Page:Encyclopædia Britannica, Ninth Edition, v. 11.djvu/513

Rh the mystic rites which were celebrated annually on the island. When Cadmus came to Samothrace, and was initiated, he received Harmonia as his wife. The gods honoured the wedding with their presence, Athene pre- sented the bride with a peplus and necklace, Electra gave the mystic rites of the mother of the gods. According to the scholiast on Euripides (Phen., i.) Cadmus with the aid of Athene carried off Harmonia ; and in the mysteries the lost Harmonia is regularly sought for. We have here an exact parallel to the Eleusinian legends. Electra and Harmonia are mere varieties of Demeter and Core. Cadmus like Plato carries off the bright daughter of the goddess to the world below to spend there the dreary winter. Hence in the Theban tale Cadmus and Harmonia leave Thebes to go away among the Encheleis, the snake people, are themselves changed into serpents, and are finally translated to the Elysian fields. We then under- stand, too, why (according to Pausanias, ix. 16, 5) Cadmus dwelt at Thebes in the temple of Demeter Thesmophoros. The necklace, wrought by Hephestus, which Harmonia received as a marriage gift, may be compared with the cestus of Aphrodite ; for it is impossible to draw a fast line between Harmonia or Core and Aphrodite. Then it is seen to be the mythic representative of some pheno- menon like the halo of dawn or the rainbow. Like the works of the German dwarfs, this necklace carried with it ill-luck, and the legends give it a history of woe. With it Polynices bribed Eriphyle to betray her husband Amphi- araus, It brought death at last to her son Alemeon. Dedicated in the temple of Athene Pronoia at Delphi, it was given by the tyrant Phayllus to his mistress; her son going mad set fire ts the house, and she perished in the conflagration.  HARMONICA is the technical name for the “ musical glasses” with the learned conversation about which the pseudo-ladies from town astonish the simple-minded vicar of Wakefield. An instrument for producing musical sounds by means of drinking glasses touched with the moistened fingers was, however, known 100 years before Guldsmith’s novel. What its exact nature may have been cannot now be ascer- tuned, but its mode of playing must have been far from perfect ; for as late as the middle of the 18th century the inusical glasses played by Mr Puckeridge were placed on a table and their pitch was fixed by the quantity of water they contained, naturally a very uncertain mode of deter- mination. It was to this instrument that the great Ben- jamin Franklin applied his improvements described in his letter to Father Beccaria of Turin. Instead of fixing the glasses he made them rotate round a spindle set in motion by the player’s foot by means of a treadle. The edge of the glasses by the same means passed through a basin of water, the pitch henceforth being determined by the size of the glasses alone. The player touched the brims of the revolving glasses with his finger, his task being further facilitated by the scale of colour which Franklin adopted in accordance with the musical gamut. Thus C was red, D orange, E yellow, F green, G blue, A indigo, and B violet. The black keys of the piano were represented by white glasses. The instrument thus improved became very fashionable in England, and a Miss Davis, a relation of Franklin’s, became a celebrated harmonica player, who per- formed at numerous concerts with great applause. It is interesting to know that the great composer Gluck was a virtuoso on the musical glasses in their earlier form, which he played, according to a contemporary advertisement, at the Haymarket Theatre, April 23, 1746. He even seems to have claimed the instrument as his own invention, and promises to perform upon it whatever may be done on a violin or harpsichord.” Nowadays the idea of a composer of repute—for such Gluck was at the time—playing on the musical glasses would appear grotesque. But the notions of artistic dignity were different in the 18th century. Many attempts have been male to increase the power and flexibility of the harmonica, and also to avoid the nervous irritability said to be caused by the friction of the vibrating glasses. Thus harmonicas played with the bow or by means of a keyboard, like that of the pianoforte, have been invented. But none of these has met with permanent success, and in all essential points the modern harmonica is such as Franklin left it.  HARMONIC ANALYSIS is the name given by Sir William Thomson and Professor Tait in their treatise on Natural Philosophy to a general method of investigating physical questions, the earliest applications of which seem to have been suggested by the study of the vibrations of strings and the analysis of these vibrations into their funda- mental tone and its harmonics or overtones. The motion of a uniform stretched string fixed at both ends is a periodic motion ; that is to say, after a certain interval of time, called the fundamental period of the motion, the form of the string and the velocity of every part of it are the same as before, provided that the energy of the motion has not been sensibly dissipated during the period. There are two distinct methods of investigating the motion of a uniform stretched string. One of these may be called the wave method, and the other the harmonic method. The wave method is founded on the theorem that in a stretched string of infinite length a wave of any form may be propagated in either direction with a certain velocity, V, which we may define as the “ velocity of pro- pagation.” If a wave of any form travelling in the positive direction meets another travelling in the opposite direction, the form of which is such that the lines joining correspond- ing points of the two waves are all bisected in a fixed point in the line of the string, then the point of the string corre- sponding to this point will remain fixed, while the two waves pass it in opposite directions. If we now suppose that the form of the waves travelling in the positive direc- tion is periodic, that is to say, that after the wave has travelled forward a distance /, the position of every par ticle of the string is the same as it was at first, then / is called the wave-length, and the time of travelling a wave- length is called the periodic time, which we shall dencte by T, so that

If we now suppose a set of waves similar to these, Lut reversed in position, to be travelling in the opposite direc- tion, there will be a series of points, distant 3/ frcem each other, at which there will be no motion of the string; it will therefore make no difference to the motion of the string if we suppose the string fastened to fixed supports at any two of these points, and we may then suppose the parts of the string beyond these points to be removed, as it cannot affect the motion of the part which is between them. We have thus arrived at the case of a uniform string stretched between two fixed supports, and we conclude that the motion of the string may be completely represented as the resultant of two sets of periodic waves travelling in opposite directions, their wave-lengths being either twice the distance between the fixed points or a submultiple of this wave- length, and the form of these waves, subject to this ccndi- tion, being perfectly arbitrary. To make the proklem a definite one, we may suppose the initial displacement and velocity of every particle cf the string given in terms of its distance from one end of the string, and from these data it is easy to calculate the form which is common to all the travelling waves. The form cf the string at any subsequent time may then be deduced by calculating the positions of the two sets of waves at that time, and compounding their displacements.