouns and pronouns, and the person and number of verbs, before being taught the relations of the words to each other? By means of the analytical method, when rightly applied, the study of grammar is made clear, logical, and easy from the very beginning. The pupil is first taught the nature of the sentence, its essential parts, and their relations to each other, and is shown how to analyze sentences of a simple character. He is troubled with but little phraseology; for all the terms that are essential to the complete distinction and designation of the parts of a sentence are subject, verb or predicate, object, attribute, and adjuncts. These being defined, and the pupil taught how to distinguish them, a complete foundation has been

thing done. Those who oppose the analytical method assert that words are the real elements of a sentence, and that any consideration of these involves, therefore, an exhaustive analysis of the sentence itself. With the same propriety might it be said that pieces of iron of various shapes are the elements of the steam-engine. They indeed compose the machine, and it can ultimately be resolved into them; but could its structure and workings be explained by taking these fragments of metal in a hap-hazard way, and noticing how they are related to others in immediate juxtaposition, without regard to the general structure of the machine, and the dependence of its operation upon a few elementary or primary parts, as the cylinder, piston, condenser, etc.? Words are not necessarily the real elements of a sentence. These are the subject and predicate and their adjuncts; and, unless these component parts of the general structure be first observed, the relations of the separate words cannot be understood. Hence, we find that those writers who have ignored a definite consideration of these logical elements, have fallen into many errors and inconsistencies.

The various systems of analysis in use differ in no essential respect, the chief variation being in the nomenclature employed to designate the elements of the sentence. The name generally applied to a proposition forming a part of a sentence is a clause, and any group of related words not making a proposition is called a phrase. The modifying elements are by some called adjective or adverbial, according as they perform the functions of adjectives or adverbs. Instead of the term adjective, adnominal is sometimes employed. The term adjunct is generally employed to designate an element subordinate to either subject or predicate. Such adjuncts may be modifying, descriptive, or appositional. A modifying adjunct changes the meaning of the element to which it is applied, generally, by making it more specific, or by restricting the class to which it belongs. Thus animal is a more general term than four-footed animal; hence, four-footed is a modifying adjunct. But the term man is no more general than man that is born of a woman, or mortal man; the adjuncts, that is born of a woman and mortal being only descriptive, not modifying. Appositional adjuncts only explain; as: He, the chieftain of them all, in which the phrase, the chieftain, etc., is only explanatory, or appositional. Adjuncts may be single words, phrases or clauses; and one of the chief advantages of sentential analysis is to show the pupil that groups of words are often used so as to perform the same office as single words. In teaching this subject, a proper gradation of topics should be observed; and much caution exercised to avoid the perplexing of the young pupil by presenting to his mind distinctions too nice to be discerned by his undeveloped powers of analysis. Various methods have been devised in order to