Calendar: 1860-1861 Page 477

478 GENERAL LITERATURE AND SCIENCE length compare the velocities at the beginning of the ascent and at the end of the descent body describes an ellipse force in focus find the law If the magnitude of the force and the square of the velocity be doubled what is the effect on the periodic time The areas described round fixed centre of force are pro- portional to the times of their description Thence find the angular velocity and show that the point Ρ in an ellipse round the centre where it is geometric mean between the greatest and least velocities is such that the circle radius CP equals the area of the ellipse coach travels 12 miles an hour what distance does the head of nail in the tire of one of the wheels travel Compare the velocity of any point in the wheel with that of the highest point Enunciate and prove Lemma VII ο 12 22 32 &c 10 Find the value of -5- when η is infinite II Eltmtntarg fEccijamcii anb SnttrojStatttiS Define the moment of force and if two forces act at point show that the sum of their moments about any other point is equal to the moment of the resultant Find the conditions of equilibrium of the screw-1 when smooth when rough Find the distance of the centre of gravity of triangle from one of its angular points An isosceles triangle whose base is the side and equal side equal to the diagonal of the square stands upon square find the centre of gravity of the compound figure ό heavy body slides down an inclined plane find the time and the velocity acquired In vertical circle find the position of that radius down which particle will descend in the same time as down the vertical diameter