Calendar: 1855-1856 Page 367

ENERAL LITERATURE AND SCIENCE 303 SENIOR MATHEMATICAL SCHOLARSHIP -ϋΗεφιηύέ J2cU ton aau comctri of tfyrcc JDtnunStonS In curves of continued curvature the chord arc and tangent vanish in ratios of equality Show in the cycloid being the vertex and Ρ Τ tangent to an arc AP that arc AP PT ultimately Explain the principle of virtual velocities and show its truth in the case of bent lever Apply the principle to find the inclination of an irregular beam placed in semicircle to the horizon semicycloid revolves round its axis find the content of the solid generated and the distance of its centre of gravity from the vertex Ρ and connected by string of given length rest upon cylinder determine their position If Ρ afterwards hang freely and the string in contact with the cylinder cover one-third of the circumference find the proportion of Ρ to person in railway carriage travelling on curve radius 1000 yards observes that weight suspended from the top of the carriage makes an tan 0ό with the vertical thence show the miles per hour the carriage is travelling The wind blowing horizontally with given velocity ball is thrown directly upwards with times the velocity of the wind determine the path of the ball and the place where it strikes the ground Find the law of force tending to the focus of an ellipse the vtlocity of the body at any point and the periodic time The earth's orbit being an ellipse major axis 190 millions of miles and eccentricity 017 find the area in yards described by the earth in an hour from the perihelion 10 Two pendulums and begin to oscillate together and are again coincident after מ oscillations of having given find