In this case the longest string vibrates as a whole when attached to the fork _a_. I now transfer the string to _b_, still keeping it stretched by the same weight. It vibrates when _b_ vibrates; but how? By dividing into two equal ventral segments. In this way alone can it accommodate itself to the swifter vibrating period of _b_. Attached to _c_, the same string separates into four, while when attached to _d_, it divides into eight ventral segments. The number of the ventral segments is proportional to the rapidity of vibration. It is evident that we have here, in a more delicate form, a result which we have already established in the case of our India-rubber tube set in motion by the hand. It is also plain that this result might be deduced theoretically from our first law. We may extend the experiment. Here are two tuning-forks separated from each other by the musical interval called a fifth. Attaching a string to one of the forks, I stretch the string until it divides into two ventral segments: attached to the other fork, and stretched by the same weight, it divides instantly into three segments when the fork is set in vibration. Now, to form the interval of a fifth, the vibrations of the one fork must be to those of the other in the ratio of 2:3. The division of the string, therefore, declares the interval. In, the same way the division of the string in relation to all other musical intervals may be illustrated.[37] Again. Here are two tuning-forks, _a_ and _b_, one of which (_a_) vibrates twice as rapidly as the other. A string of silk is attached to _a_, and stretched until it synchronizes with the fork, and vibrates as a whole. Here is a second string of the same length, formed by laying four strands of the first one side by side. I attach this compound thread to _b_, and, keeping the tension the same as in the last experiment, set _b_ in vibration. The compound thread synchronizes with _b_, and swings as a whole. Hence, as the fork _b_ vibrates with half the rapidity of _a_, by quadrupling the weight of the string we halved its rapidity of vibration. In the same simple way it might be proved that by augmenting the weight of the string nine times we reduce the number of its vibrations to one-third. We thus demonstrate the law: _The rapidity of vibration is inversely proportional to the square root of the weight of the string._