Calendar: 1851-1852 Page 313

GENERAL LITERATURE AND SCIENCE 317 Here Narcissus day by day Buds in clustering beauty gay Sipping aye at morn and even All the nectar-dews of heaven Wont amid your locks to shine Ceres fair and Proserpine Quote from ancient and modern authors descriptions of the Nightingale SENIOR MATHEMATICAL SCHOLARSHIP If μ χ cos χ η cos χ 4- χ sin χ ן or י dx Τ η sin χ χ cos χ according as η is even or odd Given that a3 cos χ -A0 -f- cos -j- A2 cos χ j- &c obtain the following relation between consecutive coefficients η a2 2n η ay Find the magnitude and point of application of the resultant of two forces which act in different directions but in the same plane upon rigid body What mechanical principle is deducible from this proposition beam rests with one end against rough wall and over vertical prop determine the position of equilibrium Given the perimeter of triangle and one angle find when its area is greatest ffxdxdy ד fir2 cos θ dr θ From י deduce JJdxdy JJrdrde and apply it to find the centre of gravity of sector of circle Express the area of triangle in terms of the coordinates of its angular points