Calendar: 1884-1885 Page 632

626 GENERAL LITERATURE AND SCIENCE The shadows of two vertical wails at right angles and which are in height are observed to be and η in breadth If be the altitude of the sun shew that cot2 m2 ri2 Prove that the area common to two circles of radii ν ψ that intersect at right angles is v2 V1V2 iW v22 tarl ""12 Enunciate and prove De Moivre's Theorem V2 If cos ν sin prove that cos β ke Is it necessary to suppose that θ is measured in circular measure 10 Sum the series cos cos β cos 2β cos η ל cos cc cos β cos 2β -1 cos מ sin 2$ sin 40 sin 60 to infinity 11 Twelve forces in act at point at successive angles of 30 find their resultant Six forces in act along the sides of regular hexagon find vheir resultant 12 What is the horse-power of steam-gun that could project 45 six-pound shots in minute with velocity of 11 000 feet per second III -gijebra &c Multiply Ό123456789 by 0987654321 to places of decimals Find within 10 per cent the mass of the earth in tons being given that it is sphere of five times the density of water cubic foot of which weighs 1000 ounces Find multiplier to convert speed of miles per hour into feet per second If twice the number of telegraph posts