HARMONIC SLIDERS, are the contrivance of Dr Tho TliaS Young, for exhibiting to the eye the effects of the un dulations or beats of tempered concords, which he has de scribed in the Journals of the Royal Institution, p. 261, and illustrated the same by a drawing, intended to represent the beating of the imperfect unison, whose ratio isti,= 50,46033/1-44m ; but which being nearly as large as the elementary semitone and a discord, is very improperly called a unison, or a beating concord.
The following is Dr Young's own account of this inven tion : 46 The combination of undulations is of acknowledg ed utility in illustrating the phenomena of musical conso nances and dissonances, and of undeniable importance in accounting for many of the phenomena of the tides. Each tide is an undulation on a large scale ; and supposing the general form of the ocean, in consequence of the attrac tion of a distant body, to coincide with that of an oblong spheroid, as it is found by calculation to do, the section of the surface of each tide, if conceived to be unbent from the circular form, and extended on a plane, would form the harmonic curve: (Young's Syllabus, IV. 151. 155.) It is remarkable that the motions of the particles of the air in sound have been generally supposed in theory to corres pond with the ordinates of this same curve, and that there is also experimental reason to believe, that the purest and most homogeneous sounds do in fact agree very nearly with the law of this curve. It is therefore by far the most natural as well as the most convenient to be assumed, as representing the state of an undulation in general; and the name of these harmonic sliders is very properly deduced from•the harmonic curve.
By means of this instrument, the process of nature, in the combinations of motion which take place in rations cases of the junction of undulations, is rendered visible and intelligible, with great ease, in the most complicated cases. It is unnecessary to explain here, how accurately both the situations and motions of the particles of air, in sound, may be represented by the ordinates of the curve at different points: it is sufficient to consider them as merely indicating the height of the water constituting a tide, or a wave of any kind, which exists at once in its whole extent, and of which each point passes also in suc cession through any given place of observation. We have then to examine what will be the effect of two tides, pro duced by different causes, when united. In order to re present this effect, we must add to the elevations or de pressions in consequence of the first tide, the elevations or depressions in consequence of the second, and subtract them when they counteract the effect of the first : or we may add the whole height of the second above any given point or fine, and then subtract, from all the sums, the distance of the point assumed below the medium.
To do this mechanically is the object of the harmonic sliders. The surface of the first tide is represented by the curvilinear termination a single board, Plate CCLXXXVIII. Fig. 1. The second tide is also repre sented by the termination of another surface ; but, in order that the height at each point may be added to the height of the first tide, the surface is cut transversely into a number of separate pieces or sliders, which are confined within a groove or frame, and tightened by a screw, Fig. 2. Their lower ends are situated originally in a right line ; but by loosening the screw and moving the sliders, they may be made to assume any other form : thus they may be applied to the surface representing the first tide; and if the similar parts of each correspond, 3, the combination will represent a tide of twice the magnitude of the simple tides.
The more the corresponding' parts are separated, the weaker will be the joint effect, Fig. 4. ; and, when they are furthest removed, the whole tides, if equal, will be annihilated, Fig. 5. Thus, when the general tide of the ocean arrives by two different channels at the same port, at such intervals of time that the high water of one would happen at the same instant with the low water of the odt4r, the whole effect is destroyed, except so far as the partial tides differ in magnitude. The principle being once understood, it may easily be applied to a multipli city of cases ; for instance, where the undulations differ in their dimensions with regard to extent. Thus, the series of sliders being extended to three or four alterna tions, the effect of combining undulations in the ratio of 2 to 1, of 3 to 1, of 2 to 3, of 3 to 4, may be ascertained, by making a fixed surface, terminating in a series of curves, that bear to those of the sliding surface the ratio required : and, by making them differ but slightly, the phenomenon of the beating of an imperfect unison in music may be imitated, where the joint undulation becomes alternately redoubled and evanescent. In Fig. 6. the pro portion is that of 17 to 18, and the curvilinear outline re presents the progress of the joint sound from the great est degree of intensity to the least, and a little beyond it."