then no wave can be produced; for after a prong has advanced and stopped moving (no matter for how short a time), if it has not compressed the air, its return motion (on the same side) cannot do anything toward making a compression.  If one such motion of 1/17000 of an inch in 1/512 of a second cannot compress the air, then the remaining motions cannot.  There is unquestionably a “union limit” between mobility and compressibility, and unless this limit is passed, mobility holds sway and prevents condensation or compression of the air; but when this limit is passed by the exercise of sufficient energy, then compression of the air results.  Just imagine the finger to be moved through the air at a velocity of one foot in one hour; is it possible that any scientist who considers the problem in connection with the mobility of the air, could risk his reputation by saying that the air would be compressed?  Heretofore it was supposed that a praeong of a tuning fork was traveling fast because it vibrated so many times in a second, never stopping to think that its velocity of motion was entirely dependent upon the distance it traveled.  At the start the prong travels 1/20 of an inch, but in a short time, while still sounding, the distance is reduced to 1/17000 of an inch.  While the first motion was quite fast, about 25 inches in a second, the last motion was only about 1/33 of an inch in the same time, and is consequently 825 times slower motion.  The momentum of the prong, the amount of work it can do, is likewise proportionately reduced.

Some seem to imagine, without thinking, that the elasticity of the air can add additional energy.  This is perfectly erroneous; for elasticity is a mere property, which permits a body to be compressed on the application of a force, and to be dilated by the exercise of the force stored up in it by the compression.  No property of the air can impart any energy.  If the momentum of a molecule or a series of molecules extending in all directions for a mile is to be overcome so as to control the character of the movements of the molecules, then sufficient external energy must be applied to accomplish the task:  and when we think that one cubic inch of air contains 3,505,519,800,000,000,000 molecules, to say nothing about the number in a cubic mile, which a locust can transmit sound through, we are naturally compelled to stop and think whether the vibrations of supposed molecules have anything or can have anything to do with the transference of sound through the air.

If control was only had of the distance the vibrating molecule travels from its start to the end of its journey, then only the intensity of the sound would be under subjection; but if at every infinitesimal instant control was had of its amplitude of swing, then the character, timbre, or quality of the sound is under subjection.  It is evident, then, that the blows normally given by one molecule to another in their supposed constant bombardment must not be sufficient to alter the character of vibration a molecule set in oscillation by a sounding body must maintain, to preserve the timbre or quality of the sound in process of transmission; for if any such alteration should take place, then, naturally, while the pitch, and perhaps intensity, might be transmitted, the quality of the sound would be destroyed.