5. Deduce the equations on which the solution of questions connected with a single-acting engine depends. 6. In evaporating water, calculate the heat expended on internal and external work. 7. Calculate the heat utilised in a double-acting engine. 8. Show how to calculate the amount of injection-water required for condensation in the steam engine. 9. Calculate the temperature produced by the combustion of fuel. 10. Mention any experiments to illustrate the conduction and radiation of heat. CHEMISTRY AND MINERALOGY. DR. APJOHN. 1. There are two distinct compounds of oxygen and hydrogen. Mention the names and write the formula of each. 2. Write the formula of gaseous ammonia. State how you would prepare it, and the compounds which are formed when it is passed into a solution of nitric and into one of sulphuric acid. 3. Nitrogen gas may be extracted from ammonium hydrate by chlorine. Explain the reaction. 4. What is the formula of Oxalic Acid, and what change does it undergo when heated with oil of vitriol? 5. How is a solution of KHO made? What are the impurities which it generally contains, and how would you demonstrate their presence? Mention also its chief use in mineral analysis. 6. How is chlorine usually insulated, and how applied in the preparation of potassium chlorate? 7. Give the action of sulphuric acid on fluor spar, and the action of hydrofluoric acid on silex. 8. There are three phosphoric acids very closely related. What is the formula and atomicity of each, and how may they be distinguished from each other? 9. Give a classification of elementary bodies grouped according to their atomicities. 10. Mention the leading gases which compose the atmosphere, and the proportions in which they are present by volume and by weight. Also a method of making its analysis. 11. What are the chief physical characters employed in distinguishing minerals from each other? 12. Enumerate the crystalline systems, explaining how they differ, and specifying those which are uniaxal and those which are biaxal. 13. Give Dana's division of the silicates. 14. What are the elements of a crystal, and what the data necessary for calculating them in the different systems? 15. Give Rose's notation, and that also of Dana, for a hexangular Dodecahedron of the second class, and of a octahedron in the fourth system. 16. A mineral analyzed by Hisinger was found to consist of— What is its formula, its name, and its crystalline system? N. B. When the written questions were disposed of, twenty mineral specimens were presented to the students, the formulæ, names, and crystalline systems of which they were required to give. GEOLOGY AND MINING. DR. HAUGHTON. 1. Write down the formations included by modern geologists under the old names : (1). Primary. (2). Secondary. 2. Describe some of the more remarkable Fishes of the Old Red Sandstone Period; and show in what respects they differed from modern Fishes. 3. Discuss the question of the probable climate of the Carboniferous Period; and that of the probable mode of formation of the Coal Beds. 4. Name the most important fossil Mammals of South America and Australia. 5. What were the zoological affinities of the genera : (a). Zeuglodon. 6. State the physical and blowpipe characters of Carbonate of Baryta, and Carbonate of Strontia. 9. There are three modes of working coal on the Long Wall System. Describe them generally, with a rough plan. 10. Name the Ores of Copper, distinguishing them into : (a). Primary Ores, (b). Secondary Ores, and describe the principle of classification. 11. Define the following terms used in metallic mining : 1. If it be granted that the direction of the resultant is the diagonal of the parallelogram of forces, prove that its magnitude will be represented by the length of the diagonal. 2. Prove that the moment of the resultant of two forces with regard to any point in their plane is equal to the sum or difference of the moments of the components, and show how to distinguish the two cases. 3. If there be a system of parallel lines, determine that one round which the moment of inertia of a given system of masses is the least. 4. If a system of forces in a given plane be in equilibrium, prove that the mechanical conditions are three, viz. : 5. Write down the differential equation of the linear motion of a point, and also the corresponding ones for the motion of a solid body round a fixed axis. 6. From the general equation of the motion of a material particle, investigate the motion of a heavy particle projected at an angle of elevation e, and with a velocity V. 7. Define the Centre of Pressure, and find its position in the case of a triangle immersed, with its plane vertical, and its base horizontal, to a given depth below the surface of the fluid. 8. Find the value of the standard atmospheric pressure in terms of kilograms per square metre from the standard height of the Barometer and the sp. gr. of mercury. 9. A body, whose weight is 1000 lbs., rests on an inclined plane whose inclination is 30°, what amount of horizontal force will be required to maintain it in its position if there be no friction? What amount if the coefficient of friction be? 10. Prove that the time of describing the chords descending from the uppermost end of the diameter of a vertical circle is constant. How is this theorem modified if friction be taken into account? MIDDLE CLASS. MR. LESLIE. 1. Calculate the relative density of steam. 2. From what equation is the temperature of steam found when the pressure is given? 3. Write the formulæ for the latent and total heat of steam. 4. Find the quantity of water necessary to condense steam. 5. Calculate the evaporating power of fuel. 6. Give any method of finding the mechanical equivalent of heat. 7. Find the mechanical effect due to the evaporation of water. 8. Assuming Boyle's law, show how to find the work done by the expansion of steam. 9. Show how to calculate work done by Simpson's rule. 10. Calculate the work by Navier's formula. DR. DOWNING. 1. Compute the number of cubic yards in an embankment for a reservoir with these dimensions :: End heights, o and 16; 16 and 24; 24 and 48; 48 and o. The lengths between these several pairs of heights being respectively, and in the above order, 330 feet, 400 feet, 600 feet, and 200 feet. Width on the top. 33 feet, and slopes, 24 to 1. Each part must be given separately in cubic yards, and the total. 2. Calculate the number of square yards of stone pitching in the slope exposed to the water; and the number of square yards in the soiling of the other, that is, the external slope. Each separate part must be given in square yards, and the total. 3. What two numbers are found in Bidder's Tables corresponding to the end heights, 25 and 50; and if the end heights were 30 and 60, how can the Tables be used to obtain the contents? 4. With a radius of 1260 feet, and a chain of 72 feet, calculate the offset at the chain end, starting from a point on a tangent 376 chains (100 feet); and if at any point a curve of contrary flexure had to be set out with either the same radius, or with the radius of 1400 feet, or again with 100 feet radius; give in each case the corresponding offsets. 5. Compute the weight which may be brought on a hollow cast iron column 12 inches external diameter, and 1 inch thick, the length being 17 feet. And give a sketch, showing how the ends, which are turned true, should be formed, the cap and base piece being separate castings. PRACTICAL CHEMISTRY. DR. TARLETON. I. Each of the three given solutions A, B, C contains a single salt; determine the acid, and the base in each of these salts. 2. One of two given substances D and E contains mercury: ascertain which. 3. The given substance F is a single salt: determine the acid and the base. 4. The given substance G contains either lead or silver: determine which metal is present. 2. The sides of a triangle are 49.872, 36.291, 28.385, respectively: calculate the magnitude of its least angle. 3. Find the distance between two places on the earth's surface, which are three degrees apart; assuming the diameter of the earth to be 7926 miles. 4. Find the differential coefficients of the expressions 5. Prove Maclaurin's theorem, and apply it to the expansion of log (1 + 2x). 6. Find the max. and min. values of sin x + sin 3x. 7. Find the values of the following integrals |