Calendar: 1865-1866 Page 540

542 APPLIED SCIENCES VII Department of tjje &pplte& gbct'ences iHatijtmattti The Mathematical Papers are the same in each case as those given for the Department of General Literature and Science MIDDLE SCHOLARSHIP -Jiatural $I tlogopi Find the distance of the centre of gravity of trapezium with two sides parallel from one of the parallel sides trapezium whose parallel sides are and feet and the other sides each equal to feet is placed with its base on an inclined plane find the elevation of the plane when the trapezium is just on the point of falling over Find the relation between the power and the weight on system of one fixed and one movable pulley with two strings each of which is attached to the weight the axes being rough neglecting the weights of the pulleys If the radius of each pulley be inches of the axes inches and sin φ 14 find the power required to raise 13 tons cwt 64 lbs Draw diagram of forces for the accompanying framework where the rafters AC and BC over which the weight is equally distributed are inclined at an angle of 30 to the horizon and are divided into three equal parts in the points and the tie beam being divided into three equal parts in Η and and into two equal parts in Show by this or any other method that the tension of CL is one-third of the whole weight of the roof What is meant by the limiting angle of resistance Explain how to find it between two given substances Find the relation between the power and the weight on rough inclined plane