# Calendar: 1854-1855 Page 353

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GENERAL LITERATURE AND SCIENCE 355 13 An indefinitely small pulley moves along an axis at the same time ball considered as point is unwound from the pulley in plane perpendicular to the axis find the solid generated by the path of the ball when the length of the string unwound equals the distance described by the pulley 14 Show that מ sin 7r η II -fHceljantcs' fictuton an& comctrn of titi tt JDtnunStouS perfectly elastic ball is projected from given point on horizontal plane and at its greatest elevation strikes another equal elastic ball at rest determine the paths of each ball after compact and the times of their reaching the ground Β is quadrant centre point Ρ starts from and ί describes while moves uniformly round find the ί locus of If and be the coordinates of the centre of gravity of an area prove that ff cos drde ff r-ux dedr rdrdB rdrde π and apply the former to r2 a2 sin β from θ to θ "- Given the velocity of sound find the range when ball at given elevation is projected towards person so that the ball and the sound of the discharge reach him at the same instant Find the content of cone by Newton's 4th Lemma Sum ך- -Γ- -- -- &c η η η α η η α η α to infinit Α Β is right-angled triangle Ν Β being the hypothe- nuse find point Ρ in Ν Β that the time from Ρ to may be minimum

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