DUH, Thanks MrF. I'll leave it anyway. May help.

BTW, isn't the cycloid also known as the 'brachistochrone'?. Wasn't this the problem one of the Bernoulli's

[Mr F adds: Johann, in fact. You need a score card to keep a track of that family ] posed to Newton and he solved it rather quickly, according to the story?. The problem was to determine the best shape for an object, such as a bearing might roll from a point P to a point Q, not directly below it, the fastest. This is the shape Newton came up with.