Source : Webster's Revised Unabridged Dictionary (1913)

Tautochrone \Tau"to*chrone\, n. [Gr. ?, for ? ? the same + ?
   time: cf. F. tautochrone.] (Math.)
   A curved line, such that a heavy body, descending along it by
   the action of gravity, will always arrive at the lowest point
   in the same time, wherever in the curve it may begin to fall;
   as, an inverted cycloid with its base horizontal is a
   tautochrone.