7. Multiply together the four factors 9x2 + 2a2, 9x2 + 6ax + 2a2, 9x2 - 2α2, 9x2 - 6ax + 2a2. 8. Divide x12 + 2x + 1 by x3- 2x + 3x1 − 2x2 + 1. 10. Show that the difference of the reciprocals of two consecutive numbers is the reciprocal of their product. SECOND PAPER. GEOMETRY AND ALGEBRA. PROFESSOR BROMWICH; PROFESSOR GIBNEY. 1. The three sides of a triangle ABC are equal to those of a second triangle PQR, prove that the triangles are equal in all respects. D, S are the middle points of BC, QR, respectively prove that AD = PS. 2. KLM is a triangle in which the squares on KL, LM are together equal to the square on KM: prove that the angle L is a right angle. 3. Divide a given line XY at Z, so that the square on XZ is equal to the rectangle XY. YZ. 4. Show how to find the shortest and greatest distances from a given point to the circumference of a given circle. Draw two circles with a given centre to touch a given circle. 5. PQ is a chord of a circle, and PT is the tangent at P; X, Y are two other points on the circumference, on opposite sides of PQ. Prove that the angle TPQ is equal to one of the two angles PXQ, PYQ, and determine which. 6. Prove that the bisectors of the angles of a triangle meet in a point, and that this point is at the same distance from each side of the triangle. (x - 13) − § (7 − x) = 8 [% x − + (x + 1)], 8. Find x, y from 10. Find the length of the hypotenuse of a right-angled triangle, in which the longer of the remaining sides is 2 feet in length, and the shorter is 18 inches less than the hypotenuse. NATURAL PHILOSOPHY. SECTION A. PROFESSOR BERGIN. 1. A uniform straight rod 12 feet long, and weighing 10 lbs. has a weight of 6 lbs. resting on it at a point 3 feet from the centre of the rod. If the whole be suspended by a string, find the tension of the string and its point of attachment to the rod which is in equilibrium in a horizontal position. 2. A mass of 4 lbs. resting on a rough horizontal plane is just on the point of being moved by a horizontal force of 3 lbs. determine the coefficient of friction of the plane, and the magnitude of its total reaction on the mass. 3. Express in pounds the force which, acting on a ton, will give it an acceleration of 2 feet per second per second. 4. A mass of 3 lbs. is projected vertically upwards with a velocity of 100 feet per second: express in foot-pounds its kinetic and potential energies at the end of three seconds. 5. What is the mechanical advantage of (1) a lever, (2) a screw? SECTION B. MR. HENRY. 1. Describe how you would determine the specific gravity of (a) a piece of metal, (b) a liquid. 2. A bubble of air has a volume of 0·1 cubic inch at a depth of 18 inches in a tank of mercury: what will be its volume when it rises to the surface, the height of the mercury barometer being 30 inches ? 3. Describe and explain the action of an ordinary suction water-pump. 4. Explain why it is possible for the pressure on the bottom of a vessel containing water to be greater than, equal to, or less than the weight of the water according to the shape of the vessel. 5. How would you proceed in order to make an ordinary barometer? Draw attention to any precautions which would be necessary in the process. FIRST UNIVERSITY EXAMINATION. SUMMER, 1902. LATIN. FIRST PAPER. PROFESSOR MACMASTER. SECTION A. GRAMMAR. I. (a) Give two masculine nouns which end in -do (genitive dinis), and four feminine nouns which end in -us (genitive -us). (b) Set down the locative cases of the following words :— Carthago, domus, Gades, Tarentum, Thebae. (c) Distinguish in meaning between the following pairs of words:-conditus, condītus; morae, mōres; palus, pālus; queritur, quaeritur; refert, refert; vincet, vinciet. (d) Quote or form phrases to show the case-constructions which are used with the words-carere, nubere, instar, tenus, fretus, peritus. (e) Give the principal parts of the verbs from which come the italicised words that follow:-nox abstulit colorem : primo avulso ramo: comptae mansere comae: defixus lumina fraus innexa: res caligine mersas: quos amor peredit: morte peremptum: custode sepulto: ossa cado texit. (f) Set down sentences that will show the construction of dependent clauses after (1) caveo, (2) gaudeo, (3) vereor. (Venus brings Aeneas the armour forged by Vulcan.) Talibus affata est dictis seque obtulit ultro: SECTION B. I. Translate the following passages, and answer the questions appended : 1. Quid moror? Irrumpunt thalamo, comes additur una Hortator scelerum Aeolides. Di, talia Graiis Instaurate, pio si poenas ore reposco. Sed te qui vivum casus, age, fare vicissim, (a) What is the case of thalamo? Explain the meaning of the name Aeolides. Parse attulerint. What is remarkable in the syntax of adires? 2. Tum pater Anchises, lacrimis ingressus obortis; (b) Parse virum and praeterlabere. What place is meant by tumulum recentem? Who is meant by hunc, and what was his relation to Augustus ? 3. Insuetum per iter gelidas enavit ad Arctos, |