Calendar: 1850-1851 Page 322

318 APPLIED SCIENCES Under what circumstances did the Emperor Frederic II engage in crusade Explain his position in reference to the popes What was his reputation What treaty did he conclude with the Saracens Essay The character and history of Lewis IX IV Department of tjje gtpplteii Sciences SENIOR SCHOLARSHIP In the case of the common catenary explain the geo- metrical construction for exhibiting the relations between the forces which keep the chain at rest Show that the tension at any point is cos θ Prove that y- ea η and ea ea Find the radius of curvature at any point of the catenary in terms of Θ and explain the mode of describing the curve on paper by means of the radius of curvature chain weighing 10 000 lbs and 20 feet long is suspended between two points on the same level 21 feet apart find the tension at the lowest point and how far the lowest point is vertically below the points of support Find the radius of curvature at any point of the chain bridge with uniform chain Having given the height of the piers and the length and weight of the road-way in the chain bridge of equal strength