Calendar: 1860-1861 Page 483

484 GENERAL LITERATURE AND SCIENCE 10 1'rove that in any curve to rectangular co-ordinates jx- λ and thence that ultimately the arc the chord Ex Find ך- when χ α Θ sin Θ cos Θ χ 11 curve is convex or concave to the axis of according as cPy and -j- have the same or different signs Ex ax Λ 12 Prove the equation in spirals p-3 -f Ex Find the equation to the Lemniscata to rectangular co- ordinates deduce the polar equation and by the preceding formula find that between ρ and MATHEMATICS -JUNIOR SCHOLARSHIP -algebra Reduce 11183542857 metres into miles assuming that 32 metres 35 yards Six pints of fluid whose specific gravity is 925 are mixed with pints of water whose specific gravity is find the specific gravity of the mixture -4 2a 15 Add together τ g-' 20 -85 and---- Find the product of 3xy 4y2 and 33 -4xy- -yi and the continued product of the factors χ-a -ax- -a2 and x2 α χ β2