How any resultant can be established as regards the time necessary for the molecule to take so as to complete a full vibration for the note C11, which requires 1/16 of a second, and for other notes up to C''''', which only requires 1/4176 of a second, as when an orchestra is playing, is certainly beyond human comprehension, if it is not beyond the "transcendental mathematics" of the present day.
Unquestionably, the able mathematicians Lord Rayleigh, Stokes, or Maxwell, if the problem was submitted to them, would start directly to work, and deduce by so called "higher mathematics" the required motions the molecules would have to undergo to accomplish this marvelous task—the same as they have established the diameter of the supposed molecules, their velocity, distance apart, and number of bombardments, without any shadow of positive proof that any such things as molecules exist.
As S. Caunizzana has said: "Some of the followers of the modern school push their faith to the borders of fanaticism; they often speak on molecular subjects with as much dogmatic assurance as though they had actually realized the ingenious fiction of Laplace, and had constructed a microscope by which they could detect the molecule and count the number of its constituent atoms."
Speaking of the "modern manufacturers of mathematical hypotheses," Mattieu Williams says: "It matters not to them how 'wild and visionary,' how utterly gratuitous, any assumption may be, it is not unscientific provided it can be vested in formulæ and worked out mathematically.
"These transcendental mathematicians are struggling to carry philosophy back to the era of Duns Scotus, when the greatest triumph of learning was to sophisticate so profoundly an obvious absurdity that no ordinary intellect could refute it.... The close study of pure mathematics, by directing the mind to processes of calculation rather than to phenomena, induces that sublime indifference to facts which has characterized the purely mathematical intellect of all ages."
Tyndall, however, states in all frankness, and without the aid of mathematical considerations, that "when we try to visualize the motions of the air having one thousand separate tones, to present to the eye of the mind the battling of the pulses, direct and reverberated, the imagination retires baffled at the attempt;" and he might have added, the shallowness and fallacy of the wave theory of sound was made apparent. He, however, does express himself as follows: "Assuredly, no question of science ever stood so much in need of revision as this of the transmission of sound through the atmosphere. Slowly but surely we mastered the question, and the further we advance, the more plainly it appeared that our reputed knowledge regarding it was erroneous from beginning to end."
Until physicists are willing to admit that the physical forces of nature are objective things—actual entities, and not mere modes of motion—a full and clear comprehension of the phenomena of nature will never be revealed to them. The motion of all bodies, whether small or great, is due to the entitative force stored up in them, and the energy they exercise is in proportion to the stored-up force.
Tyndall says that "heat itself, its essence and quiddity, IS MOTION, AND NOTHING ELSE." Surely, no scientist who considers what motion is can admit such a fallacious statement, for motion is simply "position in space changing;" it is a phenomenon, the result of the application of entitative force to a body. It is no more an entity than shadow, which is likewise a phenomenon. Motion, per se, is nothing and can do nothing in physics. Matter and force are the two great entities of the universe—both being objective things. Sound, heat, light, electricity, etc., are different forms of manifestation of an all-pervading force element—substantial, yet not material.