Calendar: 1857-1858 Page 405

APPLIED SCIENCES 407 broad and thick when its longest and shortest edges are inclined at 20 and 35 Draw the plan of the same solid when the planes of the faces and ends are inclined at 50 and 70 Draw the plan of three spheres of inches radii vesting on the horizontal plane and in contact and show by its trace plane tangential to all three VI- JJractttal ffltcfyanicS When beam without weight is supported on props at its extremities and loaded with given weight at its centre find the moment of the strain Show how to take into account the weight of thl beam What weight suspended from the centre of beam of wood would break the beam resting on supports at distance of 20 feet and having sectional area 13 inches deep and 10 broad Here 100 What is the strongest form of cast-iron beam and why An elastic string is hung at one end and supports given weight how much will it stretch Find the tension of the tie beam in an isosceles roof Explain the theory of the arch and show how friction assists in maintaining equilibrium Show how an arch may fail under load at one point Find the equation to the catenary 10 Prove that the radius of curvature at any point is equal to the normal and hence shew how to draw the curve