merator shows that twice as many of these factors are to be aplied together. Hence the value is not altered. From the preceding article it will be easily seen that a fractonal index may be expressed in decimals. EXAMPLE. Thus a2 = alo, or a0.5; that is, the square root is equal to the fifth power of the tenth root. In many cases, however, the decimal can be only an approxion to the true index. EXAMPLE. Thus a =a0.3 nearly, or a0.33333 more nearly. In this manner the approximation may be carried to any degree of exactness which is required. N.B.-These decimal indices form a very important class of umbers, called logarithms. I What is a3 equal to? : What is z1 equal to ? 1 What is yo equal to ? 4 What is equal to ? EXERCISE 46. Write the 5th root of the 4th power of a. Write the 7th power of the 9th root of d. Express a in decimals. 11 8. Express a in decimals. 9. Express a in decimals. 10. Express a in decimals. 11. Express a in decimals. 12. Express a in decimals. 13. Express as in decimals. 14. Express a in decimals. KKY TO EXERCISES IN LESSONS IN ALGEBRA.-XXVI. 9. ab2(1+b+ a2b*) + 10. 15a3+10bc2. 11. 4(xy-cm). sentatives to Parliament. It is confidently anticipated that the enfranchising of the universities, which places them more on a par with the English and Irish Universities, will have a beneficial effect on the higher education in Scotland. Of the Scottish Universities, that of Edinburgh is first entitled to our consideration, on account of its celebrity in philosophy and medical science. SESSIONS, CLASSES, AND FEES. There are two sessions of the classes in each year-namely, the summer session, which opens in the beginning of May and ends with July; and the winter session, which opens in the There is no beginning of November and ends with April. summer session in the Faculty of Arts; but tutorial classes in Latin, Greek, and Mathematics are opened for students who have attended a winter course on these subjects. In the Faculty of Arts, or Literature and Philosophy, the classes include Latin or Humanity (3), Greek (2), Mathematics (3), Logic and Metaphysics, Moral Philosophy, Natural Philosophy, Rhetoric and English Literature, Practical Astronomy, Agriculture, Theory of Music, Sanscrit, and Engineering In the classes of Agriculture, Sanscrit, and Engineering, the fee is £4 4s., and in all the other classes named £3 3s. There are eight classes in the Faculty of Theology, comprising Divinity (2), Church History, Biblical Criticism, Hebrew (2), and Hindostani (2). The fee in each class is £2 2s. In the Faculty of Law the classes are Civil Law, Law of Scotland, Medical Jurisprudence, Public Law, Conveyancing, Constitutional Law and History. The fee in Civil Law and Law of Scotland Classes is £5 5s., including the summer session, and in the other classes £3 3s. and £4 4s. In the Faculty of Medicine the classes comprise Materia 9. a23(1 − a3¿3) + x23 Physic, and General Pathology. 10. x(a-b)3. 11. (x+y). 19. a1-y*. 20. as-y3. 21. as-a2. 22. 6a2(x2-13)7. 23. (a2+b3)3. 21. 19(a-b1). 25. x+2x3y + 2x2y2 + The four Universities of Scotland-Edinburgh, St. Andrews, is £3 3s., in Anatomical Demonstrations £2 2s., and in all the other classes of the Faculty £4 48. Annual tickets of £5 5s., and half-yearly tickets of £3 3s., give admission to the demonstrations in the Royal Infirmary. The matriculation or entrance fees are £1 for the academical year, and 10s. for the short summer sessions. The ordinary curriculum in the Faculty of Arts, with a view to a degree, extends over four winter sessions; but students who pass an entrance examination in Latin, Greek, and Mathematics, showing that they are qualified to be admitted at once to the higher classes, may complete the Art curriculum, with a view to graduation, within three winter sessions, and may also dispense with a second session at the Mathematical classes. GRADUATION. By the regulations candidates for the degree of Master of Arts are examined on all the subjects of instruction embraced in the ordinary curriculum of study in the Faculty. The examination on Latin and Greek (1), on Literature, Metaphysics, and Moral Philosophy (2), and on Mathematics and Natural Philosophy (3), may take place at separate periods, although the student has not completed his attendance on the other classes composing the academical course. On completing the pass or ordinary examinations, students may graduate in Arts with honours by offering themselves for a further examination, which is conducted wholly in writing, or partly viva voce. The four departments, any one or more of which they may select, are Classical Literature, Philosophy, Mathematics, and Natural Science. In the first three of these departments there are first and second class honours. ·- 1. DEPARTMENT OF CLASSICAL LITERATURE. Cicero, "Letters to Atticus," i. Passage from a Latin author, not prescribed. General Knowledge of Roman History and Literature till the end of the Augustan Age. likely the draughtsman will deviate a little from the exact position in joining these points, three by three, by the arcs of circles, these arcs of circles or curves, with the straight lines A iv., Fiv., B iv., H iv., C iv. (Fig. 8) will form portions of a circular crown, very inexact to the truth, which will correspond to the sixteen squares into which the larger square, A c (Fig. 8), is divided, so that the mixtilineal bow a corresponds with the square a, the bow b to the square b, c to c, d to d, etc. A figure, such as a portrait, is now carefully drawn on the square AC (Fig. 8): for instance, that part of the portrait delineated in the little square a is copied into the arc or curved space, a (Fig. 8), and elongated or contracted according to the taste of the draughtsman, and so on with all the other portions of the square, A c (Fig. 8), which are transferred according to the lettering-namely, the little square marked b to the arc b, c to c, d to d, and so on with all the little sixteen squares which are gradually drawn in and transposed to the curved spaces or arcs similarly lettered. As may be imagined, an extremely irregular drawing is produced, and it is so perfectly disguised, that the outline of the portrait cannot be discovered. If, however, the distorted drawing is viewed in the cylindrical mirror by the eye placed at o (Fig. 8), and better still when the eye is raised perpendicularly on the point o (Fig. 8), at a height equal to o N (Fig. 9), the distorted picture will then appear in the mirror transformed to the original portrait. To make the change more perfectly, it is advisable to fix a piece of flat wood or brass at the point o (Fig. 8), and look through a small aperture in the same perforated at a height from o (Fig. 8) equal to ON (Fig. 9). In perusing the above description, the reader must remember that two diagrams are referred to namely, Figs. 8 and 9. The above method of bringing a distorted drawing to its proper proportions when reflected in a cylindrical mirror is equally curious and ingenious, and the effect produced will amply repay the labour incurred by any of our readers who may be painstaking enough to construct one for himself on the plan that has been given in sufficient detail for his guidance. LESSONS IN ITALIAN.-XXI. THE PREPOSITIONS SOPRA, SOVRA, SU. THESE prepositions generally denote the relation of two things or persons, one of which is on a higher locality than the other, or one of which surpasses the other with regard to some quality. Só-pra and só-vra commonly govern the accusative case, sometimes, however, the genitive and dative. Su, for the greatest part, has the accusative after it. For example:Só-pra un cár-ro é-gli se-dé-a, he was sitting on a cart. Só-pra la tá-vo-la só-pra la tér-ra, on the table, on the earth or ground. Por la má-no só-pra il pét-to, to lay the hand on one's breast. Mon-tár só-pra ú-na bár-ca, to get into (i.e., to mount on) a boat. Su quel tét-to vo-lá-va un co-lóm-bo, a pigeon flew on that roof. Un cár-ro in su dú-e ró-tè, a cart on two wheels. Só-pra as well as su frequently denote nearness, and are used for vi-cí-no, ap-prês-so, near, close, hard by, on, etc. For example: U'-na cit-tà si-tuá-ta só-pra un fiú-me, sul Ré-no, súl-la ma-ri-na, a town situated on a river, on the Rhine, on the sea-coast. Es-ser pó-sto só-pra il ma-re, to lie on the sea. Pas-sám-mo il Ré-no só-pra Co-ló-nia, we crossed the Rhine near Cologne. They also frequently coincide with the use of the English prepositions towards, about, at, etc., with regard to time. For example: Só-pra sé-ra, towards evening. Sul or in sul méz zo dì, sul ré-spro, sul tra-mon-tár del só-le, towards, about noon, or twelve o'clock, towards evening, at sunset. Pré-sta-re só-pra pé-gni, to lend on securities. Of. For example : Pen-sá-re, di-re, par-lá-re, dis-cór-re-re só-pra quál-che cổ-sa, to think, speak, talk, discourse of something. Into. For example : Qué-sta cá-sa ri-guár-da só-pra la piáz-za, this house looks out into the square. From. For example: Prén-de-re ú-na cit-tà só-pra il ne-mi-co, to take a town from the enemy. More than, above, beyond. For example: L' a-mú-va só-pra la ví-ta sú-a, he loved him more than his own life. Euphony sometimes requires the addition of the letter r to the particle su, especially before a word commencing with a: In sur ú-na piáz-za, on a square. THE PREPOSITIONS FRA, TRA, INFRA, INTRA. These prepositions generally correspond to the English prepositions between, betwixt, and among. For example :Tra il mú-ro ed il fiú-me, between the wall and the river. Fra ti-mó-re e spe-rán-za, between fear and hope. Ná-cque ú-na lí-te in-tra le dú-e dón-ne, there arose a quarrel between the two women. They also very frequently signify within, in the course of, in; as: Tra pó-chi giór-ni, in a few days. Ha pro-més-so di ri-tor-ná-re fra tre giór-ni, he promised to return within three days. In-fra un án-no tút-ti mo-rí-ro-no, all of them died in the course of one year. Before the personal pronouns me, se, etc., fra and tra have a peculiar meaning corresponding to the English prepositions to, with, and are used, as it were, in the places of dén-tro me, dénwithin me, within himself. For example: tro se, Fra se me-dé-si-mo dís-se, he said to himself. 1'-o di-cé-va fra il mí-o cuór, per-chè pa-vền-ti? I said to my heart, why dost thou tremble? Tra me so-ven-te di-cén-do, frequently saying to myself. In some phrases fra and tra merely signify in or at. For example:: Par-lár tra 'l són-no, to talk in one's sleep. So-ven-te fra 'l són-no s' al-zá-va, he frequently rose in his sleep. Tra più vol-te gli pa-gò míl-le scú-di, he paid him a thousand crowns in several instalments. Tra ú-na vól-ta e l' ál-tra, at different times. Tra (and sometimes also fra) is often used adverbially for pár-te, partly. For example :- Tra per má-la con-dót-ta e per im-pen-sá-te scia-gú-re vên-ne a fal-li-re, he became bankrupt partly through bad conduct, partly through unforeseen misfortunes. Co-stan-ti-no re-gnò più di trenť án-ni, tra nell' im-pé-ro di Ró-ma e quil-lo di Co-stan-ti-nó-po-li, Constantine reigned more than thirty years, partly in the empire of Rome, partly in that of Constantinople. Fra sometimes means together. For example: Fra uó-mi-ni e dón-ne só-no 10,000, men and women together 10,000. * Star só-pra di se means, to stand absorbed in thought, or to be in Besides these uses só-pra has other important meanings, as, doubt, to waver, hesitate; fá-re or la-vo-rá-re só-pra di se means, to in addition to. For example: work for one's self-i.e., without being a member of a tradesmen's Só-pra la feb-bre mi è ve-nú-ta la po-dá-gra, in addition to the fever I company, etc.; só-pra di se generally means, at one's own expense, have got the gout. for one's self, etc. 1. Magón-za, eit-tà sul Rê-no. 2. Fran-co-fôr-te, sul Mê-no. 3. Sul fát-to. 4. Vi pro-mêt-to súl-la mí-a fé-de. 5. Su quésta tér-ra. 6. Su quál-che ta-vo-lí-no. 7. Ric-cár-do as-sí-so su d'un sás-so. 8. Vô-glio suo-ná-re un á-ria sul mí-o cla-vicém-ba-lo. 9. Non sa-prê-i ri-spón-der-vi su tal pún-to. 10. I ba-u-li só-no súl-la car-rôz-za. 11. Ha pián-to súl-la di lui disgrá-zia. 12. Non ha di-rít-to ve-rú-no súl-la mí-a ri-co-no-scênza. 13. Ri-po-sá-te-vi súl-la mí-a pa-rô-la. 14. Quél-lo che ha in cuô-re, lo ha sêm-pre súl-le láb-bra. 15. La cá-sa dà súl-la stri-da. 16. Sul far del giór-no (or in sul ná-sce-re del giór-no). 17. Sul far dél-la sé-ra (or in súl-la sé-ra). 18. Súl-la (or in sál-la) mêz-za nôt-te. 19. In sul món-te. 20. I'-o sto fra 'l timó-re e la spe-rán-za. 21. Fra a-mí-ci si può par-lá-re li-be-ramén-te. 22. Frál-lo scô-glio e 'l fiú-me. 23. Il più sfor-tu-náto fra' ge-ni-tó-ri. 24. Dis-côr-dia fra ma-rí-to e mó-glie. 25. Ciò rê-sti fra di noi; sí-a dét-to fra noi. 26. I'-o di-cé-va fra me stés-so. 27. E'-gli ver-rà fra diê-ci giór-ni. 28. Non lo so, ma lo sa-pro bê-ne tra pô-co. 1. A'-mo i mie-i fra-têl-li e le mí-e so-rêl-le. 2. A'-mo án-che i mi-i cu-gi-ni e le mi-e cu-gi-ne. 3. I tuô-i fió-ri só-no bêl-li; i miê-i só-no án-che bêl-li. 4. Qué-sta dôn-na á-ma i suô-i fanculli. 5. Ho rice-vú to dú-e pó-mi e quát-tro pé-re da quésto giar-di-nie-re. 6. Le mí-e ci-riê-ge so-no bel-lís-si-me. 7. Ho dá-to i mie-i pó-mi a tú-o cu-gí-no. 8. Hai tu a-da-cquá-to i tad-i fió-ri? 9. Ho a-da-cquá-to i miê-i ed i tuô-i. 10. Mi-a cu-gi-na ha án-che a-da-cquá-to i suô-i. 11. I tuô-i fra-têl-li hán-no com-pri-to di-o ci-ni che só-no mól-to fe-dé-li. 12. E'. gli-no hán-no dá-to un cá-ne a mí-a cu-gí-na. 13. Le mí-e so rêl-le hán-no ri-ce-vú-to dú-e gát-ti da nô-stro zi-o, él-le-no só-no con-ten-tís-si-me. 14. I nô-stri cu-gí-ni só-no ar-ri-vá-ti. 15. Le no-stre so-rêl-le son par-tí-te qué-sta set-ti-má-na. 16. Mí-o pá-dre e mí-a má-dre só-no trí-sti. 17. Le mí-e cu-gí-ne só-no sem-pro allé-gre. 18. Ab-biá-mo a-da-cquá to i nô-stri fió-ri. 19. A-vé-te voi án-che a-da-cquá-to i miê-i. 20. I tuô-i fra-têlli hán-no ri-ce-vú-to dú-e toc-ca-lá-pis da mí-o cu-gí-no; é-gli-no só-no gli a-mí-ci di mí-o cu-gí-no. 21. Hô com-prá-to tre tocca-lá-pis per i fan-ciúl-li di nô-stro zí-o. 22. Dó-ve só-no le vô-stre so-rêl-le P 23. El-le-no só-no a Mi-lá-no. 24. Edivô. stri fra-têl-li? 25. E-gli-no só-no par-tí-ti per Pa-rí-gi. 26. Nô-stra má-dre ha com-prá-to se-i bic-chiê-ri per le nô-stre cu gí-ne. 27. Tút-ti i miê-i a-mí-ci só-no par-tí-ti. 28. Qué-sta pô-ve-ra dôn-na ha per-dú-to tút-ti i suô-i fan-ciúl-li. 29. Mí-o zí-o ha ven-dú-to tút-te le sú-e cá-se. 30. Tút-ti qué-sti tê-mi só-no fa-cil-lís-si-mi. 31. Ab-biá-mo com-prá-to tút-te qué-ste bot-tí-glie. 32. A'-mo tút-ti gli uô-mi-ni. 33. Luí-gia ha perdú-to tút-te le pén-ne. 34. In tút-te le stán-ze ci só-no quáttro spêc-chj. 35. Tút-to il tê-ma è fá-ci-le. 36. La no-stra cugí-na ha pián-to tút-ta la nôt-te. 37. Dí-o ha creá-to tút-ta la têr-ra. 38. A-vé-te ve-dú-to tút-ti qué-sti prá-ti? 39. Hai tu scrít-to tút-te qué-ste lét-te-re ? 40. I giar-di-niê-re ha man-dá to tút-te qué-ste ci-riê-ge a mí-a so-rêl-la. 41. A-vé-te voi a-dacquá-to tút-ti qué-sti píc-co-li al-be-ri e tút-ti qué-sti bêi* fiori? 42. Tút-te qué-ste cá-se só-no di mí-o zí-o. 43. Mí-o cugí-no è ar-ri-vá-to con tutt' i snô-i a-mí-ci. 44. Mí-a zí-a ha man-dá-to tút-te qué-ste pé-re e tút-ti qué-sti pó-mi a qué-sta pô-ve-ra dôn-na. EXERCISE 30 (COLLOQUIAL). 1. My brothers are very melancholy. 2. Hast thou seen our 3. Our friends are always jolly. 4. glasses and our bottles ? Where are your pocket-handkerchiefs and ours? 5. My (female) cousin has lost our pens and hers. 6. I have given (to) this poor child my pens and thine. 7. My father has sold his dogs and mine. 8. Have you also sold yours? 9. Thy wife has bought ten glasses and four bottles for her daughter. 10. I have given a lead-pencil to thy sister; she has lost hers. 11. I have lost all my pocket-handkerchiefs. 12. All these bottles belong to our uncle. 13. The whole house is beautiful. 14. I love all these beautiful flowers. 15. I think every day (i.e., all days) of Henry and of Charles. 16. Where have you bought 17. I have seen the whole town. 18. All these six glasses? your letters have (i.e., are) arrived. 19. Louisa has (i.e., is) departed with all her (female) friends. 20. Our neighbour has been shedding tears (i.e., has shed tears) the whole week; she has lost all her children. KEY TO EXERCISES IN LESSONS IN ITALIAN.-XX. EXERCISE 25. 2. He seized him by the 4. I speak for your profit. 1. I do it for pleasure, and not as a duty. cloak. 3. I took him for an honest man. 5. He turned red through bashfulness. 6. Out of regard for the 8. He suffers friend. 7. He prevailed on him by means of threats. on his account. 9. Many came to him for advice. 10. He came posthaste. 11. He comes every day. 12. I say so for your good. 13. I, for my part, should be of opinion. 14. Ah! Sir, for mercy's sake do not ruin me. 15. The blood curdles in the veins. 16. They died in the villas, in the fields, by the roads, and in the houses, by day and by 19. He was night. 17. I had well nigh fallen. 18. By his advice. buried for dead. EXERCISE 26. 1. The fathers and mothers. 2. The good fathers and good mothers. 3. The books are good. 4. The pens are good. 5. These trees are high. 6. The houses of this town are very high and very beautiful. 7. This poor man is always contented. 8. Our uncle's daughters are 10. My very contented. 9. Even the poor are often contented. sister's pens are small. 11. Henry's mother loves flowers and children. 12. John's friends have arrived. 13. My sister's friends have set out 15. for Rome. 14. The trees in our garden are still very small. These men are always dissatisfied. 16. This gardener's daughters are still very young. 17. My cousin's exercises are easy, but my brother's exercises are very difficult. 18. Your cousins are rich, but your sisters are very poor. 19. Hast thou seen the trees and flowers in our 20. There is a tree in our garden which is very high. 21. 22. In this room there are In our house there are fourteen rooms. two tables and twelve chairs. 23. Our neighbour has five children, three sons and two daughters. 24. In this garden there are twenty large trees. 25. My uncle has bought four horses. 26. We have seen thirteen pupils in the school. 27. My father has fifteen rings and six garden, * Plural of bel-lo. snuff-boxes. 28. We have a press, seven beds, and nine lookingglasses. 29. There are twelve months in a year, seven days in a week. 30. There are four weeks and two or three days in a month. 31. In our school there are ten forms. 32. Three times four are twelve. 33. Three times three are nine. EXERCISE 27. 1. Gli amici di mio zio sono ricchissimi. 2. Ho spesso veduto questi uomini. 3. I fanciulli della nostra giardinera sono ragionevoli. 4. Abbiamo trovato le sorelle d' Enrico nella chiesa. 5. Questa madre è sempre contenta, ma le nostre vicine sono spesso malcontente. 6. I vostri temi sono difficili ma i temi di Luigi sono molto facili. 7. Avete voi ricevuto questi bei fiori da Giovanni ? 8. Il nostro cugino ha tre tabacchiere. 9. Ho ricevuto da mio zio un temperino è venti penne. 10. L'amica di mia sorella ha cinque cufie. 11. Questa signora ha sette fanciulli, 12. Ho comprato due specchj e sei sedie. 13. Questo uomo ha quattro figli e due figlie, che sono molto ragionevoli. 14. Abbiamo ricevuto cinque lettere da nostra zia. 15. Il mio amico ha trovato un temperino e otto penne. 16. Ho perduto nella scuola dieci penne. 17. Cinque via quattro venti. 1. Divide 9a3y* by —3a3. 2. Divide 123≈ by 2b3. 3. Divide a b+3a2y by a2. EXERCISE 45. 4. Divide dx (a−h + y)3 by (a k+ y)3. 5. Divide a+ 8 by a. 6. Divide a by a". 7. Divide ym by ym. 8. Divide bo by l3. 9. Divide 8a+ by 4a". 10. Divide a +3 by a2. 11. Divide 12(b + y)" by 3(b + y)3. ROOTS. If we resolve b3, or bbb, into equal factors, viz., b, b, and b, each of these equal factors is said to be a root of b3. So if we resolve 27 into its three equal factors, as 3 × 3 × 3, each of these equal factors is said to be a root of 27. And when any quantity is resolved into any number of equal factors, each of those factors is said to be a root of that quantity. A root of a quantity, then, is a factor which, multiplied into itself a certain number of times, will produce that quantity. The number of times the root must be taken as a factor to produce the given quantity, is denoted by the name of the root. Thus 2 is the fourth root of 16; because 2 × 2 × 2 × 2 = 16, where 2 is taken four times as a factor to produce 16. So a3 is the square root of a6; for a3 X a3 = a6. Powers and roots are correlative terms. If one quantity is a power of another, the latter is a root of the former. As b3 is the cube of b, so b is the cube root of b3. There are two methods in use for expressing the roots of quantities; one by means of the radical sign, and the other by a fractional index. The latter is generally to be preferred; but the former has its uses on particular occasions. Thus 2a is 2 x When a figure or letter is prefixed to the radical sign without any character between them, the two quantities are to be considered as multiplied together. a; that is, 2 multiplied into the root of a; or, which is the same thing, twice the root of a. And ab is x × √b, or x times the root of b. When no co-efficient is prefixed to the radical sign, 1 is always understood; a being the same as 1a; that is, once the root of a. The cube root of a6 is a2; for a2 X a2 X a2 = a¤. Here the index is divided into three equal parts, and the quantity itself resolved into three equal factors. The square root of a2 is a or a; for a X a = a2. By extending the same plan of notation, fractional indices are obtained. Thus, in taking the square root of al or a, the index 1 is divided into two equal parts, and ; and the root is a. On the same principle, the cube root of a is a3 3, = 3√√√a. Every root, as well as every power of 1, is 1; for a root is a factor, which, multiplied into itself, will produce the given quantity. But no factor except 1 can produce 1, by being multiplied into itself. So that 1, 1, √1, "√1, etc., are all equal. Negative indices are used in the notation of roots, as well as of powers. In the preceding examples of roots, the numerator of the fractional index has been a unit. There is another class of quantities, the numerators of whose indices are greater than 1; etc. These quantities may be considered either as powers of roots, or roots of powers. as N.B. In all instances, when the root of a quantity is denoted by a fractional index, the denominator, like the figure over the radical sign, expresses the root, and the numerator the power. Thus as denotes the cube root of the first power of a; i.e., that a is to be resolved into three equal factors; for a3× aa3× as On the other hand, e denotes the third power of the fourth root of c, or the fourth root of the third power. One expression is equivalent to the other. = &. n The value of a quantity is not altered by applying to it a fractional index whose numerator and denominator are equal. Thus, a = a2 = a = an. For the denominator shows that a is resolved into a certain number of factors; and the numerator shows that all these factors are multiplied together in qu. the other hand, when the numerator of a fractional index becomes equal to the denominator, the expression may be rendered more simple by rejecting the index. n Instead of an, we may write a. n On numerator shows that twice as many of these factors are to be multiplied together. Hence the value is not altered. From the preceding article it will be easily seen that a fractional index may be expressed in decimals. EXAMPLE. Thus a = or ao-5; that is, the square root is equal to the fifth power of the tenth root. In many cases, however, the decimal can be only an approrimation to the true index. EXAMPLE.—Thus a3 = ao.3 nearly, or ao.3333 more nearly. In this manner the approximation may be carried to any degree of exactness which is required. N.B.-These decimal indices form a very important class of nambers, called logarithms. 8. Express a in decimals. 14. Express a in decimals. KEY TO EXERCISES IN LESSONS IN ALGEBRA.-XXVI. 9. ab2(1+b+ a2b$) + 10. 15a3+10bc2. 11. 4(xy-cm). sentatives to Parliament. It is confidently anticipated that the SESSIONS, CLASSES, AND FEES. There are two sessions of the classes in each year-namely, the summer session, which opens in the beginning of May and ends with July; and the winter session, which opens in the There is no beginning of November and ends with April. summer session in the Faculty of Arts; but tutorial classes in Latin, Greek, and Mathematics are opened for students who have attended a winter course on these subjects. In the Faculty of Arts, or Literature and Philosophy, the classes include Latin or Humanity (3), Greek (2), Mathematics (3), Logic and Metaphysics, Moral Philosophy, Natural Philosophy, Rhetoric and English Literature, Practical Astronomy, Agriculture, Theory of Music, Sanscrit, and Engineering In the classes of Agriculture, Sanscrit, and Engineering, the fee is £4 4s., and in all the other classes named £3 38. There are eight classes in the Faculty of Theology, comprising Divinity (2), Church History, Biblical Criticism, Hebrew (2), and Hindostani (2). The fee in each class is £2 2s. In the Faculty of Law the classes are Civil Law, Law of Scotland, Medical Jurisprudence, Public Law, Conveyancing, Constitutional Law and History. The fee in Civil Law and Law of Scotland Classes is £5 5s., including the summer session, and in the other classes £3 38. and £4 4s. In the Faculty of Medicine the classes comprise Materia Medica, Chemistry, Surgery, Institutes of Medicine, Midwifery, Clinical Surgery, Clinical Medicine, Anatomy, Practical Anatomy, Anatomical Demonstrations, Natural History, Practice of 9. a22 (1 − a3 ̧3) + 23 Physic, and General Pathology. In Practical Anatomy the fee (xy+1). 10. (a-b)3. 11. (x+y)2. 19. a*—y1. 20. as-ys. 21. as-a2. 22. 6a2(x2-13)7. 23. (a2+b3)3. 24. 19(a-b1). 25. x+2x3y + 2x2y3 + 26. a3+3265. THE UNIVERSITIES.-XI. EDINBURGH. In our former articles on the subject of the Universities, we have treated at some length on the educational advantages of those of Oxford and Cambridge. We come now to the collegiate institutions of the North. The four Universities of Scotland-Edinburgh, St. Andrews, Glasgow, and Aberdeen-are more democratic or popular in their constitution and government than the sister Universities of Oxford and Cambridge. On this account, and owing also to the comparative lowness of the class fees, many of the students annually attending those institutions are the sons of small farmers, crofters, and people in humble circumstances. The privileges and efficiency of the four Universities of Scotland were augmented by an Act passed in 1858, which made provision for improving and regulating the course of study in the universities, and also for their better government and discipline. university is now a corporation, consisting of a chancellor, rector, principal, professors, registered graduates, and matriculated students. Each In accordance with certain clauses of the "Representation of the People (Scotland) Act," 31st and 32nd Vict., the Universities of Edinburgh and St. Andrews were combined into one constituency, and the Universities of Glasgow and Aberdeen into another constituency, for the purpose of returning two repre is £3 3s., in Anatomical Demonstrations £2 2s., and in all the other classes of the Faculty £4 4s. Annual tickets of £5 5s., and half-yearly tickets of £3 38., give admission to the demonstrations in the Royal Infirmary. The matriculation or entrance fees are £1 for the academical year, and 10s. for the short summer sessions. The ordinary curriculum in the Faculty of Arts, with a view to a degree, extends over four winter sessions; but students who pass an entrance examination in Latin, Greek, and Mathematics, showing that they are qualified to be admitted at once to the higher classes, may complete the Art curriculum, with a view to graduation, within three winter sessions, and may also dispense with a second session at the Mathematical classes. GRADUATION. By the regulations candidates for the degree of Master of Arts are examined on all the subjects of instruction embraced in the ordinary curriculum of study in the Faculty. The examination on Latin and Greek (1), on Literature, Metaphysics, Philosophy (3), may take place at separate periods, although and Moral Philosophy (2), and on Mathematics and Natural the student has not completed his attendance on the other classes composing the academical course. On completing the pass or ordinary examinations, students 1. DEPARTMENT OF CLASSICAL LITERATURE. Cicero, "Letters to Atticus," i. General Knowledge of Roman History and Literature till the end of the Augustan Age. |