Calendar: 1873-1874 Page 556

556 APPLIED SCIENCES The weight of window sash feet wide is lb each of the weights attached to the cords is lbs if one of the cords be broken find at what distance from the middle of the sash the hand must be placed to raise it with the least effort Three equal forces act along the sides of an isosceles triangle of which the gteatest angle is 120 find the magnitude and line of action of the force required to balance them Find the relation between the power and weight un given smooth inclined plane when the power is inclined at given angle to the lane and draws up the weight What additional power will be required to draw up the weight along rough plane Show at what inclination the power re- quired to draw up the weight is least Find the position of the centre of gravity of portion cut off from right-angled triangle by line parallel to the base and at given distance from it State and prove Guldin's properties with regard to the volume and surface of solid of revolution Hence find the volume of the frustrum of the right cone traced out by the revo- lution of the figure in Qu about the side perpendicular to its base The pitch of roof is 45 and every square foot of it weighs 15 lbs it is supported by rafters feet apart without tie-beam and the span is 30 feet find the direction and magni- tude of the resultant pressure on every foot of the length of the side walls If the roof in the last question be supported by brick walls 10 feet high find their thickness that they may not be overturned and find the equation to the line of resistance in the wall cubic foot of brickwork weighs 112 lbs Show that any system of forces acting on rigid body can always be reduced to resultant force and resultant couple in plane perpendicular to the direction of the force State and prove the properties of the "Central Axis 10 rod without weight but loaded at one end rests over fixed point and against smooth vertical wall Apply the prin- ciple of virtual velocities to find successively and independently