Math. [f. TAUTO- + Gr. χρόνος time: cf. F. tautochrone (Dict. Trévoux, 1771).] That curve upon which a particle moving under the action of gravity (or any given force) will reach the lowest (or some fixed) point in the same time, from whatever point it starts. So Tautochronism, the property of a tautochrone; Tantochronous a., having the character of a tautochrone; occupying the same time, isochronous.
a. 1774. Goldsm., Surv. Exp. Philos. (1776), II. 142. The time spent in determining the figure of a tautochrone might have been more usefully employed in this research.
1842. Brande, Dict. Sc., etc. s.v., Newton and Hermann also determined the tautochrone in a vacuum, when gravity is supposed to be directed towards a given centre. Newton likewise showed that the cycloid is also the tautochrone in a resisting medium, when the resistance is proportional to the velocity.
1842. Exam Papers, 47 (Dubl. Univ. Cal., 1843). Prove that the cycloid is the only plane curve possessing the property of tautochronism.
1846. Smart, Suppl., Tautochronous, arriving at the same time; having the property of the tautochrone.
