VIBRATION. 



VILLEINAGE. 



particle mint describe one or other of these ellipses : one when F and 

 T an both Iraving the centra or both returning to it ; the other when 

 CM u leviug the centra ud one returning to it. In the figure, and 

 supposing cxr to be the direction of motion, T u leaving, and F 

 ratuming to, the centre. And if c M e be the circle described about 



this ellipse and K L M be always perpendicular to c e, the law of the 

 motion of the particle L is that u moves uniformly round the circle, or 

 K mores through a simple vibration. This ia exactly the law of motion 

 shown by Newton to obtain when the particle L is attracted towards o 

 by a force which varies as its distance from o ; and mechanical con- 

 siderations might easily be used to establish the whole theorem. If 

 the vibrations be thus compounded for each pair of axes, three ellipse)) 

 are obtained on the three co-ordinate planes, which are the projections 

 of the ellipse which the particle describes in space. 



We may attempt to compound two different vibrations on the same 

 line, that is, two vibrations of different durations. If in the first 

 Cgure we suppose the angular velocity of R round Q to be different from 

 that of q round o, we see that K describes a trocboidal curve, and 

 supposing such a curve to be described by uniform circular motions, 

 the motion of the projection of R upon the line of vibration will show 

 the effect of the two vibrations. Some simple instances may be readily 

 obtained from the diagrams in the article cited ; but an attempt at a 

 description of the multifarious effects of even two vibrations would 

 baffle all human power of classification. 



We now proceed to some account of the principal mechanical con- 

 siderations connected with vibrations. If any system whatsoever be 

 slightly disturbed from a position of stable equilibrium, every particle 

 makes an effort to return to that position ; and it can be shown that 

 the force of restitution varies as the distance from the position of 

 equilibrium, so that all the particles perform either simple vibrations, 

 or motions compounded of simple vibrations. Not that it is accurately 

 and geometrically true that the force of restitution always varies as the 

 distance from the position of equilibrium, but only exceedingly near to 

 it. The consequence of the restitutive force is, that the system, in 

 returning to its position of equilibrium, acquires velocity, and the 

 several particles pass through or near to their positions of equilibrium 

 with their several velocities, until the force of restitution, which begins 

 to act in a contrary direction the moment the position of equilibrium 

 is passed, destroys the acquired velocity, and causes the particles to 

 return. The same vibration is then repeated, or rather would be 

 repeated if there were no retarding forces : as it is, the resistance of 

 the air, Ac., continually diminish the extent of the vibrations, until at 

 last they become insensible. But it can be satisfactorily shown that 

 these resistances have no sensible tendency to alter the times of the 

 vibrations; and few persons are aware how much of their comfort 

 depends upon this circumstance. Whenever a sound is produced, a 

 musical note generally accompanies it ; the sound is the consequence of 

 the vibrations excited in the disturbed system, and the permanency of 

 iu musical pitch is the consequence of these vibrations being all made 

 in the same time, or very nearly so. The air does not retain tin- 

 vibration* communicated to it, but pasMS them on, so to speak ; and it 

 is therefore an agent which communicates the successive vibrations of 

 a disturbed body just as they are communicated to it. If the vibra- 

 tions gradually slackened in their lima, as they do in their excursions 

 from UM etiect of the resistances, the consequence would be that there 

 would be no untamed notes, but every sound would be a sliding 

 chromatic descent, like the cry of some animal., which are therefore 

 considered very annoying neighbours; Mid most musical instrument* 

 would be rendered unusable. 



Then is a principle in mechanic! which Is called that of the coeje- 

 q/ ribratimt, and sometimes the tptrjnntion of ribrationi, 



of any particle at any one instant, arising from the united effect of the 

 vibrations, will be the sum or difference of the disturbances arising 

 from the several different vibrations, according as they are in the same 

 or opposite directions. This is not strictly true in any case, but it is 

 very nearly true when the vibrations are small, and the more nearly so 

 the smaller the vibrations are. For instance, two stones are dropped 

 into water at two different places, and at a certain time, on a certain 

 part of the surface, the resulting waves cross one another. If there bo 

 a particle which is at the same time raised on both waves, a tenth of 

 an inch say, from one only, and three-tenths of an inch from the 

 that particle will altogether be raised four-tenths of an inch, or 

 insensibly near to it. Thus the effects of the two waves travel without 

 any apparent interference with each other, and the eye can easily 

 follow any one wave, even though a dozen disturbances should have 

 been excited at the same time. A handful of small pebbles thrown 

 into smooth water will show the coexistence of the resulting- waves 

 very satisfactorily ; and it id curious to observe how readily the non- 

 interference of the several disturbances is seen when looked for, so 

 readily, that it never is looked for unless the attention be specially 

 directed to it, 



VIBRATIONS OF HEAT. [HKAT.] 



VICAR (from the Latin rietniut, " one who discharges the functions 

 of another"). The origin, constitution, and functions of this cla*s of 

 ecclesiastical person* have been already fully treated of. [BESEFKE. J 

 One port of the subject is alone omitted in that article, namely, the 

 dissolution of vicarages. Of this it suffices to say that since the 18th 

 Elizabeth, c. 10, the property neither of a vicarage nor of any other 

 ecclesiastical office can be alienated, and that although a vicarage may 

 be dissolved, as already described, by the vicar acquiring all the rights 

 of the parson, yet the appropriator, whether lay or ecclesiastical, cannot 

 dissolve the vicarage by alienating its property or by neglecting to 

 present A vicarage may be dissolved if the parson or appropriator 

 presents the clerk to the benefice, whether by design or by accident : 

 it may also be dissolved and become a parsonage, or, to speak techui 

 cally, disappropriate, by the dissolution of the corporation to which 

 the benefice is annexed. Thus if a college which is the appropriator of 

 a certain benefice is dissolved, the vicar becomes entitled to the great 

 tithes, and his vicarage is thenceforward converted into a rectory. 

 [BENEFICE; TITHES.] 



VICAR APOSTOLIC. [CATHOLIC CHURCH (Roman).] 



VICARAGE. [VICAB.] 



VIENNA LAKE. [Cotocmxo MATTERS.] 



VIENNA, TREATY OF. [TREATIES, CHRC 



VILL. [Town.] 



VILLEIN, or VILLAIN, denotes a species of bondman subject to 

 his feudal superior. The word is from the low Latin f,. : 

 which is from the Latin word Villa. In England, during the Anglo- 

 Saxon period, a large part of the people appear to have been in a servile 

 condition, either as domestic slaves or cultivators of the land. The 

 power of the master among the Anglo-Saxons, though very extensive, 

 hod some limits. If a master beat out the eye or the tooth of hi.-, 

 slave, the slave was entitled to hie freedom ; if he killed him, he paid 

 a fine to the king, unless the slave lived a day after the wound was 

 inflicted, in which case the offence was unpunished. The Norman 

 Conquest did not materially alter the state of slavery in England. The 

 lands were transferred to Norman masters, and the slaves passed as 

 part of the property. After the Conquest there were four classes of 

 slaves : 1, Villeins in gross, who were the personal property of their 

 lords, and performed the lowest household duties. They were very 

 numerous, and were frequently sold and eveu exported to foreign 

 countries. (Walsingbam, ' UUt. Ang.,' p. 258.) 2, Villeins regardant, 

 or ]fracdial slaves, who were attached to the soil, and specially engaged 

 in agriculture. These were in a better condition than villein* in gross, 

 were allowed many indulgences, and even, in some cases, a limited kind 

 of property ; yet the law held that the person and property of the 

 villein belonged entirely to his lord, the rule being the same as that in 

 the Roman law, that whatever was acquired through the slave was 

 acquired by the lord. 3, A class called Cuttarii is mentioned in Domes- 

 day Book ; and 4, in the same book a class called Jiun/arii. But the 

 first two classes in fact comprised all the villeins. 



The legal condition of villeins in the reign of Edward IV., when 

 Littleton wrote his Book of Tenures, appears from that work, Sections 

 172-208. 



In England a few instances of pncdial servitude existed so late as 

 the reign of Elizabeth, and perhaps at a still later period. (Harrington 

 ' On the Statutes,' 274 ; Hallam's ' Middle Ages,' vol. i.) In some part* 

 of France it existed down to the time of the Revolution. [SLAVER v.] 



(Bracton ; Littleton ; Coke's Pint Intt. ; Reeves, Hitt. of Enylttk 

 Lmi- ; Blackstone's OammeiHanu.) 



VILLEINAGE was a base tenure of land. This tenure was founded 

 on the servile state of the occupiers of the soil [VILLEIN], who were 

 allowed to bold portions of land at the will of their lord, on condition 

 of performing base and menial services. Where the service was base 

 in its nature, and uncertain as to time and quantity, the tenure was 

 called pure villeinage ; but where the service, though base, was certain 



[TREATIES, CHRONOLOGICAL TABLE OF.] 



