ر ر ܐ 7. De quelle manière égayaient- 12. Quelle question l'ainé fit-il' COLLOQUIAL EXERCISE. à son père ? 8. Quel était le caractère de 13 Le père lui répondit-il sur 1. Pourquoi l'Empereur de- | 11. De quelle manière l'enfant l'aîné? le champ ? vait-il traverser la galerie? répondait-elle à cette fx9. Le cadet ressemblait-il à | 14. De quoi le cadet était-il 2. Comment était cette galerie? Veur? quoi l'aîné? joyeux ? 3. Sturquoi les fenêtres avaient. 12. De quel côté se tournaient 10. Que faisait l'aîné, un soir à 15. Que dit-il ? elles rue? les de l'enfant ? côté de son père ? 16. Que fit alors l'aîné? 4. Que vit-on lorsque neuf 13. Combion de temps les deux 11. De quoi le cadet s'occupait. 17. Quelle fut enfin la réponse heures furent sonnées ? femmes attendirent-elles ? il alors? du père ? 5. Que remarquait-on parmi 14. Qu'attendait la jeune fille ? tout ce monde ? 15. Que faisait alors l'autre? NOTES AND REFERENCES.Q. Coulaient, spent-b. from vivre; 6. Par quoi se faisait remarquer 16. Entendait-on du bruit dans I. partii., p. 110.--c. L. part ii., § 49. R. (1).-d. from recueillir; la première ? la galerie ? L. part ii., p. 102.-e leurs tisons, their fire; literally, fire 7. A quoi pouvait-on distinguer 17. Qu'arriva-t-il à onze heures? brands.f. The ils is here a poetical license; the pronoun should la seconde ? 18. Qu'annonça l'huissier ? be elles, as it relates to vertu and sagesse, which are feminine.-9. 8 De quelle couleur étaient 19. Comment Hortense désig. né, by nature; literally, born ; from naître; L. part ü., p. 96. ses cheveur ? na-t-elle l’Empereur ? h. from lire; L. part ii., p. 94.ż. from rire; L. part ü., p. 104. 9. Que disait la première à la 20. Que fit alors la jeune fille ? j. se plaisait, delighted , L. S. 39, R. 6.-k, soigneux, desirous. plus jeune ? l. faits , deeds.—m. il n'en respirait pas, he hardly ventured to 10. Que faisait-elle pour donner 21. Que fit-elle en s'écriant, breathe... from interrompre; L. part ii., p. 94.-0. from pou plus de poids à ses paroles ? grâce! grâce ? voir ; L. part ii., p. 100.--p. L. S. 39, R. 4-q. from détruire, NOTES AND REFERENCES.—a. devait, was; from devoir; L. I. part ii., p. 88.-Y. from faire ; L. S. 63, R. 2. S. 34, R. 5.-6. ayant vue, looking towards.-C. L. S. 25, R. 2.- ii., p. 76.-9. allons, du courage! come, cheer up !—h. from dire; MLLE DE LAJOLAIS. L. part ii., p. 88.-i. see note a, also L. S. 56, R. 1.-aj. L. S. 9, SECTION I. R. 7.-K. from paraître; L. part ii., p. 98.--. tenant, keeping; from tenir; L. part ii., p. 108.-M. see note k.-12. from avoir ; LA galerie que devait a traverser l'Empereur, pour se L. S.73, R. 4.-0. from voir ; L. part ü., p. 110.--p. from sortir; rendre au conseil, était une vaste pièce longue, éclairée par L. paxt ii., p. 106. q. from joindre ; L. part ü., p. 94. des croisées parallèles, les unes ayant vue sur la cour d'entrée, les autres sur les jardins.3 Neuf heures venaient dec sonner et peu à peu les deux côtés de cette galerie se remplirent deu monde, de curieux, de solliciteurs, des offi LESSONS IN ALGEBRA.–No. XII. ciers de service, des gens e de la maison. Parmi tout ce monde deux femmes se faisaient remarquer, la première (Continued from p. 330.) par sa beauté, et l'air grácieux avec lequel elle accueillait PROBLEMS IN SIMPLE EQUATIONS. les saluts respectueux de tous ceux qui passaient près d'elle; 6 et la seconde par son extrême jeunesse, par la 1. What two numbers are those whose difference is 10; and pâleur qui donnait à sa beauté un caractère extraordinaire, if 15 be added to their sum, the amount will be 43. Ans. et par ses beaux cheveux blondss tombant en boucles nom- 9 and 19. breuses sur ses épaules. 2. There are two numbers whose difference is 14; and if 9 -Allons, du courage! disaith la première à la seconde, times the less be subtracted from 6 times the greater, the du courage! remainder will be 33. What are the numbers. Ans. 17 and 31. --Je ne vous quitterai pas, disait encore la première. Puispour à 3. What number is that to which if 20 be added, and from chercher la main de la jeune fille et la serrait avec amitié. 10 of this sum 12 be subtracted, the remainder will be 10? Ans. 13. Le regard le plus expressif et le plus triste répondait à 4. A and B lay out equal sums of money in trade; A gains cette faveur ; 11 et incontinent les beaux yeux de l'enfant se £120, and B loses £80; and now A's money is triple that of B. retournaient vers la portela par laquelle devaiti paraître What sum had each at first? Ans. £180. l'Empereur. Toute cette âme jeune, aimante, exaltée, sem- 5. What number is that, of which exceeds by 72? Ans. blait avoir passé dans ses yeux;j tout le reste de son corps 864. paraissait k inanimé. 6. There are two numbers whose sum is 37; and if 3 times Deux heures se passèrent ainsi ;13 deux heures d'attente, the less be subtracted from 4 times the greater, and the rede peines, d'angoisses, et, pendant ces deux heures, ni l'une mainder be divided by 6, the quotient will be 6. What are ni l'autre de ces enfants n'avait bougé. the numbers? Ans. 21 and 16. La plus jeune, tenant? les yeux attachés sur cette porte if i3 be addeil, the amount will be 17; but if from half the 7. A man has two children, to of the sum of whose ages fermée, attendait qu'elle s'ouvrît pour respirer,l4 pour vivre; difference of their ages 1 be subtracted, the remainder will be l'autre ne détournait pas les yeux de dessus sa compagne.16 2. What is the age of each? Ans. 9 and 3 years. Le plus profond silence régnait dans cette galerie ; on n'en- ** 8. A messenger being sent on business, goes at the rate of tendait que la respiration plus ou moins agitée de tout ce 6 miles an hour; 8 hours afterwards, another is despatched monde, 16 qui attendait aussi. with countermanding orders, and goes at the rate of 10 miles Enfin onze heures sonnent, les deux battants de la porte an hour. How long will it take the latter to overtake the fors'ouvrent, 17 et un huissier annonce l'Empereur. 18 mer? Ans. 12 hours. Plusieurs personnes paraissentm à la fois. 9. 'To find two numbers in the proportion of 2 to 3 whose Lequel ? demande Maria aans la plus vive anxiété. product shall be 54. Ans. 6 and 9, Le seul qui ait" son chapeau sur la tête,lo lui répond day he worked, but for every day he was idle he should forfeit 10. A man agreed to give a labourer 12s. a day for every vivement Hortense. After 390 days they settled, and their account was even. La jcune fille n'en écoute pas davantage; ne voyanto How many days did he work? Ans. 156 days: . plus qu'un seul être dans toute cette foule qui l'environnait, 11. Three persons, A, B, and C draw prizes in a lottery. A elle sorte des rangs, s'élance aux pieds de celui qu'on lui a draws £200, B draws as much as A, together with a third of désigné,20 s'écrie : grâce! gràce! et joint, les mains avec what C draws; and C draws as much as A and B both. What force en les levant vers le ciel. 21 is the amount of the three prizes? Ans, £1,200. 8s. ears. 12. What number is that which is to 12 increased by three been despatchedd 5 days, when a second was sent after him, times the number, as 2 to 9? Ans. 8. travelling 75 miles a day. In what time will the one overtake 13. A ship and a boat are descending a river at the same the other? Ans. 20 days. time. The ship passes a certain fort, when the boat is 13 miles 35. The age of A is double that of B, the age of B triple helow. The ship descends 5 miles, while the boat descends that of C, and the sum of all their ages 140. What is the age 3. At what distance below the fort will they be together? of each ? ans. A 84, B 42, and C 14. Ans, 32, miles. 36. Two pieces of cloth, at the same price by the yard, but 14. What nuinber is that, a sixth part of which exceeds an of different lengths, were bought, the one for £5, the other for eighth part of it by 20? Ans. 480. £6). If 10 yards be added to the length of each, the sums 15. Divide a prize of £2,000 into two such parts that one of will be as 5 to 6. Required the length of each piece. Ans. then shall be to the other as 9 to 7. Ans. £1,125 and £875. 20 yards and 26 yards. 16. What sum of money is that, whose third part, fourth 37. A and B began trade with equal sums of money. The Gart, and fifth part, added together, amount to £94 ? Ans. fizet year A gained £40, and B lost £40. The second year A £120. lost of what he had at the end of the first, and B gained £40 17. Two travellers, A and B, 360 miles apart, travel towards less than twice the sum which A had lost. B had then twice each other till they meet. A's progress is 10 miles an hour, as much money as A. What sum did each begin with. Ans. and B's 8. How far does each travel before they meet? Ans. £220. A 200 miles and B 160 miles. 18. A man spent one-third of his life in England, one-fourth and 52, will make the former sum to the latter as 3 to 4? 38. What number is that, which being severally added to 36 of it in Scotland, and the remainder of it, which was 20 years, ans. 12. in the United States. To what age did he live: Ans. 48 39. A gentleman bought a chaise, horse, and harness for £360. The horse cost twice as much as the harness, and the 19. What number is that, of which is greater than of it chaise cost twice as much as the harness and horse together. by 96 ? Ans. 1,920. What was the price of eaeh? Ans. Chaise £240, horse £80, 20. A post is } in the earth, in the water, and 13 feet harness £40. above the water, What is the length of the post? Aas. 35. 40. Out of a cask of wine, from which had leaked } part, 21 21. What number is that, to which 10 being added, % of the gallons were afterwards drawn; when the cask was found to sum will be 66. Ans. 91. be half full, How much did it hold? Ans. 126 gallons. 22. Of the trees in an orchard, i are apple-trees, to pear, trees, and the remainder peach-trees, which are 20 more than 41. A man has 6 sons, each of whom is 4 years older than of the whole. What is the whole number of trees in the his next younger brother; and the eldest is three times as old orchard? Ans. 800 trees. as the youngest. What is the age of each! Ans. 10, 14, 18, 23. A gentleman bought several gallons of wine for £94; 22, 26, and 30. 42. Divide the number 49 into two such parts, that the ( and after using 7 gallons himself, sold of the remainder for £20. How many gallons had he at first ? Ans. 47. greater increased by 6, shall be to the less diminished by 11, as 24. A and B have the same income. A contracts an annual 9 to 2. Ans, 30 and 19. -debt amounting to of it; B lives upon of it; at the end of 4 be added, the sums will be as 5 to 7? Ans. 16 and 24. 43. What two numbers are as 2 to 3; to each of which, if ten years B lends to A enough to pay off his debts, and has £160 to spare. What is the income of each! Ang. £280. 44. A person bought two casks of porter, one of which held 25. A gentleman lived single of his whole life; and after just 3 times as much as the other; from each of these he drew 4 gallons, and then found that there were 4 times as inany having been married 5 years more than of his life, he had a son who died 4 years before him, and who reached only half gallons remaining in the larger as in the other. How many the age of his father. To what age did the father live? 'Ans. gallons were there in each ? Ans. 36 and 12. 84 years. 45. Divide the number 68 into two such parts, that the dif26. What number is that, of which if }, }, and be added ference between the greater and 84 shall be equal to 3 times together, the sum will be 73? Ans. 84. the difference between the less and 40. Ans. 42 and 26. 27. A person after spending £100 more than of his income, 46. Four places are situated in the order of the letters A, B, had remaining £35 more than 1 of it. Required his income. C, D. The distance from A to D is 34 miles. The distance Ans. £450, from A to B is to the distance from C to Das 2 to 3. And 1 28. In the composition of a quantity of gunpowder, the nitre of the distance from A to B, added to half the distance from was 10 lbs. more than of the whole, the suiphur 41 lbs. less to D, is three times the distance from B to C. What are the than of the whole, the charcoal 2 lbs. less than of the nitre. respective distances ? Ans. 12, 4, and 18 miles. What was the amount of gunpowder? Ans. 147 lbs. 47. Divide the number 36 into 3 such parts, that of the 29. A cask which held 146 gallons, was filled with a mix-first, of the second, and of the third, shall be equal to each ture of brandy, wine, and water. There were 15 gallons of other. Ans. 8, 12, and 16. wine more than of brandy, and as much water as the brandy 48. A merchant supported himself 3 years for £50 a year, and wine together. What quantity was there of eachAns. and at the end of each year added to that part of his stock 29 gals, brandy, 44 gals. wine, and 73 gals. vater. which was not thus expended, a sum equal to one-third of this 30. Pour persons purchased a farm in company for $4,755; part. At the end of the third year his original stock was of which В paid three times as much as A; C paid as much as doubled. What that stock? Ans. £740. A and B; and D paid as much as C and B. What did each 49. A general having lost a battle, found that he had only pay? Ans. A £317, B $951, C $1,268, and D $2,219. half of his army+3,600 men left fit for action; } of the army 31. It is required to divide the number 99 into five such +600 men being wounded; and the rest, who were of the parts that the first may exceed the second by 3, be less than whole, either slain, taken prisoners, or missing. Of how many the third by 10, greater than the fourth by 9, and less than the men did his army consist. Ans. 24,000 men. fifth by 16. Ans. 17, 14, 27, 8, and 33. 50. To find a number to the sum of whose digits if 7 be 32. A father divided a small sum among four sons: the added, the result will be 3 times the left hand digit; and if third had 9 shillings more than the fourth, the second had 12 from the pumber itself 18 be taken, the digits will be inverted. shillings more than the third, the first had 18 shillings more Ans. 53. than the second, and the whole sum was 6 shillings more than 51. To find a number consisting of two digits, the sum of 7 times the sum which the youngest received. What was the which is 5; and if 9 be added to the number itself, the digits sum divided ? Ans. 153 shillings. will be inverted. Ans. 23. 33. A farmer had two flocks of sheep, each containing the 52. There is a certain fraction such, that if you add 1 to its same number. Having sold from one of these 39, and from numerator it becomes }; but if you add 3 to its denominator, the other 93, he finds twice as many remaining in the one as in it becomes 3. Required the fraction. Ans. i. the other. How many did each flock originally contain? Ans. 53. It is required to find two numbers whose difference is 7, 147 sheep. and their sum 33. Ans. 20 and 13. 34. An express travelling at the rate of 60 miles a day had 54. At a town meeting, 375 votes were cast, and the person A was nb a Ans. Y n m12 a= elected to office had a majority of 91. How many votes had by his bargain. What did he give per gallon for his wine? each candidate ? Ans. 233 and 142. . Ans. 20s. 55. A post stands in the ground, in the water, and 10 76. A and B start at the same time and in the same direcfeet above the water. What is the whole length of it? Ans. tion, but directly opposite each other, to go round a circular 24 feet. pond 536 yards in circumference; A goes 11 yards a minute, 56. A young man the first day after his arrival in London, and B 34 in 3 minutes. In how long time will B overtake A spent of his money, the second day }, the third day ), and Ans. 804 minutes. he then had only 26 pence left. How much did he have at 77. A cask contains a certain number of gallons of rum, and first? Ans. 10 shillings. an mth part of that quantity of water: but, if a gallons of rum 57. A person being asked his age, answered that of his and b of water be added to the mixture, the water in the whole age multiplied by 1 of his age, would give a product equal to compound will be an nth part of the rum. Required the his age. How many years old was he? Ans. 16 years. quantity of each contained in the cask at first. Examine also 58. A man leased a house for 99 years; and being asked and explain the case, in which, m being equal to n, a is equal how much of the time had expired, replied that two-thirds of to nb, and the one in which it is not equal to it; and also the the time past was equal to four-fifths of the time to come. case in which x and y come out negative, x denoting the original How many years had expired? Ans. 54 years. number of gallons of the rum, and y those of the water, ri 59. On commencing the study of his profession, a man found m(nb--a) that of his life had been spent before he learned his letters, , and <= When msn, and at a public school, } at an academy, and 4 years at college. How old was he? Ans. 21. Enb, the question is indeterminate : when man, and 60. It is required to find a number such, that whether it a greater or less than nb, the values of x and y are infibe divided into two equal parts, or three equal parts, the pro- nite, and the question absurd. When u and y are duct of its parts will be equal. Ans. 6 hours. negative, the question will be changed into one in which 61. Two persons, 154 miles apart, set out at the same time the quantity of rum is diminished by a gallons, and that to meet each other, one travelling at the rate of 3 miles in 2 of the water by b gallons. hours, the other 5 miles in 4. How long will it be before they 78. Find a fraction, such that if its denominator be increased meet? Ans. 56 hours. 62. A man and his wife usually drank a cask of beer in 12 by 1, the value becomes }; while if the numerator be increased days, but when the man was absent, it lasted the wife 30 days. by 1, the value is . Ans. So. How long would it last the man, if his wife were absent? Ans. denominator be each increased by 1, the value is changed into 79. Required a fraction, such that if the numerator and 20 days. 63. A shepherd being asked how many sheep he had, replied, ; but, if they be each diminished by 1, the value becomes 3. Ans.. if he had as many more, half as many more, and 77 sheep, he would then have 500. How many had he? Ans. 197. 80. One person says to another : “If you give me half your 64. A farmer hired two men to do a job of work for him; "I shall have a hundred pounds, if you give me a third of your money, I shall have a hundred pounds." The other replies: one could do the work in 10 days, the other in 15. How long money.” How much had each? Ans. £60 and £80. would it take both together to do the same job? Ans. 6 81. At what time between 10h and 11h o'clock, are the hour days. 65. A and B together can build a boat in 20 days; with the and minute hands of a common clock exactly together? Ans. assistance of C, they can do it in 12 days. How long would At 514 minutes before 11 o'clock. 82. Find two numbers, such that one-third of the first. it take C to build the boat? Ans. 30 days. 66. There is a cistern with two aqueducts; one will fill it in the first and one-fifth of the second are together equal to 10. exceeds one-fourth of the second by 3, and that one-fourth of 30 minutes, the other will empty it in 40. How long will it Ans. 24 and 20. take to fill it, if both run together? Ans. 120 minutes. 67. Required to divide 1 shilling into pence and farthings the first and one-third of the second may be 29, and that one 83. Required two numbers, such that the sum of one-half of in such a proportion that there may be 39 pieces. Ans. 36 farthings and 3 pence. third of the first and one-fourth of the second may amount to 68. A man divided a small sum of money among his children 21. Ans, 18 and 60. in the following manner, viz. to the first he gave of the whole 84. A number expressed by three digits, whose sum is 22, is +4 pence, to the second of the remainder +8 pence, to the less by 297 than the number expressed by the same digits in a third • of the remainder + 12 pence, and so on, giving to all reversed order, and its first digit is less by one than its second. an equal sum till he had distributed the whole. Required the What is the number: Ans. 679. number of shares and the sum distributed. Ans. 5 shares and 85. A bill of £100 may be paid by 50 bank notes of one value each, and by 38 of another; or it may be paid by means of 75 69. A hare has 50 leaps the start of a hound, and takes 4 leaps of the former kind, and 17 of the latter. What are the values while the hound takes 3; but 2 leaps of the hound are equal of the notes ? Ans. Those of the first kind 21 shillings each, to 3 of the hare. How many leaps will the hound take in and those of the second 25 shillings. catching the hare? Ans. 300. 86. Two persons set out from a certain place on the same 70. A and B start at the same time and place to go round an day, and proceed in the same direction, the one travelling 30 island 600 miles in circumference. A goes 30 miles a day, miles the first day, and going each day a mile less than he did and B 20. How long before they will both be at the starting on the preceding; while the other travels at the constant rate point together, and how far will each have travelled. Ans. 60 of 20 miles a day. When will they next be together: Ans. days; and 1,800 and 1,200 miles. At the end of 21 days. 71. A has £100, B £48. A robber takes twice as much 87. How many lines are contained in a page of a book, and from A as from B. A now has 3 times as much as B. What how many letters at an average in each line of that page, if it was taken from each! Ans. £44 from B. be found that by adding one line to each page, and making 72. It is required to divide £1,200 between A, B, and C; Beach line contain an additional letter, the page will be increased has £256 +3 of A's share; C has £270 + 1 of B's. What by 96 letters; while, by adding two lines to the original page, was the share of each ? Ans. A $312, B £412, and C £476. and making each line contain four additional letters, the num 73. There are 3 pieces of cloth of different value. The ber of letters will be increased by 286? Ans. 44 lines, each average price of the first and second is 79. per yard, that of the containing 51 letters. second and third is 9s., and the average price of all is- of the 88. Two persons get each a legacy of £300, and one of them third. What are the several prices ? Ans. 125., 2s., and 16s. is then found to be worth three times as much as the other; 74. A pipe will fill a cistern in 11 hours. After running but had the legacy to each been £800, the one would have 5 hours another is opened, and then the two fill it in 2 hours. been worth only twice as much as the other. How much had In what time would the last fill it? Ans. 51 hours. each originally Ans. £1200 and £200. 75. A man bought a cask of wine, and } of it leaking out, 89. A cistern can be filled by three pipes; by the first in 80 he sold the rest at 258. per gallon, and neither gained nor lost I minutes, by the second in 200 minutes, and by the third in 360 120 pence. minutes. In what time will the cistern be filled when all three with the illustrious Lord Palmerston at the head of the inquiry, pipes are cpen at once? Ans. In 48 ininutes. are anxiously and earnestly engaged with the great question SO. Two gentlemen play at billiards ; A, before he began to of the education of the people in general, with that of the proplay, had £12, and B £24. Each lost and won in turn, when A found he had five times as much as B had remaining. How priety of opening the old Universities to the public generally, much did A win. Ans. £13. without regard to religious creed, and with that of the utility 91. What capital is that which, with five years' interest at 4 of giving a still more liberal constitution to the University of per cent., will amount to £8,208. Ans. £6,840. London. This is therefore the nick of time for our students 92. A capital was put out for one year at 41 per cent. per to come forward in a body by petition and representation, annurn; at the expiration of the year there was received back, as capital and interest, £13,167. What was the amount of the respectfully to urge their claims to be examined as to the learning capital ? Ans. £12,600. which they have most industriously and often painfully 93. A fortress has a garrison of 2,600 men, among whom are acquired, and to be rewarded with those sweet honours which nine times as many foot soldiers anủ three times as many ought to be conferred on them if they succeed. Let us not artillery as cavalry. How many are there in each corps ? Ans. be behind ancient Greece in this respect; but let us be up and 200 cavalry, 680 artillery, and 1,800 foot. 94. Divide the number 46 into two parts, so that when the be doing what we can to rescue the sons of the soil from the 95. From the first of two mortars in a battery 36 shells are circulated in the Minutes of the University of London. "The Popular Educator' Office, the second; the second mortar requiring as much powder for La Belle Sauvage Yard, 3 charges as the first does for 4. It is required to determine Ludgate Hill, London. after how many discharges of the second mortar the quantity 1st February, 1834. of powder consumed by it is equal io the quantity consumed by the first. Ans. 189. "Sir, I have the honour to request that you will have the 96. Suppose the crown of Hiero of Syracuse weighed 100 goodness to lay the accompanying Memorial before the meetounces; suppose thetwo crowns, one gold and the other silver; ing of the Senate of the University of London this day; and weighed the same, 100 ounces each; and supposing what would permit me also to request that a number of letters addressed be very nearly the case, that the gold crown, weighed in water, lost 5 ounces : the silver one lost 9 ounces; and supposing the to me, as Editor of “The Popular Educator,' on the subject of compound or mixed crown lost 6 ounces; it is required to find the Memorial, and nlaced by me in the hands of Mr. Moore, the proportion of gold and silver in the crown of Hiero. Ans. Clerk to the Senate, may also be laid before the meeting as 75 oz. gold, and 25 oz. silver. evidence of the statements set forth in the Memorial. I hope 97. Å footman agreed to serve his master for £8 a year and that at the next meeting I shall be able to submit further evia livery, but was turned away at the end of 7 months, and re: Idence of the same description, and also to add many names to ceived only £2 13s. 4d, and his livery. What was its value: Ans. £4 16s. the prayer of the Memorial, which it was impossible to obtain, 98. A fish was caught whose tail weighed 9lbs.; his head owing to the rapidity with which the Memorial was prepared, weighed as much as his tail and half his body; and his body and to the non-arrival of the members of Parliament and weighed as much as his head and tail ; what is the weight of others in town, who should have been most willing to put the whole fish? Ans. 72lbs. 99. If A and B together can perform a piece of work in eight their names to the document. days, A and C together in nine days, and B and C together in I have the honour to be, ten days, how long will each person take to perform it alone? “Sir, Ans. A, 1314; B, 1731 ; and C, 23.1. “ Your most obedient servant, 100. The forewheel of a carriage makes 6 revolutions more " ROBERT WALLACE." than the hindwheel in going 120 yards; but if the circumference of each wheel be increased by 3 feet, the forewheel makes “R. IV. Rothman, Esq., only 4 revolutions more than the hindwheel; what is the cir- Registrar, fc." cumference of each wheel: Ans, 12 feet and 15 feet. [We have here given our students a centenary of problems to Inclosure.] exercise themselves in Algebra. We hope they will do their best to solve them; we shall be happy to insert their solutions, " To the Right Honourable the Earl of Burlington, with their names attached to them, if they be performed in the LL.D., F.R.S., Chancellor, the Honourable shortest and easiest possible manner, just as we have done John George Shaw Lefevre, Esq., C.B., H.A., with the Exercises in Geometry.] F.R.S., Vice-Chancellor, and the Right Roverend and Bonourable the Senate of the Univer. sity of London: UNIVERSITY OF LONDON.-No. VI. We feel assured that all of our subscribers will be gratified by « The Memorial of the Subscribers, the perusal of the following papers which we have the pleasure “ Sheweth, to lay before them in reference to our efforts on behalf of the “That in consequence of the increasing demand for the difself-educating students and others of the British realms. These fusion of useful knowledge, the extension of the blessings of papers were presented to the Senate of the University of Lon-education, and the equitable distribution of the honours and don, on the 1st of the present month, and read at the meeting rewards of learning, among all classes of the community, it on that day. It will now be necessary, if our self-educating would seem to be both wise and politic, on the part of a liberal students be in real earnest, and we have every reason to believe and paternal Government, to throw open the Royal Road to that very many of them are so, from the letters which we have the valuable and permanent distinctions which the University received, that this movement should be followed up not only of London confers upon its members, to all the aspiring and by an application and petition to the Senate of the University self-taught Students of the British Empire, irrespective of their of London, but by an application and petition also to Govern- various conditions in life, or of the different places and ways in ment itself. We know that Her Majesty's present Government, which they may have acquired their learning. sono: “ With this view, your Memorialists are induced, by the Eignth. That ignorance being the mother of immorality and accustomed suavity, kindness, and liberality for which the vice, and the father of crime and violence, sedition and anarchy, Noblemen and Gentlemen composing the Senate of the Uni- it seems to behove the Senate of the said University, on the versity of London are distinguished, to solicit on behalf of all principles of its free constitution and liberal administration, to such Students, and especially of the self-taught, that you would, employ the mighty lever which it possesses, in raising all classes as a body, apply to Her Majesty's Government for such a to the level of an honourable and useful rank in society, by the renewal and extension of the Royal Charter as will enable you bestowment of its valuable honours and degrees on all who are to confer the honours and degrees of the University upon found duly qualified, irrespective of their original condition. them, without requiring their attendance for a term of years at "And lastly. That the security of Government, the advanceany of the affiliated Colleges or Institutions connected there- ment of religion and morality, the suppression of crime, the with, provided that they be found competent at the period of removal of juvenile delinquency, and the rapid progress of the Annual Examinations of the University, upon the payment humanity towards a peaceful and happy state of civilization, of the necessary fees, and upon their presenting at the same are greatly dependent on the free extension of the blessings of time such certificates of moral character as shall be deemed education to all classes of the community, and on the free adsatisfactory to the members of the Senate, or to the Inspectors mission to the distinction which it confers on its enlightened that may be appointed by that body to decide upon the merit possessors, in whatever manner it may have been acquired; and validity of such certificates, and for the following rea- and that though there be no Royal Road to Learning, yet there may be a generous, noble, and illustrious road to its honours “ First. That it appears from the present Royal Charter and thrown open to the Learned by Royal Favour; a consummafrom the Laws and Regulations of the University, that no tion which your Memorialists earnestly wish, and respectfully student, however well qualified he may be, is permitted to come press upon your attention. forward to the Annual Examinations for degrees, unless he has attended a certain number of academical years at one of “ROBERT WALLACE, A, M, Glasguensis, formerly First Professor of Mathematics in the Adthe affiliated Colleges or Institutions connected with the University. dersonian University, Glasgow, and Pro“Second. That by the said Charter, Laws, and Regulations, fessor of Mathematics and Physics in Homerton and Stepney Colleges. numerous self-taught and other students in the British Empire are excluded from the attainment of those honours and the M.D. HILL, Q.C., Recorder of Birmingham. possession of these degrees, to which their perseverance in the EDWIN HILL, Inland Revenue Office. acquisition of literary and scientific knowledge would justly S. MORLEY, Wood Street, entitle them. ROWLAND HILL, General Post Office. “ Third. That the University of London, by its metropolitan WILLIAM ELLIS, Champion Hill. JOHN MORLEY, Wood Street, position, its free and liberal constitution, its high and impartial standing, and the well-known ability of its Examiners, is better Thomas Muir, formerly one of the Magistrates of the City of Glasgow. qualified than any other Academical Body in the Kingdom, to extend and consolidate the advantages of a literary and scien FREDERIO HILL, Late Inspector of Prisons for Scotland, tific education among the masses of the people. “ Fourth. That there exists among the community at large, ARTHUR HILL, Bruce Castle School, Tottenham. both in the United Kingdom and in the Colonies, a desire for JOHN CASSELL, Ludgate Hill." the acquisition of that honour which arises from the possession In order to assist our stu ents in following up the preceding of real knowledge, to the exclusion of that surreptitious honour efforts on their behalf, we propose that the following short which is conferred by the purchase of titles and degrees to which the possessor has no claim on the score of literary and petition to the Senate of the University of London should have as many of the names as possible of our Subscribers, readers, scientific merit. Fifth. That the middling and lower classes of the people should be forwarded by us immediately to that learned body for and others whom it may concern, appended to it, and that it aspire to the attainment of such honours and degrees as the its serious consideration. We shall be glad to receive these names University of London can confer, from a sincere conviction that these are truly valuable and praiseworthy, and constitute by post as soon as possible, so that no time may be lost, while the subject is fresh in the minds of the members of the Senate, an enviable distinction among men. and while the questions connected with it are just on the point « Sixth. That the conviction just mentioned is one of the of being brought before Parliament. brightest and most hopeful signs of a great change for the better among those classes of the community; that it is fraught To the Right Honourable the Earl of Burlington, with the seeds of such an amelioration in the condition of the LL.D., F.R.S., Chancellor, the Honourable human race as ought not to be overlooked by a wise and intel John George Shaw Lefevre, Esq., C.B., M.A., ligent Government; and that it is, in truth, the harbinger of F.RS., Vice-Chancellor, and the Right Rovethe accomplishment of that ancient prophecy referred to by rend and Honourable the Senate of the UniverLord Bacon in the motto to his • Instauratio Magna,' namely, sity of London : • Multi pertransibunt, et scientia augebitur.' “ Seventh. That the enlightened improvement of the Postage The Petition of the Subscribers, system having mightily conduced to the diffusion of useful knowledge, this favourable result requires to be fostered and Humbly Sheweth, extended by the free and generous opening of the honours and That, having carefulay perused memorial presented degrees of the University of London to all Her Majesty's sub- by the Editor of the POPULAR EDUCATOB and others, to the jects without let or hindrance, under proper regulations as Senate, on the 1st of February, 1854, in reference to the subbefore mentioned. ject of throwing open the University of London to all self |