, per question, (52.) Let z be the numerator, that no possible difficulty can arise. Thus oxygen, meaning Then I + 1 is the new numerator, “ the acid former," signifies a gas which entered into all the And 2 (x + 1) the denominator. acids, the composition of which had been determined in the 1 era of Lavoisier, of which acids it was said to be the acidifying Whence principle. Not the slightest idea appears to have been enter 2(x + 1) +3 3) iained by Lavoisier that hereafter acids might come to light Again, as Or, 3x = 2x + 5, removing fractions, &c. in whose composition oxygen did not even enter. Therefore x = regards combustion, the gas chlorine was known to Lavoisier And 2(x + 1) = 12; Consequently is the fraction. (53.) Let x be the greater number. Whence 23 – 7 = 33, per question, Or, 2x = 40; Therefore x = 20, And x--7= 13. (54.) Let x be the greater number of voters. Then x - - 91 is the less number of ditto, who introduce new terms should ever remember. The precept Whence 2x - 91 = 375, per question. of naming things in reference to some evident property, not Or, 2x = 466 ; some theoretical one. Thus the term chlorine, expressive as Therefore x = 233, it is of a yellowish-green colour, is totally independent of any And a 91 = 142, And 5x = 120 ; Compounds of Chlorine with other Bodies.-Although the pre- Therefore x = 24. Then x x x = x, per question. Whence ? = , Or, tex = 1, by reduction and dission by x; Therefore x = 16. Then 99 - x is the time to come, Whence śr= }(99 — x), per question. Whence 22x 1188; Therefore 2 = 64. Or, 21% = 3.x + 7x + 7x + 84, (60.) Let u be the number required. Then x x ft x şx = 4x x x, per question, information has taught him how to recognise chlorine when And * = *x?, br multiplication, free or uncombined ; taught him by the following signs. Whence 4.x = 27z2, by clearing of fractions, (2) Free chlorine alone is that which dissolves gold leaf and Or, 4x = 27, by dividing by **. bleaches, although chlorine, in any soluble condition, yields Therefore x = 6. with soluble silver salts the chloride of that metal, Note.- Dele the word hours in the answer. As the one travels it miles per huur, We have life +"="56, per"question, Or, 6x + 5x = 616, Whence 11% = 616; Therefore x = 56. (62.) Let x be the number of days required. As the wife drinks 1 th per day, 30 1 -th And both drink 1 1 1 + per question. The man 36 ; We have Or, 5x = 60 + 2x, by clearing of fractions, Therefore x = 20. Then x + x + 3x + 7) = 500, per question. Therefore 2 = 197. 1 Then, as one man can do Tóth of the work per day, 3.0 ; Whence 30x 20x = 600, per question. 30.x = 1800, Then 2x is what was taken from A. 48 -- * what B had left. And 2.x = 88. Then 256 + 1x is B's share, 256 + x = 412, And 398 + 4x = 476. Then (2 x 7) - x= 14 - x is the price of the second. x = 2, 1 Then is the part filled by the first pipe in an hour 11 1 1 10 15 Therefore x = 6. 1 1 1 Then, as before, per question. 20 Or, 3.2 3x = 60, And 2x = 60, Therefore a = 30. (66.) Let x be the number of minutes required. 1 Then, one aqueduct fills th of the cistern per minute, 30 1 1 1 per question. Thurefore x = 120. Then 39 - x is the number of pence. *3. Then 4x + 4 is the share of the first child, the second child. Therefore 1 = 120. Then 3:4::X: $i; starting. 8x + 100, 3 Therefure x = 300. Then 30x is the distance travelled by A. 11 Therefore x = 5. 2 Then is the part remaining of each gallon, Whence x = 20. Then 11x is the space travelled by A. Therefore * = 804. Then is the number of gallons of water at first. m 12 mn 3 , per question, 2000 -- 50% t + 12b * to a Whence 75x + 17 =2000, per question Or, 38 Or, 2850x + 17 (2000) — 850x = 38 (2000); And 2000x = 21 (2000), Therefore x = 21, 2000 - 50 x = 25, 38 (86.) Let x be the number of days required. - x for the distance travelled on the last (78.) Let x be the denominator. day by the one, Then (a + 1) is the numerator. And (30 + 31 — x) x the whole distance travelled by 1(x+1)+1 the same one. Also, 20x is the whole distance travelled by the other, Whence 20x = }(61 — X)x, per question. Or, 20 = (61 – x), And 40 = 61 – x; Therefore x = 21, (87.) Let a be the number of lines in a page. And y the number of letters in a line. Then xy is the number of letters in a page. If x + 1 be the number of lines, And + 1 the number of letters, Then (5+1) (y + 1) = xy + xty+1, is the num. ber of letters in a page. Again, if x + 2 be the number of lines, And y + 4 the number of letters, Then (r + 2) (y + 4) = xy + 4x +2y +8 is the rum. (80.) Let x be the money of the one. ber of letters in a page. Then 100 ha is the money of the other, Whence xy ++y1=ay + 96, per question, And x +y = 95; equation A. Also, ay + 4r + 2y + 8 = xy + 286, per question, And 4x + 2y = 278. Or, 2x + y = 139; equation B. By subtracting equation A from equation B, we have 3 = 44; (81.) [Having explained the nature of this problem very fully And from equation A, we have y = 95 - x=51. (88.) Let x be the money of the one, 2 + 300 Then 4 (}x – 3) is the second. Then 300 = 14 200 is the money of the Whence *x + $(fx – 3) = 10, per question, other. Or, 5x + 16 (1x – 3) = 200, Whence x + 800 = 2(43 — 200 + 800), per question, Or, x + 800 = ji + 1200; And tax = 400; Therefore 2 = 1200, And ta 200 = 200. (89.) Let x be the number of minutes required. 1 1 Then 3 (29 - 12) = 87 – fx is the second, 1 1 Then + + per question. 80 200 300 Whence 153 to 6. + 4x = 1200. And 25x = 1200, Therefore x = 48, (90.) Let x be the sum won by A. Then 42 +- x = 5(24 -- x), per question. Whence 12 + x = 120 - 5.x, And 6x 78, units' digit, (91.) Let & be the capital. Then x + 5(745x) = 8208, per question, Whence x 8208, And 6x = 41040, Therefore x = 6840. (92.) Let & be the capital. 412 = 13167, per question. 100 Whence 100x + 4x = 1316700, (85.) Let x be the value of one kind in shillings. And 200x + 9.4 2633400, Therefore x + 12600. (93.) Let å be the number of cavalry, Then x + 9x to 31 - 2600, per question, 3 Then at Now, Z 8 : 1 Also, ܪ +1 per question. 00 + Therefore x = 200, And 80x 72.c + 90x = 1440; Whence 98.x = 1440, And 49% = 720. Therefore x = 141$; 1 1 1 41 Then 46 -- is the other part, 1431 720 Whence 20:1 1 : 21= 17 il; 1 31 9 ; 720 And 39 = 23.1. In the answer, 133$ is misprinted for 1114. the second began, Then x + 6 is the number of the hind-wheel. 120 Also, is the circumference of the fore-wheel, charges. 120 And the circumference of the hind-wheel. +6 120 120 +4= (96.) Let ä be the ounces of gold in Hiero's crown. Whence, 120 120 +1 Then 100 - x is the ounces of silver in it. 2+-6 = 20 is nearly the specific gravity of gold, 303 30.r+180 Or +1= i 120+2 126+3 100 100 Whence 39rt'80 317120 And 120.c+ 126+3 Whence (126 + x)(31x + 120)=(120 + x)(30x +180), ; And a2 + 246.0=6180. To solve this equation, which is an adfected quadratic, by the Hindoo method, as we have been requested, we first multiply both sides by four times the co-efficient of the first terın (that is, of *"), and we have Then x + 23 is his 7 months' wages, 4x + 984x = 25920; Aridx + 8 his 12 months' wages. we next add to both sides of this equation, the square of the Whence x +8: x + 21 :: 12:7, per question. co-efficient of the second term (that is, of x) in the former Or, 12.x + 32=73 + 56; equation, and we have And 5x = 24, 4.1? +984x + (246)= 86436; Therefore x = = 43, or £4 16s. we now extract the square root of both sides of this equation, (98.) Let u be the weight of the body. and we have Then 9 + 4x is the weight of the head. 2x + 246 = 294; Whence by simple equations, we have Therefore cte=30. Also, = 5 yds, or 15 feet, (99.) Let a be the time A takes alone. And = 4 yds, or 12 feet. We have thus completed the solutions of the whole Cen- Many of have freely availed ourselves, in order to encourage then to particularise the names of all the students who solved every individual problem, otherwise we should have filled a whole number with their names repeated from fifty to 100 times, We give, however, in the following list, the names of those who succeeded in their solutions, and the number of problems which they solved : H. D. Davis, Maida Hill, 100 problems; James Wardle, Dean Mills, Bolton, 94;* James Russell, Chislehurst, Kent, 61; Antodiductos, Knottingley, 60; J. Buchanan, Murray. field, Edinburgh, 50; R. Parkinson, Everton, 50; W. Ward, 35; D. Hornby, Driftield, 31; M. C, Gascoigne, Amersham. road, New Cross, 30; John Pogson, Quick View, Mossley, 30;. A. Sorr, Highgate, 21; W. Kérslake, Carlisle, 25; J. II. Eastwood, Middleton, 24; G. Smith, Manchester, 19; T. Bocock, Great Warley, 16; T. K. B., Stalybridge, 15; J. 1 Johnson, Marske, 13; J. Jenkins, P mbroke Dock, 12 ; J. 10 per question. Redfern, 12; Anna Pringle, Ferry Hill, Duchain, 3; W. Martin, New Swindon, 7; A. Smith, Marske, 7; J. Marchall, • Mr. Wardie solved 18 problems in pp. 329, 330, vol. iv. = 24 30 ! BIT Sandyford, Newcastle, 6; T. Grisdale, Penrith, 6; J. Wilkin The Falling followed by the Rising. son, Guildford, 6; E. Lowe, Cheshire, 4 ; J. Parker, Norfolk, 1. “I would rather gò than stay." 4; J. Verini, Welbeck-street, 4; G. Fox, Bedford, 2; and 2. “ I would rather walk than ride." W. Cotcheifer, West York Militia, 1, the last, which is an 3. “He travelled for health, not pleasure." adfected quadratic. It is proper to remark that some of those 4. “He pronounces correctly, not incorrectly." who solved the fewest, selected the most difficult; and thus 5. “ It is the falling, not the rising inflection.” they showed that they were able to do the rest. The result of these solutions is, on the whole, very gratifying to us, as Examples of Circumflex. many of the students have assured us that they never had any Tone of Mockery. “I've caught you, then, at lâst !" instructions in algebra, but what they received in the P.E. Irony. “ Courageous chief!-the first in flight from pain!" It shows, also, that our national system of education has Punning. " And though heavy to wèigh, as a score of fat been very successful. sheep, He was not, by any means, heavy to sleep.” Example of Monotone. Ave and Horror. “ I could a tāle unföld whose lightest word Would hārrow ūp thy soul, frēeze thy young blood, * INFLECTIOX' in elocution signifies an upward or downward Māke thy two ēyes, like stārs, start from their sphērer, *slide' of voice, from the average, or level, of a sentence. Thy knõtted and combined locks to pârt, There are two simple inflections' or 'slides,'--the upward And each particular hāir to slānd on ēnd, or 'rising,' and the downward or “falling. The foriner is Like quills upon the frētsul pòrcupine," usually marked by the acute accent [']-the latter, by the grave accent (). Rules on the Rising Inflection. The union of these two inflections, on the same syllable, is RULE I. The intensive' or high rising inflection, expresses called the circumflex,' or wave. When the circumflex com. mences with the falling inflection, and ends with the rising, it surprise and wonder.. Example. — * Há! laugh’st thou, Lochiel, is called the 'rising circumflex, —-{marked thus']; when it my vision to scórn?”. begiris with the rising, and ends with the falling, it is called Rule II. The moderate rising inflection takes place where the falling circumflex,'-(marked thus ^]. the sense is incomplete, and depends on something which fol. When the tone of the voice has no upward or downward lows. Example.-* As we cannot discern the shadow moving slide, but keeps comparatively level, it is called the 'mono- along the dial-plate, so we cannot always trace our progress tone,'--marked thus -). in knowledge. Examples. Rising in flection :--Intensive,' or high, upward Note. Words and phrases of address, as they are merely slide, as in the tone of surprise, “ Ha! Is it possible !" In introductory expressions, take the moderate rising inflection. 2. “Sír, I the usual tone of a question that may be answered by Yes or Example 1. -"Friends, I come not here to talk." No, " Is it really so " Moderate' rising inflection, as at the deny that the assertion is correct." 3. “Soldiers, you fight end of a clause which leaves the sense dependent on what for home and liberty !” follows it. “If we are sincerely desirous of advancing in Exception.-In emphatic and in lengthened phrases of address knowledge, we shall not be sparing of exertion.” “Slight' the falling inflection takes place. Example 1.-"Ön! ye rising inflection, as when the voice is suddenly and unex- bràve, who rush to glory or the grave !” 2. • Soldiers ! if my pectedly interrupted: "When the visitor entered the room_" standard falls, look for the plume upon your king's helmet!". 3. “My friends, my followers, and my children! the field we The last mentioned inflection may, for distinction's sake, be have entered, is one from which there is no retreat." 4. "Genmarked as above, to indicate the absence of any positive up- tlemen and knights--commoners and soldiers, Edward the ward or downward slide, and, at the saine time, to distinguish Fourth upon his throne, will not profit by a victory more than it from the intentional and prolonged level of the mono- you." tone.' Rule III. The suspensive,' or slight rising inflection, Falling inflection :— Intensive,' or bold and low downward occurs when expression is suddenly broken off, as in the folslide, as in the tone of anger and scorn: “Down, soothless lowing passage in dialogue. insulter!" Example. - Poet. “The poisoning dame - Friend. You The 'full' falling inflection, as in the cadence at a period : " All his efforts were in vain." P. I don't. F. You do." The moderate' falling inflection, as at the end of a clause Note. This infection, prolonged, is used in the appropriate which forms complete sense : “Do not presume on wealth; it tone of reading verse, or of poetic prose, when not emphatic, may be swept from you in a moment." “ The horses were instead of a distinct rising or falling inflection, which would harnessed; the carriages were driven up to the door ; the have the ordinary effect of prosaic uiterarice, or would divest party were stated : and, in a few moments, the mansion was the expression of all its beauty, left to its former silence and solitude." The suspensive,' or slight falling inflection, as in the mem. Examples. bers of a series,' or sequence of words and clauses, in the 1. “Here waters, woods, and winds in concert join." same syntactical connexion : "The force, the size, the weight 2. “And flocks, woods, streams around, repose and peace of the ship, bore the schooner down below the waves." impart." irresistible force, the vast size, the prodigious weight of the 3. “The wild brook babbling down the mountain's side ; ship, rendered the destruction of the schooner inevitable." The lowing herd; the sheepfold's simple bell; 'Ile suspensive' downward slide is marked as above to disti: guish it from the deeper inflection at the end of a clause, The pipe of early shepherd, dim descried or of a sentence. In the lone valley ; echoing far and wide, The clamorous horn, along the cliffs above; The hollow murmur of the ocean tide; The hum of bees, the linnet's lay of love, 1. “Will you gó, or stay?” And the full choir that wakes the universal grove." 2. Will you ride, or walk?" 4. "White houses peep through the trees; cattle stand 3. “ Did he wavel for health, or for pleasure." 4. “Dues he pronounce corréctly, or incorrectly;" cooling in the pool; the casement of the farm-house is covered 6,"Is it the nsing, or the failing infection;" • Shouting tone. mean "The |