ROSTOFF 



ROTATION 



817 



&c. ; exports grain, wool, flax, and cattle ; owns a, 

 mercantile fleet of 750 vessels of some 150,000 tons ; 

 and is entered annually by more than 900 vessels 

 of about 120,000 tons. Vessels above 200 tons un- 

 load in part at Warnemiinde, at the mouth of the 

 river. The industries are very varied, the most 

 important being shipbuilding, the making of 

 machinery, tanning, brewing, distilling, the manu- 

 facture of hats, tobacco, &c. The university, 

 founded in 1418, but rebuilt in 1867, is the chief 

 of the public institutions ; it has 40 teachers, 360 

 students, a library of 140,000 volumes, an observa- 

 tory, and an experimental agricultural colony. 

 Amongst the churches are St Mary's (1398-1472), 

 one of the finest Gothic churches of north Germany, 

 in which is a monument of Grotius, and St Peter s, 

 with a tower 414 feet high. The ducal palace 

 (1702) and the 14th-century Gothic town-house 

 also deserve mention. There is a handsome public 

 park. The statue of Bliicher, a native of the town, 

 adorns one of the squares. Pop. (1875) 34,172; 

 ( 1890) 44,388. Rostock, an ancient Slav town, was 

 burned to the ground by Waldemar of Denmark in 

 1161. In 1314 it came to Mecklenburg. About 

 this time it enjoyed great repute as a powerful 

 member of the Hanseatic League, and secured 

 important rights of self-government. It still pos- 

 sesses a thoroughly republican municipal constitu- 

 tion, and forms a separate estate in the Meck- 

 lenburg Assembly. See history by Koppmann 

 (Rostock, 1887). 



RostofT, ( 1 ) a town of south Russia, stands at 

 the head of the delta of the Don and on the rail- 

 way (1875) from Moscow to the Caucasus. It 

 owes its origin to the foundation of a fortress 

 here in 1761, since which time the progress of the 

 town, owing to its advantageous situation, has 

 been remarkable. Pop. (1881) 44,500; (1885) 

 61,256. It exports corn, linen, and wool to the 

 value of 3,000,000 a year ; its imports only 

 reach 30,000. The manufactures are growing 

 rapidly, the principal articles produced being ropes, 

 tobacco, macaroni, soap, and leather ; but there 

 are also shipbuilding-yards, wool-cleansing estab- 

 lishments, and caviare-factories. Two important 

 fairs are held here every year. (2) One of the 

 oldest towns of Russia, stands on a small lake, 129 

 miles by rail NNE. of Moscow, and has celebrated 

 market-gardens, a large fair, an extensive trade, 

 tallow-works, and coarse linen manufactures. Pop. 

 11,898. 



Rostopchine, FEODOR VASSILIEVICH, COUNT, 

 a Russian general, was born in the government of 

 Orel, March 23, 1763, and entered the Russian 

 military service as a lieutenant in the Imperial 

 Guard. He won great influence over the weak 

 mind of the Emperor Paul, who promoted him to 

 various offices in rapid succession. In May 1812 

 the Emperor Alexander appointed him governor of 

 Moscow. He it was, according to the French 

 writers, who planned and began with his own 

 hand the burning of Moscow. But in 1823 he 

 published La VtriU sur I'Incendie de Moscow 

 (Paris, 1823), in which he rebuts the charge, 

 affirming that this action was due in part to a few 

 of the inhabitants, and in part to the violence and 

 negligence of the French. Nevertheless, he subse- 

 quently recalled this denial and admitted his share 

 in the burning, in that he at least set fire to his 

 own mansion-house. He died at Moscow, January 

 30, 1828. His works, which include a number of 

 historical memoirs, two comedies, &c., in Russian 

 and French, were published at St Petersburg in 

 1853. See life by Schnitzler (Paris, 1863) and by 

 8<$gur ( Paris, 1872). 



Roswitha. or HROTSWITHA. See DRAMA, 

 Vol. IV. p. 83. 

 41(1 



Rot. See FLUKE, DRY ROT. 



Rotation. When all points of a body are 

 moving with the same Velocity (q.v. ) the motion 

 is one of pure translation, and is easy to compre- 

 hend. When, however, this condition is not ful- 

 filled there must exist the kind of motion known 

 as rotation. As simple examples, take the whirl 

 ing of a flywheel or the motion of the hands of a 

 watch. In such cases we readily see that there is, 

 in the rotating body, a row of points which does 

 not itself move. This row of points is called the 

 axis of rotation, and every other point in the body 

 describes a circle about it. To specify the motion 

 completely we must know not only the position of 

 this axis, but also the rate of rotation and the sense, 

 clockwise or counterclockwise, with which the body 

 is rotating about the axis. The rate of rotation 

 may be measured by the number of revolutions 

 made in a chosen time. It is more scientific, how- 

 ever, to measure it in terms of the angular speed. 

 If the body is rotating uniformly the angular speed 

 is the angle described in unit time by any plane 

 drawn in the body parallel to or containing the 

 axis of rotation : e.g. with the unit of time one 

 sidereal day, the earth's angular speed about its 

 axis is 2ir or 360 ; but with the second as the unit 

 of time the angular speed is a quarter of a minute 

 of arc, or -000073 in radians. 



In a simple geometric way a given rotation may 

 be represented by a directed line taken of length 

 numerically equal to the angular speed, and drawn 

 along the axis of rotation in that direction which 

 is related to the sense of rotation exactly as the 

 to-and-fro motion of a right-handed screw is to the 

 rotational motion of the screw. Such a directed 

 quantity of definite length and of definite line 

 position is called by Clifford a rotor. It is a Vector 

 (q.v.) under the restriction that its lie in space is 

 limited to a particular straight line. 



So long as the axis of rotation is fixed with 

 reference to lines which appear steady to us, there 

 is no difficulty in apprehending the character of 

 the motion. Take, however, the case of a carriage 

 wheel or boy's hoop rolling along the road. Here 

 we may regard the wheel as rotating about an axis 

 drawn through the centre, while the axis is at the 

 same time travelling forward with a definite linear 

 speed i.e. we may regard the motion as a combin- 

 ation of translation and rotation. In this par- 

 ticular case we may, however, represent the motion 

 at each instant as one of pure rotation about an 

 axis coinciding with the instantaneous line of 

 contact of the wheel with the road. For, with 

 rolling and no slipping, this line of contact with 

 the road is for the moment at rest. And it is 

 almost self-evident that, if at any instant there 

 exists in rigid connection with a moving body an 

 axis momentarily at rest, the instantaneous motion 

 must be of the character of a rotation about this 

 axis. The above is a simple example of what 

 holds generally in uniplanar motion i.e. motion 

 in which every point of the body jnoves in a plane 

 perpendicular to a fixed direction. The general 

 theorem is that any uniplanar displacement what- 

 ever (which is not a pure translation) can be 

 effected by a pure rotation about a determinate 

 axis. Since any given motion may be regarded 

 as consisting of a succession of displacements, it 

 follows that any such uniplanar motion can be 

 effected by a succession of rotations about instan- 

 taneous axes whose successive positions in space 

 and in the body are determinate. 



In uniplanar motions generally it is clear that 

 the instantaneous axis of rotation, however much 

 it may move both in space and in the body, must 

 always remain parallel to the same direction, 

 discontinuous motion be excluded and all natural 

 motions are continuous this instantaneous axis 



