Calendar: 1848-1849 Page 261

APPLIED SCIENCES 39 18 If sensible gravity at tbe equator be 288 times that of the centrifugal force show that if the earth's angular velocity were increased 17 fold bodies would cease to have any weight 19 ball is projected with given velocity along the inside of hollow cylinder determine its path and rove that its vertical descents at each revolution will be as the numbers &c 20 Integrate III -Statu When given forces act on body having fixed axis show how to determine the moment of the friction of the axis and the work done by the friction in one revolution Having given the weight position of the centre of gravity radius of the wheels &c of four-wheeled railway carriage standing on level rails find what force applied horizontally at the highest point of one of the wheels will be just sufficient to move the carriage Determine the relations between χ and ν χ in the common catenary uniform chain is suspended between two points on the same level at given distance from each other and the tension at tbe lowest point is half that at the highest determine the length of the chain Find the equation between χ in the catenary of equal strength Find the radius of curvature at any point of the chain of chain bridge neglecting the weight of the suspension rods Show how to draw on paper the curve in which the chain of chain bridge hangs Show how to determine the law according to which the thickness of the chain must vary so that the chain bridge may be one of equal strength