steadily as possible, and ascending as high as his voice will allow (with the cork, if necessary, to keep his mouth open), and with the most careful observance of the following directions. Expand the ribs, so that they press against the dress at the sides, and, by drawing in the muscles of the lower belly, keep the ribs thus xpanded. This will allow free and easy play to the lungs. For courses of exercises on these subjects, see the small book named in Lesson V.

The sounds of the voice, in singing, should be delivered promptly and easily. If the voice is given out carelessly, it comes roughly through the throat, and is called guttural; and if produced in a forced manner, it is driven through the nose, and so becomes nasal. Correctness in singing depends upon mental effort, for it is the mind which commands the delicate muscles of the larynx and throat. Lazy singing is always flat and miserable; hence we always sing musically better when our hearts are most engaged in the song.

A note may be loud or soft. The loudness or softness of the voice is called its force. It is very important to cultivate the habit of using a medium force of voice, so that it may be always easy to sing a note or strain more loudly or more softly than

the rest. This habit is important to comfort and pleasure in singing, and absolutely necessary for expressior, and refinement. The medium voice of one person is, of course, different from that of another, according to the size of the larynx and the strength of the lungs.

The suggestions given above must be kept constantly in mind in every daily practice. If you enjoyed the advantage of a private teacher, such points as these would be constantly in his mind, and he would see that you observed them. Indeed, one of the chief uses of a private teacher is to keep us to our work. The self-educator, however, must summon to his aid sturdy determination and steady perseverance. A lady went to a distinguished teacher of singing, to receive a course of costly lessons in the art. For a large proportion of these lessons, in the early part of the course, he did not permit her to sing a single note, but made her simply pace the room, expanding her lungs, and taking breath in every way which was required to give her command of the material of which voice is made. Even great public singers do not think of omitting the daily practice of the scale and chord in long “holding" notes, as we have recommended.

LESSONS IN FRENCH.-XXII.

SECTION XLVIII.-IMPERSONAL VERBS AND THEIR

USES.

chirurgien ? 18. Il faut lui envoyer de l'argent, il en a grand besoin. 19. La modiste a-t-elle tout ce qu'il lui faut ? 20. Elle n'a pas tout ce qu'il lui faut. 21. Combien vous faut-il? 22. Il me faut cinq francs. 23. Ne vous faut-il pas davantage?

Il faut, il a fallu.

Il me faut écrire un thème. Où nous faut-il aller ?

study.

EXERCISE 92.

1. What must we do? 2. You must bring your book and to-day? learn your lesson. 3. Is it necessary to write to your brother been necessary to speak to your father? 4. It is not necessary to write to him. 5. Has it sary to speak to him. 6. It has been neces

7. Is it necessary to go to D. to-day? 8. It is necessary to go there (y). 9. Must I go to your sister? 10. You must go to her, she wishes to speak to you. 11. How much money must your brother have? 12. He must have ten francs fifty centimes. 13. How many books does your sister want ? 14. She must have many books, she reads (lit) much. 15. What will you send to the surgeon? him our horse; his own (le sien) is ill. 17. Must he not have 16. We must send

paper ? 18. He must have some; he has letters to write. 19. Must he have much? 20. He must have a quire (main, f.). 21. Do you want anything more? (See No. 13, in the French Exercise above.) 22. I need something more. have ten dollars. 23. I need nothing more. 24. Must you have one hundred francs ? must have money to (pour) pay his debts. 25. I must 26. What does the surgeon want? 27. He 28. Has the tailor all that he wants ? 29. He has not all that he wants. milliner has received all that she wants. 30. The 31. What must you have for your trouble? 32. How much do you want? 33. How much do we want? 34. What must I do ? 35. You must write a letter. 36. What must she write? write four pages. 37. She must 38. She must go to church.

LESSONS IN ARITHMETIC.-XX.

RATIO AND PROPORTION.

francs?

EXERCISE 91.

Fort, very, very much. Modiste, milliner. Ouvrage, m. work. Pay-er, 1. pec. [S 50 (2)], to pay. Peine, f. trouble. Quand, when.

1. Que faut-il faire aujourd'hui ? 2. Aujourd'hui il faut travailler. 3. A-t-il fallu beaucoup travailler pour finir l'ouvrage à temps? 4. Il a fallu travailler toute la journée. 5. Quand faut-il écrire à notre ami ? 6. Il faut lui écrire aujourd'hui. 7. Me faut-il aller trouver mon père? 8. Il vous faut aller le trouver, il désire vous parler. 9. A-t-il besoin de quelque chose? 10. I lui faut des livres, des plumes, et de l'encre. 11. Ne lui faut-il pas aussi de l'argent? 12. Il lui en faut beaucoup pour payer ses dettes. 13. Vous faut-il encore quelque chose? 14. Il ne me faut plus rien, j'ai tout ce qu'il me faut. 15. Ne faut-il pas du papier à votre sœur ? 16. Il ne lui en faut pas davantage.t 17. Que faut-il envoyer au

* Another form of this and the following sentences will be found Section 21. 1, 2.

†This adverb, in modern usage, is not employed with a noun.

This latter relation-namely, that which is expressed by the quotient of the one number or magnitude divided by the otheris called their Ratio.

The It

Thus the ratio of 6 to 2 is 62, or 3. The ratio of 7 to 5 is 75, or, as it would be written, the fraction . numbers thus compared are called the terms of the ratio. The two first term is called the antecedent, the last the consequent. will be seen that any ratio may be expressed as a fraction, the antecedent being the numerator, and the consequent the denominator. A ratio is, in fact, the same thing as a fraction. When we talk of a ratio, we regard the fraction from rather a different point of view, namely, as a means of comparing the magnitude of the two numbers which represent the numerator and the denominator, rather than as an expression indicating that a unit is divided into a number of equal parts, and that so many of them are taken.

2. The ratio of two numbers is often expressed by writing two dots, as for a colon, between them. Thus the ratio of 6 to 3 is written 6: 3; that of 3 to 5, 3 : 5, etc.

exactly the same thing. The expressions and 3: 5, it must be borne in mind, mean

A direct ratio is that which arises from dividing the antecedent by the consequent.

the two numbers. Thus, the inverse ratio of 3: 5 is the ratio An inverse or reciprocal ratio is the ratio of the reciprocals‡ of of : }, or otherwise expressed, which is the same as §, or otherwise expressed, 5: 3.

Hence we see that the inverse ratio of two numbers is expressed by inverting the order of the terms when the ratio is

The reciprocal of a number or fraction is the number or fraction obtained by inverting it. Thus, the reciprocals of 5,,, etc., are respectively, 3, 6.

Different pairs of numbers may have the same ratio. Thus, the ratios, 12, 3, are all equal.

When two pairs of numbers have the same ratio, the four numbers involved are said to form a proportion; and they themselves, in reference to this relation subsisting among them, are called proportionals. Thus, 3, 4, 12, 16, are proportionals, because the ratio, or 3: 4 = the ratio 3, or 12 : 16.

A proportion is expressed either by writing the sign of equality (=) between the two equal ratios, or by placing four dots in the form of a square, thus, :: between them.

Thus, the proportionality of 3, 4, 12, 16, might be expressed in any one of the three following ways:

= 13; 3:4 12:16; 3:4 12:16.

The last expression would be read, 3 is to 4 as 12 is to 16. The first and fourth terms of a proportion are called the extremes; the middle two, the means.

4. If four numbers be proportional, the product of the extremes is equal to the product of the means.

Take any proportion, 3: 4 :: 9: 12, for instance. Expressing this in the fractional form, we have = , and reducing these fractions to a common denominator 12 x 4, we get

Any set of numbers are said to be respectively proportional to any other set containing the same number when the one set can be obtained from the other by multiplying or dividing all the numbers of that set by the same number. Thus, 3, 4, 5 are proportional respectively to 9, 12, 15, or to 3, 4, §.

7. To divide a given number into parts which shall be proportional to any given numbers.

Add the given numbers together, and then, dividing the given number into a number of parts equal to this sum, take as many of these parts as are equal to the given numbers respectively. EXAMPLE.-Divide 420 in proportion to the numbers 7, 5,

and 3.

These parts are evidently in the proportion of 7, 5, and 3, and their sum, 196 +140+ 84 = 420.

8. The same method will apply if the given number or quantity is to be divided proportionally to given fractions. EXAMPLE.-Divide 266 into parts which shall be respectively proportional to,, and .

Following exactly the same method as before, the answer, without reduction, would be} × 266, × 266, and +++ 星++1

} + 1 + 1

Or we may proceed thus:

x 266.

Reducing the fractions to their least common denominator, which is 60, we get

18, 18, and 13.

7. Insert the first term in the following proportions- -: 3 :: 5:6; -:48:9; -:::2:1.

8. Find a fourth proportional to 2:13, 579, and 3.14159, correct to 5 places of decimals.

9. Divide 100 in the ratio of 3 to 7.

10. Two numbers are in the ratio of 15 to 31, and the smaller is 75; find the other.

11. What two numbers are to each other as 5 to 6, the greater of them being 210?

12. Two numbers are in the ratio of 16 to 27, the smaller being 112; find the other.

13. Divide 921 in the ratio of 1 to 3.

14. Insert the first term in the following proportion, -:8:: 14:56. 15. What two numbers are to each other as 15:36, the greater of them being 756?

16. Find a fourth proportional to 8.76, 9'81, and 183.96.

17. Two numbers are in the ratio of 18 to 91, the larger being 3549; find the smaller.

18. Find the third term of the proportions, 17: 27::--: 81; 16: 29::: 174.

19. Give the second term of the proportions, 16:- -:: 21: 147; 8.5: 178.5 :: 35'7.

20. Insert the fourth term in the proportions, 3:14 :: 86: —; 81981: 901:-.

21. Two numbers are in the ratio of 86 to 981, the smaller being 6622; find the larger.

As tests by which the correctness of the processes of addition, subtraction, multiplication, and division may be ascertained, were given in Lessons in Arithmetic, II. to V., it has not been thought requisite to give answers to the Exercises already given in abstract Arithmetic. The answers will, however, be supplied to future examples in concrete Arithmetic.

LESSONS IN SHORTHAND.-IX.

EXERCISE 29.

ON THE ABBREVIATING HOOKS, ETC., IN LESSON VIII. To be written by the pupil in Phonography, and in longhand. N HOOK.

1. cone, town, deign, chin, Jane, pine, bean, run (upward r). 2. cones, towns, deigns, chins, Jane's, pines, beans, runs (upward ). 3. shine, then, fawn, vein, lawn, earn (downward r), known, moan. 4. shines, fawns, veins, lawns, leans, earns, man's, moons.

FOR V HOOK.

5. dove, devour (upward r), divide, above, approve, brave, chaff. 6. groove, rough, pave, scoff, serve, tough, turf, serf, surf, crave. 7. rife, achieve, brevity, advent, advert, defer, derive, deprave. 8. divine, divinity, dovetail, defend, refer, reference, profit, mischiet. -TION HOOK.

9. auction, addition, additional (downward ), admission, admonition, 10. affliction, aggravation, animation, anticipation, approbation. 11. commendation, compassion, confession, confusion, consideration, 12. temptation, pension, nation, mansion, invention, intention. HALVING PRINCIPLE, ADDING T or D.

13. ask, asked; aim, aimed; attack, attacked; avail, availed. 14. bake, baked; bath, bathed; bawl, bawled; boil, boiled. 15. calm, calmed; cheer, cheered; chip, chipped; deem, deemed. 16. elope, eloped; envy, envied; fail, failed; fear, feared; fill, filled. 17. glue, glued; guide, guided; howl, howled; her, heard (tick h). 18. jump, jumped; keep, kept; knock, knocked; kneel, knelt. 19. leaf, left; loathe, loathed; lodge, lodged; laugh, laughed. 20. maim, maimed; move, moved; match, matched; nip, nipped. 21. ooze, oozed; pair, paired; pick, picked; pitch, pitched. 22. quill, quilt; reach, reached; rob, robbed; rock, rocked. 23. save, saved; shame, shamed; spare, spared; subdue, subdued. 24. touch, touched; thaw, thought; thatch, thatched; wage, waged. ST AND STR LOOPS.

25. abased, abreast, attest, boast, bust, cast, chaste, crust, durst, dust. 26. fast, fist, ghost, grist, infest, inmost, jest, just, last, list, lost. 27. mast, mist, most, next, nest, oppressed, paste, pest, post, quest. 28. request, roast, stage, steal, steam, suggest, text, trust, utmost. 29. castor, Chester, faster, fluster, Leicester, Manchester, minister. 30. monster, muster, poster, punster, Ulster, Winchester, youngster.

S-TION HOOK.

31. decision, disposition. vexation, possession, position, opposition. 32. exposition, physician, compensation, organisation, transition.

(In the last three words, turn the ns circle on the left.)

LENGTHENED CURVE, ADDING THR, DER.

33. asunder, founder, slander, provender, thither, father, thunder. 34. adventure, mother, matter, September, November, December. 35. temper, neither, another, dissenter, laughter, rafter, letter. 36. latter, alter, fetter, fender, order, salter, smatter, weather, wither. EXERCISE 30.

(To be written in Shorthand.)

Do as you wish others to do to you. When you feel angry, it is well to think long before you speak. Try to do that which is right, and avoid that which is wrong. There is a time for play, and there is a time for work; a time to think, and a time to talk ; a time to keep silence, and a time to speak. When you speak, think to whom you speak, of whom you speak, and say only that which you know to be just and right.

The pupil should now test his progress, by submitting his work to the examination of a competent phonographer. He is recommended to send a shorthand transcript of Exercise No. 30, (with interlined longhand, leaving a blank line under every two lines thus filled, for corrections,) to some first-class member of the Phonetic Society for examination, and correction if necessary. His request will be cheerfully complied with, and he will be invited to forward other exercises for correction. The lesson should be accompanied by a stamped and directed envelope for its return. A List of the Society for the current year may be obtained through any bookseller, of Mr. F. Pitman, 20, Paternoster Row, London, or of Mr. Isaac Pitman, Bath, by post, price 2d.

GENERAL RULES FOR WRITING.

143. POSITIONS OF WORDS.-Phonographers, who wish to become reporters, should cherish reporting habits as soon as they can write the system fluently. In following a rapid speaker it is impossible to insert many vowels. If then we can, by a difference in the POSITION of a consonant outline, INDICATE the vowel, or principal vowel, of the word, it will facilitate the reading of the report. In the Reporting Style, a word that contains only one or two consonant strokes is written IN POSITION, in accordance with its vowel, or accented vowel, as explained in paragraph 139. As a general rule, no advantage would arise from placing IN POSITION a word that contains three or more consonant strokes, because in such cases there is seldom any other word written by the same outline for which, if left unvocalised, it could be mistaken.

144. A word composed of a horizontal and a down or up stroke, has its position determined by the down or up stroke, and not by the horizontal one; or, in other words, a horizontal letter, when initial, written a little higher than usual to accommodate itself to the position in the first position, and followed by a perpendicular stroke, must be followed by an upstroke, it must be written a little lower, for the same of the following stroke; and when initial, in the first position, and

reason.

145. A word written by a double-length curve takes three positions if the letter be horizontal; two positions, ON and THROUGH the line, if sloping; and one position, THROUGH the line, if perpendicular. See par. 139.

146. CIRCLE SS.-The large circle ss (par. 35) cannot be added to a hook or a half-sized consonant. In the former case, it could not be distinguished from s; and in the latter, it would take up nearly the whole of the letter. The titles Misses (plural of Miss,)

and

Mrs, should be written thus, for the sake of distinction. 147. VOCALISATION OF THE LARGE CIRCLE.-The large circle ss may be supposed to contain the short vowel No. 2, namely, sez or zez, for the plural of nouns, and the third person singular of verbs. Other vowels may be expressed by placing the vowel-sign within the circle; thus, exist (ekzist), Crassus, persuasive, precisely, exercise. No distinction can, in this case, be made between aw, ō, and ōō; or between wah, weh, and wee, etc.

148. STROKE-VOWELS.-Theoretically a stroke-vowel is at a right angle with the consonant, but in practice it may be written at any angle that is distinct; thus, instead of |_ true.

149. VOCALISATION OF HALF-LENGTH CONSONANTS.-When the circle s follows a half-sized consonant, it must be read after the t or d added to the primary letter; thus, pat, pats (not past), Spant,pants. No final vowel can be placed AFTER the t or d added by halving; thus would not be India, practice, M .are the

faulty, but iniad, prackits, faulit: ju

correct forms. This rule requires particular attention: it is frequently misunderstood by learners.

150. OMISSION OF VOWELS IN PL, PR, ETC.-It is seldom necessary to mark an unaccented vowel in a double consonant of the pl and pr series; thus, permit, _____ vocal. In accented syllables, the vowel should be inserted; thus, \ pervért, ~ pérvert.

151. Two VoWELS CONCURRING.-When two vowels occur either

before or after a consonant, the vowel that is sounded nearest to the consonant should be written nearest to it; thus, - iota, Messiah. When two vowels occur between two consonants, one is placed to each; thus, fuel. The diphthongs i-a, oi-a may be written thus, diamond, royal.

152. DISSYLLABIC DIPHTHONGS.-The following form a series:4 ah-e, | eh-e, | ee-e, 7| aw-e, 70-e,

ار

00-e.

This series of signs may represent diphthongs composed of an accented long vowel and ANY short vowel except oo; thus, the first sign may be written in "solfaing" and "solfaers," also for ay (yes); the second in " saying, clayey, aerated, bayonet; " the third in "being, real, theory, museum;" the fourth in both soil (one syllable) and sawing (two syllables), etc. In alien, folio, create, etc., where the first vowel is not accented, the yah series of vowels should be used, rather than the third of the above series.

153. FRENCH VOWELS AND NASALS.-In the French language