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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 follow kings. Men obey the king.

There are neuter nouns which belong to this class. The stem of these neuter nouns ends in r and in кт, as yaλa, milk, yaλakr-og, of milk. As the laws of euphony do not endure a Tor KT at the end of a word, the r and the кr disappear in the nominative, or pass (as in ovç, g. ouros, an ear) into . 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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Αμαρτημα, άτος, το, a failing, a fault, sin.

Βοηθημα, άτος, το, help. Πραγμα, ατος, το, a deed, thing.

Ρημα, ῥημᾶτος, a thing spoken, a word. Χρημα, ατος,το, a thing for use; in the plural, goods, property.

ίδρως, ίδρωτος, ό, sweat. Сερажεiα, aç, ý, care, service. Ταυτολογία, ας, ή, saying the same thing again, repetition. Νύμφη, ης, ή, a nymph. Ικέτης, ου ό, an entreater, petitioner.

Μυθος, ου, o, a speech, word.
Χωρισμός, ου, ό, a separation.
Μικρός, α, ον, small.
Hokiλog, n, ov, various, varie-
gated.

Φαύλος, η, ον, radically bad.
Xpηotos, n, ov, useful, good.
Βαστάζω, I bear, carry.
rvuvalo, I exercise.
EO, I accustom.
Σπεύδω, I hasten.
Enεvow, I pour out, make a
libation.

'ATTоμаι, I hang on something,
I touch (gen.)
Γευομαι, I taste (gen.)
Διαμειβομαι, Ι exchange.

EXERCISES. GREEK-ENGLISH.

Εν χαλεποις πραγμασιν ολιγοι έταιροι πιστοι εισιν. Tns αρετης πλουτον ου διαμειβόμεθα τοις χρημασιν. Οἱ ἱκεται των γονατων ἁπτονται. Ο θάνατος εστι χωρισμός της ψυχης και του σώματος. Ο πλουτος παρέχει τους ανθρωποις ποικιλα βοηθηματα. Μη πειθου κακων ανθρωπων ῥημασιν. Μη δουλευε, ω παι, τη του σώματος θεραπεια. Οι Έλληνες ταις Νυμφαις κρατήρας γάλακτος σπεύδουσιν. Εθιζε και γυμναζε το σωμα συν πόνοις και ίδρωτι 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 ακόνομεν. Μη εχθαιρε φιλον μικρου ἁμαρτήματος ενεκα. Γευου, ω παι, του γαλακτος. Οἱ στρατιωται δορατα βασταζουσιν.

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11.

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(3.) The infinitive present is used in French after certain verbs, which are, in English, joined to other verbs by the conjunction and :

Allez chercher mon père.

1 Go and fetch my father.

(4.) We might give as a general rule, that a verb immediately preceded and governed by another verb (avoir and être excepted), or by a preposition (en excepted), is put in the present of the infinitive:

Tout ce qu'elle s'imaginait tenir, lui échappait tout-à-coup.

FénéLon Vos raisons sont trop bonnes d'elles-mêmes, sans être appuyées de ces secours étrangers.

RACINE.
Vous pensez tout savoir.
PIEYRE,
Croit-il le pouvoir rompre?

TH. CORNEIlle.

All that she fancied that she held, escaped her suddenly.

Your reasons are too good in themselves to need that foreign assistance.

You think that you know everything.

Does he believe he can break it?

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Accourir, to run Aimer mieux, to prefer

Aller, to go

Apercevoir, to perceive
Assurer, to assure
A vouer, 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 listen

Entendre, to hear

Espérer, to hope
Envoyer, to send
Faire, to make
Falloir, to be necessary
Imaginer (s'), to imagine
Laisser, to let, to suffer
Mener, to take, to lead
Nier, to deny

Observer, to notice, to observe
Oser, to dare

Paraître, to seem

Penser, to think, to funcy

Pouvoir, to be able

Prétendre, to pretend

Préférer, to prefer

Protester, to protect

Rappeler (se), to remember

Rapporter, to report

Reconnaître, to acknowledge

Regarder, to look at

Retourner, to return

Revenir, to come back
Savoir, to know
Sembler, to seem
Sentir, to feel
Souhaiter, to wish
Soutenir, to maintain
Témoigner, to testify
Valoir mieux, to be better
Venir, to come
Voir, to see
Vouloir, to be willing

19

de pudends vous fruiter comme RACINE, mon propre Ala But to thin de ses flota erdrossdr la Lane, Avant que tes faveurs aortout de ma memoire Bou BAU,

I intend to treat you as my own 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.

And the Rhine will go and swell the Loire with its waves, before the remembrance of thy goodness leaves my memory.

D. D. CAUSALITY: For something of the Art of Photography, see the "Magazine of Art." For proving your Apothecaries weights, apply to her Majesty's inspector of Weights and Measures in your own district.-A. LISPER (D-d): We know of no cure for lisping but a strong effort of the will to speak without hisping.-R. LAMBIR (Glasgow): Cassell's French

/ tat. Venus nequiring the PuPOSITION BEFORE AN Dictionary will be completed in two divisions-1, French-English, which INFINITIVE,

The pr') placed after the verb shows it to be reflective.

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Etre, être à lire, ] to be reading,
a corire, &o ( writing, de,
Entendre (a), to be expert în
Evertner (8), de strive
Expeller, Anw

Exeter, & de

Exhorter, fo mohant

Expower (s'), lo expose one's self
Fatiguer (e), fo weary one's se

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is now published, price 43. in stiff covers, or 5. in cloth. The English-
French 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 Erchanges in our
Arithmetic, this will be considered; and we shall soon give an inkling of it
As to the conversion of the money of differen
under the head of Reduction.
nations, see Kelly's Universal Cambist," or Macculloch's Commercial
Dictionary, "JAMES WARDLE Dean Mills): Right.

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APOLLO (Cheltenham) should apply to R. Cocks and Co., New Burlingtonstreet, about Musical Instruments, &c.-T CHope Hartland: His sug Ediar. The gestions are good, and will be considered.-J. HOULDEN, Jr Porgenai dimanae extends only from 1738 to 1830-Isquisit.va Liverpodast omit the word of in the sentences to which he refers books which are deemed authorities for excellence of style, we say Addison's paprs in the "Spectator," and his writings generally; Dean Swin's - Guiver's Trave's," and his writings generally; and Dr. Samuel Johnson's papers in the “ Ramber" and his writings generally. Macaulay, our me wcert à storia", is admired for his style, but it is too £ ppant for us; those of Sir James Macintosh, Dugald Stewart, and Professor Flaylar, are vasty $-0. ACHOLZ St. Peter's: KL-H. S.: We can't The plants referred to, grow from seeds that preTARNERS Jood & Dem. G Pay" Chemistry of the Seasons” is pood and astia... I cert is a larger ection than the is, zze which is greatly imperet.

QUINTIN PRINS Gasgow): Hasistūns of the teak and pine prestan

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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

Fig. 1.

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 rule, 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

10 20

30 40 50 60 70 80 90 100 10 20 30 40 50 610

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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 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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I intend to treat you as my own | 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.

son.

And the Rhine will go and swell the Loire with its waves, before the

remembrance of thy goodness leaves

my memory.

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Apprêter ('), to prepare

Aspirer, t aspire

Assigner, to summon

Assujettir (s), to subject one's self

Attacher (s') to apply

Attendre (s') to expect

Attendre, to put off

Augmenter ('), to increase
Autoriser, to authorise

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

A voir peine, to have difficulty in Balancer, to hesitate

to

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
Consentir. to consent

Consister, to consist

Conspirer, to conspire
Consumer, to destroy
Contribuer, to contribute

Convier, to invite
Coûter, to cost
Déterminer, to induce

Déterminer (se), to resolve

Disposer (se), to prepare one's self
Divertir (se), to amuse one's self
Employer, to employ, to devote

Encourager, to encourage
Engager, to induce

Enhardir, to encourage

Enseigner, to teach

L'homme n'aime point à s'occuper de son néant, et de sa bassesse. MASSILLON. Avez-vous jamais pensé à offrir à Dieu toutes ces souffrances ?

THE SAME.

Etre, être à lire, to be reading,

à écrire, &c. writing, &c.
Entendre (s'), to be expert in
Evertuer (s'), to strive
Exceller, to excel
Exciter, to excite
Exhorter, to exhort

Exposer (s'), 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
Ob-tiner (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, 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 said 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 bands 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

་་

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.-A 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.

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. 18. 6d.-G. J. B ANVERS had better write to Professor De Lolme. SAMUEL ESQUIRE (Logierait) will find an explanation of his diffi culties 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 Bouλn 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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Now ready, price 4s. in stiff Wrapper, or 58. strongly bound in cloth, the First Part complete, consisting of the French and English, of CASSELL'S FRENCH DICTIONARY: the entire work in two Parts-1. French and Eng lish: 2. English and French. The French Department carefully Edited by Professor De Lolme, and the English Department by Professor Wallace and H. Bridgeman, Esq., will be completed in Twenty-six Threepenny Numbers, and will form one handsome Volume of eight hundred and thirty-two pages. Price 8s. 6d. bound in cloth, or the Two Divisions may be had separate. volume, price 2s. in stiff covers, or 2s. 6d. neatly bound in cloth. CASSELL'S LESSONS IN FRENCH (from the " Popular Educator"), in a neat

A KEY TO CASSELL'S LESSONS IN FRENCH, containing Translations of all the Exercises, with numerous references to the Grammatical Rules, price 1s. paper covers, or 1s. 6d. cloth.

GERMAN.

CASSELL'S GERMAN DICTIONARY is now issuing in Weekly Numbers, at 3d. each; Monthly Parts, 1s. each. CASSELL'S LESSONS IN GERMAN (from the "Popular Educator "), price 28. in stiff covers, or 2s. 6d. cloth.

MISCELLANEOUS EDUCATIONAL WORKS. CASSELL'S EUCLID-THE ELEMENTS OF GEOMETRY. Containing the First Six, and the Eleventh and Twelfth Books of Euclid. Edited by Professor Wallace, A.M., price ls. in stiff covers, or 1s. 6d. neat cloth.

CASSELL'S ELEMENTS OF ARITHMETIC (uniform with Cassell's EUCLID) is now ready, price ls. In stiff covers, or ls. 6d. neat cloth.

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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

Fig. 1.

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.

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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 In fig. 1, from A to B there is a common six inch rule, with inch and 8 tenths of an inch; 20 hundredths or 2 tenths of a the inches marked on it from 1 to 6 each inch being sub- foot is 2 inches and 4 tenths of an inch; 30 hundredths or divided into tenths of an inch; this, then, is a decimal inch-3 tenths of a foot is 3 inches and 6 tenths of an inch; 35

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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 & 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
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 o to D are

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