ROT 



R O T 



covered with a kind of brufhwood without leaves. Cook's 

 Voyage by HaA'kefworth, vol. iii. p. 264. 



ROTALA, in Botany, lo named by Linnaeus, from rota, 

 a wheel ; apparently in allufion to the fpoke-like appear- 

 ance of its numerous radiating whorled leaves. — Linn. 

 Mant. 2. 143. Schreb. 33. Willd. Sp. PI. v. 1. 189. 

 Vahl. Enum. v. 2. 26. Mart. Mill. Diet. v. 4. Juff. 

 303. — Clafs and order, Triandria Monogynia. Nat. Ord. 

 Caryophyllei, fell. 3, Linn. Caryophylleis effinc, Juil. 



Gen. Ch. Cal. Perianth inferior, of one leaf, tubular, 

 membranous, three-toothed, permanent. Cor. none. Slam. 

 Filaments three, capillary, the length of the calyx ; anthers 

 roundifh. Pijl. Germen fuperior, ovate ; ftyle thread- 

 (haped; ftigma three-cleft. Peru. Capfule ovate, ob- 

 fcurely triangular, inclofed in the calyx, of three cells, 

 and three valves. Seeds numerous, roundifh. 



Eli'. Ch. Calyx three-toothed. Corolla none. Capfule 

 of three cells, with many feeds. 



1. R. vcrticUlaris. Linn. Mant. 2. 175. (Ene pael ; 

 Rheedc Malab. v. 9. 159. t. Si.) — Native of wet iitua- 

 tions in the Eaft Indies, from whence it was fent by Koenig 

 to Linnxus. A (mall annual herb, quite fmooth, four 

 inches, or more, in height, ereft, branched, having the 

 afpeel of an Ammanma, as Vahl, from the infpe&ion of the 

 only known fpecimen, in the Linnaean herbarium, remarked. 

 Root with many rows of whorled fibres. Stem and branches 

 reddifli ; quadrangular in the upper part. Leaves from 

 four, or five, to eight in each whorl, feffile, linear, entire, 

 bluntifh, or fomewhat emarginate, at the end, about half 

 an inch long ; paler, with a prominent rib, beneath. 

 Flowers aicillary, fmall, feffile, folitary, pale ; their per- 

 manent calyx membranous and pellucid, globular, inverting 

 the fruit, about the lize of a muftard feed. 



ROTAS, in (Jeography, a town of Hindooftan, in 

 Lahore, 815 miles N.W. by N. from Lahore. N. lat. 

 32° S 8'. 



Rotas, a circar of Hindooftan, in the foubah of Bahar, 

 bounded on the N.E. by Boujapour, on the E. by Bahar 

 Proper, on the S. by Palamow, on the W. by the circar 

 of Bid/igur, on the N.W. by Chunar ; its form approaching 

 to a fquarc about 58 miles each way. The chief towns are 

 Rotafgur and Saferam. » 



ROTASGUR, a town of Hindooftan, in the above- 

 mentioned circar, fituated on the river Soane ; 94 miles 

 S.W. of Patna. N. lat. 24- 38'. E. long. 84 2'. 



ROTATA, COROLLA, in Botany, a monopetalous co- 

 rolla, whofc tube is as fhort as poffible, and the limb hori- 

 zontally extended, like the form of a wheel. This differs 

 from a falver-fliaped corolla, in the want of an elongated 

 tube. See Coroi./.a. 



ROTATION, in Mechanics, is a term ulcd to denote 

 the motion of the feveral parts of a folid body about an 

 axis, called the axis of rotation, and which may be either 

 fixed or fpontaneous, accordin I body is con drained 



to make its revolution about a determinate point or line, 

 or it. tree to revolve in any direction from a momentum im- 

 prefled upon it in [pace 



We have already treated ol feveral cafes of rotatory 

 motion, under our articles CENTER of Gyration, PERCUS- 

 SION, Oscillation, Sec, and it therefore only remains, 

 in this place,' to offer fome general remarks with regard 

 to fuch motion, and to enumerate a few of the moll im- 

 portant particulars relating to this interfiling branch of 

 mechanics. 



When a folid body turns round an axis, retaini 

 fhapc and dimenfions unaltered, every particle is absolutely 

 defcribing a circle round this axis , which axis | 



Vol. XXX. 



through the centre of the circle, and is perpendicular to its 

 plane. Moreover, in any inilant of its motion, the particle 

 is moving at right angles with the radius vector, or iine 

 joining it with the centre of rotation : therefore, in order to 

 afcertain the direction of the particle, we may draw a line 

 from that particle perpendicular to the axis of rotation. 

 This line will be in the plane of the circle of rotation of 

 that particle, and will be its radius vector ; and a line drawn 

 from the particle, perpendicular to its radius veftor, will 

 be a tangent to the circle of rotation, and will reprefent the 

 direction of the motion of this particle. 



The whole body being fuppofed to turn together, it is 

 evident, that when it has made one complete rotation, each 

 point has defcribed the circumference of a circle, and the 

 entire paths of the different particles will be in the propor- 

 tion of thefc circumferences, and therefore of their radii : 

 and this is alfo true of any portion of thefe circumference* . 

 that is, the velocities of the different particles are propor- 

 tional to their radii veftores, or to their diftances from the 

 axis of rotation ; and all thefe motions are in parallel planes, 

 to which the axis of rotation is perpendicular. Hence it 

 follows, that when we compare the motion of different re- 

 volving bodies with refpect to velocity, it is evident that it 

 cannot be done by directly comparing the velocity of any 

 particle in one of thefe bodies with that of any particle of 

 the other ; for as all the particles of each have different ve- 

 locities, this comparifon can eftablifh no ratio. But we may 

 familiarly compare fuch motions, by the number of com- 

 plete turns which they make in any equal portions of time ; 

 and, therefore, as the length or number of feet defcribed 

 by any body, in reftilinear motion, is a proper .meafurc of 

 its progreffive velocity, fo the angle defcribed by any par- 

 ticle of a revolving body is a proper meafure of its motion 

 or rotation : and in this manner may the motion of two or 

 more bodies be compared, and this velocity is with pro- 

 priety called the angular velocity. 



Again, with refpeft to the motion of bodies at liberty to 

 move freely by the aftion of any force impreffed : if any 

 fuch body receives an impullion in any direction, which 

 does not pafs through the centre of gravity, the motion 

 which enfues is a rotatory one. For if, at the fame mo- 

 ment, a body is impelled according to any direftion A B, 

 (Plate XXXVII. Mechanics, Jig. 9.) not paffing through 

 the centre of gravity, an equal and oppolite force is ex- 

 erted upon the body in a parallel direction, C G paffing 

 through the centre of gravity, that centre will manifeflly 

 be kept at reft : neverthelcfs it is clear, that the other parts 

 of the body will not be in a Hate of quiefcence, becaufe the 

 two forces, though equal, are not directly oppofite ; fo 

 that the only motion that the body can have, its centre of 

 gravity being atreil, i> evidently a motion of rotation about 

 that centre. Now the fixed axis, about which the body re- 

 volves, is preflcd by the impelling force, while it generates 

 rotatory motion ; but the axis, being by In potnefis im- 

 moveable, re ..cts equally againfl that prcflure ; and, when 

 it pafles through the centre of gravity, would, as above 

 llated, caufe each particle to move with the lame velocity, 



and in the direction of the force. If, then, the force which 

 prefles againfl a fixed axis, in given circumftances, be ascer- 

 tained, tie- motion of the body in tree Space, when the axis 

 n moved, will be known ; tor the latter motion will con- 

 fill of the rotatory motion about the axi-; pilling through 

 the centre of gravity, confideredas fixed, compounded with 

 motion of the cent! of gravity caviled by the force now 

 ■ if. 1, in impel the centre, the fixed axil which paflei 

 through u being ri movi d. 



Wlii 11 a fi lid body receive- an impulfe on any one point, 

 4 li or 



