TAURUS

(Lat. the Bull.) In Astronomy, the second in order of the twelve zodiacal constellations. There are several remarkable stars in this constellation: Aldebaran, of the first magnitude, in the eye; the well-known cluster called the Pleiades, in the neck; and the Hyades, in the face. See Constellation, Zodiac. time),TAUTOCHRONE in Mechanics, is (Gr.a curveravros,line the having same,this and ypovoc, property, that a heavy body descending along it by the action of gravity will always arrive at the lowest point in the same time, wherever the point from which the body begins to fall be taken in the curve. Huygens first showed that this is a property of the common cycloid when the motion takes place in a vacuum, and gravity is supposed to act in parallel straight lines. (See Cycloid.) 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 (Principia, b. ii., prop. 26); and Euler first determined the nature of the curve when the resistance is proportional to the square of the velocity (Mechanic a vol ii ) See also Joh. Bernoulli, Opera, vol. Hi. ' [s. 1232]