Letters on Natural Magic; Addressed to Sir Walter Scott, Bart.

by David Brewster

Let us now suppose two pipes, AB, BC, to be joined together as in Fig. 42, and to be separated by a fixed partition at B; and let a spiral spring be fixed in each. Let the spring AB be now pushed to the end A, while the spring BC is pushed to C, as in No. 1, and back again, as in No. 2, but always in opposite directions; then it is obvious that the partition B is in No. 1 drawn in opposite directions towards A and towards C, and always with forces equal to each other: that is, when B is drawn slightly towards A, which it is at the beginning of the motion, it is also drawn slightly towards C; and when it is drawn forcibly towards A, as it is at the end of the motion of the spring, it is also drawn forcibly towards C. If the partition B, therefore, is moveable, it will still remain fixed during the opposite excursions of the spiral springs; nay, if we remove the partition, and hook the end of one spiral spring to the end of the other, the node or point of junction will remain stationary during the movements of the springs, because at every instant that point is drawn by equal and opposite forces. If three, four, or five spiral springs are joined in a similar manner, we may conceive them all vibrating between their nodes in the same manner.

Upon the very same principles we may conceive a long column of air without partitions dividing itself into two, three, or four smaller columns, each of which will vibrate between its nodes in the same manner as the spiral spring. At the middle point of each small vibrating column, the air will be of its natural density, like that of the atmosphere; while at the nodes B, &c. it will be in a state of condensation and rarefaction alternately.

If, when the air is vibrating in one column in the pipe AB, as in Fig. 41, No. 2, 3, we conceive a hole made in the middle, the atmospheric air will not rush in to disturb the vibration, because the air within the pipe and without it has exactly the same density. Nay, if, instead of a single hole, we were to cut a ring out of the pipe at the middle point, the column would vibrate as before. But if we bore a hole between the middle and one of the ends, where the vibrating column must be either in a state of condensation or rarefaction, the air must either rush out or rush in, in order to establish the equilibrium. The air opposite the hole will then be brought to the state of the external air, like that in the middle of the pipe; it will become the middle of a vibrating column: and the whole column of air, instead of vibrating as one, will vibrate as two columns, each column vibrating with twice the velocity, and yielding harmonic sounds along with the fundamental sound of the whole columns, in the same manner as we have already explained with regard to vibrating strings. By opening other holes we may subdivide a vibrating column into any number of smaller vibrating columns. The holes in flutes, clarionets, &c. are made for this purpose. When they are all closed up, the air vibrates in one column; and by opening and shutting the different holes in succession, the number of vibrating columns is increased or diminished at pleasure, and consequently the harmonic sounds will vary in a similar manner.

Curious as these phenomena are, they are still surpassed by those which are exhibited during the vibration of solid bodies. A rod or bar of metal or glass may be made to vibrate either longitudinally or laterally.

An iron rod will vibrate longitudinally, like a column of air, if we strike it at one end in the direction of its length; or rub it in the same direction with a wetted finger, and it will admit the same fundamental note as a column of air ten or eleven times as long, because sound moves so much faster in iron than in air. When the iron rod is thus vibrating along its length, the very same changes which we have shown in Fig. 41, as produced in a spiral spring, or in a column of air, take place in the solid metal. All its particles move alternately towards A and towards B, the metal being in the one case condensed at the end to which the particles move, and expanded at the end from which they move, and retaining its natural density in the middle of the rod. If we now hold this rod in the middle, by the finger and thumb lightly applied, and rub it in the middle either of AB or BC with a piece of cloth sprinkled with powdered rosin, or with a well-rosined fiddle-bow drawn across the rod, it will divide itself into two vibrating portions AB, BC, each of which will vibrate, as shown in Fig. 42, like the two adjacent columns of air, the section of the rod, or the particles which compose that section at B, being at perfect rest. By holding the rod at any intermediate point between A and B, so that the distance from A to the finger and thumb is one-third, one-fourth, one-fifth, &c. of the whole length AC, and rubbing one of the divisions in the middle, the rod will divide itself into 3, 4, 5, &c. vibrating portions, and give out corresponding harmonic sounds.

Fig. 43.

A rod of iron may be made to vibrate laterally or transversely, by fixing one end of it firmly, as in a vice, and leaving the other free, or by having both ends free or both fixed. When a rod, fixed at one end and free at the other, is made to vibrate, its mode of vibrating may be rendered evident to the eye; and for the purpose of doing this, Mr. Wheatstone has contrived a curious instrument, called the Kaleidophone, which is shown in Fig. 43. It consists of a circular base of wood AB, about nine inches in diameter and one inch thick, and having four brass sockets firmly fixed into it at C, D, E, and F. Into these sockets are screwed four vertical steel rods C, D, E, and F, about thirteen or fourteen inches long; one being a square rod, another a bent cylindrical one, and the other two cylindrical ones of different diameters. On the extremities of these rods are fixed small quicksilvered glass beads, either singly or in groups, so that when the instrument is placed in the light of the sun or in that of a lamp, bright images of the sun or flame are seen reflected on each bead. If any of these rods is set vibrating, these luminous images will form continuous and returning curve lines in a state of constant variation, each different rod giving curves of different characters, as shown in Fig. 44.

Fig. 44.