"In a memoir presented to the Royal Society of Göttingen in 1858, but afterwards withdrawn, and only published in Poggendorff's Annalen in 1867, after the death of the author, Bernhard Riemann]deduces the phenomena of the induction of electric currents from a modified form of \frac{\mathrm{d^2}V}{\mathrm{d}x^2} + \frac{\mathrm{d^2}V}{\mathrm{d}y^2} + \frac{\mathrm{d^2}V}{\mathrm{d}z^2} + 4 \pi \rho= \frac{1}{a^2} \frac{\mathrm{d^2}V}{\mathrm{d}t^2}where V is the electrostatic potential and a velocity. This equation is of the same form as those which express the propagation of waves and other disturbances in elastic media. The author, however, seems to avoid making explicit mention of any medium through which the propagation takes place. The mathematical investigation given by Riemann has been examined by Clausius, who does not admit the soundness of the mathematical processes, and shews that the hypothesis that potential is propogated like light does not lead either to the formula of Weber, or to the known laws of electrodynamics."
Quote Details
Added by wikiquote-import-bot
Unverified quote
0 likes
Original Language: English
Available Languages (1)
Sources
James Clerk Maxwell, A Treatise on Electricity and Magnetism (1881) Vol. 2, p. 446.
https://en.wikiquote.org/wiki/Bernhard_Riemann
Revision History
No revisions have been submitted for this quote.
Categories
Bernhard Riemann
Georg Friedrich Bernhard Riemann (September 17, 1826 – July 20, 1866) was an influential German mathematician who made lasting and revolutionary contributions to analysis, number theory, and differential geometry.
69 quotes on TrueQuotesView all quotes by Bernhard Riemann →
Related Quotes
"As is known, scientific physics dates its existence from the discovery of the differential calculus. Only when it was…"
"Magnitude-notions are only possible where there is an antecedent general notion which admits of different specialisat…"
"Definite portions of a manifoldness, distinguished by a mark or by a boundary, are called Quanta. Their comparison wi…"
"If in the case of a notion whose specialisations form a continuous manifoldness, one passes from a certain specialisa…"
"Measure-relations can only be studied in abstract notions of quantity, and their dependence on one another can only b…"
"For Space, when the position of points is expressed by rectilinear co-ordinates, ds = \sqrt{ \sum (dx)^2 }; Space is …"
"Let us imagine that from any given point the system of shortest lines going out from it is constructed; the position …"
"With every simple act of thinking, something permanent, substantial, enters our soul. This substantial somewhat appea…"
"Mind-masses entering the soul appear to us as ideas, the quality of the latter depending on the inner state of the fo…"
"Nevertheless, it remains conceivable that the measure relations of space in the infinitely small are not in accordanc…"