FOR ADMISSION INTO THE ROYAL MILITARY ACADEMY AND THE ROYAL MILITARY COLLEGE FOR THE YEARS 1899-1908 EDITED BY E. J. BROOKSMITH, B.A., LL.M. = ST. JOHN'S COLLEGE, CAMBRIDGE; LATE INSTRUCTOR OF MATHEMATICS AT AND R. M. MILNE, M.A., LATE SCHOLAR JESUS COLLEGE, CAMBRIDGE; MACMILLAN AND CO., LIMITED 1909 COLLEGE JUN 15 1909 LIBRARY Bowditch fund TABLE OF CONSTANTS. I metre 100 cm. = 1000 mm. = 0.001 km. I yard = 3 ft. = 36 in. =0·9144 metre. I mile = 8 fur. = 320 po. = 1760 yds. I hectare = 100 ares = 10,000 sq. metres. I acre = 4 roods = 4840 sq. yds. = 0 ̊4047 hectare. I litre I c.dm. 100 cl. = 0.01 hl. = 0.001 c. metre. I gallon = 4 qt. = 8 pt. = 0.1606 c. ft. = 4'546 litres. = 32 pk. = 64 gal. I kilogram = 1000 g. =0'001 tonne. I quarter = 8 bush. I lb. = 16 oz. = 7000 grains = 453'6 grammes. I ton = 20 cwt. = 80 qr. =2240 lb. I litre of water weighs 1 kg. I c. ft. of water weighs 62.3 lb. A circle of radius has a circumference of length 2πr and has an area of 2 where = 3'1416. Base of natural logarithms is e = 2.7183. The acceleration of a falling body is 32.2 ft. per sec. per sec. or 981 cm. per sec. per sec. I kilowatt = 102 kilogram-metres per second. I horse-power = 550 footpounds per second. I atmosphere = 760 mm. of mercury = 103 kg. per sq. cm. = 147 lb. per sq. inch. GLASGOW PRINTED AT THE UNIVERSITY PRESS BY ROBERT MACLEHOSE AND CO. LTD. MATHEMATICAL EXAMINATION PAPERS I. Reduce to their simplest forms: ++, 22%, and 24-, and divide the product of these three expressions by 12+38-2. 2. A tradesman, having promised me 12 per cent. reduction from a bill for 16. 16s. 8d. takes off only 10 per cent. By what sum am I entitled to further diminish his bill? And how much per cent. is this of 3. Define the average of a set of numbers, and find the average of 213, 217, 199, 201, 208, 209, and 211. If the height of a number of men is measured; and the average of the first six is 5 ft. 5 in., of the next seven, 5 ft. 51⁄2 in., and of the next eleven, 5 ft. 4 in.; what is the average height of the whole number of men to the 4. Two trains start at the same time, one from Liverpool to Man- chester, and the other in the opposite direction, and running steadily |