Calendar: 1899-1900 Page 777

FACULTY OF SCIENCE י CXXV ABCD is quadrilateral In the diagonal AC is taken any point and through it is drawn EF parallel to BD meeting AD AB respectively in Ε and D0 CE cut at and BO CF at If AG AH meet CD CB respectively in Κ and prove that KL is parallel to EF 13 If straight line is perpendicular to two straight lines it meets in plane prove that it is perpendicular to the plane piece of straight wire is bent into three portions each of the outer portions being twice the middle portion and at right angles to the plane containing the other two Prove that the distance between the extremities of the wire is three times the middle portion 14 Name and define the regular solids Prove that the section of regular octahedron by plane parallel to one of its faces is hexagon and prove that the regular hexagon so formed is half as large again as face of the octahedron SECOND AND THIRD YEARS Explain how the work done by force can be conveni- ently represented geometrically heavy chain of given length is suspended from one end which is fastened to pulley find the work required to coil up the first half of the ohain on the pulley and show that it equals three times the work required to coil up the second half Describe the principle of the steam indicator and explain the use of the steam indicator diagram drawbridge AB whose breadth is 12 feet and weighing half ton is kept in horizontal position by chain 20 feet long made fast to and to point in wall vertically above Β find the tension of the chain In roof weighing 30 lbs per square foot the rafters are feet apart the pitch is 60 and the side walls 40 feet apart find the vertical and horizontal components of the thrust along each rafter and the direction of the pres- sure of the roof on the side walls