Mathematical Methods in Science (1977)
Context: Life is full of surprises: our approximate condition for the fall of a body through a resisting medium is precisely analogous to the exact condition for the flow of an electric current through a resisting wire [of an induction coil]....
m\frac {dv}{dt} = mg - Kv
This is the form most convenient for making an analogy with the "fall", i. e., flow, of an electric current.
... in order from left to right, mass m, rate of change of velocity \frac {dv}{dt}, gravitational force mg, and velocity v. What are the electrical counterparts?... To press the switch, to allow current to start flowing is the analogue of opening the fingers, to allow the body to start falling. The fall of the body is caused by the force mg due to gravity; the flow of the current is caused by the electromotive force or tension E due to the battery. The falling body has to overcome the frictional resistance of the air; the flowing current has to overcome the electrical resistance of the wire. Air resistance is proportional to the body's velocity v; electrical resistance is proportional to the current i. And consequently rate of change of velocity \frac {dv}{dt} corresponds to rate of change of current \frac {di}{dt}.... The electromagnetic induction L opposes the change of current... And doesn't the inertia or mass m..? Isn't L, so to speak, an electromagnetic inertia?
L\frac {di}{dt} = E - Ki
“When a constant electric current flows along a cylindrical wire, its strength is the same at every part of the section of the wire. But if the current is variable, self-induction produces a deviation from this… induction opposes variations of the current in the centre of the wire more strongly than at the circumference, and consequently the current by preference flows along the outer portion of the wire. When the current changes its direction… this deviation increases rapidly with the rate of alternation; and when the current alternates many million times per second, almost the whole of the interior of the wire must, according to theory, appear free from current, and the flow must confine itself to the very skin of the wire. Now in such extreme cases… preference must be given to another conception of the matter which was first presented by Messrs. 0. Heaviside and J. H. Poynting, as the correct interpretation of Maxwell's equations as applied to this case. According to this view, the electric force which determines the current is not propagated in the wire itself, but under all circumstances penetrates from without into the wire, and spreads into the metal with comparative slowness and laws similar to those which govern changes of temperature in a conducting body.
…Inasmuch as I made use of electric waves in wires of exceedingly short period in my experiments on the propagation of electric force, it was natural to test by means of these the correctness of the conclusions deduced. As a matter of fact the theory was found to be confirmed by the experiments…”
"On the Propagation of Electric Waves by Means of Wires" (1889) Wiedemann's Annalen. 37 p. 395, & pp.160-161 of Electric Waves
Electric Waves: Being Researches on the Propagation of Electric Action with Finite Velocity Through Space (1893)
Help us to complete the source, original and additional information
Heinrich Hertz 4
German physicist 1857–1894Related quotes
Quote of Naum Gabo (1957), as cited in: Gabo: Construction, Sculpture, Paintings, Drawings, Engravings. p. 164.
1936 - 1977
Source: The Principles of Political Economy and Taxation (1821) (Third Edition), Chapter VII, On Foreign Trade, p. 91
“But youth is as a flowing stream, on whose current the shadow may rest but not remain.”
Other Gift Books
“O'er the wires the electric message came,
"He is no better; he is much the same."”
On the Illness of the Prince of Wales (1910)
An 1871 poem on the illness of the Prince of Wales, although there is some doubt that Austin actually wrote this part. That classic compendium "The Stuffed Owl: An Anthology of Bad Verse" (2d ed. 1930; Capricorn paperback 1962) includes a dozen quotations from Austin but attributes this particular couplet (p. 17) to a "university poet unknown." It also provides a metrically more accurate first line, "Across the wires the gloomy message came," plus "not" for "no" in the second line.
On the Illness of the Prince of Wales (1910)
“Most artists have retired too absolutely; they grow rusty, inflexible to the flow of currents.”
November 26, 1932
Diary entries (1914 - 1974)
Context: This abdiction of life demanded of the artist is to be achieved only relatively. Most artists have retired too absolutely; they grow rusty, inflexible to the flow of currents.