Brachistochrone raceway

This model is a kinetic demonstration of the brachistochrone, or curve of quickest descent.  The problem was proposed, so the story goes, by Johann Bernoulli in the journal Acta Eruditorum in 1696 to "the most brilliant mathematicians in the world". 

Isaac Newton, who received a letter from Bernoulli with the challenge, solved the problem overnight and sent the solution in anonymously, however Bernoulli recognized the author immediately, exclaiming that he "recognized the lion by his claw mark".

Newton, who apparently could be kind of a jerk, responded that "I do not like to be dunned [pestered] by foreigners about mathematical things..."

If you look at the raceway, you see the ball starts and ends at the same position for each track.  The first is a straight line (shortest distance), the next two have increasing degrees of drop which accelerates the ball but also increases the path length.  Can you tell which curve represents the brachistochrone?