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concern,

or

woe,

g in sieg (victory), are written thus, 5 ch, so gh; as in thus, air, 6

ray,

tare, Wtory, fear, fury, floch (Scotch, lake), -5: ich (German I), L's Dach pare, perry, car, carry, cheer, y cherry, (German, roof), Sieg. The phonotypes are "X, 4.”

Easter, history, Sir, star, earn, run, 155. WELSH LL.-The Welsh ll, which is the surd dr whispered

airs, rose, rise,

stern, source. form of the English 1, is represented by Ý ll; thus, Ć Llan.

167. The rule for the downward final r does not apply when r is The phonotype for this sound is 'l.

156. Nominal Consonant. It is sometimes necessary to express preceded by g, th,r, or m, after which the upward r only is conveone or more vowels or diphthongs without a consonant. In this case nient (except in

go

straggler, etc., where the previous part of the T! I may be employed as outlines which have no specific values ; word makes the downward r easy); nor when it would carry a word thus, I E for Edward or Emma, .J I for Isabel, I ah! more than one descending stroke below the line. 'or Leh? or aye (e, ever). The stroke-vowels may be struck 168. In the case of a word that contains no other stroke-conThrough the nominal consonant, as T O for Oliver, tă, 1 oo. sonant than, with a vowel both before it and after it, write the Christian names should be written in full when they are known. The downward r if there is only a vowel before; as, 5 area, 3 areas, nominal consonant may be joined to any other consonant, and be array, 8 arrays, Yarise; but if there is MORE THAN a vowel written in any direction; thus, Fort Thomas Eah.

before, write the upward r; as, (sorry, y story, . serene,

Styrian, o serious.
CONSONANT OUTLINES.

169. PL AND PR SERIES.- The pl and pr series of double conso157. Seeing that in the Phonographic Alphabet s, r, w, y have du. nants should be kept, generally, for such words as contain no vowel plicate forms, that three other letters (sh, 1, h) may be written either between the two consonants, or only an obscure one ; thus, pray, upward or downward, and that many groups of consonants may be ex apple; and the two single consonants should be written when pressed either by their alphabetic forms or by abbreviations, it is evi

peer, V pole. dent that many words may be written in more than one way. For any a clearly-sounded vowel comes between ; as, giren word the writer should choose that form which is most easily and

170. PAST TENSE.—The past tense of a verb ending in t or d is rapidly written, and is at the same time capable of being clearly vocal written thus, V part, V. parted, not v part, y parted. ised. The briefest outline to the eye is not always the most expeditious Verbs that end with the sound of z, are written in the past tense to the hand. The student will insensibly acquire a knowledge of the with Psd, not with the loop st; thus, of gazed, ng 'mused. best forms by practice and observation, and especially by reading some book printed in Phonography. The following special rules embrace

171. STROKE AND CIRCLE S.-Words that contain no other conso. the principal CLASSES of words that admit of various outlines, and a nants than ss, are written with the stroke and the circle, or the circle list of nearly all other common words of this kind is given in par. 177. and the stroke, as may be convenient. It is well to keep the form

158. STROKE W, Y, H.—The stroke-letters for w, y, h are written for ss, and 9 for sz. The former may then be vocalised into cease, in words that contain no other consonant (except - you), in prefer- sauce, etc., and the latter into seize, size, etc.; but the outlines of ence to the vowel signs ce wah, weh, wee, yah

, yeh, yee, 2. see, ). say, 5 saw, etc., should not be changed to ) sees, etc. etc., and the dot h; thus, Y co

yea, 8 hue.

172. FL, FR, ETC.-In words containing no other consonant 159. STROKE H.-The upward h may be joined to p, t, ch, thus, stroke, “fr, vr, fr, dr” should be employed in words beginning with a V behave, 6 Takiti, fie Jehovah; to f, th, thus, vowel, as offer, ether; and "fr, vr, or, &r” in words beginV Pohi; to s and sh, thus, X (first writing > >, and ning with a consonant ; as Vyfry, )- throw. In other cases select forming the circle when vocalising); to n, ng, thus,

the stroke which makes the easiest outline. When the outlines are kance; and to the upstrokes for r, w, y, h, thus, Rehob. equally convenient, fi, ul, 01, dl, should be written cca C.

en

160.— The downward h may be joined to ck (or the correspond and fr, vr, ør, dr, thus, 12), in accordance with the pl, pr. ing thick letter), thus; % Jehu ; to s, thus, % Soho; or to s series of letters ; to prevent the reading off for fr, etc., or the contrary,

when the difference in the size of the hook is not accurately observed. and sh, thus,

(first writing} 7, and making the circle 173. JOINED VOWELS.-At the beginning of a word, a vowel when vocalising); and to k, m, l, and the downward r, thus, Ž may be joined to a consonant in the following cases :-war, wỏ,

before k, , (up), n, m, tr, chr, and shr; the diphthong i, before cohort, 7 Mahomet, ila Elihu, of Režum (Ezra iv. 8).

t, sh, s, th, p, f, r (down); and the triphthong wi before t, th, f; 161. Dor H.-The dot aspirate cannot be used AFTER A CONSO- thus, walk, 7 water, Vi item, wife; also in such NANT; thus, lvis Appii (Acts xxviii. 15), not Ap-hy.

cases as r orol, w about, b due, new, continue. 162. GENERAL RULE FOR L AND R.- The following rule, which 174. Hooks.—A hook may occasionally be written when voca.. and r : – If equally convenient to the writer, the up stroke is used lising ; thus, first write y, then make it into og university. when a vowel follows, and the down stroke when a vowel precedes. 163. INITIAL L.-When joins easily to the following letter, it is

175. When ns, following a curve, ends a noun in the singular, or written downward if a vowel precedes, and upward otherwise ; thus,

a verb in the infinitive, write the STROKE n, not the hook ; thus,

ve fence, Cu alike, <like, alum, 6 element, lament.

176. The following compounds are thus written: Almighty, 164. FINAL L.-After f, or the upward r, L is written downward

almost, already, although, altogether, when final, and upward if followed by a vowel; thus, feel, always, also. Vafollow. After sk, sh (down), ng, and n, the downward / is most convenient. After p, t, ch, k, sh (apward), s (stroke), th, 1 (upward), (downward), m, and skr, use the upward l; also after the circle s,

CORRESPONDENCE IN FRENCH.-I. except when preceded by f, th, or n. The corresponding heavy As a suitable pendant to our “ Lessons in French" and "Readletters follow the same rules. 165. INITIAL R.-When r is initial, and

ing in French," we now bring under the notice of our readers a

followed by p, k, sh, valuable series of model business letters in English and French, (stroke or circle), 1, 7, or n (stroke or hook), the down-stroke is relating to the various transactions of commercial life. used if a vowel precedes; and the up-stroke otherwise ; thus

Under each heading the student will first find a model letter 2-ark, rock, V earl, 1 rule,

error,

couched in language appropriate to the subject under considera

tion in English. Immediately after is given, in every case, a 166, FINAL R.-A final < (with or without a hook, circle, or loop) close but idiomatic translation of the English model letter into is written upward if a vowel follows the r, and otherwise downward; French.

ofences.

rare.

It is unnecessary to do more than point out that any one who 3.-CIRCULAR NOTIFYING THAT A BUSINESS HAS CHANGED has carefully studied the “ Lessons in French," which have

HANDS. already appeared in the POPULAR EDUCATOR, may soon become Messrs. Roger & Co., Brussels.

Bremen, August 17, 1866. an adept in French commercial correspondence by means of these model letters of business. We would recommend the constrained me to retire from business, which in future will bo

Gentlemen,-The natural infirmities incident to old age have learner first to copy the English form without looking at the conducted by my two sons in their name. French translation below; then endeavour, by aid of his dictionary and grammar, to translate the English form thus copied tinue your correspondence with them, and take note of their

While making known to you this change, I beg you will con. out into French; and, lastly, compare his work with the French

respective signatures. model that follows the English form, and correct his translation

I have the honour to remain, Gentlemen, by its aid. He should also practise himself in translating each

Your very obedient servant, French model into English, afterwards correcting his translation

FRANZ MEYER. by the English forms.

Mr. Louis Meyer will sign : MEYER BROS. 1.-CIRCULAR ON THE RETIREMENT OF A PARTNER IN A FIRM.

Karl Meyer will sign : MEYER BROS.
Amsterdam, August 16, 1866.
Messrs. Legrand & Co., London.

Bremen, le 17 Aout, 1866. Gentlemen,--We take the liberty of informing you that our

Messieurs Roger & Cio, à Bruxelles. Mr. Jean Van Steen will, in conformity with a long-expressed gagent à renoncer aux affaires du commerce, que je remets dès

Messieurs, Les infirmités inséparables de la vicillesse m'en. desire, retire from this date from our firm.

Though we regret being deprived of his active co-operation ce jour entre les mains de mes deux fils pour qu'ils les dirigent and long experience, the fact of his retirement will not interfere

en leur nom. with the conduct of our business.

En vous annonçant ce changement, je vous prie de vouloir We are, Gentlemen, your obedient servants,

bien continuer avec eux votre correspondance, et prendre note J. & B. VAN STEEN.

de leurs signatures.

Je suis, Messieurs, avec la plus parfaite estime,
Amsterdam, le 16 Août, 1866.

Votre très-obéissant serviteur, Messieurs Legrand & Cie, à Londres.

FRANZ MEYER Messieurs, -Nous prenons la liberté de vous faire part que M. Louis Meyer signera : MEYER FRÈRES. notre sieur Jean Van Steen, désirant quitter les affaires, se retire Karl Meyer signera : MEYER FRÈRES. à dater de ce jour de notre maison.

Sa retraite, quoique nous laissant le vif regret d'être privés 4.-CIRCULAR ON THE CESSATION OF EXISTENCE OF A de sa co-opération active et de son expérience, ne changera rien

FIRM AND WINDING-UP OF AFFAIRS, dans la marche de nos affaires.

Bordeaux, August 18, 1866. Nous avons l'honneur, Messieurs, de vous saluer, Messrs. Thomas & Co., London.

J. & B. VAN STEEN.

Gentlemen,- It is with deep regret that I have to inform you 2.-CIRCULAR ANNOUNCING THE ESTABLISHMENT OF A of the sad and premature death of my husband, Mons. Martin New HOUSE OF BUSINESS.

Auber, only existing partner of the firm of Auber & Co., of Messrs. Petit & Co., Marseilles.

London, August 15, 1866. this town.

As both my sons are still too young to continue the firm Gentlemen,-We have the honour to inform you that we have founded by their father, I have but to fulfil the sad duty of this day established a house of business under the firm of

thanking my late husband's correspondents for their confidence, Masters & Johnstone.

and to inform them that the firm Auber & Co. has ceased to We are in hopes that ample capital, our joint experience, and exist, and that I intend to superintend the liquidation myself. acquaintance with business matters, will enable us to give satis

Begging you to take note of my signature, faction to all who may honour us with their confidence.

I have the honour to be, Gentlemen, Begging you to take note of our respective signatures, we

Your obedient servant, refer you to the undermentioned firms,

MARIE AUBER, Widow. And have the honour to be, Gentlemen,

Mme. Auber will sign : AUBER & Co., in liquidation.
Your very obedient servants,
FRED. MASTERS.

Bordeaux, le 18 Aout, 1866.
ANDREW JOHNSTONE.

Messieurs Thomas & Cie, à Londres. Fred. Masters will sign: MASTERS & JOHNSTONE.

Messieurs,—C'est avec la plus vive douleur, que j'ai à vous Andrew Johnstone will sign: MASTERS & JOHNSTONE. annoncer la perte douloureuse et prématurée de mon époux, le References permitted to

sieur Martin Auber, seul chef de la maison Auber et Cie, de Messrs. H. Bake, London.

cette ville. Changarnier, Lyons.

Comme mes deux fils sont encore trop jeunes pour diriger la Lilienskin, St. Petersburg.

maison fondée par leur père, il ne me reste que le triste devoir Mackay, Glasgow.

de faire mes remerciements aux correspondants de feu mon mari

Londres, le 15 Août, 1866. pour la confiance qu'ils lui ont accordée, et de les prévenir que Messieurs Petit & Cie, à Marseille.

la maison Auber et cie n'existe plus, et que je dirigerai la liqui. Messieurs,---Nous avons l'honneur, de vous prévenir que nous dation moi-même. venons d'établir une maison de commerce sous la raison sociale En vous priant de prendre note de ma signature, et are Masters et Johnstone.

l'assurance de ma parfaite considération, Nous nous flattons que des capitaux suffisants, l'expérience et

J'ai l'honneur d'être, Messieurs, la connaissance des affaires, nous mettront à même de satisfaire

Votre humble servante, tous ceux qui voudront bien nous honorer de leur confiance.

MARIE AUBER, Veuve. En vous priant de prendre note de nos signatures respectives, Mme. Auber signera : AUBER & Cir, en liquidation. nous nous référons aux maisons ci-dessous, et avons l'honneur d'être avec une parfaite considération, vos très-humbles serviteurs, 5.-LETTER OF INQUIRY AS TO SOLVENCY OF A FIRM,

FRED. MASTERS.
Messrs. Lafitte, Paris.

Havre, August 19, 1866.
ANDREW JOHNSTONE. Gentlemen,-We beg to confirm our letter of the 26th of July

, Fred. Masters signera : MASTERS & JOHNSTONE.

and request you to be good enough to let us know your opinion Andrew Johnstone signera: MASTERS & JOHNSTONE. of the solvency of Messrs. Henry Smith Bros., who have reRéférences :

ferred us to you for the said information. Messieurs H. Bake, Londres.

We shall be obliged if you would also indicate to us the Changarnier, Lyon.

amount of credit we may safely give them.
Lilienskin, St. Petersbourg.

You may rely upon our discretion.
Mackay, Glasgow.

MERIVALE BROTHERS.

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Le Havre, le 19 Août, 1866.

REDUCTION BY DIVISION. Messieurs Lafitte, à Paris. Messieurs, -- Nous vous confirmons notre lettre du 26 Juillet as a factor, the equation is reduced by dividing every term on

165. When the unknown quantity contains any known quantity, dernier, et vous prions de vouloir bien nous donner des renseigne- both members by this known quantity. ments sur la solvabilité de MM. Henry Smith frères, qui nous

EXAMPLE.- Reduce the equation ax + b – 3h= d. ont indiqué votre maison comme pouvant nous les fournir.

Here, by transposition, we have ax = d + 3h - b; and Vous nous obligeriez aussi en nous indiquant l'étendue du crédit que vous jugeriez convenable de leur accorder.

dividing by a, we have a =

d + 3h b.

Ans. Vous pouvez compter sur notre discrétion.

MERIVALE FRÈRES.

166. If the unknown quantity has co-efficients in several terms, the equation must be divided by the sum of all these co

efficients. LESSONS IN ALGEBRA.-XV.

EXAMPLE.-Reduce the equation 3x – bæ = a - d.
Hero, 3x – bx = (3 — b); and (3 - 6) Xa= a -

-d.
SIMPLE EQUATIONS (continued).

Whence, dividing by 3 – b, we have x = Ans. REDUCTION BY MULTIPLICATION.

3 - 6 160. WHEN the unknown quantity is connected with a known

167. If any quantity, either known or unknown, is found as a quantity by the sign of division, the reduction is effected by factor in every term, both members of the equation may be multiplying both members of the equation by the latter, if it be divided by it. On the other hand, if any quantity is a divisor the divisor; and by the former, if it be the divisor.

in every term, both members of the equation may be multiplied In this case, it will be particularly useful to remember a rule by it. In this way, the factor or divisor will be removed, and formerly given, namely, that a fraction is multiplied by its de- the reduction may be effected as before. nominator, by removing the denominator ; or, in other words,

EXAMPLES.-(1.) Reduce the equation ax + 3ab = bad + a. patting down the numerator as the product. Also, that after this

Here, dividing by a, we have x + 36 = 6d +1; and, by

60 +1- 3b. Ans. process has been performed, transposition is still to be employed transposition, x = as in the preceding examples.

b_h-a (2.) Reduce the equation

D3 + 1 EXAMPLE.—Reduce the equation 1. +a =+d.

Here, multiplying by x, we have x +1-b=h-d; and, by Here, multiplying both sides by c, we have, for the product, transposition, x=h-d+b-1. Ans. * + ac = bc = cd; and, by transposition, æ = bc + cd - ac. 168. A proportion is converted into an equation by making the 161. Though it is not always necessary, yet it is often conve- product of the extremes

, one member of the equation ; and the nient, to remove the denominators from fractions consisting of product of the means, the other member. known quantities only. This is done in the same manner as in EXAMPLE.-Reduce to an equation ax:6:: ch: d. the preceding rule.

d h

Here the product of the extremes is adx, and the product of EXAMPLE.-Reduce the equation

the means bch; the equation is, therefore, adx = bch. Whence c

bch ad ah

Ans. Here, multiplying by a, we have x= + ; again, multi ad"

b plying by b, we have bæ ad +

169. An equation may be converted into a proportion, by resolv; lastly, multiplying by c, ing one side of the equation into two factors, for the middle terms

acd + abh we have bcx = acd + abh. Whence <=

Ans. of the proportion; and the other side into two factors, for the bc

extremes. 162. An equation may be cleared of fractions by multiplying

EXAMPLE.—Convert the equation adx=bch into a proportion. both members by all the denominators.

Here the first member may be divided into the two factors ax 163. In clearing an equation of fractions, it often happens and d; the second into ch and b. From these factors we may that a numerator becomes a multiple of its denominator (i.e.,

form the proportion ax:b:: ch: d. can be divided by it without a remainder), or that some of the

EXERCISE 27. fractions can be reduced to lower terms. When this occurs, the

d operation may be shortened by performing the division indicated, 1. Reduce the equation 2x =

+ 4b. and by reducing the fractions to their lowest terms.

2. Reduce the equation ax + x = h - 4. 164. In clearing an equation of fractions, it will be necessary

& + d to observe, that the sign prefixed to any fraction, denotes

3. Reduce the equation a that the whole value is to be subtracted, which is done by 4. Reduce the equation ** (a + b) - & -b= d * (a + b). changing the signs of all the terms in the numerator.

5. Reduce to an equation a +6:0::h-m:y. d

6. Reduce to a proportion the equation ay + by = ch EXAMPLE.-Reduce 36 – 2hm – 6n

7. Reduce the equation 16x + 2 = 34. (a-d),

8. Reduce the equation 4 - 8 = - 3x + 13. sp - 36 + 2hm + 6n

9. Reduce the equation 10x – 19 = 7x + 17. EXERCISE 26.

10. Reduce the equation 8x - 3+9 = - 7x + 9 + 27. 1. Reduce the equation + 5 = 20.

KEY TO EXERCISES IN LESSONS IN ALGEBRA.

EXERCISE 25. 2. Reduce the equation +d= h.

1. x=b + 4.

6. x= 11.

11. æ= 7.

2. y = 2ab - 2hm - a. 7. a = 20. 3. Reduce the equation +7= 8. 3. x=b-7h-d-22.

13. y = 16. 4. x = 8bh + 9.

9. = 8.

14. x= 24. 5. a = 15.

10, x= 6. 4. Reduce the equation

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LESSONS IN MUSIC.-XXII. EXERCISES—“HONEST FELLOW” "AULD LANG SYNE." In our last Lesson in Music (Vol. III., p. 398) we gave the learner a great deal of necessary and valuable information on the different kinds of voices of men, women, and boys, proper enunciation, and singing in parts. We now propose, in accordance with our promise, to set before our pupils some exercises in part-singing; but before any student commences to practise these, | it will be as well for him or her, as the case may be, to read over

10

once more the lesson to which we have referred, that our remarks another of Burns's heart-stirring lyrics, "Auld Lang Syne," or on the regulation of the voice, its pitch, quality, and strength, may “Old Long Ago,” if there be any need to put the expression, be fresh in the memory of our readers when they begin to sing which must be familiar to all, in an English dress. It may, in concert the exercises that are now brought under their notice. however, be as well to say, for the benefit of those of our readers

In the first of these exercises, some words by Martin Farquhar to whom some of the Scotch words introduced into the poetry Tupper are set to an old English tune which admirably suits may be new, that braes means hill-sides ; gowans, daisies or any the rhythm of the poetry. In the second the learner will find wild flowers growing in hedge or meadow; and burn, a brook

EXERCISE 36.-HONEST FELLOW, SORE BESET.-Key D. M. 80.
(Tune, Old English. Words from the last Edition of “ Ballads for the Times,” by M. F. TUPPEB, Esq.)

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2. Though the night be dark and long,

Morning soon shall break serene;
And the burden of thy song,

“HOW MUCH WORSE IT MIGHT HAVE BEEN."

1. Honest fellow, sore beset,

Vexed by troubles quick and keen,
Thankfully consider yet

"HOW MUCH WORSE IT MIGHT HAVE BEEN."
Worthily thy faults deserve

More than all thine eyes have seen;
Think thou, then, with sterner nerve,

“HOW MUCH WORSE IT MIGHT HAVE BEEN."

God, the Good One, calls to us,

On his providence to lean,
SHOUT, THEN, OUT, devoutly thus,

" HOW MUCH WORSE IT MIGHT HAVE BEEN."

We have here separated the established notation from nor keys will be a difficulty to them.] This piece is arranged its accompanying interpreter, thus offering a better exercise for for three voices—two trebles and a bass or baritone. We should the pupil. Da Cape means "return to the beginning.” [The not, however, omit to point out that, as compared with the dots between the lines of the staff mean the same thing. The "air" and "second treble," the "base" is written an octave students of the old notation will notice the “ bass clef,” now too high in the new notation ; but this creates no confasion in first introduced. But they must be guided by the place of practice, as the bass voice is naturally an octave lower thru the key-note indicated by the square note, and neither clefs the treble.

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THE SAME IN THE NEW NOTATION, BUT FOR TWO EQUAL VOICES.

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2. We two have ran about the braes,

And pulled the gowans fine;
But we've wandered many a weary foot
Since ola "lang syne."

For old, etc.

Bat seas between us broad have roared
Since old "lang syne."

For old, etc.
4. And here's a hand, my trusty friend,

And gi' us a hand of thine;
And we'll take the cup of kindness yet,
For old " lang syne."

For old, etc.

3. We two have paddled in the burn,

From morning sun till dine :

To illustrate still further this subject of the different , accompanying. The laws of harmony will tell you why the voices, we give our present song-first (in the old notation) as accompaniments in the two cases are different. "DAL SEGNO it may be sung by two female voices and one male voice-and, means " return to the sign." The curiously-marked s is put again in the new notation), as it should be sung by two for that sign, and the word " fino” shows where you are to female voices, or by two male voices, without a third voice! close.

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