37 



NODAL POINTS AND LINES. 



NODAL POINTS AND LINES. 



hereditary possession, these privileges might fall to persons who had 

 not wealth or the means of obtaining it, nor the influence and power 

 which wealth brings with it. 



When once society had thus established an order and regulated the 

 means by which persons might be admitted into it, the desire would 

 become general of admission to the privileges and advantages which 

 belonged to it, in persons who had any pretensions to aspire to such 

 advantages. It was then easily discovered that society had thus an 

 unexpensive way opened to it of rewarding very eminent services. 

 A community has not always manors and lands to give to the man 

 who performs for it such services, nor are money pensions out of the 

 taxes, continued from generation to generation, agreeable to those who 

 contribute to the payment of them. But a society accustomed to such 

 an order, and sensible of the benefits which attend the existence of 

 such a state of things, willingly sees advanced into it men who are 

 distinguished by very eminent talent, very eminent services, or very 

 eminent virtues. It is a reward not given all at once, but through 

 long succession of years. 



In the different countries of modern Europe there are nobles various 

 in their titles and various in the privileges belonging to them. In 

 England, Scotland, and Ireland, the heads of the families which are 

 noble are either dukes, marquesses, earls, viscounts, or barons ; all, 

 except the last, originally names of office, originated in that state of 

 society where the nMlei were all men in actual political employ- 

 ment. To the heads only are political privileges given, the chief of 

 which is, that the English peers have seats in the House of Lords, and 

 consequently a voice in all projected changes of the law. But the 

 junior members of the family are accounted noble, and have certain 

 titles or honourable distinctions united with their names. 



By the English constitution the privilege of placing a family in 

 the rank of the nobility is vested solely in the sovereign. The 

 phrase by which this is usually expressed is, that the sovereign is the 

 fountain of honour. It is done by letters-patent declaring that such 

 or such a person is created to the dignity, &c., to descend to the 

 lifirs male of his body, or in such manner as the crown may choose 

 to direct. 



The persons admitted into the order of "nobility in England are now 

 usually 1, Peers of Scotland or Ireland ; 2, Persons distinguished for 

 services in the army, navy, diplomacy, and for political services ; 3, 

 Younger branches of families already noble; 4, Persons of ancient 

 wealth, with sometimes, though rarely, persons of large fortunes which 

 have been recently acquired ; and 5, Persons promoted to high judicial 

 appointments, as the lord chancellor, the chief justice of the King's 

 Bench, and others, usually called the law-lords. 



New creations are essential to keep up the order, as extinction is 

 perpetually taking place in a nobility such as the English, where few 

 of the titles descend in any other way than to the male descendants of 

 the person first ennobled. 



There are modern communities, such as the United States of North 

 America, in which there is no nobility in any respect resembling that 

 of Europe. Wealth of course gives some influence and importance to 

 the possessor, but it is also an object of jealousy, which must always 

 be the case, more particularly in democratic constitutions. Office, so 

 long as it ia held, gives greater distinction than wealth ; but office is 

 only held for a short tune, and wealth, although it may be acquired 

 by an individual, is seldom transmitted to a single person, but is 

 usually distributed in moderate or small portions among several 

 persons. Thus it has been observed, that in the United States a family 

 seldom maintains any great wealth or importance for more than two 

 generations. Names which have been made illustrious by an indi- 

 vidual are remembered only because of him who first elevated them to 

 distinction, and the descendants of the wealthy lose with their wealth 

 the remnant of that importance which their ancestor acquired. Thus 

 one family of distinction after another sinks into obscurity, and its 

 H soon filled by a name before unknown. 



NODAL POINTS AND LINES. Nodal points are those points 

 in the length of a string extended between two fixed objects, or in a 

 column of air confined at one or at each extremity, which, when 

 the string or column is put in a state of vibration, are found to 

 remain at rest; nodal lines are corresponding lines which exist on 

 the surface of an elastic body, usually a plate, whose parts are in a 

 itate of vibration. 



It 5fl well known that if a string or a metallic cord be attached 

 at its extremities to a board or plate, on causing it, when in a state 

 of tension, to vibrate transversely, there may be distinguished, besides 

 the principal sound, which is due to the length of the string, several 

 others which have a greater degree of acuteness; these are called 

 harmonic tounds, and they are conceived to result from some property 

 of the extended string, by which, when in a state of vibration, it 

 becomes a sort of moving axis, having on it points, at distances from 

 H.ther equal to some aliquot part of the whole length of the 

 string, at which points a contrariety in the directions of the vibrations 

 of the particles keeps the latter in a state of rest. Such are called 

 nodal points ; and they may be conceived to form themselves in con- 

 'ice of inequalities in the thickness or density of the string, or of 

 different degrees of flexibility in its different parts. The string between 

 *,wo such points is in the same condition as if it were attached at 

 : points to fixed objects; it 1'ailh' vibrations are consequently 



such as are due to the distances between the points, and hence arise 

 the secondary or harmonic sounds. 



A string of considerable length, on being made to vibrate, will be 

 found to have several such nodal points, and the curves which the 

 intervals assume in consequence of the vibrations, though alternately 

 on opposite sides of the axis of the string, are equal and similar to one 

 another. The situations of the nodal points may be made evident by 

 placing, at intervals, across the string, pieces of paper notched or bent 

 in the form of an inverted V ; those which are at the places of the 

 nodes remaining at rest, while the others experience considerable agita- 

 tions, or are thrown entirely off. 



If a string, in a state of tension, have its extremities attached to a 

 board or plate of metal, and be made in some part of its length, to pass 

 over a bridge resting in the centre of the board or plate, the vibrations 

 of the string, when a violin-bow is drawn across it, will be communi- 

 cated to the plate ; and if over the latter some light dust or powder such 

 as fine sand or lycopodium be sifted, that dust will be agitated and 

 made to arrange itself on lines at which the surface of the plate is in a 

 state of rest : these are called nodal lines, and the figures which they 

 form are called A caustic Jiyures. Again, if a glass rod be cemented at 

 one end to the centre of a disk of the like material, and be excited by 

 being rubbed, for example, with a wet cloth, so as to be put in a state 

 of vibration longitudinally, those vibrations will be communicated to 

 the disk, and light dust strewed over the latter when in a horizontal 

 position will arrange itself in acoustic figures. Or, if a glass rod be 

 connected at each extremity to a glass disk at right angles to its length, 

 on exciting one of the disks by drawing a violin-bow across its edge, 

 the vibrations of that disk will, by means of the rod, be communicated 

 to the other ; and if light dust be strewed over both it will arrange 

 itself in figures : when the disks are equal and similar to one another, 

 the figures are alike on both ; otherwise they differ. 



If a column of air in a cylindrical tube which is closed at either or 

 at each end be acted upon by the force of the breath, for example, 

 applied at an aperture in any part of its length ; it will spontaneously 

 divide itself into portions in which the particles are subject to equal 

 and similar vibrations [ACOUSTICS ; VIBRATION] : these portions are 

 separated from one another by sectional areas in which the particles 

 are at rest ; the condensations, or rarefactions, of the air being, in those 

 areas, greater than in any other parts of the tube in consequence of the 

 particles moving in contrary directions, and with equal velocities 

 towards, or from, them. Such areas are called nodal sections, and 

 several may exist at the same time in the tube. Their existence is 

 rendered evident by boring small holes in different parts of the 

 sides of the tube and covering them with pieces of thin paper 

 slightly adherent to the surface : at the nodal sections the papers 

 will be scarcely affected, while, in the intervals, they will be greatly 

 agitated. 



If, in the side of a tube containing a column of vibrating air, any 

 aperture exist by which that air is enabled to communicate with the 

 atmosphere, the air in that section becomes in equilibrio with the latter, 

 and, in that section, there is consequently neither condensation nor 

 rarefaction : this section corresponds to the middle point between two 

 nodes in a vibrating string. 



Vibrations corresponding to those which are produced in strings or 

 rods and in columns of air may be conceived to take place in any solid 

 bodies or in any elastic fluids whatever be the figure of their mass : in 

 such a mass there may be several places at which the vibrations are 

 performed in contrary directions so as to produce nodal lines ; and 

 these, when they occur on the surface of the mass, may become 

 sensible by means of light dust strewed over it. Some of the vibra- 

 tions are found to take place parallel to the surface, and others perpen- 

 dicular to it : the former being called tangential, and the latter normal 

 vibrations. In one case the particles of dust glide upon the surface in 

 directions which tend alternately towards and from the nodal lines 

 (the movements in the former direction being always more rapid than 

 those in the other) till they come to a state of rest on those lines ; in 

 the other case the particles alternately rise from and fall back upon 

 the surface at the places where the latter is in a state of vibration ; 

 and, dispersing from those places, they become quiescent in the lines 

 of no vibration. 



Galileo was the first who observed (Dialoyhi dellc Scienze Nuave) that 

 the vibrations of elastic plates might be rendered visible by covering 

 the plates with fine sand ; and he remarked that the sand became 

 accumulated at the parts where the vibrating plate was in a state of 

 rest : but this subject was extensively investigated by Dr Chladni, of 

 Wirtemberg, who first discovered the longitudinal vibrations of solid 

 bodies; and, 1787, published, in a work entitled Entdeckim,en iiber die 

 Theorie ties Klanges, an account of numerous experiments which he had 

 made on the nature of the vibrations produced in plates of glass of 

 different forms. 



The plates with which such experiments may be performed should 

 be of good window glass ; and, if square, from 4 to 8 inches on each 

 side ; if circular, their diameters may be within the same limits : in 

 making an experiment the plate must be held horizontally between 

 a finger and thumb, or it may be fixed within the lips of a clamp 

 screw or of suitable tongs, the points of contact being furnished with 

 cork ; and when it is required to prevent any particular part of the 

 from vibrating, that part, if on the edge, may bu pressed again.it 



