equivalent to the simple fraction oz. But fractions may be still 10. Paisciple 1.-If the numerator and denominator of a fraction be both multiplied by the same number, the value of the fraction is not altered, that is, the value of the fraction remains the same as before; and if the numerator and denominator be both divided by the same number, the value is not altered, that is, the value remains the same as before. This principle is the same in effect as that general principle in division laid down in vol.I., p. 380, col. 1, No. V., viz., that if the divisor and dividend are both multiplied or both divided by the same number, the quotient will not be altered. Here we have only to substitute the words denominator, numerator, and value for the words divisor, dividend, and quotient respectively, and the principles are one and the same. But in order to illustrate the former, let us take the fraction or ; if we multiply both numerator and denominator of this fraction by 10 its value will not be altered, for it then becomes or. Now, whether a unit be divided into 10 equal parts, and 5 of them be taken, or into 100 equal parts and 50 of them be taken, it is plain that half the number of parts is taken in either case, and that the value of these parts is of the whole in both fractions, so that the value of the fraction remains unaltered; that is, no-oor. Again, let us take the fraction or ; if we divide both numerator and denominator of this fraction by 25, its value will not be altered, for it then becomes;. Now whether a unit be divided into 100 equal parts and 75 of them be taken, or into 4 equal parts and 3 of them be taken, it is evident that three fourths of the number of parts is taken in either case, and that the value of these parts is of the whole in both fractions: for 25 parts is 3 of 100 parts, and as 75 is 3 times 25, therefore 75 parisis # of 100 parts; also, 1 part is ; of 4 parts, and 3 parts is # of 4 parts; so that the value of the fraction remains unaltered; that is so-#. 11. Paisciple 2.-If the numerator only of a fraction be multiplied by any number, the denominator remaining the same, the value of the fraction is increased as many times as that number denotes; or, if the denominator only of a fraction be divided by any number, the numerator remaining the same, the value of the fraction is increased as many times as that number denotes. This principle combines two of the general principles in Division, laid down in vol I. p. 380, col. 1, Nos. 1. and IV., viz.:-If the divisor re mains the same, to multiply the dividend by any number is in effect | multiplying the quotient by that number; and, if the dividend remains the same, dividing the divisor by any number, is in effect multiplying the quotient by that number. Here we have only, as before, to substitute the words denominator, numerator, and value, | for the words divisor, dividend, and quotient respectively, and the principles are one and the same, as before. To exemplify the former, let us take the fraction so, and let its numerator be multiplied by the number 4, its denominator remaining the same; the result is #3. Now, taking any unit of which the value of the fraction is can be easily found, say a pound Avoirdupois; it is plain that as is of a pound is 1 ounce, so or of a pound is 3 ounces, and !3 of a pound is 12 ounces; but 12 ounces are 4 times 3 ounces; therefore, multiplying the numerator of the fraction or by any num. ber, 4 increases its value, viz., 3 ounces, as many times as that number denotes, viz., to 4 times 3 ounces or 12 ounces. Again, let the denominator of the fraction of be divided by the number 4, its numerator remaining the same; the result is #. Now, taking the same units as before, we find that or of a pound is 3 ounces, and # of a pound is 12 ounces (3 of a pound being 4 ounces); but, as be: fore, 12 ounces are 4 times 3 ounces; therefore, dividing the denominator of the fraction & by any number 4, increases its value 3 ounces, as many times as that number denotes, viz., to four times 3 ounces, or 12 ounces. Besides, we know that {{. ; for if both the numerator and denominator of the fraction ## be divided by any number, say 4, its value will not be altered. Whence, multiplying the numerator only of a fraction, or dividing its denominator only, by the same number, multiplies the fraction by that number. 12. PRINCIPLE 3.-If the numerator only of a fraction be divided by any number, the denominator remaining the same, the ralue of the fraction is diminished as many times as that number denotes; or, if the denominator only of a fraction be multiplied by any number, the numerator remaining the same, the value of the fraction is diminished as many times as that number denotes. This principle combines the two general principles of Division laid down in Vol. I., p. 380, col. 1, Nos. II. and III., viz. If the divisor remains the same, dividing the dividend by any number, is in effect dividing the quotient by that number, and if the dividend remains the same, multiplying the divisor by any number is in effect dividing the quotient by that number. Here, again, if we substitute the words denominator, numerator, and value for the words divisor, dividend, and quotient respectively, the principles will be found to be identical. To exemplify the former, let us take fraction {3, and let its numerator be divided by the number 4, its denominator remaining the same; the result is no. Now, if we suppose the unit to be a pound Avoirdupois as before, then it is evident that 33 of a pound is 12 ounces, and or of a pound is 3 ounces; but 12 ounces divided by 4 gives 3 ounces; therefore, dividing the numerator of the fraction #3 by any number 4, diminishes its value, viz., 12 ounces, as many times as that number denotes; for 12 ounces + 4 = 3 ounces. Again, let the denominator of the fraction +3 be multiplied by the number 4, its numerator remaining the same; the result is ##, which by principle 1, Art. 10, is for; for # = or, by dividing both numerator and denominator by 4. Hence, multiplying the denominator only of the fraction {3 by any number 4, diminishes its value as many times as that number denotes, for, 12 --4-3, and #* as before. Whence, dividing the numerator only of a fraction, or multiplying its denominator only, by the same number, divides the fraction by that number. derer. 1. If he had not been able to perform the work, he would not have undertaken it. 2. Will he be able to fulfil his promise 2 3. He has not been able. 4. We ought not to promise more than we are able to perform. 5. Are you able to deliver a better explanation upon this subject 2 6. I am indeed able, but I have no time now. 7. Does the boy go for my stick freely 2 8. When he does, it is unwillingly; I would rather go myself. 9. Do you like to see your relations 2 10. Yes, I do like to see them. 11. When you have need of those books, then I will lend you them freely. 12. He needed money yesterday, therefore he desired me that I would give him some. 13. Therefore it is useless to ask for more, when you already owe so much. 14. Who would not freely heal the wounds of a wounded heart. 1. Had your friend not become ill, he would certainly have embellished the feast by his presence. 2. If you were more prudent, you would not have met with this inconvenience, 3. I would have settled your business, if you had mentioned it to me. 4. His brother would have been better received, if he had had letters of recommendation. 5. He would have better friends, if he were more agreeable. 6. You would have had more difficulties, if you had not followed the advice of your friends. 7. I should not have the least doubt, that you would have succeeded, if you acted more prudently. 8. We should set sail for Holland, if we had a fair wind. 9. He would be the first among our merchants, if he were more sociable. 10. If I had had the power, I should have acted in another manner, because I should not have had so much patience. 11. What would be the felicity of man, if he always sought his happiness in himself? 12. You would be richer, if you were more enterprising. ANSWERS TO CORRESPONDENTS. Juvex is DiscIPULUs (Wigton) should consult a variety of works on the ancient laws to which he refers. He will get information in some of the large Classical, Dictionaries recently published.—Cos: His solution is right. We shall be glad to see his perpetual calendar.—J. W. D. (Lambeth): The distance M. N. measures 243 equal parts, and the distance P. M. measures 225 equal parts.-CHARLEs, Hughes (London) has made a good selection of studies; let him go on and prosper. Cassell's Arithmetic is intended for those who are desirous of H."; more rapidly with that subject than with, any other-B. P. (Islington): See Bradshaw’s “Continental Guide,” or M'Culloch's "Commercial Dictionary.”—J. A. (Leicester): The “Spec tator” was an old “standard periodical work.” Complete copies cfit may now be had in any bookseller's shop, or at any book-stall. T Hoxas M'LAREN (Grandtully): We have already said Liddell and Scott's Lexicon.—L. W. F. : Correct.—E. P. (Wigan) should study Dr. Beard's Lessons in English first, and then the French. Exercises must of course be written out, and we would advise the rules also to be written out in a book; for by carefully writing out to: eren once, you thereby fix it in the memory.—SINE PRECEPTonk (Fife) is right; there are some misprints and inaccuracies in the places to which he refers. We shall take an opportunity of rectifying them.—FENELox (Stockwell): Thanks for the following corrections: in vol. 1., p. 76, col. 2, line 20 from bottom, for mauvais read mauvaise; p. 78, col. 1, line 32 from top, for boiteaux read boiteux; col. 2, line 2, for amusunt read amusant; p. 171, col. 1, line 25 from bottom, for the first chantons read chansons; p. 261, col. 2, line 1, for barber read barbar, in the German.—SIGMA (Dollar): Thanks for his observations and suggestions; they will be attended to.—CAEsAR (Walworth): Thanks.-C. W. STYRING (Doncaster); Soon.-APPRENtice (Edinburgh): Only two errors in 1 and 5.-R. H. HAMMoRD : We can't exactly say.—P. (Milford Haven): Her verses are very creditable indeed.—J. J. Newton (Bridgewater): Right.—D. D. (Kincardinshire): Rue St. Honore.—J. W. (WAcer): Thanks for his suggestions.—H. Wilson : On the different kinds of galvanic or hydro-electric batteries, see Peschell's Physics, vol. III., p. 75–91. AN ALGEBRA1c Studext has proposed two questions which, from their manner of statement, are literal absurdities, thus: 1. “To find the side of a square whose area is equal to twice the sum of the sides; and 2. To find the side of a cube whose solid content is twice its surface.” An area or a number of square inches can never be equal to a length or number of long inches; and a solid, or a number of cubic inches, can never be equal to a surface or a number of square inches . . Yet the number which expresses an area may be equal to the number which expresses a length; and the number which expresses a solid content may be equal to the number which expresses a surface. In these senses, and in these only, can the preceding questions have any meaning; their solution is quite easy. 1. Put the square of a (the side of the square", equal to twice four times ar, or twice the sum of the sides, and you find z is equal to 8, the first answer. 2. Put the cube of a (the side of the cube), equal to 6 times the square of r, or the surface of the cube, and you find a *6, the second answer.—QUADRANT: Really we cannot say.—George AMD Rose DAMERHAM: Riddle's Young Scholar's English-Latin Dictionary 5s., and Latin-English Dictionary 7s. Both together 12s.-R. J. (Tavistock): Right.—SusANNE (Newington): It is by no means necessary to go back to poihooks and strokes; many persons would admire her writing; we admire her desire for improvement; and recommend her to write two or three copy-books of the teart, or large hand, from A to Z; then two or three copy-books of the half-tert, or next size of writing, from A to Z; and lastly, two or three copy-books of the court-hand from A to Z; and if she will attend to the method of holding the pen, and of sitting at the table, which we have recommended in Lesson I. of Penmanship, we feel quite certain that her next letter to us will both astonish her and ourselves. A SUBscribert : There is an “express” almanack for the P. E. and it is not the same as the one for the “Illustrated Exhibitor,”—see Literary .Notices.—J. BRiggs (Neverston): Thanks for his suggestions; he should try and give each an hour or two a-week, and not alternately.—UN Soldat ANGLo-INDIEN : Quand and lorsque are very nearly, if not entirely synonymous, when applied to the indicative mood; grand, when applied to the subjunctive, is a synonyme for si; your note is pretty correct.-J. A. F. (Bristol): We recommend J. S. Knowles as a teacher of Elocution, and of course his book on that subject.—F. P. F. (Hounslow): See p. 288, vol.I. col. 2, line 49.-S. G. (London); Terpsichore, pronounced terp-sick'-o-reIs AAc DAYKIN (Leicester): There is some truth in his remarks; they will be attended to.-J. T. (South Shields) need not expect to find corresponding terms for life-boat and wreckers in any common French dictionary.-J. B. (Wolverhampton): A scalene triangle may also be a right angled triangle. To prove this; make a triangle of which the sides'shall be respectively 3, 4, and 5 inches in length; and it will be a scalene right angled triangle.— Juvenile CHEMisr, &c. (Notting-hill): We do not see the application of his citation from Newton. Right in the arithmetical question. But his own must lie over at present. LITE R A R Y NOTICES. THE UNCLE TOM'S CABIN ALMANACK ; or, Tue Apolitioxist MEMENTo Fon 1853.-The most complete work on the question of slavery that has hitherto been published. Everybody who has read “Uncle Tom's Cabin” should possess themselves of a copy of this book, which more than verifies all the statements in Mrs. Stowe's thrilling narrative. This work is splendidly Illustrated by George Cruikshank, Esq.; J. Gilbert, Esq.; W. Harvey, Esq.; H. K. Browne, Esq.(“Phiz"); and other eminent artists; and contains upwards of 70 pages super-royal 8vo., replete with the most stirring incidents—Lives of Escaped Negroes; the Workings of the Fugitive slave Law; Anecdotes, Narratives, and Historical and Descriptive Accounts of American Slavery. The sale already is very large, nearly 20,000 copies having been disposed of in a fortnight. Illustrated Exhibiton ALMANAck, Thirty splendid Engravings, 5d. Porular Educator ALMANAck, Notices and Essays on Education, od. TEMPERAN ce. ALMAN Ack, Tale by the Atitholicss of Uncle Tom, &c., od ProTest ANt Dissenters' ALMANAck, with new Historical Notices, &c.5d. CAssell's EleMENTs of AR1Thristic, 1s. paper cover; is. Ga. theatly bound in cloth. Printed and Published by John CAssell, La Belle Sauvage Yard, Ludgatohull, London, November 27, 1852. 137 UN I W E R SITY OF LOND ON.— No. I. NUMERous applications having been made to us regarding the inquiry whether self-taught students are permitted to Matriculate at the University of London—that is, to enroll their names in the list of UNDER-GRADUATEs of the said University, we have made special inquiry into this matter, and we are enabled to announce to our students that it is quite competent for any of them, whether self-taught or not, to become a member of the University of London by passing the Eramination for Matriculation, and even to take honours at the said Examination. The following are the REGULATIONs of the University on this head, which we extract from the “University Calendar for 1853.” A RTS. M A TRICULATION. The Matriculation Examination shall take place once a-year, and commence on the first Monday in July. No Candidate shall be admitted to the Matriculation Examination unless he have produced a Certificate showing that he has completed his Sixteenth year. This Certificate shall be transmitted to the Registrar at least fourteen days before the Examination begins, A Fee of Two Pounds shall be paid at Matriculation. No Candidate shall be admitted to the Examination unless he have previously paid this Fee to the Registrar. If a Candidate fail to pass the Examination, the Fee shall not be returned to him, but he shall be admissible to any subsequent Examination for Matriculation without the payment of any additional Fee. The Examination shall be conducted by means of Printed Papers; but the Examiners shall not be precluded from putting, for the purpose of ascertaining the competence of the Candidates to pass, vied voce questions to any Candidate in the subjects in which they are appointed to examine. Candidates for the Matriculation Examination shall be examined in the following subjects: [PASS EXAMINATION.] MATHEMATICS. ARITHMETIC AND ALGEBRA. The ordinary rules of Arithmetic. Vulgar and Decimal Fractions. Extraction of the Square Root. Addition, Subtraction, Multiplication, and Division of Algebraical Quantities. Proportion. Arithmetical and Geometrical Progression. Simple Equations. GeoMETRY. The First Book of Euclid. NATURAL PHILOSOPHY.* MECHANICs. Explain the Composition and Resolution of Statical Forces. Describe the Simple Machines (Mechanical Powers), and state the Ratio of the Power to the Weight in each. Define the Centre of Gravity. Give the General Laws of Motion, and describe the chief experiments by which they may be illustrated. State the Law of the Motion of Falling Bodies. HYDRostatics, HYDRAULics, AND PNEUMATICs. Explain the Pressure of Liquids and Gases, its equal diffusion, and variation with the depth. Define Specific Gravity, and show how the specific gravity of bodies may be ascertained. - a o. only of these subjects in Natural Philosophy will be i. such as may be attained by attending a Course of Experimental ectures. WOL. II. Describe and explain the Barometer, the Siphon, the Common Pump and Forcing-Pump, and the Air-Pump, Acoustics. Describe the nature of Sound. OPTICs. State the Laws of Reflection and Refraction. Explain the formation of Images by Simple Lenses. CHEMISTRY. The Atmosphere. Its general nature and condition; its cemponent parts. Oxygen and Nitrogen; their properties. Water and Carbonic Acid. Proportions of these substances in the air. Chlorine and Iodine, as compared with Oxygen. Water. Its general relation to the atmosphere and earth; its natural states and relative purity. Sea-water, river-water, spring-water, rain-water. Pure water: effects of heat and cold on it; its compound nature; its elements. Hydrogen. Its nature and proportion in water; its presence in most ordinary fuels; its product when burnt. Sulphur, Phosphorus, and Carbon generally. Nitric Acid, Sulphuric Acid, Carbonic Acid; their elements. Hydrocholoric or Muriatic Acid. Alkalies, Earths, Oxides generally. Salts. Their nature generally; Suiphates, Nitrates, Carbonates. Metals generally. Iron, Copper, Lead, Tin, Zinc, Gold, Silver, Platinum, Mercury. Powers of Matter. Aggregation, crystallization, chemical affinity, definite equivalents. Combustion. Flame; nature of ordinary fuel; chief results of combustion, i.e., the bodies produced. Heat. Natural and artificial sources; its effects. Expansion; solids, liquids, gases. Thermometer; conduction; radiation; capacity; change of form; liquefaction; steam. The chief elements of Vegetable bodies; of Animal bodies. CLASSICS. THE GREEK AND LATIN LANGUAGEs. One Greek and one Latin subject, to be selected one year and a-half previously by the Senate from the works of the undermentioned authors:* Homer....One Book. Xenophon... One Book. Virgil ....One Book of the Georgics, or the Sixth Book of the AEncid. Horace....One Book of the Odes. Sallust.... 1ne Conspiracy of Catiline, or the War with Ju urtha. Caesar ....The Civil War, or the Fifth and Sixth Books of the Gallic War. Livy...... One Book. Cocero ....The Treatises De Senectute and De Amicitiã; or two of the shorter, or one of the longer Orations. THE ENGLISH LANGUAGE. Candidates shall not he approved by the Examiners unless they show a competent knowledge in 1. Classics;” 2. Mathematics; 3. Natural Philosophy; 4. Chemistry; 5. Either French or German. In the first week of examination the Examinations shall be conducted in the following order: Afternoon. Monday ............French, 2 to 4. Monday .. .....German, 4 to 6. ..... English History, 3 to 6 .....Chemistry, 3 to 6 Thursday ..... Natural Philosophy, 3 to 6. Friday ............The English Language, 2 to 5. Morning. Tuesday............Mathematics, 10 to 1. Wednesday ........Greek Classic and History, 10 to 1 Thursday ..........Mathematics, 10 to 1. Friday ............ Roman Classic and History, 10 to 1. On Monday Morning at Nine o'clock in the week next but one ensuing, the Examiners shall arrange in Two Divisions, each in alphabetical order, such of the Candidates as have passed. EXAMINATION FOR HONOURS. Any Candidate who has passed [the previous Examination] may be examined for Honours in Mathtmatics and Natural Philosophy, Classics, Chemistry, and Natural History. Candidates for Honours in MAt HEMAtics AND NATURAL PHILosophy shall be examined in the following subjects: Attithm ET1C AND ALGEBRA. Geom oth Y. PLANE AND SPHERICAL TRIGoxoMETRY. CoNic Sections. The EleMENts of STATIcs AND DYNAMICs. The EleMENTs of HYDRosTATICs. The ELEMENTs of OPTICs. This Examination shall take place on Tuesday, Wednesday, and Thursday, in the week next but one after the Matriculation Exa. mination; in the Morning from Ten to One, and in the Afternoon from Three to Six. In determining the relative position of Candidates, the Examiners shall have regard to the proficiency in Mathematics evinced by the Candidates at the Matriculation Examination, The Examiners shall publish in the course of the following week a list of the Candidates who acquit themselves to their satisfaction, in the order of proficiency; and Candidates shall be bracketed together unless the Examiners are of opinion that there is a clear difference between them. Candidates for Honours in CLAssics shall be examined in the following subjects: THE GREEK AND LATIN LANGUAGEs. Homer. ....The First Six Books of Iliad, and Books IXXII. of the O yssey. Joschylus.... Prometheus. Euripides....Me, ea. Sophocles.... Antigone. Thucydides ... Book I. Herodotus.... Book II Lemosthenes...The Olynthiacs and .g. Plato .......Apology of Socrates and Crito Xenophon.... I he Memorabilia. Virgil. ......[All the Books.] Horace.......[All the Books.] Sallust ...... he Wars with Catiline and Jugurtha. Liry ........ Books XXI. and XXXI. Cicero ...... De Sen clute; DeAm citia; the Orations against Catline, Pro Miloue, Pio Archià, and the 2nd Phil p, ic. Tacitus...... Agricola; G. rimania; and Annals, Book I CoMP'osi 10x is Latin AND IN ENGL1sh. Latin, I'r se. Translation and retranslation. En lish Prose. An olysis of any of the subjects selected for examination; original com, osition upon questions arising out of h c as-ie -l authors -elect d for examina ion. The papers i Casies shal consis or possages to be translated, accom on d by questions in Grammar, History, and Geography. This Examina on “hol, take place on luesday, Wednesday, and Thursday, in the week following the Examinati u tor Houours in * Including the Fnglish Language, History, and Geography. Mathematics and Natural Philosophy; in the Morning from Ten to One, and in the Afernoon from Three to Six. In determining the relative position of Candidates, the oxa. miners shall also have regard to the proficiency in Classics, His ory, and Geography, ev-nced by the Candidates at the Matriculation Examination. The Examiners shall publish in the course of the following wee: a list of the Candidates who acquit themselves to their satisfaction, in the order of proficiency; and condidates shall be bracketed together unless the Examiners are of opinion that there is a clear difference between them. Candidates for Honours in NATURAL. History shall be examined in one or both of the following subjects: BotANY.” The Examination for Honours in Chemistry shall take place on the Friday in the week next but one after the Pass Examination, in the Morning from Ten to One; and the Examination in Natural History on the same day, in the Afternoon from Two to Five. Such Candidates for Honours in Chemistry and in Natural History as acquit themselves to the satisfaction of the Examiners, shall be arranged in the order of proficiency in each subject. II, in the opinion of the Examiners, any Candidate shall possess sufficient merit, the Candidate who shall distinguish himself the most in Mathematics and Nattoral Philosophy, and the Candidate who shall distinguish him-elf the most in Cla-sics, shall each receive an Exhibition of Thirty Pounds per annum for the next Two Years, if continuing during that period Students at one of the Institutions in connexion with this University. Under the same circumstances, the Candidate who shall distinguish himself the most in Chemistry, and the Candidate who shall distinguish himself the most in either branch of Natural History, shall each receive a Prize of Books to the value of Five Pounds.” Hitherto we find in the list of under-graduates who passed the Matriculation Examination, no less than 165 names to which are attached the words Private Tuition; and in the list of those who took honours at that Examination, no less than 23 names to which are attached the same words. From the date of this announcement, we hope and trust that some of our self-taught students will endeavour to get their names enrolled as members of the University of London, next year, and that their names will appear in the register with the words self-tuition attached to them. It is quite possible that of those who have been already enrolled in the list with the words Private Tuition attached to their names, many may have been self-taught, and that, consequently, this term is included in the former. But the fact that self-taught students are admissible into the University, is now placed beyond a doubt. The Examination for Matriculation, whether with or without honours, takes place in July. This year, 1852, it took place for passing on the 6th, 7th, 8th, and 9th of July, and for honours on the 20th, 21st, 22nd, 23rd, 27th, 28th, and 29th of the same month. We add the following important notification from the Calendar: “Candidates for Degrees are requested to take notice that it is necessary for them to attend in person at the Apartments of the University at Somerset House, before the commencement of the Examinations, for the purpose of entering their names on the Register.” must be able to explain if required. |