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(re.) Give in square feet the area of a figure 800 ft. long, 60ft. wide at one end and 140 ft. wide at the other; and also the area in square feet of a triangle 200 ft. in the base and 300 ft. in the perpendicular.

Fourth Day.—Time : 9 a.m. to 12 noon. Subject 10. — A Knowledge of the Different Bocks where Gold, Silver, Tin, Copper, Zinc, Lead, and Antimony are found, and on the Formation of Lodes and Leads. What are the most commonly worked ores of the following metals : silver, copper, tin, manganese, tungsten, chromium, and antimony ? Give a short description of each, and mention where they are found in New Zealand, and the mode of their occurrence.

Subject 11. — A Knowledge of Arithmetic, and a Method of keeping Accounts. (ft.) The base of a triangle is 36ft., and the perpendicular 48ft. ; find the length of the third side. (b.) Find the cube root of 259694072. (o.) Multiply 86785432 by 70169. (d.) How many solid feet are there in a block of stone 6ft. 6in. long, 2ft. lin. broad, and lft. 3in. thick. (c.) If the wages of 6 persons for 21 weeks are £120, what wages would 14 persons make in 46 weeks at the same rate ? (/.) In a triangular piece of timber the base is 29in., the perpendicular 17|in., and the length 12ft.: how many solid feet are there contained?

Subject 12.—A Knoivledge of Part 111. of " The Mining Act, 1886." Oral examination.

" COAL-MINES ACT AMENDMENT ACT, 1890." Fiest-ceass Ceetipicates.—Fiest Day.—Time : 9 A.M. TO 12 NOON. I. — On the sinking of Shafts and Construction of Main Boadways, opening out a Mine, and the Division of a Mine into Districts. 1. What preliminary operations would you undertake in starting to sink a rectangular shaft? 2. After sinking through soft, water-bearing strata, describe your operations on reaching the solid rock if metal tubbing has been used. 3. In a shaft 200 fathoms deep, what thickness of metal tubbing would you use (1) at 50 fathoms, (2) at 150 fathoms ; and show by calculation how you arrive at these results ? 4. What size would you drive a stone drift 700 ft. long, lying at 1 in 4, which would be used as intake for air, and up which an output of 500 tons per day must be drawn ? Enumerate the considerations which would guide you (1) in very hard strata, (2) in soft strata. 5. Give sketch showing how you would lay off your levels and drawing-roads with 50 fathoms cover, dip lin 3, coal both to dip and rise. Give the widths and height you would drive them in an lift, seam of very soft coal. 6. Give two cases in which you would divide the mine under your charge into districts. Give an instance in which you would not. Explain your reasons fully. 7. Mark on sketch the size of shaft-pillars you would leave to protect a shaft 420 ft. deep, a 7ft. seam, and lying at 1 in 3 —(1) with a sound floor, (2) with 6ft. of soft fireclay pavement and a strong roof.

11.- — The various Methods adopted in securing Shafts and Workings in a Mine, showing the relative Advantage and Efficiency of each Class of Material used. 1. In a shaft 350 ft. deep, 14ft. by 6ft., with very soft strata for the first 150 ft., what sizes of lining, cover-pieces, and guides would you use? What kinds of timber, and show by sketch how you would secure the buntons, what form of joint you would have for guides, stating why. 2. What are the avantages of brick-lining compared with wood ? 3. In opening-out in a very soft seam sft. by sft. levels, what size and kind of timber would you use, and if the floor were also soft how would you proceed.? 1. Sketch how you would put up a 6in. by Bin. cap-piece, and give your reasons. 5. How would you work a 7ft. seam of coal with good roof and pavement? 6. What method would you adopt in working an 18ft. seam free from spontaneous combustion, and with a strong shale roof ? 7. In long-wall working, what is the first difficulty you have to contend with ? and in working a seam by that method with hard pavement, lft. 6in. coal, lft. shale, and 2ft. coal, and tough shale roof, explain how you would proceed, giving width of roadways, building, and walls. Where would you get your pack ? Would you break the wall-faces or keep them abreast, and why ?

Time : 2 p.m. to 5 p.m. lII. — -The Various Methods of Ventilation, and the Construction of Airways, so as to Produce a good Circulation of Fresh Air in any part of the Mine. 1. State what you know of the principles of natural ventilation. 2. If one of your return air-currents was of an explosive nature, what precautions would you adopt in leading it to upcast when ventilating by furnace ? How far from the upcast would yon place your furnace ?