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proceed at once to the verbs. The verb is the life of a language, and he who knows the verbs thoroughly has mastered the chief difficulty of his task. The remaining kinds of words will be taught and discussed in the same natural order.

out the leading errors which Englishmen commit in pronouncing Italian. The reason of this is, that men are apt to transfer involuntarily the peculiarities of their own language to that which they are studying. The first effort therefore in learning to pronounce Italian, should be to forget your native peculiarities. In the mastery of the pronunciation of the continental languages, and particularly of Italian, the Englishman's great diffi

These lessons will contain, if I may so speak, two grammars. Presuming that I may find two classes of readers,-one anxious for knowledge by the most easy and rapid manner, the other with more preparation, inclination, and leisure for study,-Iculty is in the vowels. have so shaped my labour as to combine in a form sufficiently The Englishman, perhaps from childhood, has heard no vowel marked though not separated, an elementary grammar which sounds but those of his own island-his four sounds of a, his shall give the before-mentioned indispensable foundation and four sounds of o, his three sounds of u, his two sounds of e, and skeleton; and a grammatical treatise which shall, with philo-his two sounds of i,-sounds little swayed by rule, and changing sophical reasons, satisfactorily explain the ornaments, the continually. He begins Italian, but carrying to the study the delicacies, the accidents, and exceptions of the language. complex vocal habit of his language, it must be some time As I have said, I shall not divide my grammar into parts of before he can comprehend and practise the simplicity and perspeech, but into paragraphs. In the paragraphs I shall dis- manence of the sound of one Italian a. one Italian 1, one Italian u, tinctly mark the line of separation between the elementary two Italian e's, and two Italian o's. He therefore pronounces no grammar and the grammatical treatise by the title of "ADDI- vowel purely, and wherever he may move in Italy, his insular TIONAL REMARKS. The student who only desires to learn the nativity will be instantly recognised by the facchino of any language sufficiently to enable him to read, speak, and write village inn, from his inveterate habit of giving to the Italian a, with tolerable accuracy, need only attend to the numbered that most comical of sounds to a Tuscan ear, of a in hat and fat. paragraph; but he who would learn the language thoroughly, Another radical error committed by Englishmen in promust follow me closely and carefully in all I may find occasion nouncing Italian, arises from two opposite principles which to say in the additional remarks. may be said to be the fundamental rules of the accentuation of the languages. In English, every word has its leading, marked, or strongly accented syllable-generally speaking the root of the word; and it follows that while this syllable is distinctly marked by the voice, the subordinate unaccented fade away in the utterance into an airy nothingness that can hardly be described. It is quite different with Italian. It has its accented syllables just as English, but the accent on the one does not destroy the vocal enunciation of the others. On the contrary, full and substantial justice must be done to every syllable, each being clearly sounded, full and roundly with the vowels, and in a resonant or vibrating tone with the consonants. The contrast may be observed in the pronunciation of any of the many words of a kindred sound in both languages derived from the same classic stock. Take the following: English. Difficulty. Voluntarily.

Each paragraph will be complete in itself—a decided step in knowledge of the language. Every principle of the language will be clearly illustrated by examples, including vocabularies and exercises.

I have now only to ask the earnest and patient attention of my pupil readers.

I.

I shall teach the pronunciation of the Italian language in more detail than is generally pursued in English tuition. The profit to be derived from the study of any living language is much less if we are unable to pronounce it correctly. We can make little practical use of our theoretical acquirements, if in communication with those to whom this language is the mother tongue, we can neither make ourselves understood when we speak, nor understand when we are spoken to. And besides, no man, though he may gather the sense, can relish or even comprehend the beauties or delicacies of great poets, and prose writers too, in any language, and more especially in that of Italy, without an accurate knowledge of the sounds. In reading such poets as Ariosto or Tasso, the pleasure does not consist altogether in appreciating the thoughts or even shades of thoughts, but in the faculty to enjoy that divine harmony to which they have attuned the language. One may relish the beauty of the rose, but if he is deprived of the sense of smell, he can admire only a lifeless beauty. Such students of the Italian poets, to use a more homely figure, may read their poetry with the satisfaction with which one might admire a Turkey carpet, who has seen the reverse side only. There is no insuperable or even very considerable difficulty in mastering Italian pronunciation; but a thoughtful attention to some leading principles, and a student-like diligence, are conditions essential to success. My thoughtful and industrious pupils will very soon find that a prolixity in this the very outset of my labours which might seem trifling, is really most important-one of the fundamental parts of the language.

I am aware that I am writing for the most part for adult readers; but let them for a little space forget the dignity of manhood; for every learner of a language, be he as old as Cato was when he learnt Greek, should be regarded as a child learning to express his thoughts. Indeed the more he is taught a foreign tongue as the child his mother's speech, the better for him.

A living language can never be accurately and completely expressed by signs. They who profess the contrary only mislead the uninformed. But a tolerable approach to accuracy in fixing pronunciation may be made by letter-signs representing analogous sounds familiar to the ear in one's own language. If one has made himself so familiar with the imitated sounds, as to have acquired a considerable vocal command of the leading ones, he may very soon accurately and permanently acquire them, by a few brief communications with an educated native.

Perhaps the most useful beginning I can make, is to point

Detestably.

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Italian.
Dif-fi-col-tá.

Vo-lun-ta-ria-men-ti.
De-te-sta-bil-men-te.

Ge-ne-ro-sa-men-te.

In-dif fe-ren-te-men-te.
Re-pe-ti-zi-o-ne.

This peculiarity of the English language, it may be remarked, is the great obstacle which every English poet has encountered in the effort to naturalise the classic measures of antiquity. Contrasted with the open limpid vocalisation of Italy, the pronunciation of the English is to an Italian so obscure or indistinct, as very frequently not to be even understood. It might be presumed that in a word so sonorous as detestabilmente or volontariamente it would be impossible to miss the true sounds, yet an Englishman will, generally speaking so slur over what he would from the analogy of his own language conceive to be the subordinate parts of the word, as to be often quite unintelligible to an Italian.

A third and radical difference between the two languages, as regards the principles of pronunciation, proceeds from what may be termed the vocal mechanism or the physical principles of enunciation. Shortly stated, the physical difference is this, in England, they speak from the mouth; in Italy, from the chest. The Englishman whispers his words through the palate, tongue, teeth, or lips; the Italian throws them out with the vigour of his lungs. When therefore the Englishman attempts the pronunciation of Italian after his accustomed mode, he confines the open sounds of Italy to the limited mechanism of his hissing or lisping articulation above the throat, and turns Italian melody into harmonious discord, now a croak, now a hiss.

These are the radical differences and difficulties which my readers must strive to overcome. This is only to be accomplished by a constant recollection of these points of difference in connection with the rules I am about to state and illustrate, and by reading aloud, and with a clear and distinct voice uttered from the chest, every Italian word which I may have occasion to give in the course of the grammar

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Α.

D. N.A.V.
GD.

λαιλάπ-οιν

λαρυγγ-οιν

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Οψ, οπος, ή, voice; (Lat. vox.)
Ωψ, ωπος, ή, the countenance,
fair.

Λιξ, αιγος, ή, a she-goat.
Μαστιξ, ίγος, ή, a whip,
scourge.
Όρτυξ, υγος, ο, a quail.
Σύριγξ, ιγγος, ή, a shepherd's
pipe, Pandean (from the
rural divinity, Pan) pipes
Τεττεξ, ἔγος, ὁ, the grasshopper.
Φορμιγξ, ιγγος, ή, the harp.
Κολαξ, άκος, o, a fatterer.
Μυρμηξ, ηκος, ό, the ant.
Φεναξ, άκος, o, a deceiver.

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EXERCISES.GREEK-ENGLISH.

Οἱ κορακες κρωζουσιν. Τους κολακας φευγε. Απεχου του φενᾶκος. Οἱ ανθρωποι τέρπονται φόρμιγγι και ορχηθμῳ και φδη. Οἱ ίπποι μαστίξιν ελαυνονται. Αἱ φορμιγγες τους των ανθρωπων θυμους τερπουσιν. Τεττιξ μεν τεττιγι φίλος, μυρμηκι δε μυρμηξ (sc. εστιν). Οἱ ποιμενες προς τας συριγγας ᾅδουσιν. Παρα τοις Αθηναίοις και ορτυγων και αλεκτρυόνων αγωνες ησαν. Οἱ ποιμενες τας των αιγων αγέλας εις τους λειμωνας ελαυνουσιν. μυρμηκων και ορτυγων βιος πολυπονος εστιν. Πολλοι αγαθην μεν ωπα, κακην δε οπα εχουσιν.

ENGLISH-GREEK.

I avoid a flatterer. Ravens croak. You are delighted by the harp. Dances delight men. They drive the horses with (dat.)

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λαμπας κορυς

ορνις

αναξ

ἐλμινς

λαμπάδος κορυθος ορνιθος ανακτος έλμινθος
λαμπάδι κορύθοι ορνίθι ανακτι ἑλμινθι

λαμπάδα κορυν ορνῖν
λαμπας κορυς ορνις
λαμπάδες κορυθες ορνιθες
λαμπάδων κορυθ-ων ορνίθων
λαμπάσι* κορύ- σι* ορνι-σι*
λαμπάδας κορυθας ορνιθας
λαμπάδες κορυθ-ες ορνιθες

ανακτ-α έλμινθα αναξ ἑλμινς ανακτ-ες έλμινθες ανακτ-ων ελμινθων αναξι* ἑλμισι* ανακτ-ας έλμινθας ανακτες έλμινθες

D. N.A.V. λαμπάδε κορυθσε όρνιθε ανακτε έλμινθε λαμπάδον κορυθ- οιν ορνίθων ανακτ-οιν έλμινθοιν

G.D.

The noun ὁ, ἡ παις, child, has in the vocative παι. Here belong the adjectives in us and t, (gen. ίδος, ἴτος) as ὁ, ἡ ευχαρις, το ευχαρι, (g. ἴτος), pleasing, graceful; also, those in ας, (gen. άδος), as ὁ, ἡ φυγας, (g. φυγάδος), an exile, or banished person ; those, too, in ης, (g. ητος), as ὁ, ἡ αργης, (g. ητος), white; those, moreover, in ως, (β. ωτος) as ὁ, ἡ αγνως, (Β. αγνωτος), unknown; and those in is, (g. ίδος), as ὁ, ἡ αναλκις, (§. αναλ είδος), without strength; ἡ πατρις (se. γη land,) g. πατρίδος, one's native country; Gnally, those in ῢς, (g. ύδος), as o, νεηλυς, (g. νεηλυδος), recently come.

VOCABULARY.

Γελως, ωτος, ό, laughter.
Έρως, οτος, ὁ, love (English
erotic, as in erotic poems).
Κακότης, ητος, ἡ baseness.
Νεότης, ητος, ή, youngness,
youth.

Ομοιοτης, ητος, ή, likeness,
resemblance.

Χαρις, ἴτος, ή, loveliness, plea
singness, favour, benefit,
gratitude (Lat. gratia, Eng.
gratis).

Έρις, ερίδος, ή, strife.
Ελπις, ελπίδος, ή, hope.
Παις, παιδος, ό, ή, a child, son,
daughter.

Φροντις, ίδος, ή, care.

Νυξ, νυκτος, ή, night.
Πενης, πενητος, ὁ, ἡ, poor.
Κουφος, η, ον, light, light-
minded.

Απορία, ας, η, want of means,
destitution, need.

Φιλοχρημοσύνη, ης, η, love of
money, avarice.
Πας, πασα, παν, every; in the
plural, παντες, all,
Απας, ἁπασα, ἁπαν, another

form of πας, πασα, παν, the
å giving the force of toge-
ther, all together, so of com-
biration.

Αδελφος, ου, o, a brother.
Αδελφη, ης, ή, a sister.
Πλουτος, ου, o, wealth.
Πλουσιος, α, ον, rich.
Εγείρω, I stir up, arouse,

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Οἱ ορνίθες αδουσιν. Χαρις χαριν τίκτει, ερις εριν. Μακαρίζομεν. την νεοτητα. Απορια τίκτει εριδας. Πλουσιοι πολλακις την κακοτητα πλουτῳ κατακρυπτουσιν. Ω καλε παι, στεργε τον αγαθον αδελφον και την καλην αδελφην. Ἡ φιλοχρημοσυνη μητηρ κακότητος άπασης εστιν. Οἱ πενητες πολλακις εισιν ευδαιμονες. * The iota, which is subscript with small letters, is written | Η σοφία εν τοις των ανθρωπων θυμοις θαυμαστους των καλων by the side of capitals, but not sounded; thus φδη becomes | ερωτας ενεγείρει. Ο θανατος τους ανθρωπους φροντίδων απολύει. Ἡ φιλια δια ὁμοιοτητος γιγνεται. Οινος εγείρει γελωτα. Εν νυκτι Ωιδη, and ᾄδω becomes Αιδω. βουλη τοις σοφοις γιγνεται. Οἱ σοφοι κολαζουσι την κακοτητα. Οι άνθρωποι πολλακις κουφαις ελπισι τερπονται

+ Note, sc. stands for scilicet (that is, scire licet) and points out that a word is understood, that is, left out, and is to be supplied: sc. is therefore equivalent to our that is, or supply: so here sc. εστιν means that the verb εστι, is, being omitted by the author, is to be supplied by the reader.

* Instead of Λαμπαδσι, κορυθσι, ορνιθσι ανακτσι, and ελμινθσι,

1

ENGLISH-GREEK,

Birds sing. Favour is begotten by favour, strife by strife.. By (dat.) wisdom (there) is awakened in men's minds a wonderful love of good things. I am delighted with the song of birds. The songs of birds delight the shepherd. We delight in (dat.) birds. Men foilow kings. Men obey the king.

There are neuter nouns which belong to this class. The stem of these neuter nouns ends in 7 and in кt, as yaλa, milk, yaλakt-oç, of milk. As the laws of euphony do not endure a Tor Kr at the end of a word, the 7 and the Kт disappear in the nominative, or pass (as in ovç, g. ouros, an ear) into o. Thus, το σωμα, σώματος, a body ; το γονυ, γονατος, a knee ; το γαλα, γαλακτος, milk, and το ους, ωτος, an ear, are declined as follows.

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Εν χαλεποις πραγμασιν ολιγοι έταιροι πιστοί εισιν. Tns αρετης πλουτον ου διαμειβόμεθα τοις χρημασιν. Οἱ ἱκεται των γονατων ἁπτονται. Ὁ θανατος εστι χωρισμός της ψυχης και του σώματος. Ο πλουτος παρέχει τοις ανθρωποις ποικιλα βοηθηματα. Μη πειθου κακων ανθρωπων ῥημασιν. Μη δουλευε, ω παι, τη του σωματος θεραπεια. Οἱ Ἕλληνες ταις Νύμφαις κρατήρας γάλακτος σπενδουσιν. Εθιζε και γυμναζε το σωμα συν πονοις και ιδρωτι, Οἱ αδολεσχαι τείρουσι τα ώτα ταις ταυτολογίαις. Την ψυχην εθιζε, ω παι, προς τα χρηστα πράγματα· Οἱ φαυλοι μυθοι των ωτων ουχ άπτονται. Τοις ωσιν ακουομεν. Μη εχθαιρε φίλον μικρου ἁμαρτηματος ενεκα. Γευου, ω παι, του γαλακτος. Οἱ στρατιωται Oi δορατα βασταζουσιν.

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(5.) The French language preferring the active to the passive voice, requires the use of the active verb in the following and similar cases wherein the English use the passive voice :

Cette dame est bien à plaindre.

Cette maison est à vendre.

That lady is much to be pitied. This house is to be sold. La chose est de trop peu de conThe matter is of too little consaséquence pour la traiter sérieuse-quence to be treated seriously. ment. VOLTAIRE.

§ 129.-GOVERNMENT OF VERBS.

Some verbs are in English governed by prepositions different from those which connect or govern the same verbs in French. Some, again, which are in English joined by prepositions, require none between them in French. We give below lists of verbs with the appropriate prepositions, according to the best French authorities.

§ 130.-VERBS REQUIRING NO PREPOSITION BEFORE ANOTHER VERB IN THE INFINITIVE.

Accourir, to un
Ammer mieux, to prefer

Aller, to go

Apercevoir, to perceive
Assurer, to assure
Arouer, to confess
Confesser, to confess
Compter, to intend
Courir, to run
Croire, to believe
Déclarer, to declare
Daigner, to deign

Désirer, to desire
Devoir, to be obliged
Ecouter, to hear, to lister‹
Entendre, to hear
Envoyer, to send
Espérer, to hope
Faire, to make
Falloir, to be necessary
Imaginer (s'), to imagine
Laisser, to let, to suffer
Mener, to take, to lead
Nier, to deny

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Accorder (s'), to agree

Accoutumer, to accustom

Acharner (s'), to strive
Admettre, to admit, to permit
Aguerrir (s'), to become inured
Aider, to help in
Aimer, to like

Appliquer (8'), to endeavour, to
Apprendre, to learn

Apprêter (8'), to prepare
Aspirer, to aspire

Assigner, to summon

[apply

Assujettir (s'), to subject one's self

Attacher (s'), to apply

Attendre (s'), to expect

Attendre, to put off

Augmenter (s'), to increase
Autoriser, to authorise

Avilir (8'), to debase one's self
Avoir, to have

Avoir peine, to have difficulty in
Balancer, to hesitate

Borner (se), to confine one's self
Chercher, to endeavour
Complaire, to delight in
Concourir, to co-operate

Condamner (se), to condemn one's self

Condescendre, to condescend

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Exceller, to excel

Exciter, to excite
Exhorter, to exhort

Exposer (8'), to expose one's self
Fatiguer (se), to weary one's self
Habituer (s'), to become used to
Hasarder (se), to venture
Hésiter, to hesitate
Instruire, to instruct

Intéresser, to interest

Inviter, to invite
Mettre, to set, to put
Mettre (se), to commence
Montrer, to show, to teach
Obstiner (s'), to persist in
Offrir (s'), to offer
Pencher, to incline
Penser, to think, to intend
Persévérer, to persevere
Persister, to persist
Plaire (se), to delight in
Prendre plaisir, to take pleasure
Préparer (se), to prepare
Porter, I to induce, to excite,
Provoquer, to urge
Pousser, to urge
Réduire, to constrain
Réduire (se), to tend, to end
Renoncer, to renounce
Répugner, to be repugnant
Résigner (se), to be reconciled
Rester, to tarry too long
Réussir, to succeed
Risquer, to risk

Servir, to serve

Songer, to think, to intend

Suffire, (not unip.), to suffice.
Tarder, to tarry
Tendre, to tend

Tenir, to intend, to aim
Travailler, to labour

Viser, to aim
Vouer, to devote

Man does not like to contemplate his nothingness and his vileness.

Have you ever thought of offering all these sufferings to God?

ANSWERS TO CORRESPONDENTS. HARRIET STYLE: The German is very correctly translated into English; not so the English into German, as might be expected. All substantives should begin with a capital letter, and the final s should not be used anywhere else than at the end of a word. The inverted arrangement, according to which the verb is placed at the end of a sentence, only takes place in relative and other subordinate clauses.

W. MABRAISON: We cannot, as we have before said, undertake to correct exercises. Those sent by our correspondent contain a good many errors. In translating from German to English, he appears more anxious to make some sort of sense than to get at the exact meaning of the original. Thus he renders: Was sonst als was die Nachtigall einst zu der Lerche sagte? by "Wherefore as the nightingale aaid to the lark." The proper translation is: "What else than what the nightingale once said to the lark ?" Again, machte er seinen Gruss unter allen Göttern der Juno zuerst, does not mean " he made his salutation to all the gods of Juno first," which is scarcely sense at all, but "he made his obeisance to Juno first of all the gods (and goddesses)." It is not English to say-"those which my brother in his hands has had." This is carrying literal translation too far. Our correspondent seems to have forgotten that in writing German two distinct characters are used for the letter s. He puts the final one at the

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beginning and in the middle of the words. Welcher Regenschirm haben Sie cannot be right. It should be Welchen, accusative masculine to agree with Regenschirm. We have not time or room to point out more mistakes.

D. D. CAUSALITY: For something of the Art of Photography, see the Majesty's inspector of Weights and Measures in your own district.-A. Magazine of Art." For proving your Apothecaries weights, apply to her LISPER (D-d): We know of no cure for lisping but a strong effort of the will to speak without lisping.-R. LAMBIE (Glasgow): Cassell's French Dictionary will be completed in two divisions-1, French-English, which is now published, price 43. in stiff covers, or 53. in cloth. The EnglishFrench Division will be completed in December. The entire work will be published, bound, at 8s. 6d.-S. GRAHAM (Liverpool): We have had lessons on Floriculture and Horticulture in view; and we shall by no means lose sight of them.-J. M. (Aberdeen): We have seen some American (U. S.) publications on Book-keeping, and they are so extremely similar to our own, that it is very evident that brother Jonathan is indebted to us for this as well as many other lessons relating to the business of human life. There is one difference which must be carefully looked into, viz., that of Federal Money instead of Sterling Money. When we come to Exchanges in our Arithmetic, this will be considered; and we shall soon give an inkling of it under the head of Reduction. As to the conversion of the money of differen nations, see Kelly's "Universal Cambist," or Macculloch's "Commercial Dictionary."-JAMES WARDLE (Dean Mills): Right.

APOLLO (Cheltenham) should apply to R. Cocks and Co., New Burlingtonstreet, about Musical Instruments, &c.-T. CHOPE (Hartland): His sug gestions are good, and will be considered.-J. HOULDEN, Jr. (Edinr.): The Perpetual Almanac extends only from 1758 to 1830!-INQUISITIVE (Liverpool) must omit the word of in the sentences to which he refers. As to books which are deemed authorities for excellence of style, we say Addison's papers in the "Spectator," and his writings generally; Dean Swift's "Gulliver's Travels," and his writings generally; and Dr. Samuel Johnson's papers in the Rambler," and his writings generally. Macaulay, our most recent historian, is admired for his style, but it is too flippant for us; those of Sir James Macintosh, Dugald Stewart, and Professor Playfair, are vastly superior.-G. ARCHBOLD (St. Peter's): Right.-H. S.: We can't tell.—À LEARNER (Swaffham): The plants referred to, grow from seeds that preceded them. Griffith's "Chemistry of the Seasons" is good and useful. There is a larger edition than the 4s. one which is greatly improved.

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QUINTIN PRINGLE (Glasgow): His solutions of the teak and pine question are correct.-G. S. (Cupar): See p. 223. vol. III., P. E.—J. L. (Duke-st.): Binding 2d. vol. 1s. 6d.-G. J. B. ANVERS had better write to Professor De Lolme.-SAMUEL ESQUIRE (Logierait) will find an explanation of his difficulties in a note to the Article Duodecimals of the 1st vol. of Hutton's Mathematics, at pp. 63 and 64 of the 12th edition.-ZENO (Glasgow): We

strongly advise him to persevere at self-education in the midst of all his difficulties and discouragements, as he will be ultimately rewarded. The errors to which he refers are now corrected. συν becomes συμ when combined with Bovλn for the sake of euphony.-G. ELTON (Beatton): The writing out of the French Exercises is generally considered all that is necessary; and the committing of the rules to memory in the best way you can; but we may be allowed to remark that the writing out of a rule once is equivalent to reading it carefully, at least, six or seven times.-W. TAYLOR: The best and the cheapest are seldom combined; we know of no case where this is certain, but the Bible. As to globes, try Smith in the Strand.-S. O. (Camberwell): Right.-T. HUNTER should add the study of English to that of Chemistry.-J. Russell (Kingscavil): Received.

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INSTRUMENTAL ARITHMETIC.-No. II.

THE PLANE SCALE; ITS CONSTRUCTION AND USE. In our first lesson on Instrumental Arithmetic, we explained the nature and use of an apparatus called the Neperian Abacus. In this lesson, we propose to explain the construction and use of the Plane Scale. This scale is usually found in a case or box of Mathematical Instruments, and is one of the most useful inventions we know for the purpose of the practical Mathematician, the Artist, the Mechanical Draughtsman, and the Designer and Drawer of Plans, whether relating to Architecture, Machinery, or Civil Engineering. In our illustrations, fig. 1 and 2, we have given an example of a Plane Scale of the most useful construction, for there are several varieties in this respect, which we shall have occasion to explain. This example is a fac simile of an ivory Plane Scale which has been in our own possession for more than thirty years, and a more useful instrument in the solution of practical problems in Mathematics is not easy to be found. This instrument, although only six inches long, contains the same Lines as those which are put

mark it; you can then take 5.5 inches from the scale and mark it in a straight line with the former; then the whole length will be that of the line of 11.5 inches required. Under the line or rule thus described, there is another consisting of six inches divided into 5 equal parts, and having these parts in like manner subdivided into tenth parts. These parts are marked at every large division, thus: 10, 20, 30, &c., which means 10 hundredths, 20 hundredths, 30 hundredths, &c., of a foot, or 1 tenth, 2 tenths, 3 tenths, &c., of a foot. This, then, is a decimal scale of a foot, containing tenths and hundredths of a foot without regard to inches; and from it you may lay down or measure lengths of lines very accurately to hundredths of a foot, as far as it goes, and it may be extended to the laying down or the measurement of a line longer than the scale itself by doing it by parts as shown above.. Thus, if you wished to lay down a line of 2.37 feet, that is, 2 feet 3 tenths of a foot and 7 hundredths of a foot; you would draw an indefinite straight line, and repeat the length of the scale four times in succession on that line, this would give the length of the 2 feet, then stretch the legs of your compasses so that the distance between the two points of the legs may extend from the

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upon one side of the Gunter s Scale, called the Common Gunter by sailors who use this instrument, and who solve their problems in Navigation by its means. The Common Gunter is 24 inches long, and contains on the other side of it, Lines representing the Logarithms of the numbers which are represented by the Lines on the one side just alluded to. In explaining the nature and use of the Plane Scale, therefore, we are explaining the nature and use of one side of Gunter's Scale, so useful in the study and practice of Navigation.

extremity a to the 7th vertical division beyond that marked 30, and this will give the length of the 37 of a foot; next place this length on the straight line above mentioned, in continuation of the 2 feet already laid down, and you will have a line of the whole length of 2.37 feet as required. By comparing the two scales extending from A to B, just explained, at the points where their divisions coincide, you will see that 5 hundredths of a foot is 6 tenths of an inch; 10 hundredths or 1 tenth of a foot is 1 inch and 2 tenths of an inch; 15 hundredths of a foot is 1 inch and 8 tenths of an inch; 20 hundredths or 2 tenths of a foot is 2 inches and 4 tenths of an inch; 30 hundredths or 3 tenths of a foot is 3 inches and 6 tenths of an inch; 35 Fig. 2.

In fig. 1, from A to B there is a common six inch rue, with the inches marked on it from 1 to 6 each inch being subdivided into tenths of an inch; this, then, is a decimal inch

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scale, and you may measure or lay down the lengths of lines by,
its means very accurately to tenths of an inch, as far as it
extends. Thus, if you stretch the legs of a pair of compasses,
so that the distance between the two points of the legs may
extend from the extremity A to the fourth vertical division
beyond that marked 3, you have in this distance the measure
or the length of 3.4 inches or 3 inches. If you wish to
If you wish to
measure or lay down a longer line, you can do it from the same
scale by parts; thus, to measure or lay down a line of 11.5
inches, you can first take 6 inches complete from the scale and

VOL. IV.

hundredths of a foot is 4 inches and 2 tenths of an inch; 40 hundredths or 4 tenths of a foot is 4 inches and 8 tenths of an inch; 45 hundredths of a foot is 5 inches and 4 tenths of an inch; and so on, according to the length of the scale.

We come now to the most useful and accurate Scale drawn on this Instrument, fig. 1, we mean the Diagonal Scale of Equal Parts. The larger Divisions of this scale are sometimes an inch, as on the Common Gunter, which is 2 feet long; and sometimes half an inch as on the Plane Scale, which is only half a foot long. In fig. 1 the larger divisions from c to D are 80

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