“ The intrinsic equation is s = 4a sin ψ, and the equation to the evolute is s = 4a cos ψ, which proves the evolute to be a similar cycloid placed as in fig. 2, in which the curve QOP is the evolute and QPR the original cycloid. The radius of curvature at any point is readily deduced from the intrinsic equation and has the value ρ = 4 cos 1/2θ, and is equal to twice the normal which is 2a cos 1/2θ. ”

“ References.—Geometrical constructions relating to the curves above described are to be found in T. H. Eagles, Constructive Geometry of Plane Curves. For the mechanical and analytical investigation, reference may be made to articles Mechanics and Infinitesimal Calculus. ”