rest. Thus a series of nodes and ventral segments will be produced whose number will depend upon the tension and the frequency of the alternate motions communicated to the moveable end. So, when a string fixed at both ends is put in motion by a sudden blow at any point of it, the primitive impulse divides itself into two pulses running opposite ways, which are each totally reflected at the extremities, and, running back again along the whole length, are again reflected at the other ends. And thus they will continue to run backwards and forwards, crossing one another at each traverse, and occasionally interfering, so as to produce nodes; so that the motion of a string fastened at both ends consists of a wave or pulse continually doubled back on itself by reflection at the fixed extremities. Harmonics generally co-exist with the fundamental sound in the same vibrating body. If one of the lowest strings of the pianoforte be struck, an attentive ear will not only hear the fundamental note, but will detect all the others sounding along with it, though with less and less intensity as their pitch becomes higher. According to the law of co-existing undulations, the whole string and each of its aliquot parts are in different and independent states of vibration at the same time; and as all the resulting notes are heard simultaneously, not only the air, but the ear also, vibrates in unison with each at the same instant (N. 181). Harmony consists in an agreeable combination of sounds. When two chords perform their vibrations in the same time, they are in unison; but, when their vibrations are so related as to have a common period, after a few oscillations they produce concord. Thus, when the vibrations of two strings bear a very simple relation to each other, as where one of them makes two, three, four, &c., vibrations in the time the other makes one; or, if it accomplishes three, four, &c., vibrations while the other makes two, the result is a concord which is the more perfect the shorter the common period. In discords, on the contrary, the beats are distinctly audible, which produces a disagreeable and harsh effect, because the vibrations do not bear a simple relation to one another, as where one of two strings makes eight vibrations while the other accomplishes fifteen. The pleasure afforded by harmony is attributed by Dr. Young to the love of order, and to a predilection for a regular repetition of sensations natural to the human mind, which is gratified by the perfect regularity and rapid recurrence of the vibrations. The love of poetry and dancing he conceives to arise in some degree from the rhythm of the one and the regularity of the motions in the other.