Calendar: 1857-1858 Page 398

400 GENERAL LITERATURE AND SCIENCE weight and length moving in vertical plane round given weight is suspended by string fixed at and passing through ring at Find the position of equilibrium Find the centre of gravity of triangle ABC and show thzt3 GA' GB GC AC BC AB1 If two weights each equal to the weight of the triangle be respectively placed at and find the centre of gravity of the triangle and the two weights Prove that if be space the accelerating force of gravity and time that igt particle describes in the second of its fall space equals times the space in the second find the whole space described Two weights connected by string rest upon smooth vertical circle Find their position of equilibrium and the tension of the string 10 perfectly elastic ball is projected at an angle of 60 and strikes plane inclined at 30 to the ground and passing through the point of projection find the greatest height the ball will attain after the impact 11 In any equation if Mx" be the first negative term and Ρ the greatest negative coefficient -f- '3 greater than the greatest root 12 Express Σ am Sec being roots of an equa- tion in terms of the coefficieuts of the equation JUNIOR MATHEMATICAL SCHOLARSHIP -SUgtbra airtf Crtgonomttru If in the expansion of Ώ be four con- secutive coefficients prove that Β Bn B' 2B