When a number of single and separate sounds follow each other in rapid succession, they produce a continued sound, in the same manner as a continuous circle of light is produced by whirling round a burning stick before the eye. In order that the sound may appear a single one to the ear, nearly sixteen separate sounds must follow one another every second. When these sounds are exactly similar, and recur at equal intervals, they form a musical sound. In order to produce such sounds from the air, it must receive at least sixteen equally distant impulses or strokes in a second. The most common way of producing this effect is by a string or wire A B, Fig. 40, stretched between the fixed points A, B. If this string is taken by the middle and pulled aside, or if it is suddenly struck, it will vibrate between its two fixed points, as shown in the figure, passing alternately on each side of its axis A B, the vibrations gradually diminishing by the resistance of the air till the string is brought to rest. Its vibrations, however, may be kept up, by drawing a rosined fiddle-bow across it, and while it is vibrating it will give out a sound corresponding to the rapidity of its vibrations, and arising from the successive blows or impulses given to the air by the string. This sound is called the fundamental sound of the string, and its acuteness or sharpness increases with the number of vibrations which the string performs in a second. [Illustration: _Fig. 40._] If we now touch the vibrating string A´ B lightly with the finger, or with a feather at the middle point C, Fig. 40, it will give out a more acute but fainter sound than before, and while the extent of its vibrations is diminished, their frequency is doubled. In like manner, if we touch the string A´´ B´´, Fig. 40, at a point C, so that A´´ C is one-third of A´´ B´´, the note will be still more acute, and correspond to thrice the number of vibrations. All this might have been expected; but the wonderful part of the experiment is, that the vibrating string A´ B´ divides itself at C into two parts A´ C, C B´, the part A´ C vibrating round A and C as fixed points, and the part C B´ round C and B´, but always so that the part A´ C is at the same distance on the one side of the axis A´ B´ as at A _m_ C, while the part C B is on the other side, as at C _n_ B. Hence the point C, being always pulled by equal and opposite forces, remains at rest as if it were absolutely fixed. This stationary point is called a _node_, and the vibrating portions A´_m_ C, C _n_ B´ loops. The very same is true of the string A´´ B´´, the points C and D being stationary points; and upon the same principle a string may be divided into any number of vibrating portions. In order to prove that the string is actually vibrating in these equal subdivisions, we have only to place a piece of light paper with a notch in it on different parts of the string. At the nodes C and