the music passes directly from FAH to TU or from TE to FI. See two cases in tunes well-known,-one in the "May Fly," and the other in "Lightly Tread." Both are solfaed in the "Tonic Solfa Reporter," No. 4, (Ward and Co.) "Natural modulation," says Dr. Goss, "that is, modulation into related keys, may be performed either gradually or suddenly. The gradual method is that in which we take some doubtful chord (or chord which may be considered to belong either to the key we are in or to that into which we are going), and from this chord proceed to a modulating chord, or chord which clearly marks the change of key, by exhibiting a new sharp or flat." Dr. Marx calls this preparatory chord the "mediating chord." See also Dr. Crotch and Mr. Hickson. This "convertible" note, from which transition is taken, should be indicated, in solfaing, by pronouncing the syllabic name it bears in the old key together with that which it takes in the new. Thus ME converted into LAH of the new key would be pronounced M'LAH, DOH converted into son would be pronounced D'soн, and so with the rest. The mention of the first syllabic name gives help to the ear (by association) in striking the note, and the sliding into the new syllable prepares the ear for the interval by which we leave the note, and makes us feel our place in the new key. In writing, this "convertible" note may have the initial of its first syllabic name placed before and above that of its second and new name. Thus m111, or, dig or sr. When music is solfaed in this, the more perfect way of denoting transition, Tu of course becomes the new TE, and FI is the new FAH. As the old notation, however, does not mark the "doubtful" or "convertible" note, and leaves us unprepared for the change until we come actually upon a distinguishing note of the new key, we are often obliged to translate that distinguishing note by the syllables TU or FI, and con EXERCISE 39. tinue solfaing as though we wese still in the old key. This d " And in the phrase given below, you are compelled to feel that the peculiar use of LAH and FAH has made them "bold and strong" notes, or, in other words placed you in the key of FAH -the "subdominant." d MELCOMBE. LESSONS IN GEOGRAPHY.-No. XXIV. MAP OF NORTH AMERICA. NORTH and South America form but one vast irregularly shaped continent, being connected with each other by the Isthmus of Panama or Darien; it occupies a part of four zones, extending from the north frigid zone, across the north temperate and the torrid zones, and stretching into the south temperate zone. North America is bounded on the north, by the Arctic Ocean; on the south, by the Gulf of Mexico and the Pacific Ocean; on the east, by the Atlantic Ocean; and on the west, by the Pacific Ocean. This continent extends from Latitude 76° 45' N. to Latitude 8° 1' N., and from Longitude 52° 18' W. to Longitude 168° W. The most northerly point of North America is considered to be Cape Clarence, in North Somerset (Arctic Regions), in Lat. 76° 45' N. and Long. 77° 40′ W.; the most southerly, is Burica Point, Costa Rica, in Lat. 89 1′ N. and Long. 82° 50′ W.; the most easterly point! is Cape Charles, Labrador, in Lat. 52° 18′ and Long. 55° 31 W.; and the most westerly point is Cape Prince of Wales, Russian America, in Lat. 65° 16' N. and Long, 1689 W. The latter point, situated in Behring's Strait, is said to approach the easternmost point of Asia, within a distance of 36 miles, a short enough sail for European migrators to accomplish even in an open boat, and, having done so, to people the new world. Within the limits above mentioned the greatest length of North America is 4,817 miles from north to south; and its greatest breadth, from east to west, is 3,614 miles. The surface of this continent, including that of the West Indies and other islands belonging to it, may be reckoned about 10 millions of square miles, and the population about 30 millions; thus giving on an average about 3 inhabitants to every square mile. The great inland seas and gulfs of North America are the following:-Hudson's Bay, which runs through Hudson's Strait into the British territory, and is connected with the Arctic Seas by Fox Channel, Fury and Hecla Strait, Prince Regent's Inlet, Barrow Strait, and Wellington Channel; it is also connected with Baffin's Bay by Lancaster Sound; Hudson's Bay terminates in James's Bay to the south. Baffin's Bay is connected with the Atlantic Ocean by Davis's Strait, Lancaster Sound, and other sounds and inlets on the north. The Gulf of St. Lawrence is the broad estuary of the river of the same name, having the large island of Newfoundland with other smaller ones at its embouchure (river mouth). The area of Hudson's Bay is reckoned at 350,000 square miles; its length from north to south being about 1,000 miles, and its breadth about 500 miles. Baffin's Bay is about 1,500 miles long, and about 300 miles broad; its surface is not less than that of Hudson's Bay, being at least 400,000 square miles. The Bay of Fundy runs from the Atlantic between Nova Scotia and New Brunswick. It is remarkable for its high tides, which have been known to rise 90 feet. The Gulf of Mexico, which is about 1,100 miles long, and about 500 miles broad, washes the southern shores of the United States, and the western shores of the Mexican States; it is connected with the Carribbean Sea, which washes the shores of the West India Islands, and of the northern part of South America; the latter sea is about 1,800 miles, and on an average about 1,000 miles broad. The Bay of Campeachy is the southern part of the Gulf of Mexico. The gulf stream rushes from the Gulf of Mexico through the strait of Florida, between Cuba and the peninsula of Florida, and crosses the Atlantic in an easterly direction, preserving its higher temperature in the middle of the ocean, and being sensible in this respect when it reaches the Azores. In the Caribbean Sea, to the south-east, are the Gulf or Bay of Honduras, the Mosquito Gulf, and the Gulfs of Darien and Venezuela. On the Pacific side of North America are the Gulfs of Panama, Tehuantepec, and California; and a variety of small bays and sounds stretching to Behring's Straits, and even beyond that strait into the Arctic Ocean. The most important straits have been already mentioned in the preceding remarks; besides these, there are: Frobisher Strait leading from Davis's Strait to Fox Channel; Sir Thomas Roe's Welcome, between Southampton Island and the main land; the Strait of Belle Isle between Newfoundland and Labrador; the Gut of Canso between Cape Breton Island and Nova Scotia; and others of less importance. The following is a list of the countries, kingdoms, empires, and states of North America, similar to our former lists of the old continents. Many of the Latitudes, and Longitudes are only approximate, having been taken from maps; but they were taken from the latest published. In islands, where a town or capital is not given, the Latitude and Longitude is that of some known point in the island. COUNTRIES, KINGDOMS, EMPIRES, AND STATES IN NORTH AMERICA. Bathurst, Cape Parry, and Cape Felix, in the British territory; also Cape Rennel, Cape Clarence, Cape Hay, Cape Adair, Cape Roper, Cape Walsingham, and Cape Enderby; Cape Chudleigh, in Labrador; Cape Sable, in Nova Scotia; Cape Cod, Cape Charles, Cape Hatteras, Cape Look-out, &c., all on the east coast of the United States; Sable Point, in Florida; Cape Catoche, in Yucatan; Cape Gracias-à-Dios on the Mosquito coast; Cape Blanco, Central America; Cape Corrientes, Mexican States; and Cape St. Lucas, Lower California. St. Bartholomew's Hospital. St. George's Hospital. BACHELORS OF ARTS. Alfred Barnes William Leech Charles Jerom Murch UNIVERSITY OF LONDON.-No. III. London, 4th May, 1853. This day we had the pleasure of witnessing the ceremony of the presentation of the students of the various colleges and institutions in connection with the University of London, to the Chancellor of the University, the Earl of Burlington, for the conferring of degrees, and for the reception of scholarships. exhibitions, medals, and prizes. This ceremony took place in the large hall of King's College, Somerset House, at 2 P. M. and was attended by a considerable number of spectators, consisting of ladies and gentlemen, professors and students from the different colleges and institutions, and the office-bearers of the University. The proceedings went on with very great eclat, and many a student's heart then bounded with becoming joy at the reception of the honours gained by their praisewor thy labours in the acquisition of knowledge. Not a few would also be stimulated by the rewards which they saw conferred on their fellow students, to go and nobly endeavour to deserve the same honours at no distant period, by giving fresh vigour George William Hewitt Fletcher to their studies, and by fanning the flame of honourable ambi-Burford Waring Gibsone tion for lasting distinction among men. The impetus thus Walter Battershell Gill, M.B. given to climb the hill of science among the students of the different colleges and institutions of the University, we desire to communicate to our students in the Popular Educator, and we hope that the perusal of the following list of those who reaped the honours of this day will have the desired effect. We shall continue to watch the proceedings of the University, and we shall rejoice to find the names of many of our selftaught and other students, in the lists of the honourable and honoured men of future presentations at the University. The registrar having read a short report, the presentation for degrees then took place. The students were generally presented by one of the professors of the college or institution to which they belonged. The registrar having read out the name of the candidate to be presented, the gentleman appointed to present him addressed the chancellor in these words:-"My lords and gentlemen,-in the name of College, I present to you [A. B.] to be admitted to the degree of Each candidate, after presentation, immediately proceeded to the table on the left of the chancellor, and there inscribed his name in the register. The order for presentation for degrees was as follows: William Frederick Teevan Frederick Alfred Johnson cellor, the presentation of Scholars, Exhibitioners, Medalists, The Graduates having been severally presented to the Chanand Prizemen then took place. The names of all Candidates who obtained Honours in the course of the past year were read; but those Gentlemen only who obtained Scholarships, Exhibitions, Medals and Prizes were presented to the Chancellor in the following order : PRIZEMEN. Robert Braithwaite Batty, M.A. University College, Medal in Ma- Robert Ainslie Redford, M.A. Spring Hill College, Medal in Thomas King Hornidge, M.B. St. George Hospital, Scholarship in Surgery. Joseph Lister, M.B., University College, Scholarship and Medal Thomas Morley Rooke, M.B. Guy's Hospital, Scholarship and Frederick William Pavy, M.B. Guy's Hospital, Medal in Medicine. matics. Frederick William Farrar, B.A. King's College, Scholarship in Henry Enfield Roscoe, B.A. University College, Prize in Chemistry. The following have passed M.B. First Examination :Henry Power, St. Bartholomew's Hospital, Exhibition and Medal in Anatomy and Physiology. John Zachariah Laurence, University College, Medal in Anatomy George Buchanan, B.A., University College, Medal in Chemistry. Henry Power, St. Bartholomew's Hospital, Medal in Botany. ANSWERS TO CORRESPONDENTS. H. W. K. informs us that Alison's "History of Europe" is being issued in weekly numbers at three-halfpence each. Every separate subject in a letter should have a separate paragraph. His poetry and handwriting will both bear very considerable improvement.-W. BOOTH, we cannot insert his poetry verbatim. R. N. wishes to become a good speaker; this is right; but we can give him no advice such as he wants from us unless we know his aim or object in being a good speaker. There are various sorts of eloquence; which of them does he mean to choose? There are-1. The eloquence of the Bar; 2. The eloquence of the Pulpit; 3°. The eloquence of the Senate; 4°. The eloquence of Democratic Asseinblies; 5°. The eloquence of Debating Societies; 6°. The eloquence suited to street mobs; and 79. (according to his account). The eloquence of Codger's Hall! We have some notion of all the preceding eloquences, except the last. Who Codger is, or what his hall is for, we don't know; but we hope that, as is his name, so is not the man. R. N. has mentioned the names of Burke, Canning, and Brougham, among the modern orators, and those of Demosthenes and Cicero among the ancients: such names are reckoned towers of strength among men but we know not whether any of these orators attended a Codger's Hall, or anything approaching thereunto. We have heard that Demosthenes studied in the great hall of nature, under the glorious canopy of heaven, and that his first auditors were the mighty billows of the deep; "Wielded at will, the fierce democracy, 'twas thus that he And fulmin'd over Greece, to Macedon both means the same thing.-A WORKING MAN (Leeds) who wants the so- IMPORTANT ERRATUM. Vol. II. p. 355, col. 2, line 35, dele and c. LITERARY NOTICES. EXTENSION OF JOHN CASSELL'S SYSTEM OF BY THE PUBLICATION OF VALUABLE DICTIONARIES. H. T. B. (Hoxton): Hebrew? yes. Grammar? Bagster's, Paternosterrow.-T. CARTER (Barking): His idea of good French authors is in contemplation.-E. T.: Genesis, ch. vii., v. 19; 2nd Peter, ch. iii., v. 5—13. -MAESTRO: The expression 141788.801, is an exponential one, 1-7 being the index or exponent, and signifying that the number 14 is to be raised to the power which it denotes, that is, to the 1% power or the power. This would be done arithmetically by raising the number 14 to the 17th power, and extracting the 10th root! But the operation is easily per-readers and students of THE POPULAR EDUCATOR, JOHN CASSELL has just formed by a table of logarithms, thus:-Take the logarithm of the number 14, which is 1146128, and multiply it by the index 17; the product will be 1-9481176; look for this product among the logarithms in the table, and you will find that the number corresponding to the logarithm nearest to it, is 88-801; and so of other examples. To meet the want of masses of the People, and the wishes of the numerous commenced publishing a Series of the most valuable and useful Dictionaries in different Languages, upon a plan which will place them within the reach of the humblest individual. The publication of THE POPULAR EDUCATOR, and the wonderful success which has accompanied it from its first appearance, twelve months since, has led a vast number of its subscribers to study the Latin, French, and German Languages. As a natural and necessary result, a demand has immediately been made for Dictionaries in each of these Languages at a moderate price. But where were they to be obtained? The high prices at which good Dictionaries of these Languages are published was found to be an insuperable bar to progress in learning, and especially to such a desirable progress as would give the students of the Lessons in THE POPULAR EDUCATOR the power of speaking and writing these different Languages. It is universally acknowledged that the Lessons and Vocabularies of the Latin, French, and German tongues are unrivalled for simplicity and clearstudent cannot be limited to these; he must be furnished with a copious Dictionary of the Language he desires to master, and which the Lessons in THE POPULAR EDUCATOR have taught him he is able to master, if he has only the suitable instrumentality. As it is the high price of Distionaries which has hitherto prevented the march of improvement thus happily begun, JOHN CASSELL has determined to publish a good and useful Dictionary of each Language, on a plan that will enable the student to obtain it upon terms equally easy with those on which he has obtained the Lessons themselves. The Dictionaries will be published in Weekly Numbers, Threepence each, and in Monthly Parts, One Shilling each. They will be printed in demy octavo; each NUMBER will contain thirty-two pages, and each PART one hundred and twenty-eight pages. Though these Dictionaries are thus published in periodical portions, to suit the convenience of a majority of purchasers, it will be found that the entire volume will cost no more than if it were purchased at once. J. RUSSELL (Kingscavil): We must really drop the multiplying money by money question, notwithstanding his ingenuity and rhymes.-E. Č.: See our Literary Notices.-E. J. R.: The annotations on the glass objects exhibited in Class 24, in the Illustrated Catalogue of the Great Exhibition, will most likely answer your purpose, especially those by W. C. A.-J. E. G. (Hastings) and J. M. E.: Thanks.-F. F. (Plymouth): Of Josephus we have seen only two translations, L'Estrange's and Whiston's; of these the latter is the best. Liddell and Scott's Greek Lexicon, price two guineas.-T. HIGGINBOTTOM (Salford): The answer to the query about the 100 ships, which he sent us is wrong. The question worked by the rule for finding the sum of any number of terms in Geometrical Progression (See Cassell'sness, as well as for the extent of information they convey; but the ardent Arithmetic, p. 142), is found to be £1,320,469,375,237,738,959,892,399,172 58. 3 d., as sent to us by S. H. J. R. (Paisley), and NIDUS ELEPHANTIS (Falkirk).-FR. WHITE (Cambridge): In the answer to the questions in Cassell's Arithmetic, p. 36, Ans. 3, the space should be between 6 and 1, instead of between 1 and 6.-AN ANXIOUS INQUIRER (Bridgewater): This little boy must wait till he grows a man, before he assumes so much importance as to request a young lady's name and residence.-FACTORY OPERATIVE (King's Cross): Such questions as he has proposed will come soon under the head of Lessons in Algebra.-CONSTANT SUBSCRIBER (Tunstead) asks too much; we cannot be supposed to have time or space to give translations of long passages out of Caesar. Besides, there are many translations for the use of schools easily to be had.-UN ETUDIANT (Southwark): His inquiry is answered in a previous number.-H. J. KEATING: Every vowel that comes before two consonants, like the first u in summus, is pronounced or reckoned long.-Mare instead of mari is an error; the other matters are quite right.-C. H. F. (Petersfield): We really cannot give advice in the matter to which he refers.-E. W. HARRIS (Bristol) must not be in a hurry, but allow nature to take its course. Lessons in English by all means, and Geometry if he has time.-F. GOODHEART (Smithfield) will find better lines than his own on the same subject in "Young's Night Thoughts," a work well known, and universally admired.-A SUBSCRIBER (Paisley) whose name we cannot make out, has the merit of so completely puzzling us with his bad writing on some question in bookkeeping, that we cannot really answer him, although we are humbly of opinion that we know something of that art.-W. ELPHINSTONE (Alexandria): His algebraic exercises are very nearly correct.-J. MURPHY (Tramore): His note is not too polite certainly; but we shall give the wished for information immediately.-PHI LOMATHES: His question is a very curious one; we shall insert it when we can get an opportunity.-SCRUTATOR (Scarborough): We regret that we cannot give him exact information on the subject as to money matters; we think that he should matriculate in the University of London, whether he changes his profession or not; the latter is a grave consideration, and should not be attempted without great reflection and inquiry of those who are better able to give it than we are.-W. ROBERTS (Exeter) wishes to know who was the author of the papers in the Spectator signed R. TILSDEN (Broadstairs): His questions are really more curious than useful; as to the position of the Equator, were the whole of the water drained off the earth's surface; who can tell? As to the crown of Hanover ever reverting to England; we can't tell; but we hope that it never will, lest we should get embroiled in continental quarrels VOTRE ECOLIER (Bromley): See pp. 283, and 289 vol. II., for answers to his questions.-WEST QUAY (Greenock): How does he know that the casks of molasses found with their bung upwards in the vessels on landing have not had them downwards in the course of the voyage?-A. (Leeds) should study the 6d. Lessons for pronunciation in French; and the Popular Educator lessons for a knowledge of the language. Let your eye alone; to meddle with it is very dangerous.-E. COLLINS (Love Clough): As much again and twice as much, The first Dictionary which will be published will be that of French and English, and English and French, with a complete Treatise on French Pronunciation. This Dictionary will embrace a greater number of Scientific, Mythological, Geographical, and Historical Names than is to be found in any other Dictionary published in this country. The price of the work complete will be Eight Shillings and Sixpence, or twenty-six weekly Numbers, price Threepence, of thirty-two pages, or sixty-four columns. Covers for binding the volume, when completed, will be issued at 9d. The French department carefully edited by Professor De Lolme, and the English department by Professor Wallace and H. Bridgeman, Esq. The German Dictionary will shortly follow upon a similar plan of publication. Also the Latin Dictionary, which will be edited by Dr. Beard. Orders for the French Dictionary in Numbers ought to be immediately given CASSELL'S LESSONS IN FRENCH (from the "Popular Educator"), are just issued in a neat volume, price 2s. in stiff covers, or 23. 6d. neatly bound in cloth. The German Lessons (uniform with this volume) will follow in a few days. CASSELL'S EUCLID.-THE ELEMENTS OF GEOMETRY. Containing the First Six, and the Eleventh and Twelfth Books of Euclid. Edited by Professor Wallace, A.M., price ls. in stiff covers, or 1s. 6d. neat cloth. THE SELF AND CLASS EXAMINER IN EUCLID, containing the Enunciations of all the Propositions and Corollaries in Cassell's Edition, for the use of Colleges, Schools, and Private Students, is now ready, price 3d. CASSELL'S ELEMENTS OF ARITHMETIC (uniform with Cassell's EUCLID) is now ready, price ls. in stiff covers, or 1s. 6d. neat cloth. THE ANSWERS TO ALL THE QUESTIONS IN CASSELL'S ARITHMETIC, for the use of Private Students, and of Teachers and Professors who use this work in their classes, is just issued, price 3d. |