n- THE TEACHEli'S MANUAL. THE NORMAL: METHODS OF TEACHING THE COMMON BEANOHES,. ORTHOEPY, OKTnOGEAPHY, GEAMMAE, GEOGEAPHY, AEITHMETIO AND ELOCUTION: ur<3L0DiKa TfiS OUrLENES, TECHNICALITIES, EXPLANATIONS, ZJEMONSTRATfOMS, DEFINITIONS ^AND METHODS, OITeODUCTOEY AND rECUUAR TO EACH BRANCH. y By ALFRED HOLBROOK, FBOKKPAL OF NORMAL SCHOOL, LBBAKOIT, FOXTP.ra F.DITI-OK. NEW YORK : PUBLISHED BY A. S. BARNES & BURR, 51 i2^ Q .^ g S' |o c u ..- . ,■13 '5 p>i5 « a g 5 III § ^^ . -9 c3 .Sir tss: S a -^ aj ' . ' m < i ill »-5 O O " Grammar. (39) LANGUAGE. HISTORY. 1 ORIGIN OF SPOKEN LANGUAGE. Language was a divine gift. Spoken Lan. guage was used undoubtedly by our first parents. Adam gave names to all cattle, and to fowls of the air, and to every beast of tbe field, before there was ^ helpmeet for him ; so says the Bible. He is also represented as talking directly with that Being, from whom he derived the faculty of speech, and who trained him in its use. Let us. Teachers, remember who was the first of our profession; and not only so, but that no profession has been more highly honored, ^ 2 ORIGIN OF WRITTEN LANGUAGE. The first account we have of Written Language, is the writing of the decalogue on the tablets -of stone. It is remarked that all the Hebrew char- acters except one or two unimportant marks, which have since been added to the language, are found in the Ten Commandments. Before Written Language, Pictures, Monu-. ments, and Medals were used to commemorate events, and to some slight extent to commu- nicate ideas between those of the same age. These forms, however, represented things^ and not (40) LANGUAGE. 41 sounds used in words. Tlie Eomanic letters, which we use, are evidently derived from the Greek letters ; while the Grreek letters, according to their historians, were brought by Cadmus from Phenicia, B. C, 1493. The Phenician alphabet is similar, in some resi^ects. to the. Hebrew, as is also the Greek. Mr. Pitman, in forming his Phonographic Alphabet, seems to have imitated the Hebrew more nearly than any other, especially in his vowel system. Thus we have in the latest and most improved form of Written Language, a restoration of the original characters to some extent, as taught to Moses on Mount Sinai. 3 DIVERSITY OP LANGUAGES. Profane History assigns no reason for the mul- tiplicity of languages. Sacred History gives us an account of the " confusion of tongues," at the Tower of Babel, and the consequent dispersion of mankind. This may account for the existing number and variety of languages ; or, if, as many commentators suppose, the " confusion of tongues" refers to a disagreement of the builders in their plans, and the consequent irreconcilable quarrels^ which drove these early inhabitants into diverse parts of the earth, then the changes which take place in the pronunciation and signification of many words in a few years in modern society, even though language is fixed by written charac- ters, and the diversity of pronunciation in difier- ent localities in the same country, where there is 42 LANGUAGE. much and frequent intercourse, will sliow that when tribes have wandered far from each other, with no written language, with no intercourse, their language, though originally the same, will, in a few generations, become so changed as to become entirely unintelligible to others than the tribe or tribes in more immediate proximity. The great diversity of languages ceases to be a won- der, then, even though men were originally of one blood, used one language, and no miracle inter- posed to confound their language. 4 TIME OF HIGHEST DEVELOPMENT. Both Greece and Kome, at the time of their highest political power, enjoyed the greatest refine- ment in the arts and sciences. Language is no exception to the rule. Gradual improvement may be traced in the style of their authors from the earliest historical dawn of those nations to the period of their highest glory respectively. This improvement may be noticed in all the qualities which constitute excellence of language ; some of which are precision, euphony, flexibility, and sus- ceptibility of nice shades of difference in expres- sing thought or feeling. At the present time, the several spoken langua- ges have attained a higher degree of polish and power than at any previous period. Among these modern languages, the German is highly cultivated for the expression of thought, and the Italian for the exhibition of the emotions ; while the Eng- lish yields to no other in its strength, flexibility, LANGUAGE. 43 and delicacy of expression for both thought and feeling. 5 CHIEF DIFFERENCE BETWEEN ANCIENT AND MODERN LANGUAGES. This lies in the more highly mechanical struc- ture of their verbs and nouns ; the nouns of the ancient languages having more methods of de- clension, and each declension more terminations than any of the modern nouns. This variety of termination gives equal precision, with much greater latitude of arrangement. The cases ot modern nouns are determined to some extent by their position with relation to the verb. The cases of ancient nouns depend entirely on their termination, and not in the least on their position in the sentence. Hence the ancient languages give a Jletter opportunity for securing harmony in the arrangement than the modern. The verbs of the ancient languages are muoh more complete in their terminations, and of course make use of less auxiliary verbs. None are nec- essary save that denoting heing^ which is used only in the passive voice. 6 DEFINITIONS, EXPLANATIONS, AND REMARKS. 1. Language. Any method of communicating thought or feeling. 2. Natural Language. Instinctive methods of communicating thought or feeling. Remark. Brute animals possess their own instinctive forms of language; many of which forms are understood by other species than those which use them. 44 LANGUAGE. Artificial Language. That Tvhich must be learned before it can be used. Vocal Language. That produced by the organs of speech. 7 Written Language. Any method of commu- nicating thought by visible characters, depicted on a surface. Symbolic Language. That form of written language in -which the characters are designed to represent ideas and not sounds. Phonetic Language. That form of written language in which the characters are designed to represent sounds. Pictorial Language. That form of symbolic language in which the ideas are plainly repre- sented. Hieroglyphic Language. That form of symbolic language in which the ideas are so obscurely represented as to need an interpreter. Syllabic Language. That form of phonetic language in which the characters represent syl- lables. Alphabetic Language. That form of pho- netic language in which the characters represent separate articulate sounds. Equivocal Alphabetic Languages. Those in which a letter represents more than one sound, and in which a sound is represented by more than one letter. The Unequivocal Alphabetic Languages, are those in which the number of letters equals the number of separate articulate sounds — giving LANGUAGE. 45 but one sound to each letter, and but one letter for each sound. GrESTicuLATE LANGUAGE. Any method of communicating or impressing thought or feeling, by motions, postures, or appearances of the animal form, not producing or representing articulated sounds or written characters. 8 GrENERAL OR UNIVERSAL GRAMMAR. That form of grammar which treats of all those princi- ples and usages which are common to all lan- guages. Particular Grammar. That form of gram- mar which treats of all those principles, usages, characters, and sounds, comprised in any particular language. English Grammar. That branch which treats of the English language. 9 Orthoepy. That division of grammar which treats of articulate sounds, and of their correct use in pronunciation. Orthography. That division of grammar which treats of letters, words, and spelling. Etymology. That division of grammar which treats of the derivation and formation of words. Orthogeny. That division of grammar which treats of the classification of words according to their uses. Lexicography. That division of grammar which treats of the signification of words. Syntax. That division of grammar which treats of the arran2;ement of words in sentences. 46 LANGUAGE. Analysis. That division of grammar, which treats of the separation of sentences into their elements. Prosody. That division of grammar, which treats of versification and punctuation. General Remarh. The definitions of Cognate Branches in Phrenics, including Grammar, will be found in Part I, pages 16 and 17, Section 10. ORTHOEPY. Nature, Sound. \ Limit of Vibration, Rate of progress. '■I I Articulatory, Organs. ^ Vocal, Respiratory. Articulate sounds. | |®® f^^*'"^ jiation. -l [ Rules. \ Articulation, Divisions. \ C Common, Accent. \ giscriminatire. Pronunciation. ^ i ^mphatic, ' ' Poetic, 1st., 2nd. 1. Drill in articulate sounds. M.thods o£ Teaching. \ I g^lVw^SpZelSi;!'"""""' 4. Parse words Orthographically. ■^ ORTHOEPY. 10 DEFINITIONS, EXPLANATIONS, AND REMARKS. Orthoepy. That division of grammar, which treats of articulate sounds, and their correct use in pronunciation. Sound. A sensation produced on the auditory nerve by the rapid vibratory motion of air or other elastic substance. Remark 1. The vibration that produces the sound is often called sound, as, we say "sound travels," &c. Remark 2. Limit of Vibrations. The least number of vibrations in a second, that can yield a sound to human ear, is 32. The highest num- ber is 30,000 ; though other animals may perceive vibrations more or less rapid than these limits. Remark 3. Rate of Progress. Sound travels through air at the rate of seven hundred sixty- three miles per hour, or eleven hundred twenty feet per second ; through liquids and solids at a rate many times greater. 11 Organs of Speech. All those distinct parts of the human system, which are necessarily used in producing the sounds of language. (47) 3 48 ORTHOEPY. Articulatory Organs. Those organs of speech which are used in modifying or obstructing sound as produced by the other organs. They are labia, (lips,) dentes, (teeth,) palatum, (hard palate,) uvula, (soft palate,) nasal fossa3, (cavities of the nose,) larynx, with its cartilages and muscles. Vocal Organs. Chordae Vocales, (vocal chords.) These are two pair of membranes, extending back- wards and forwards, opposite to each other, through the larynx. They are attached by their two ends and one side, to the walls of the larynx, leaving an open space between them, through which air is drawn in and forced out by the respiratory organs Voice or Vocal Sound. That sound produced by the vocal chords. Eemarh. The vibration of these chords during the emission of vocal sound, may be perceived by placing the fingers on the larynx, externally, at the projection of Adam's apple. The vibration can be detected at no other time. Respiratory Organs. Those organs of speech used in forcing air through the other organs. They ara trachea, (windpipe,) bronchi, (bronchial tubes,) pulmo, (lungs,) diaphragm, and the inter- costal, dorsal, and abdominal muscles. Articulate Sound. That made by the organs of speech, and used in language. Voiced Sound, or Voice. A sound made by the vibration of the vocal chords. Vocal Sound, or Vocal. A voiced sound, ORTHOEPY. 4D modified but not obstructed by tlie articulatory organs. Simple Voc\l. A vocal, made without a change in the position of the articulatory organs during its emission. Compound Vocal. A vocal, made by a change in the position of the articulatory organs, from that required by one simple vocal to that required by another, during its emission. Remark. This change commences with the emission of the sound, and continues until the close ; hence the elements of the compounds arc *not heard in their purity. CoALESCENT. An articuIatc sound, that always precedes, and unites with, a vocal. 13 SuBvocAL Sound, or Subvocal. A voiced sound modified and obstructed by the articulatory organs. Aspirated Sound or Aspirate. An artic- ulate sound made without the vibration of the vocal chords. Pure Aspirate. An aspirate, modified but not obstructed by the articulatory organs. Obstructed Aspirate. An aspirate, modified and obstructed by the articulatory organs. 14 Labial. An articulate sound, modified or obstructed at the lips. Remark. The vocals and pure aspirates are modified only, while the subvocals and the other aspirates are obstructed also. Dental. An articulate sound modified or obstructed at the teeth or gums. \ 50 ORTHOEPY. Palatal. An articulate sound, modified or obstructed at the hard palate. Guttural. An articulate sound, modified or obstructed at the soft palate. * Remark 1st. Sounds are obstructed at the lips by the lips alone, or by the teeth and lips. Remark 2d. Sounds are obstructed at the teeth, gums, or hard palate, by the tip of the tongue ; ard at the soft palate, by the root of the tongue. 15 Abrupt, (also called Explodentand Mute.) An articulate sound, made by such a perfect contact of the organs as entirely, prevents the escape of air externally. Continuant, (also called Subvocal.) An artic- ulate sound, made by such partial contact of the organs, as to admit of escape of air externally. Liquid. A continuant, susceptible of simulta- neous combination with other obstructed sounds. The liquids are I and r. Nasal. A continuant, made by the escape of air through the cavities of the nose only. Cognate Sounds. Those sounds made by the articulatory organs, in the same positions, and dif- fering only in the vibrations of the vocal chords. 16 Pronunciation. The enunciation of the sound.s of a word with correct articulation and accent. Articulation, (joining.) The distinct enun- ciation of the sounds in words. Accent. The greater stress given to one sylla- ble of a word than to others; also, the greater force given to long syllables in poetry. ORTHOEPY. 51 Common Accent. That given in the ordinary pronunciation of a word, without reference to any other word. Discriminative Accent. That given to words of the same articulation to distinguish different parts of speech. ♦ EXAMPLES. 1. Nouns from Verbs. Ac'cent, accent'; con'cert, concert'; in'sult, insult', etc. 2. Adjectives from Verbs. Ab'sent absent'; com'- pound, compound'; fre'quent, frequent', etc. Emphatic Accent. That in which the stress is transferred from the ordinary syllable to another, for the purpose of giving antithetic emphasis more distinctly. Poetic Accent. That which is placed on long syllables of a poetic foot; even though those syl- lables should be monosyllabic words. 17 SIETHODS OF TEACHING PRONUNCIATION. DRILL IN articulate SOUNDS. Commence with vocals as given in Chart No. 1. 1. Repeat each long sound twice in order. 2. Direct the class to do the same in concert with yourself. 3. Direct the class to do the same without your aid. Continue this process until the large major- ity make the sounds correctly, and in the order of the chart. 4. Drill individuals failing, before the class, in groups, or singly, till each pupil masters all the difiQculties. p».3.3 K^.>s ► ►^ ° m ® S « o o a, o O -^ s„- , org •o § 3 cL o a s "S-? o oO o O (52) 4 -e ^ "« ^ ^ -1^^ fl fl ^ 03 mi BBB eS a: 2r 5 5 ? rf 2 -w -»- ** 1 . 2 O 13 ^g o aj a a -2 •^ bCO ^ so p- 0, bO cS •S-9 K -J- 3 « OTS -2 o 5Q 1-3 o o --i &: ^ S ^ & 5 ^ o te; ^ — ^ — ^.^ -S I ^ot gsl §^? « §^ -S^-* ^ -M ^ '^ 3 e :3 ^^^ ^f:.^ ^-H * a * TO 1 — o TO ( a* * TO S oT ^.^ TO-^ g-l Subvocils,! Liquids. < Sub vocals,! , Nasals. ( ego G0<1 ■i -1 1 1 6 ^ g 1 (54) -1 -a -s T ^ ORTHOEPY. 55 5. Pursue the same course witli the short vocals. 6. Alternate the cognate vocals on Chart No. 2, and in case a cognate is wanting, say " wanting." 7. Repeat and vary these drills until every scholar can go through the vocals long and short, and name the organ at which the sound is modi- fied. 9. Pursue a similar course with the obstructed sounds beginning with the aspirates and follow- ing with the subvocals on Chart No. 1 ] then with cognate sounds, on Chart No. 2. 18 DRILL IN THE NOTATION OF DICTIONARIES. Take Chart No. 3, and go over in concert, the names of sounds as given, with the sounds follow- ing, and the notation of any dictionary used in school. Thus : Long a — a, notation a. with a short horizontal mark over it. Short a — a, notation a, with a curved line over it. Broad a — e, notation a, with a circumflex over it. Italian a — q, notation a, with a diaeresis over it. Medial a — ^, wanting in Webster's dictionary. This will be sufficient to show the drill on the notations- It need be followed no further in this form. 2. Require the scholars to look out words in their dictionary, and describe the marks to signify the irregular sounds of the consonants, as city, cane, off, of, church, chaise, etc. 3* 56 ORTHOEPY 19 SPELLING WORDS PHONETICALLY. 1. This should be practiced more or less in con- nection with every exercise, in concert, the Teach- er accompanying; next, the class in concert without his aid, lastly, individual scholars, always giving opportunity for the members of the class to criti- cise the spelling of the individuals, — they jfirst raising their hands for permission to do so. 2. Let the Teacher select such phonotypic char- acters in order, from Chart No. 1 or No. 2, as shall form words. The class will pronounce each sound, as its representative is touched with the pointer, until the elements of a word are thus separately pronunced, then, a signal given, they are expected to pronounce the word together. This exercise should begin with monosyllables, and from these proceed to the most complicated and difficult words. 20 CRITICISM ON PRONUNCIATION. In recitation of all studies, opportunity should be given the classes for mutual criticism on pronun- (/iation, as well as in other particulars. This matter of criticism is managed thus . The teacher asks, " Are there any errors in pro- nunciation?" Pupils who have noticed errors, raise their hands. The teacher calls upon such a scholar as is least in the habit of criticism, to mention the error. ORTHOEPY. 57 The scholar doeg it in this form : "Mr. A. B. pronounced * heard' * heerd.' He should have given the close sound of e rather than the long." The scholar continues, "he pronounced 'demon- strate' ' demonstrate,' accenting the first syllable instead of the second." In case of doubt in the mind of any one, either pupil or teacher, a scholar is requested to examine the authorities, Worcester's or Webster's diction- ary, which should always be on the teacher's table, and in the pupil's desk. >, 1 ■ 2 © fi ea 5 ^ s i CI. c5 C5 (O tc o "" "H "H ^ 3 3 C_i a o © ^1 § o .ii .2 C5 O © D "g "P O O © QJ © o © { .S e« BJ oJ o •i O c m 1>^ 6 fcO .2§ o 3 o 8. •3§ o -CI P. P •r? "rr o o ►> © (ua> isle it own on move wolf 1.- . ■ Ph f2 ■r '''' f"" - V f§ i ' h o o fe 'S3 335 -03 -.03 c« 'H,0 50<0<;3 a jji rt o '^ . c 'Ph o -g '"^-^cJ ♦ :c3 * eflt'OO* irH.p^ O O :0 O 5 I s ■ in ^ ^ yj<^ '^ \^ ^/^ (. \ © © >» « '^ c 'rt _: "o tJ 3 S ^^"S ^'^•2;5'^ ^ctf S boti bo-S bc-S b«t2° C O C O C o cot:! O j3 O ^ O J tJ 02 .-5 02 J 02 o ^ 2 H^02 S *— , -» V ^ ^■^v-*-- ^ J srf-V^^ KJ ^ ■» bb >4 Q-S :2 -S-^ .— ~ a a; ^ s bc>o •s:juBuosuoo •siuoq^qdy > (59) ORTHOGRAPHY. Italic. ' Typical. • Roman. (DlJ) €ngli3[). ©erman ®cvt. .ORNAMENTAL Forms. • Classes. I'^^J^,^ Capital, . /^"^^^^ GramcQatical. < Rules. | Small. ' Italic, : Rhetorical. • SMALL CAP. LARGE CAP. ■S . 3 Bold Faced. r DIaaiand. Agate, Pearl. Nonpareil, Minion, Brevier, Bourgeois, Sizea. • Long Primer, Small Pica, Pica, English, Great Primen Arrangement in Classes, ( See Chart Genera, Species, etc. I No. 3. .««p--^^^^--il^^K^r"^'*"^^ (60) OETHOGRAPHY.— Continued OETHOGRAPHY.— ContimiBd. (62) •gaisiiTfj otqclTjagoq^JQ JOJ tnjoj OETHOGRAPHY. 21 Orthography. That division of grammar which treats of letters, syllables, words, and spel- ling. Letter. A visible character, representing by itself, or with one or more besides, an articulate sound; also used to determine signification. Typical Forms. These are given in the names that distinguish them in the classification. There are many ornamental forms in use, not given. Grammatical Forms. These are used for em- emphasis or other rhetorical distinction. Power of a Letter. The sound which a letter represents in a word; also the influence which one letter exerts upon the representative character of another. 22 Yowel. a letter used to represent a vocal sound ; the basis of a syllable. Consonant. A letter used to represent a sub- vocal or aspirate sound, modifying the basis of a syllable. Remarh. Phonographers write many syllables without a vowel as a basis, contending that a sub- vocal is often the basis of a syllable, e.g. apple, often. They claim that there is no vocal heard in (63) 64 ORTHOGRAPHY. the second syllable, and that they should be writ- ten apl, oftn, or ofn. It seems to me, however, more in accordance with the principles of our orthography to consider a vocal, accented or unac- cented, plain or obscure, as the basis of every syl- lable. Aphthoxg, or Silext Letter. A letter which represents no sound, but is used either to modify the representative character of another, or merely to determine signification. Remark. An aphthong may be a vowel or a consonant aphthong, according to the more com- mon use of the letter. Explanation. U, in the word lade, chancres the sound of a from short to long ; also ^, in sign, changes the sound of i short to long; also lo in write, determines the signification of the word, and distinguishes it from that of rite ; also, b in dumb, determines signification, since dum has no signification. 23 Diphthong. One or two vowels, representing a combination of two vocal sounds. Explanation. The diphthong i represents a combination of Italian a and long e. The diphthong long u represents a combination of long e and close o. The diphthong oi represents a combination of broad a and short i. The diphthong ou represents a combination of Italian a and close a. These are all the proper diphthongs in the Encrlish Lan!>;ua2;e. ORTHOGEAPHY. 65 A Vowel Digrafh, or improper diphtliong, is a combination of two vowels, in wliieli only one receives a sound, the other being a modifier. A Conjoined Yowel Digraph is one in which the two vowels are not separated by a consonant. A Disjoined Vowel Digraph is one in which the two vowels are separated by one or more eon- sonants. A Consonant Digraph is a combination of two consonants, one or both of which are required to represent a sound. Remark. A consonant not required to repre- sent a sound of the word, is an aphthong, whether modifying the representative character of a letter or not. Thus, in the consonant digraph pi, in the word condign, the g modifies the sound of ^, but is not necessary for the representation of the final sound, and hence is an aphthong. A Combined Digraph is a combination of a consonant and a vowel to represent a subvocal or an aspirate sound. Explanation. The consonant t, and the vowel i are used in the terminal syllable iion, to represent the aspirate sound yf sh or cli. CV, ce, and si, are used in a similar manner. Vowel Trigraph. A combination of three vowels, representing one or two sounds. Remark. Eau in heau, represents one sound; in heauty, it represents two combined. Disjoint:d Trigraph. One in which a conso- nant occurs between two of the vowols. 66 ORTHOGRAPHY. 25 Syllable. One or more sounds uttered at one impulse of the breath ; also, the letters represent- ing any sound or sounds so uttered. Ultimate Syllable. The last syllable in a word. Penultimate Syllable, or Penult. The last syllable but one in a word. Antepenultimate Syllable. The last sylla- ble but two in a word. Pre antepenultimate Syllable. The last syl- syllable but three in a word. Remarh. The syllables of a word are also described in their numerical order, commencing at the left, as first, second, third, &c. Base op a Syllable. The vocal or vowel used in its formation. Modifier. Any sound preceding oi succeed- ing the base of a syllable, or letter or digraph representing such sound. Antecedent. Any -sound preceding the base of a syllable; or letter or digraph representing \ such sound. j Consequent. Any sound succeeding the base ! of a syllable; or letter or digraph representing such sound. Remarh. A letter representing a sound, pre- j ceding another, is parsed as an antecedent, though the order of the letter should differ from that of the sounds represented by them. ORTHOGRAPHY. 67 26 "Word. The received sign of an idea, expressed in one or more articulate sounds, or in visible characters representing such sounds. Simple Word. One which cannot be divided into separate words without radically altering the signification, CoMPouxD "Word. One which can be divi- ded into separate words without radically alter- ing their signification. Primitive Word. One which cannot be re- duced to a simpler form, without radically altering its signification. Derivative Word. One which can be re- duced to a simpler form, without radically altering its signification. Remark. A compound word is considered primitive, if all its parts are primitive, otherwise a derivative. A derivative is considered simple, unless it plainly comes under the definition of a compound. The Base of a Compound Word is that word representing the fundamental idea. The Modifier ix a Compound Word is that word which describes the other. The Base of a Derivative Word is the prim- itive word from which it is derived. The Modifiers in a Derivative Word are the prefixes or suffixes, or both. Prefix. One or more syllables, not used as a word of similar meaning in the English language, but placed before words to modify their significa- tion. 68 OUTHOGRAPHY. Suffix. One or more syllables, not used as a word of similar n.eaning in the English language, but placed after ^orch to modify their significa- tion. m Mo'i^osYLL/.mM A word oi one syllable. Dissyllable. A word of two syllables. Trisyllable. A word of three syllables. Accented Syllable. One that is pronounced with more fores than others in the same word. Remark 1. Accent may be primary when it is greu.w ''■^iin that received by some other syllable in the sati.w ^ordj or secondary, when it is less than that receive x by some other syllable in the same word. Remark 2. In prosody, an accented syllable is long in quantity, an unaccented syllable, short in quantity, i. e. of time taken to pronounce it. 28 Spelling. A distinct expression of the letters or sounds of a word, in their proper order. Orthographic Spelling. The expression of the letters, of which a written word is composed, and in their proper order, according to the received f uthority. Phonetic Spelling. The separate expression of the elementary sounds of which a word is com- posed, and in their proper order, according to es- tablished usage. GENERAL RULES FOR SPELLING. Rule 1. Write no word unless sure of ita orthography and signification. ORTHOGRAPHY. 69 Rule 2. Consult the dictionary in case of .loubt. Rule 3. Apply the rules for derivatives. Remark. The special rules for spelling are to be found in every good grammar, and spelling- book, and need special attention. All grades, except primary, should be thoroughly drilled in their use. It is not enough to memorize them. More than one-half the bad spelling found in school exercises, as well as in business operations, may be justly charged to ignorance .of these special rules. TEACHLNG THE ALPHABET. 29 teacher's preparation. The preparation necessary for the successful teaching of Phonotypy, the all-important prepara- tion, I might say, is a thorough practical knowl- edge of the articulate sounds of our language: an ability to enunciate them distinctly, either sep- arately or in combinations, and to give such direc- tions to others as will, when followed, enable them to do the same. 30 PREPARATION OP PUPILS. The only preparation necessary for the pupils, is, that they should be of a proper school age, that the school should be properly organized, and that the teacher should so gain the confidence of his young pupils by a pleasant conversation, or other means, as to lead them to speak and act with the freedom of children in a well-regulated home. I very much prefer that they should know nothing of any alphabet. 31 TEACHING THE ARTICULATE SOUNDS. The first eifort in imparting instruction should be to give them some knowledge of articulate sounds. In doing this, avoid the use of techni- calities. Select a few such words as saw, say, so, (70) TEACHING THE ALPHABET. 71 see, and taking one of them, as saiv, call upon the pupils to speak it carefully a few times. The teacher should now resolve it into its elements; enunciating them at first, with a long pause, as, s o, then with less and less pause, as, s e, s 0, s e, s - - 0, s - 0, leading them, if possible, to perceive that those sounds, if enunciated by one impulse of the voice, would constitute the word saio, without his thus uttering them. But if this can not be done, the teacher may pronounce the word; after which, he should separate it into its elements, and proceed as before. Now he should take the elements of another word, as, sa?/, without calling their attention to the word by pronouncing it, and enunciate their elements, as in the other case; asking after each enunciation, what the word would be if the sounds were spoken together. Generally, if this is skil- fully managed, there will be a correct response ; after which the sounds should be uttered more and more rapidly, to show them clearly that they were right. Now, take another word, as, see, using special care that they shall perceive from the separate elements, what word they constitute. 32 TEACHING TO READ. If we have succeeded thus far in cultivating our pupils' powers of observing sound, there will be little trouble in teaching them the letters that represent those sounds. 72 TEACHING THE ALPHABET. - Calling their attention to the first sound in " see, " let us print ujDon the blackboard the letter "s" as the representative, the ^^ picture''^ of that sound. We should now cultivate their powers of observation, by calling upon them to find a simi- lar letter on the charts ; of which there should be at least two suspended before the class: also, among the tablets. ( These are pieces of card-hoard with a letter upon each.") As each child finds the letter on a chart or on a tablet, he should enun- ciate the sound represented. The name of the letter should not be taught them. If any of them, already knowing the name, should call the letter " Es, " say " Yes, that is its name, but what sound does it represent? What sound are you to make when you see it ? 33 * LESSON SECOND. Review the first lesson, calling their attention, as before, to the analysis of "saw?, sai/, so, see, " and to "s" as the representative of the initial sound of those words. Now teach them "8 " as the rep- resentative of the final sound in " see. " 34: COMBINING LETTERS TO REPRESENT WORDS. The pupils have already discovered that sounds combined form spoken words ; ayd they now know the representatives- of two sounds. The combining of these representatives may now be taught them. Print those letters on the black- board thus : TEACHINQ THE ALPHABET. 73 S------8 8 - - - - 8 S - - 8 S8 Now call upon them to enunciate those sounds, as jou point to the letters. Pass the index slowly from one letter to the other in the upper line, and more rapidly as you descend, until they blend the two sounds, and pronounce the word "see. " Printed cards, with the lessons on them, should also be used, but they should not supersede the use of the black-board. 35 SUBSEQUENT LESSONS. Proceed in a similar manner to teach them the letters a, 9, m, and w; and they will read several words and a few sentences. They should now be taught to spell by sound all the words they can read ; after which they may learn other letters, always using each new letter in combination with familiar ones. The Phonetic Primer should be given to the children at this stage, and they should be permit ted to read from it in connection with the black- board and charts. Some teachers succeed finely with the black-board and Primer, without charts or tablets. 36 WORDS OF THREE LETTERS. When they are to be taught words of three let- 74: TEACHING THE ALPHABET. ters, familiar words of two letters, followed by a third letter also familiar, may be presented on the black-board thus : h5 - -• - s h^ - s The class should pronounce the word h^, and then enunciate the sound represented by S, as the teacher points from the one to the other, moving his index more and more rapidly, until uncon- sciously they find themselves pronouncing the word h3S. Other words, as mst, matj tam^ should be taught by similar means. Now take the tablets, and show them a similar word, as mc, and after they have pronounced it, drop the hand that holds the word, and with the other hand present a tablet having the letter t on it. The class will enunciate it ; when the other hand should be raised and the tablets held so as to form the word met. Then, with the right hand, present the m only, and after the enunciation of the sound, remove that hand, and present the word 8t with the other. After they pronounce the word st, prefix the m to it, and they will pronounce the word mst. If they fail to pronounce the word at the first trial, make another efibrt. By no means pronounce the word for them. Manage skilfully, and the pro- nunciation of the word will come from the class. TEACHING THE ALPHABET. 75 37 Now take other words of three letters, and pro- ceed with them in the same manner: choosing such as will leave words, after removing either the inital, or the final letter, as mat; which, by remov- ing the initial letter, leaves at, or the final leaves ma. After this, when a pupil, in reading, comes to a word of three letters, which he cannot pronounce, instead of pronouncing it for him, hide the initial or final letter from his view, and after the remain- der of the word has been pronounced, permit him to see the whole word, and, usually, he will pro- nounce it. Longer words may be taught thent in a similar manner. After all the Phonetic letters are learned, the children should continue reading Phonotypy until they can read well in the Second Phonetic Keader ; after which they may make the transition to Ko- raanic reading. r TRANSITION TO ROMANIC READING 38 I must caution the young teacher against per- mitting his pupil to make the. transition too soon. Children sometimes make the transition success- fully, after having barely read the Phonetic Prim- er, but sometimes they find it very difficult. But by waiting, as I have suggested, nothing is neces- sary but to permit them to read in the Second Reader of any series, and it will be found that they will need much less instruction than children reading in the same book that were taught in the common way, and they need no special instruction. They may be taught as others are. 39 SPELLING. Without the direct aid of the teacher, they will now have learned the names of the Roman letters, and they may be taught the common orthography as other children are ; and it will be found that they will by far excel children taught ii the com- mon way, not only in articulation^ but in spelling also. 40 EMPLOYMENT FOR THE CHILDREN. "What has been written refers only to class in- (,76) SPELLING. 77 btruction. For employment between recitations, the children should be permitted and encouraged^ not required and compelled^ to print on slates all the exercises they read, copying them from the exer- cises placed on the black-board by the teacher, oi from cards suspended before them, or from theii Primers. 41 TEACHING ORTHOGRAPHY TO PRIMARY CLASSES, Many teachers use no other Spelling Book than the Reading Books ; thus teaching their pupils to spell the words they are daily using in their les- sons. In this way they have, or should have, a correct idea of the meaning of the words of their spelling lessons, though they may not, at this early age, be able to define them. 42 STUDYING SPELLING LESSONS. While making, and after having made, the tran- sition from the Phonetic print, children should be required to study spelling lessons. The best way to do this is to p)rint them on th^ir slates, until they learn the script form of letters ; when they should use that form, or write their lessons. The practice of requiring pupils to study their lessons a given number of times, only teaches them to hurry over their study ^ and not to study to any purpose. It is not the numher of times a lesson has been studied that should be considered the mark of success, but the ability to spell every word in the lesson. , i 78 PRIMARY TEACHING. 43 MANNER or CONDUCTING RECITATIONS IN SPELLING. We cannot vary the mode of conducting spelling recitations as much as with the more advanced classes. One very good method, and perhaps the best one, is to require them to read the lesson from their slates ; each one pronouncing a word, and then spelling it and again pronouncing it. Every pupil should give notice of any mistake observed, by raising the hand. In this way, the teacher can ascertain whether they have studied their lessons aright. The side of the slates, con- taining the lesson, should be held up to the teacher for criticisms: and the criticisms should embrace, not only the size and appearance of the letters, but the proper arrangement of the words in col- umns. The slate should now be laid down on the reci- tation seat or on the floor, with the side containing the lessons from the pupils, and the words pro- nounced for them once, and only once; and a pu- pil should be permitted to try to spell the word once, diiidi only once. If he cannot spell it on the first trial, he has not learned his lesson ; and he is now on the floor to be examined in reference to that matter, and not to learn his lesson. It is a good plan, frequently, to call upon some pupil in the class to pronounce the words for the class, under the eye and ear of the teacher. If a word is misspelled, it should be made a part of the next lesson. SPELLING 79 44 SECURING THE ATTENTION. Pronouncing a word but once, will go far to- wards securing the attention of every pupil; but in addition to this, when a word is misspelled, an- other pupil should be called upon to spell it with- out being spoken to. A movement of the eye, or hand, or some other sign, is all the notice that is necessary, if the pupils are giving their attention j and a failure on the part of the pupil to receive this notice, should be considered as much a failure as the misspelling of a word. 45 KEEPING UP AN INTEREST. A variety of methods may be resorted to, though not as great a variety as with»older pupils. The class may commence all standing, as each one spells he may sit down, until all are- seated. The class may then rise in order as they spell, un- til all are up. The practice of having a head and foot to a class is often resorted to, and with good effect, if properly managed. If this practice is found to discourage any in the class, it should be abandoned. A better method is for the teacher to call on the scholars at the close of the recitation for the num- ber each one has missed, which should be recorded, and have a bearing on the grade of the tickets given them to take home weekly. The respelling of misspelled words by those who misspelled them, and then by the class in concert, is another method. 4* ■ . "1 80 PRIMARY TEACHING. 46 SPELLING WITH OTHER RECITATIONS, In reading exercises, if a word is mispronounced, attention should be called to its orthography. In their exercises in Mental Arithmetic, words that they use, and other words, should occasionally be ipelled by the pupils, and so in other studies. TEACHING SPELLING TO SECONDARY CLASSES. 47 Remarks. — I make use of no spelling book, but assign a definite part of a reading lesson as a spel- ling lesson. The advantage of this is, that schol- ars learn the forms of words in connection with their use in sentences, and associate their forms rather with their signification than with their pla- ces on the page of the spelling book. What teacher has not seen instances, in which a scholar could spell every word in the Spelling book, perhaps, without any one to "put out the words; " while, if called upon to write an essay, or a letter, that same scholar would misspell the most common words ? Such words, as, there their, are air, two too to, plain j)lane, are almost cer- tainly misspelled in writing by spelling book spel- lers. 48 ORAL METHOD. Let the class stand in a line, in order of their numbers as determined at the close of the last spelling exercise ; save that No. 1 takes his place at the foot of the class. Pronounce a word for No. 2, who now stands at the head. He spells it. All in the class who (81) 82 SECONDARY TEACHING. think lie spelled it wrong, will raise the hand. If the word was spelled right, those who raised their hands go below those who did not: all the schol- ars of each kind keeping their relative places with those of the same kind ; but all the scholars who were mistaken will take their places below all who were right in their opinion of the spelling as given by scholar No. 2. If the scholar misspelled the word, then the first scholar in order who raised his hand is called upon to spell the word, then the next, and so on till all who thought the word mispelled are tested. Those who are thus tested and fail, then take their places below with those who indicated that they thought the word spelled correctly, by not raising their hands. This method never fails to secure the attention of all in the class, and involves no confusion or disorder, if the teacher follow the direction of keeping every scholar of each kind in his place relatively with others of his own kind. The two kinds being : first, those who spell correctly or in- dicate correctly by raising their hands or not r.ais- ing them ; and second, those who spell incorrectly or indicate incorrectly, it being understood that all who show that they were mistaken take their places below all who show that they were right. Successive scholars are called upon to spell words, and the same indications taken and the same course pursued, till the time allotted fcr the exercise is exhausted. SPELLING. 83 At the close of the exercise, the teacher calls upon each member of the class, as he has him en- rolled in his class book, for the number of times he was mistaken in his opinion of the spelling, and he is graded accordingly. The class is then dismissed in order, No. 1 spea(i:ing his number and going to his seat; No. 2 following in the same manner. So of all the rest. Short sentences, or phrases, containing as many words as the class can well recollect, may be pro- nounced at once, instead of single words. This method has the advantage of more distinctly im- pressing the meaning of words in connection with their spelling TEACHING SPELLING TO SECONDARY CLASSES BY USE OF SLATES. Words or sentences, which have been studied, are dictated to a class of scholars sitting on a rec- itation seat or at their desks, till perhaps they have written twenty words, each, on their slates. Slates are then exchanged. Some scholar is then called upon to give orally the spelling of the first word written on the slates. Teacher says, " How many agree?" All who think his spelling right, raise the hand. Teacher says, " How many disa- gree?" All such raise the hand. Teacher notes those who are wrong. Teacher then says, "How many slates are wrong?" All who have slates with the word incorrectly spelled, raise their slates to a vertical position on their knees, or on their 84 SECONDARY TEACHING. desks. Tbey are tlien called on in order, to give the correct spelling ; or, to save time, tlie teacher says, after one has given an incorrect spelling, " How many slates have that spelling ? " He thus continues with the word till he gets all the false spellings and determines also the bad spellers. The next word is then taken up and treated in a similar manner. It takes much time to describe this method, but it is really the most expeditious and thorough method of getting at the knowledge of a class, and makes a more durable impression, perhaps, of the correct spelling and of the evil of bad spelling than any other method that has ever been devised for secondary scholars. 50 ANOTHER METHOD WITH SLATES. Let the teacher write one or more sentences, which the scholars have studied, on the black- board, with many of the words misspelled, involv- ing such errors as the class would be most likely to fall into. The scholars sitting at their desks are required to copy the matter on the black-board, and to cor- rect the errors in spelling and capitals. The teacher afterwards examines their slates or papers, and grades them according to the accuracy, or Want of it. OETHOGRAPHY TO ADVANCED CLASSES. 51 1. Criticism op Reports Written on the Black-board. — The criticism of spelling comes next in order after tho criticism of pronunciation. It is done by the class in the usual way by raising the hand at the instance of the teacher. Illustration. — A scholar in an advanced class in Grrammar has had the subject of the noun assigned to him, on which to give a report before the class. Having had a day for preparation, he writes out the classification of his subject on the black-board from memory^ without referring to notes or book. He then gives, in the order of his classification, all necessary explanations, definitions, and illus- trations of the subject, orally. When the pupil has gone through with his report, the teacher calls on the class for criticisms ; first, in pronunciation; second, in spelling ; and so proceeds with the other items till the subject is thoroughly sifted. 52 2. Criticism of Compositions. — The teacher notes words misspelled in compositions, by draw- ing a lead mark under them. The scholar is re- quired to go to his dictionary and obtain the correct spelling of these words, and to make arec- (85) 86 TEACHING HIGHEK CLASSES. ord of them in the two forms in a blank book, which he keeps for this purpose, called The Spel- ing Book. Every advanced scholar, who is not an accurate speller, should have such a book. These spelling books are arranged with two columns on each page, one headed with the name of the pupil, the other with the name of the au- tlior of the Dictionary which he consults. In the . column under hi& own name, he writes his bad spelling. In the other column, be writes the cor- rect spelling according to his authority. Scarcely will a scholar fall into a second blunder with regard to the spelling of a word, after having made such a record of his error. Teachers must, of course, have a i^gular and definite time for examining these spelling books, or they will soon ftill into neglect. Without them, the criticisms on bad spelling in compos-itions, will not amount to muclu ADVANCED METHODS OF TEACHING. 53 TEACHING ORTHOGRAPHY BY CHARTS. The methods of using the charts are explained in articles 21 to 28. These charts can be copied in an enlarged form by the teacher, or by scholars, on to one or more large sheets of printing paper, with a crayon. Charts of orthography are sold frequently for two dollars. Such a chart would cost the teacher not over a half dime, including paper and crayon, and will serve as good a purpose as the most expensive. If scholars are permitted to make such charts, they have the advantage of learning them by the process, and of cultivating their taste in drawing and writing. 54 TEACHING ORTHOGRAPHY BY DERIVATIVES. It is an excellent practice to give spelling les- sons in the derivatives. Let the teacher propose two or three roots for a lesson : as, press, act, etc. The scholars, at the recitation, are required to write as many derivatives as they have been able to obtain ; either on their slates, or on the black- board. They should, of course, be provided with dictionaries in the preparation of such a lesson. They can also make use of tables of prefisies and (87) :-] 68 ADVANCED TEACHING. suffixes. They will also bring into use the spec- ial RULES for spelling derivatives. The definitions of the derivatives should be re- quired as a part of the exercise. Many teachers make use of Mc Elligott's or Town's analysis. The exercise can be made very profitable without them, with the use of a dictionary and the tables of prefixes and suffixes defined. These tables can be copied from Mc Elligott on to large sheets of paper and into the "spelling books" of the pupils, as described in article 52. 55 Examples in formation of derivatives, with the rules for spelling, according to Goold Brown. WITH SUFFIXES. Act. a primitive word, signifying to do or to make. Actor. The person who acts. Actress. The female who acts. Action. The result or process of acting. Acts. Does act. Actest. Dost act. AcTETH. Does act. Acted. Did act. Acting. Continuing to act. Actionable. Admitting of an action. Actionably. By admitting an action. AcTioNARY. I A person who has a share in an Actionist. j action. Active. Inclined to act. c,- SPEJ.LING, 89 Activity. | Rule VI. | r The state or qual- AcTivENEss. j Eule YII. j ( ity of being active. Actively. Rule VII. In an active manner. Actual. Real in acting or being. . * j- The state of beino' actual. Actualness. j Actually. In an actual manner. Actuate. To cause to act. WITH PREFIXES AND SUFFIXES. CoACT. To act together with force. CoACTioN. The process of coacting. CoACTivE. Inclining to coact. Counteract. To act against. Counteraction. The process of acting against. Enact. To act in making a law. Enactment. The process or result of enacting. Inactive. Without action. Inaction. An inactive" state. Inactively. Rule VII. In an inactive man- ner. Inactivity. Rule VI. An inactive state. Exact.— Verb. To act in forcing out of. Exacting. Continuing to exact. Exaction. The process or result of exacting. Exactor. The person who exacts. Exact. — Adjective. Acting from rule. Accurate. Exactly. In an exact manner. Exactness. ) m, , , « r • ^ y ihe state ot beinsj exact. Exactitude. ) React. To act again. To act back. Reacting. Continuing to react. Reaction. The process of reacting. 8 90 ADVANCED TEACHING. Reactiye. Inclining to react. Reactively. Rule VII. In a reactive manner. SuBACTioN. The process of acting to place under. 56 Pel. An inseparable radical word, signifying to drive or force. From FtllOj Pulsus. With the only suffix — Pulsion. The act of driving. With preJ&xes and suffixes — Compel. Compelled, Rule III. Compelling, Rule III. Compulsion. Compulsive. Compul- sively, Rule VII. CoMPULs-ivENEss, Rule VII. Compulsory, etc. 57 From the root Press, nearly two hundred deriv- atives can be obtained. From the inseparable root Gress, a long list can be formed. These two examples, Act and Pel, will be suffi- cient to illustrate the method of spelling by the use of prefixes and suffixes in forming derivatives from separable and inseparable primitives. 58 DRILLING ON THE SPECIAL RULES FOR SPELLING. The class should be required to memorize these as they are given in the grammar used, with the exceptions and remarks. They should so memor- ize them, that they can give them as they are called for by the teacher promiscuously. They should then be required to write, or spell orally, words as SPELLING. 91 tliey are dictated, or pronounced from the exam- ples contained in the grammar, under each rule, in order, until- every scholar shows that he is able to apply the rules correctly. Sentences may then be dictated for writing, con- taining derivative words coming under the rules promiscuously. Sentences may be written on the board by the teacher in which these rules are violated. The scholars are expected to rewrite the sentences on slates or paper, with references by number to the rules which were violated. This course should be pursued day after day, for weeks, until the scholars have formed the habit of noticing the application of these rules in spel- ling. We find that the larger part of misspelling in the compositions of advanced scholars, is in viola- tion of these rules, until they have been thor- oughly drilled in them. ORTHOGRAPHIC PARSING. EXERCISES IN ORTHOGRAPHIC PARSING. The following lists of words are selected with the design cf bringing in as large a variety of combinations both of syllables and letters as possible. It is presumed that the teacher, by care- fully examining the methods by which these words and the letters and sounds of which they are composed, are disposed of, under the FouM OF Orthographic Parsing, given on page 62, will be able to parse any words, letters or sounds in the language. List of words analyzed : — Pin, Called, Through, Ewe, Manlike, Inkstand, Condition. List of words whose letters and sounds are analyzed : — Sound, Chaise, Xenophon, Rough, Lough, Phthisic, Motion, FiliaL List of words parsed orthographical ly in full : — Impossibility. In commencing to teach Orthographic Parsing, it is well to divide the subject, and, at first, drill the class on words, includ- ing spelling, afterward upon letters and sounds, and finally com- bine the two. DRILL ON WORDS INCLUDING SPELLING. P«M is a simple, primitive, monosyllable, spelled orthographi- cally (naming the letters) p, i, n, and phonetically (enunciating the sounds) p, i, n. Called is a simple, derivative monosyllable, except in poetry, where it is sometimes a dissyllable, accented orT the first. As a derivative, its base is call, modified by the simple suffix, ed, sig- nifying did. The signification of called is, did name, summons, invite, &c. Spelled orthographically, c, a, ll,e, d, phonetically, k, e, 1, d. ThroygJi is a simple, primitive monosyllable. Spelled, ortho- graphically, t, h, r, 0, n, g, h ; phonetically, t,r, co. Ewe is a simple, primitive monosyllable. Spelled, orthograph- ically, e, w, e, phonetically, y,i|. Manlike is a compound, primitive dissyllable, accented (slight- ly) on the first. Spelled, orthographically, m, a, n,l, i, k, e, pho- netically, m,a, n,l, j, k. The base of the word is man ; which is modified by the word like, signifying resembling in manner, or appearance. The signification of the word is, resembling a man. _ Inkstand is a compound, primitive dissyllable, accented on the first. Spelled, orthographically, i, n, k, s,- 1, a, n,d, phonetically, i,g,k, s,t, a, n, d. The base of the word is stand, modified by (92) ORTHOGRAPHIC PARSING. 93 the word ink, signifying (here,) a fluid for •writing. Tho word signifies a vessel for holding the fluid. Condition is a simple, primitive trisyllable, accented on the second ; spelled, orthographically, 0,0, n,d, i, t, i,o,n, phonetically, k, 0, n, d, i, J, 0, n. DRILL ON LETTERS AND SOUNDS. Sound. S is a consonant, antecedent to the base of the sylla- ble, ou, and represents its own proper sound, s ; {enunciate the sound,) which is an aspirate, obstructed at the gums by a partial contact of the organs: producing a dental and a continuant. Ou, the base of the syllable, is a diphthong, representing its own proper sound, •» ; {enunciate,) which is an open, compound vocal, modified (in the commencement of the sound,) at the soft palate, and at the conclusion at the lips. N is a consonant, and the immediate consequent of the base of tho syllable, representing its own proper sound, n; {enunciate,) which is a subvocal, obstructed at the hard palate by a contact made perfect there, but with an opening of the nasal cavities, through which there is an escape of air externally, and, hence, obstructed by a partial contact of the organs ; producing a pala- tal, a continuant, and a nasal. D is a consonant, and the remote consequent of the base of the syllable, representing its own proper sound, d; {enunciate,) which is a subvocal, obstructed at the teeth or gums, (at the teeth by some, and at the gums by others,) by ti perfect contact of the organs, producing an abrupt, and a dental. Chaise. Ch is a consonant digraph, the antecedent of the base of the syllable, ai, final e, and represents the sound of sh, J; {enunciate,) which is an aspirate, obstructed at the hard palate, by a partial contact of the organs ; producing a palatal and a continuant. Ai — e, the base of the syllable, is a disjoined trigraph, repre- senting the long sound of a, a; {enunciate,) which is a long, simple vocal, modified at the hard palate. S is a consonant, having its position between the parts of the disjoined trigraph, which forms the base of the syllable, and rep- resents the sound of z, z; {enunciate,) which is a subvocal, ob- structed at the gums by a partial contact of the organs ; produc- ing a dental and a continuant. Xenophon. X is a consonant, antecedent to the base of the first syllable, e. and represents the sound of z, z ; {enunciate,) which is a subvocal, obstructed at the gams, by a partial contact of the organs ; producing a dental and a continuant. E, the base of the first syllable, is a vowel, representing the short sound of e, e ; {enunciate,) which is a short, simple vocal, modified at the hard palate. N is a consonant, the consequent of the base of the first sylla- ble, and represents its own proper sound, n; {enunciate,) which is a subvocal, obstructed at the hard palate by a partial contact of the organs; producing a palatal, a continuant, and a nasal. 0, the base of the second syllable, is a vowel, representing its 94 ORTHOGRAPHIC PARSING. own long sound, o ; (enunciate,) which is a long, simple vocal, modified at the lips. Ph is a consonant digraph, antecedent to the base of the third syllable, o, and represents the sound of f, f ; (enunciate,) which is an aspirate, obstructed at the lips by a partial contact of the organs, producing a labial and a continuant. 0, the base of the third syllable, is a vowel, representing its own short sound, o; (enunciate,) which is a short, simple vocal, modified at the short palate. N is a consonant, the consequent of the base of the third sylla- ble, and represents its own proper sound, n; (enunciate,) which is a subvocal, and is obstructed at the hard palate, by a partial contact of the organs; producing a palatal, a continuant, and a nasal. Rough. R is a consonant and is antecedent to the base of the syllable, ou ; representing its own proper sound, r ; (enunciate,) which is a subvocal, obstructed at the hard palate, by a partial contact of the organs, producing a palatal, a continuant and a liquid. Ou, the base of the syllable, is a conjoined vowel digraph, rep- resenting the short sound of u, u ; (enunciate,) which is a short, simple vocal, modified at the hard palate. Gh is a consonant digraph, and the consequent of the base of the syllable, representing the sound of f, f; (enunciate,) which is an aspirate, obstructed at the lips by a partial contact of the organs; producing a labial and a continuant. Lough. L is a consonant, and the antecedent of the base of the syllable, ou ; representing its own proper sound, 1; (enunci- ate,) which is a subvocal, obstructed at the hard palate, by a partial contact of the organs, producing a palatal, a continuant and a liquid. Ou, the base of the syllable, is a vowel digraph, representing the sound of short o, o; (enunciate,) which is a short, simple vocal, modified at the soft palate. Gh is a consonant digraph, and the consequent of the base of the syllable, representing the sound of k, k; (enunciate,) which is an aspirate, obstructed at the soft palate, by a perfect contact of the organs ; producing a guttural and an abrupt. Phthisic. Ph are two aphthongs and remote antecedents of the base of the first syllable, i, and are used to modify the repre^ sentative character of the digraph th, and to determine the sig- nification of the word. Th is a consonant digraph, and the immediate antecedent of i, the base of the first syllable, representing the sound of t, t; (enunciate,) which is an aspirate, obstructed at the teeth or gums, by !i perfect contact of the organs, producing an abrupt and a dental. 1, the base of the first syllable, is a vowel representing its own short sound, i ; (enunciate,) which is a short, simple vocal, modi- fied at the teeth. S is a consonant, the consequent of the base of the sylIaW» and represents the sound of z, z ; (enunciate,) which is a subvo- cal, obstructed at the gums, by a partial contact of the organs , producing a dental and a continuant. ORTHOGRAPHIC PARSING. 95 I, the base of the second syllable, is a vowel^ representing its own short sound, i ; [enunciate,) which is a short, simple vocal, modified at the teeth. C is a consonant, and the consequent of the base of the sylla- ble ; representing the sound of k, k ; {enunciate,) which is ai aspirate, obstructed at the soft palate, by a perfect contact of th« organs ; producing a guttural and an abrupt. Motion. M is a consonant, and the antecedent of o, the has*- of the first syllable ; representing its own proper sound, m ■ {enunciate,) which is a subvocal, obstructed at the lips, by a par- tial contact of the organs ; producing a labial, a continuant, ai>l H nasal. 0, the base of the first syllable, is a vowel, representing iwi own long sound, o; {enunciaief) yvhXoh is a long, simple voca.-. modified at the lips. Ti is a combined digraph, and the antecedent of o, the base ',1 the second syllable ; representing the sound of sh, J ; {enuuciate,) which is an aspirate, obstructed at the hard palate, by a partis contact of the organs ; producing a palatal and a continuant. 0, the base of the second syllable, is a vowel, representiu* the sound of short u, u; {enunciate,) which is a shorty simpU vocal, modified at the hard palate, N is a consonant, and the consequent of the base of the sylla- ble, representing its own proper sound, n ; {enunciate,') which i. a subvocal, obstructed at the hard palate, by a partial contact of the organs; producing a palatal, a continuant, and a nasaL Filial. F is a consonant, and the antecedent of the base o* the first syllable, representing its own proper sound, f; {ennn-' date,) which is an aspirate, obstructed at the lips by a partia contact of the organs ; producing a labial and a continuant. J, the base of the first syllable, is a vowel, representing its owr short sound, i; {enunciate,) which is a short, simple vocal. L is a consonant, and the consequent of the base of the first eyllable : representing its own f roper sound, 1 ; {enunciate,) which is a subvocal, obstructed at tbe hard palate by a partial contact of the organs; producing a palatal, a continuant, aad a liquid. I is a consonant, and the antecedent of the base of the second Byllable, representing the sound of y, y ; {enunciate,) which is a vocal and a coalescent, modified at the teeth. A, the base of the second syllable, is a vowel, representing its own short sound, a; {eminciate,) which is a short, simple vocal. L is a consonant, and the consequent of the base of the second syllable, representing its own proY>er sound, 1; {enwiciate,) which is a subvocal, obstructed at the hard palate, by a partial contact of the organs ; producing a palatal, a continuant, and a liquid. DRILL IN PULL ORTHOGRAPHIC PARSING. Impossibility is a, sim-^la, derivative polysyllable, accented on the fourth and second syllables. Possible, the base of the word, is modified by the prefix im, signifying not, and the suffix ity, signifying the state or condition. The word signifies, ''that which can not be." 98 ORTHOGRAPHIC PARSING. It is spelled, orthographically, i, m, p, o, s, s, i, b, i, 1, i, t,y, and phonetically, i, m, p, o, s, i, b, i, 1, i, t, i. I is a vowel, the base of the first syllable, representing its own short sound, i ; {enunciate,) which is a short, simple vocal. M is a consonant and the consequent of the base of the first syllable, representing its own sound, m; (envnciate,) which is ft subvocal, obstructed at the lips by a partial contact of the organs, producing a labial, a continuant and a nasal, P is a consonant, and the antecedent of the base of the secorvd syllable, representing its own sound, p; {enunciate,) which is an aspirate, obstructed at the lips by a perfect contactof the organc? producing a labial and an abrupt. 0, the base of the second syllable, is a vowel, representing it^ own short sound, o; {enunciate,) which is a short, simple vocal, S is a consonant, and the consequent of the base of the secop4 syllable, representing its own propersound, s; {inundate.) whic-G is an aspirate, obstructed at the gums, by a partial contact of th* organs; producing a dental and a continuant. 1, the base of the third syllable, is a vowel, representing it* own short sound, i ; {enunciate,) which is a short, simple vocal B is a consonant, and the antecedent of the base of the four*^ syllable, representing its own propersound, b; {enunciate,) which is a subvocal, obstructed at the lips by a perfect contact of ths organs; producing a labial and an abrupt. I, the base of the fourth syllable, is a vowel, representing li'* own short sound, i; {enunciate,) which is a short, simple vocal. L is a consonant, and the subsequent of the base of the fourt^h syllable, representing its own proper sound, I ; {enunciate,) whicii is a subvocal, obstructed at the hard palate by a partial contact of the organs ; producing a palatal, a continuant and a liquid. I, the base of the fifth syllable, is a vowel, representing its own short sound, i ; {enunciate.,) which is a short, simple vo.^?J. modified at the teeth. T is a consonant and the antecedent of the base of the sixth syllable; representing its own proper sound, t; {enunciate,) which is an aspirate, obstructed at the teeth or gums, by a perfect con tact of the organs : produci'ag a dental and an abrupt. Y, the base of the sixth syllable, is a vowel, representing tha short sound of i, i ; {enunciate,) which is a short, simple voca' modified at the teeth. PART III. GRAMMAR. METHODS OF TEACHING ORTHOGENi:, SYNTAX, AND ANALYSIS. INTRODUCTION. PROPER AGE FOR COMMENCING THE STUDY OP GRAMMAR. There is no subject of school study about wMch there is a greater disparity of opinion prevailing among teachers than that of the age at which chil- dren may commence the study of Grammar. Some teachers would have children commence Grammar as the first stvdy in books after they have learned to read well, or even before ; others of our best educators would defer it till the faculties of the mind are all measurably developed; a third class would not have Grammar studied at all, as a distinct science. I conceive that, by an adapta- tion of which the subject is susceptible, children may commence Grammar as soon as they can read fluently and intelligibly. Geography may be in- troduced before children can read fluently, as a means of securing study in reading lessons, and of training the hand and eye in drawing maps. I should, therefore, introduce Geography at this point, in this volume, were it not for breaking in upon a systematic arrangement of the branches. Object lessons in common things, and Natural History; also experiments in Chemistry and Natu- (99) 100 GRAMMAR. ral Philosophy, may well precede the study of Grammar also. ORAL INSTRUCTION BEFORE THE BOOK. No lesson should be required of a young pupil in the text-book, till he has had a preliminary drill ; and the teacher is satisfied that he comprehends the subject so far as his lesson in the text-book extends. Should the teacher fail in making the class, or any member of a class, understand any particular part of the subject, by the preliminary drill, it would be worse than in vain to require such a class, or individual, to memorize it from the text -book. Such a pupil or class must lay aside that subject for awhile, and take up some other more simple ; Dr, lay aside the study of Grammar till the mind is more matured. THE 3IETH0DS OF PRELIMINARY DRILL. The main object of the following pages, given to PRIMARY TEACHING, is to illustrate and exemplify the method of preliminary drill, preparatory to lessons to be memorized from the text-book. A similar course has been pursued with numer- ous classes in the Model Department of the Normal School, and Grammar has never failed to be a treat for the children. THE ORDER OF LESSONS. The order pursued in the following pages, in taking up the different subjects for lessons, is that of simplicity; commencing with tie most simple INTRODUCTION. 101 and obvious of subjects, viz : the noun, and pro- ceeding witli its modifications and classes, as the child can bear tbem, and so advancing to other parts of speech and their modifications and classes, till the whole -ground shall have been passed over in its plainest form. All exceptions, idioms, and irregularities, save such as are obviously violations of rules, are studiously avoided in this method of primary teaching, as tending to confuse the mind by too great a degree of complexity and obscurity. METHOD OP INTRODUCING RULES. No rule should be introduced till the necessity for it is understood by the class. There is, then, no difficulty in their memorizing it even in the oral drill. Children will thus obtain the great fundamental principles of construction, of syntax, while they are learning to distinguish the parts of speech, their classes and modifications. WRITING EXERCISES. There are many advantages in the plan of writ- ten exercises proposed in parsing; some of which are: 1st. It secures study in the preparation of a parsing lesson, which otherwise might be evaded under various pretexts. 2d. It affords a means of teaching spelling, as explained in article 52, page 85. 3d. Rapid improvement in penmanship can be secured by close attention to this matter on the part of the teacher. 4th. It paves the way to composition, by the scholars taking a part of the difficulties, before entering upon them in eombina- 102 GRAMMAR. tion. 5tli. It effects the more equal advancement of a class, by securing more equal amounts of ap- plication outside of the recitation. Remark. — The ordinary writing book may be "Ased for this exercise, and the time otherwise given to writing from copies. GENERAL PLAN OF CONDUCTING RECITATIONS. The method of conducting a recitation in Grram- mar, as explained in the subsequent pages, illus- trates the general onefJiod of conducting recitations in all branches. It assumes, that the class is an organized assembly, with the teacher for Chairman. No scholar has a right to the floor (using parlia- mentary language) till he is recognized by the teacher. The raising of the hand signifies, that he wishes to obtain the floor, but does not gi^e him a right to it without the assent of the Chair- man. The teacher should be particularly watch- ful on this point; otherwise scholars conceive, that whenever they raise the hand they may speak. Thus the object of raising the hand is defeated, and disorder is the result, MUTUAL CRITICISM OF SCHOLARS. Scholars are required, in tlie recitations, to criti- cise each other. Without special care, on the part of the teacher, he will deprive the scholars of this privilege by doing too much of it himself. Schol- ars will learn vastly more by criticising, than by being criticised. " It is more blessed to give than teceive." INTRODUCTION. 103 They should also be encouraged to criticise each other out of school hours — of course, in a kindly manner. METHOD OF USING PART III. For Primary classes in Grammar, it is not sup- posed that the teacher consulting this work will be governed mechanically by my divisions of the general subject into Lessons, or that he will follow implicitly my arrangement of the parts of speech, and their classes and modifications, in his Steps. With the exception of the adjective and the parti- cles, which for want of room are not provided for, I conceive the arrangement adopted the best; though other teachers may prefer to follow the arrangement of their text-bo^ks. The main object in view in the preparation of these primary lessons will be to exhibit, as clearly as possible, the combination of oral instruction with memoriter lessons from text-books; and it is believed that if a teacher will consult these suc- cessive Lessons and Steps in his own preparation for the successive recitations and exercises, he will obtain some hints which may serve as guide boards or beacon lights in his course. The methods of using the Outlines and Defini- tions, etc., under the head of Advanced Teaching, ?ill appear sufficieptly in connection with them. METHOD OF TEACHING GRAMMAR TO PRIMARY CLASSES. 1 PRELIMINARY REMARKS AND EXPLANATIONS, The class should be able to read fluently and intelligently. They should be provided with books, grammars of some kind, and all of the same kind. It is not necessary nor desirable that they should have primary grammars. The larger and fuller grammar has to be purchased, after the primary has been used one session. Most Normal Schools, throughout the country, now make use of either Brown's or Clark's Gram- mars as text books. My references will be made chiefly to Clark's Grammar, revised edition. 2. LESSON I. First Step — Nouns. Let the teacher define a Noun in the simplest possible manner, i. e., as a name, and illustrate the definition by examples, thus : Teacher. A noun is a name. Every noun is a name, and every name is a noun. Your names are nouns, and my nr^me is a noun. Can you think of any other nouns? (104) PRIMARY TEACHING. 105 The scholars raise tlieir hands. Teacher says to one — ^' John, you may mention some noun." John mentions some name, as "house," "stone," " boy." Teacher, Why is house a noun, John? Jolm. Because it is a name. So the teacher should proceed with every mem- ber of the class, until all can not only give nouns, but can define them correctly. 3. Second Step — Nouns — Immaterial Objects. As scholars will in the first place select the names of material substances, the teacher will secondly bring to their notice the names of immaterial sub- stances and abstract qualities, thus: Teacher. Is mind a noun? As many as think it is may raise the hand. Several do not raise their hands, perhaps ; among whom is Samuel. Teacher. Samuel, why is n't mind a noun? Samuel. I never saw a mind. Teacher. But then you have a mind, I suppose; or are you all body and clothes? There are many things which you cannot see, which still must have names, as we have to talk about them. Did you, any of you, ever see the wind? or did you ever see a love or a friendship? Yet you do n't doubt that you possess and enjoy these things. Each one of the class may give such a noun. The teacher will then call on the pupils individ- ually by name, when such nouns as sound, health, 106 GRAMMAR. goodLGSs, breatii, life, deatli, weight, lightness, smell, etc., may be brought out by the class; possi- bly some adjective, as new, or soft, or sweet, by Jane. Teacher. Jane, why is sweet a noun? • Did you ever see a sweet? Jane. No, sir; but I have tasted of a sweet apple. Teacher. True, you have tasted of an apple, and the apple was sweet. But what sort of a thing is the sweet without the apple? Now, how many of the class can tell me the name of that quality of the apple which makes it taste sweet? Hands are raised. Teacher. Sarah. • Sarah. Sugar. Teacher. Sugar is a substance, not a quality. James. Juice. Teacher. Juice is also a substance, not a qual- ity. If I were speaking of the quality which makes the apple sweet, I should not call it the Bweet of the apple. "What would I call it? All hands come up, and eyes glisten. Teacher. Mary. Mary. Sweetness. Teacher. Yes, that is the name of the quality. Can you give me any other quality, of apples? Each scholar may think of some quality of an apple and give it, when called on. James, what quality do you think of? James. Hardness. Teacher. Susan. PRIMARY TEACHING. 107 Susan. Softness. The teacter sliould pursue this course, till the class are familiar with the names of qualities taken abstractly. 4. Third Step. Drill in the Grammar. Direct the scholars to turn to page 148 of Clark's Gram- mar, Sentence I. Teacher. You may tell me all the nouns you see in the second line : " A large ship traversing the ocean by the force of the wind." James. Ship — ocean — wind. Teacher. Why are these words nouns? James. Because they are names. Teacher. Are there no other names in that line? James, perhaps, hesitates. Teacher. Class. [Several hands rise.] Remark. It will be noticed that when the teacher uses the word "Class," that no pupil speaks ; but all who are able to respond raise their hands. The teacher then calls on some one to give the answer. Teacher. Mary, you may give me the other nouns in that line. Mary. Large, and force. Teacher. Why is force a noun, Mary? Mary. It is the name of something. Teacher. Yery well. Why is large a noun? Mary. It is a name. Teacher. Name of what? Did you ever see a large? 108 GRAMMAR. Mary. I never saw a force either. Teacher. What property of the wind dri-ves the ship? Is it not the power of the wind? What other name is there for power? Cla,ss. [Hands rise.] Susan. Susan. Force. Teacher. Is not force then the name of that which drives the ship? Could the wind drive the ship, if it had no force? Let us now see about large. Is large the name of anything, Mary? Mary. Yes, sir ; a large house is a name. Teacher. House is a name of that in which people live ; but what sort of a thing is a large? How many think large is the name of anything, now? In a similar way, each member of the class may be called on to give the nouns in a line. The teacher will select such lines from Clark's Gram- mar, or any other, as may be best adapted to the particular scholar with whom he is dealing. Chil- dren will most easily and certainly select the names of material objects. The lesson assigned for the scholar to learn from the book, is, in this case, nothing more than the definition of a noun. And the teacher will be careful in these primary exercises to require the class to learn nothing from the book which he has not made plain, and pleasant, in the preliminary drill. •^ — ^^^ PRIMARY TEACHING. 109 5. LESSON II. First Step — Recitation of Lesson assigned. Teaclur. How many can define a noun? Hands rise ; and the teaclier calls upon those who were the dullest in the previous exercise, to give the definition. Having thus satisfied himself as to the amount of study bestowed, he proceeds to another preliminary drill, on the modifications of nouns, taking them in the order of their sim- plicity, taking those modifications first, always, which are the most obvious to the child. 6. Second Step — Number. Teaclier. I will tell you something more about nouns. They are sin- gular or plural. If a noun means one of that thing which it is the name of, it is singular ; if it means more than one it is plural. For instance, horse is a singular noun, because it means a single horse ; but horses is a plural noun, because it means more than one horse. Teaclier. The class, all together. Is bird sin- gular or plural? The class answer in concert without raising hands when the words "all together" are used. Teacher. Is birds singular or plural? Glass. Plural. Teacher. How is it with boy? Class. Singular. Teacher. Give me the plural of boy. Class. Boys. ^ "^ 110 GRAMMAR. 1 Teacher. Is girls singular or plural? Class. Plural. Teacher. Give me the singular of girls. Class. Girl. Teacher. Very well; now tlie plural of fox. Class. Foxes. Teacher. Box. Class. Boxes. Teacher. Ox. Class. Oxes — oli no, oxen. I' Teacher. Yery well; try again. Mouse. Class. Mice. Teacher. Louse. Class. Lice. Teacher. , r House. Class. Ilice — no, no, houses. Teacher. You are right now. Again ; Moose. Class. Mooses. Teacher. Papoose. Class. Papooses. Teacher. Goose. Class. ! [ Gooses; ha, ha, geese. 1: 1' Third Step — Gender. Teacher. Now, chil- dren, I wish to tell you about gender. The name of a male is a noun of the masculine gander. The name of a female is a noun of the feminine gender. For instance; hoy is a noun of the masculine \ gender, girl is a noun of feminine gender. Floor • [ is a noun of the neuter gender. Teacher. What gender is man? All together.' Class. Masculine. Teacher. How many can tell me why man ia masculine? [Hands rise.] Teacher. Samuel. Satmiel. It is the name of a man. Teacher. Jane. Jane. It is the name of a female. Teacher. What gender is lady? [Hands rise.] Teacher. Mary. Mary. Feminine. ^ PRIMARY TEACHING. Ill Teacher. What gender is desk? [No hands rise.] What gender did I tell you those nouns were which were neither masculine nor feminine? [Hands rise.] Teacher. Sarah. Sarah. Neuter. Teacher. Yery well. What gender is desk, then? [All hands up.] Teacher. All together. Class. Neuter. 8. Fourth Step — Parsing. The class are now prepared to commence the process of parsing. The teacher will lead the way by giving an ex- ample thus. Teacher. You may all look at the first noun in the first line of Sentence I. 148, of Clark's. Grammar, and I will parse it for you. Science is a noun, singular number, neuter gen der. Do you think you can parse a word now? — [Some hands rise.] i Teacher. Jane, you may parse mind, in the same line. Jane. Mind is a noun. Teacher. What number? Jane. Singular. Teacher. What gender? Jane. Neuter. Teacher. Now, you may parse it again. Jane. Mind is a noun, singular num- ber, neuter gender. Teacher. Very well. You may all parse i^ in concert. Class. Mind is a noun, singular number, neu- ter gender. Teacher. "Very well. Sarah, you may now parse ship. 112 GRAMMAR. Sarah. Ship is a iiotid, neuter gender, singu lax number. Teacher. You may all parse ship. Class. Ship is a noun, {in confusion) singular number, neuter gender, neuter gender, singular number. Teacher. You may give the number before the gender. Take the noun, John, in the line: "I, John, saw these things." James, you may parse it. James. John is a noun. Teacher. Why? James. It is a name. Teacher. Go on. James. Singular number. Teacher. Why? James. It means only one. TeacJier. What gender? James. Masculine. Teacher. Very well. You may all parse John. Class. John is a noun, singular number, mas culine gender. 9. Fifth Step — Person. Teacher. I will now tell you something else about nouns. If a noun is the name of the speaker or writer, it is in the first person. If it is the name of a person spoken to, it is in the second person; and if it is the name of a person or thing spoken of, it is in the third person. For instance: John, in the sen- tence we have just had, is in the first person, be- cause John was the name of the writer. If I should say, "George, shut that door," George would be in the second person, because it would be the name of the person spoken to. But door would be in the third person, because it is spoken of. c.-^ PRIMARY TEACHING. 113 Wbat person is Daniel, in tlie expression used by the King : "0, Daniel! servant of the living God?" All together. Cla^, Second person. Teacher. Why? Class. Daniel is spoken to. Teacher, Now, we will parse a iew words. I will parse John for you first. John is a noun, third person, singular number, masculine gender. You may follow the same order in parsing that I did in giving person, number and gender. Teacher. Eliza, you may parse Esther in the second sentence, in Lesson II. Uliza parses as directed, in this manner : Esther is a n6un, third person, singular number, feminine gender. Teacher. You may all parse it in concert. The Class p^rse in concert. They can be kept together by the teacher's beating with his hand, or pointer. It will be noticed, that no definitions are called for, while parsing, as is practiced by most teachers and recommended in most grammars, since the days of Kirkham. However, if the scholar is wrong, or hesitates, showing doubt or ignorance of any point, the teacher at once calls for the defi- nition necessary to set the scholar right. If the scholar parsing cannot give the required definition, the teacher says, '^ Class:" when all who can give it raise their hands ; and the teacher calls on the scholar most unlikely to give it. If he fails, then on another, and so on till the definition is correctly given. 114 GRAMMAR. 10. Sixth Step — Classes of ISJouns. Teacher Nouns are divided into two classes, for tbe purpose of sliowing us where to use capital letters. General names, or such as apply to many per- sons or things,^ are called common nouns; for the reason that they belong in common to many ob- jects. The noun man is common } it belongs in common to many persons. James Buchanan is called a proper noun; it belongs, properly, or pe- culiarly, to one person. I will give you several common nouns, and you may give proper names that belong to the same class of things. For in- stance : under the common noun, girl, we fiitd the proper nouns, Susan, Mary, Eliza, etc. What proper noun comes under the common noun boy? ^ Class raise their hands. Teacher. William. William. Samuel. This course may be pursued with each of the scholars, until they arc all able to distinguish the classes of nouns. Then the teacher calls on them to parse ; giving the class of the noun first in order after the noun, then the modifications as before. The exercise is closed by assigning to the class, for a lesson to be learned from the book, the defi- nitions of the two classes of nouns, as well as the definitions of person, number, and gender. These definitions are pointed out in the grammar by the teacher; and some one of the duller scholars is asked to show, in his own book, what the lesson PKIMARY TEACHING. 115 ig, 111 order that the teacher may be sure that the class understand what they are to learn for the next recitation. 11. LESSON III, First Step. The recitation of the lesson as- signed, and the grading of the scholars according to their merits, in the teacher's register. 12. Second Step — Case. Verb. Teacher. Nouns have one more property, or modification ; that of case. In order that you may understand this prop- erty, I shall introduce you to another kind of word ; or, as the grammarians call it, another part of speech. A verb is a word that denotes action, or being, or state of being. When I say, "The bird flies," the word flies de- notes the action of the bird, or tells what the bird does; hence, it is a verb. In the sentence, "Mary reads ;" reads is a verb for a similar reason. In the sentence, " The stone lies on the ground," the word lies does not express action, but simply state of being. Now, you may give me the verbs in these sen- tences; all together: " The horse runs." Class. (In concert.) Runs. Teacher. Why? Class. It tells what the horse does. Teacher. Does it denote action or being? Class. Action. Teacher. " The boy chops wood." In this sen- tence, what is the verb, John? John. Chops. Teacher. AVhy? John. It denotes action. Teacher. Very well. 116 GRAMMAR. 13. The Third Step — Drill in Verbs. Teacher. You may nov/ open your grammars to the G5th page and find sonae of the verbs in Sentence I. James, in the first sentence, what is the verb, and whyl James. Feels, because it denotes action. Teacher. Sarah, in the next sentence ? Sarah. Rose ; it denotes action. This course may be pursued till the class have all been reached, and can give the verbs in these simple sentences, and the reason for such words being verbs. It will be noticed, that aj^pear and seeins are verbs, because they denote being, or state of being. 14. Fourth Step — Subject and Object. Teacher^ If I say, "The boy drives a team;" what is the subject of the remark, what is the principal thing talked about? Class raise their hands. Teacher. Susan. Susan. Boy. Teacher. Right. The subject of a sentence is that word in a sentence about w^hich the verb as- serts something. Now, the verb drives asserts an action of the subject, boy; and the noun, boy, is in the condition of a subject. Grammars call this condition the '• nominative case." They might better call it the "subjective case," or condition. But, since nearly all grammars agree in this mat- ter, we will call it so too. Teacher. Let us take the same sentences again. What obje'^t does the boy drive? PRIMARY TEACHING. 117 Class raise hAnds. Teacher. Jolin. John. Team. Teacher. Yes. Then team is in the condition of an object, and we will say, that it is in the objective condition or case. We can now parse these nouns, boy, and team, in full. I will parse boy for you, but will first write the form by which I parse it, on the board. [The teacher writes.] Species? Class? Person? Number? Gender? Case? Construction? Rule? Now, I will parse it by this form ; then, you may all parse it by the same form, in concert. The teacher using the pointer, as he proceeds, parses thus: Boy is a noun, common, third, singular, masculine, nomi- native, because it is subject of the verb, drives. He then calls on the class to parse the same word, guiding them by pointing at the successive ques- tions in the form, on the board. The same courso is pursued with team, the teacher giving, as its "construction," "being the object of the verb drives." The teacher assigns for the next lesson, those definitions which he has brought out and exempli- fied in this exercise. This lesson is to be studied and prepared for the next exercise. The defini- tions to be assigned, are these, viz: of the noan, common noun, proper noun; gender, masculine, feminine; person, first person, second person, third person; number, singular number, plural number; case, nominative case, objective case. 118 GRAMMAR. 15. LESSON IV. First Step — Recitation. The manner of con- ducting this recitation is this : The scholars being seated on the recitation bench, the teacher calls one most likely to fail, by name. He or she rises. The scholaf rises for several reasons. 1st. He feels more responsibility in the recitation, when thus made more promi- nently the object of observation. 2d. The rest of the class can hear what he says more plainly. 3d. Other scholars, who are sitting, cannot so easily prompt him without being heard by the teacher. The teacher then proposes one word for definition, not the first, necessarily ; perhaps the most diffi- cult. If the scholar fails in this, the teacher pro- poses it to the class, for the purpose of keeping their attention, by saying, " Class." All who are able to answer, raise their hands ; and the teacher calls upon those least likely to do so, to give the definition or answer the question. This course is pursued till every member of the class is reached, and his merit or demerit ascertained and recorded in the class register. 16. Second Step — Parsing. The teacher directs the class to turn to page 65 of Calrk's Grammar, or to any similar collection of sentences, in any other grammar. He writes out the form fm^ ^oars- ing a noun on the board, as given before, in section 14, page 117. Then some one ©f the more apt Bcholars is called on to parse Science in the sen- V.-.. PRIMARY TEACHING. 119 tence, "Science enlarges and strengtliens tli3 mind," by the form — standing while lie parses ; the rest of the class signifying any error by rais- ing their hands; when the teacher calls on some one, so signifying, to correct the error, or the sup- posed error. A scholar having parsed a word, is excused, and the class parse in concert ; the teach- er keeping time for them by pointing in succession to the several questions in the/or?7i. I will parse the words Science and Mind, in the manner they should be parsed in this exercise. Science is a noun, common, third, singular, neuter, nominative, being the subject of strengthens and enlarges, according to the llule, A noun or pro- noun which, is the subject of a finite verb, must be in the nominative case. Mind is a noun, common, third, singular, neuter, objective, being the object of the verbs strengthens and enlarges, according to the Kule, The object of a transitive verb must be in the objective case. The teacher will be careful to give only such nouns to parse, as are subjects or objects of verbs; introducing or requiring nothing in the parsing exercise, which has not been fully understood by previous explanation and drill. If the book does not furnish a sufficient number of appropriate examples, sentences may be written on the black- board. In parsing, the words person, number, gender, and case, are omitted; because they are given in the form on the blackboard, and because they are just as plainly signified, when omitted, as when 120 GRAMMAR. expressed. No definitions are required, we repeat, when parsing, unless the pupil, in his parsing, makes an error or hesitates ; when he is corrected or prompted by the teacher's calling for the appro- priate definition ; the forgetting or neglecting of which was the cause of the pupil's error or hesi- tancy. The hour, or half hour, for the recitation, is thus occupied in parsing, by individuals, and by the class in concert, leaving only time enough to assign another lesson. 17. Third Step — Assigning a Lesson in Writing. The next lesson is the parsing of the words in writing, which have been parsed orally in the class. Teacher. Scholars, you will hand me, at the next recitation, a written parsing lesson. You may write, on paper, with ink, very neatly, and with correct spelling, the parsings of the same words which have been parsed in this recitation. Now, you will be careful to have paper, ink, and pens, all ready at the regular hour in which you study this lesson, and I will help you a little then, if necessary. I would like to have you fold your papers neatly, as merchants and lawyers fold their papers for filing, and write your name across one end, on the outside. The teacher will then show the manner of folding by taking a half-sheet and folding it before the class. He will write his name, on the folded paper, as he wishes the schol- ars to write theirs. PRIMARY TEACHING. 121 18. LESSON V. First Step — Criticising Written Exercises The written exercises are collected by one of the scholars ; and the teacher reads one of them aloud for the class to criticise. They are directed to watch for errors and to raise their hands if they notice any. Should any hands rise, the teacher calls on some one who raises his hands to mention the error and correct it. If he should fail, then the teacher calls on others, till the error is cor- rected. The pupil who made the error is required to give the definition or rule which he neglected or violated in making the error. The same course is pursued till this paper and the others are disposed of. The teacher will be careful to bestow any praise, that is deserved, for neatness in the execu- tion of the mechanical part of the exercise, and he will grade the pupils in his register according to their accuracy in parsing and spelling; and accord- ing to the neatness evinced in writing and fold- ing, and superscribing their own names on the papers. Time should be reserved for another drill in oral parsing, even though all the written exercises are not criticised before the class. They may be criti- cised by the teacher out of school hours, and the errors corrected with a lead pencil or red ink, on the paper, so that the scholar will understand them, and the paper returned to him at the next recita- tion. 122 GRAMMAR. 19. Second Step — Drill in Orai, Parsing. This drill may consist of parsings of the same class of words as before, provided the class are found quite deficient in their written exercises ; and the same course may be pursued through several lessons until the majority of the class are able to parse the words assigned, according to their stage of ad- vancement, correctly. 20. LESSON VI. First Step — Criticising Written Parsings. Second Step — Possessive Case. The possess- ive case may be introduced, and the declension of nouns ; and, after being explained, the definition of the possessive case and other cases, also, the declensions of nouns may be assigned for study, in connection with some nouns to be parsed in writ- ing, which have not been parsed orally, and which are in the constructions already explained, viz : the subject of a verb, the object of a verb, the pos- sessive case, denoting possession, origin, design, etc. (See Clark's Grammar, pages 83 and 84.) 21. LESSON VIT. First Step — Recitation of definitions of cases, and the declensions of nouns. Second Step — The Examination of the paper of one of the scholars, while the other scholars, having their papers in their hands, give their agreement or disagreement with the paper read. PRIMARY TEACHINa. 123 Third Step — Introduction of the Pronoun. — Teacher. If I should say : " Jane studies with all Jane's might?" how could you better express that idea? [Hands rise.] Teacher. Susan. Susan. ''Jane studies with all her might," would sound better to me. Teacher. Right. What word do you use in- stead of Jane's? Class. [Hands rise.] Teacher. Mary. Mary. Her. Teacher. Then her is a pronoun, because a pronoun is a word used instead of a noun. Now, you may all open to page 209, and see if you can tell me which are the pronouns. How many of you see a pronoun in the sentence : " The evil which he .feared has come upon him." [Hands rise.] Teacher. Henry. Henry. Which. Teacher. What does which stand in place of? Henry. Evils. Teacher. Right. Samuel, what pronoun in the same sentence? Samuel. He. Teacher. Why is he a pronoun 1 Samuel. Because it stands in the place of John. Teacher. Right. Do any of you see another pronoun in the same sentence 1 [Hands rise.] Teacher. Ellen. Ellen. Him. Teacher. What does him stand in place of? Ellen. Hllen. It stands m the place of he. Teacher. Right. The same course may be pursued till the major- ity of the class can distinguish pronouns. The next lesson assigned for study, will include the definition of the pronoun, and a new parsing les- Bon of nouns; the teacher being careful to assign 124 GRAMMAR. no nouns in different constructioiiS from ttose he has alreadj explained. 22. LESSON VIII. First Step — IlECiTATioisr of tlie definition oi pronouns. Second Step — Classes and Cases of Pronouns. Teacher. There are three classes of pronouns. I will endeavor to describe them, so that you can tell them apart. Let me have your attention very closely. A personal pronoun is one that always stands for the same grammatical person. A relative pronoun is one that may stand for any grammatical person, and connects clauses. An interrogative pronoun is one that is used for asking a question. The pronoun he always stands for the third person or some person spoken of. The pronoun I always stands for the speaker or for the first per- son. Thou, always stands for the second person. He, I and thou, are, therefore, personal pronouns. The pronoun who may stand for any one of the three persons; for the first person, second person, or third person. In the expression, "I, who teach," what person does who stand for? Class. [Hands rise.] Teacher. Susan. Susan. First person. Teacher. In the expressions, " You, who study ;l' '•Our Father which art in heaven," what person do who and which stand for? [Hands rise.] John. Joh7i. The third person. Teacher. What does who stand for, John? John. It stands for you. PRIMARY TEACHING. 125 Teache)\ Right. What does you stand for, when E say, "You, who study?" Does it stand for the person spoken of, or the person spoken to? John. it stands for the person spoken to. Teacher. Then who stands for the person spoken to, for it stands for the same that you does. In the expression, "Thou who runnest," what person does who stand for? [Hands rise.] Teaclier. Jane. Jane. Sec- ond person. Teacher. Very well. Then you see that who does not always stand for the same gram- matical person, as ih.Q pronoun I does. In the question, " Who comes there?" who stands for the answer of the question, and for that reason is a pronoun. It is also used for asking that question, and is for that reason an interroga- tive pronoun. How many can tell the pronouns in the line, "I, who was present, know the particulars." [Hands rise.] Teacher. Julia. Julia. I and who are pronouns. Teacher. Yes. Now I will write those definitions that I gave you, of the difterent kinds of pronouns on the board, and you may copy them on to your papers and recite them at your next recitation. You may also learn the declensions of the personal pronouns, on page 89. I do not wish you to learn the definitions of the different classes of pronouns in the grammar ; they will only per plex you. 23. LESSON IX. First Step — Recitation of the Definitions given on the blackboard and copied the day pre- 126 GRAMMAR. vious; also of the Declensions of personal pro* nouns. Second Step — Form of Parsing Pronouns. — This may be written on blackboard thus : Speciesf Class? (^Suh-class?) Agreement? Person? JS^iim- ber? Gender? Rule? Case? Construction? Rule? Teacher. I will now parse a pronoun for you by the form. In the sentence, " When the Saxons subdued the Britons, they introduced their own language," they is a pronoun, per- sonal, and agrees with Saxons in the third, plu- ral, masculine, according i-o the rule, A pronoun must agree with its antecedent, or the noun or pronoun which it represents, in person, number, and gender. They is in the nominative case, be- ing the subject of the verb introduced, according to the rule; A noun or pronoun, which is the sub- ject of a finite verb, must be in the nominative case. Now, you may parse the same word in concert, as I point to the form The class then parse this word in concert. Their, in the same sentence, is parsed by some one of the pupils, following the form, and the teacher asking for definitions when the pupil errs or hesi- tates. Then the class parse the same word in con- cert, following the form as the teacher points to the several questions in it. This exercise is co itinued with other pronouns, on the same page, till the time expires ; when the teacher assigns the same pronouns for a parsing esson in writing, for the next recitation. PRIMAJIY TEACHING. 127 . 24. LESSON X. First Step — Criticism of one of the written exercises, witli the comparison of the other exer- cise by the scholars. The teacher then collects the papers, for criticism out of school hours. Second Step — Relative Pronouns. Teacher. I wish you to attend now more particularly to the relative pronouns. How many can give me the definition of a relative pronoun? [Hands rise.] Teacher. Sarah. Sarah repeats the definition. If she fails or errs, some other pupil is called on for it. Then the class is called on to repeat it, in concert, several times, till all can give it correctly. Teacher. A relative pronoun is one used to intro- duce a sentence, which qualifies its own antecedent. Turn to page 91, and see who can tell nie what sentences, who connects'^ [No hands rise.] Teacher, I will tell you ; " The youth was applauded," is one sentence, and " Who was speaking," is another, since they both have verbs in them, as every sen- tence must have a verb in it. Now, try the next sentence. — What is said about hel Samuel. Sa^ muel. " Man whom you described." Teacher. No. " We saw man," is one sentence ; what is the other 1 — Samuel. " Whom you described." Teacher. And what connects the two sentences'? Samuel. Whom, I guess. Teacher. You guess right. Then what kind of a pronoun is whom 1 Class. [Hands rise.] Teacher. James, James. Relative. Teacher. Why? James. It connects those sentences. Teacher. Very well. Who can tell me the relative pronoun in — . 128 GKATtlMAE. the next sentence? [No hands rise.] Teacher, ^' Mount the horse." is one sentence; what other sentence is there included in it? . [Hands rise.] Teacher. Susan. Susan. " Which I have chosen." Teacher. Right, and what stands for horse and connects the clauses ? [Hands rise.] Teacher. Mary. Mary. Which. Teacher, Very well. Now, Mary, you may parse which by the form. Mary parses which; any corrections, signified by the class, or otherwise necessary, are made by the teacher, by calling on Mary for the appropriate definitions. The class then parse it in concert, till they all are able to harmonize. The parsing lesson now assigned for writing, is these same relative pronouns, which have been parsed by the class orally. 25. LESSON XI. Second Step — The Verb — Tenses. Teache9\ We will resume the study of the verb. How many can give me the definition of the verb. [Hands rise.] Teacher. Sarah. Sarah. A verb is a word used to express the act, being, or state of a person or thing. Teacher. Right. The class may give the defi- nition in concert. The class repeat the definition until all can give it correctly. The course to be pursued with the verb is simi- lar to that pursued with the noun, viz : taking the most obvious feature first, and others in order, as they become more complex. The distinction of PRIMARY TEACHING. 129 cense appears to me the simplest and easiest modi- fication, in connection with the verb. Teacher. There are three kinds of time: pres- ent, past and future. All actions are performed in present time, or past time, or future time. Each kind of time has two tenses ; the first and second. The first tense of each kind is called the present, past, future. The second of each kind is called the prior present, prior past, and prior future. I will give you the form of these tenses with the verb learn: Present^ I learn; Past^ I learned; Fu- ture^ I shall or will learn. The class may give the forms in concert as I call for thorn. Teacher. Pres- ent. Class. I learn. Teacher, Past. Class. I learned. Teacher. Future. Class. I shall or will learn. Teacher. I would like to have you give the same tenses of some other verbs. Take study, and go through with it in the same way. The class may all follow the teacher in inflecting the present tense, with the persons and numbers, giving them the proper pronouns. Teacher. You will be able to get the forms of the tenses more easily by means of these signs : now^ being the sign or test of the present ; yester- day., the sign or test of the past; and, shall or ivillj the signs of the future. You will not find the signs, noto and yesterday, often in connection with verbs, in books; but you can always apply them to their respective tenses and make sense. They are applied in this way: Present, I learn now ; jPa.s^, I learned yesterday; Future, I shall or v/ill learn. U 130 GRAMMAR. Now, you may give, in concert, the verb write, in these three tenses, with the signs. I will beat time and you may give them. .Class. Present. I write now ; Fast. I wrote yesterday; Future^ I shall or will write. Teacher. Pretty well. You may give them again. The drill is continued with tenses in a variety of verbs, until all are able to give the tenses cor- rectly. If any scholar is slow and careless in the concert exercise, he is called on to give the tenses separately, till his attention is secured. 26. Second Step — Prior Tenses. Teacher. The prior tenses have these signs. The prior present, havCj hadst, or has;" prior past, had or hodst; prior future, shall or will have; I will apply them to the verb learn. Prior present, I have learned ; Prior past, I had learned ; Prior future, I shall or will learn. Now, you may give them as I call for them. Teacher. Prior present. Class. I have learned. Teacher. Prior past. Class. I had learned. Teacher. Prior future. Class. I shall or will have learned. Teacher. Prior future. Class. I shall or will have learned. Teacher. Very well. Now take the verb write and give the names of the prior tenses and their forms as I beat time with the pointer. It may be well in any more difficult concert ex- ercise, in which many of the class hang behind or fail of getting the exercise^ to require the class to PRIMARY TEACHING. 131 give each form twice. The laggards will then be able to catch the forms. Teacher. You may now give all the six tenses, with their signs, as I call for them, and you may all give each form twice. All together. Present. Class. I learn now, I learn now. Teacher. Prior present. Class. I have learned, I have learned. Teacher. Past. Class. I learned yesterday, I learned yesterday. Teacher. Prior past. Class. I had learned, I had learned. Teacher. Future. Class. I shall or will learn, I shall or will learn. Teacher. Prior future. Class. I shall or will have learned, I shall or will have learned. Teacher. You may now copy these signs from the board as I write them, and they will be your lesson for the next recitation. [The form of writing them will be found in See. 58.] The teacher writes on the board : "Signs of the tenses." Indicative mood. Present^ (now.) Prior present^ have, hast, or has. Past^ (yesterday.) Prior past^ had or hadst. Future^ shall or will. Prior future^ shall or will have. You may learn the names of the tenses, and their signs, for your next lesson, so that you can all write them on the black board, at the next recitation, with- out looking on your papers. You may also learn the definitions of th^se tenses as given on pages 115- 116 of Clark's Grammar. 27. LESSON XII. First Step — Kecitation of definitions of tenses; and writing out the tenses, and their signs on the board ir on slates. 132 GRAMMAR. Second Step — Moods. Teacher. There are several difierent manners of expressing actions or states of being. Tliese different manners gram- marians call moods. The indicative mood, that which you have been learning thus far, simply in- dicates a fact or asks a question, as. He learned, Did you study? The potential mood expresses power, possibility, liberty or necessity, and always uses these auxiliary or helping verbs, may, can, or must; and might, could, would or should. I will give you the four tenses in this, mood ; then you may see if you can give them in concert: Present. I may, can, or must learn ; Prior present^ I may, can, or must have learned ; Past, 1 might, could, would, or should learn ; Prior past, I might, could, would, or should have learned. Now, you may see if you can give the present tense, with its different persons and numbers. Give each twice, all together. First person. Class. I may, can or must learn, I may, can, or must learn. Teacher. Second person. Class. Thou mayest, canst, or must learn. Thou, etc. Teacher. Third person, etc. This drill may be continued in this form, till the class are all familiar with the variations of these signs, as applied to the different persons and num- bers. Then the other tenses of the potential may be taken up in the same manner. Teacher. I have told you the signs of the four tenses in the potential mood. I will repeat these signs, once more ; and you will notice that they are taken in pairs; that the perfect tenses differ from the others by taking, after them, the word have. PRIMARY TEACHING. 133 The teaclier repeats these tenses ; then calls on the class, thus : Teacher. You may give me these tenses of the potential mood, in concert, each twice. Present. Class. I may, can or must learn, etc. Teaclie-r. Prior Present. Class. I may, can or must have learned, etc. Teaclier. Past. Class. I might, could, would, or should learn, etc. Teacher. Prior Past, Glass. I might, could, would, or should have learned, etc. The concert exercise must be continued till all the class can join in promptly and correctly. In case any pupil fails, he should be taken, separately, and drilled, till he overcomes the difficulty. 28. TfflRD Step — Parsing Verbs. Teacher. You may now turn to page 91. I will take a verb and parse it for you, as far as you will he able to under- stand me. In the third sentence, have been, is a verb, in the indicative mood, prior present tense, first person, singular number, to agree with its subject, I, according to rule, on page 195. A verb must agree with its subject, or nominative, in person and number. I will now write the partial form, on the board, for parsing the verb, by which I parsed this verb, thus: Species? Mood? Tense? Person? Num- her? Cons f ruction? Rule? You may now parse the same verb, by this form, and give each particular called for, by the form, twice, as I point. The class now follow the form, as directed, and 134 GRAMMAR. parse the verb, have been ; then other verbs : the teacher calling on individuals to select the succes- sive verbs as they occur, and to parse them. Then, after a verb has been parsed correctly, by an indi- vidual ; or, after he has been corrected by the class and teacher, in the manner before described, the class, in each instance, are called on to parse the same verb, in concert; giving the entire parsing, twice only, repeating each particular once, in each parsing. 29. Fourth Step. The teacher prescribes for the next lesson, the definitions of the words; verb, mood, indicative mood, potential mood, tense, pres- ent tense, prior present tense, past tense, prior past tense, future tense, prior future tense; also, for a parsing lesson, in writing, the same verbs as have already been parsed, orally, in this exercise. 30. LESSON XIII. First Step — Recitation of lesson prescribed, and examination of the written exercises, and the hearty approval of every point in every scholar that admits of it; especially, the neatness in fold- ing papers, and superscribing their names; neat- ness in the arrangement of the writing on the page; freedom from blots and blurs, etc. 31. Second Step — Imperative Mood. Teacher. — There are three other moods beside the indicative and potential. You will know them by these pe- L PRIMARY TEACHING. 135 culiarities, whidi I shall give you. The imperative mood is used for commanding, entreating, exhort- ing and permitting. It has no subject expressed. Take, for example: ''George, shut the door." Shut, is a verb in the imperative mood, because it is used for commanding, etc. The teacher should give exa-mples of all the different particulars em- braced in the definition of the imperative mood, and then proceed to parse a verb in this mood by the form already given. The class should also parse, individually, and in concert, other exam- ples, in preparation for writing. 32. Third Step — Infinitive Mood. A similar course may be pursued with the infinitive mood, and embracing the signs of two tenses ; to, being the sign of the present tense; to have, the sign of the prior present tense. Fourth Step. -A lesson should be prescribed, embracing the definitions pertaining to the verb, as far as the class have advanced ; also, a parsing lesson, to be prepared, in writing, embracing verbs in the imperative and infinitive moods. 33. LESSON XIV. First Step — Recitation, and Examination of written exercises. Second Step — Yoice. Teacher^ I wish now to explain the most difficult thing to understand, that you will find in the whole subject of Gram- mar. It is Voice. J 136 GRAMMAR. Voice shows the relation of action expressed by the verb, to its subject. If the verb shows that the subject acts, it is in the active voice. If the verb shows that the subject is acted upon, it is said to be in the passive voice ; because, passive means re- ceiving or suffering an action or influence. For example : "George runs." In this sentence, the verb shows that the subject, George, acts; also, in the sentences, "The boy drives the horse;" "The stove warms the room ;" the verbs show that the subjects act. But, in this sentence, " The horse is driven by the boy," the subject is acted upon, or receives the action, or is passive to it. The verb is said to be in the passive voice, because the sub- ject is acted upon, or is passive to the action. Now, you may look at some verbs in the Gram- mar, and tell me, if you can, whether they are in the active or passive voice. Turn to page 118, and take the verbs as they oc- cur in Sentence 37, and tell me whether they are active or passive, and why ? John, you may select the last verb, and tell me which voice it is in. John. Have been happier. Teacher. Susan. Susan. I don't think happier is a verb. Have been, is a verb. Teacher. Right, Susan. John, can you tell me what voice have been is in? John. I don't know. [Hands rise.] Teacher. How many think have been is in the active voice? [Several hands rise.] Teacher. How many think have been is in the passive voice? [Several other pupils raise their hands.] Teacher. How many don't know anything about it? [All PRIMARY REACHING. 137 raise tlieir hands, witli a smile.] Teacher. I seo you don't understand it. I told you that voice was a difficult matter to get hold of. The truth is, that verb has no voice, according to my definition, as it does not denote action. What was my definition of the active voice? [Hands rise.] TeacJier. Mary. Mary. The active voice shows that the subject acts. Teacher. Very well. How many can give me the definition of the passive voice? [Hands rise.] Teacher. Sarah. iSarah. The passive voice shows that the subject of the verb is acted upon. Teacher. Very well. Have been, or the verb to be, and other verbs which do not denote action, ai-e said to be in the active or passive voice, according to their form. If such verbs have the form of verbs, whose subjects act, we will say they are in the active voice ; or, if they have the form of verbs whose subjects are acted upon, we will say, they are in the passive voice.' Now, William, take another verb, and give its voice. William.' Hast been taught, is a verb in the passive voice. Teacher. Why? William. Because the subject is. acted upon. Teacher. Kight. Samuel, another verb. Samuel. Had not found, is neither active nor passive, as I see. It don't de- note action, but that there wasn't any action. He did n't find them. Teacher. Not, is no part of the verb. You may omit not. Now, tt.l me what voice had found is in, Samuel. Sam.uel. The ac- tive voice. Teacher. Why? Samuel. Because it shows, that the subject acted, if you leave out not. Teacher. Very well, Samuel. 138 QKAMMAK. So the class are all called on, individually, tor give tlie voice of one or more verbs. Third Step — Parsing by the form. Fourth Step — Prescribing a Lesson. This should include a review of definitions, for the verb and its modifications, also definitions written out on the blackboard, for voice, active voice, and passive voice. These definitions should be copied by the scholars on to their slates, or on to paper, so that they may have no excuse for not learning them. These definitions are m&t all foun& in any Grammar, M. LESSON XV. First Step — ^Recitation. Second Step — Classes. It will hardly be necessary to go through -with the method of drill for the classification of verbs. The classification which we adopt does not agree with Brown's ; consequently, if that Grammar is used, definitions must be written out on the board. Such definitions may be found in this volume, Part III, Section 60. 35. Third Step — Parsing. The complete form for parsing verbs may now be given ; and the class will need drilling on this form, in connection with the form for pronouns and nouns, for many days — perhaps weeks — in conn©<^tion with written lessons. PRiMAHY TEACniPfG. 139 38. general dibections. The remaining Parts of Speech. The Adjective, Participle, xVdverb, Preposition, Conjunction, and Exclan:iation, may be made sub- jects of lessons, occasionally, to give variety to the drills in parsing verbs, pronouns, and nouns. The adjective would have been introduced more properly, immediately after the nouns, in this course of lessons; but, from its greater simplicity, it was thought preferable to give all the space to the more complex forms and facts involved in the noun, pronoun and verb. 37, THE RULES OF SYNTAX. The most important of these rules will be learn- ed in connection with the drills already given, without assigning special lessons for learning them. Such lessons should, however, be given, sooner or later, and the scholars should be required to give them hy mimher, as they are called for, pro- miscuously, by the teacher. The advantage of this is, that they can afterwards refer to them by num- ber; thus saving much time and labor in the pars- ing lessons, both oral and written. The more dif- ficult rules for construction, as, for example, that for the predicate nominative, should have special drills, and entire lessons devoted to them ; other- vise, they ne^er will be well understood. 140 GRAMMAR. 38. It is an excellent plan to give parsing lessons in the examples of false syntax, furnished for cor- rection in the grammar used, confining the attention of the class chiefly to the words which violate the rules ; requiring, that a pupil, before parsing the word assigned him, correct it, and give the reason for his correction ; then that he parse it in full. 39. HORIZONTAL PARSINa. Much more progress may be made, in a given time, after a class shall have become tolerably familiar with all the parts of speech, by pursuing the horizontal -method of parsing. The First Step, in this method, is to call on the class for the parts of speech, only, as they occi\r in any given passage. The Second Step is to give the class only to which each word belongs; for example, (see Clark's Grammar, pages 104, 119, and 154). Let the scholars, in succession, as they sit, give the classes of the words, as they occur, thus : A, indefinite; man, common ; of, not classi- fied ; a, indefinite ; lively, common or qualifying ; iTuagination, common; has, irregular, transitive, etc. Thibd Step — The cases only, of nouns and pronouns. Fourth Step — The constructions only, of the nouns and pronouns. Fifth Step — The rules only, which apply to the cases of nouns, pronouns and verbs. Sixth Step — The construction and eui^s of all the words, as they occur, in succcession. 1 PRIMARY TEACHING. 14j Much time may be saved, by adopting any one of these steps, which the class may seem most to need. Thus, those points on which the class are well posted, may be laid aside, for the time, and their attention directed, exclusively, to those in which they are found' most defective. 40. GENERAL CAUTIONS. This entire plan demands the exercise of the closest watchfulness, on the part of the teacher, that no material points are omitted ; that nothing, which has once been passed over, should be so long neglected, in the drills, as to be forgotten. The FORMS OP PARSING, for all the parts of speech, should be well memorized, and so frequent prac- tice should be given, in the use of them all^ that no one can be forgotten. Care should be taken, that only one construc- tion be given to each word, except to double rela- tives, which, from supplying two cases, are in two constructions. Nouns and pronouns, in apposition, are too frequently parsed as if also in the same construction as the word with which they are in apposition. The fact of their being in apposition, is sufficient to determine their case, and any other construction would be superfluous. The Predicate Nominative, is not unfrequently parsed by teach- ers who enjoy some reputation, as being in the objective case, and governed by an intransitive t)r passive verb. The scholar should be drilled long, and thoroughly, on this point, till he accustoms 142 GRAMMAR. himself to ascertain that an intransitive or passive verb is used; and, that .the noun after it, means the same thing as the noun before it. In the distinction of personal and relative pro- nouns, there is generally more obscurity and error than in any other part of Grrammar. It arises, in part, from their inappropriate names ; but chiefly, from the erroneous or obscure definitions used for them. A personal pronoun is too frequently defined as one which relates to persons, and a relative pro- noun as one which relates to an antecedent. Both of these definitions are abominable in themselves, and lamentable in their results. In all the parsing exercises, constant care should be exercised in selecting such sentences and WORDS, for drill, as will best exemplify the princi- ples presented. From a want of such care, arise confusion, embarrassment, disgust and discourage- ment. Again ; scholars should neither be required, nor permitted, to parse a word any farther than the class have been taken along together, and a form has bejn given. Note. — The various models found in Clark's Grammar, pp. 104, 105, and 154, may be profitably consulted by the teacher. METHOD OF TEACHING ADVANCED CLASSES. 41. PRELIMINARY REMARKS. Wlieii, by the method described in the foregoing pages, or by any other, a cLass can distinguish all the parts of speech, and parse them in the more obvious constructions, a review of the entire sub- ject should be commenced, with the use of outlines. Some teachers decry outlines altogether, and confine themselves and their scholars to the order and substance of the text-book, or what is worse, to DO order or substance, except to such as appears in gas and vanishes in forgetfulness. My experience is, that classes making use of outlines as guides to investigation, are much more independent, thorough and critical, in their study; and, that they obtain more correct, liberal and comprehensive views from such investigation, than without outlines. Outlines, used properly, will never limit investigation ; but every well-trained pupil understands, that any facts, or principles, or items not provided for in the outlines, must be incorporated into it by himself; and he thus en- joys the satisfaction of an original discoverer. Not only so, but it is an excellent plan to re- quire a class, having used outlines enough to ap- preciate the logic of their arrangement, to make V (143) 144 GRAMMAR. out outlines, eact pupil for liim^olf, and to present tliem, on paper, to the teacher, for examination. Then the teacher may select some one or more of these, for presentation to the class. The pupil will copy his own work on to the board. 42. METHODS OF USING OUTLINES. First 3fetliod. Instead of assiornins: a given o o o number of pages, in the text-book, for scholars to study, for recitation, an outline of a subject may be copied on to the blackboard, by one of the pu- pils, from a manuscript prepared by the teacher. The class will all copy the outline on to slates or loose paper.* It is then expected, that at the next recitation every pupil will be prepared to give the whole of the outline on the board, entirely from memory ; also, any definitions, explanations, and applications, that the outline or the subject may call for. The teacher does not, ordinarily, call on one individual to write out the whole outline, but distributes it in such portions, as may be conveni- ent, to different pupils. These portions, so as- signed, they may write, immediately, on the board ; and describe them, when they are again called on, by the teacher. After having assigned the differ- ent topics of the outline, to the ctass, (and each of the topics, if the class is large, may be given to several different scholars,) the teacher may occupy any time, before scholars who have had topics as- signed them are ready to report, in examining oth- ers, who have had no topics assigned them, orally, by questions*; or, by proposing topics for them to ADVANCED TEACHING. 145 discuss, witliout having written any portion of the outline on the board. Such a course would be ne- cessary, with a large class and a small blackboard. Teachers using outlines, should not lay aside the ordinary methods of assigning lessons, and of recitations, entirely. They may adopt this method of reporting, occasionally, in advance lessons; al- ways in review lessons; or, as the nature of the subject, and the aptitude and discipline of the pupils may require. 43. Second Method. An outline may be assigned to only one pupil, for him to use in investigating and mastering a subject. He will be expect'ed to give his report, on that subject, at the next recitation, either without the written outline before him, in any form, or with the outline written on the black- board, from memory/, in presence of the class. In the latter case the pupil, in* giving his report, takes his place, at the board, with the pointer, and directs the attention of the class to the several topics, sub topics, and distinct items, as he ampli- fies them with definitions, explanations, exemplifi- cations, illustrations and applications. These may be drawn from books, or from the pupil's own ex- perience and observation. It is perceived, that the scholar thus obtains the power, almost unconsciously, of speaking system- atically, and, at length, on any subject that he may have properly and thoroughly investigated. To such pupils as are the best disciplined, advance suhjeds may be assigned, without outlines. It is 146 GRAMMAR. tlien expected that tliey will prepare their own outlines, and present them, as their own, on the blackboard, at the time of giving their report. A definite time should be appointed, for giving the report; also, a definite amount of time, in which to give it; as five minutes, ten minutes, or fifteen minutes, according to the age of the pupil, the time occupied by the whole recitation, and the demands of the subject assigned for investigation. The most interesting public examinations that I have ever attended, have been conducted on this plan. Special subjects were assigned to individual pupils, on which to report or deliver lectures before the public audience. The audience, of course, are informed of the plan adopted, in the preparation for the examination ; and, that it is not designed so much to exhibit the scholars' knowledge of the branches generally, as to test their mental power in grasping a subject, and in communicating their views under embarrassing circumstances. The audience should be urged to criticise the pupil, during the delivery of his lecture. Other pupils also, especially members of the same class, should consider themselves free to criticise, to correct misstatements, or to fill up omissions. 44. METHOD OF CRITICISING REPORTS. The scholars should do most of the criticising. They will learn much more by criticising than by being criticised. But system should be secured in these criti- PRIMARY TEACHING. 147 cisms; or nothing definite, or satisfactory, will be accomplislied. The order to be followed may be this : at the conclusion of a report, before the pupil reporting has taken his seat, the teacher may call on the class for criticisms, on — 1st, Pronunciation ; 2d, Spelling; 3d, Arrangement of the Outline, includ- ing, also, omissions or repetitions; 4th, Defini- tions ; 5th, Promiscuous matters. Lastly, the teacher makes any additional criti- cisms, remarks, or explanations required. The pupil having a special subject assigned him, is, of course, excused from preparing the lesson as- signed to the class. By giving the subjects, in order, to difierent pupils, on successive days, reviews will be accom- plished in a manner more interesting and impres- sive than in that generally pursued. The subjects having been passed over once in review, as far as the class have advanced, the same order may be pursued by other pupils, as by those who first had them for special study and reporting. 45. Ordinary Method of conducting a recitation with an advanced Grrammar Class. The teacher has a register for this class as for all others. He calls the names of the pupils, as he finds them in his register ; sometimes in the direct order, sometimes in the inverse order ; sometimes in the direct order, omitting alternate names ; then in the inverse order. By this method of calling on the members of a class, he secures uncertainty, r 148 GRAMMAR. on the part of a pupil, as to when he may be called on ; and, certainty, on his own part, that no pupil is neglected in the recitation. He grades each pupil as he recites ; which grading shows who has been called on. A scholar's name being called, he rises, and the subject of a section is proposed for him to discuss. If he should fail to reach all the matter of the section, the teacher will reach his knowledge or ignorance of those points, by questions. In the case of parsing, or correction of false syntax, the pupil, when called on, rises and parses the word, or corrects the sentence, without inter- ruption from the class; but when he concludes, the teacher calls on the class for criticism, by pro- nouncing the word "Class." Other pupils, who have criticisms to offer, raise their hands, and are called on, by name, separately, to give them. The teacher will call on those first, who are generally the least inclined to offer criticisms. He will also call on any pupil, for criticisms or corrections, who is seen to have remitted his attention or interest in the recitation. Such criticisms are given, by the pupil, sitting. No pupil, when standing, resumes his seat, without permission from the teacher. It is well, in case a pupil fails in a topic or question proposed to him, to pass it to the next pupil, and if he fails, to call on the class. That being dis- posed of, a second topic or question is proposed to the scholar first having failed; and so on, till the teacher is satisfied, as to his grade, for tha recita- tion. l: ADVANCED TEACHING. 149 46. OUTLINES. RemarJc. The following outlines are accompa- nied only by the definitions of such words as, I conceive, are inadequately, or incorrectly defined, in most G-rammars. It is not supposed, that this number of The Normal is to be used as a text-book. But, it is hoped that both teachers and scholars will find it serviceable as a reference book, in their daily preparation for recitations. 47. GENERAL OUTLINE OF GRAMMAR. Remark. This outline was introduced, in Part 11, page 49, and the definitions and explanations given, in connection with it, for the purpose of keeping the chain of Outlines unbroken from the General Outlines of Knowledge, in Part I, to those of Orthoepy and Orthography, in Part II. OUTLINE OF ORTHOGENY. C Noun, extended on page 150. Verb, " « 157. Pronoun, « " 162. Orthoottnt J Adjective, URTHOGENT, ^ Participle, Adverb, 1 Conjunction (. Interjection or Exclamation. 48. DEFINITIONS, EXPLANATIONS, AND REMARKS, Orthogeny. For definition, see Part II, page 45, section 9. For definitions of the parts of speech, see any text-book in general use. 49. 1 OUTLINE OF THE NOUN. .H-Sl § tf « S ,2 eS u £ '^ ^Of^ 2 a fe" T""^ .'a -§ Q> c S c 'H s a •^ «3 s fcO« fc. u a >>>>> aj ^ ^ ? s « 2 ^o ^-pqMM S) a "^ e .9'5 3 '5 i^ J- ^ S g 1 -a J Collective and Verbal and no Abstract and ( DiminQtive ac 1 Singular, 1 Plural. if forming the P ( Masculine, Fei I Common, Neu I of Feminine, • [ 1st, 2d, ! 3d. tended on next (2 o o " « « w» &. - « .. .2 « s < ^ s -? S 11 S^ o "3 ft . ^® &,a *>^^ >>>> JS| ^ ^' . ' (3.2 a S -»f ^ C3 fl 83 t3 a 3 R<< •Jf \ f ft ilg-.^S ■^ E. •e wj £ " '-3 ^-« o a noun of diffe a noun of same e as the nomina iiii- a transit an inf ir a prepos dicate, on, nt. iting iting Sam Object of Subject of Object of In the pre In apposit Independe a a-r' tfiS •.as g CCP. g ts o 152 GRAMMAR. 50. DEFINITIONS, EXPLANATIONS AND REMARKS. Noun — A name. Remark. Terms inclnde all those teclmieal words necessary to an understanding of the sub- ject, and not elsewhere introduced into the outline. They should all be defined, by the pupil, in giv- ing a report. Classes. Results of an arrangement of similar things, according to some definite plan Remarh. The sub-classes of common nouns are only noticed in parsing, when the noun falls into one of the sub-classes in the first vertical column. Modification. Any form or condition of words, used for grammatical distinction. 51. CONSTRUCTIONS. Construction.. The method of framing a word into a sentence or phrase, by which it acquires any given modification. Remark. Examples of nouns, in some of the more difficult constructions of the several cases, will be given, in which I differ somewhat from both Clark and Brown. 52. Nominative in - •< [to] follies) ( have committed | ^°'°p (That) f desire | my ((That) [desire I my he tJ ( (*'^^*^) is dishonest 1 ^^ 1 ^^^ is manifest. \ ( may ir improve. COMPOUND SENTENCE. J (that exTiect i^^® (^"') i ^ e*P ^ 1 ^m come ) intend I to return 81. EXPLANATIONS. 1. Sentences and elements of the same rank, stand in the same vertical column. Hence, in the analysis of a sentence, the principal elements stand ADVANCED TEACHING. 175 in the first column ; subordinate elements of tlio first degree stand in tlie second, and so on. 2. To prevent a subordinate sentence from ap- pearing like two elements, it is preceded by a brace. 3. Words supplied, to make out a construction, are enclosed in brackets. 4. Words not forming a part of the construction, although expressed in the sentence, are enclosed in a parenthesis. Such words are conjunctions, and independent forms. 5. Words having a double use, have a line drawn under them. Such words are relative pro- nouns, since they are used as connectives and pro- nouns ; also, conjunctive adverbs, since they are used both as connectives and modifiers. 6. Double relatives must be separated into their two parts, in written anaylsis ; since the antece- dent part belongs in the principal sentence, and the relative part, in the subordinate. 82. ABRIDGMENT. DEFINITIONS, EXPLANATIONS AND REMARKS. Abridgsient. That? part of analysis which treats of contracting sentences, by rejecting con- nectives, suppressing subjects of verbs, and chang- ing the verbs from the finite moods to infinitives and participles. Abridged Sentence. One whose verb is an in- finitive or participle. Substantive Abridged Sentence. One that is used as the subject or object of a verb. 8* 176 GRAMMAR. Adjective Abridged Sentence. One tliat is used to modify a noun, pronoun, or substantive clause. Participial Abridged Sentence. One whoso leading word of construction is a participle. Infinitive Abridged Sentence. One wLose leading word of construction is an infinitive. Absolute Abridged Sentence. One whose leading word of construction is the nominative case absolute. Method of Abridgment. Remove the connec- tive, change the finite verb to an infinitive or par- ticiple, and suppress the subject, provided it is the same as that of the verb in the principal sentence. ORDER OP ANALYSIS. 1st, Analyze in the abridged form. 2d. Expand the sentence by supplying the connective and sub- ject, and changing the mood of the verb to a finite mood. 3d. Analyze in the complete form. Remarh. In written analysis, these two forms of the subordinate sentence, njay be connected by a curving sign of equality. ]NJoTE. — Teachers, who use Clark's Grammar, -will find the various sentences classified and exhibited with great precision by the use of his System of Diagrams. PAKT IV. METHODS OF TEACHIJSfG GEOGRAPHY. INTRODUCTION PROPER AGE FOR COMMENCING THE STUDY OP GEOGRAPHY. As soon b.3 the child is able to read well enough to obtain ideas from what he reads, in as difficult a class of sentences as those found in the primary Geography, proposed to be used, it is desirable that he have the advantages of the variety which the Geography will give to his reading lessons. It would be folly, of course, to set such a child t\) studying a book designed for higher classes. It is a great mistake to keep a child confined to one book, whether Speller, Pieader, or Geography; or to keep him confined to books entirely ; a slate and pencil are indispensable concomitants of books, from the first. ORAL INSTRUCTION BEFORE THE BOOK. I may repeat here, what I said in reference to Grammar. No lesson should be required of a young pupil, in the text-book, till he has had a preliminary drill, and the teacher is satisfied that he can comprehend the subject, so far as the les* son in the text-book extends. (179) 180 vJEOGRAPHY. NECESSITY OF APPARATUS IN TEACHING GEOGRAPHY. Some teachers 'suppose, that apparatus is only necessary in High Schools and Colleges ; others, that it does not belong to them to purchase it; and multitudes of others do not know what it is, and would not know what to do with it, if it were placed in their hands. This is obvious, from the manner in which the apparatus, furnished by the State of Ohio, has been abused, neglected and de- stroyed, in the large majority of schools, where it has been placed. " It is of no account," says one. " I don't know what to do with it," says another. " Take away your fly-traps," says a third. " Them things will do for play things; I don't know what other use to make on 'em," says the fourth; and so on through every variety of ignorance and stu- pidity. Of the twenty thousand dollars' worth of appa- ratus supplied to the schools by the State of Ohio, if at this time all that remains in our country schools were put up at auction, to be bid for by the teachers who have used the apparatus, I doubt whether one hundred dollars would be offered for it. Such is the lamentable ignorance prevalent among teachers in this direction, that Normal In- stitutes should be established in every county, to be in session long enough to instruct every teach- er, at least, in the use of the blackboard and globe, and then no certificate should be granted to any one who could not show a good degree of facility *n applying the illustrations. INTRODUCTION, 181 I say, then, that a globe is indispensable to the correct teaching of primary classes in Geography. I know of a child who had learned Parley's little Geography, " by heart," at school and could repeat it from one end to the other, who, when she saw a small globe, in her father's hand, as he brought it home, addressed him thus : " Pa, what is that round thing in your hand?" The father replied; ^'It is a globe, Fannie." ''A globe? What is that?" " Why it shows what' shape the world is." " Why, Pa, is th« world round like that?" ''Hav'nt you repeated a hundred times, the world is round and like a ball flies swinging in the air?" " Oh, yes, Pa, but I never knew 'it before." If that girl's teacher had had a globe, she would not, probably, have known what use to make of it. A globe of the most convenient size only costs a dollar. . If the teacher has n't a dollar to buy a globe, and cannot borrow it, he ought to make one, or make use of an orange or an apple ; or, if he cannot spare those, for such a purpose, he might use a piece of chalk, a potato, or his fist. OBJECTS TO BE AIMED AT IN TEACHING PRIMARY GEOGRAPHY 1st. Learning to Study. Study is necessary to any desirable progress in learning to read ; for if the scholar only reads while he is engaged in his class, he can only be familiarizing his eye with the forms of words some fifteen or twenty minutes, at most, during the day ; while the scholar who studies^ — 1 -. I i 182 GEOGRAPHY. may be engaged in the same operation seyeral hours each day. The progress of the latter will be more than proportionally rapid and satisfaciory. 2d. Learning to Draw. The use of the hand and eye, in drawing, is conceded, by all intelligent Educators, to be an important aim in the education of every person. The drawing of Maps, on the slate, blackboard or paper, is an easy and excellent introduction to the art. Map Drawing also impriats the local geography on the mind, more correctly and permanently than any other method ; it also affords the necessary va- riety to school exercises, to make them healthful and pleasant. 3d. Learning to Read. The consideration af this object has been forestalled in discussing the others. 1 will, however, add, that since Geography may be made more interesting than any reading lesson^ it will more thoroughly arouse the pupil to voluntary effort in the preparation of his lessons, which, of course, will secure more rapid advancement in intel- ligent and intelligible reading. ' V^ 4th. Learning Geography. This is a worthy object, but less in importance, in my estimation, than any other mentioned, at the age at which a scholar should commence the study. METHODS OF PRELIMINARY DRILL. Many of the following pages will be given to the various plans to be adopted in preliminary drills, involving the use of the globe, of the black board, of the neighborhood and township; and of any INTRODUCTION. 183 travel that the scholars may have enjoyed, for il- lustration; also, of maps both small and large. METHODS OP CONDrCTING RECITATIONS. The methods of conducting recitations have been BO fully explained and exemplified, in the preced- ing branches, that comparatively little attention will be given to them in Part lY. METHOD OF USING PART IV. The teacher will consult it, in his daily prepara- tion for his classes. TEXT-BOOKS USED. Monteith & McNally's series of Geographies are highly recommended as the best now before the public ; and I shall refer to them continually, in the following pages, for the material of illustration and exemplification in the methods described. OBJECT LESSONS. In connection with the lessons in Geography, it is well for a teacher to make use of various objects^ not only for illustration, such as globe and maps, but of common things, such as corn, wheat, ap- ples, woods of various kinds, etc.; also to bring before the class, the productions of fereign coun- tries, or to induce the scholars to do so. Such objects serve by suitable conversation, to aiouse thought, to train children to observe, and to oud- nect hooh lessons, with existing thinos. METHOD OF TEACHING GEOGRAPHY TO PRIMARY CLASSES. 1. PRELIMINARY REMARKS AND EXPLANATIONS. Remark 1. The class should be able to read the simple style of the Primary Geography used, in- lelll gently; not necessarily, fluently. They should all be provided with some Primary Geography, and all with the same kind. Remark 2. The teacher should be provided with a five-inch globe, at least. Such a globe, mounted on a stand, can be purchased for one dol- lar. It would be well for the teacher to provide himself also with maps of the town, township, county and state, in which his school is situated. Remark 3. It is understood that Geography is the first branch of science, to which the jDupil is introduced ; that it comes in connection with a Second or Third Reader, but does not displace it. 2. LESSON I. First Step — How to secure Books. The teacher having called a reading class to the recita- tion seat, ascertains how many have Geographies, and how many have the right kind. He finds the children wide awake with the idea of taking up a (184) l_ PRIMARY TEACHINa. 185 new study, in a new book. It is only necessary for him to say, tliat tliose who can obtain the book used by the class, can study Greography, and that it will be impossible for others to join the class. He will then inquire how many there are who think they cannot get the book. If any, he should visit the parents, or write a note and send it by the hand of the pupil, who will use all a child's eloquence, in connection with the note, to obtain the desired book. The child will not fail, unless the parent is absolutely too poor or too drunken to purchase it; in which case, the teacher should sup- ply the book himself, or apply to the Directors, or other benevolent individuals, to do it. No child will be permitted to remain behind his class, from poverty, by the True Teacher. 3. Second Step — Exciting an Interest. Teacher. You have new G-eographies, some of you ; by to- morrow, I hope you will all have them. You see it is full of pictures and maps ; and reading that tells you about the pictures and explains the maps. Q-eography is a very interesting study. Why, see ; here is the picture of the Natural Bridge, which is ten times as high as this house, and is one solid rock. A boy once climbled to the top of it, by cutting steps, with his jack-knife, into the rock. When he got up so high that he could n't jump down, he tried to go down by his steps, and couldn't doit, without falling; then all that he could do, was to try to cut his way to the top of the bridge, several hundred feet. Bo you suppose he 1S6 GEOGRAPHY. ever readied the top? He did, and all the people, for miles, had collected on the bridge to see him. Then, here is a picture of Bunker Hill Monu- ment, where the British soldiers were mowed down by the bullets of American farmers and me- chanics, when the British wanted to make slaves of them. Here also, are beautiful pictures of a great many fine buildings and large cities. By studying Geography, you will find out all about them. Is not Geography an interesting study? 4. Third Step — Explanation of Maps. Teacher. Now, I want to show you about these maps, that are painted so prettily. See, here is the map of the Western Hemisphere. How many can tell me what a map is for? [Hands rise.] Well, John, what do you think a map is for? John. (^Hesitat- ingly.^ Maps show how the countries look. [Several hands spring up.] Teacher. Isaac. Isaac. I don't think the countries look that way, all red and yellow. Teacher. No ; the country is generally green in the summer. Maps are not designed to show the color of countries, but their shape on the surface of the earth. Here, I'll draw a map of our school yard for you, on the blackboard. [Teacher draws.] See, here is where the front fence runs ; here are the side fences. Now, where shall I put the school-house? Here? Where the wood-house? Here? And, here the pump stands ; and here the outhouse, and here the walk to the gate, etc., etc. In the same way I could draw a map of the town, and could shew PRIMARY TEACHING. 187 you, on tbe map, where each one of you lives. How many would like Jo learn to draw maps? [All hands come up.] Well ; I will show you to- morrow. 5. Fourth Step — ^The Globe. Here is a Globe. It is designed to show the shape of the Earth, in which we life. Yo'U see it has maps on it. Now, I can show you where the country is, in this globe, on which you live. See, here is North America, and here are the Great Lakes, and just about there, [sticking a pin,] is where you are now. This globe is five inches in diameter, or through it ; and fifteen inches, or a little more than a foot, in circumference, or around it. How large do you suppose this great ball is, on which we stand? (^Stamping.') Why, it is eight thousand miles through it, and twenty-five thousand miles around it, and it takes a whole year to travel round it. Perhaps, some one of you knows some person that has sailed round the world. G. Fifth Step — Assigning a Lesson. Teaclier. You may now open your books, those of you that have books, to this picture of the Earth, and we will see if we can read Lesson I. I will read the fine print, and you may read the coarse print. All look on, now, and see if I read right. [Teacher reads.] "What is the planet, on which we live, called?" John you may read the coarse print. [^Jolm reads!] "It is called the Earth." Teaclier. Very well. You see that the coarse 188 GEOGRAPHY. print answers the question in fine print. I will read the next question. [Reads.] "What is the shape of the Earth?" Mary, you may read the an- swer. 3£ary reach. "It is very nearly round." Teacher. Now Samuel, you may read the next question. Samuel reads. "Do we live on the out- side or inside of the Earth?" Teacher^ Susan, you may read the answer. Susan reads. " On the out- side." Teacher. Very well. Now you all see how to read this. I wish you to read over the questions and answers, so many times to yourselves, when you go to your scats, that you can give me the an- swers without looking on the book, when you come to me, to recite to-morrow. How many of you think that you will be able to answer all the questions in Lesson I, by to-morrow morning? [All hands rise.] Very well. You may take your books home to-night, if you have a mind to, and study your lesson at home ; I shall not be surprised if you get two les- sons, but I shall only hear you recite one. You may go to your seats now, in order. 7. LESSON II. First Step — Have all Books? Teacher. — How many have books today? [Books rise.] If any have not yet got the books, the teacher decides in his own mind, how they may be provided, and informs the scholars deficient, how it can be done. 8. Second Step — Recitation. The teacher having enrolled the names of the pupils in his register, calls from the register the name of one pupil ; say, PRIMARY TEACHINa. 189 Amanda. [Amanda rises.] .Teacher. [With Globe in his hand.] "What is the planet, on which we live, called?" Amanda. " It is called the Earth." Teacher. Very well. Amanda is excused. James, [James rises.] " What is the shape of the Earth?" James. "It is round." [Hands rise.] Teacher. Sarah. Sarah. " It is very nearly round." Teacher. Eight, Sarah. James is excused. Remark. Scholars, when offering criticisms or corrections, do it sitting; but- never without per- mission from the teacher. Teacher. I will. ask you all a question not in the book. Is the earth round, like a plate, or like the stove pipe, or like this ball? How many can tell? [Hands rise.] Maria. Maria. It is round like a ball. Teacher: Then it is a ball, is n't it? How deep must a hole be, to go" through this globe, right through the center. [No hands rise.] — Teacher. Five inches. But how deep would a well have to be to go down through the Earth, right through the center? [No hands rise.] How far through did I say the Earth was, yesterday? [Some hands rise.] Henry. Henry. Eight hun- dred miles. Teacher. Eight thousand miles ; and how long would it take to go through such a well or tunnel, if you could go in a railroad car, with the speed of thirty miles an hour? Well, it would take more than twenty days, traveling twelve hours a day. That would be a long journey, in a tunnel, would n't it? Thus the lesson is pursued, by proposing the J 190 GEOGRAPHY. questions, in the book, till all tlie Sv'holars have been reached, one or more times. If any scholar fail on one question, he is tried on another; and then on another, till the teacher satisfies himself as to the amount of study the scholar has be- stowed on his lesson. He is then graded, accord- ingly, in the register. 9. Third Step — Drawing on Slates. Teacher. I wish you to draw this map of the Western Hem- isphere, on your slates, for a part of your next les- son ; and bring your slates when you come to re- cite. I will draw it for you, on the blackboard. The teacher first draws the circle by taking, a string as a radius, holding one end, in one hand, stationary, on the board ; the other end, wilh a piece of chalk, in the other hand, he carries around on the board, forming the circle. He then draws the continent, with the general divisions, prints the names, and makes a dot, in a small figure, rep- resenting his own State, in the map. The children are thus encouraged to do what they see done, and perhaps will even try to excel the master, in drawing a map. He requires them only to draw the outline for the first lesson. 10. Fourth Step — Dismissing the Class. The next lesson being assigned, and the grades of the class being read aloud for their encouragement or incite- ment, they are dismissed f- cm the recitation seat, in order, by calling their numbers, as written in the class register. PRIMARY TEACHING. 191 11. LESSON III. JFirst Step. The teacher examines the slates, points out the excellences and errors of each draw- ing ; gives his attention to the evenness of the curve ; the shape ^nd position of the countries ; the size and regularity of the letters in the print- ing. He finds several of the class who could not make a circle, and so failed of doing anything. Instead of scolding thorn, or making any discour- aging comparisons, he takes a slate and makes a circle ; then tells all the scholars to make one. He then proceeds to draw the map, on the slate, re- questing them all to follow him on their own slateSj as he draws, holding his slate before the class. Thus by encouragement, by aid judiciously given, map-drawing is fairly commenced, and will not be laid aside, till the study of Geography is abandoned. It will be well to include the consideration of map -drawing, in the grading. Second Step — Recitation. Third Step — Assigning the next Lesson, in- cluding the drawing of the same map, with the gulfs and lakes, in addition to the outline of the continent. 12. LESSON IV. First Step — Examination of Drawings. Second Step — Recitation. This recitation should be conducted, with the globe in the hand of the teacher ; and the scholars should be called 9 192 GEOGRAPHY. upon to decide wliicli is land and wliich is water, on the globe ; also wliicli is tlie Western and wliich is the Eastern Hemisphere, and the Northern and the Southern Hemisphere, on the globe. In fact, the globe should be constantly in use, in every recitation, to give correct ideas of the rel- ative size of countries; their true direction from each other, which never can be obtained from maps. Third Step — Assigning next Lesson, including another drawing lesson. It may be the same map, with the lakes, seas, islands, and all the details as far as given. 13. LESSON V. First Step — Examination of Maps. Second Step — Recitation. Third Step — Points of Compass. The teacher should be careful, that the scholars get clear and correct ideas of direction, not only on the map, but on the Earth itself. He should begin with the school-room, and have the class understand defi- nitely the four cardinal points of the compass, in the school-room. The pupils should obtain them from the rising and setting sun. He should also use the globe, in this connection, and show how these directions lie on the globe. Having explained the eight most important points of compass, in connection with the globe, the teacher proceeds, somewhat thus, in question- ing the class. Teacher. (^Holding the globe in his hand.) — - Which way is North America, from South Amer- PRIMARY TEACHING. 193 ica, on tliis globe? You may all answer together. How many of you can point towards South Amer- ica, on' the Earth? As many as can, may do it. Which way is Europe from North America, on the globe? Now, if you were about to start for Europe, which way would you travel? "Which way is Asia from North America? The scholars give various answers. One says East ; another. West ; another, it is on the other side, etc. Teacher. You may point now, if you can, to- wards Asia. The class have the same difficulty in pointing as in telling the direction. Teacher. If a fly were walking on this globe, which way would it go from North America to raach Asia. All together. Class. East, West, (in covfusion.) Teacher. Would it not reach Asia, if it should walk, continuously, in any direction? East, West, North or South? Then, which way would you go on the Earth's surface, to reach Asia? But, you may now point directly towards Asia, without reference to traveling. Most of the scholars point downwards. Teacher. Some of you are right ; Asia is ou the other side of the Earth, but not directly oppo- site to us. If a hole were dug down through the Earth, where would it come out? Class. In Asia. In the ocean. 194 GEOGRAPHY. Teacher. Some of you are right and some wrong. A hole would not come out in Asia, if dug directly down ; it would have to be inclined somewhat towards the north. Do you think a person, in going through such a hole or tunnel, would come out head foremost or feet foremost in Asia? Such a hole will never be made, but the people, in Asia, stand with their heads pointing nearly in the same direction that our feet do. Thus, no pains should be spared to connect the words of the hook with the ideas of existing things. The great and crying evil of teaching, is, that hooh knowledge is kept isolated from real knowl- edge ; and the evil, generally, begins with the first lessons of the child, and ends with the last lessons of the collegiate graduate. 14. LESSON VI. Conclusion of Primary Teaching. I shall conclude these explanations of Primary Teaching, by a few general remarks. Remark 1. The most common phenomena, as the rising and setting of the sun, should be ex- plained to a primary class, from time to time, in order to give interest and variety to the study. Remark 2. The globe should be kept con- stantly in hand, that no erroneous impressions may be derived from maps, with regard to the true position of places. Remark 3. The same map should be assigned to the class, for drawing lessons, several days in succession . They should only be required to draw PRIMARY TEACHING. 195 the outline, on tlie first day. Then, in successive days, they should make new drawing's, embracing all the work of the previous days, and should add, in order, first the larger bodies of water, and islands, if any; secondly, rivers and mountains; thirdly, boundaries of political divisions ; and, lastly, localities of cities and towns. The printing of names should keep pace with the other work. Remark 4. The drawings may be made on pa- per, after a sufficient practice on slates. Drawing, of course, will not be confined to maps ; though every map in the book should be so learned, that the scholars can go to the blackboard and draw it, without looking on the book, at all, while drawing it. Remark 5. The teacher should instruct the class to look out the pronunciation of the geo- graphical names in the vocabulary, at the end of the book. Remark 6. Frequent reviews should be taken ; sometimes, by the maps; sometimes, by outlines, prepared by the teacher; sometimes, by asking promiscuous questions on the matter passed over in one week. Scholars should have opportunity to prepare themselves for reviews, as well as for advanced lessons. A wide awake teacher will ex- cite more interest in the review lesson tli?n in the advance lessons n METHOD OF TEACHING INTERMEDIATE CLASSES. 15. PRELIMINARY REMARKS AND EXPLANATIONS. Remark 1. The class should be able to read the style of the Intermediate Geography, intelli- gently and fluently. They should be able to write a legible hand, with facility ; and should be train- ed in the use of the dictionary, in ascertaining the pronunciation, spelling and meaning of words. They should, of course, all be provided with dic- tionaries, either Webster's Academic, or Worces- ter's Comprehensive. Remark 2. The teacher should be provided with a five- inch globe, and a set of Outline Maps. Instead of Outline Maps, the teacher can make use of any maps whatever, of large size, situated so far from the class, that the names cannot be recognized. The beautiful Maps in McNally's Geo- graphy are well adapted to this use. The pupil can draw a series of outline maps of a larger size, making use of McNally's maps for his guide (omit- ting all the small cities and towns), and introducing the course of rivers and all boundary lines — and when finished, tack them to the wall, or blackboard, for class exercises, (196) SECONDARY TEACHING. 197 16. Remark 3. It is supposed, tliat those wTio study Intermediate Geography, are also studying Arithmetic, Reading and Spelling. Remarh 4. In graded schools, a half hour should be devoted to this recitation. In ungraded district schools, not less than fifteen minutes are required to arouse any degree of interest that will be profitable in the least. Remark 5. Some teachers require their pupils to purchase "Topic Books," at an expense nearly half as great as that of the Geography. I think all the advantages of Topic Books can be secured without them, and more. Instead of the pupil's using a Topic Book, when he is learning his les- son, and reciting, he will do better to write on pa- per, or on his slate, the topics of his lesson, when he is studying; and use- them in the recitation, in the manner described below. All speculations in books, and, especially, in those which are not in- dispensable, are likely to raise complaints from parents, and to impair a teacher's influence. Should a teacher introduce any books whatever, he will find it a matter of economy to furnish them to his scholars at cost. • 17. • LESSON I. First Step — Topic Lists. Teacher. My young friends, we commence, to-da}^, in a new Geogra- phy. You will pursue a very difierent course, In this work, from what you did in studying the Pri- mary Geography. I was accustomed to ask you 198 GEOGRAPHY. tlie questions, in that book, and you to answer them, in the very words of the book. I shall not ask the questions, in this book, but wish you to prepare Topic Lists, when you study your lessons, and to recite your lessons from them. I will write the first one for you, on the board. [He writes.] GeograpTiy? Earth? EariKs Stirface? Land? Water? Natural Divisions? Artificial Divisions? Political Divisions? Mathematical Divisions? Phys- ical Geography? Includes ivhat? Political Geogra- phy? Includes what? Mathematical Geography? Includes what} Divisions of Geography? I will let this Topic List remain on the board, and you may copy it, on to loose paper, or into your writ- ing books, in a very neat style, and study your lesson by it. Kome of the topics you will find discussed or explained, in the coarse print, in the answers of the book; arid some of them, in the fine print, in the questions. 18. Second Step — Explanation of the Method op Reciting. Teacher. Children, when you come to recite, I shall ask you no questions. But, I wish each one to bring his Topic List, and to re- cite from that. I shall give each of you an equal amount of time, to recite in ; and we will see who can go over the most ground, and in the most cor rect manner. 19. Thikd Step — Concert Exercise on Map ani> Globe. Teacher. We will now take a short exer- cise on an Outline Map. SECONDARF TEACHING. 199 The teaclier places a Map of the World, in a conspicuous position, and calls on the class to go over with him, in a concert exercise, the principal fcodies of land and water ; also, the H-emisph^jres, Eastern and Western, Northern and Southern. In the concert exercise, the class give each name twice, as they proceed; that, at the second pronun- eiation of the word, all may join in. When it shall be found that all can harmonize, in the concert exercise, as the teacher only points to the different localities, a scholar may be called \ Materials T , , ( How situated? rr-n [thrown out? Island, I How surrounded? °'"' ■o . 1 ( How situated? -.r ,, Peninsula, j jj^^ surrounded? ^^"^^' S -^ T Au \ Connects what? -n «. J-i Isthmus, i Lies between what? ^^^^'^^ (^ s Projects from what? ou >^ ^- CaP«' 1 Projects into what? ^^^^^^^' ,, . . ( Where situated? >^ .9 Mountain, j Extending in what <^°^^^^ (^ [direction? Teacher. In studying your lesson, by the topic list, you will learn the definitions of all the natural divisions, as continents, islands, etc.; then you may look out three such divisions, on your map, and describe them as the topic list requires. For instance, when you come to Isthmus, you 208 GEOGRAPHY. will learn tlie definition as you find it in the book. Then you will find an isthmus on the map of the world, or any other map, and describe it, by telling what two bodies of land it connects, and what two bodies of water it lies between. Then find two more, and prepare yourselves to describe them, in the same way; and so of all the natural di\dsions of land. You may also, each one, prepare yourselves to draw, on the board, without any map before you, some continent, island, peninsula and cape ; so that the rest of the class can tell what division you have drawn. You will practice in drawing these on your slate. 30. LESSON IX. First Step. The teacher will assign some kind of natural division of land, to each pupil, for draw- ing on the board. If the board is not large enough,, some of the pupils may use slates. Second Step. While the oJass are thus engaged in drawing, the teacher will call on individuals, in succession, from his register, to recite their lesson from the topic list, the scholar having the topic list in hand, but using it as little as possible. Third Step. When all have thus recited, return- ing to their drawings, as they are excused, from the topic list, each drawing may be examined thus: Taking, for instance, the drawing of some one, who was required to draw an Island, the teacher Bays : How many can tell what island? As many as can, may raise the hand. [Hands rise.] Teach- SECONDARY TEACHINa. 209 er. Mary. Mary. Madagascar. Teacher. How many agree with Mary? [Hands rise.] How many disagree? [Hands rise.] Susan, what do you tliink it is? Susan. I do n't know ; I don't think it is Madagascar. It runs East and West ; Madagascar r^ns Nort^k and South. Teacher. Well, H-enry, you drew this : what did you design it for? Henry. Cuba. Teacher. It is quite similar to Cuba, both in direction and shape. In this way, each drawing may be examined and criticised. 31. First Step — WRrmsrG Topic List, ^1^ 0EOGRAPHT. You will pursue the same course, in prepariirg this lesson, with these topics^ as with those of yes- terday ; also, m drawing, LESSON X. First kStef^ — A&sign-ino ]>ivisk>n& ©f Water FOR Drawing. Second Step-— Regitatio^n. Third Step — ^Assigning a Les&on, ^011 will next take a lesson on the Map of North America. I wish you to practice, in drawing Nqrth America, so that you can draw the )x)undane& of all the countrie-s in it, and locate the capitals. You need^ not draw the bodies of water any farthei* than they form boundaries. You may also prepare ycurseWes ta give the boundaries of the countries, from the outline map, either before you have drawn them, or after you have drawn them ; also, to give the name of the capital of each country, 3S, lesson xi. First Step^ — Dra-vving the Maf of North America, either on the board or on slates. Second Step — Becitation. While the class are generally engaged in drawing, individuals are called on, successively, to give the boundaries of North America, and each of the countries; also, the capital of each. Third Step — Assigning a Lesso'n. Teacher. For your next lesson, you may practice, in draw- ing the outline of North America, and the princi- SECONDARY TEACHING. 211 pal islands, peninsulas, capes, and mountains; also prepare yourselves to describe them by the topic lists, I gave you, a few days since. How many have the topic lists? [Hands rise,] John, you have the topic lists ; you may write, on the board, the topic list for natural divisions of land. Su- san, you may write the topic list, for natural di- visions of water, on the board. Now, those who have lost them, can copy them, and then, I hope, ibey will copy them into their Topic Books. GENERAL DIRECfiaNS FOR THE STUDY OF COUNTRIES, EMPIRES, EINQDOMS, AND STATES. Remark. I do not deem it advisable to confine scholars, for any lesson, exclusively to map studies, as is proposed in Monteith & McNally's Geography, I would make map-studies a part of every lesson, in connection with every country, empire, king- (i'.offi, or state. 34. Direction I.— Map-Drawing. The practice of map-drawing, should be kept up, without inter- mission. Besides drawing on slates, and on black- board, pupils should be required, in order, one or more every day, to bring in a finished map, drawn on paper, not always, necessarily, of the country assigned for study of the class. These may be drawn, mathematically, and proportionally, larger or smaller than the map in the atlas or book, by drawing th6 marginal lines first, in proportion to 212 GEOGRAPHY. the marginal lines of the printed map, taking them one-half, two-thirds, or twice as large, or in any other proportion. Then the scholar will use divid- ers,„and divide the marginal lines into as many equal parts as those of the printed map ; then draw the lines of latitude and longitude. If these lines are curved, he can bend a piece of whalebone or hickory, prepared for the purpose, by extending a string from end to end, to keep it bent in the proper curve. By loosening or tightening the string, the curve can be varied to meet the de- mands of any line, on any map. The lines having thus been drawn and numbered, with the degree of latitude or longitude, the paper is ready for com- mencing the map. By the use of these squares, thus formed by the lines of latitude and longitude, noticing the posi- tion of each point, and direction of each line, as to which square it is in, and which part of the square, and the proportional distance, in each correspond- ing square, a map can be drawn with correctness and beauty. The lines of latitude and longitude should be drawn in ink ; the boundaries, rivers, etc., should first be drawn with a pencil, afterwards with ink. 35. Direction II. — Preparation and Use of Topics. Scholars should, in the main, prepare their own topics, as they have only to copy them from the bold faced type, as Boundaries, Situation, etc. Such natural divisions of land and water may be added, as occur in the country assigned for a les- SECONDARY TEACHING. 213 son. These may be proposed, or written on the blackboard, when the lesson is assigned, at first, by the teacher. Soon, however, the scholar will be able to bring in these topics, without any direc- tion from the teacher. I think the writing of such topic lists, a valuable exercise for the pupil, and that he ought not to be deprived of it by using printed topics. The method of recitation, by top- ics, has already been fully described, and I will merely add, that scholars should be encouraged to recite, without looking at the topic list^ and with- out any prompting or questioning from the teacher. As has before been stated, a definite length of time should be assigned, for each pupil to use in reciting; and the more he can accomplish, in this time, and the better he can do it, the higher should his grade be, on the class register, for each recita- tion. Strict attention should be given to penmanship, in preparing topics and copying them into the Topic Book, for review lessons. Much care should be bestowed, on precision and propriety of lan- guage, in the recitations. Such attention and care, are generally the most efi'ectual when given in the form of encouragement, rather than in the form of fault-finding. 36. Direction III. — Keview Lessons. Keview les- sons should be assigned frequently. I prefer to give them, in connection with the divisions of the subject-matter, rather than to assign them periodi- cally, as many teachers do. In completing the 214 GEOGRAPHY. study of the States, on any map, for instancft, 1 wonid propose a review of those States ; so, in com- pleting the study of the Grand Divisions, I would have the whole reviewed, cvdn if it should take several lessons to accomplish it. 37. Direction TV. — Pronukciation. Scholars should be required to consult the pronouncing vocabulary, before they come to the recitation. If there should be none, in the Geography used, they should have access to some dictionary that contains one ; or, if this is not practicable, the teacher, at least, should have such a dictionary, or gazetteer, on his table : and no geographical name should be permitted to pass, without a definite and certain knowledge of its pronunciation. The teacher will do well, in case any doubt arises, to require some scholar to look out the word, during the time of recitation. METHOD OF TEACHING ADVANCED CLASSES. 38. INTRODUCTORY LESSON. In commencing a term of school, it is desirable for the teacher to define the position that Geogra- phy holds in Science, in relation to other branches. This can be done by referring to Part I. The teacher should make an introductory exercise, as the scholars are not prepared for recitation, by presenting so much of the General Outline as is necessary for the purpose. It may be given thus: f Mathematical, I^mTc^H Zoology. Arts. Having written so much of the General Outline, he should present the definition of every term used, beginning with Knowledge. These definitions are found in Part I. But the teacher should not confine himself to bare definitions ; he should oc- cupy the whole time, allotted to this recitation, in such illustrations and exemplifications of these definitions, as will make them intelligible and in- teresting to his pupils. He will thus have deliv- 10 (215) 216 GEOGRAPHY. ered a systematic introductory lecture, and ■will have given his pupils an earnest of his ability to manage the class in a novel and interesting man- ner. The scholars should be requested to copy the outline so presented, in order that they may be able to report on it from time to time, and that each may have an entire course of outlines, em- bracing the whole subject of Geography. The teacher will also assign a lesson for the next exer- cise ; state, if possible, at what time the class may expect to be called on for a recitation. As it is supposed that the class are already familiar with Geography, to a considerable extent, it is not de- sirable, perhaps, to follow the course of any text- book that may be used in the class, but to follow the course marked out in the Outline of Geography, as presented below. The teacher will give as much of it, for successive lessons, as his class can well man- age. It will be seen, however, that a variety of text- books, in an advanced class, is no bar to its pro- gress, but decidedly a means of greater interest and improvement. There is no objection, however, to all the class having a book of the same kind; but all the class should be in possession of one or more besides the common text-book. They should all have access to Physical Geography, which may be found in the new edition of McNally's Geogra- phy ; also to some good system of Histories, as Wil lard's School Histories. Before proceeding further with the method of teaching advanced classes, it will be necessary to present the Outline of Geography. ADVANCED TEACHING. 217 39. I. Mathematical Geography. f Sun, 95 million miles, Distance J Moon, 210 thousand miles, from, J Other planets, variable, ( Nearest fixed star, 40 trillion miles. Inclination of axis —23= 28 min. Direction of axis Form of Orbit ( paiaii^i >T 111- -I Ellipse, \ C2 j Proofs that the I Earth I is globular. I Proofs that the I Earth is an ob- [late spheroid, ( towards North Star. I parallel with itself. ra:ijor axis, minor axis, eccentricity. Circumnavigation. Appearance of ship at sea, Shadow on the Moon, Appearance of Polar Star, ^J.5. Appearance of Clouds in Horizon, 6. Suspenflcd weights, 7. Force of Gravity, 8. Analogy. 9. Actual Measurement. 1. Varying vibration of pendulum, 2. Centrifugal Force, 3. Analogy, 4. Measurement of degrees of latitude. B t ( Equatorial, 7924 miles, ) ,. , \ Polar, 7898 " J- nj (Mean, 7912 « j ^ ^"^ fferenoo 28 milea. Circumference, 25.000 miles. Area, 197,000,000 square miles: Lk Diurnal, Annual, In common I with I solar (^ system. Velocity at Equator 1000 miles per hour, f Table turns under pendulum, j Falling body strikes east of ver- Proofs, \ tical line, I Necessary assumption in all as- [ trnnomical calculations. Velocity, 68,000 miles per hour in orbit. ("Aberration of light, p » j Change of Seasons, froois, -^ Necessary assumption in all aa- (^ ^ tronomical calculations. i Velocity per hour 3,500 miles. ( Approaching and receding of Proof, < fixed stars in opposite parts of j the heavens. 218 GEOGRAPHY. Mathematical Geography — Concluded, r Points, \ Lilies, (^ Divisions, .} f 1. Axis, 2. Pules, 3. Diameter, 4. Circumference, 5. Equator, 6. Tropics, 7. Polar Circles, 8. Parallels of Latitude, 9. Meridians of Longitude, 10. Zones, 11. Hemispheres, 12. Horizon, \ ««"^'^^t' * I rational, U3. Colures. fl. Globe, I 2. Tellurian, 6. Means Of Representing,]^. ^J^^j.^^^^^ «P^°^«' I 5. Maps, •6. Charts. II. 40. Physical Geography. 1. Structure £ind Materials. f Igneous Rocks, \ ieology, 1 I Metamorphic V Inorganic, \ ^ f Primary, Mineralogy, j I Aqueous Rocks— Organic, I TerSr^""^' L [ Quaternary, Chemistry. 2. Temperature. ( At the surface variable, Temperature, < Depth of invariable temperature, ( Increase of temperature downwards. 3. Land. Extent, Proportion, Distribution, Analogies of Continents. ( 1. Continent, 2. Island, 3. Peninsula, Divisions, < 4. Isthmus, 5. Cape, 6. Promontory, ( 7. Shore or Coast, 8. Banks, 9. Shoals. ADVANCED TEACHING. 219 Physical Geography — Continued, c i Mountain, Hill, Plain, Valley, 1. Ranges, 2. Systems, , 3. Groups, ' 4. Peaks. 5. Volcanoes High, Fertile, f Directions, Distribution, Analogies, Slope, Counter-Slope. Active, lotermittent, ( Extinct. ( Table Land, \ Plateau, C Prairie, J Selva, j Pampa, I Steppe, r Sandy, Barren, -^ Salt, t Alkaline, Jl Causes and Uses. 4. Water. Fresh, Salt, Mineral, ' Oceans and Seas •] ( Soft, I Hard, ( Ocean, I Lake, r Acidulous, ] Chalybeate, j Sulphurous, t Saline, Characteristics, - r Localities, I Composition, •j Weight, Points of \ ebullition, L { congelation. I Fresh, Lake, < (Salt, color, saltness, temperature, ' depth, quantity, level, extent, taste, motions, fl. with Inlets and Outlets, 2. with Inlets and no Outlets, 3. with Outlets and no Inlets, 4. with neither Inlets nor Outlet^ I 5. Subtf/rranean, te. Periodical. "1 220 GEOGRAPHY. Physical Geography — Continued. r ( in Mountains, Gulf, 1. Extent, Source, -^ in Lakes, Mouth, ( in Springs. Bay, 'stagnant, gentle, Strait, 2. Telocity o|]-P;?j,^ Channel, Cataracts, [ Cascades, Sound, riength, 3. Magnitude, ■{ breadth, t depth, c r extent, _o 4. Drainage, < Water-Shed, , . (.Basins or Bottoms, j g^ j^ p River, ■ Estuary, 1 Fluvial, 5. Delta, -| Lacustrine, ( Maritime. 6. Direction, f Ordinary, 7 Locality ^ Subtern nean, ^' ] On elevations of their own form- Canal, ■ ( ( for what vessels, Well, 8. Uses, 4 Navigable, ) ( 1 to what extent. 5. Atmosphere. Composition, essential, accidental. Color, Height, 1 how determined. I Torrid Zone, Temperature, Limits on surface, in -| Temperate Zone, ( Frigid Zone, at surface. Weight, at height of three miles, ratio of diminution upward. Fluidity. Elasticity. Moistare, Limits of ratio to the atmosphere. Dew, Fogs, Clouds, Rain, Hail, Snow, Frost. .. .. . .^ . :;::. : .^._......,.^. - ...^ _,..::'■_. ,j ADVANCED TEACHING. 221 Physical Geography — Continued. Climate, Classes, Ubcb, Circumstances modifying, Isothermal Zones. Salubrity, Natural, Artificial. K Continental or excessive, / Insular, f Latitude, Height above the Sea, Proximity to bodies oJf water, Slope of country, Position and direction of Moun- tain Chains, . Nature of soil, I Degree of cultivation. I Prevalent winds, [Annual quantity of rain. ' Torrid, 1 . Hot, I Boundar33, Warm, I Temperate, (How determined. Cold, I Frigid, J Productions. C Temperatifre, ) Soil, Causes I modifying, j 1 Moisture, l^ Cultivation. 8. Productions. r a S o -^ Non-combusti- ble, .2 I Coal, Naphtha^ \ Petroleum Sulphur Aml3er. fAir, I Water, I Building materials, \ Statuary " Ornamental " Drug, " Chemical " i Anthracite, \ Bituminous, Cannel, Liquids, Distribution, Abundance, i- i Locality, j tUses. ' — " - - -'l 222 GEOGRAPHY. Physical Geography — Continued, rooid. Planner of deposition, Distribution, >'""«.■ \^Z'\\ Abundance, Liocalities, [ Mercury, Comparative value, J . Uses. < .sT Intermediate, Aluminum, | j Deposition, properties, 1 value, uses, abundance. 3 ■ ' Iron. S s Tin, C Manner of deposition, Distribution, Abundance, . Base, Zinc, Localities, Cobalt, Arsenicum, Comparative value, [Uses. Antimony, '^Bismuth, J ' ■ Mosses, Lichens, Cryptogamous, ■ Fungi, Ferns, Sea-weed, r ' ' Palms, . . Grasses, c o %. Endogens, • Cereals, Lilies, 1- Canes, etc. *i r Apple, 5 Phenogamous, • 1 Pear, T-.,:f» J Peach, Fruits, j Q^^^g^^ h4 Exogens, Grape, n t etc. S^ Forest Trees, § Banian, etc. > d o s 3 Torrid Flora, Temperate Flora, I. / Description, . -| Most important ( plants. i Description, \ Most important ( plants, J fFood plants, Spices, • { Narcotics, Dyes, t Ornamental. :2 " w P , i Description, ) Trees, ^['S'*^ ] Most important }■ \ Mosses, ^^°'^^' plants, ) Lichens, S 1 Arrangement of i Plants of Vertical, -J plants on -J tho several ^ ( Mountains. Zones. L_ _J ADVANCED TEACHING. 223 Physical Geographf — Concluded. 'Homo — man. Quadrumana — monkey, ape, etc, Carnivora— lion, bear, cat, dog, etc, I Marsupalia — opossum, kaagaroo. I Rodentata — beaver, squirrel, rat, 1. Mammalia, <( etc. Edentata — e!oth, armadillo, etc. Pachydermata— olephaut, horse, . hog, ebe, Ruminata — camel, ox, sheep, etc. -2 ' 2 I ,2 ^ y- I. Bird!, 3. Reptiles 4. Fishes. 5) i 2. Moleuscous 3. Articulated, 4. Radiated, (0; ( Ml Whale, Dolphin, Horizontal, Vertical, Marine, Oyster, Snail, Mussel, Insects, Worms, Lobsters and Crabs. Coral, Zoophyte. Geaeral description — pe- culiar animals of each grand division. Temperate ) ( ^«"fral description of an- — ^ "^ ^ imals common and pecu- liar to each division. General description of an- imals common and peculiax to each grand divisioo, ( Arrangement of animals \ • on mountains. Torrid Fauna. 1) Fauna, C Frigid Fauna, 10* ^ 224 GEOGRAPHT. 41. , III. Phenomenal Geography. 1. Astronomical Phenomena. 1. Day and night— variation in length of day and night. 2. Change of Sun's declination. 3. Rising and setting of the Sun north of east and west, is Summer. 4. "Where on the Earth's surface do the days begin'f o. Difference of time. 6. No absolute up and down, east or west. 7. Change of Seasons. 8. Appearance of the Sun in the frigid zones. 10. Changes of the Moon. 11. Precession of Equinoxes. 12 Mptpors f Shooting Stars, 1^. Meteors, | Rawing Stars. 2. Terrestrial Phenomena. Formation and structure of the Earth. ■r . 1 u f S Depth of invariable temperature, internal neat, | j^^^j^ ^^ increase downwards. Elevation of Mountains. Elevation and subsidence of Continents. Elevation and subsidence of Islands. Volcanoes — Causes of Eruptions. Earthquakes — Causes, Movements and Effects. ) explanation, uses. Perpetual, Intermittent, Periodical, 8. Springs, ■{ Artesian Wells, Salt Springs, I Hot Springs, | 1^ Fire Springs. J f Origin, Formation of channels. Formation of bottoms. Rivers, ■{ Formation of oxbows, bayous, and islands, Formation of deltas, Elevation of bed above surrounding country, .Running up hill. I „1 10. Caves, j Motintain, Subterranean, Causes, Stalactites, Stalagmites, Gases, Rivers, Lakes. ADVANCED TEACHING. 225 Phenomenal Gteography — Continued, 11. Natural Bridges, rsT'remarkable. cause. 12. Causeways, } columns, \ '^^P^' ' \ size. 3. Oceanic Phenomena. 1. Saltness, Causes, Limits of percentage. 2. Temperature, in Torrid, Temperate, and Frigid Zones j in currents. 3. Depth, Deepest Sounding, Method of Sounding. 4. Density, at surface, at depth of a mile. c T „„„! S Variation, Apparent \ < elevation of land, 3. i.evei, 1 Variation, i I depression of land. 'Cause, Height— "Billows mountain high"? oo Force, Direction, $ Rate of tmvel, The Bore, , Uses. ' Causes, Tide opposite the Moon, Direction and rate of travel. , Later daily recurrence. « Tides in rivers— many at the same time, i Spring and neap tides, What six concurring circumstances will give the highest tide? Extraordinary local tides— causes. «. Motions,' US€ s. 'Antarctic drift, Pacific equatorial, Indian « Atlantic " ' causes. South Atlantic, extent, S *^* Brazil, direction, a 1 South connecting, force. £ . s- Cape, ■1 tempera- 3 o O Gulf Stream, j f' ^^°«^' Arctic, l^^^^T^' Japan, ture, color, effects. Grassy Sea, J Counter, | ( means of determining, I Under, f I effects. U . 226 GEOGRAPHY. Phenomenal Geography — Continued. 6. Periodical Currents, T. [of Red Sea, ^ ) of Persian Gulf, { I causes, of India Ocean, \ \ effects, of China Sea, J ( No. of genera and species, Coral animalculae, < description, ( habits. rReef, .' Branch, Classes, Ccral, ^ Atolse, |{Keefs. J Chalk beds, j Brain. [ Organ pipe, etc. i habitable part, "j \ lagoon, encircling, barrier, fringing, J how formed, how forming. f causes, I shape, \ localities, I uses, I dangers. 1. Weight, 4. Atmospheric Phenomena. \ cause, methods of determining, rate of diminu tion upwards, effects, force. f preserves liquidity of water, I prevents vacuums, I raises water in pump and si* •{ phon, I raises mercury in barometer, I combination with water to [ maintain life of fish. f flying of birds, J difference of descent, 'j retarding velocity of railroad [ cars. 4. Temperature — cause of variation, rate of diminution upward. 6. Boiling point of 'Viler — variation upward and downward. 2. Pressure, 3, Resistance, {cause, illustrations, effects. cause, illustrations, effects. - — '- i-n 1 — — ■ '^ " ADVANCED TEACHING. 227 ; Phenomenal Geography — Continued. I Heat, ) ;atises, -I Electricity, V operations of each ( Revolution of the Earth, ) Velocity and ) force of, \ 1 Gentle, Brisk, High, Violent, Hurricane. Direction, means of determining, upper and lower currents. ' explanation, 1 equatorial, zones of calms, \ . . , ( northerc Constant or Trade, ' I *^«P^°^^' 1 southern. Limits, ) l"^'^^ ^°^J*^'J^^' ' ] East and West. Uses. ) ( localities. Land and Sea breezes, V J explanations, J / periods. Periodical, J, T^Ton.nor.. \ I localities. Etesians, J- \ explanations, i Northers ) (extent, ' ^ periods. Ci ^localities. fa o explanations, , Simoom, Variable, \ Local, < Rhamsin, Harmattan, Sirocco, Pamperos, Bora. Whirlwinds,, , , ,..'. Typhoons? * (chief periods. ( locality, Water Spouts, J. explanation, I ( "attending phenomena. 1 r Former ignorance in relation to. Late improvements. Navigation, ^ , from.Europe to America, jGen'I principles, « JJ.' f ; ^o fc^o, I ^ " U.S. to China. ^ 228 GEOGRAPHY. Phenomenal Geography — Continued, r , proofs. Evaporation, -j average annual ( Temperate Zone, ^ from sq. rod, ( Torrid Zone. ' explanation. ■n„, -^r i depending on what? Dew point, } J^^ determined? Dew, -i Dew at midday— "pitcher sweats," circumstances favoring, ) ( exnionation circumstances preventing, ) < ^ ' Frozen — frost. ,uses? ' explanation, Mists, or condition of moisture, Fogs, • localities of dense fogs, . periods of fogs. ' explanation — how differ, height, , Cirrus, , Clouds, ■ Classes, ] g,",7jg"'| description of each. 1 ^Nimbus', ' uses, 1' ' explanation, a" r from equator to polos, from sea to interior, r<„ -.1 «„-„„:v.i„=. J on east and west shorei General principles, i .^ Tropics, b-' .2 s :2 ' llain, to in Temperate Zone, [ in Frigid Zone. ^ ( Rainless, i Regions, ^ Periodical rains, V where. ( Frequent rains, ) 'explanation, snow crystals, Snow, ^ exteilt superficially. in Torrid Zone, Snow line, •< in Temperate Zone, in Frigid Zone. ' explanation, character and appearance of ice, Glaciers, - localities, extent, motions. effects. ADVANCED TEACHING. 229 Phenomenal Gteographt — Concluded. I explanations, Avalaaches, < localities, ( effects, explanation, dimensions, 1 extent, I cool southern climate, [flea, { effects, -< distribute rocks over bottom of ( boulders on present continents, explanation, dimensions, localities, effects. IV. — Electrical Phenomena. Hail, Thunder and Lightning. 'Explanation, , Zigzag, ^ Heat. ^ f / inventor, I -p. J, j extent of protection. Protection, J ^^^^> 1 best materials, I ^ best arrangement. I. Localities to be avoided, , Localities, — when most abtmdant. 2. Mariner. Light.. i-PjS?"' j i explanation, 3. Aurora Borealis. < appearance, ! ( localities. j V. — Optical Phenomena. I [explanation of j P^^ry. 1. Eainbow. \ classes, 1 1^^^^, 2. Halo, Corona. j-P'-'r- 2 { Mock Sun, | j explanation^ • ( Mock 3Ioons. J ( localities. I explanation, 4. Mirage. k localities, ( effects. 5. In^rting images in air. \ fiX^'' { esplanatiixn, ». Ignis fatuus. •? localities, * effect*. 230 QEOGKAI HT. VI. — Political Geography, GoYernment^ 1. Patriar&baL Absolute Monarchj. 3. Li Baited Monare'ay. r Political divisions, < Chief officer, I Subord'te officers, f Political Divisions, I Chief Officer, ! Subord. Officers,, j Branches of Gov- t erniucnt, 'Political Bivisioas, | Chief Officer, | 4. Aristocracy. -( Coordinate branches ) of Governmeat, ) f Political divisions, ' Chief Officer. I Coordinate branches ) I of Governraent, ) f Political divisions, ( I Chief Officer, { 6. Republic. ■{ Coordinate branches I of Government^ \ L term of service, ■( how appointed, I extent of power. Empire, Kingdom. L time of service, ■{ how appointed,, f extent of power. i how established. < extent of jurisdiction, f officers, how app^tcd Empire, Kingdoca. j how appointed, j extent of power, j how established, •< extent of jurisdiction, f officers, how app'teci. { how appointed, ( extent of power, i how established, •7 extent of jurisdiction, ( officers, how app'ted^ State, Dachy. i time of service, < how appointed, ( extent of power. i how established, •< extent of jurisdrctioBi f officers, how app'ted. 1. Caucasian,. 2. Mongolian, 3. Malay, 4. American, 6. African. Races. Color, — skin, hair, eyes. Features '> ^^^^' ^'^'^^' eheekbones, forehead^ ' t mouth, lips, ehin, hair. Nations included. Number estimated, "l Distinguishing eharaeteristks^ Government, Languages, Civilization,. Religioa. r- ADVANCED TEACHING. 231 Political Geography! — Continued . / State of Society. ' f-^llSaa issrra f Attainments in Arts and o ni„ . „ „„ f Enlightened, s 1 Sciences, 2. Classes as j civilized, | J Systems of Education, to social con- ^ Half Civilized, C ] Political power, d^fcion. (savage, ' Religion, ^ Humane institutions. Religion. r ' Founders, Ecclesiastical system, 0«io-s. l^-a-X'-. .2 1, Roman Catholic, , 'm 2. Greek Church, 1 ^ Books of authority, 6 3. Protestant, j 4. Nestorians, ^ worship, \^ Sects, iH Number, Embraced in what nations. ^Founders, Ecclesiastical System, Officer'' i ^^^ appointed, Ulticers, 1 g^^gjjj, ^j p^^gj.^ 2. Jews. Books of authority, Sects, Number, Scattered through what nations? ' Founder, Ecclesiastical System, Officers \ ^°^ appointed, Utlicers, 1 g^^g^^ ^j power. 8. Mahometans. - Books of authority, Sects, Number, Embraced by what nations! 'Books of authority, 4. Pagans.' Sects, Number, r:-^ .Embraced by what nations? '^\ 232 GEOGRAPHY. Political Geography — Continued, Artificial Productions. ■ r Beef, ) Butter, Animal, • < Mutton,)- < Lard, P^^^ I Pork, ) 1 Tallow, etc. [Rye, etc. ^^°^' \ Cereals— Wheat, Corn, Oats, Barley, . Vegetable, 4 Fruits— Apple, Peach, Pear, etc. t Roots— Potatoe, Beet, Turnip, etc. 2 p c'o"""^- \¥i^^^:^^&^^' ^" 1 Aoi.a,s tor Labor, \^^l^'^^' -p., , ( Animal— Tallow, Lard. * "®'' \ Vegetable-Wood, Charcoal. ( Cordage— Hemp, etc. [mint, ct« Miscellaneous, \ Medicines— Castor Bean, Oil of Pepper- y. { Dyes— Madder, Indigo, etc. j j ' Ores and precious stones Clay and Sand, Raw, Stone, Timber, Ivory, Horn, etc. '' Metals, Hewed Stone, Wrought, ^ Lumber, Brick, Yarn and Cloth, Kaaufacturei. . Leather, etc. 'Machinery, Cutlery, Crockery, Houses, Furniture, Finished, - Clothing, Shoes, Hats, Clocks, L Diamond Ornaments, < Agate, L L ( Opal, etc. 'Food— Fish, Game, etc. p , Coal — Bituminous, Anthracite, Co„dio,en.!!"' }_§;«-; I-. sugar, Miscellaneous - T-v ( Mineral — Calomel, etc. ^r"=3, ^ Vegetable-Strychnine, etc. Perfumes, Paints, Dyes, .Poisons — Corrosive Sublimate, Arsenic, etc. t-^ J ADVANCED TEACHING. 233 Political Gteograph y — Continued, Employments. I Farmer, Gardener, Fruit Grower, ete. Agriculture.' •< Grazier, Shepherd, Drover, Butcher, eto, I Teamster, Chopper, Sawyer, etc. Fishery. Whaleman, Codfisher, Oysterman, etc. Manufactures. •! JJ^^f ' Quarryman, Lumberman, Trapper, \ Mechanics. L Importers, Merchants, -^ Jobbers, { Retailers. f Sailors, Boatmen, rp-o.,c,.^„^-„.^ J Railroadmen, Transporters, ^ g^^^^ ^^^^^^ ^^^ ^^.^^ i Teamsters and Dr«^vmeI^ (.Stevedores, f Architects, I Designers, I Musicians, { Painters, I Sculptors, I Engravers, [Daguerreans, . Teachers. J Ministers, "j Physicians, . ^ Lawyers. Commeroe, \ Artists, Professions. History. Ancient Countries. Modern Countries. Dynasties, ] ^^"^f j '^^*^^- Extent of f over what ecuntries, Conquests, J under what kings and generals, I Decline 1 under what king, and Fall, \ by what nation and king subdued. Change of ( by whom effected, I Govern- < causes of decay, ments, { effects on civilization and religion, fdate, I locality, I number of men engaged on each side. Battles, { generals, I causes, I number slain on each side, (.consequences. Extent of \ over what countries, , Conquests, ) under what kings and goueraia. 234 GEOGRAPHY. Political Geography — Concluded^ Education;. 1. Diffusion and extent of ( among the common people^ Knowledge, ( among higher classes. tPublic, fby whom established, '* 2. Libraries, \ -jnumber of volumes, fPrivate, ('conditior^ of use. %\ f Universities, "| ( Public, I Normal S-cbools, or \ Elgh Schools, j. { Free, | Common ^ classified t Schools, \ unclassified, Number of Teaenenf I Number of Pupils^ J L P.-iv»fP f Universities, j (endowed, rnvate j- jf^rmal Schools, I J „t,__„ ^"^ 1 High Schools, \ \ ^^^^f ^' f rn t, , LGrfmmar Schools, I I ^""^«'- ^^ Teachers, Chairs, amomits.- Fay. ' J I, Number of Pupils. Literature, Sciences, Arts, Literatijre, Bcieiices, and Arts, what form the most generally "] Historical? cultivated? [Periodical? what form the most highly | Poetical? cultivated? J MetaphoricalT most noted works, I °^^^^f;, what the most generally understood? what the most highly cultivated? {character? discoveries? consequencesT .what the most generally cultivated? 'what the most highly cultivated? most noted inventions? \ | character? >• < inventors? most noted works? ) ( consequences? Miscellaneous. Natural Curiosities, Artificial Curiosities, Places and obj«otf of Interest, Distinguished Persons, Manners and Customs^ Lan- guages, Traveling Facilities, etc., etc. iDVANCED TEACHING. 2 43. Beschiftive Geographt. i. Boundaries, 2. Latitude aud Longitude, 3. Surface, 4. Moantains, 6. Volcanoes, 6. Plains, 7. Islands, 8. Peninsula, 9. Capes, 10. Isthmus, H. Bodies of Water^ m Kiversy 13. Noted Springs, 14. Climate, 15. Isothermal Line, 16. Soil, 17. Natural Currents, 18. Natural Productions^ 19. Square Miles,^ 20. Population, 21. Race, 22. State of Society, 23. Capital, 24. Chief Towns, 25. Employments, 26. Facilities for Traveling, 27. Agricultural Productions, 28. Manufactured Productions. ■ Slares, 29. Miscellaneous Productions, I f^^^^^*^ (.Tar, etc. 30. Religion, 31. Education, 32. Morality, 33. Manners and Customs, 34. Languages, 35. History. 36. Literature, Arts »ad Ssienoes, 235 236 GEOGRAPHY. 44. SUCCEEDING LESSONS. The class will pursue this course of Outlines, in successive lessons, with frequent reviews, till it shall have been mastered. Then they will commence Descriptive Geogritphy, taking one or two Political divisions for a lesson, using the Topic List on page 235, in the prepara- tion and recitation of their lessons. The Teacher of an ungraded or country school, can make a division of the class, according to the ability of the scholars, by assigning the wholo Topic List, as a guide for the lesson of the most advanced scholars, and only such topics as are found in the text-book used, to scholars less ad- vanced. These two divisions may recite as one class. The general plan of managing the recitation of an advanced class, is the same as for a secondary class, the difference being in the greater range of topics examined, and in the greater amount of time allowed each scholar for a recitation. USE OF APPARATC S. 45. The remaining pages of Part IV. will be given to the description and use of the Globe and Tellu- rian, and their use in the explanation of Astro- nomical Phenomena. The matter was originally written by me, several years since, for a text-book, to accompany Holbrook's School Apparatus. Most of it was transferred to the Teacher's Guide to Illustration, a work prepared by F. C. Brownell, for a similar purpose, and published in Hartford, Ct., 1857. That is a valuable work, and should be in the hands of every teacher. TERRESTRIAL GLOBE. (237) .^...^, ^ 238 GEOGRAPHY. 46. A Globe should invariably precede tlie use of maps, to avoid the erroneous impression, with chil dren, that the earth is flat ; and the Hemisphere Globe may be used in connection with the Hemis- phere Map. For several reasons, a five-inch globe is prefera- ble, in a common school, to one of any other size. While it shows the spherical form as well as any other, and is large enough to give a distinct view of the principal divisions of land and water to all the members of any ordinary class in Geography, it is not so large but that it can be held in the hand conveniently for familiar illustration; nor is it so large but that it can be made of solid, firm material, without too much increase of weight, which secures it against destruction in case of a fall. Again, anything that is desirable to be taught by the use of a globe to an ordinary Geography class, can be taught better with a small globe, ele- vated on a simple pedestal, or suspended by a cord, than by a large globe, costing ten or twenty times as much, surrounded and encumbered by a frame work, horizon and meridian, as such globes usually are. The fact, that where both a large and a small globe are in possession of teachers, the former is shoioed to visitors, and the latter used to instruc* scholars, is a sufficient indication of the compara- tive utility of the two. But an outline globe is preferable, in primary in USE OF APPARATUS. 239 struction, to one so much crowded with names as to render the forms of seas and continents obscure and incorrect. The details of particular countries are studied better on maps than on globes. If the minutiae of Geography should be studied on globes, then ought globes to be large enough to embrace the details of countries and towns, which, of course, is impossible within any ordinary limits of expense. 47. APPLICATION'S. I. — THE SHAPE OF THE EARTH. That the earth is spherical, appears from the following proofs and illustrations : Proof \st. The earth has been traveled around. Illustration. As a fly crawling around the globe, in any continuous direction, comes back to the starting point, so travelers have passed around the earth, in nearly all directions, and returned to their homes. Proof 2d. The shadow of the earth on the moon is always circular. Plustration. The globe always casts a circular shadow, whereas no other body, in all positions, will do so. Try a cylinder, a cone, oblate and prolate spheroids, and then the globe. Proof 3IGES OF THE MOON. The changes of the Moon are the result of its opacity and its revolution about the Earth. We have new and full Moon once in twenty-nine and a half days, from the fact that its revolution around the Earth once in twenty-eight days, in connectior. with the common motion of these bodies around the Sun, bring them all into the same relation with re- gard to each other in that period. This period is called a lunation or lunar month. Placing a strong light on the Tellurian, as be- fore, turn the arm so as to briftg the moon between the sun and earth. Evidently the dark side of the moon is now toward the earth, and this is the position of the three bodies at new moon. Thus situated, the sun and moon arc said to be in con- junction. Turn the arfti again, and bring the moon around on the side of the earth opposite the sun. ♦Note. — The diflerence of a sidereal and a synodical revolution ca« be shown in a manner similar to that of illustrating the difference of» Bidereal and solar ^Jay. 260 GEOGRAPHY. The illuminated side of tlie Moon is now present- ed to the Earth. This is full moo7i, and the Sun and Moon, in this position, are said to be in opposi- tion. As the Moon's orbit is not on the same plane with the Earth's orbit, the Moon is some- times above and sometimes below the plane of the Earth's orbit or ediptic at new and full. Hence we do not always see exactly the same hemisphere at full moon, or the crescent pointing in the same direction at new moon. The horns of the crescent will, however, always point away from the Sun, whether above or below ; or, as we say, the Moon runs high or runs low ; all of which carl be clear- ly shown b}^ the Tellurian. The intermediate phases, as the quadrants and octants, are also seen by the Tellurian, but perhaps more clearly by the use of the Lunarian. 67. ECLIPSES. An eclipse is nothing more than an obscuration of the Sun or Moon by the interception of the Sun's rays. An eclipse of the Sun, or a solar eclipse^ is shown by turning the Tellurian arm until the moon casts a shadow on the earth's surface. An eye, situated at the place of the shadow, could not, of course, see the luminous part of the candle. So, on the earth's surface, wherever the shadow of the Moon falls, the Sun can not be seen, as it is in an eclipse. A solar eclipse commonly happens at new moon, and can be total when the Moon's center is USE OP APPARATUS. 261 in, or very near, the ecliptic, or when the Moon is at one of its nodes. Since, as shown by the Tellu- rian, the Moon is sometimes above and sometimes below the ecliptic, at this period, it is obvious that an eclipse can not happen at every new moon. A par^ia? eclipse will occur where rer a part of the Sun's disk is obscured 'by the intervention of the Moon. A lunar eclipse is shown by turning the Tellu- rian arm until the moon comes into the shadow of .he earth, either partially or entirely ; giving a partial or total eclipse. Neither of these can hap- pen at every full moon, in consequence of the obli- quity of the moon's orbit to the ecliptic. The construction of the instrument is such that the moon's orbit plane will come into the same rela- tion to the earth's plane once in eighteen revolu- tions of the earth around the sun. This ar- rangement corresponds to the Chaldaic period in nature, which gives the recurrence of nearly the same order of eclipses once in eighteen years and ten days. By means of this period, the an- cients were enabled to foretell eclipses, but with no great degree of precision. 68. TIDES. Tides are the result of the unequal attraction of the Moon on the water on the Earth's surface, and on the inflexible mass of the Earth itself. They are influenced likewise by the Sun, and by the form and position of coasts and harbors. 262 - GEOGRAPHY. Since the water tinder the Moon ia 4,000 miles nearer to it than the centre of the Earth, it will be attracted by as much greater force than the Earth as the square of 240,000 is greater than the square of 2365000* Hence the water is heaped up under the Moon, and this elevated mass of water will pass around the Earth as far as continents will permit, once in twenty-four hours, or as often as the Earth revolves under the Moon. This will account for a tide once a day. But there are two tides daily. How is this ? Since the Earth's centre is 4,000 miles nearer to the Moon than the water on the Earth's surface opposite the Moon, the Earth is drawn away from this water on its surface opposite the Moon. And as the water under the Moon is drawn away from the Earth, so the Earth is as much drawn away from the water on the side opposite the Moon Hence, there will be a tide opposite the Moon as well as under it, and the two tides will be equal, or nearly so. This will give any place within the reach of tide -water two tides in a day. 69. LATER DAILY RECURRENCE OF TIDES. Tides happen about fifty minutes later everyday, in consequence of the motion of the Moon in ita orbit around the Earth. This may be shown by giving motion to the Tellurian arm and the globe on its axis at the same time. Observe that any place on the earth must make more than an entire revolution to como USE OF APPARATUS. 263 around the second time under the moon, whereas if the moon were stationary, then a co/nplete revolu- tion would bring the same meridian again under it. 70. SPRING AND NEAP TIDES. It is found by observation, that the influence of the Sun on the tides is about one-fourth as great as that of the Moon. By the Tellurian, it is shown, that when the Sun and ?»Ioon are either in opposition or in conjunc- tion, their influences combine to produce a tide equal to the sum of the tides they would produce separately. This is called a spring tide, and will happen either at new or full moon. Again, it is shown, that when the Moon is at its quadratures, the tide will be equal to the difi"er- ence of the Sun's and Moon's tides separately. This is called the neap tide. The highest tide possible^ at any given place, will happen under the concurrence of ihe follow- ing circumstances, viz : The Earth in its perihe- lion, the Moon in its perigee, at one of its syzygies, and in the zenith or nadir. 71. PRECESSION OP THE EQUINOXES. The precession of the Equinoxes is the recur- rence of the Equinoxes or any other period of th^ year before the Earth has made an entire revolution around the Sun. It it is found that a year is twenty minutes and 12 264 GEOGRAPHY. seventeen seconds less than the time reqiired for an entire revolution. This is occasioned by a change, not on the inclination of the Earth's axis, but on the direction of that inclination. To fihow this clearly, take hold of the lower movable pulley with the thumb and finger, and turn that pulley half the way round. In so doing, you will cause the axis of the Earth to point south instead of north, but with the same inclination still. In nature, it requires 12,934 years to make the change, and 25,868 years to bring the axis back again into its present position. Now, if you start the arm from the east, where the globe will be in the position of the autumnal equinox, and while you turn the arm, you at the same time turn the axis so that it shall incline easterly, you have only to carry the arm around to the south to bring the globe into the position of the autumnal equinox again ; i. e., a quarter of a revolution of the axis produces a precessioa of the equinox — equal to a quarter of the Earth's orbit. The precession, then, we see, is equal to the part of a revolution that the axis makes. It really makes a change of 50". 1 in a year, and the precession is the same, and it requires twenty minutes and seventeen seconds for the earth to pass that part of its orbit. Hence, as before stated, the year is so much less than the time required for an entire revolution. PART V, METHODS OF TEAOHING MENTAL, PRACTICAL, AND THEORET- ICAL ARITHMETIC. INTRODUCTION MENTAL ARITHMETIC. The objects aimed at By the true teacher for his class in Mental Arithmetic, are — 1st. Distinct mental conceptions. Some teachers make use of numeral frames, and a variety of othci' expedients, to aid their pupils in realizing the powers of numbers. I am of the opinion that such aids may be relied on too far ; so far as to retard the operation of the mind in forming its own con- ceptions. The large majority of pupils will ad- vance more rapidly and self-relyingly. without any visible representations whatever, and should they be needed, marks on the blackboard answer every purpose. 2d. Clear views of cause and effect. From the very first exercise in Arithmetic, the relation of cause and efi'ect is ever before the mind ; equally as much in answering the question, One and one are how many? as in the most complex problems^ requiring a long continued course of analysis and synthesis for solution. In fact, every operation is (267) 268 ARITHMETIC. but an application, in some form, of the law of cause and effect. Hence Arithmetic, and especially Mental Arithmetic, affords a fine field for the cul- tivation of the reasoning faculties. There is no better, if properly managed^ 3d. Certainty in the courses of reasoning. This should be aimed at just as much, in the simpler steps, in the first lessons, as in the higher walks of more advanced stages. For if entire certainty^ is not secured in the preliminary steps, what else may be expected of the more advanced exercises than conjecture, doubt and uncertainty in the processes and results? 4th. Precision in language. This implies not only a clear distinction of abstract and concrete quantities, and the use of the necessary language to make such distinction without tautology, if pos- sible; but it does not admit of any forms of false or doubtful syntax in the enunciation or solution of questions. 5th. A thorough understanding of Fractions. — There is no aspect in which a Mental Arithmetic class can appear to so good advantage before an examining committee, as in the ready and success- ful management of fractional numbers. A knowl- edge of powers and multiples is indispensable to free use of fractional quantities. 6th. Rapidity in tlie solution of questions. Cer- tainty should be aimed at from the very first, but as the class advances emulation should be brought into play in exciting the minds of the whole claiss to rapid combinations and evolutions. Most INTRODUCTION. 269 astonisliing results may be attained, even witli sluggish min(l.ri, in this direction. 7th. Artifices for abridging labor. These should never be introduced till the scholar is well drilled in the full and logical forms of procedure, but then they may be used with great interest and effect. 8th. Cultivation of Memory. To this end no book should be used by the class, during recita- tion ; and at every lesson more or less impromptu and *' random questions" should be given. Ex- amples of these will appear in the following pages. WRITTEN ARITHMETIC. The OBJECTS to be aimed at in Written Arith- metic, are — 1st. Correctness in operation. Written Arith- metic looks more particularly to operations in dollars and cents, in the counting room, workshop, or market; and the teacher who should tolerate any want of accuracy in the operations of the pupil would be false to his interests. 2d. Rapidity in operation. When it is known, that by practice, two or throe long columns of fig- ures can be added with as much rapidity as one is, ordinarily, it is seen that there is abundant room for improvement, not only in scholars but in most teachers. Multiplication and division are equally susceptible of condensed operations, yielding re- mote results -n "less than no time" to the expert calculator 270 ARITHMETIC. 3d. Artijices for ahridging labor. Every possi- bility of cancellation should be familiar, every contraction in the fundamental rules, every use of aliquot parts, and factors, should be so frequently and so long dwelt upon by a class, that the "short- est method" will always afterward present itself, in business life, as if by intuition. 4th. Ready and reliable means of proof . As there are no " answers" to real business transac- tions, except such as the business man obtains for himself, it seems to me altogether preferable to accustom scholars in practical arithmetic, to prove their work from the first. Of course the " best methods" should be sought by the teacher, and practiced by the pupil, till he has little occasion for " the answer in the book." Books without answers are desirable for this end ; but the teacher should be the more watchful and exacting in the matter of proofs, if the text book is furnished with answers. THEORETICAL ARITHMETIC. The objects to be aimed at in Theoretical Arithmetic, are — 1st. A thorough iinderstdnding of all the i^ecullar and common properties of numbers as high as twelve. The demonstration and use of these properties are equally useful and interesting. 2d. Development of reasoning facidties. Geom- etry is frequently resorted to for this purpose and for no other. Theoretical Arithmetic is no less cfi'ectual, if pursued with as much rigor as the sub- INTRODUCTION. 271 ject demands. The definitions and axioms should be as clearly stated, and the propositions as well connected, and as logicaLy proved as those of Geometry; while for the great majority of pupils there is immeasurably a greater demand for the use of the principles of Arithmetic than for those of Geometry. 3d. Cultivation of the power of accurate expres- sion of tho2(ght. There is no department of science where we find so much looseness in definitions and rules, as in Arithmetic, notwithstanding the multi- tude of text books on this subject, and the higher claims of each successive author, in this particular. This very looseness in authors affords the critical teacher a fine field, if not for display of his own acumen; yet for arousing the energies of his pupils to excel their text book. 4th. A hnowledge of the curiosities of the science. 5th. An acquaintance with the works of various authors. It will be found a very desirable prac- tice, in pursuing a course of Theoretical Arith- metic, to consult the various authors who have written on the subject. A more liberal and sym- metrical view of the science is thus obtained than from any one author. Kespect for authors is thus diminished, while the love for tb^ truth is en- hanced. 12* METHOD OF TEACHING MENTAL AEITH- METIC TO PRIMARY CLASSES. LESSON I. 1. First Step — How to secure Books. A course similar to thafdescribecl on page 184, Sec. 2, may be pursued. Second Step — Counting. Teaclier. — Children, how many of you can count a hundred? [A ma- jority raise their hands.] As many as can count ten may raise the hand. [Nearly all hands rise.] Now we will see. I will make some marks on the blackboard and you may all count them as I make them. The teacher makes the marks, (circles,) on the board, and the children count in concert. He soon learns the ability of the class in counting; and drills those unable to count ten in counting marks, buttons, fingers, desks, windows, panes of glass, etc., till they can tell the number of objects as high as ten. They may then be required to make as many marks on the board as the teaclier designates. (272) MENTAL ARITHMETIC. 273 2. Third Step — PRELimNAiiY Drill on Lesson I. Ray's Mental Arithmetic. Teacher. — Children, you may now open your books to Lesson I., on page 8, as many as have books. Those who have no books may look over others' books to-day, but all who remain in the class must have books to-morrow. "We can have no looking over after to-day. Have you all found it? Charles, you may read the first question, beginning " James had an ap- ple." Charles reads the question. Teacher. — How many can answer it? As many as can may raise the hand. [All hands rise.] Sarah, you may answer it. Sarah. — Two. Teacher. Susan, you may read the next question. Susan reads. Teacher. — How many can answer this ques- tion? The teacher will be careful to call on those pupils who are the most backward or inattentive. In a similar manner, this lesson, or so much of it as the class can bear, is passed over in prepara- tion for studying it. Teacher. — Now I wish you to study this lesson which you have been reading, so that you can answer all the questions without the book, when you come again to recite. I will read the ques- tions and you may answer them without looking on the book at all. How many will study this lesson and learn it well? [All hands rise.] The class is now dismissed in order, and notes written to parents for the necessary books. 274 MENTAL ARITHMETIC. L ESS ON II . 3. First Step — Recitation. The teacher reads the question to the whole class, and calls on one pupil by name for an answer. He will be careful not to omit any, but he should not pursue the order in which they sit. He may follow the order of his register for this class, forwards or backwards, taking all the names as they stand, or taking them alternately, backwards or forwards : or he may depart from this order, when he sees any scholar inattentive, by giving him a question. Making Figures. As each scholar answers his question, he may go to the blackboard, and make the figures corresponding to the numbers used in the question and answer, and perform the opera- tion by adding the figures as in Written Arithmetic. Of course, the mental operation comes first and the answer by this means. With a primary class it is much better thus to combine Written with Mental Arithmetic as they proceed. Second Step — Preliminary Drill for next les- son. Remark. The class will pursue the course de- scribed in Lesson II, for many days, until they acquire a knowledge of counting, of the use of figures, and the power of making them correctly on the slate or blackboard, till they can perform the operation of addition and subtraction by either the mental or written process ; but when multipli- cation is reached the regular steps of a solution should be taught, whi^h are as follows : — MENTAL ARITHMETIC. 275 4. ADVANCED LESSON. Recitation. Teacher reads a question for the whole class: " At 7 cents apiece what will 3 mel- ons cost?" After waiting till most of the class have raised their hands as each has obtained the result, he speaks the word " class." Then all who have obtained the result raise their hands together. He calls on one pupil by name to give the result; then on all who agree with this result to raise their hands ; then on all who have another result, to raise their hands; then on some individual, from his register, in order, by name, to give a solution of the question, which is done in the manner de- scribed in the following section. 5. solutions. First Step — Scholar rises and repeats the Question. If he fails, the teacher says, " Class, who can give him the question?" Hands rise. The teacher then calls on some one to repeat the question. He repeats it without rising. First scholar, still standing, also repeats it. Second Step — Scholar gives the Analysis, or explains the method of solving the question. If he fails, pursue the same course to correct him as in the first step. Third Step — Scholar performs the Operations, and obtains the result. Fourth Step — Scholar gives the Conclusion, as nearly as possible in the language of the ques- tion. 276 MENTAL ARITHMETIC. Remark. After the teacher has drilled the class in solutions, in multiplication, they may return to addition for a few solutions. 6. FIRST EXAMPLE. — ADDITION. Teacher reads, James had five cents, and he found seven more; how many had he then? When it is seen by hands rising that nearly all the class have obtained the result, he says " Class." Then all who have solved the question raise their hands together. Teacher. — Henry, what is the result? Henry. — Twelve. Teacher. — How many agree? [Hands rise.] How many have a different result? [Hands rise.] Mary. Mary. — Twelve cents. Teacher. — Very well. Sarah, you may give the solution. Sarah, rising, repeats (not reads) the question. First Step. James had five cents, and he found seven more, how many had he then? Second Step. He had as many as the sum of five cents and seven cents. Third Step. Five cents plus seven cents are twelve cents. Fourth Step. Therefore, if James had five cents, and fouF.d seven more, he then had twelve cents. 7. . SECOND EXAMPLE. — SUBTRACTION. The teacher having read the question — ilfana, rising, gives the solution ;hus : MENTAL ARITHMETIC. 277 j First Step. A boy having eiglit marbles, lost five of tliem, how many had he left? Second Step. He had as many as the differ- ence between fiv« marbles and eight marbles. Third Step, Eight minus five are three. Fourth Step. Therefore, if James, having eight marbles, lost five of them, he had three mar- bles left. 8. THIRD EXAMPLE — ADDITION AND SUBTRACTION, Peter ^ rising, repeats the question. First Step. A lady bought a comb for twenty five cents, some pins for ten cents, and some tape for six cents; she gave the shopkeeper seventy-five cents ; how much change ought she to receive? Second Step. She ought to receive as many as the difference between seventy-five cents and the sum of twenty-five cents, and ten cents, and six cents. Third Step. Twenty-five plus ten, plus six, are forty one. Seventy-five minus forty-one are thirty-four. Fourth Step. Therefore if a lady bought a ' comb for twenty-five cents, some pins for ten cents, and some tape for six cents, and gave the shop- keeper seventy-five cents, she ought to receive forty-one cents ia change, 9. FOURTH EXAMPLE — MULTIPLICATION. Samuel^ rising, gives the solution thus: First Step. At four dollars a pair, what will five pairs of boots cost? 278 MENTAL ARITHMETIC. Second Step. If one pair cost four dollars, five pairs will cost five times four dollars, Third Step. Which are twenty dollars. Fourth Step. Therefore, at four dollars a pair, five pairs of boots cost twenty dollars. m riFTH EXAMPLE. — DIVISION. Susan, rising, gives the solution thus: First Step. If a man laid out one hundred dollars for cows, and paid twenty dollars for each cow he bought, how many cows did he buy? Second Step. If one cow cost twenty dollars, he bought as many cows for one hundred dollars I as twenty is contained times in one hundred, { Third Step. Which are five times. Fourth Step. Therefore, if a man laid out one hundred dollars for cows, and paid twenty dollars for each cow that he bought he bought five cows* 11. SIXTH EXAMPLE. — ^DIVISION. William, rising, gives the solution thus : First Step. If you should buy six oranges for twenty-four cents, how much would you pay for each orange? Second Step. To pay one cent for each orange would require six cents ; then you would pay as many cents for each orange as six cents is con- tained times in twenty-four cents, Third Step. Which are four times. Fourth Step. Therefore, if you should buy six oranges for twenty-four cents, you would pay fout cents for each orange. MENTAL ARITHMETIC. 279 Remarh. In examples of this kind the pupil is inclined to take it for granted that one kind of concrete quantity is contained in another kind of concrete quantity. Hence his analysis is likely to be thus: " Since you buy six oranges for twenty- four cents, each orange will cost as many cents as six is contained times in twenty-four." Six what is contained times in twenty-four what? should be asked by the critical teacher. For further examples and solutions I refer th^ teacher to Ray's Mental Arithmetic. 12. VARIATIONS IN THE MANAGEMENT OF CLASSES. 1st. If a class is large, it will be better for each pupil, as his name is called from the register, to take but one step in a solution. Thus more of the class will be reached in a given time, and more general attention secured with less difficulty. 2d. It may be well occasionally to combine the second and third steps Jn one, i. e., let the pupil give the process and result of each operation pro- posed in the method of solution ; thus, JELenry^ rising, gives the solution. First Step. If three tuns of hay cost twenty- one dollars, what will five tuns cost? Second and Third Steps. If three tuns of hay cost twenty-one dollars, one tun will cost one-third of twenty-one dollars, which is seven dollars; and if one tun cost seven dollars, five tuns will cost five times seven dollars, which are thirty-five dollars. Fourth Step. Therefore, if three tuns of hay 280 MENTAL ARITHMETIC. cost twenty-one dollars, five tuns will cost thirty- five dollars. 13. RANDOM EXERCISES. A random exercise is sucli as is engaged in hy the class without previous study, the teacher leading. These should be commenced with small integral numbers ; and the teacher should proceed slowly in his lead, at first bringing in only addi- tion and subtraction. As a class improves under the exercise, the operations of multiplication and division may be introduced ; also, involution and evolution; also, fractional quantities. I will give a few examples. 14. Example 1st. Teacher. Class, take seven, add five, add eight, add five, subtract nine, subtract eight. How many have the result? The pupils, as many as have followed the teacher and have obtained the final result, are expected to raise their hands. ♦ Teacher. — James. James. — Twelve. Teacher, How many agree? [No hands rise.] How many have a diff'erent result. [Hand rises.] Sarah. Sarah. — Eight. Teacher. — How many agree with Sarah? [Hands rise.] Yery well. How many can give the operations aloud? [Hands rise.] Susan. Susan. Take seven, add five, which gives twelve ; add eight, which gives twenty ; add five, which gives twenty-five; subtract nine, which gives sixteen ; subtract eight, which gives eight, the final result. Teacher. — Very well, Susan. MENTAL ARITHMETia 281 15. Example 2d. Teacher. — Class, take fourteen, divide by seven, multiply by twelve, multiply by two, add two, divide by twenty-five ; bow many have the result? The same course is pursued in bringing out all the scholars, in ascertaining how many have fol- lowed the question, and how many have not, as before. 16. Example 3d. Teacher. — Class, take nine, square it, subtract seventeen, take square root, double it, take the square root, take the square root ; how many have the result? > 17. Example 4th, Take one hundred, multiply by nine-tenths, multiply by eight-ninths, multiply by seven-eighths, multiply by six-sevenths, multiply by five-sixths, multiply by four-fifths ; how many have the result? - 18. Example 5th. Take eight, divide by four-fifths, divide by five-sixths, divide by six-sevenths, divide by seven-eighths. Hovr many have the result? I 19. Example 6th. A monkey started up a mast sixty feet high ; he ran up twenty feet, down eight feet, up fifteen feet, up seventeen feet, up six feet, jumped up five feet, and where was he? 24 282 MENTAL ARITHMETIC. 20. The variations of random exercises are, of course, endless. They serve for variety, and if properly managed will arouse any desirable amount of e-n- thusiasm in a class. They should not, however, be relied on, to any great extent, as a means of suitable training, in Mental Arithmetic. I will give one more example, involving a few contractions, which may be reached by the class in the appropriate successive drills on each contrac- tion. 21. EXAMPLE IN CONTRACTIONS. Take eighteen, multiply by five, multiply ly twenty-five, multiply by ten, take the square root, add ten, multiply by twelve and a half, divide by thirty-three and a third, multiply by ten, divide by sixteen and two-thirds, and what is the result? Explanation. 18x5=18x^=90, 90x25=90 X'r=2250. 160 xl2-i=160x'r =2000, 2000-^- 33J=2000xTeo=60, " 60x10=600. 600^16| r=600XT^j=S6, METHODS OF TEACHING WRITTEN ARITHMETIC. PRELIMINARY REMARKS. 22. Remarh \st. Written Arithmetic should be commenced with Mental Arithmetic. Scholars in Mental Arithmetic should be provided with slates, and they should be permitted to work out the examples, while studying iJiem, on the slate. They should also be required to work them on the slate or blackboard after having solved them mentally. 23. Remark 2d. In the management of a large class in Written Arithmetic, the principal difficulty to be overcome is that of reaching all the schol ars at everi/ recitation. Unless this is done schol- ars are liable to remit their efforts, especially on such days as they may think the chances are against their being called on to recite. This difficulty must be met, if possible, and every scholar must know that he will be held re- sponsible at every recitation, for a thorough prepa- ration of all the lesson. If in the division of time (283) 284 WRITTEN ARITHMETIC. among the several classes it shall be found impos- sible to give time enough to Arithmetic, to reach every scholar, in each recitation, it will be better to have the recitation every other day, and the Grammar recitation every alternate day. Thus double the amount of time could be had for each recitation in these two leading subjects, by having them occur only half as often. By proper management in the use of blackboards and slates, every scholar in the largest class may be reached. 24. Remark 3cZ. The blackboard should be suffi- ciently capacious, if possible, to accommodate all the class at once. To this end all the space on the walls of the room not taken up by windows and doors, to the height of six or seven feet, should be occupied by blackboard. It is sufficient to paint a hard firm wall that is laid on brick. If laid on lath, it should first be covered with the thickest, firmest wall paper that can be had, and then paint- ed black. If, then, there is not room enough to accommodate all the scholars at the same time, those who cannot find room on the board for working examples, can work them on their slates as they sit on the recitation seats ; and the teacher can pass around and look over the work of each scholar as often as a new example has been as- signed and wrought. 25. Remarh 4:t7i. In the earlier steps, especially, it is better to give the same example to all the class, "WRITTEN ARITHMETIC. 1^85 to work simultaneously. But in review lessons, and in a more advanced class, it is better to assign different examples to each pupil, unless some ex- amples more difficult than others should be as- Bignod to several different pupils, or taall of them. 26. Remark dth. Some teachers think it necessary that scholars should understand the reasons of every rule, before they are permitted to use it in working out examples. This is plausible, but will be found to work badly. It is. better, gener- ally, for scholars to learn the practical working of a rule first, and thus have their curiosity excited to inquire why they have to do so and so, as the rule directs, to obtain the result; rather than to force the reasons upon them before they have any desire to know them. With a few of the quicker scholars, the latter plan will work well enough ; but with the majority of most classes the former course is decidedly preferable. There is no trouble in feeding a hungry child, but the same food only disgusts him when he has no appetite. First ex- cite the desire to know ; then administer to the mind's cravings. 27. Eemark 6th. It hardly seems desirable to me to require scholars to give arithmetical rules pre- cisely in the language of the book. I prefer that they should describe the processea in their own lan- guage ; a rule in Arithmetic being " a description of a process for obtaining a required result." It 286 WRITTEN ARITHMETIC. is more necessary, perhaps, to require the rules verbatim from beginners. 28. Remark 7th. Books without answers are pref- erable, for the reason that a strong temptation is removed to copy the answers from the book with- out solving the questions; for the reason also that scholars are more self-relying, and are made, by this means, better practical reckoners and account- ants. If answers are not desirable in Mental Arithmetic, why in Written? 29. Remark Sth. I would, if possible, avoid any text book in Arithmetic or Algebra which has a printed key in market. Keys are paralyzers, nuisances, and the teacher should be particularly watchful that keys are not resorted to by pupils in any of his classes. 30. Remark 9th. The skilful teacher will always prepare his class for any difficulty which may meet them in the advance lesson. He may explain the difficulty orally ; he may solve an example, not in the book, which shall meet the difficulty ; he may give the class a preliminary drill on a rule, or on a series of more difficult examples under any rule, or in miscellaneous examples under a number of rules. Such preparation, judiciously given, more than anything else, is calculated to keep up the ambition of all a class, by removing all excuses for laziness and discouragement. WRITTEN ARITHMETIC. 287 31. Remark l^th. Small scholars should be re- quired to bring their examples, wrought on slates or on paper, to the recitation, which the teacher will examine, a-s the First Step in every recitation. This will not prevent their working them again during the recitation. Remark llfh. The manner of conducting dif- erent recitations in Written Arithmetic are so similar that I shall give but two Lessons — as ex- amples. 33. .PRIMARY LESSON. First Ste? — The Teacher examines the Slate or paper of each pupil, to determine how much of the lesson assigned has been prepared, and how well the work has been executed. He points out the errors as he proceeds, giving as much encour- agement in every case as possible, and as little censure. Second Step — Eecitation of Rules or Tables assigned for the lesson. Third Step — Working the Examples on the slates or blackboard. As in few schools there is blackboard enough to accommodate all the schol- ars, they will be called up in sections to the board without books, and will follow the orders of the teacher. 13 288 WRITTEN ARITHMETIC. 34. Order 1st. — Prepare the hoard. This is done by erasing any former work, and dividing the board by vertical lines into equal spaces for each scholar. Each scholar draws a line at his right. Order 2d. — Write the example. The teacher then dictates the example and all write it, both those at the board, on the board; and those on the recitation seat, on their slates. Order ?»d. — Perform the example. The teacher now has opportunity to note the readiness and correctness of each pupil in his work as he pro ceeds, whether at the board, or on the seat; or the failure or errors of any, or their inclination to copy from others' work. Order 4:th. James, you may explain your work. James proceeds to explain the example as he has solved it; and the teacher, at any error, either in the work or in the explanation, looks for the rais- ing of hands by other members of the class, and if no pupil notices the error, he calls attention to it by the question, Why do you thus? or by any other that the case may require. When James has concluded his explanation, the class is called on for criticisms. After these are settled, the teacher may inquire, "How many understand James' explanation?" Hands rise. *•' How many do not understand the example?" If hands rise he may call on James again to explain the exam- ple, or on some other pupil, or he may explain it himself. Order bth. — Be seated. Vv^RITTEN ARITHMETIC. 289 35. The teacher then calls up another section, and proceeds in a similar manner with them in the v/orking of another example ; and so on till the time has expired, or so far expired that he can only have time for the fourth step. Fourth Step — Preliminary explanation and DRILL for the next lesson. 36. ADVANCED LESSON. Remark. The same course may be pursued with an advanced class as that described for a pri- mary class, or the following method may be used. First Step. Teacher. — Any who have reports to give may prepare their work on the board. Scholars, then, to whom any classification, de- monstration, or explanation was assigned at any previous recitation, for this recitation, take their places at the board and make any necessary prepa- ration, as writing out the classification or work necessary for a demonstration. Second Step — Recitation of Rules or Tables by the rest of the class. Third Step — Scholars at the board give the demonstration ; and the same order of criticism from the class and from the teacher, as was de- scribed in the Primary Lesson, is pursued. 37. Fourth Step — Working the examples. The course to be pursued is the same as described ia the Primary Lesson, except that it will be found 290 WRITTEN ARITHMETIC. necessary to give each pupil a diiferent example. These may be assigned by number to each pupil, he having the book in hand from which to take his data. Fifth Step — The explanation op examples. It is supposed that the teacher, in a preliminary drill has himself explained the working of the rule; and demonstrated the principles on which its different points are based. In this stage of the recitation, one pupil is called for the demonstration of one principle in connection with his example; and another for the demonstration of the same principle or another in connection with the ex- planation of his example. All under the same course of criticism, from other scholars and teach- er, as has been before described. Sixth Step — Pheliminary explanation and DRILL for next recitation. THEORETICAL ARITHMETIC. 38. Remarh. Instead of presenting the method of teacliing Theoretical Arithmetic, I shall give a condensed view of the subject itself; leaving it for the teacher to apply the methods before described for Grammar and Geography. I. — ARITHMETIC. f (Euclid, B. C. 300, Greek Notation. Ancient, -| Archimedes, B. C. 250, Greek Notation. (Diophantes, A. D. 250, " •' History, \ f Lucca de Borga, A. D. 1484, Arabic Notation. Modern J Nicholas Pike, A. D. 1776, « y Warren Colburn, A. D. 1825, Mental Arith'c. ' Definition, Solution, Rule, Demonstration, \ 't^'^^. Terms, Problem, Corollary, Scholium, Lemma. Theorem. Proposition Hypotheses, Axiom, Discussion TT •*. n „ *•*„ i Magnitude. Unit, Quantity, j Multitude. Integral, ) \ Abstract, Even, ) ( Simple, Odd, i I Comp'nd. Rational. ) Surd. 1 . Fractional, i \ Concrete, j I j ( Cardinal, | ( Prime, ) ^25 [ \ Ordinal, i 1 Composite, \ As to uses : — Abstract, Applied. Classes, \ As to characters: — Particnlar, General. As to operation : — Mental, Written, Theoretical. r Preliminaries SS^*^'*«"/- \ Numeration. r Addition, Fundamental J Multiplication, Diyisions, Increase. Operations, Diminution. I Subtraction, . Division, " 1 Comp. Numbers, 2 Com. Fractions, 3 Decimals, 4 Ratio and Proportion, A«r^i;naf?«r,« J ^ Percentage, 6 Partnership, 7 Alle- Appiication., -J g^tjQQ^ 8 Exchange, 9 Partnership, I 10 Involution, 11 Evolution, 12 Men- {.suration, 13 Analysis. (291) ^92 THEORETICAL ARITHMETIC. 39. \' DEFINITIONS, EXPLANATIONS AND REMARKS. Arithmetic. The Science of Numbers History. Notice of the most prominent wri* ters, and of the progress of the Science of Arith- metic. Ancient History. That which applies to time previous to A. D. 1400. Modern History. That which applies to time subsequent to A. D., 1400. Euclid was the first writer on Mathematics whose works have come down to us. He wrote on Geometry and Optics, as well as on Arithmetic. He established a school for Mathematics at Alex- andria in Egypt, which Ptolemy Lagus, the Egyp- tian Monarch, attended. When the pupil inquired of Euclid, if there was no easier method of learn- ing Mathematics, Euclid replied, " There is no royal road to Geometry." Although he was the first writer on Mathemat- ics, he was indebted to Thales and Pythagoras, celebrated teachers, for much contained in his works. Archimedes flourished in Syracuse. He made many discoveries in Mathematics, and inventions in Mechanics. One of the former was the ratio of the cylinder to the inscribed sphere ; one of the latter was an arrangement of mirrors by which he Bet the Roman fleet on flre. He also discovered the means of obtaining the specific gravity of bodies. Several fragments of his writings are extant, but nothing on Arithmetic. THEORETICAL ARITHMETIC. 293 BiOPH ANTUS flourished at Alexandria. The time at which he wrote is not definitely known. But his works remain, both on Arithmetic and Alge- bra. He was the first writer on Algebra. Lucca de Borga is worthy of note, as being the first European writer who made use of the Arabic Notation. 40. Definition. Such a description of an object as includes everything of the kind, and excludes everything else. Solution. A process by which a required re- sult is obtained. EuLE. A description of a general process for obtaining a required result. Demonstration. A course of reasoning by which the propriety of a Rule is made obvious ; also a course of reasoning by which a proposed truth is established. Direct Demonstration. One that commences with known truths ; and by a course of reasoning establishes the proposed truth. Indirect Demonstration. One which assumes the proposed truth to be false, and then proves that an absurdity will result from the assumption. This is also called a Reductio ad absurdum. Proposition. That which requires a solution, or a demonstration. Problem. A question proposed for solution. Theorem. A truth requiring a demonstration to establish it. 294 THEORETICAL ARITHMETIC. Corollary. A truth deduced from a preceding proposition. Scholium. A remark on a preceding proposi- tion, showing its application, restriction, or exten- sion. Lemma. A subsidiary proposition. Hypothesis. A supposition made either in the statement or demonstration of a proposition. Axiom. A self-evident truth. Discussion. A course of investigation by which the properties, relations, and applications of any number, proposition, or rule, are demonstrated. 41. Quantity. That which can be increased, dimin- ished, or measured. Magnitude. Undivided Qi^tity; also that form of quantity which answer.»4fte question, How much? Multitude. Quantity made up of distinct parts; also that form of quantity which answers the ques- tion. How many? Unit. A single thing, either a whole or a part. Number. One, or more, or less; also an expres- sion for Quantity. Integral Number. An expression for one or more whole or entire units. Fractional Number. An expression for one part of a unit, or more than one equal parts of a unit. Abstract Number. A number taken without reference to substance, time, space, or their prop* erties. THEORETICAL ARITHMETIC. 295 Concrete Number. A number applied to sub- stance, time, space, or their properties. Even Number. One which, can be divided by two without a fractional quotient. Odd Number. One which cannot be divided by two without a fractional quotient. Simple Number. One in which the units ex- pressed, are all of the same value. Compound Number. One in which the units expressed are of different values. Cardinal Number. One used to denote multi- tude, or how many. Ordinal Number. One used to denote the order or rank of an object. Prime Number. An integral number which can be divided by no other integral number than itself and unity without a fractional quotient. Remark. There is no term in Mathematics which has had so many bungling, worthless defini- tions, as this. Ray's definition: "A prime number is one that can only be exactly divided by itself and unity." {since every number can be exactly divided by every other, with either an integral or fractional quotient, there is no prime number according to this definition. Again, in Ray's Higher Arithmetic, we find this : "A prime number is one that can be exactly divided by no other whole number but itself and unity." Since every whole number will exactly divide every other number whether fractional or integral, there can be no prime number according to this definition ; moreover, the grammatical sequence of hut to other, is, to say the least, inharmonious. Again, Thompson's definition is still worse : *•' A prime num- ber is one which cannot be produced by multiplying any two or more numbers together, or which cannot be exactly divided by any whole number except a unit and itself." Since every num- ber can be produced by multiplying itself by unity, or some in- tegral number by some fractional number, there is no prima number according to Thompson. Loomis' definition involves the same absurdity, rf Leach & Swan's definition is passable. Davies' definition is the best, most simple and concise 296 THEORETICAL ARITHMETIC. Rational Number. One whose exact root can be expressed by figures. Surd Number. One whose exact root cannot be expressed by figures. 42. Classes. Results of arrangement according to a given plan. Abstract Arithmetic. That form of Arith- metic which makes use of abstract numbers. Applied Arithmetic. That form of Arithmetic which makes use of concrete numbers, Rcmarh. Book-keeping and Mensuration may be mentioned as examples of Applied Arithmetic. Particular Arithmetic. That form of Arith- metic which makes use of figures to express par- ticular values. General Arithmetic. That form of Arithme- tic which makes use of letters ta express general values. It is also called Algebra. Mental Arithmetic. That form of Arithmetic in which the operations are carried on entirely in the mind, without the use of visible characters. Written Arithmetic. That form of Arithmetic in which the operations are carried on by the aid of visible characters. Theoretical Arithmetic. That form of Arith- metic which investigates principles, and demon- strates rules; also, that gives a clear, connected, and systematized arrangement of all the principles and rules involved in the subject. 43, Preliminaries. Preparatory processes. THEORETICAL ARITHMETIC. 297 Fundamental Operations. Processes on which all others ar3 based ; or those without which no others can be performed. Applications. All other processes than the preliminary and fundamental. 44. II. — NOTATION. Signs, __ ^. r Increase +, X, ab () of Operation ^ ^. . ^. ' . a^^^,, „ I Diminution f--^, a)b(, ^ of Relation =, :,-::, > , <. of Deduction .*. , [of Aggregation , (),[], j | . f History, I Forms, I, V, X, L, C, D, M, " Roman) | Origin of each. increase, j ^ 'luUi r"'""' Characters, Arabic \ or > .Figaral,) Laws of arrangement History, Forms, 1, 2, 3, 4, 5, 6, 7, 8, 9, 0. {Significant, or digits. Classes, -|Zero, cypher, or naught. (Separatrix. Origin of each. Radix, Fundamental Law. ^^^-^tE'Taf' 45. DEFINITIONS, EXPLANATIONS AND REMARKS. Notation. Any visible method of indicating operations or relations ; also of expressing quan- tity. Sign. A mark or combination of marks to in- dicate an operation or relation, deduction or ag- gregation. Operat'on. Process involved in a solution. 298 THEORETICAL ARITHMETIC. Ih CREASE. Augmentation. The act or result of making largir. Diminution. Decrease. The act or result of making less. Relation. Bearing. 46. The sign -|- signifies add to; and is read, jplm- It has its origin in the fact that two lines thus placed seem to be the simplest manner of express- ing the act of addition. The sign x signifies multiply hy, and is read into. It has its origin in tallying, or keeping accounts of several successive additions of the same quantity, which consists in crossing obliquely oth- er marks. This is an abridged or simplified form of tallying. The sign of contiguity, as represented in ab, is Msed only in letters, or in Algebra. The sign O"^, or the exponent, signifies that the quantity immediately before it, or the quantity contained in the parenthesis to which it is attached, is to be multiplied by itself a number of times, one less, than there are units in the sign. The sign — signifies subtract from, and is read minus. It se^ms to have originated in the sign -j- ; one of the marks having been taken away, suggesting the idea of subtraction ; and the mark left, a difi"erence. The sign ~r- signifies divide hy; and is read, divided hy. Its origin is plainly, that of dividing or separating one line into two parts, by the use of another. IHEORETICAL ARITHMETIC. 299 The sign J signifies divide hy^ or the result of having divided one quantity by another, and is read over, as a over b ; or in this example, jf) sev- enteen over thirteen. The sign a)b( signifies that the quantity at the right of the first curved line is to be divided by the quantity at the left. In Algebra the divisor is placed at the right of the line curving to right. The sign y^, or the radical sign, signifies that the square root of the quantity to which it is pre- fixed, is to be taken. If a figure is placed before the sign, then such a root is to be taken as is indi- cated by the figure, which is called the index. 47. The sign = signifies eqiiality, and is read, is iqual to. Its origin is found in the fact that it is the simplest method of expressing to the eye the idea of equality. The signs ><^ signify inequality, and are read is greater than, and is less than; the greater quantity being placed at the opening, and the less at the apex of the angle. The sign of ratio : is an abridged form of the sign of division. In the French form of writing the ratio, however, the divisor is JJlaced before the sign, and the dividend after it. It is read, as, as, in the first couplet and to in the second. The sign of proportion : : is an abridged form of the sign of equality ; the extremities only of the line being used. It is read so is. The sign of deduction . *. seems to have its ori- gin in the fact that there are throe terms in a syl- T] 300 THEORETICAL ARITHMETIC. loglsm; tlie two first being true the third must follow. It is read therefore. 48. The signs of aggregation are the bar , which signifies that the numbers over which it is placed are to be taken together as one number ; also, the parenthesis, (); the brackets, []; and the braces, j j , which signify that the quantities enclosed by them respectively are to be taken together, as one quantity. Remarh. The use of technicalities not hitherto defined in this work, for the explanation of the signs, is not strictly philosophical; but as this classification is only used in reviews, and as the signs are an inseparable part of Notation, the de- mands of the case seem to warrant this departure from rigid philosophical usage, in the arrange- ment. 49. Characters. Any written or visible forms used to express numbers. Verbal Characters, or Verbal Notation. Visible words used to express numbers. Roman Notation. That notation which makes use of seven Caprtal Letters, to express numbers. Arabic Notation. That which makes use of ten figures to express numbers ; also a separatrix. 50. History of the Roman Notation. Notwith- standing the Roman alphabet seems to be but a modification of the Greek alphabet, the Romans adopted an entirely difi'erent notation for numbers. THEORETICAL ARITIJ.METIO. 301 While the Greek notation makes use of the letters ^ in their original order and number to express numbers, the Roman notation, in part, seems to have been in use before the Roman people adopt- ed the Greek letters or formed an alphabet at all, as their origin will show. The several capital let- ters, which more nearly corresponded to the ori$^i- nal marks of the notation, were subsequently adopted. Origin of the Koman Characters. In count- \ ing, or in keeping an account, it is obvious that j one or more vertical lines is as simple a method as \ could be adopted for the first few units. The let- | tcr I was afterwards used as most nearly resem- | blin^ such a vertical line. ! When the number equal to the fingers and i thumbs on both hands had been reached, it was i natural and easy to cross the vertical lines signi- | fying ten. In transferring this method of tally- ing, or of keeping accounts, it was after a while discovered that a simple cross would answer as well afi all the marks of the original tally. Hence | a cross was adopted for tea, and afterwards an X j for the cross. ; Either half of the cross was used for five, but j the letter Y, corresponding to the upper half, was I finally adopted. The initial of Centum, which signifies one hun- dred, was adopted, after the introduction of the alphabet, to save the trouble of writing ten cmssea j or X's. Either half of the letter C in its angular form C 302 THEORETICAL ARITHMETIC. was used to represent fifty ; but since the letter L corresponds to the lower half it was finally adopted. The initial of Mille, which signifies one thou- sand, was also used to represent one thousand. Following the law of taking halves, a half of thi? letter was taken for five hundred. It was finally supplanted by the letter D, the letter which seemed most nearly to correspond to it. Katio of Increase. From the origin of these characters it is seen that they increase in the alternating ratio of five and two. Laws of Arrangement. 1st. A letter, not of greater value, being placed after another gives the sum of the values represented by the letters sepa- rately. 2d. A letter of less value being placed before another, gives the difi'erence of the values repre- sented by the two letters standing separately. 3d. A horizontal line drawn over any letter or letters increases their value one thousand times. 51. History of the Arabic Notation. The Ara- bic figures were introduced into Europe during the tenth century, by the Crusaders. From the Arabic these figures have been traced to the sacred books of the Brahmins in India. The Brahmins claim that they are a gift of the god Brahma. They are probably the invention of some inge- nious priest of that heathen deity. Origin of the Figures. In keeping accounts, one mark would naturally represent one. Two horizontal marks with a connecting line would THEORETICAL ARITHMETIC. 303 stand for two, thus : ^. Three horizontal marks with connecting lines would stand for three, thus : 3 ', and four marks, either arranged in the form of a square or triangle, would stand fcr four, thus : Q, 4'« Five marks in this form ^ ^^^ the original figure five of this notation. Six marks, thus ; □, the original figure six. The figure eight was made by placing two squares near each other, thus: g; and seven, by omitting one of these marks, thus: rn : nine by adding one more mark to the figure eight, thus : H. The zero was originally a circle, and seems to have been suggested from counting around the fingers and thumbs, as held in a circu- lar position. Hence once around was denoted by the figure 1, and 0. Twice around by 2 and 0, and so on. From this last arrangement seems to have been suggested the law of the notation, in which its superior utility consists. For, by placing any other figure in the place of the zero to make the numbers between ten and twenty, we have the law established. Separatrix. a mark used in the Arabic nota- tion to separate units from tenths, in other words, integers from decimal fractions. Remarh. The separatrix is always written, or supposed to be written, at the right of the unit's place. Though not called a figure, it is still the most important character in the notation. Radix of the Arabic Notation. The number expressing the number of times the value of any figure is increased or diminished as it is removed 304 THEORETICAL ARITHMETIC. one place to the left or right, to or from the sepa- ratrix. It is ten. Fundamental Law of the Arabic Notation. Every significant figure has its value multiplied by ten every time it is removed to the left, towards or away from the separatrix; and divided by ten every time it is removed one place to the right, towards or away from the separatrix. 52. Remark 1st. Figures at the right of the sepa- ratrix express, obviously, by the law of the nota- tion, fractional quantities; as tenths, hundredths, etc. Such figures are called decimal figures, and the quantities expressed by them are called deci- mals, or decimal fractions. Remark 2d. The removal of figures is often accomplished relatively by changing the place of the separatrix. This can also be done in whole numbers, by annexing cyphers or other figures; and in the fractional figures by interposing cyphers or other figures between the separatrix and the given figures. Simple value of a Figure. Its worth when standing in the first place at the left of the sepa- ratrix. Local Yalue of a Figure. Its simple value multiplied or divided by such a power of ten as is indicated by the order of the place that the figure occupies at the left or right of the place of unity. THEORETICAL ARITHMETIC. 305 53. III. — NUMERATION, Orders.— Units, Tens, Hundreds, Thousands, et«. Periods. — Units, Thousands, Millions, Billions, etc \r ,■ , < French. ISational, ] English. Methods, iPra^tica!, ||S'^^''^' Derived, ] by Hundreds, etc. 54. DEFINITIONS, EXPLANATIONS AND REMARKS. Numeration. Any method of expressing the values of figures in words. Orders. Places occupied by the several figures being counted towards the left and right from the separatrix. Units. The first order, at the left of the separ- atrix ; also, the first order of integral numbers or integers. Tens. The second order of integers. Hundreds. The third order of integers. Tenths. The first order at the right of the separatrix; also the first order of decimal fractions. Hundredths. The second order of decimal | fractions. i Periods. Groups of orders, named and used to i facilitate numeration. ! French Method. That method of numeration in which three orders constitute a period. English Method. That in which six orders constitute a period. j Remark. The names of the orders in bot!i methods are the same as far as the ninth, or hun- dreds of millions; after which they take different 306 THEORETICAL ARITHMETIC names, the tenth being called in the French meth- od, billions, and in the English method, thousands of millions. Namks of thk Terjods.— 1st, Units. 2d, Thousands. 3d, Millions. 4tb, Billions. 5th, Trillions. 6th, Quadrillions. 7th Quintillions. 8tb, Sextillions. 'Jth, Septillions. 10th. Octil lions. 11th, Nonillions. 12th, Decillious. 13th, Undecillions, lith, Duodecillions. 15th, Tridecillions. 16th, Quadrodecil lions. 17lh, Quindecillions. 18th, Sexdecillions. 19th, Septo docillions. 20th, Octodecillions. 21st, Nonodecillions. 22d Yingintillions. 23J, Unvingintillions. 24th, Duo-vingintil lions, etc. 32d, Trigintillions. 42d, Quadrogintillions. 52d Quingintillions. 62d, Sexagintillion.s. 72d, Septuagintillions 82d, Octdgintillions. 92d, Ninogintillions. 102d, Centillions 103d, Unccutiilions. 104th, Duocentillions, etc. 202d, Duo- centillions, etc. 1002d, Millillions, et-c. Derived Methods of Reading Numbers. These are veadings with the assumption of some other order than units as the base. Example. — SOi.OG may be read as tens, thus : thirty tens, and four hundred and six thousandths of a ton. The same number may be read as tenths, thus : three thousand and forty tenths, and 8ix tenths of a tenth. 56. TOPIC LIST FOR DISCUSSION OF FUNDAMENTAL OPERATION. 1. Definition. 2. Terms, and definitions. 3. Signs — form, signification, reading. 4. Rules, Demonstrations. 5. Proofs, Demonstrations. 6. Comparison with other operations 7. Contractions, Demonstratione. 8. Use of negative quantities. THEORETICAL ARITHMETIC, 307 Remarh. The four fundamental operations may each be discussed very thoroughly by following this Topic List as a guide in the investigation, I shall omit many of the most obvious considera- tions in my discussion, as these can be obtained from all Arithmetics. Pupils, however, should be required in these discussions to reach every point, whether obvious or obscure. 57. DISCUSSION OP ADDITION. 5. Proof 1st. Add the columns downwards. Proof 2d. Reject the ]?^ines from each quan- tity, also from these excesses so obtained, also from the sum of the quantities; then, if the ex- cess of the excesses of the several quantities is equal to the excess of the sum of the several quantities, the work is supposed to be right Dernionstratmn. Since by the sixth Theorem — Bay's Algebras — the difference of the same powers of any two numbers is divisible without a fraction- al quotient, by the difference of the numbers, any power of ten, minus any power of one, is diivisible by ten minus one. In other words, any power of ten is one greater than a multiple of nine. This may be expressed thus : (10)°— (l)'^ is divisible by 10—1 without a fractional quotient, or (10)" — 1 is divisible by 9, without a fractional quotient. But if a unit of any integral order gives one for a remainder, when divided by nine, then any fig- ure in any order will give itself for a remainder when its local value is divided by nine. Hence 308 THEORETICAL ARITHMETIC. the figures expressing any integral quantity will express so many remainders, when the quantity is separated into the parts expressed by the local values of the several figures used to express it, and each part is divided by nine. Now if the sum of these figures, or remainders, be divided by nine, the true remainder for the whole quantity will be obtained. Thus, 7896, separated into parts as described, gives 7000 and 7 remainder, 800 and 8 " 90 and 9 " 6 and 6 " The true remainder from the given quantity is thus obtained by rejecting the nines from these figures, either as they stand in the vertical column or in the given quantity. 58. One example will suffice to show the process of Rejecting Nines, and of proving addition by this process. EXAMPLE FOR PROVING ADDITION BY REJECTING NINBS. 4 y Excesses l^nal excess, ll^ZlT''''^'- r7896 Quantities, ] 4567 (3864 sum. Sum, 16327 Process. First quantity. 6-)-8=14, which gives 5 as an excess, 5-|-7=12, which gives 3 as an excess 3 is placed in the column of excesses. It will be noticed that no attention is paid to the figure 9. THEORETICAL ARITHMETIC. 309 Second quantifi/. 7-|-6=13 ; 4, excess. It will be noticed that no attention is given to 4 and 5, as they are equal to nine. Third quantity. 4-|-6==10 ; 1, excess. l-[-8 =9, hence 3 is the excess of the third quantity. Rejecting nine from these excesses, we have 1 for a final excess. Rejecting nine from the sum of the quantities, which is done by simply noticing that 7-f-2=9 and 3-|-6=9, 1 remains as the excess of the sum of the quantities. This being equal to ihe filial eKcess of the quantities as before obtained, the work is supposed to be right. The concluding link in the chain of demonstra- tion is this : Since we have found the remainders of the several quantities, when divided by nine, to give a final remainder equal to the remainder from the sum of the several quantities, the sum is sup- posed to be correct. Remark 1st. Any other figure would answer as well as 9 for this form of proof, save that 9 gives us its remainder more readily by this meth- od of rejection^ than other figures would their re- mainder, by the process of division. Remark 2d. This' property of nine, viz.: that it will divide any number loitli the same remainder^ as that ichich the sum of the figures, expressing the mimher gives, ivhen divided hy nine, results obvi- ously from its being one less than the radix of the notation. If the radix were eight, seven would have the same property. 310 THEORETICAL ARITHMETIC. Proof 3d. Reject the Elevens from differ- ence of the sums of the alternate figures in the several quantities ; also from the difference of the sums of the alternate figures in the sum of the several quantities ; then if the excess of the ex- cesses, from the several quantities, is equal to the excess of the sum of the quantities, the work is supposed to be right. Deinonsiration. By theorem 8th, Ray's Alge- bras, the sum of the same odd powers of two quantities is divisible without a fractional quotient by the sum of the quantities. Hence (10)'*-|-1'^ is divisible by lO-j-l, or 11, when n is an odd number. Then lO-fl, 1000-fl, 100,000+1, etc., are divisible by 11 ; in other words, the odd pow- ers of ten lack one of being divisible by 11, or give — 1 for a remainder. If the figure 1 in all the odd places taken in its local values gives — 1 for re- mainders, then any other figure will give itself with the minus sign for a remainder, — i. e., as 10, 1000, 100,000, or any other odd power of 10 gives —1 for remainders. 20, 2000, 200,000, etc., will give — 2 for remainders, when divided by 11. Hence every figure in any odd place may be taken with the minus sign, for the remainder, when its own local value is divided by 11. In a similar manner, by Theorem 7th, Ray's Algebras, it may be proved that each figure in the even places will give itself with the plus sign for a remainder, when its local value is divided by 11. THEORETICAL AR1TH3IETIC. 311 Now if the sums of these two series of remain- ders are equal to each other, they will cancel each other, and there will be no remainder when the quantity which the figurea express is divided by 11; or if these sums are not equal, their diflfer- ence gives the same remainder as the quantity which they express gives when divided by 11. If there should be an excess of the negative figures, the true remainder will be obtained by subtracting that excess from 11. Such being the case, we can add the two sums of alternate figures, and find the difi'erence of the two sums, remembering that the series of figures in the odd places give minus re- mainders. This process is much abridged, by subtracting the left hand figure of each quantity from the next, and the resulting remainder, from the next figure, and so on. The final remainder will always be the remainder with the proper signs. 60. EXAMPLE FOR PROVING ADDITION BY THE REJECTION OF ELEVENS. . 7896 ^ ,.,. ) 58731 Quantities, < <^Qg 41 Sum, 66874 I n >■ Excesses. .^ final PTPPsq f from exeeseea nnai excess, | ^^^^ ^j^^ ^^^ Taking the first quantity: 8— 7==:1, 9—1=8, 6 — 8= — 2 the excess. Taking the second quantity . 8 — 5=3, 7 — 3=4, 3— 4==— 1, 1— (— 1)=2. U 312 THEORETICAL ARITHMETIC, Taking the third quantity: 0—2=— 2, 6~(-'2) =+8. Taking the fourth quantity: 1 — 4i= — 3. Then the sum of these excesses, arranged at the right of their respective quantities, is +5. Taking the sum of the quantities: 6 — 6=0, 8— 0=+8, 7— 8=— 1, 4— (— l)r=: + 5. 61. Demonstration of this method of finding the difference of the sums of alternate digits. Let a, b, c, dz=:four figures expressing any quan- tity, including four orders. Then b— a, c— (a— b), d— [c— (b— a)] will represent the several steps of the subtraction. The last quantity, being reduced, so that each letter shall have its essential sign, and then ar- ranged, the result will be d — c-f-b — a, which cor- responds to the demands of the case. Again, take an odd number of letters repre- senting the figures standing in the several orders, perform a similar operation, and the result will also correspond with that obtained by subtracting the sum of the figures in the even places from the Bum of the figures in the odd places. JSchoIium. It will be noticed that in those quantities expressed by slvl even number of figures, that the process of subtraction must commence at the left, or the excess obtained will be aff'ected with the wrong sign. THEORETICAL ARITHMETIC. 313 Comparison of addition with other fundamental operations. 1st. It is similar to multiplication ; both being operations of increase. 2d. It is the opposite of subtraction. 3d. It is the indirect opposite of division. 63. Contractions. 1st. The addition of two or more columns at once. 2d. Multiplication is but a contraction of addi- tion, in the case in which the quantities to be added are alike. 64. Use of Negative Quantities. Remark 1st. The Teacher will do well to give his classes practice in the negative quantities un- der all the fundamental rules. Remark 2d. My limits will not permit the discussion of the other fundamental operations; but the discussion becomes more interesting as the class proceeds, from one to the other, in order. Remark Zd. The contractions in multiplication and division are worthy of close study; and de- mand thorough demonstration, each of them. Leach & Swan have given a better variel y of such contractions than other authors. 314 THEORETICAL ARITHMETIC. 65. COMPOUND NUMBERS. Terms, — Simple Numbers, Denominate Numbers. I National,) f Tables, [taining. /-Currency, -| State, > -j Standard unit, and means of ob- 1 Foreign, ) Coins — Gold, Silver, Copper, [ Comparison of each with others. I Avoirdupois, ) ( Tables, Weight, "I Apothecaries,)- -j Uses, [ing. I Troy. ) I Standard unit, means of obtain- t Comparison of each with others. Measure, Time, Linear— Long, Cloth, 'j Superficial — Square, Land, | I Soli I ••I Cubical, ?fy'., (Wine L'^'^^^'lBeer, Tables, Standard unit, means of obtaining it. Tables, Uses, Standard unit and the means of ob- taining. Comparison, f Increase, Operations, j Dimintition, I Reduction, J Addition < Multiplioation, ( Subtraction, \ Division, ( Ascending, j ( Descending, J ' Rules, and Demonstrations. Proofs, and Demonstrations. Remark. All the standard units are determined, directly or indirectly, from the length of the day or the time of a revolution of the Earth on its axis, as ascertained by astronomical observation. A pendulum, beating seconds, has a certain length. A linear foot is now determined by the pendulum. Dry and liquid measures are determined by the number of solid feet or inches. A cubic foot of pure water weighs 1000 ounces, and the standard pound is thus determined. Hence it is seen that any variation in the length of the day will cause a variation in all the denomi- nations, of every kind. THEORETICAL ARITHMETIC. 315 66. COMMON FRACTIONS. PBBLIMINARI£S. XC ambers, Classes, ^ Properties, Factoring, Greatest ) Common >- Divisor. ) Least I Common >• Multiple,) Tenns,- Classes, ^ Terms — Unit, Integer, Factor, Reciprocal, Root, f 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12. Demonstration of the properties of each number. Remark. — Properties,of 9 and 11, depend on their relation to the radix, .10. ( by inspection, I by division. Scholium. — UEe the primes no further than the square root of the number to be resolved. Demon- ^ strati on. ( by primes, I by division. Demonstration. i Divide the G. C. D. of numerators by ■j the L. C. M. of denominators. (. Demonstration. ( 1st. primes, U^ rs, ■ ■ Rules, Rules for integers, i Rule for Fractions, I Rule for '^ Fractions, , Rules for } J by ) egers, ) |j^y. jjy;gjQjj^ Demonstration. (Divide the L.C. M. of numerators by the G. C. D. of denominators. Demonstration. ESSENTIALS. -Numerator, Denominator. { as to value — Proper, Improper, and Mixed Numbers. \ as to form — Simple, Compound, Complex, r Equal to "j Value, ■< Greater than > Unity. [Less than J r« .-.^o.'o^., «* T?..n«*:^„ 1 fNumerator= Dividend, Comparison of Fraction I Denominator=Divisor with Division, i \valuo=Quotient. Propositions, 1, 2, 3, 4, 5, 6. Demonstrations. OPERATIONS. f Integers or mixed numbers to fractions, I Fractions to integers or mixed numbers. Fractions to lower or higher terms, \ Compound Fractions to Simple, I Complex Fractions to Simple, I Fractions tc equivalent fractions, with C. D# I. Fractions tc eq. Frao. with L. C. D. Reduction of Fractions Simple NumberS; of ) of \ ibers, J r 316 THEORETICAL ARITHMETIC. 'rr 1] Multiplication W-^'; Diminution, J Division, J 1 f j^ f Addition,— Sabtraction. Increase •] i M„u,-.i,-.af;n« ^ ^-Integers by fractions, Fractions by integers, Fractions by frnctions, "ixed No. by Mixed No. f Fract. of one denomination to frac. of another, •p , . . I Integers of different denominations to fraction of Fraction-- 1 ' ^^ ^'S^*''" ^^-^^^'^^^^^ons, f C d M Fractions of higher denomination to integers of Nu"ber"° -' lower denomination, ^ ''• I Quantity of several denominations to fraction [ of another quantity. 67. DEFINITIONS, EXPLANATIONS AND REMARKS. A Common Fraction. A Fraction -whose nu- merator and denominator are both expressed Preliminaries. Preparatory steps. Terms. Words not otherwise introduced in the classification. Unit. One, either integral or fractional. Integer. A whole number, or a number con sisting only of entire units. Factor of a Number. A divisor which gives an integral quotient. Remark. Factors are more generally considered integers, unless otherwise designated. Reciprocal of a Number. The result of divid- ing unity by that number. This result is said to be the reciprocal of the given number. Remark. The reciprocal of a numb^ may be obtained by changing it to the fractional form, if it be a mixed or integral number, and then invert- ing the fraction. Root of a Number. Any factor, whether frac- tional or integral, which being multiplied by itself THEORETICAL ARITHMETIC. 317 shall produce a given number. Explanation. Such a factor of a number is called, if multiplied into itself once, its square root ; twice, its cube root; thrice, its fourth root; and so on. Classes. Results of arrangement according to some given plan. Prime Number. Any integer which can only be divided by itself and unity without a fractional quotient. Absolute Prime. The same as a prime. Relative Primes. Integers which have no common integral factor, save unity. Composite Number. Any integer resulting from the product of other integers than itself and unity. Multiple of a Number. Any product, which results from taking a given number, either frac- tional or integral, an integral number of times. Such product is called a multiple of the given number. Pow^ER OF A Number. The result of taking a number a given number of times as a factor. Explanation. A number taken once as a factor, is the number itself, and is the first power. A number taken twice as a factor, is multiplied, or is to be multiplied into itself once, and is the second power. A number taken three times as a factor is the third power, and so on. The nought power of every number is unity, or the result of dividing a number by itself. Remark. Pupils should be well drilled in primes and their Pov/ERfl before commencing the study of 318 THEORETICAL ARITHMETIC. the Least Common Multiple. It is a good plan for the teacher to call for the primes, in concert, from the class, and to notice which of the class can go the farthest in giving them. It is well for the class to give each prime twice in the concert exercise, that the slower pupils may learn them. The powers of the smaller primes should be learned by a similar method. No pupil should be per- mitted to do anything with Least Common Multi- ples till he thoroughly understands the nature of primes and powers. 68. PROPERTIES OF NUMBERS. 1 is the nought power of every number. 1 is any power of itself. 1 is any root of itself. 1, used as a multiplier, does not increase the multiplicand. 1, used as a divisor, does not diminish the divi- dend. 2 is a factor of any integral number whose unit figure is divisible by 2, without a fractional quotient. Demonstration. Every integral number ex- pressed by more than one figure is made up of tens and units. The tens are divisible by 2 ; if the unit figure is also divisible by two without a fractional quotient, then the whole number is divisible by 2. 3 will divide any number without a fractional quotient, the sum of whose figures it will divide in the same manner. THEORETICAL ARITHMETIC. 319 Explanation. The figures of any number are the figures used in writing the number. Remarh. This property of three depends on its being a factor of 9. Remark. The properties of the other numbers are discussed in most Arithmetics, and my limits forbid my pursuing them further. The properties of nine and eleven, however, are discussed in section 58, page 310. Factoring. The process of separating numbers into their prime factors. Remark. Long and numerous drills must be given in factoring before commencing the study of the Greatest Common Divisor, and Least Common Multiple. The teacher will commence such drills by giving small numbors, and requiring the class to separate them by the mental process, and to give what power of lach prime factor is contained in each given nunibev. 69. Demonstration of Scholium. Since every di- visor smaller than the square root of a number, must give a quotient larger than the square root, and every divisor larger than the square root must give a quotient smaller ; if every prime number smaller than the square root proves not to be a factor, no prime number larger can be, for the reason, as before stated, that it must give as a quotient one of the primes less than the root, which is impossible; as they have already been tried, and fouitd not to be factors. 14* 320 THEORETICAL ARITHMETIC. 70. Demonstration of Rule by divisioD for finding the Greatest Common Divisor. The Gr. C. D. of two numbers must be the same as that of the smaller number and the remainder after the smaller number has been taken out of the larger number as many times as possible. Illustration. Take the two lines A B C I I? D, apply the shorter to the longer; it is evident that after the shorter shall have been applied to the longer as many times as possible, that the greatest common divisor or measure of the two lines A B, and C D, must also divide or measure the difference E D, after it has exactly measured the line C E, which is but the line A B, repeated on the line C D. Since then the Gr. C. D. of the remainder after division of the larger number by the smaller, is the same as that of the two given numbers, if this remainder is not itself the G. C. D., it may be taken out of the smaller as many times as possible, and then the G. C. D. of what remains after this second division will be the G. C. D. of the less of the given numbers and the remainder, and if so, then of the two given numbers. This process of dividing the last divisor by the last remainder must evidently be continued till there is no re- mainder, then the last remainder, which is also the last divisor, is the G. C. D. of the two given numbers. THEORETICAL ARITHMETIC. 321 71. RULES FOR OBTAINING L. C. M. BY PRIMES. 1st. Multiply /jOgetlier the highest powers of each of the prime factors contained in any of the given quantities. Demonstration. The L. C. M. is the product of the highest powers of each of the prime factors, found in any of the given quantities; for it must contain as many of each kind of prime factor a^s any number contains, or it would be impossible to divide by that number. No more factors of any one kind can be taken out the L. C. M. than it contains; but if any given number should contain more of such factors than the L. C. M., in attempt- ing to divide the L. C. M. by such a number it would be attempting to take out more of one kind of prime factor than the L. C. M. contains, which would be impossible. Nor should the L. C. M. contain more of any one kind of prime factor than the largest number of such prime factor contained in any one of the given quantities, as suoh would obviously be superfluous. 2d. Take the largest of the given numbers, mul- tiply it by such factors contained in the other numbers as are not provided for in the largest number, or by factors already taken from other numbers. Example. 12, 18, 20, 24, 50, By the first rule, 8 is the highest power of 2 contained in any of the given numbers, nine is the highest power of three, 25 the highest power of 5 and there are no other prime factors in the 322 THEORETICAL ARITHMETIC. numbers, save 1, wliicli does not affect tko L.C. M. Hence 8x9x25 = 1800, =L. C. M., for it con- tains all the 2's in all the numbers, since it con- tains as many as there are in 24, which contains more than any other. So also 1800 contains all the S's since it contains as many as 18, which has more than any other. So also of the 5's in 50. By the second rule I take 50, which contains one 2 and two 5's, but 24 contains three 2's. as factors, hence two of them are not provided for in 50, but must be by multiplying 50 by 4. Again, the 3 in 24 is not yet provided for; this must also be mul- tiplied into the former product of 50 and 4. All the factors of 20 are provided for, but 18 has two 3's, and as only one 3 has as yet been put into the L. C. M., another must be multiplied into it. Hence we now have for the L. C. M., 50x4x3x 3=1800. 2nd Example. 20, 30, 40, 50, 60. By the first rule we have 8x3x25 = 600=L, CM. By the second rule we have 60x5x2=600=L. CM. 3d Example. 24, 34, 44, 54. By the first rule we have 8x27x11 xl7=L. C M. By the second rule we have 54x2x11x17x2 «L. C M. 4th Example. 23, 33, 43, 53. By the first ru'.e we have 3x11x23x43x53=- L. C M. THEORETICAL ARITHMETIO. 323 By the second rule we have 53x43x3x11x23 = L. C. M. 72. Demonstration of the rule for obtaining the L: C. M. by division. Take the numbers 6, 8, 9, 12, 15, 18, 20, 24, 25 ; divide these by 2, and we shall obtain the quotients and undivided numbers, 3, 4, 9, 6, 15, 9, 10, 12, 25. Now this divisor 2 will answer for all the first powers of 2 contained in any of the given numbers; consequently those first powers of 2 are all rejected, and this divisor 2 is retained for them in the L. C. M. Dividing again by 2 we shall obtain the quo- tients and undivided numbers, 3, 2, 9, 3, 15, 9, 5, 6, 25. This second divisor 2 will answer for all the second factors of 2 in any of the given num- bers. It is therefore retained, a? a factor of the L. C. M. Dividing again by 2 we obtain 3, 1, 9, 3, 15, 9, 5, 3, 25. This third divisor 2 answers for all the third factors of 2 contained in any given numbers. Hence it is obvious that dividing by the several prime factors as long as two or more of the given numbers can be divided without a frac-* tional quotient, is merely for the purpose of re- jecting superfluous factors, and retaining the necessary factors, for the L. C. M. Remark. How much easier and shorter is the process of selecting the necessary factors according to Rules 1st or 2nd than to reject the unnecessary factors, according to the Rule, by division. Ac- cording to Rule 1st the necessary factors are 8x9 324 THEORETICAL ARITHMETIC. X25=1800. According to Rule 2d they are 25x8x9=1800. The L. C. M. is thus obtained at a glance, with scarcely any effort. Remark. The skillful teacher will not permit his pupils to learn the Rule by division at all ; or, if they have already learned it, he will drill them on the other rules ii\) they will be glad to let it alone. 73. ESSENTIALS. Terms of a Fractio^^. The numbers used to express it. Numerator. That term of a fraction which is written above the line, and expresses the number of parts taken, by the fraction. Denominator. That term of a fraction which is written under the line, and shows the number of parts into which the unit of which the fraction expresses a part, is taken. It also names the parts taken. 74. propositions. 1. Multiplying the numerator multiplies the fraction. 2. Multiplying the denominator divides the fraction. 3. Multiplying both terms by the same num- ber, does not alter the value of the fraction. 4. Dividing the numerator divides the fraction. 5. Dividing the denominator multiplies the fraction. THEORETICAL ARITHMETIC. 325 6. Dividing both terms by the saJiie number does not alter the value of the fraction. DEMONSTRATIONS. Prop. 1. Because it increases the number of parts while their size remains the same. Prop. 2. Because it diminishes the size of the parts while their number remains the same ; and it diminishes the parts, because the unit is thus divided into a greater number of parts, and of course each part becomes as many times less, as the divisor is times greater. Prop. 3. Because it increases the number of parts, as many times as it diminishes their size. Prop. 4. Because it diminishes the number of parts while their size remains the same. Prop. 5. Because it increases the size of the parts while the number remains the same ; and it increases the size of the parts because the unit is thus divided into a less number of parts ; each part being as many times greater as the divisor is times less. Prop. 6. Because it diminishes the number of the parts as many times as it increases their size. 75. Reduction. Change of form without changing the value. Remark. From want of room I shall only dis- cuss a few of the oj)erations of fractions; and those, to show the application of the propositione in their demonstrations. 326 THEORETICAL ARITHMETia REDUCTION OF FRACTIONS TO LOAVER TERMS, Demonstration^ Prop. 6. REDUCTION OF FRACTIONS TO HIGHER TERMS. Demon slration^ Prop. 3. REDUCTION OF COMPOUND FRACTIONS TO SIMPLE. Demonstration. Take |- of §. Since multiplication is taking one number as many times-as there are units or parts of a unit in another, taking -J of §- is a ease of multiplica- tion; hence may be expressed thus: f X|. Then 3 times | (Prop. 1,) is V, but since the multiplier is \ of 3, this product is four times too large, and must be divided by 4. But (Prop. 2,) y-f-4=5|. By observing the two operations it is seen that the numerators have been multiplied together for a new numerator, and the denominators for a new denominator. Hence the ordinary rule is demon* strated. 76 • Remarh 1. Reduction of Complex Fractions to Simple is demonstrated in a similar manner, after having first shown that it is a case of division. Remarh 2d. In examining classes this may be considered a test question, " Why does dividing the denominator multiply the fraction?" Such an answer as this is often given, " Because it shows that the fraction is divided into a less number of parts;" or this, " Because it increases the parts:' or this, " Because the number of the parts is less, therefore they must be greater." All these an- swers are worthless, the latter, which is more fre- THEORETICAL ARITHMETIC. 327 quently given, is absurd. This answer may be given, Because by dividing the denominator we divide the unit of which the fraction expresses a part, into a less number of parts : consequently, each one of the parts is of greater value. Remark. The analytical method of demonstrat- ing the operations of fractions should not be neg- lected. I will give one example of this method in division. Divide f by |. 1-1=1. l~i=Q. i-f-J=f. i--4=:^?«=V. |-^|=V'-^5=j'x«j=i|. By noticing the last steps of this process it is seen that they correspond to the ordinary rule for the division of one fraction by another; viz: Invert the divisor and proceed as in multiplication. 77. Reniarlc Zd. The division of a mixed number by a mixed number without reducing them to im- proper fractions gives an excellent drill, and should not be omitted. Such an example as this for instance, 19|)3994f(, involves a difficulty that few scholars will surmount without help; for, in performing the division it is found that the divisor is not contained twice in 39, and if it is assumed that it is contained once the second partial quo- tient is 10. The difficulty may be overcome in two ways ; first assume that the divisor is contained twice in 39-}-to5 which assumption holds, as the second nine is -^o of a unit standing in the place of the first nine. Secondly, assume that it is con- tained once in 39, thus making the first quotient 328 laEuiil^TICAL ARITHMETIC. figure 1, then the second partial quotient will be 10 ; the first figure of which being added to the former figure makes the first figure of the quotient 2. as before. The second quotient figure will be 0. It is not claimed that this method of dividing one mixed number by another, is of any practical value in business operations ; only, that it gives a clearer view of the theory of the Arabic Notation ; and that it affords the means for an excellent drill in a class of apt scholars. Remarh Ath. In reducing a fraction of a larger denomination to integers of lower denominations, a course is too often pursued which involves ab- eurdity in the notation. For instance, if ^ of a mile is to be reduced to integers, the work is gen- erally performed thus, ^^m x8= Vfur.^^S^ fur. r. 40=rr'?° rodsr=17; rods X 16^=16* ft.=:=22* ft.xl2 =z%^ inchesrz:4^ inches. This is plainly a string of absurdities ; for 8 times ^ of a mile is ''^ of a mile, and not --^^ of a furlong. Again, 3 1 fur. X 40 is not equal to ^^ rods, but is equal to 120-|-'f" furlongs. A better method is this : ^m= '4 fur.r=:3;^ fur., ^ fur.z='i' rod=r=17^ rods, ^ rod=:i6fr ft — 2^4 ft., ** ft.= 7 inchrzr47 inches ; then ^ miler=:3 fur- longs, 17 rods, 2 feet, 42 inches. Remarh bth. Nearly every operation in frac- tions admits of several different methods ; that of dividing one fraction by another admits of at least twenty different methods. It is an excellent plan to propose to a class to bring out all the dif- ferent me*^hods which they can discover or invent THEORETICAL ARITHMETIC, 329 for each operation ; also the demonstrations for the several methods. 78. DECIMAL FRACTIONS. "ti~LTi3 — Separatrix, Price, Cost, Quantity, Unity, tn, •„• „>„a < Notation — Rule. .xVf xiMinanes, ^ Numeration-Rule. -^- [ ' ^"^ ' ( No. of figures — method of determining. si f Origin, ^ Notation, Rule, ^ I Circulating, Numeration, Rule, •{ Value: how determined, { Pure, ) ( Single, (^ Classes, < Mixed, ) \ Double, etc. I f Imperfect, ''Repetends, •! fist, [Perfect, \l^' isd, I' ,4th. j r. , .' c\ rCom. toDec. .Reduction ofl Uec. to Com. ^Fractions ot V j p^^.^^j ^^ j^^^^. ^^^^^^ ^^ ciimpie JNos. J 1^ Decimal to higher terms. ,2 I Increase — Addition, Multiplication, ) ( Rules, "S •{ Diminution — Subtraction, Division, i I Demonstration, r> , ,. e^ f Decimal of higher denomination to integers Reduction of^ ^ ^ ° Fractions of ' ' ' ^ J M Integers of lower denomination to decimaJ t Compound T j ^f higher, !-< umbers, J \^q^^ quantity to decimal of another. 79. DEFINITIONS, EXPLANATIONS, AND REMARKS. Decimal Fraction. A Fraction whose denom- inator is not expressed ; but is understood to be 5i;ch a power of ten as is indicated by the number of figures at the right of the separatrix. Criticism. In consulting Ray's Higher Arithmetic, I find this definition of a decimal fraction : "A Decimal Fraction is one which derives its name from the Latin word decern, meaning ten ; and is so called, because its denominator is always 1 with cyphers annexed ; being either 10 or the product cf several lO's." This detitiition is worthless because it includes a large class of common fractions. Read Prof. Davies, in his University Arith- metic — " A decimal fraction is one in which the unit is divided itccordinfj to the scale of tens." 330 THEORETICAL ARITHMETIC. Remarlc. The separatrix is the most important character used in decimals, and no pains shonld be spared to impress this on the minds of pupils. Rule for Notation. 1st. Write the separatrlz. 2d. Determine the place of the given denomina- tion. 3d. Assume this place, so determined, ?.^- zh^ place of units, and write the given quantity, p^^ ic whole numbers. Remarh \st. The difficulty in most rules for writing decimals is that the pupil is compelled to write them twice; once, to obtain the correct num- ber and arrangement of figures, and again, to place them in proper relation to other decimals with which he may wish to combine them. By. this rule he will write them where he wants them in the first instance. Remark 2d. In large classes of Teacliers I have seldom found more than two or three individuals (frequently none) who were able to write decimals correctly. Take examples of these kinds, for in- stance :* One hundred million ten-thousandths. Fifteen million fifteen thousand and fifteen hundred ten-milliohths. Forty-five million forty-five thousand and forty- five hundred thousandths. Forty-five million forty-five thousand and forty- five hundred-thousandths. Remark od. Such common fraictions as ^o^off and (To-Joff, having denominators of many more figures than the numerator are the proper examples to ■^ THEORETICAL ARITHMETIC. 33"i test a class in reducing common fractions to deci- mals. It is not an uncommon thing for a class to obtain almost as many different results as it contains pupils, in consequence of the misplace- ment of the separatrix. A thorough teacher will pay particular attention to this matter. 80. Demonstration of the rule for multiplication of decimals. Rule. Multiply as in entire numbers and point off as many figures from the right of the product as there are in both of the factors. Demonstration. Assume that both factors are entire numbers, then since removing the separatrix towards the left divides either of the factors, as many times by ten, as there are figures thus placed at the right of the separatrix; and since the pro- duct must be as many times divided by ten as both the factors, it follows that the rule rs correct. 81. Demonstration of the rule for the division of decimals. Rule. Divide as in whole numbers, and poini off as many figures, at the right of the quotient, for decimals, as the decimal figures in the dividend exceed those in the divisor. Demonstration. Assume first that both dividend and divisor are whole numbers, then of course the quotient is also a whole number: but since divid- ing the dividend divides the quotient, and dividing the divisor multiplies the quotient, and since re- 332 THEORETICAL ARITHMETIC. moving the separatrix towards the left divides either quantity as many times by ten as there are figures thus placed at the right of the separatrix, in each of the numbers, it follows then as many more times as the dividend has thus been divided than the divisor, so many times must the quotient be divided by ten; in other words, so many figures must be cut off from the right of the quotient as the dividend has been divided more times by ten than the divisor has been thus divided. RATIO. Terms — Antecedent, Consequent, Couplet, Value of Ratio. Signs- ; I I" of subtraction — how much greater? — Difference. Relations i ^^ division — how many times greater? — Quotient. M of involution. l.of evolution. ,a3 to arrangement, j t^"^^!.?^' Classes, French. . • • < Direct, as to origin, \ j^^^^^^ as to combination, j g^J^^^j. as to value, j of equality, ' < of greater inequality, (.of less inequality. ( Antecedent=T)ividend. Comparison "i f ^^^^ Division, j Consequent=IHvisor, Ratfo^^ I I i Antecedent=Numerator. • '' *• with Fractions, < CoDsequent=Denominator. ( Value=Value. ( Antecedent=Divisor, n^™»,«..;»^„ ^ r ^i'^ Division, •< Consequent=Dividend. of Freich U ^ Value=Quotient. Ratio I I • ( ■^ot6<'6dent=Denominator, ' '' ^ with Fractions, < Consequent=Numerator, ( Value=Value. Scholium, — Ratio can only exist between quantities of tho sam« kind. Rule for finding value of Ratio. THEORETICAL ARITHMETIC. 333 {English ) J 1. Ant.— Con?.xValue of Ratio. Ratio, ) ( 2. Cons.— Ant,-?- Value of Ratio. French l ( 1. Ant.-Cons.^Value of .Ratio. Ratio, ) / 2. Con3.— Ant.XV'alue of Ratio. Geometric Series, j y'^^^^ Propositions, 1, 2, 3, 4, 5, 6. 83. DEFINITIONS, EXPLANATIONS, AND REMARKS. Ratio. A combination of two or more terms in pairs, for the purpose of comparison by division. Reinarh. The result of such division is often called ratio; more correctly, it is the value of the ratio. Terms. The numbers between which the com- parison is instituted. Antecedent. The first or lefthand term of a pair comprised in a ratio. Consequent. The second or righthand term of the pair comprised in a ratio. Couplet. A pair of terms including an ante- cedent and consequent. Value of Eatio. The quotient arising from dividing one term of a ratio by the other. Relations. Bearings. Relation as determined hy subtraction, answers to the question. How much greater is one number than another? It is the same as the difference. Relation as determined hy division, answers the question, How many times is one number greater than another? It is the game as the quotient. Relation as determined by involution or evolution answers the question, What power or root is one number of another? It is the same as the expo- 334 THEORETICAL ARITHMETIC. nent or index of one number, when placed equai to another, as its power or root. English Katio. That in which the antecedent is to be divided by the consequent. French Ratio. That in which the consequent is- to be divided by the antecedent. Remark. It is not to be supposed that all Eng- lish mathematicians adopt what is called the Eng- lish Katio, or that all French mathematicians use what is called the French Ratio. Davies seems first to have introduced the inverted or French ratio into American books. He did not follow the French author wliose work he translated in this particular. Most works on Natural Science retain the old or English form, and in their ratios suppose that the first term is to be divided by the second. Several of the more recent Arithmetics have adopted the English Ratio, as Stoddard's, Dodd's, etc. '84. Direct Ratio. That in which more requires more ; or less requires less. Inverse Ratio. That in which more requires less ; or less requires more. Remark. Many arithmeticians reject this dis- tinction as useless. In my opinion, however, it affords a fine means of drill, in the discussion of problems in compound«proportion. Simple Ratio. That involving but one couplet. THEORETICAL A.RITHMETIC. 335 Compound Ratio. That involving two or more eimple ratios, combined with the sign of multipli- cation. Katio of Equality, That In which the terms are equal; or that in which the value is unity. Ratio of Greater Inequality. That in which the value is greater than unity. Ratio of Less Inequality. That in which the value is less than unity. Remark. It will be noticed that a French Ra- tio of greater inequality may be identical with an Engjish Ratio of less inequality. Series. A succession of terms, each of which is derived from one or more preceding terms by some known law. Geometric Series. One in which each term ia derived from the preceding term by a constant multiplier or divisor. It is sometimes called Con- tinued Proportion. Remark. This constant multiplier or divisor is equivalent to the value of any single ratio, or couplet comprised in the sieries. Propositions. The same as those for fractions, substituting the terms antecedent and consequent for numerator and denominator. 16 336 THEORETICAL ARITHMETIC. 85. PROPORTION. Terms, — Proportional, Mean Proportional, Last Proportional, Third Proportional, Fourth Proportional, Homologous, Analogous, Extremes, Means. Signs,-, -,=,=,,.,} 11*"°°' .as to origin, jDi-N, Classes, ■{ | Simple, ■•I as to combination, -^ Compound, Conjoined. {First term=First Antecedent=First Extreme. Second term=First Coaseqaent=First Mean. Third term=Second Antecedent=Sec'd Mean. Fourth term=Sec'd Consequent— 2d Extreme, r First and Second=First Couplet, I First and Third=Antecedents, Names of ) First and Fourth=Extremes, Pairs of Terms, ) Second and Third=Means, I Second and Fourth=Consequents, (Third and Fourth=Secoud Couplet. f Fandamental, Product of Extremes=Product of Means. Laws, •< (1. Product of Extremes-^one mean=other [Derived, -j mean. [treme. 1 2. Product of Means-^one extreme=other ex- Rules for statement, \ I''' ^'"^P^^ Proportion ' ( for Compound Proportion. il. by Fundamental Law, 2. by Ratio, 3. by Cancellation. 86. DEFINITIONS, EXPLANATIONS, AND REMARKS. Proportion. A combination of two equal ra- tios, with the sign of equality. Proportional. Any one of the terms of a pro* portion. Mean Proportional. One of two equal means in a proportion. Third Proportional. The fourth term of a proportion in which the means are equal. Remark. Such a proportion is often written with only three terms ; thus: (4:8:16) = (4:8::8:16). THEORETICAL ARITHMETIC. 337 Homologous Terms. Those occapying the same place in two or more couplets. Two or more consequents are homologous terms ; also tv/o or more antecedents. Analagous Terms. Such as are found in the same couplet. Extremes. The first and last terms of a pro- portion. Means. The second and third terms of a pro- portion. Signs. Symbols indicating a relation, operation or sequence. Sign of Ratio. .(:). It is an abridged sign of division, and is read as in this Example, 4:6::8:12. Reading. — As 4 is to 6, so is 8 to 12. Sign of Equality, (::). It is an abridged form of the ordinary sign of equality, being the extrem- ities of the lines. It is read as in the example above, "so is." Sign of Sequence or Deduction, (.•.). It is explained, section 47, page 299. Direct Proportion. That which involves di- rect ratios. Inverse Proportion. That which involves in- verse ratios. Simple Proportion. That which consists of simple ratios only. Compound Proportion. That which contains one or more compound ratios. Conjoined Proportion. That form of a com- pound proportion, in which each antecedent is equal in value to its consequent. 338 THEORETICAL ARITHMETia Remarh. Conjoined proportion is used in re- ducing coins of tlie two countries through the medium of other countries. It is often called the Chain Rule. Demonstration of fundamental law: 1st. Take 6:8::12:16. • Expressing each ratio fractionally I==y|. Multiplying each fraction by 6, we have 8='|-^s; for, multiplying equals by equals the products will be equal. Again, multi- plying the last two equal quantities by 12, we have 8x12=16x6, which gives the product of the means, 8 and 12, equals the product of the ex- tremes, 6 and 16. 2d. . Take 6:8::12:16. Since every consequent is equal to its antecedent multiplied by the value of their ratio : 8 = 6x|; and 16=12Xj. Hence we perceive that the extremes 6 and 16 contain the same factors as the means 8 and 12. 6.12 and I being the factors of the extremes; 6, |, and 12, being the factors of the means. Since the products of equal factors are equals, and the means and extremes contain equal factors, the products of the extremes and means must be equal. Methods of Solution. By Ratio. Multiply the first term of the second couplet by the value of the ratio, obtained from the first couplet. By cancellation. Consider all antecedents, excepting the last, as denominators, all consequents and the last antecedent as numerators of a compound frac- tion. Then cancel as in the reduction of a com- pound fraction. THEORETICAL ARITHMETIC. 339 87. PJKKCENTAGE. Terms, — Percent, Rate percent. Notation, — Rule, Consider hundredths as units, and writo as in whole numbers. Sign (%\ This sign has been recently introduced ; and is read percent. 1st, To find any given percent of a number, Rule. Cases, J 2d, To find what percent one No, is of another, Rule. 3d, To find a No. when any percent of it is known, Rule. ,4tb, To find a No. when any percent greater or less is given, Rule, 88. GAIN AND LOSS. EemarJc. 100 percent represents the IVo. on which any gain or loss accrues. ID Cases, < o >'=the same general cases in percentage. 89. COMMISSION. Itemarh. — 100 percent represents the No. on which commission is charged. fp ( Agent, Commission-Merchant, Factor, Correspondent, ' \ Principal, Rate of Commission. (2] Cases, < 2 >-=the same general cases in percentage. Uj BROKERAGE. {Consigner, Consignee, Bill of Exchange, Check, Draft^ Bond, Rate of Brokerage, Proceeds or cost. [2] Cases, ■( 3 V =the same general cases in percentage. 90. STOCKS. 'Joint Stock Company, Stock, Share, Certificate, Stockholders, Dividend, Rate of Dividend. Par Value, Face, Nominal Value, Real Value, Market Value, Rise and Fall. At par, Above par, Below par, At a premium, At a discount. Discount. Stock Broker, Stock Jobber, Investment, CommisBion, t Rate of Commission, Cases,==Cases in Percentage. Terms, 840 THEORETICAL ARITHMETIC. 91. INSURANCE. Terms, Policy, Premium, Underwriter, Out-Door, Rate of Insurance, Take a Risk, Cover. fFire, 1 Marine, Life, Health, Stock, etc. Case.?,=Ciise3 in Percentage. TAXES. Classes, !>'-'. i?Ser.y, Indirect, Tare, Customs) ( Ad valorem, ) ( n'^'pl or I J Allowances, M- i^'J^i^' Duties, f ] Specific, f ] Leakage,^ reakage. C sp'? \ ^'^^ specific duties, Rule, •*'■■ ' 1 for ad valorem duties — Cases=Cases in percentage. 92. INTEREST. f Principiil=P. Compound Interest=C. I. Interest=A. Compound Amounti=C. A. I Rate=R. Logarithm=Log. ^ ( Years=T. Time in < Months=m. ( Days=d. Amount— A.=P+I. Simple, Compound, Annual, Mixed. Mi., FI. Ca., Mi., Wis., lo. Legal Rates, I 10, Texas. 1 6, In all other States and in U. S. Courts, Remark. 100 percent represents the principal. ( General. PxTxR=I. Quantities and Symbols, Classes, Mixea. fS, Ga., Ala., 7, N. Y., S. 3, <^ 5, La. 1 Given i T*. R: (T. Given, i L (R. THEORETICA L ARITHMETIC. P. 3il equirea, I. PxRxT=I. _ P. Given, < I. Required, R. Rule ] I T. ' P. Required, T. Rule r^-T. PXTx,Oi i-i < PXK Given, -j R. Required, P. Rule j ^rT^--=P. =R. Required, P. Rule j -^^^^--^^P. A. ^ Required, I. Rule A — o - Given, in. |T. (A. Given, ^ R. (T. IP- Given, ■{ R. Required C A. Rule Px(l+R)'^=C A. P' i R*. R( (T. Jr. It. (CI n, \ R. (t. 2 Given, $1,+RXT. Required C I. Rule PX( 1+R) T— P.=C I. C A. c A Given, -l R. Required P. Rule --—;-==?. (1+R)i CI. CI Given, -l R. Required P. Rule rrr-fTT^— r"P. (1+R)T— 1 Given, { P. Required R. Rule V i^— 1=R. ( T. ^ Given, i ?. ^Required T. Rule ^^-^-^ -El^T. i B. Log. (l+R.) 342 THEORETICAL ARITHMETIC. BANKING. Banks, Officers ( of Iss ^ of Dii I of De (Direetoi Preside] Ciishierj of Issue, iscount, iposit, Di rectors, ident. Tellers. Classes, Essentials, Persons, {Negotiable, Non negotiable, Bank, of hand. . Signature, J Date, i Promise to pay, * Value received-. Maker, Payee, " Ider; Endorser. , Ma Term (Face, Protest, Payable on Demand, Payable on Time, Payable on Sight, Proceeds, Avails, Cost, Time to Run, Day of Maturity, Nominally Due, * Legally Due. Partial Payments, Discount, ■ .Remark. — Interest must not draw interest. I J United States, Rules, j Connecticut, ' ' Vermont. f Face of Note, A. I Avail or Cost, C. Rate, R. Quantities, •{ Classes, Cases of) Bank V Discount) I in Years— T. Time, •< in Months — m. ( in Days — d. Bank Discount — D. True Discount,— I=PxRXT. Bank Discount,— D=AxRxT. '1. To find discount of a note. AxRxT=D. 2. To find proceeds of a note. A-AXRXT=C. 3. To find face of a note for given prooeeds, 1-RxT- =A. r' .„ . . ^ 1 THEORETICAL ARITHMETIC. 343 ! 94. 1 EXCHANGE. ( Foreign, Classes, -l Domestic, ( Circular. Bill.., j lis",^'^''^'"' E-dorsoo-ent., ' f/'gtj/t. Acceptance. -* Rate i *° ^^^^'■' "^^®' 1 against. Standard— Amount of pure gold or ailTer ia oottt. Eeductidn of ) direct, Currencies, ) circular=chain ml©. fK'^ fir- Foreign Coi.,,|Germa.,U;^„^.„^_ , Russian. J ''®^*^- 95. Iin^OLUTION. (Degrees, '•o-.JExpooen,, JP:^';-. r Adding exponents multiplies, the quantities. PrAT.AfiU?«n« J Subtracting exponents divides the quantities, rroposiuons, < Multiplying an exponent involves the quantity. . Dividing an exponent evolves the quantity, fof 1. Every power of 1 is 1. P-nnarfJoo J of numbers less than 1. Powers, higher than properties, < ^^^ ^.^^^^ ^^^ ^^^^ ^^^^ ^^^ number. (.of 0th power of numbers. Always=l. i n»}^ i Demon3tratic\i, *''^^®' 1 Applications. 96. * EVOLUTION. C Degrees, «««'- \!&, (.Fractional Exponent. "• Propositions. The same as in Involution. ("of 1. Every root of 1 is 1. Prnn«rfifl \ Common difference=d. Symbols, ) Number of terms=n. t Sum of series=3. h ) i ISui (a. ,1 Given, ^n. Required 1. Rule, a-f d(n— 1)=J. n' 2 Given, ^1. Required a. Rule, 1— d(n— l)=a (d. Cases, 3 Given, 4 Given Required d. Rule, — -=d. n— 1 ■I (a. iven, •. should like to know how the children are to go to school to-morrow. They sha n't go through such w-^ather; I am determined. No; they shall stop at hfme and never learn anything, (the blessed crea- t'M-es!) sooner than gq and get wet! And when they grow up, I wonder who they '11 have to thank for knowing nothing; who, indeed, but their father, i-eople who can't feel for their own children ought lever to be fathers. 101. Plaintive. " Oh ! cease not yet to beat, thou vital urn ! Wait, gushing life, oh, wait my love's return ! Hoarse barks the wolf, the vulture screams from far, The angel, pity, shuns the walks of war ; Oh ! spare, ye war hounds, spare their tender age, On me, on me," she cried, " exhaust your rage." Then, with weak arms her weeping babes caressed, And, sighing, hid them in her blood-stained vest. 102. Denunciafo)y. I ask now, Verres, what thou hast to advance against this charge ? Will you pretend to deny it ? . Will you pretend that anything false, that even any- thing exaggerated is alleged against you ? Had any prince, or any State committed the same outrage against the privileges of Roman citizens, should we not think we had reason for declaring immediate war against them ? What punishment, then, ought to be VOCAL CULTURE. 425 infiicted on a tyrannical and wicked preetof, who dared, at no greater distance than Sicily, within sight of the Italian coast, to put to the infamous death of crucifixion that unfortunate and innocent citizen, Publius Gavius Cosanus, only for having asserted his privilege of citizenship ? The unliappy man, arrested as he was going to embark for his native country, is brought before tk« wicked prfetor. With «yes dart- ing fury, and a countenance distorted with cruelty, he orders the helpless victim of his rage to be stripped, and rods to be brought, and the infamous punish- aaent to be inflicted, 103. CopAempfAmus. Banished from Rome I What's banished but set free? " Tried and convicted traitor ! " Who says this ? Who '11 prove it at kis peril on my head ? Banished ! I thank you for it. It breaks my chain I held some slack allegiance till this hour, But now my sword 's my own. Smile on, my lords I I scorn to count what feelings, withered hopes, Strong provocations, bitter, burning wrongs, I have within my heart's core shut up, To leave you in your lazy dignities; But here I stand and scoff you ! Here I fling Hatred and full defiance in your face ! Your Consul 's merciful — for this, all thanks ; He dares not touch one hair of Cataline. 104. Ironical, " But, Mr. Speaker, we have a right to tax Amer- ica." Oh, inestimable right ! Oh, wonderful, trans- cendent right! the assertion which has cost this country thirteen provinces, six islands, one hundred thousand lives, and seventy millions of money. Oh ! invaluable right ! for the sake of which we have sacri- ficed our rank among nations, our importance abroad, and our happiness at home ! Oh, right, more dear to us than our existence ! which has already cost us bo 426 VOCAL CULTURE. muclij and which seems likely to cost us our adr. In- fatuated man ! miserable and undone country ! not to know that the claim of right, without the power of enforcing it, is nugatory, idle. We have a right to tax An'ierica. This is the profound logic which com- prises the whole chain of Ins reasoning. Not inferior to this was the wisdom of him who re- solved to shear the wolf What, shear a wolf ! have you considered the resistance, the difHculty, the dan- ger of the attempt ? No, says the mad man, I have considered nothing but the right. Man has a right of dominion over the beasts of the forest, and there^ fore I will shear the wolf. 105. Angri/. Ye dark, designing knaves ! ye murderers ! parri- cides ! how dare you tread upon the earth, which has drank the blood of slaughtered innocents, shed by your hands ; how dare you breathe the air which wafted to the ear of heaven the groans of those who fell a sacrifice to your accursed ambition ! But if the laboring earth doth not expand her jaws, if the air you breathe is not commissioned to be the minister of death, yet hear it and tremble ! The eye of heaven penetrates the darkest chambers of the soul ; traces the leading clue through all the labyrinths which your industrious folly has devised ; and you, however you may have screened yourselves from human eyes, must be arraigned, must lift your hands, red with the blood of those whose death you have procured, at the tremendous bar of God. 106. PERSONATING STYLE OF DELIVERY. Remark. The personation of the passions is somewhat different from the delivery of passages when really under the influence of such passions, as has been supposed in the preceding sections. For instance, the personation of Love, presupposes \ that the individual is under no restraint from any ' i VOCAL CULTURE. 427 observer; that he is alone, or only in the presence of the object of his aifectioji. It is farther taken for granted by the audience, that every such per- sonation is somewhat over-acted, whereas in the former styles of delivery, directed really to the audience, no audi overaction is tolerated. The Persona f in ff Style ^ therefore, may, perhaps, more properly be called the Caricaturing style, though not designed, in all instances, to provoke humor by any means. 107, Love^ Strange! that one lightly-whispered tone Is far, far sweeter unto me, Than all the sounds that kiss the earth Or breathe along the sea; But, lady, when thy voiee I greet, Not heavenly mu.sic sounds so sweet. 108. Fear. Ah! what sound w%is that? — The trap-door fallen? and the spring-lock caught — Well, have I not the key? — Of course I have! 'Tis in this pocket — ^o. In this? — No. Then I left it at the bottom of the ladder — Ha! 'tis not there. Where then? — Ah mercy, HeavenI 'T is in the lock outside? What's to be done? Help, help ! Will no one heur? \ would that I Had not discharged old Simeon! — but he begged Each week for wages — would not give me credit. I'll try my strength upon the door — Despair I I might as soon root up the eternal rocks As force it open. Am I here a prisoner, And no one in the house? — Horrible fate [ I sink^— I faint beneath the bare conception. .J 428 VOCAL CULTURE. 109. Hate. How like a fawning publican he looks 1 I hate him, for he is a Christian; But more, for that, in low simplicity, He lends out money gratis, and brings dowa The rate of usance with us in Venice. If I can catch him once upon the hip, I will feed fat the ancient grudge I bear him! He hates our sacred nation; and he rails, Even there where merchants most do congregate, On me, my bargains, and my well-won thrift, Which he calls interest.— Cursed be my tribe, If I forgive him. 110. Anger, Thou slave ! thou wretch ! thou coward ! Thou little valiant, great in villainy! Thou ever strong upon the stronger side, Thou fortune's champion, thou dost never fight But when her humorous lady's hiss is by To teach thee safety! Thou art perjured too, And soothest up greatness! What a fool art thou, A ramping fool, to brag, and stamp, and sweat, Upon my party. Thou coldblooded slave. Hast thou not spoke like thunder on my side? Been sworn my soldier? bidding me depend Upon my stars, thy fortune and thy strength? And dost thou now fall over to my foes? Thou wear a lion's hide? Doif it for shame, And hang a calfskin on those recreant limbs. 111. PERSONIFICATION OF NATIONAL PECULIARITIES. Irish. 0> Mulligan. 'Pon me sowl, if it 's not yourself that I see. Sobersense. How now, Pat, what news? OM. News! it's meself that's afther telling ye that! Ye see I 'm jist like a letther rite out of the mail, that's come by tiligraph, walking over the thrack like a staim taekittle; and sure as me name VOCAL CULTURE. 429 is Pat 0' Mulligan, that owld boy of a stLudent has made a diskivery in chimistry that '11 make a great man of him all his days. And has not he been of- fered a dale of money for it, and a chance to be a teacher in the siminary? /Sob. Why surely, Pat, you must be dreaming, foi he was here but a short time since, and he said noth • ing about it. 0'7I£ The divil a bit am I a dhraming. It 's like the likes o' him to say niver a word at all, at all. Did he iver till how he supported the poor mither of his all the time he was afther studying the books? Shure and was n't he the dacentest boy this side of the ould counthry? Sure and it 's meself that 's just from the post office with news. 112. Dutch. Mr. Foreman and Toder Jurymens: — Hans peen dried for Murder pefore you, and you must pring in te verdict; put it must pe 'cordin' to law. Der man he killed vash n't killed at all, as vash broved; he is in ter jail in Morristown, for sheep stealing. Put dat ish no matter; te law say ven ter ish a doubt you give him to ter brisoner; put here ter ish no doubt. Zo you see ter brisoner is guilty, Pesides, he is a great loafer. I have known him fifty years, and he has not done any work in all dat times; and dere ish no one depending upon him for dere living, for he ish no use for nopody. I dinks, derefore, Mr. Foreman, he petter pe hung next Fourth of July, as der militia is going to drain in anoder county, and dere will pe noting going on here. 113. TRANSITION. Transition. A sudden change in the manner of delivery. Explanation. In commencing new paragraphs, or in personating several characters in the delivery of one piece, we find the most common and impor- 430 VOCAL CULTURE. tant u?e for Transition. There are many other forms of transition^ however, some of which I shall exemplify* 114. TRANSITION IN PARAGRAPHS. Remark. Most of our reading books heiflg as absurdly divided into verses as is the Bible, this kind of transition is precluded. Appropriate ex- amples may be found on pages 419 — 20; others should be found by the teacher in some book, and all the pupils should be trained in this form of delivery. Rule. The transition from one paragraph to another, or from one topic of a discourse to anoth- er, generally requires a lower pitch, slower rate, and subdued force; also, a slight change in the po- sition on the stage. 115. TRANSITION IN STYLE. Remark. Dialogue and colloquy afford the best examples of this form of transition ; though narra- tive pieces, having conversations interspersed, are often more difl&cult to deliver, requiring also a fre- quent transition from the narrative to the colloquial style. Examples of both kinds will be given. 116. Transitions in Colloquial Style. \_Sir Robert Bramble and Humphrey Dobbins.'] Sir R. I'll tell you what, Humphrey Dobbins, there is not a syllable of sense in all you have been saying. But I suppose you will maintain there is. Hmn. Yes. Sir R. Yes ! is that the way you talk to me, you old boor ? What's my name ? VOCAL CULTURE. 431 Hum. Kobert Bramble. Sir JR. An't I a baronet ? Sir Robert Bramble of Blackberry Hall, in the county of Kent ? ' Tis time you should know it, for you have been my clumsy, two-fisted valet these thirty years: can you deny that ? ITum. Hem ! Sir R. Hem ? what do you mean by hem ? Open that rusty door of your mouth, and make your ugly voice walk out of it. Why don't you answer my question ? Hum. Because, if I contradict you, I shall tell you a lie, and when I agree with you, you are sure to fall out. Sir R. Humphrey Dobbins, I have been so long endeavoring to beat a few brains into your pate, that all your hair has tumbled off before my point is carried. .Hum. What then ? Our parson says iBy head is an emblem of both our honors. Sir R. Ay ; because honors like yoisr head are apt to be empty. Hum. No ; but if a servant has grown bald under his master's nose, it looks as if there was honesty on one side, and regard for it oo the other. Sir R. Why, to be sure, old Humphrey, you are as honest as a — pshaw ! the parson means to palaver us ; but, to return to my position, I tell you, I don't like your fiat contradiction. Hum. Yes you do. Sir R. I tell you I don't. I only love to hear men's arguments. I hate their flummery. Hum. What do you call flummery ? Sir R. Flattery, blockhead ! a dish too often served up by paltry poor men to paltry rich ones. 117. Transition from Narrative to Colloquial, [_The Gouty Merchant and the Stranger.'] In Broadstreet building, (on a winter night,) Snug by his parlor-fire, a gouty wight Sat all alone, with one hand rubbing His feet, rolled up in fleecy hose, With i'o^Aerhe'd beneath his nose 19 432 VOCAL CULTURE. The Public Ledger, in whose columns grubbing, He noted all the sales of hops, Ships, shops, and slops ; Gums, galls, and groceries ; ginger, gin, Tar, tallow, tumeric, turpentine, and tin ; When lo ! a decent personage in black, Entered and most politely said — ^'■YoMvfootman^ sir, has gone his nightly track To the King's Head, And left your door ajar^ which I Observed in passing by ; And thought it neighborly to give you noticej' " Ten thousand thanks ; how very few do get, In times of danger, Such kind attentions from a stranger 1 Assurdly that fellow's throat is Boomed to a final drop at Newgate : He knoivs^ too, (the unconscionable elf,) That there's no soul at home except myself^ " Indeed,'' replied the stranger (looking grave), "Then he's a double knave, He knows that rogues and thisves by scores Nightly beset unguarded doors : And see, how easily might one Of the-se domestic foes. Even beneath your very nose, Perform his knavish tricks ; Enter your room as I have done, Blow out your candles — thus — and thus— Pocket your silver candlesticks, And — walk off- — thus,' — So said, so done ; he made no more remark, Nor waited for replies, But marched off with his prize, Leaving the gouty merchant in the dark. 118. TRANSITION IN PARENTHESIS. Examples have before been given of ordinary parenthesis, — I shall here add one of rather extra- ordinary character. It affords the material for an excellent drill. VOCAL CULTURE. 433 119. Example of Transition in Parenthesis. \_Ode to an Infant Son.'] Thou happy, happy elf ! (But stop, first let me kiss away that tear,) Thou tiny image of myself ! (My love, he 's poking peas into his ear,) Thou merry, laughing sprite. With spirits, feather light, Untouched by sorrow, and unsoiled by sin, (My dear, the child is swallowing a pin !) Thou little tricksy Puck ! With antic toys so funnily bestruck, Light as the singing bird that wings the air, .(The door! the door! he'll tumble down the stair!) Thou darling of thy sire ! (Why, Jane, he'll set his pin-afore afire !) Thou imp of mirth and joy ! In love 's dear chain so bright a link, Thou idol of thy parents; — (Hang the boy! There goes my ink !) 120. Transition from Male to Female Voice, Mister Socrates Snooks, a lord of creation, The second time entered the married relation ; Xantippe Caloric accepted his hand. And thought him the happiest man in the land. But scarce had the honeymoon passed o'er his head, When, one morning, to Xantippe, Socrates said, " I think, for a man of my standing in life, This house is too small, as I now have a wife: So, as early as possible, carpenter Carey Shall be sent for to widen my house and my dairy. "Now, Socrates, dearest," Xantippe replied, " I hate to hear everything vulgarly mxfd; Now, whenever you speak of your chatties again, Say, our cow house, our barn yard, our pig pen." " By your leave, Mrs. Snooks, I will say what I please O^my houses, mg lands, my gardens, my trees." "Say Our," Xantippe exclaimed in a rage. "I won't Mrs. Snooks, though vou ask it an age ! " 434 VOCAL CULTURE. Ob, woman! though only a part of man's rib, If the story in Genesis don't tell a fib, Should your naughty companion e'er quarrel -with you, You are certain to prove the best man of the two. In the following case this was certainly true ; For the lovely Xantippe just pulled off her shoe, And laying about her, all sides at random, The adage was verified — " Nil desperandum." Mister Socrates Snooks, after trying in vain, To ward off the Wows which descended like rain, — Concluding that valor's best part Avas discretion — • Crept under the bed like a terrified Hessian : But the dauntless Xantippe, not one whit afraid. Converted the siege into a blockade. At last, after reasoning the thing in his pate, He concluded 't was useless to strive against fate; And so, like a tortoise protruding his head, Said, "My dear, may we come out from under our bed?* v'Hah! hah!" she exclaimed. "Mr. Socrates Snooks, I perceive you agree to my terms, by your looks: Now, Socrates, — hear me, — from this happy hour, If you'll only obey me, I'll never look sour." Tis said the next Sabbath, ere going to church, He chanced for a clean pair of trowsers to search : Having found them, he asked, with a few nervous twitches " My dear, may we put on our new Sunday breeches ? " [ From Kidd' 8 Elocution. ^ GESTICULATION. CLASSES. As to Origin, Natural, Artificial. ^s to Style, Colloquial, Oratorical, Dramatic As to Order, Principal, Subordinate. As to Combination, Simple, Complex, Compound. As to Use, Introductory, ( To an Audience, \ Of a Speech, a Paragraph, etc. Demonstrative, j t^^^^^'Z^S!- ^^^ f Of Assent, Denial, 1 Approbation, Disapprobation, Significant, • Request, Command, Prohibition, Threatening, . Silencing, Directing, etc. Emphatic, Earnest, Rhetorical. Of Joy, Grief, Love, Hate, Contempt Fear, Horror, Despair, Surprise, Impassioned, • Astonishment, Fright, Pride, Arrogance, Humility. Servility, Shame, Bashfulnesa, etc. 'Of Personal Peculiarities. Of National Peculiarities. .Imitative, . Of Feminine or Masculine Peculiarities. 1 Of Cockney Peculiarities, t Of Clownish Peculiarities. Concluding, ( Departure from Individual. ( Retreat from the Stage. (435) 436 GESTICULATION, Feet, USE OF THE PARTS. Right. Left. ( 1st, 2d, 3d, 4th.. I Contracted. Positions. ■{ Extended. Parallel. 1. Introverted, r Advancing. changes ^t^stng. ^ Kicking. J [Errors- ' Conditions. -1, 2, 3. Firm, Rigid, Feeble, Trembling. I "" ""■ / Straight, Bent, Kneeling. Lower Limbs, •( \f *■• g \ Bending, Kneeling* Shaking } Staggering. [Errors— 1,2, 3. Conditions, Ereuth ( nd ^ ips, I Mouth and Lipi Conditions, Condition, Actions, forwards, averted, downwards, upwards, around, on vacancy, fixed, smiling, glistening,' winking, frowning, weeping, closing, distended, starting, staring, wild, phrensied, bloodshot, etc. I closed, gaping, grinning, pouting, down in the moutb, ' with stiff upper lip. j laughing, hissing, yawning, sneering, flouting, hooting, . chuckling, spitting, whistling. QUALITIES. Magnificent, Just, Constrained, ^ol<^» •'. Appropriate. Tame, go^rSf t^c, Forcible, Feeble, !?"«?' Select, •• Monotonous, ^'°^Pl6> Adequate, Theatrical. ^«^' :•; Sufficient, Excessive, g'"«^.ef^J. Suitable, Awkward Precise, Well-timed, Ill-timed. METHODS OF DRILL. 1. In gestures alone, j j Simple, AT r 1 Complex, 3. In gestures with voice,) ( Compound. Oratorical, Dramatic, 438 GESTICULATION. REMARKS AND EXPLANATIONS. Remark I. Most of the text books oa Elocution, virtually ignore the subject of Gesticulation, by saying that it cannot ba taught by pictures; or by referring it to teachers, who, for the most part, are iinacquainted even with its nomenclature. Remark 2. Having given an outline of Gesticulation, em- bracing its nomenclature, I shall have room only for the defi- nitions of such terms and explanations of such parts of it as seem most to require them. Remark 3. Almost any teacher, by going over this classifi- cation and familiarizing himself with its terms and details, and by practicing them in his private room, will be able to in- troduce tbe following drills on Gesture into his school with good cifect. They can take the place of other gymnastic exercises during recesses or intermissions. Remark 4. An abridged notation may b§ secured by using capital initial letters for the positions and motions of the head, eyes, mouth, also for the lower extremeties; and small initial letters for the motions, positions, and conditions of all other parts. In case the initial letters are alike in two terms, the first two letters must be used ; and when the first two are alike, the first three can be used. The letter added to an initial capital should be small. This notation is convenient in guid- ing drills ; also, for noting the errors or defects of pupils un- der drill in order for efficient criticism. Remark 5. All tha*has been gained by the drill in the Management of the Person, as treated of on pages 357 — 365, will be valuable as introductory to Drills in Gesticulation, Gesticulation. See page 55, section 7. CLASSES. Natural Gesticulation. See page 43, section 6. Aetificial Gesticulation. See page 44, section 6. Colloquial Gesture. That which occurs in ordinary con- versation. GESTICULATION. 439 Explatiaihn. This oftea consists in metions of the head | only ; not ualrequentlj, however, the motions of the hand j and forearm are used; seldom the motions of the arm. ! Oratorical Gesture. That used in the pulpit, arid in i legislative assemblies. i Explanation. This consists of the positions and motions | of all parts ef the system, except such attitudes and highly I wrought displays, as are necessary to exhibit the stronger { emotions, as of fright, horror, despair, etc. It forbids the i use of the forearm, by itself, entirel}'. ' Dramatic Gesture. That which is saitiible for the drama .j or theater. j Explanation. It includes all oratorical gesture ; also, the ; appropriate portrayal of the strongest passions and emotions of the soul. i Simple Gesture. That made by one member or equally fey a pair of members, when designed to give expression to only one gush of thought or feeling. \ CosPLEX Gesture. That which involves the motions of \ two or more members, a part of which motions are subordi- ' aate to others. i Compound Gesture, Gesture continued from one thougiit or feeling to another, with, or without change. \ Principal Gesture. That which in a complex gesture is i the most prominent. i Introductory Gesturs. That which is designed to accompany the introduction of a speaker to an audience, or i to prepare the minds of an audience for a new speech or a new ■,^ paragraph. ; Explanation. The bow is commonly addressed to the ! audience, when a speaker is introduced both by the speaker | and the person introducing him ; also, a downward oblique '\ oatward gesture with the right hand, by the latter. { Reniarh. For want of room, I shall be compelled to omit ; the definitions and explanations of other classes of Gesture. They will, for the most part, explain themselves to any intel- ligent teacher, { 19^- ! li L_ZZ ZT"^ 440 GESTICULATION. POSITIONS AND MOTIONS OB THE FEET. 1st Position. Body on the left foot, right foot forward, liead erect, hands down. I 2d Position. Body forward on the right foot; the left foot behind, resting on the toe. i 2d Position. Body on the right foot, the left in front. 4th Position. Body on the left foot, the right behind, \ resting on the toe. Contracted, Feet nearly touching. Extended. Feet far apart. Parallel. Both feet in the same direction. Introverted. Feet with toes turned inward. Remark. The motions of the feet will explain them- selves; and for want of room, I shall leave the Outline on the Trunk and Shoulders for the ingenuity of the teacher »Jid pupil to master. POSITIONS OF THE ARM. lIouizoNTAL. Extended in a straight line from the shoul- i \ der, neither elevated nor depressed. Downward. Depressed 45° from the horizontal position. Upward. Elevated 45° from the horizontal position. Zenith. Pointing vertically upward. Rest. Hanging by the force of gravity only. ' [ Forward. Extending in a straight line, neither inclining i I to right or left. i i Oblique. The right arm inclined 45° towards the left; the f left arm extended 45° towards the right. j \ Both arms are in the rfght oblique position, when inclined 45° towards the right; and in the left orliqub POSITION, when inclined 45° towards the left. Across. The right arm diiected towards the left, or the left arm directed towards the right, in contact with the breast. Extended. Directed outward, 90° from forward. Backward, leaking an obtuse angle with foru-ard. J \ GESTICULATION. 441 Folded. Wrapped across the breast, and enclosing each other. KiMBo. With the elbow extended, and the hand placed on the hip. Arrogant. The elbows in contact with the person, and the thumbs in the arm-holes of the vest. Reposed. With one hand covering the other over the Etomach. A feminine position. Remark. Outline of Motions must explain itself. It gives at least 96 different gestures with each arm, without inclu- ding any changes of the hand or fingers. DIVISIONS OF GESTURE WITH THE UPPER EX- TREMITY. Preparation. This consists in such elevation of the hand and arm from the position of Rest as is necessary to perform the gesture. Commencement. The first part of the motion, which is given with less force than the Stroke. Stroke. Climax or telling point of the gesture, which must be given with greater energy than that of the motion preceding it. Conclusion. The falling back of the hand and arm to the state of Rest. POSITIONS OF THE HAND. Prone. Palm downward. Supine. Palm upward. Inward. Palm toward the body. Outward. Palm away from the body. Vertical. Pointing directly upward. Forward. Palm turned forward, the arm being at rest, or in one of the extended or backward positions. Backward. Palm turned backward, the arm being at rest, or in one of the extended or backward positions. DISPOSITION OF THE FINGERS. Natural. The fingers all a little bent in towards the palm, and the extremity of the thumb a little beni outward; the same arrangement as when offered for shaking hands. 442 GESTICULATION. Clinchkd The fingers firmly closed, and thumb pressing over them. Extended. The fingers separated from each other, accord- ing to the excitement of the speaker. Index. The fore finger extended, the other fingers being closed. Collected. The ends of the fingers inclined towards, or touching the end of the thumb. Holding. The fore and middle fingers pressed at their middle against the thumb, the other fingers being more or less contracted. Hollow. The hand supine, and the fingers curved with- out touching. Thumb. The fingers closed, the thumb being used as an index. COMBINED POSITION OP THE HANDS. Applied. The palms, fingers and thumbs mutually pressed against each other. Clasped. All the fingers inserted between each other, and closed, as far as possible. Folded. The fingers of the right hand laid between the thumb and forefinger of the left, the, right thumb crossing the left. Crossed. One hand laid on the breast and the other laid over it. Inclosed. One hand so laid within the other that one thumb lies over the other. GESTURES WITH HAND AND ARM. Pointing. Indicating the direction of any object. Noting. The right hand as an index descending gently and repeatedly; often towards the palm of the other hand, hollow. Repelling. The arms first retracted, being pushed for- ward with the hand vertical and outward. Waving. The fingers first downward, being raised quickly by extending the joints of the hands and arms. GESTICULATION. 443 Beckoning. The hand inward, and brought repeatedly towards the breast. Rei'Ressing. The hand outward, being carried repeatedly forward. It is the opposite of the preceding. Advancing. The hand first moved downward and back- ward, then regularly /orz^arc? to the horizontal; a step being made forward to aid in the gesture. Springing. The hand having nearly arrived at its limit in a gesture, being suddenly thrown forTtard making the stroke of the gesture. This must be simultaneous with the enunciation of the accented syllable in the empnatic word. Striking. The arm being thrown towards the person ad- dressed, as it were, by the force of the gesture. Threatening. The hand suddenly clinched, is raised into a posture of offence. Pressing. The hand already laid on some part, the elbow being raised and the fingers pressed more forcibly on that part, denoting greater violence of the emotion. Retracting. Withdrawing the arm preparatory to ges- ture. Rejecting. Pushing the hand forward toward an object, at the same time averting the face. METHOD OP DRILL WITHOUT \ OICE. Remark 1. A few minutes spent in these or similar drills of gesticulation, every day, in connection wjth reading les- sons, or at recesses or intermissions, will be sufficient to give propriety, force and beauty to the expression of gesture, where otherwise there is the greatest backwardness, or the most re- pulsive awkwardness in gesticulation. Remark 2. It is not to be supposed that these drills as laid down here are the only drills by which a class ought to be trained. They are only given as specimens for the com- mencement of the training in Oratorical Gesticulation; for want of room, drills in Dramatic Gesture are omitted. Remark 3. The constrained and feeble action of Collo- quial Gesticulation calls for no training otherwise than to break it up in. Reading, Declamation and Oratory. 444 GESTICULATION ORATORICAL GESTICULATION. DIRECTIONS TO THE TEACHER. Direction 1. Arrange the members of the class on the floor, at such distances that their hands cannot meet. Let them stand as many as possible so that their feet can be seen. Direction 2. Having cleared off your table, take your stand on it, in order that your entire figure may be seen by every pupil in tl^e class. Direction 3. Illustrate every nevr position and motion to the class by examples, cautioning them against the various awkward errors to which they will be liable, illustrating such errors also by example. Direction 4. Let the class take the same position and go through with the same evolutions, many times, in concert with yourself; then by themselves in compliance with your directions, while your attention is given to the faults of indi- viduals, so that you can correct them in the repetition of the exercise. If simply describing the error does not enable the pupil to correct it, you will illustrate it, or caricature it, till he will be glad to abandon it. Direction 5. When the class shall have become familiar with the meaning of the words used describing positions and motions, either by practice in the drills or by study of the Outline and Definitions, you can introduce a random exer- cise ; firstly, requiring the class to follow your lead as closely as possible; secondly, requiring them to comply with your random verbal directions. teacher's directions to pupils. Explanation 1. Words in italics in the following direc- tions are technical ; they will be found in the Outline on Gesticulation in their proper places, and their definitions are given so far as has been thought necessary among the Defini- tions following the Outline. Explanation 2. The word Position, when commencing with a capital, v«ill refer to the position of the f^et; and the word Best, to the hands and arms. GESTICULATION. . 445 INTRODUCTORr AND CONCLUDING GESTURE. Series I. Take your places. First Position Second Po- Bition with the bow, First Position, Second Position with the Introductory/. (^Explanation. This is given by raising the right hand from Rest^ gracefully and in the natural posi- tion, as if to shake hands. It is used to introduce a speech or a new paragraph.) First Position with Rest. Third Po- sition, Fourth Position, and Introductory with the left hand. Third Position and Rest^ concluding bow. First Position, with a step backward. Series 2. First Position. Second Position with a bow and sweep of the right hand towards the right. Second Po- sition with a bow and sweep of the left hand towards the left. First Position, Introductory and Second Position. First Position and sweepinrj bow, retiring one or two steps to the First Position. POSITIONS AND MOTIONS OF THE HANDS AND ARMS. Series 1. First Position, arms horizontal forward^ hands natural^ prone^ supine, forward, clinched, Rest. Hands natural, arms forward, with second Position; doion- ward, horizontal, upicard, zenith. Rest. Right hand index, arm north. Right arm Rest, with the left hand index, arm south. Left arm Rest, with the right hand index, arm east; Right arm Rest, with the left hand index, arm west. Rest. With the right index, point to me, to the clock, to the zenith, etc. Remark. These gestures must be given with vivacity, in graceful curves, rather than with awkward, angular motions; also with the spring, making the stroke. First Position, arms horizontal oblique, with hands supine; arms folded, kimho, horizontal extended with hand forioard, arms arrogant, with trunk swaggering; hands applied; arms upward, extended, with hands natural; hands wringing. Rest. Remark to the Teacher. By studying the Outline and Defi- nitions you will be able to carry on such exercises, varying them, ard bringing in new positions, motions, and combina- 446 GESTICULATION. tions, until youi* class shall becorae familiar with the noio- enclature of Gesticulation, and are able to gesticulate with freedom, grace and effect. DRILL IN GESTICULATION WITH VOICE. Several authors on Gesticulation have given a variety of pieces with the appropriate gestures of all the different parts of the system marked, either with figures or letters. I have found it difficult to make any good use of either kind of no- tation, without devoting more time to learn them than a teacher can well afford, who is fully occupied in teaching the various branches of a common school. Neither have I found the cuts representing the various positions of any real service; and if they were, it would amount to little, zs motions cannot be represented, which of course are the most difficult to acquire and to teach. The method of drill which I have found most serviceable is the declamation of short pieces, in concert, with the pupils, after they have had opportunity to memorize them: giving one or two such pieces at each read- ing lesson, to be memorized for recital and practice in ges- ticulation, a few moments, at the next reading exercise. I shall leave it to the judgment and taste of the trainer tc select examples from these following, or from other books, and to give appropriate gestures in their delivery. EXAMPLES FOR DRILL IN GESTICULATION AND VOCAL DELIVERY. Demonstrative Gesture. Though you, though all the world, though an angel from heaven were to declare the truth of it, I could not believe it. From xsTorth to South, from East to West, in all its wide extent, our country calls on heaven for blessings this day. Oh that they may descend without nieas- ure, and sweep crime and oppression from all tb© land. Are not you, sir, is not your honorable colleague sitting near you, are you not both the proscribed and predestined objects of punishment and of vengeance? ^ GESTICULATION. 447 Is there not rain enough in the sweet heavens to Fvash this crimson hand as white as snow? thou that rollest above, round as the shield of my fathers! Whence are thy beams, Sun, thy everlasting light? Thou comest forth in thy awful beauty; the stars hide themselves in the sky, the moon cold and pale sinks in the western wave. But thou, thyself movest alone; who can be a companion of thy course? Know -ye this, my friends, that he who reigneth in Heaven, whose footstool is the solid globe, who at a glance taketh in all things, whose essence filleth all space, the immensity of the universe, regardeth us, the creatures of his wisdom and his bounty, not as objects to be cast away or repelled from his presence, but as beings to whom his heart is ever open, his hand ever extended. He will take us to his arms, as a mother taketh her child! — IFrom Fitzgerald's Exhi- bition /Speaker. Ye crags and peaks, I 'm with you once again 1 hold to you the hands you first beheld To show they still are free. Methinks I hear a spirit in your echoes answer me And bid your tenant welcome to his home Again I sacred forms, how proud you look! How high you lift your heads into the sky! How huge you are I how mighty and how free I Ye are things that tower, that shine — whose smile Makes glad, whose frown is terrible, whose forms, Robed or unrobed, do all the impress wear Of awe divine. Ye guards of liberty, j I 'm with you once again. I call to you •, ^ With all my voice. I hold my hands to youj To show they still are free. I rush to you As though I could embrace you ! Demonstrative, Emphatic, Significant and Impassioned Gesture. HOHENLINDEN, Oh Linden, when the sun was low, All bloodless lay the untrodd'n snow, And dark as winter was the flow Of Iser rolling rapidly. 448 GESTICULATION. But Linden saw another sight, When the drum beat at dead of night, Commanding fires of death to light The darkness of her scenery. By torch and trumpet fast array' d, Each horseman drew his battle blade; And furious every charger neigh'd, To join the dreadful revelry. Then shook the hills with thunder riv'n^ Then rush'd the steeds to battle driv'n, And louder than the bolts of heav'n, Far flashed the red artillery. And redder yet those fires shall glow On Linden's hills of bloodstained snow; And darker yet, shall be the flow Of Iser rolling rapidly. 'Tis morn — but scarce yon lurid sun Can pierce the war clouds, rolling dun, Where furious Frank, and fiery Hun Shout in their sulph'rous canopy. The combat deepens — On, ye brave, Who rush to glory, or the grave! Wave, Munich, all thy banners wave! And charge with all thy chivalry! Few, few shall part where many meet! The snow shall be their winding sheet, And every turf beneath their feet. Shall be a soldier's sepulchre. THE Seminole's defiance. I 've scared ye in the city, I scalped ye on the plains; Go, count your chosen, where they feU Beneath my leaden rain ! I scorn your proffered treaty ! The pale-face I defy I Revenge is stamped upon my spear, And blood my battle cry. Ve 've trailed me through the forest, Ye 've tracked me o'er the stream; r GESTICULATION. 449 And struggling through tkc everglades, Your bristling bayonets gleam; But I stand as should the warrior, With his riiie and his spear; The scalp of vengeance still is red, And warns ye^ — Come not here! I loathe ye in my bosom, I scorn ye with mine eye, And 1 11 taunt ye with my latest breath, And fight ye till I die! I ne'er will ask ye quarter, And I ne'er will be your slave; But I '11 swim the sea of slaughter, Till I sink beneath its wave! THE MISER, The wind was high — the window shakes; With sudden start the miser wakes! Along the silent room he stalks; Looks back, and trembles as he walks! Each lock, and every bolt lie tries, In every creek, and corner pries; Then opes his chest with treasure stor'd. And stands in rapture o'er his hoard. But now with sudden qualms possess'd, He wrings his hands, and beats his breast — By conscience stung, he wildly stares; And thus his guilty soul declares: Had the deep earth her stores confined, This heart had known sweet peace of mind. But virtue's sold! Good gods! what price Can recompense the pangs of vice? Oh, bane of good ! seducing cheat. Can man, weak man, thy power defeat? Grold banish' d honor from the mind, And only left the name behind; Gold sowed the world with every ill; Gold taught the murd'rers sword to kill; 'T was gold instructed coward hearts In treach'ry's more pernicious arts. Who can recount the mischiefs o'er? Virtue resides on earth no more. 450 GESTICULATION. ELIZA. O'er Minden's plain spectatress of the fight. Sought with bold eye, amid the bloody strife, Her dearer self, the partner of her life ; From hill to hill the rushing host pursued, And viewed his banner, or believed she viewed. i Pleased with the distant roar, with quicker tread, I Fast by her hand one lisping boy she led; ( And one fair girl, amid the loud alarm, i Slept on her kerchief, cradled by her arm; j While around her brows bright beams of honor dart^ And love's warm eddies circle round her heart. \ Near and more near the intrepid beauty press'd, { Saw through the driving smoke his dancing crest; j I Saw on his helm, her virgin hands inwove, I i Bright stars of gold, and mystic knots of love; I I Heard the exulting shout, " They run, they run! j I Great heav'n," she cried^ "he's safe! the battle's won!" I I 4 bail now hisses through the airy tides, j j (Some fury winged it, and some demon guides!) i j Parts the fine locks her graceful head that deck, j Wounds her fair ear and sinks into her neck; I The red stream issuing from her azure veins, I i Dyes her white veil, her ivory bosom stains. j I "Ah me!" she cried, and sinking on the ground, j I Kiss'd her dear babes, regardless of the wound; I I " Oh! cease not to beat, thou vital urn! . I I Wait, gushing, oh, wait my love's return!" j j Hoarse barks the wolf, the vulture screams from far, , The angel. Pity, shuns the ranks of war ! I "Oh! spare, ye war-hounds, spare .their tender age; j On me, on me," she cried, " exhaust your rage!" I Then with weak arms her weeping babes caressed, And, sighing, hid them in her bloodstained vest. I From tent to tent the impatient warrior flies, 1 Fear in his heart, and frenzy in his eyes; Eliza's name along the camp he calls, — "Eliza" echoes through the canvas walls. [tread. Quick through the murmuring gloom his footsteps O'er groaning heaps., the dying and the dead; Vault o'er the plain, and in the tangled wood Lo ! dead Eliza, weltering in her blood. Soon hears his listening son the welcome sounds, GESTICULATION. 451 With open arms and sparkling eyes he bounds; "Speak iow/' he cries, and gives his Httle hand, "Ehza sleeps upon the dew cold sand:" Poor weeping babe, with bloody fingers press'd And tried with pouting lips, her miikless breast, "Alas we both with cold and hunger quake — Why do you weep? Mamma will soon awake." — "She'll wake no more!" the hapless mourner cried, Upturn'd his eyes, and clasped his hand and sigh'd; Streitched on the ground awhile entranced he la.y, And pressed warm kisses on the lifeless clay: And then upsprung, with wild convulsive start, And all the lather kindled in his heart. "Oh, heavens," he cried, "my fii-st rash vow forgive; These bind to earth, for these I pray to live!" Round his chill babes he wrapt his crimson vest, And clasped them, sobbing, to his aching breast. ROLLA TO HIS SOLDIERS. They follow an adventurer whom they fear, and obey a power which they hate. We serve a monarch whom we love, a God whom we adore I Whene'er they move in anger, desolation tracks their progress; whene'er they pause in amity, affliction mourns their friendship! — They boast they come but to enlarge our minds, and free us from the yoke of error. Yes; they will give enlightened freedom to our minds, who are .themselves the slaves of passion, avarice and pride! They offer us their protection. Yes; such protection as vultures give to lambs, — -covering and devouring them! They call on us to barter all the good we have inh&rited and proved, for the despei^ate chance of something better which they promise. Be our plain answer this: — The throne we honor is the people's choice: the laws we reverence are our brave forefather's legacy; the faith we follow teaches us to live in peace with all mankind, and die with hopes of bliss beyond the grave! RIUNZI TO THE ROMANS. Friends 1 I came not here to talk. Ye know too well The story of our thraldom. We are slaves! The bright sun rises to his course, and lights A race of slaves! He sets, and Jiis last beam 452 GESTICULATION. Falls on a slave! not such as, swept along By the full tide of power, the conqueror leads To glory and undying fame, — But base, ignoble slaves! — slaves to a horde Of petty tyrants, feudal despots; lords, Rich in some dozen paltry villages; Strong in some hundred spearmen; only great . In that strange spell, a name! Each hour, dark fraud Or open rapine, or protected murder, Cry out against them. But this very day An honest man, my neighbor, — there he stands — Was struck — struck like a dog, by one who wore The badge of Ursini! because, forsooth. He tossed not high the ready cap in air, Nor lifted up his voice in servile shouts, At sight of that great ruffian. Be we men And suffer such dishonor? Men, and wash not The stain awaj' in blood? Such shames are common. I have known deeper wrongs. I that speak to ye — I had a brother once, a gracious boy, Full of all gentleness, of calmest hope, Of sweet and quiet joy. There was the look Of heaven on his face, which limners give To the belov'd disciple. How I loved That gracious boy! Younger by fifteen years, Brother at once and son! He left my side, A summer bloom on his fair cheeks — a smile Parting his innocent lips. In one short hour The pretty, harmless boy was slain. I saw The corpse, the mangled corpse, and then I [slaves! Cried for vengeance! Eouse, ye Eomans! Eouse ye Have ye brave sons? Look in the next fierce brawl To see them die. Have ye fair daughters? Look To see them live, torn from your arms, distained, Dishonored; and if ye dare call for justice Be answered by the lash! Yet this is Rome, That sat on her seven hills, and from her throne Of beauty ruled the world! Yet, we are Romans "Why, in that elder day, to be a Roman Was greater than to be a king. And once again — Hear me, ye walls, that echoed to the tread Of either Brutus — once again I swear The Eternal City shall be free. CONTENTS. PART I. CLASSIFICATION OF KNOWLEDGE. Page. Introductiox, 7 — 11 Outline of Knowleogb, 11 — 12 Odtlinbs of Departments and Branches of Literature, 11; Sciences, 12; Arts, 13, 11—13 Definitions, for Outlines of Knowledge, 14 — 27 Definitions of Departments of Literature, 15 ; of Sciences, 15; of Arts, 16; of Branches of Phrenics, 16; Theotics, 17; Chronics, 18; Epistatics, 19; Geotics, 20; Therapeutics, 21; Mathematics, 22; Physics, 23; Technics 24; Graphics, 25; Polemics, 26; Cosmics, 26 — 27. Method of using the Outline of Knowledge, 27 — 28 Schemes of Mental Training, 29 — 32 PART 11. ORTHOEPY AND ORTHOGRAPHY. Introduction 35 — 38 General Outline op Grammar, 39 Language, 40 — 46 Definitions, Explanations, and Remarks for Outline of Grammar, 43 — 46 ORTHOEPY. Outline of Orthoepy. Definitions, etc., 51 — 57 Methods OP Teaching Pronunciation, 51 — 57 Chart No. 1. Physiological Classification of the Articulate Sounds, with Phonotypic, Web- sterian, and Worcesterian Notation, 52 — 53 Chart No. 2. Cognates of Articulate Sounds, 54 ORTHOGRAPHY. Chart No. 3. Orthographic Arrangement of Letters and Sounds, 58 — 59 Outline of Orthography. Definitions, etc., 60 — 69 Form of Orthographic Parsing, 62 Definitions for Outlines of Orthography, 63 — 69 Phonetic Method op Teaching the Alphabet, 70 — 75 Transition to Romanic Reading, 76 — 80 Method of Teaching Spelling to Secondary Classes, 81 — 84 Method of Teaching Spelling to Advanced Classes, 85 — 91 Exercises in Orthographic Parsing, 92 — 98 (453) •" ■~~' 454 CONTENTS. PART III. GRAMMAR. Introductiok, 99-^103 104—142 143—176 149 150—156 157—161 162—165 165—166 167—176 171 173—17*. 175—176 179—183 184—195 196—214 207 209 211—214 215—236 217—218 218—223 224—229 229—234 235 237—264 237 238—248 249 249—264 267—271 272—282 283—290 291—344 291—297 297—304 305—306 306 307—313 314 315—329 329—332 Method of Teacbino" Advanced Classes Outline of the Verb. Definitions, etc Outline of the Pronoun. Definitions, etc, .... Outline of Syntax. Remarks, etc., Outline of Analysis. Definitions, etc., ,. Methods of Oral Analysis, jIei'hods of AVritten Analysis .<«•< . . . \bRIDGEMBNT ...<..... .4. ,.441 4 ..<.< PART IV. GEOGRAPHY. Method of Teaching Primary Classes, Method of Teaching Secondary Classes, Topic List for Natural Divisions of Water, General Directions for the Study of Political ArTTTfTnn nf TpnoViino" Advnnfpd Clas