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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-(3-1)+3(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:

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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 un-
known 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 expla-
nation: "Given 7x2-28x+14=238, to find the
value of x. In order to do this, I wish so to trans-
form 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 subtract-
ing 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 x. 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 x2-4.x con-
stitutes the first two terms of the square of a
binomial of which the square of half the coeffi-
cient 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. Ex-
tracting 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, ob-
taining .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 ex-
planation, 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, constitut-
ing 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

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principle that equals divided by equals give equal quotients," etc. Again, while it is admissible when the purpose is to fix attention upon any particular transformation, to omit the reasons for some of those previously studied, it is far better that these be omitted pro forma, than that something which is not an exposition of reasons be given. Thus, if the present purpose is to secure drill in the theory of completing the square, after having enunciated the problem, the pupil may say: "Having reduced the equation to the form -42-32," etc., proceeding then to give in full the explanation of the process under consideration. But it is well to allow no recitation on such a subject to pass without having at least one full explanation. These remarks apply to study and recitations designed to give intelligent facility in reducing equations. In what may be called "Applications of equations to the solution of practical problems" the purpose is quite different, and so should be the pupil's explanation. In these, the statement is the important thing, and should be made the main thing in the explanation. In most such cases, it will be quite sufficient, if, | after having given the reasons for each step in the statement, thus fully explaining the principles on which he has made the equation, the pupil conclude by saying simply: "Solving this equation, I have," etc. Outlines of demonstrations and synopses of topics are exceedingly valuable as class exercises. For example, it requires a far better knowledge of the demonstration of Sturm's theorem to be able to give the following outline than to give the whole in detail: (1) No change in the variable which does not cause some one of the functions to vanish, can cause any change in the number of variations and permanences of the signs of the functions; (2) No two consecutive functions can vanish for the same value of the variable; (3) The vanishing of an intermediate function cannot cause a change in the number of variations and permanences; and (4) The last function cannot vanish for any value of the variable; and, as the first vanishes every time the value of the variable passes through a root of the equation. it by so doing causes a loss of one, and only one, variation. We, therefore, have the theorem [giving the theorem]. Finally, no subject should be considered as mastered by the pupil until he can place upon the blackboard a synoptical analysis of it, and discuss each point, either in detail or in outline, without any questioning or prompting by the teacher. The order of arrangement of topics, i. e., the sequence of definitions, principles, theorems, etc., is as much a part of the subject considered scientifically as are the detailed facts; and the former should be as firmly fixed in the mind as the latter.

ALGERIA, a division of N. Africa, which was formerly a Turkish pashalic, but has since 1830 been in possession of the French. The boundaries are not defined, and the tribes dispute the claims of the French to large tracts on the border. The territory claimed by the French is estimated at about 258,317 sq. m.; of which about 150,568 are subject to the civil, and the

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ALPHABET

remainder to military, government. The population according to the census of 1872 was 2,416,225, of whom 245,117 were Europeans and their descendants; 34,574 native Jews; the remainder were Mohammedans. In regard to religion, 233, 733 were Catholics, 6,006 Protestants. 39,812 (including those of European descent) Jews, and 140 had made no declaration. The Catholics have an Archbishop and two Bishops; the Protestants three Consistories, under which both the Lutheran and Reformed Churches are placed. In regard to public instruction, Algeria constitutes a division, called the Academy of Algeria and headed by a rector. The number of free public schools in 1866 was 426, with 45,375 pupils; for secondary instruction there are four colleges and one Lyceum (at Algiers, Bona, Constantine, Philippeville, and Oran), the secondary institution at Tlemcen, and the free school at Oran. A special system of instruction has been arranged for the Mohammedan popuiation. It comprises the douar (village or camp) schools, the law schools (zaïuas), the schools of law and literature (medresas), the French Arabic schools, and the French Arabic colleges. Algiers, the capital, has special schools of theology and of medicine. The educational progress of this country derives a special interest from the fact that it illustrates the influence which the government of a Christian country can exercise upon a Mohammedan dependency. See BLOCK, Dictionnaire général de la politique. A full account of the French laws regulating public instruction in Algeria may be found in GREARD, La Législation de l'Instruetion Primaire en France, tom. III., art. Algéri ́.

ALLEGHENY COLLEGE, at Meadville, Pa., was founded in 1817, and is under the direction of the Methodist Episcopal Church. The number of students in 1874-5 was 132, more than one half of whom were pursuing the collegiate course. It has classical, scientific, and biblical departments, and is open to both sexes. its library contains about 12,000 volumes. Rev. L. H. Bugbee, D.D., is the president of the faculty.

ALMA MATER (Lat., fostering mother) is a name affectionately given by students of colleges and universities to the institution to which they owe their education.

ALPHABET. The alphabet of any language is the series of letters, arranged in the customary order, which form the elements of the language when written. It derives its name from the first two letters in the Greek alphabet, which are named alpha, beta. The letters in the English alphabet have the same forms as those of the Latin language, which were borrowed from the Greek. The Latin alphabet, however, did not contain all the Greek letters. The letters of the Greek alphabet were borrowed from the Phonician, which was that used by many of the old Semitic nations, and is of unknown origin. It consisted of 22 signs, representing consonantal sounds. Into this alphabet the Greeks introduced many modifications, and the changes made by the Romans were also considerable. Its use in English presents many variations from its

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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 ages. The twenty-six letters of our alphabet have been thus classified with regard to their history: (1) B, D, H, K, L, M, N, P, Q, R, S, T, letters from the Phoenicians; (2) A, E, I, O, Z, originally Phoenician, but changed by the Greeks; (3) U (same as V), X, invented by the Greeks; (4) C, F, Phoenician letters with changed value; (5) G, of Latin invention; (6) Y, introduced into Latin from the Greek, with changed form; (7) J, V, graphic Latin forms raised to independent letters; (8) W, a recent addition, formed by doubling U (or V), whence its name.

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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, e (hard) and k, q and k, and ks. (2) Different sounds are expressed by the same letter; as c in cut and cell, g in get and gin, s in sit and as, ƒ 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.

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as in end

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hat ask

what, not " sit

love, luck

tion. This process must, of course, be not only long and tedious, but exceedingly dry and uninteresting to a child, since it affords no incentive to mental activity, no food for intelligence. By a careful selection and discrimination, however, in presenting the letters to the attention of the child, its intelligence may be addressed in teaching the alphabet by this method. The simple forms, such as I, O, X, S, will be remembered much more readily than the others; and these being learned, the remainder may be taught by showing the analogy or similarity of their forms 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.

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a

The letters which closely resemble each other in form, such as A and V, M and N, E and F, and C and G, among capitals, and b and d, e and e, p and q, and 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. By "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. schools a piece of apparatus, called the roading

From this table it will be seen that the letter a is used to represent seven different sounds; e, fire 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-C'book, 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

In some

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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, Early 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 alumnœ.

AMHERST COLLEGE, at Amherst, Mass., is one of the chief seats of learning in the United States. It was founded in 1821 by the Orthodox Congregationalists, especially for the education of young men for the ministry; but its charter was not obtained till 1825. Its first president was the Rev. Zephaniah S. Moore, who in 1823 was succeeded by the Rev. Heman Humphrey, to whose strenuous and prudent efforts the college owed much of its success. He continued in office till 1845, when he was succeeded 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

ANALYSIS

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, must consist of a verb with or without adjuncts. These constitute all the parts, and all the relations, involved in the construction of a sentence. A few words, such as interjections, may be used independently of them. Grammar has been defined as the "art of speaking and writing correctly," or as the "practical science which teaches the right use of language"; and for general purposes this account is, perhaps, sufficiently explicit. It does not, however, truly distinguish grammar from the other arts concerned in teaching 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

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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

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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

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