(b) "the hotë fire"-what concord, now disused, do these words illustrate ? (c) What change do you perceive to have taken place in the pronunciation of the words science and colour? Is there any rule for this alteration of accent, and can you give other examples of it? (d) Analyse the last four lines. (e) Parse and explain the words in italics. Geography.-1. Give notes of a lesson on "The United States" under these heads. (a) Boundaries and extent; (b) mountains; (c) rivers; (d) history; (e) constitution; (f) trade manufactures and great towns. Illustrate by a map. 2. Compare the shape, size, and general character of the Atlantic and Pacific Oceans. History.-1. What explanation would you suggest of the fact that England has not had a second sovereign named either Stephen or John ? 2. How did we acquire the Cape of Good Hope? Trace the progress of British dominion in South Africa. 3. When was publication of debates in the House of Commons first tolerated? What part was taken by the City of London in obtaining that toleration ? Composition.-Write a short essay on Light and its uses. Euclid.-1. Draw a straight line from a given point in a side of a parallelogram which shall bisect the parallelogram. 2. If there be two straight lines, one of which is divided into any number of parts, the rectangle contained by the two straight lines is equal to the rectangles contained by the undivided line, and the several parts of the divided line. What is the corresponding formula in Algebra ? 3. If a straight line be divided into two equal parts and also into two unequal parts, the squares on the two unequal parts are together double of the square on half the line, and of the square on the line between the points of section. 3. A man was employed on the condition that for every day he worked he should receive 3s. 6d., but for every day he played he should forfeit 2s. 6d.; at the end of forty days he received £4. How many days did he work? Mensuration.-1. The sum of the sides of an isosceles triangle is 306 feet, and each of the equal sides is five-eighths of the third side; find its area. 2. The sides of a right-angled triangle are 27 and 43 feet; find the area of the circle described on the hypotenuse as diameter. ANSWERS. CANDIDATES.-Males: 1. 3s. 6d. 2. £38 7s. 6d. to each question. 3. £1,861 11s. 3 d. 4. 12,800 people. 5. £3 1s. 10 d. Females: 1. £24 15s., £39 11s. 2d., £139 Os. 11 d., £651 5s. 10d., £12 16s. 8d.; total, £867 9s. 7 d. 2. £353,094 18s. 9 d. 3. £114,417 17s. 9 d. 4. £387 7s. 101d. FIRST YEAR.-Males: 1. Sum = 41261989, difference = ·32211484. 2.2.4. 3. .0472279+. 4. 99. 5. 031134259 of a day every four years. Females: 1. 4s. 4d. 2. 9d. 3. 8 men. 4. 1818 feet. SECOND YEAR.-Males: 1. £398 2s. 6d. 2. He has gained £3 7s. 6d. 3. 5s. 10 d. 4. £1 2s. 6d. 5. £3 6s. 8d. Females: 1. 2191. 2. T. 3. 12. 4. left. 672 Euclid.-1. The converse is that if the three angles in the one triangle be equal to the three angles in the other, each to each, then the triangles shall be equal. Not true. Take any point E within AE and BF are greater than CE and DE are greater than . twice the sum of AE, BE, 2. Draw any quadrilateral figure ABCD. the circle, and join third angles of figure. AB; BE and CE are greater than BC; DC; DE and AE are greater than DA. CE, and DE is greater than sum of AB, BC, CD, DA. .. sum of AE, BE, CE, and DE is greater than half the sum of AB, Similarly if E be taken outside the figure. THIRD YEAR.-Males: 1. £2,364 2s. 1d. 2. 1s. 10 d. B, £126; C, £90. 4. 16s. 5. £7 12s. 6d. 394. 3. 15 35 miles on each of the first three days. 4. 20 BC, CD, DA. 3. A, £210; Females: 1. 00021. 2. Euclid.-1. Let AC and CD be parallel to EF, FG. Then AB, BD, are parallel to EH, HG. Draw OP, cutting the figures in K, L, M, N. .. CD and EH are parallel to FG, and AB to CD; the angles OKH, KLB, LMD, and MNG are all equal; and OKH being equal to KLB, EH is parallel to AB. Similarly BD is parallel to HG. 2. Euclid I. 47. Algebra.-2. Let a and b be the quantities, d their G.C.M.; and let a = pd, b = qd, so that P and q will have no common factor. Then the least quantity which contains p and q = pq, and the least quantity which contains pd and qd: pqd, L.C.M. of a and b. But pqd = pd × qd — axb = d = d 3. 2. 1,520 tons. Females: 1. 4 FOURTH YEAR.-Males: 1. Loss of 61 per cent. 528 days. 4. £6,947 18s. 4d. 5. £1 11s. 4 d. years. 2. 500 reams. 3. £243 11s. 6d. 4. 10 per cent. = Euclid.-1. Let ABCD be parallelogram, and E a point in one side. From D cut off DF = BE. Then AF EC. Join E, F. EF bisects the parallelogram. AF is equal and parallel to EC, therefore AE is equal and parallel to FC, and triangle AEF CEF. And triangle ABE = DFC, on equal bases and between the same parallels. Wherefore ABEF= DCEF, and EF bisects ABCD. 2. Let a = one line, b = the other, and let a be divided into parts m, n, p. Then ab = bm+bn+bp. Algebra.-1.2-4. 2. x = 109, y=107; x=, or -43. 3. 30 days. Mensuration.-1. 3,468 square feet. 2. 2024 72047+ square feet. REVIEWS. MAJOR'S GRADUATED EXERCISES IN ARITHMETIC, 2s. 6d.— This book should be in the hands of every teacher and student of arithmetic, containing as it does over 2100 graduated problems, given at the following examinations:-Pupil Teacher, Queen's Scholarship, Certificate, University Local Examinations, Civil Service, London Univeraity Matriculation, &c. It is conveniently divided into three parts: Part I. containing 981 exercises on simple and compound rules, Practice, and Proportion; Part II. furnishes 456 exercises on Fractions (vulgar and decimal); Part III. 688 exercises on Interest (simple and compound), Discount, Stocks, &c. I find it an invaluable help in the preparation of my large classes of P.T.'s and Candidates for Queen's Scholarship, Certificate Examinations, &c. MAJOR'S PUPIL TEACHERS' GEOGRAPHY (America & Oceans), ls. -We have in this little book 90 pages of valuable information. It will be found especially useful to pupil teachers, there being over 40 pages of matter on the Oceans, written in an intelligent, scient fic manner, and containing the most recent researches of Dr. Carpenter and expedition of H. M.S. Challenger. This alone should recommend it to every pupil teacher, for the ordinary geographical text-books are singularly deficient in information on this subject. An index of contents would improve it. MAJOR'S KEY TO PUPIL TEACHERS' YEAR BOOK IV., 1s.-In the key to Book IV. we have the exercises in arithmetic and algebra carefully worked out in a clear and concise form. It will be found a great boon to any student who cannot obtain the services of an instructor in these subjects. MAJOR'S PUPIL TEACHERS' YEAR BOOK IV., 2s. 6d.—As its name implies, this book embraces all the subjects required by pupil teachers for this year of apprenticeship. It contains much valuable information, and the questions already given at various examinations which it contains will be found very useful. Of necessity the style of writing is very concise, and occasionally a little dry. MR. WATKINS, P.T. Instructor, Leicester School Board. MAJOR'S PROBLEMS IN ARITHMETIC, in Six Standards.—Well calculated to make arithmetic what it ought to be a logical training for the schoolboy mind. MAJOR'S MUSIC FOR SCHOOLS, 3d., contains in a emall compass and at a small price the essentials of the "old notation." With copious vocal exercises to go with it, the book would prove quite enough for any elementary examination. MAJOR'S CROWN DRAWING BOOKS, 2d. each, in seven books, are well graduated. The examples are elegantly drawn, and the course must be a capital preparation for South Kensington candidates. MAJOR'S CROWN READERS, 6d., 8d., 18., 1s. 4d., ls. 6d., 2s., in a preface claim ten grounds for preference, and, after going through three of the books, I think the claim well sustained. The series is strongly bound, well printed and illustrated, and contains an unusual number of new extracts. Considerable aid is given in teaching spelling by well selected columns of words. The subject matter is dlversified, and a good proportion of it affords scope for intelligent, supplementary oral teaching. I can cordially commend the "Crown Readers" to practical teachers. WILLIAM HUGH, High Pavement Schools, Nottingham. 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