Question: Explain how to determine the time of vibration of a given tuning-fork, and state what apparatus you would require for the purpose.
Answer: For this determination I should require an accurate watch beating seconds, and a sensitive ear. I mount the fork on a suitable stand, and then, as the second hand of my watch passes the figure 60 on the dial, I draw the bow neatly across one of its prongs. I wait. I listen intently. The throbbing air particles are receiving the pulsations; the beating prongs are giving up their original force; and slowly yet surely the sound dies away. Still I can hear it, but faintly and with close attention; and now only by pressing the bones of my head against its prongs. Finally the last trace disappears. I look at the time and leave the room, having determined the time of vibration of the common “pitch” fork. This process deteriorates the fork considerably, hence a different operation must be performed on a fork which is only lent.

~~[Dubious]~~ If you want to find the secrets of the universe, think in terms of energy, frequency and vibration.

A physicist will tell me that this armchair is made of vibrations and that it’s not really here at all. But when Samuel Johnson was asked to prove the material existence of reality, he just went up to a big stone and kicked it. I'm with him.

A plain, reasonable working man supposes, in the old way which is also the common-sense way, that if there are people who spend their lives in study, whom he feeds and keeps while they think for him—then no doubt these men are engaged in studying things men need to know; and he expects of science that it will solve for him the questions on which his welfare, and that of all men, depends. He expects science to tell him how he ought to live: how to treat his family, his neighbours and the men of other tribes, how to restrain his passions, what to believe in and what not to believe in, and much else. And what does our science say to him on these matters?
It triumphantly tells him: how many million miles it is from the earth to the sun; at what rate light travels through space; how many million vibrations of ether per second are caused by light, and how many vibrations of air by sound; it tells of the chemical components of the Milky Way, of a new element—helium—of micro-organisms and their excrements, of the points on the hand at which electricity collects, of X rays, and similar things.
“But I don't want any of those things,” says a plain and reasonable man—“I want to know how to live.”

Any opinion as to the form in which the energy of gravitation exists in space is of great importance, and whoever can make his opinion probable will have, made an enormous stride in physical speculation. The apparent universality of gravitation, and the equality of its effects on matter of all kinds are most remarkable facts, hitherto without exception; but they are purely experimental facts, liable to be corrected by a single observed exception. We cannot conceive of matter with negative inertia or mass; but we see no way of accounting for the proportionality of gravitation to mass by any legitimate method of demonstration. If we can see the tails of comets fly off in the direction opposed to the sun with an accelerated velocity, and if we believe these tails to be matter and not optical illusions or mere tracks of vibrating disturbance, then we must admit a force in that direction, and we may establish that it is caused by the sun if it always depends upon his position and distance.

As a man who has devoted his whole life to the most clear headed science, to the study of matter, I can tell you as a result of my research about atoms this much: There is no matter as such. All matter originates and exists only by virtue of a force which brings the particle of an atom to vibration and holds this most minute solar system of the atom together. … We must assume behind this force the existence of a conscious and intelligent mind. This mind is the matrix of all matter.

But in the heavens we discover by their light, and by their light alone, stars so distant from each other that no material thing can ever have passed from one to another; and yet this light, which is to us the sole evidence of the existence of these distant worlds, tells us also that each of them is built up of molecules of the same kinds as those which we find on earth. A molecule of hydrogen, for example, whether in Sirius or in Arcturus, executes its vibrations in precisely the same time. Each molecule, therefore, throughout the universe, bears impressed on it the stamp of a metric system as distinctly as does the metre of the Archives at Paris, or the double royal cubit of the Temple of Karnac ... the exact quantity of each molecule to all others of same kind gives it, as Sir John Herschel has well said, the essential character of a manufactured article and precludes the idea of its being external and self-existent.

Do not Bodies and Light act mutually upon one another; that is to say, Bodies upon Light in emitting, reflecting, refracting and inflecting it, and Light upon Bodies for heating them, and putting their parts into a vibrating motion wherein heat consists?

Fourier’s Theorem … is not only one of the most beautiful results of modern analysis, but it may be said to furnish an indispensable instrument in the treatment of nearly every recondite question in modern physics. To mention only sonorous vibrations, the propagation of electric signals along a telegraph wire, and the conduction of heat by the earth’s crust, as subjects in their generality intractable without it, is to give but a feeble idea of its importance.

How, indeed, can there be a response within to the impression from without when there is nothing within that is in relation of congenial vibration with that which is without? Inattention in such case is insusceptibility; and if this be complete, then to demand attention is very much like demanding of the eye that it should attend to sound-waves, and of the ear that it should attend to light-waves.

I have read somewhere that the resistance offered by a wire ... is affected by the tension of the wire. If this is so, a continuous current of electricity passed through a vibrating wire should meet with a varying resistance, and hence a pulsatory action should be induced in the current ... [corresponding] in amplitude, as well as in rate of movement, to the vibrations of the string ... [Thus] the timbre of a sound [a quality essential to intelligible speech] could be transmitted ... [and] the strength of the current can be increased ad libitum without destroying the relative intensities of the vibrations.

I must own I am much in the dark about light. I am not satisfied with the doctrine that supposes particles of matter, called light … May not all the phenomena of light be more conveniently solved, by supposing universal space filled with a subtle elastic fluid, which, when at rest, is not visible, but whose vibrations affect that fine sense in the eye, as … the ear … in the case of sound … May not different degrees of the vibration of the above-mentioned universal medium occasion the appearances of different colors? I think the electric fluid is always the same; yet I find that weaker and stronger sparks differ in apparent color; some white, blue, purple, red; the strongest, white; weak ones, red.

If you want to find the secrets of the universe, think in terms of energy, frequency and vibration.

In the heavens we discover [stars] by their light, and by their light alone ... the sole evidence of the existence of these distant worlds ... that each of them is built up of molecules of the same kinds we find on earth. A molecule of hydrogen, for example, whether in Sirius or in Arcturus, executes its vibrations in precisely the same time. Each molecule therefore throughout the universe bears impressed upon it the stamp of a metric system as distinctly as does the metre of the Archives at Paris, or the royal cubit of the Temple of Karnac.
[Footnote: Where Maxwell uses the term “molecule” we now use the term “atom.”]

In this communication I wish first to show in the simplest case of the hydrogen atom (nonrelativistic and undistorted) that the usual rates for quantization can be replaced by another requirement, in which mention of “whole numbers” no longer occurs. Instead the integers occur in the same natural way as the integers specifying the number of nodes in a vibrating string. The new conception can be generalized, and I believe it touches the deepest meaning of the quantum rules.

Is it a fact—or have I dreamt it—that, by means of electricity, the world of matter has become a great nerve, vibrating thousands of miles in a breathless point of time?

It has just occurred to me to ask if you are familiar with Lissajous’ experiments. I know nothing about them except what I found in Flammarion’s great “Astronomie Populaire.” One extraordinary chapter on numbers gives diagrams of the vibrations of harmonics—showing their singular relation to the geometrical designs of crystal-formation;—and the chapter is aptly closed by the Pythagorian quotation: Ἀεὶ ὁ θεὸς ὁ μέγας γεωμετρεῖ—“God geometrizes everywhere.” … I should imagine that the geometry of a fine opera would—were the vibrations outlined in similar fashion—offer a network of designs which for intricate beauty would double discount the arabesque of the Alhambra.

It’s intriguing that the chair is mostly empty space and the thing that stops you going through it is vibrations or energy fields. But it’s also fascinating that, because we’re animals that evolved to survive, what solidity is to most of us is something you can’t walk through. Also, the science of the future may be vastly different from the science of today, and you have to have the humility to admit when you don’t know. But instead of filling that vacuum with goblins or spirits, I think you should say, “Science is working on it.”

My theory of electrical forces is that they are called into play in insulating media by slight electric displacements, which put certain small portions of the medium into a state of distortion which, being resisted by the elasticity of the medium, produces an electromotive force ... I suppose the elasticity of the sphere to react on the electrical matter surrounding it, and press it downwards.
From the determination by Kohlrausch and Weber of the numerical relation between the statical and magnetic effects of electricity, I have determined the elasticity of the medium in air, and assuming that it is the same with the luminiferous ether I have determined the velocity of propagation of transverse vibrations.
The result is
193088 miles per second
(deduced from electrical & magnetic experiments).
Fizeau has determined the velocity of light
= 193118 miles per second
by direct experiment.
This coincidence is not merely numerical. I worked out the formulae in the country, before seeing Webers [sic] number, which is in millimetres, and I think we have now strong reason to believe, whether my theory is a fact or not, that the luminiferous and the electromagnetic medium are one.

Pure mathematics is much more than an armoury of tools and techniques for the applied mathematician. On the other hand, the pure mathematician has ever been grateful to applied mathematics for stimulus and inspiration. From the vibrations of the violin string they have drawn enchanting harmonies of Fourier Series, and to study the triode valve they have invented a whole theory of non-linear oscillations.

Scientists are supposed to live in ivory towers. Their darkrooms and their vibration-proof benches are supposed to isolate their activities from the disturbances of common life. What they tell us is supposed to be for the ages, not for the next election. But the reality may be otherwise.

The external resistance may also be varied. For instance, let mercury or some other liquid form part of a voltaic circuit, then the more deeply the conducting wire is immersed in the mercury or other liquid the less resistance does the liquid offer to the passage of the current Hence the vibration of the conducting wire in mercury or other liquid included in the circuit occasions undulations in the current…

The final result of our researches has widened the class of substances sensitive to light vibrations, until we can propound the fact of such sensitiveness being a general property of all matter.

We believe that each molecular vibration disturbs the ether; that spectra are thus begotten, each wavelength of light resulting from a molecular tremor of corresponding wavelength. The molecule is, in fact, the sender, the ether the wire, and the eye the receiving instrument, in this new telegraphy.

We have reached the end of our journey into the depths of matter. We have sought for firm ground and found none. The deeper we penetrate, the more restless becomes the universe…: all is rushing about and vibrating in a wild dance.

When external objects are impressed on the sensory nerves, they excite vibrations in the aether residing in the pores of these nerves... Thus it seems that light affects both the optic nerve and the aether and ... the affections of the aether are communicated to the optic nerve, and vice versa. And the same may be observed of frictions of the skin, taste, smells and sounds... Vibrations in the aether will agitate the small particles of the medullary substance of the sensory nerves with synchronous vibrations... up to the brain... These vibrations are motions backwards and forwards of small particles, of the same kind with the oscillations of pendulums, and the tremblings of the particles of the sounding bodies (but) exceedingly short and small, so as not to have the least efficacy to disturb or move the whole bodies of the nerves... That the nerves themselves should vibrate like musical strings is highly absurd.