4. Describe Acetic Acid as regards its mode of formation, constitutional relation to Alcohol, properties, and the principal salts which it forms, (Acetates). How is Ethyl Acetate prepared? 5. What is the chemical constitution of Chloroform? From what materials is it usually prepared? Describe the process, and explain in a general manner the probable re-actions that take place, as suggested by your knowledge of the chemical affinities of the elements or radicals involved. 6. Compare the chemical compositions of tallow, common soap, glycerine, palmitine, nitroglycerine, dynamite. PRACTICAL CHEMISTRY-ADVANCED COURSE. TIME: THREE HOURS. 1. Find the specific gravity of the Water sample A (Mineral Water), and describe the operation fully, noticing every precaution necessary to ensure accuracy. Give results obtained, with any requisite calculations, including deducted weight of bottle, (a previously unweighed bottle without counterpoise to be used). 2. Describe in detail the ordinary method of analysis of an Iron Ore, with necessary calculations. Find by analysis the amount of metallic iron in the sample B. State the several processes to which you have subjected it, and the results obtained. PRACTICAL CHEMISTRY-ELEMENTARY COURSE. TIME: THREE HOURS. 1. Find (1) one Acid, and (2) one Base in each of the Solutions, numbered,, &c., to.. x 3T, or in as many of them as you can 2. Write out carefully the results of your determinations. In any case of failure, or uncertainty, point out probable or possible cause. Standing of candidates will be calculated from number of accurate determinations, minus number of erroneous ones,-due value being allowed for explanations given under question 2. Examiner BOTANY. PROFESSOR LAWSON. APRIL 9TH.-10 A. M. TO 1 P. M. Five questions only to be answered. 1. Give a general description of a vitally active Vegetable Cell, noticing particularly (a) the structure, nature and functions of its protoplasm, (b) the Cell Wall, its composition, special modifications, lignification and mineralization, (c) plastids, (d) protein granules, (e) starch, (ƒ) crystals. 2. Compare, as regards their form and structure, (a) parenchyma cells, (b) epidermal cells with their trichomes and stomata, (c) cork cells, (d) wood cells, (e) spiral and dotted vessels or ducts, (f) bast cells, (g) cribrose cells, (h) latex cells, -and classify them. 3. Give a description of the modes of arrangement of the several tissue elements into tissues, of the tissues into systems, and the systems into organs. 4. Give a detailed account of the Circulation of Protoplasm in cells, Rotation, Amoeboid movement, relations of protoplasmic movements to heat (giving optimum, maximum and minimum temperatures), continuity of protoplasm. 5. Relations of the Plant to the soil, absorption, ash constituents and their offices; transfer of water through the plant; compare transpiration and evaporation, and state effects of the former upon the plant, the air, and the soil. 6. Describe fully the process of Assimilation, or appropriation of carbon by the plant, describe the assimilating system of the plant, noticing fully the essential constituent of the assimilative cells, the raw materials required for assimilation, effects of light. Briefly, appropriation of Nitrogen by the plant. 7. Transmutation or changes of organic matter in the plant. Respiration. Classify principal organic products of the plant. 8. Give a sketch of the grouping or classification of plants into the larger groups, distinguished by the absence or presence of true seeds, the nature of the embryo, structure of the stem, venation of leaves, number of parts in the floral verticil, position and mutual relations as regards adhesion or separation of the calyx, stamens, petals and ovary, the presence of a spadix, and the texture of the floral envelopes (whether petaloid or glumaceous). 9. Give a brief account of each of the following Natural Orders, pointing out the most important characters by which they are distinguished:-Cruciferæ, Umbelliferæ, Leguminosa, Compositæ, Coni feræ. 10. Give an account of each of the following orders, with examples, and point out their essential distinctive characters :--Liliaceæ, Amaryllidaceæ, Trilliaceæ, Araceæ, Glumiferæ. = 1. Either of the following Problems. (1) Given cos (AC) cos B cos (A-B+C): to prove the tangents of A, B and C in Harmonical Progression. Or (2) given that the sines of A, B, C are in Arith metical Progression, to prove that tan A. P. 2. Given sin A B C tan , " 2 tan are also in 2 3. A rectangular field is twice as long as it is broad, and the distances of a tree in it from three corners are a, b, c respectively. Find an equation for determining the sides. 4. Take an exponential expression for sin 0, and hence express sin" in a series of descending multiples of 0. when n is even. 5. Resolve x2n - 2x" cos 0+1=0 into Quadratic factors, and apply the result to decompose similarly x2n - 2a "xn cos 0+a2n, when = 6. From B, the end of the diameter of a circle, measure off n arcs, BC, CD, DE, &c., all equal to each other, and from C, D, E, &c., draw chords to the other end of the diameter: then, if the first chord be in summing to n terms the series (cos 0+√−1 sin 0) + (cos 0 + √ − 1 sin 0)2+(cos +√−1 sin 0)3+ &c. 8. Deduce, from your knowledge of the theory of Equations, stating any objections if you have them, that = (1-402) (1 of the calculus, that 1 Φ tan = 4 2 π2-02 + 32 π2-02 + &c. 9. Given the latitude of the place and the sun's altitude and declination to find the hour of the day (solar time). : 10. If ax2+ bxy+cy2 = 1 be cut by the line mx + ny=1: shew the meaning of ax2 + bxy +cz2 — (mx + ny)2=0: invent a problem which this equation would enable you to solve. Also adapt the method to the general equation, ax2 + bxy + cy2+ dx + ey+j=0. 11. Jf a = 0, B = 0, y = 0 be the equations to the sides of the triangle ABC, shew that the equation to the line joining the centres of the inscribed and circumscribed circles is, a (cos B cos C)+B (cos C -cos A)+y (cos A − cos B) = 0. - 12. Investigate the condition that the lines, lu+mv + nw = 0, l'u + m'v + n'w =0 may be at right angles to each other. II. ANALYTICAL GEOMETRY AND CALCULUS. APRIL 17.-3 TO 6 P. M. 1. Find the polar equation to the line joining the points whose polar co-ordinates are (r, 0) and (r¡¡, 0). What does the equation become when one of these points is the origin? and what is the condition that the two points given and the third point (rg, 0g) may be in the same straight line? 2. Deduce the equation to the tangent of the ellipse or hyperbola in terms of the angle it makes with the axis of x from considering the ultimate position of the secant y = mx + c. 3. In either of the same curves, prove that the rectangle of the perpendiculars on the tangent drawn from the foci is equal to the square of the minor or conjugate axis. 4. Chords are drawn through the focus of an ellipse at right х 5. Explain the "eccentric angle" in the case of the ellipse: and y prove that if a be the eccentric angle cos a + 1/1/ sin a1 is the equation to the tangent to the ellipse. α 6. If any straight line be drawn cutting a hyperbola and its asymptotes, the intercepts on it between the asymptotes and the curve are equal. Prove this simply by drawing a tangent to the curve parallel to the line. 7. If in the reduction of the general equation, ax2+ bxy +cy2+ &c. = 0, it turn out that b2-4ac, by what steps do you proceed to the inference that tho locus is a parabola? A 8. Shew by considering the points at which the escribed circle of a triangle, opposite angle A, touches the sides, that cos Va + sin B C 2 √B + sin 2 √7=0 is the equation of this circle: a=0, B=0, y=0 being the equations to the sides. 9. Lines are drawn from the vertex of a parabola making angles a and ẞ with the axis, and meeting the curve in P and P. Prove that PP, is divided by the axis in the inverse ratio of the tangents of these angles. 10. Shew that McLaurin's Theorem for the expansion of f(x) is only a case of Taylor's Theorem. 11. What are the circumstances in which Taylor's Theorem is said to "fail"? Taylor's Theorem needs Cox's or Lagrange's to to complete it and what is the principle on which Cox's demonstration depends? III. DIFFERENTIAL AND INTEGRAL CALCULUS. APRIL 19.-10 A. M. To 1 P. M. 1. An ellipse is made to revolve (1) round its major axis: (2) round its minor axis. Cut the greatest cylinder out of each of the solids so formed, the axis of the cylinder coinciding in each case with the axis of revolution, and compare their volumes. 2. If v and u be each a function of x, prove that dn-1 + &c., after the analogy of the binomial theorem. (Leibnitz's Theorem.) 2 d2 u -x du 3. If u=(sin1x) prove (1-22) dx2 - dx 5. Shew that if a straight line cut two axes of reference in such a manner that the product of the intercepts of them is constant, its envelope is a hyperbola. 5. Write the tests for concavity and convexity of a curve. (1) in rectangular co-ordinates, (2) in polar co-ordinates; and deduce from the expression for Radius of Curvature, that in general at a point of inflexion an infinitesmal portion of the curve is a straight line. 6. If r0a be the equation to a curve, shew that its polar subtangent is constant; and if r2 a2 cos 20, prove r = a2p, where p is the perpendicular from the pole on the tangent. 7. Given the curve y"= (x-α) √x b; if ab there is a conjugate point: find if there are asymptotes. 8. Shew methods of integrating any two of the following expres sions : |